Alicia Lardennois

Gabriella Pásti

Teresa Ferraro

Flora Llense

Pierre Mahou

Julien Pontabry

David Rodriguez

Samantha Kim

Emmanuel Beaurepaire

Christelle Gally

Michel Labouesse An

Keywords:

REMERCIEMENTS

Cette expérience a été déterminante pour moi. La science n'était pas mon premier choix de carrière, mais la vie en a décidé autrement. J'en ai tiré le meilleur parti et aujourd'hui, je suis très heureuse du résultat.

Je tiens avant tout à remercier mon directeur de thèse, Michel, de m'avoir confié un projet aussi intéressant et stimulant et de m'avoir fait confiance pour le mener à bien. Merci pour ta patience, ta motivation, ton enthousiasme et tes immenses connaissances. Tes conseils m'ont aidé tout au long de cette thèse et de son écriture. Cela n'a pas été facile tous les jours, mais cela en valait la peine. Merci également de m'avoir encouragée lorsque j'en ai eu besoin et d'avoir trouvé les mots justes.

Ce fut un honneur de travailler avec Flora, ma superviseure dans l'équipe, et je suis extrêmement reconnaissante de ton soutien et de tes conseils au cours de ces quatre années intenses. Merci de m'avoir encouragée jusqu'au bout, surtout pendant les moments difficiles. Merci pour ton aide pour les expériences, tes conseils scientifiques et nos discussions très stimulantes (scientifiques ou autres).

Je voudrais également exprimer ma profonde gratitude à Teresa. Sans ta contribution scientifique, ma thèse n'aurait pas été la même. Merci pour ton soutien, nos diverses discussions scientifiques et celles plus légères.

En plus de Michel, Flora et Teresa, je voudrais également remercier tous les anciens membres et membres actuels des équipes Labouesse et Robin: François pour nos échanges scientifiques approfondis (en particulier sur le cytosquelette) mais aussi pour tes précieux conseils Saurabh pour m'avoir appris quelques manipulations de base sur C. elegans et la conception des CRISPRs Shashi pour ta disponibilité à chaque fois que j'avais des questions sur les protocoles ou autres (en particulier sur les CRISPR ou VAB10…) Loan pour avoir supporté avec bonne humeur de partager la paillasse avec moi pendant deux ans et pour ton aide avec les injections Serena pour nos grandes conversations scientifiques (ainsi que celles sur les chats et United Wizard) Asma pour ta gentillesse et notre passion partagée pour Harry Potter Camille, Thanh, Xinyi, Vlad et Dilyana pour nos conversations sur la science et le reste en général. Je tiens à remercier les étudiants qui m'ont aidée sur les expériences : Antoine, Leïla et Camille. Merci également aux membres de l'équipe Galy pour leur accueil chaleureux chaque fois que nous injectons. Et surtout merci à tous d'avoir été présents, j'ai beaucoup apprécié votre compagnie au cours de ces quatre dernières années.

Je n'ai pas de mots pour exprimer ma gratitude envers Emma, Manon et Dylan, qui ont toujours été là pour moi, particulièrement dans les moments très difficiles. Vous m'avez supportée à chaque fois que je parlais de ma thèse, de mon papier, de mes difficultés et surtout de la frustration qui en découlait. Je vous dois beaucoup (nous sabrerons le champagne bientôt !).

Merci particulièrement à Michel, Flora et Teresa pour la correction de ma thèse, ainsi qu'Emma et mes parents pour en avoir perfectionné la mise en page au cours des derniers jours.

Enfin, je remercie profondément ma famille, et Nounoutte, mon chat adoré. Merci, papa et maman, pour votre soutien inconditionnel et votre amour et pour être à mes côtés à chaque fois que j'en ai eu besoin. Cela fait quinze ans que vous me faites confiance, quel que soient mes choix de vie, même les plus difficiles. Votre confiance a fait de moi ce que je suis aujourd'hui, je n'aurais pas pu le faire sans vous. Je ne serai jamais assez reconnaissante.

ABSTRACTS

(in English and in French)

RÉSUMÉ COURT

Les processus morphogénétiques impliquent des changements de forme de cellules, via des forces mécaniques, qui doivent être stabilisés. Ma thèse vise à élucider comment l'embryon de C. elegans, matériau élastique, s'allonge progressivement sous l'effet des contractions musculaires.

Un crible ARNi en fond pak1(Ø), kinase de l'épiderme impliquée dans une cascade de mécanotransduction en aval des muscles, a identifié SPC1/αspectrine, comme partenaire probable.

Les embryons spc1()pak1() s'allongent jusqu'à 1.5fold, puis reviennent à leur taille initiale sous l'effet des muscles. Avec la microscopie à superrésolution, j'ai montré que leurs faisceaux d'actine épidermiques sont très désorganisés ; suggérant que le remodelage de l'actine pourrait contrer l'élasticité des cellules. Avec un crible en fond spc1()pak1(), j'ai identifié deux protéines de fragmentation aidant à rompre les filaments d'actine quand les muscles les courbent fortement. Par ailleurs, la formine de "pontage" FHOD1 induit aussi une rétraction dans des embryons fhod1( );spc1(). J'ai surexprimé une construction FHOD1(ΔFH2/DAD) tronquée en Cterminal qui a partiellement sauvé la rétraction spc1()pak1() suggérant que FHOD1 bloque la dépolymérisation de l'actine à chaque cycle de contraction. Pour tester cela, j'ai modélisé l'embryon en tant que matériau KelvinVoigt soumis à une force épidermique et à la tension musculaire et prédit son allongement en utilisant un composant viscoplastique symbolisant le raccourcissement de l'actine.

J'ai donc caractérisé un réseau cellulaire conférant une plasticité mécanique et stabilisant la forme des cellules dans un processus morphogénétique.

RÉSUMÉ LONG

En tant qu'organismes vivants, nous interagissons avec notre monde grâce à nos sens. Nous sommes continuellement exposés à des signaux mécaniques, et il en va de même pour nos cellules.

Ces dernières ont la capacité de détecter leur environnement physique en traduisant des forces mécaniques et des déformations en signaux biochimiques. À leur tour, ces signaux peuvent ajuster les structures cellulaires et extracellulaires. Au cours des deux dernières décennies, de nombreux processus biologiques répondant à des stress mécaniques ont été mis en évidence tels que : le changement de pression de turgescence dans la réponse au toucher chez Mimosa pudica, la différenciation variable des cellules souches mésenchymateuses en fonction de la rigidité du milieu de croissance sousjacent, la cicatrisation des plaies ou encore la prolifération et la dissémination des cellules cancéreuses. Les différents mécanismes par lesquels le tissu cellulaire convertit le stimulus mécanique en une activité électrochimique ou biochimique sont appelés mécanotransduction. La mécanotransduction est à l'origine d'un certain nombre de sens et de processus physiologiques dans le corps, notamment la proprioception, le toucher, l'équilibre et l'audition. Au niveau cellulaire, elle est importante pour de nombreuses fonctions telles que l'adhésion, la migration, la prolifération, la différenciation et l'apoptose et elle est essentielle au développement d'organes.

Une étape clé du développement de l'animal est la mise en place de l'axe du corps définissant sa forme finale lors de la morphogenèse. Ce processus détermine la forme et la structure des tissus, des organes et des organismes. Plus spécifiquement, la morphogenèse embryonnaire désigne des modifications de la forme et de la position des cellules dans l'embryon, en particulier de l'épithélium.

L'importance de la morphogenèse épithéliale a été rapportée dans des processus de développement cruciaux tels que la gastrulation (étudiée de manière approfondie dans les ascidies, la drosophile, le poisson zèbre ou le xénope) ou dans la formation du tube neural. Cette étape dépend de manière critique des changements de forme de cellules, euxmêmes dépendants de l'interaction entre les À l'aide d'outils génétiques et d'approches d'imagerie in vivo, une ancienne doctorante de l'équipe, Gabriella Pàsti, a montré que l'αspectrine et PAK1 interagissent génétiquement. En effet, elle a constaté que chez les mutants spc1 () pak1 (), les embryons s'allongent jusqu'à « 1,5fold », puis se rétractent jusqu'à leur taille initiale (phénotype de rétraction). Fait intéressant, ce phénotype avait déjà été décrit suite à la dépolymérisation massive de l'actine, via l'usage d'une drogue, suggérant que le réarrangement de l'actine pourrait fonctionner comme un verrou lors de la morphogenèse embryonnaire. Mon travail a donc consisté à caractériser plus en détail cette interaction entre le cytosquelette d'actine et l'αspectrine en répondant aux questions suivantes :

-Comment fonctionne le mécanisme de verrou au niveau moléculaire ? -Comment les câbles d'actine sontils remodelés au cours du temps ? -Quels sont les rôles des différents acteurs identifiés ? -Peuton modéliser l'allongement progressif de l'embryon pour comprendre comment les forces contribuent au remodelage de l'actine ?

Phénotype de rétraction et activité musculaire

Sachant que les embryons spc1() pak1() amorcent leur rétraction lorsque les muscles comment à être actifs, j'ai essayé de déterminer la manière dont l'apport musculaire affecte la rétraction des embryons. Précédemment, Gabriella a montré que si l'activité musculaire était bloquée que chez des mutants spc1() pak1(), grâce l'utilisation d'un ARNi contre unc112 (kindlin homologue et composant essentiel des muscles), cela empêchait la rétraction des embryons. J'ai terminé cette expérience en ajoutant plusieurs contrôles supplémentaires en mesurant l'élongation des vers unc112(); pak1() et unc112(); spc1(). Ils ont montré une croissance plus lente très semblable aux vers unc112() seuls. Pour comprendre comment les contractions musculaires contribuent au phénotype de rétraction, j'ai quantifié la différence de comportement entre embryons de type sauvage et mutants en utilisant des points de repère sur l'actine épidermique. J'ai mesuré le temps de contraction / relaxation et l'ampleur de la contraction / relaxation. Les doubles mutants ont présenté des contractions plus rapides et plus profondes que les embryons de type sauvage et pak1(). Ces deux expériences ont montré que l'apport musculaire est crucial pour le phénotype de rétraction bien qu'il soit perturbé dans le double mutant spc1() pak1().

Remodelage et

2.b. Remodelage durant l'élongation

Tous ensemble, les résultats décrits cidessus établissent un lien entre l'activité musculaire et désorganisation de l'actine chez les embryons spc1() pak1(). L'hypothèse la plus simple est que l'activité musculaire induit chez les embryons normaux une rupture et une stabilisation de l'actine bien contrôlée qui se détériore chez les embryons spc1() pak1(). En effet, une autre analyse sur ces images a montré que la circonférence de l'embryon diminuait de 20% au cours de l'allongement, impliquant que les filaments d'actine dans les cellules dorsoventrales doivent également se raccourcir. Pour comprendre au niveau moléculaire comment ce remodelage pourrait se produire, j'ai effectué un crible ARNi en fond sensible spc1() pak1() à la recherche d'un sauvetage du phénotype de rétraction. De manière remarquable, avec l'aide de Flora Llense, maître de conférences dans l'équipe, nous avons identifié des homologues de deux « protéines de fragmentation » de l'actine, la gelsoline et la villine suggérant que les contractions musculaires Effectivement j'ai observé que 2/3 des embryons exprimant la construction FH2/DAD ne se rétractent plus et qu'ils sont significativement plus longs que les doubles mutants spc1() pak1().

Modélisation de l'élongation

Pour rendre compte de l'élongation du ver à l'échelle mésoscopique, nous avons développé un Considérant cela, nous avons décidé de modéliser l'embryon de C. elegans comme un matériau de KelvinVoigt soumis à deux forces actives principales : la force épidermique, qui est une force positive continue, et la force musculaire, qui est une force pulsatile puisque les muscles se contractent alternativement. En utilisant un ensemble d'équations mathématiques, nous avons pu prédire l'allongement de l'embryon en introduisant un composant viscoplastique dans le système, symbolisant le raccourcissement de l'actine. Grâce à cela, nous avons également pu modéliser la rétraction des doubles mutants spc1() pak1(). Comme la continuité des filaments d'actine est modifiée chez ces mutants, leur résistance au stress provenant des cellules latérales ne serait pas maintenue et la force épidermique diminuerait progressivement, ce qui réduirait la longueur du système. L'absence combinée de SPC1 et de PAK1 coïncide avec l'incapacité d'étendre plastiquement la longueur du tissu.

Globalement, nos résultats identifient deux groupes de protéines impliquées dans la stabilisation de la forme des cellules dans un épiderme soumis à un stress répété : SPC1, PAK1 et FHOD1 qui stabilisent les câbles d'actine lors du remodelage, GSNL1 et VILN1 qui les sectionnent pour les aider à raccourcir. Ce réseau cellulaire confère une plasticité mécanique (en termes physiques, il implique une déformation irréversible sous contrainte) stabilisant la forme des cellules pendant la morphogenèse. Comprendre comment les cellules s'adaptent à un stimulus mécanique est essentiel et pourrait aider à élucider les dernières étapes de la morphogenèse chez C. elegans.

Dans un contexte plus médical, la dérégulation de PAK1 et des spectrines a été décrite dans de nombreuses pathologies. PAK1 apparaît surexprimée dans de multiples formes de cancers humains tels que le cancer du pancréas, de la prostate, du sein ou encore les mélanomes. De nombreuses études ont montré que la capacité à détecter une entrée mécanique, sa transduction dans la cellule et sa réponse sont défectueuses dans les cellules cancéreuses. In fine, nos résultats pourraient aider à mieux comprendre la dérégulation de la réponse à un stress mécanique lors de maladies.

INTRODUCTION

INTRODUCTION

The range of animal forms is immense, both in terms of obvious external appearances and in terms of the internal anatomies of organs and tissues. Observing the vast number of different shapes, we can wonder how does this diversity arise? Morphogenesis means the generation of form, and usually in the context of developmental biology it means the generation of tissue organization and shape in animal and plant embryos. It is one of three fundamental aspects of developmental biology along with the spatiotemporal control of cell growth and cellular differentiation. The process controls the organized spatial distribution of cells during the embryonic development of an organism.

Morphogenesis can also take place in a mature organism, in cell culture or inside tumor cell masses.

Some of the earliest ideas and mathematical descriptions on how physical processes and constraints affect biological growth, and hence natural patterns such as the spirals of phyllotaxis, were written by D'Arcy Wentworth Thompson [START_REF] Thompson | On Growth and Form[END_REF][START_REF] Montell | Morphogenetic Cell Movements: Diversity from Modular Mechanical Properties[END_REF] and Alan Turing [START_REF] Turing | The Chemical Basis of Morphogenesis[END_REF]. Thompson explained animal body shapes as being created by varying rates of growth in different directions, for instance to create the spiral shell of a snail. Turing correctly predicted a mechanism of morphogenesis, the diffusion of two different chemical signals, one activating and one deactivating growth, to set up patterns of development, decades before the formation of such patterns was observed [START_REF] Hiscock | Orientation of Turinglike Patterns by Morphogen Gradients and Tissue Anisotropies[END_REF]. The first major approach to investigating morphogenesis was to look at the intrinsic morphogenetic properties of cells. It showed that randomized aggregates of cells from a mix of amphibian embryonic tissues would not only sort themselves out into their cell types but also generate some structure [START_REF] Townes | Directed movements and selective adhesion of embryonic amphibian cells[END_REF].

They demonstrated that the cells themselves had morphogenetic properties that they could use and stimulated a great deal of work in the '60 '70s and '80s on the morphogenetic abilities of cells. A second approach was to analyze cell behavior in tissues that that will develop in culture where they can be experimentally manipulated. As chick and amphibian embryos are large and accessible, they have been the model species of choice for studying morphogenesis (e.g. neural crest and nerve migrations, corneal development, gastrulation, and epithelial morphogenesis) [START_REF] Trelstad | Cell contact during early morphogenesis in the chick embryo[END_REF][START_REF] Summerbell | Cell density and cell division in the early morphogenesis of the chick wing[END_REF][START_REF] Summerbell | Precision of development in chick limb morphogenesis[END_REF][START_REF] Meier | Development of the chick embryo mesoblast: morphogenesis of the prechordal plate and cranial segments[END_REF][START_REF] Heasman | Fates and states of determination of single vegetal pole blastomeres of X. laevis[END_REF][START_REF] Weliky | Notochord morphogenesis in Xenopus laevis: simulation of cell behavior underlying tissue convergence and extension[END_REF]. The mouse Mus musculus, the zebrafish Brachidanio rerio, the fruitfly Drosophila melanogaster and the roundworm Caenorhabditis elegans have also supplied continuous and extensive insights into cellular and molecular aspects of morphogenesis [START_REF] Knust | Drosophila morphogenesis: orchestrating cell rearrangements[END_REF][START_REF] Chisholm | Epidermal morphogenesis[END_REF][START_REF] Ellertsdóttir | Vascular morphogenesis in the zebrafish embryo[END_REF][START_REF] Riverapérez | The Dynamics of Morphogenesis in the Early Mouse Embryo[END_REF].

Morphogenesis was a major area of research in the 70s and early '80s, but activity then declined as the focus of research in development moved to discovering and studying the genes involved in networks that regulate differentiation. However the discovery of molecules controlling tissue organization and the development of transgenic animals led to an enormous amount of work in the first decade of the 21st century that has explained much about the molecular basics of morphogenesis, but less is known about how these are integrated at the cellular level.

For decades, the morphogenesis of epithelial tissues has fascinated scientists at the interface of cell, developmental, and molecular biology. Epithelial morphogenesis includes the various processes by which epithelia contribute to organ formation and body shape. During embryonic development, definitive epithelial organs often arise from preexisting epithelial tissues. Indeed, epithelia form transient structures, such as the neural tube, somites, and the precardiac epithelium, that serve as progenitors for the development of more complex organs [START_REF] Affolter | Tube or not tube: remodeling epithelial tissues by branching morphogenesis[END_REF][START_REF] Mango | elegans pharynx: a model for organogenesis[END_REF][START_REF] Bryant | From cells to organs: building polarized tissue[END_REF]. Different epithelia acquire diverse morphological forms appropriate for their specific functions, such as the kidney tubules or the complex branching structures found in the lung for example [START_REF] Miura | Models of lung branching morphogenesis[END_REF][START_REF] Marciano | A Holey Pursuit: Lumen formation in the Developing Kidney[END_REF]. Recently, the characterization of some of the molecular mechanisms involved in epithelial morphogenesis has provided an abundance of new information on the role and regulation of the cytoskeleton, cellcell adhesion, and cellmatrix adhesion in these processes [START_REF] Ding | The cytoskeleton and epidermal morphogenesis in C. elegans[END_REF][START_REF] Blankenship | Multicellular rosette formation links planar cell polarity to tissue morphogenesis[END_REF][START_REF] Armenti | Adherens junctions in C. elegans embryonic morphogenesis[END_REF][START_REF] Bosveld | Mechanical control of morphogenesis by Fat/Dachsous/Fourjointed planar cell polarity pathway[END_REF][START_REF] Chauhan | Epithelial morphogenesis: the mouse eye as a model system[END_REF].

Here I will first discuss the epithelia as layers of cells and their cellular characteristics. Then I will detail the dramatic change they undergo to drive morphogenetic processes, such as shape changes, increase in number, or rearrangements. Finally, I will talk about the mechanical forces, generated by actomyosin and transmitted by adhesive junctions, driving most of these changes.

I. Epithelia in morphogenesis

Maintaining the homeostasis of a multicellular organism requires compartmentalization of the internal environment of the external environment. In metazoans, the epithelial tissues fulfill this function. These tissues consist of epithelial cells that line the entire body and cavities of the body. In addition, these cells are histologically compact and rest on a basal lamina. Nevertheless, the epithelium denomination includes tissues with vastly different forms and functions within the same organism. Thus, the different epithelia can first be classified empirically according to the overall morphology of their cells (squamous morphology, cubic or cylindrical). Epithelia can also be distinguished by the number of layers of the tissue: layered epithelia consisting of several stacked cell layers (eg. skin epithelium), pseudostratified epithelia (eg. tracheal epithelium) and simple epithelia, consisting of a single layer of epithelial cells light (ex: epithelium of the jejunum) [START_REF] Marieb | Human Anatomy and Physiology[END_REF][START_REF] Guillot | Mechanics of epithelial tissue homeostasis and morphogenesis[END_REF].

Biologically, epithelia support the structures of organs and protect the body from the outside pathogens. They separate the interior from the exterior environment as a barrier or control the substance exchange across the plasma membrane as a regulated barrier. They also take part in sensing the environment, repairing wounds, contributing to various steps of development, and playing a pivotal role in shaping organs. To fulfill these roles, the epithelial cells can present additional specific structures, such as microvilli (eg intestinal epithelium), vibratile eyelashes (eg bronchial epithelium) or stereocilia (eg inner ear cells). However, despite this morphological and functional diversity, epithelial cells have a set of molecular characteristics that define them. They have an apicobasal polarity that allows polarized secretion, communication, and uptake of material from extracellular sources. This epithelial polarity is central in the biology of epithelia [START_REF] Munro | Cortical lows powered by asymmetrical contraction transport PAR proteins to establish and maintain anterior-posterior polarity in the early C. elegans embryo[END_REF][START_REF] Houk | Membrane tension maintains cell polarity by confining signals to the leading edge during neutrophil migration[END_REF][START_REF] Stetina | PAR6, but not Ecadherin and βintegrin, is necessary for epithelial polarization in C. elegans[END_REF] (Fig. 1). Indeed, its implementation precedes and is required for the morphogenesis of epithelial tissues and the maintenance of their homeostasis. Epithelial cells can form tissues of very different shapes and functions within the same organism. Nevertheless, their apicobasal polarization is required for morphogenesis to take place. Adapted from Kévin Sollier's thesis.

In addition, they also have several cytoskeletal elements with distinct functions that allow both their shape maintenance and force generation. Finally, they have multiple sets of junctions and attachment structures that allow them to form layers with each other and to set up connection with neighboring tissues. These contacts do not solely serve structural and barrier functions: they allow intra and intertissular communication in two ways. One is the classical, chemical signaling. The other one involves physical forces generated in one cell or tissue, which are transmitted and turned into biochemical signals in another cell or tissue. This way of communication is termed as mechanotransduction that is a wellcharacterized process in sensory mechanisms. On the other hand, a relatively new and dynamically developing research field establishes its role in various developmental processes, as for instance epithelial morphogenesis. This crossing point of epithelial morphogenesis and mechanotransduction stands in the very center of our research limelight.

I.1. General characteristics and function of the epithelia

Epithelia, along with the connective, the muscle, and the nervous tissue, are one of the four basic animal tissue types. Epithelia are continuous sheets of cells (one or more layers thick) that cover the exterior surfaces of the body, line internal closed cavities and body tubes that communicate with the outside environment (the alimentary, respiratory and genitourinary tracts), make up the secretory portions of glands and their ducts, and are found in the sensory receptive regions of certain sensory organs (e.g. ear & nose). Epithelia cover and lining surfaces (e.g. skin), take part in absorption (e.g. the intestine), secretion (e.g. glands), can be sensory (e.g. neuroepithelium)

or contractile (e.g. myoepithelial cells). They secrete a basement membrane which supplies a site of attachment for the epithelium, and acts as a selective filtration barrier. There is little intercellular material. Epithelia do not have their own blood supply (avascular), they rely on diffusion for exchange of oxygen and metabolites. Epithelia hold specialized cellcell junctions that bind adjacent cells to each other. They also have communicating junctions (gap junctions) that allow communication between adjacent cells. Cells in epithelia show a polarity along the axis between the external and internal environment, called apicalbasal polarity. When organized in epithelial sheets, they can also exhibit a planar polarity, defined as polarity in a plane other than the apicobasal axis.

All the three germ layers, the endoderm, mesoderm, and ectoderm can give rise to epithelial tissues.

The main functions of an epithelial tissue are:

to protect the tissues that lie beneath from radiation, desiccation, toxins, invasion by pathogens, and physical trauma the regulation and exchange of chemicals between the underlying tissues and a body cavity the secretion of hormones into the circulatory system, as well as the secretion of sweat, mucus, enzymes, and other products that are delivered by ducts (Quitin et al., 2016) to provide sensation [START_REF] Takeichi | Dynamic contacts: rearranging adherens junctions to drive epithelial remodelling[END_REF] Beyond that, the epithelium oversees the formation of the invertebrate exoskeleton as well (e.g. cuticle in worms and arthropods, mineralized shell in molluscs). The role of the exoskeleton is isolation and protection. But it also serves as an insertion for the muscles that enables the active movements and displacement of these animals [START_REF] Wolpert | Principles of Development[END_REF]. In vertebrates the epidermis can be keratinized and can form various structures like hair, nails and claws or protective structures (like spines, scales, or carapaces).

I.2. The organization of an epithelial cell

Epithelial cells have evolutionary conserved features at the level of their structural organization. First, they have an apicobasal polarization that enables polarized secretion, helps to better fulfill their barrier function, and allows polarized communication with their environment [START_REF] Johnston | Cell polarity in eggs and epithelia: parallels and diversity[END_REF]. This polarization divides the epithelial cells into an apical side that is most commonly in contact with the environment and could have various surface structures (membrane protrusions, microvilli or sensory structures) and a basolateral side that is in contact with the internal environment, with the neighboring tissues and it also secretes the basal lamina (Fig. 2). A typical vertebrate epithelial cell is shown with components of the polarized vesicle sorting machinery and the apical junctional complex depicted. Note that invertebrate (for example in Drosophila) epithelial cells lack primary cilia and the junctional complex is organized differently with adherens junctions (AJs) located more apically than the sealing junction (named septate junction instead of tight junction). In C. elegans, AJs and sealing junctions are combined into a single structure. Adapted from RodriguezBoulan and Macara, 2014.

Second, epithelial cells have multiple sets of cell junctions that are relatively conserved in form and to some extent also in function throughout the evolution. They set the barrier between the apical and the basolateral side of the cell, this way promoting polarity maintenance. Furthermore, they are the elements that hold together the epithelial cells. They are important in resisting and transmitting forces within an epithelial sheet, which is pivotal during the different morphogenetic processes [START_REF] Lecuit | Ecadherin junctions as active mechanical integrators in tissue dynamics[END_REF].

Epithelial cells also possess four main interconnected cytoskeletal systems. Microtubules (MTs), intermediate filaments (IFs), and actin are the commonly discussed "classical" cytoskeletal networks, shared by all animal cells. Although there is a fourth skeletal network, the spectrin skeleton. It has been initially characterized and extensively studied in red blood cells and its role was little understood in nonerythroid cells for long. Nevertheless, recent research efforts started to recognize the impact of nonerythroid spectrins that seem to be just as important as the first three cytoskeletal entities [START_REF] Machnicka | Spectrinbased skeleton as an actor in cell signaling[END_REF].

I.2.1. Epithelial junctions

Epithelial cells are tightly connected to form a sheet. This tight connection is achieved through specialized junctions. They interconnect the membrane of adjoining cells, or between a cell and the extracellular matrix (ECM). They also build up the paracellular barrier. The primary function of cellcell junctions is to resist the external forces that pull cells apart. For instance, epithelial cells must remain tightly linked when they are stretched and pinched. These junctions are dynamic to accommodate the changes in cellular environment such as growth and remodeling.

In epithelia, junctions can be divided into six distinct types, tight junctions, adherens junctions (AJs), desmosomes, gap junctions, hemidesmosomes (HDs), and focal adhesions (FAs) (Fig. 3). At the apical pole, some types of junctions can even combine to form junction complexes.

The apicalmost junction in vertebrates is the tight junction or zonula occludens, responsible of the paracellular gating function [START_REF] Hartsock | Adherens and tight junctions: structure, function and connections to the actin cytoskeleton[END_REF][START_REF] Meng | Adherens Junction: Molecular Architecture and Regulation[END_REF]. The intercellular space where tight junction happens is very narrow and filled with this dense junction material. Therefore, the passage of substances between epithelial cells is impossible because the intercellular space is sealed [START_REF] Sullivanbrown | Neural tube closure: the curious case of shrinking junctions[END_REF]. Its analogous structure in Drosophila is the septate junction (Hall and Ward, 2016), while in C. elegans the paracellular gating is established through different mechanisms and the zonula occludens ortholog protein functions differently [START_REF] Labouesse | Epithelial junctions and attachments[END_REF].

Below the tight junction can be found the cadherincateninbased AJs: ubiquitous type of linkage between epithelial cells, responsible for maintaining cellcell adhesions. These junctions employ cadherins and catenins to link the cytoskeleton of one cell to that of its neighbor, in the presence of calcium [START_REF] Lecuit | Ecadherin junctions as active mechanical integrators in tissue dynamics[END_REF]. In C. elegans, AJ are composed of two complexes commonly referred to as the C. elegans Apical Junction (CeAJ) [START_REF] Labouesse | Epithelial junctions and attachments[END_REF]. First, the cadherin catenin complex (CCC) is the most apical within the CeAJ [START_REF] Koppen | Cooperative regulation of AJM1 controls junctional integrity in Caenorhabditis elegans epithelia[END_REF][START_REF] Mcmahon | Assembly of C. elegans apical junctions involves positioning and compaction by LET413 and protein aggregation by the MAGUK protein DLG1[END_REF]. It is analogous in composition and to a large extent in function to the cadherincatenin complex found in flies and vertebrates [START_REF] Costa | A putative catenincadherin system mediates morphogenesis of the Caenorhabditis elegans embryo[END_REF]. Second, the DLG1/AJM1 complex (DAC) is formed by two membraneassociated proteins: a Drosophila Discslarge homologue (DLG1), and a coiledcoil protein AJM1 [START_REF] Bossinger | Zonula adherens formation in Caenorhabditis elegans requires dlg1, the homologue of the Drosophila gene discs large[END_REF][START_REF] Firestein | DLG1 is a MAGUK similar to SAP97 and is required for adherens junction formation[END_REF][START_REF] Koppen | Cooperative regulation of AJM1 controls junctional integrity in Caenorhabditis elegans epithelia[END_REF][START_REF] Mcmahon | Assembly of C. elegans apical junctions involves positioning and compaction by LET413 and protein aggregation by the MAGUK protein DLG1[END_REF]. They are mutually dependent on each other for proper localization in vivo [START_REF] Koppen | Cooperative regulation of AJM1 controls junctional integrity in Caenorhabditis elegans epithelia[END_REF][START_REF] Mcmahon | Assembly of C. elegans apical junctions involves positioning and compaction by LET413 and protein aggregation by the MAGUK protein DLG1[END_REF][START_REF] Segbert | Molecular and functional analysis of apical junction formation in the gut epithelium of Caenorhabditis elegans[END_REF].

Another complex has a key role in resisting shear stress, the desmosomes. Like AJs, they are attached to cytoskeleton IFs and allow the transmission of tensile forces between epithelial cells [START_REF] Delva | The desmosome[END_REF]. However, the desmosomes do not form a continuous belt, but circular patches randomly arranged on the lateral side of the cells, to increase the stress resistance of the intra epithelial attachments [START_REF] Wolpert | Principles of Development[END_REF]. They are also located more basally compared to AJs: they are distributed over the lateral membranes, with an up limit of AJs. Desmosomes are absent in Drosophila and in C. elegans.

Unlike all other types of junctions, gap junctions connect the cytoplasm of two neighboring cells directly. As implied in its name, a gap junction allows the direct pass of various molecules, ions, and electrical impulses between two cells. One gap junction includes two connections, also called hemichannels, to form a homodimer in the intercellular space. The homodimer of connections can undergo a conformational change between close and open in different conditions and thus functions as a regulating gate between cells. Gap junctions are found in many tissues, especially in neurons and nerves, where they are called an electrical synapse [START_REF] Kelsell | Human diseases: clues to cracking the connexin code?[END_REF][START_REF] Willecke | Structural and functional diversity of connexin genes in the mouse and human genome[END_REF].

Focal adhesions (FAs) serve as the mechanical linkages to the ECM, and as a biochemical signaling hub to concentrate and direct numerous signaling proteins at sites of integrin binding and clustering. Within the cell, the intracellular domain of integrin binds to the cytoskeleton via adapter proteins such as talin, αactinin, filamin, vinculin and tensin. Other intracellular signalling proteins, such as focal adhesion kinase, also bind to and associate with this integrinadapter protein cytoskeleton complex. FAs are highly dynamic structures that grow or shrink due to the turnover of their component proteins in response to changing mechanical stresses (e.g. actomyosingenerated forces, external forces exerted by or through the surrounding matrix) [START_REF] Zamir | Dynamics and segregation of cellmatrix adhesions in cultured fibroblasts[END_REF][START_REF] Ballestrem | Marching at the front and dragging behind: differential alphaVbeta3integrin turnover regulates focal adhesion behavior[END_REF][START_REF] Rid | The last but not the least: the origin and significance of trailing adhesions in fibroblastic cells[END_REF][START_REF] Holt | Quantifying cellmatrix adhesion dynamics in living cells using interference reflection microscopy[END_REF]. For example, new adhesions are formed at the leading edge of migrating cells and grow and mature as the cells move over them (Partridge and Marcantonio, 20006). In stationary cells, they serve as anchorage devices that maintain the cell morphology. In Drosophila embryos FAs mediate surfacerigidity dependent development [START_REF] Brown | Integrins as mediators of morphogenesis in Drosophila[END_REF][START_REF] Delon | Integrins and the actin cytoskeleton[END_REF]. C. elegans present dense bodies similar to vertebrate focal adhesions but only in muscles cells not in the epithelia [START_REF] Cox | Sticky worms: adhesion complexes in C. elegans[END_REF]. Finally, the HDs are the most basal junctions. Under the electron microscope, they have a similar structure as desmosomes. However, while desmosome links two epithelial cells together, HDs link the cell to the ECM. HDs are asymmetric as they connect the basal face of the cell to the basal lamina. They include two rivetlike plaques. The plaques and the anchoring fibrils and filaments are collectively called HDstable adhesion complex. The HDstable adhesion complex forms a continuous link between the epithelia and the underlying basement membrane zone [START_REF] Bornslaeger | Breaking the connection: displacement of the desmosomal plaque protein desmoplakin from cellcell interfaces disrupts anchorage of intermediate filament bundles and alters intercellular junction assembly[END_REF][START_REF] Walko | Molecular architecture and function of the hemidesmosome[END_REF]. Therefore, HDs can transmit the forces between them, like the AJs.

I.2.2. Extracellular matrix (ECM)

The extracellular matrix is an evolutionary conserved, ancient structure present in all the metazoans. The ECM participates in keeping tissues separated, providing structural support or providing a structure for cells to migrate on. It is a complex network of macromolecules (collagen, laminin, and fibronectin, among others) that are secreted locally and assembled into sheets, fibers, and gels. Multisubunit transmembrane receptors called integrins are used to bind to the ECM.

Integrins bind extracellularly to fibronectin, laminin, or other ECM components, and intracellularly to microfilamentbinding proteins αactinin and talin to link the cytoskeleton with the outside. Integrins also serve as receptors to trigger signal transduction cascades when binding to the ECM [START_REF] Frantz | The extracellular matrix at a glance[END_REF][START_REF] Theocharis | Extracellular matrix structure[END_REF]. Different organisms have evolved different macromolecules for ECM, yet they are not so different in their functions. For instance, ECM related integrins have roles during neural development of Drosophila such as axonal growth and synapse formation [START_REF] Broadie | Extracellular matrix and its receptors in Drosophila neural development[END_REF]. Another example is the Drosophila zona pellucida (ZP) domain protein, dumpy, located in the apical ECM of epithelial cells. It has been shown to interact with numerous proteins notably during embryonic tracheal development and wing development [START_REF] Prout | Autosomal mutations affecting adhesion between wing surfaces in Drosophila melanogaster[END_REF]Walsh and Brown, 1998;[START_REF] Carmon | Dumpy interacts with a large number of genes in the developing wing of Drosophila melanogaster[END_REF]. In C. elegans, the apical ECM promotes elongation. The ZP domain proteins NOAH1 and NOAH2 are important for muscle anchoring and mechanical input from muscle contractions, which are essential for elongation (VuongBrender et al., 2017). The matrix can also become calcified and hard as rock in case of bones and teeth or produce carapace as in turtles.

I.2.3. Cytoskeleton

The cytoskeleton is present in all type of cells in the body. It organizes cells in space and helps cells to interact mechanically with each other and with the environment. It is a complex network in a remarkable system of filaments that extend throughout the cytoplasm, from the plasma membrane to the nucleus (Fisher and Fowler, 2015). The structure, function, and dynamics of cytoskeleton can vary. They depend on the behavior of three families of filaments: intermediate filaments (IFs), actin filaments, and microtubules (MTs). Each type differs in their composition, biological role, dynamics, and mechanical properties. Actin filaments determine the shape of the cell's surface and are necessary for wholecell locomotion and cell membrane pinching during cell division. MTs determine the positions of the membrane bound organelles, direct intracellular transport, form and orient the mitotic spindle that segregates the chromosomes. IFs supply the mechanical strength.

A network of proteins regulates the cytoskeleton. Accessory proteins, which include a variety of motor proteins such as myosins or kinesins control the assembly of cytoskeletal filaments in specific locations. [START_REF] Howard | Molecular motors: structural adaptations to cellular functions[END_REF][START_REF] Fehon | Organizing the cell cortex: the role of ERM proteins[END_REF].

I.2.3.1. Actin and myosin

Actin is a family of globular multifunctional proteins that form microfilaments. It is found in essentially all eukaryotic cells. Its mass is about 42kDa, with a diameter of 4 to 7 nm. An actin protein is the monomeric subunit of two types of filaments in cells: microfilaments, one of the three major components of the cytoskeleton, and thin filaments, part of the contractile apparatus in muscle cells. It can be present as either a free monomer called Gactin (globular) or as part of a linear polymer microfilament called Factin (filamentous), both of which are essential for cellular functions (Alberts, 2002, Amon, 2012). Factin is a semiflexible polymer with a bending stiffness much greater than that of flexible biopolymers such as DNA, but significantly more flexible than rigid rodlike macromolecules such as MTs. It has very high compressive strength however actin binding proteins (ABPs) decrease this and allow bending. These physical properties suggest that Factin itself may function as a highly dynamic tension sensor [START_REF] Galkin | Actin filaments as tension sensors[END_REF]. Its interaction with various ABPs allow the actin cytoskeleton to promptly adapt to intracellular and extracellular mechanical forces affecting its structure and dynamics [START_REF] Harris | Mechanotransduction by the actin cytoskeleton: Converting mechanical stimuli into biochemicals signals[END_REF].

While providing mechanical support to the cells, the actin network is also connected to trans membrane adhesion proteins [START_REF] Doherty | Mediation, modulation, and consequences of membranecytoskeleton interactions[END_REF]. This connection eases the transduction of intracellular and extracellular mechanical signals, which allow cells to detect and respond to both chemical and mechanical signals from their extracellular environment. Indeed, the actin skeleton conducts a broad range of functions in epithelial cells, including muscle contraction, cell motility, cell division and cytokinesis, vesicle and organelle movement, cell signaling, and the establishment and maintenance of cell junctions and cell shape [START_REF] Huber | Emergent complexity of the cytoskeleton: from single filaments to tissue[END_REF][START_REF] Xu | Actin, spectrin and associated proteins form a periodic cytoskeletal structure in axons[END_REF][START_REF] Suraneni | A mechanism of leadingedge protrusion in the absence of Arp2/3 complex[END_REF][START_REF] Tsopoulidis | T cell receptortriggered nuclear actin network formation drives CD4+ T cell effector functions[END_REF].

In vertebrates, three main groups of actin isoforms, α, β, and γ have been identified. The α actins, found in muscle tissues, are a major constituent of the contractile apparatus. The β and γ actins coexist in most cell types as components of the cytoskeleton, and as mediators of internal cell motility. Although the amino acid sequences and in vitro properties of the isoforms are highly similar, these isoforms cannot completely substitute for one another in vivo [START_REF] Khaitlina | Functional specificity of actin isoforms[END_REF]. Actin has been one of the most highly conserved proteins throughout evolution because it interacts with a large number of other proteins. It has 80.2% sequence conservation at the gene level between Homo sapiens and Saccharomyces cerevisiae, and 95% conservation of the primary structure of the protein product [START_REF] Gunning | The evolution of compositionally and functionally distinct actin filaments[END_REF].

Although the monomers of actin assemble the helical ropelike filaments, these filaments are modified by and interact with other proteins to carry essential cellular functions (Sackman, 2015).

This process is called actin remodeling. It is a cyclic pattern allowing the dynamic alterations of cellular organization (Fig. 4). During the remodeling process, actin monomers polymerize in response to signaling cascades that stem from environmental cues [START_REF] Stossel | Cell surface actin remodeling[END_REF]. The cell's signaling pathways cause actin to affect intracellular organization of the cytoskeleton and often, the cell membrane. Over the course of the cycle, actin begins as a monomer, elongates into a polymer with the help of attached actinbindingproteins, and disassembles back into a monomer so the remodeling cycle may commence again [START_REF] Stossel | Cell surface actin remodeling[END_REF][START_REF] Rottner | Actin dynamics and turnover in cell motility[END_REF]. The dynamic function of actin remodeling is directly correlated to the immense variability of cell shape, structure, and behavior. First, there is uncapping of the barbed end by the removal of barbed end capping proteins and ABPs that sever actin filaments [START_REF] Stossel | Cell surface actin remodeling[END_REF]). This step is followed by de novo nucleation of new actin microfilaments from the existing sides of Factin by the Arp2/3 complex and formins [START_REF] Begg | The visualization of actin filament polarity in thin sections. Evidence for the uniform polarity of membraneassociated filaments[END_REF]. It is helped by polymerization promoters and barbed end capping inhibitory proteins. The elongation phase begins when the concentration of short, Factin polymers is significantly larger than at equilibrium. At this point, both termini accept the addition of new monomers (although primarily at the barbed end) and the actin microfilament lengthens [START_REF] Kuhn | Realtime measurements of actin filament polymerization by total internal reflection fluorescence microscopy[END_REF]. It results in the overall stabilization of the actin filament network. The cell uses crosslinking proteins of diverse sizes to carry out different means of stability within the binding network. Small ABP's such as scruin, fimbrin, and espin function by solidifying actin filament bundles [START_REF] Stossel | Cell surface actin remodeling[END_REF]. Larger ABPs that exhibit coillike qualities such as filamin function in the promotion of orthogonal organization. Actin crosslinking provides a framework for which the cell may transport signaling intermediates needed for other steps within the actin remodeling cycle [START_REF] Begg | The visualization of actin filament polarity in thin sections. Evidence for the uniform polarity of membraneassociated filaments[END_REF][START_REF] Dos Remedios | Actin binding proteins: regulation of cytoskeletal microfilaments[END_REF][START_REF] Winder | Actinbinding proteins[END_REF][START_REF] Lappalainen | Actinbinding proteins: the long road to understanding the dynamic landscape of cellular actin networks[END_REF].

Recycling

Profilin, Tβ4 Srv2 / CAP Nucleation Arp2/3 complex, formins, Spire, Cobl

Elongation and capping

Profilin, capping proteins After a while, the immobilization by interpenetration of actin filaments results from two distinct ABP families. The gelsolin protein family is believed to be the most efficient in the disruption of actin filaments and is considered a strong severing protein. These proteins respond to an increase in Ca 2+ and cap the barbed end of the recently severed Factin [START_REF] Kalwat | Signaling mechanisms of glucoseinduced Factin remodeling in pancreatic islet β cells[END_REF]). The increased level of Ca 2+ may also destabilize the actinfilament network by interfering with the binding of crosslinking proteins [START_REF] Nicholsondykstra | Actin dynamics: growth from dendritic branches[END_REF]. The ADF/cofilin protein family also serves to severe actinfilament networks through the weak severing of actin networks. This form of weak severing does not tightly cap the barbed ends but does allow for the disassociation of actin monomers and thus the disassembly of Factin [START_REF] Begg | The visualization of actin filament polarity in thin sections. Evidence for the uniform polarity of membraneassociated filaments[END_REF]. Finally, thymosin and profilin prevent the spontaneous nucleation of new actin trimers. Actin filaments break back down into monomers and the cycle is completed. Despite its complexity, actin remodeling may result in complete cytoskeletal reorganization in under a minute [START_REF] Lodish | [END_REF].

Disassembly and depolymerization

ADF

Apart of the actin remodeling proteins, other regulators can also contribute to actin dynamics.

Indeed, in the epithelial cells the internal force generation occurs through an actomyosin contractile system, with the contribution of nonmuscle myosins: molecular motors that convert chemical energy by ATP hydrolysis into mechanical force generation. To note, several nonmuscle myosins, like nonmuscle myosin I and VI could also contribute to epithelial contractility [START_REF] Dai | Myosin I contributes to the generation of resting cortical tension[END_REF][START_REF] Biro | Cell cortex composition and homeostasis resolved by integrating proteomics and quantitative imaging[END_REF], but the most relevant force generator is nonmuscle myosin II.

Nonmuscle myosin II is composed of a pair of heavy chains (MHC), a pair of essential light chains (MLC) and a pair of regulatory light chains (RLC). The MLC contain calciumbinding EFhand domains, interacting with the neck region of the MHC (Fig. 5a). The MLC are responsible for the structural integrity of the motor domain, while the regulatory light chains regulate the myosin II ATPase activity [START_REF] Ruff | Singlemolecule tracking of myosins with genetically engineered amplifier domains[END_REF]. Together they form an hexameric protein complex socalled positive end motor: its progressive movement is directed towards the plus end of the actin filament (Fig. 5b). The motor part of the protein is situated in the Nterminal globular head domain of the MHC, containing the actin and ATPbinding sites, required for motor activity. ATPbinding and hydrolysis causes conformational changes in the head domain which results in displacement. Myosin II motors by their own are unipolar and hardly processive, they do not perform a contractile activity.

But following their activation, they form bipolar complexes, consisting of several NMYII hexamers in an antiparallel organization, interacting through the MHC tails. In this arrangement NMYII mini filaments become highly processive, their motor domains associate with oppositely oriented, antiparallel actin filaments and pull them together. The attachment and detachment of NMYII and actin happens in a cyclic manner and is coupled to the ATPase activity of NMYII. The phosphate release upon ATP hydrolysis produces the energy for the conformational change, which triggers the actin movement. At the end of the movement ATP replaces ADP at the motor domain and NMYII detaches from actin. This mechanism is the heart of the actomyosin contractility that creates cortical tension in the epithelial cells [START_REF] Krendel | Myosins: tails (and heads) of functional diversity[END_REF][START_REF] Levayer | Biomechanical regulation of contractility: spatial control and dynamics[END_REF]. (a) The subunit and domain structure of NM II forms a dimer through interactions between the αhelical coiled coil rod domains. The globular head domain contains the actinbinding regions and the enzymatic Mg 2+ ATPase motor domains. The ELCs and the RLCs bind to the heavy chains at the lever arms that link the head and rod domains. In the absence of RLC phosphorylation, NM II forms a compact molecule through a head to tail interaction. This results in an assembly in competent form (10S; left) that is unable to associate with other NM II dimers. On RLC phosphorylation, the 10S structure unfolds and becomes an assemblycompetent form (6S). S1 is a fragment of NM II that contains the motor domain and neck but lacks the rod domain and is unable to dimerize. Heavy meromyosin (HMM) is a fragment that contains the motor domain, neck and enough of the rod to effect dimerization. (b) NM II molecules assemble into bipolar filaments through interactions between their rod domains. These filaments bind to actin through their head domains and the ATPase activity of the head enables a conformational change that moves actin filaments in an antiparallel manner. Bipolar myosin filaments link actin filaments together in thick bundles that form cellular structures such as stress fibers. Adapted from [START_REF] Vicentemanzanares | Nonmuscle myosin II takes centre stage in cell adhesion and migration[END_REF] In Drosophila, a single gene encodes for each subunit: zipper for MHC, spaghetti squash (sqh)

for MLC and mlcc essential light chain [START_REF] Yamashita | Identification and analysis of the myosin superfamily in Drosophila: a database approach[END_REF]. C. elegans has two MHC genes (nmy 1, nmy2), a single MLC gene (mlc4) and a single essential MLC gene (mlc5) [START_REF] Chisholm | Epidermal morphogenesis[END_REF]Gally et al., 2009). In vertebrates at least one regulatory light chain (MRLC2) and three MHC isoforms can be found: NMHCIIAC [START_REF] Conti | Nonmuscle myosin II moves in new directions[END_REF]. Actin forms contractile structures with myosin motor proteins to form crosslinks and to slide compared to one another. As epithelial cells do not need to generate a high amount of contractile tension compared to muscle cells, they only have a small amount of actomyosin II bundles. The regulation of these contractile bundles' activity is through the phosphorylation of myosin light chain.

One important function of these contractile bundles is to provide mechanical support for cells.

Actomyosin bundles can assemble into cortical stress fibers to connect epithelial cells to adjoining cells or ECM through AJs (Sackman, 2015). Also, actomyosin can generate forces inside epithelial cells for their remodeling, as well as the regulation of cell adhesion and migration during morphogenesis [START_REF] Zelenka | Regulation of cell adhesion and migration in lens development[END_REF][START_REF] Blaser | Migration of zebrafish primordial germ cells: a role for myosin contraction and cytoplasmic flow[END_REF]Wirshing and Cram, 2017).

I.2.3.2. Microtubules (MTs)

MTs are complex and highly dynamic cytoskeletal components. The subunits of MTs are tubulins, which are heterodimers formed by two closely related globular proteins: α and β tubulins.

Assembly of tubulins forms hollow, helical tubes of MTs, which can grow up to 50µm long tubes of 24nm in diameter [START_REF] Weisenberg | Microtubule formation in vitro in solutions containing low calcium concentrations[END_REF][START_REF] Pilhofer | Microtubules in bacteria: ancient tubulins build a fiveprotofilament homolog of the eukaryotic cytoskeleton[END_REF]. These tubes are assembled of short (8nm long) protofilaments. Thirteen such protofilaments line up side by side to close a concentric tube, but the neighboring filaments are not completely aligned: there is a 0.9 nm shift between them, which gives the tube a spiral structure. MTs exist in a dynamic instability and are quasi constantly remodeled: there is a fastgrowing plus end, where filament polarization and depolymerization happen, and a minus end often anchored to the centrosome or the microtubule organizing center (MTOC) [START_REF] Desai | Microtubule polymerization dynamics[END_REF][START_REF] Marshall | Cell division: The renaissance of the centriole[END_REF]. The dynamics instability that MTs undergo is profoundly influenced by the binding and hydrolysis of GTP. The dynamics and organization of MTs are also modulated by the polymerstabilizing/destabilizing drugs and MT binding proteins [START_REF] Weisenberg | Microtubule formation in vitro in solutions containing low calcium concentrations[END_REF][START_REF] Weisenberg | Tubulinnucleotide interactions during the polymerization and depolymerization of microtubules[END_REF]. Apart of α and β tubulins, γ units also exist, but they do not contribute to such tube formation. These units are acting as nucleators that cap the minus end of the tubes. They are found at the highest concentration in the nucleus, but they are present within the whole cell architecture, at several nucleation sites of the MTs network.

A major function of MTs is to enable motor proteins to transport cargos within the cells. Two families of MTbased motors, kinesins, and dyneins move along MTs to transport vesicles and even organelles during interphase (Berg et al., 2002). This MTmediated transport is an essential element of various cellular processes and it plays a significant role during cellular movements and shape changes as well (Alberts et al., 2002). It is well established that MTs are central components of cell mechanics during tissue morphogenesis [START_REF] Kirschner | Beyond selfassembly: from microtubules to morphogenesis[END_REF]Mathur and Hülskam, 2002;[START_REF] Cearns | Microtubules, polarity and vertebrate neural tube morphogenesis[END_REF][START_REF] Singh | Polarized microtubule dynamics directs cell mechanics and coordinates forces during epithelial morphogenesis[END_REF]. Our lab has recently discovered that MTs also contribute to the process of embryonic morphogenesis as transport machinery (Quitin et al., 2016). Another example is the neuronal morphogenesis in the developing brain. The MT cytoskeleton provides physical support to shape the fine structure of neuronal processes. MTbased motors play important roles in nucleokinesis and centrosomal positioning [START_REF] Sakakibara | Microtubule dynamics in neuronal morphogenesis[END_REF]. The centrosome, as major organizer of MTs, also has essential functions in regulating cell shape, polarity, cilia formation as well as the position of cellular structures, including the mitotic spindle. Therefore, centrosomes and MTs have important roles during morphogenesis by controlling cell fate decision during tissue and organ development [START_REF] Tang | Centrosome positioning in vertebrate development[END_REF]. However, MTs still play key roles in development even when they are not centrosomally organized. For example, during early Drosophila wing epithelium development, individual cells are mechanically autonomous. They contain a polarized apical noncentrosomal MT cytoskeleton that bears compressive forces. In these cells, the Fat planar cell polarity signaling pathway couples MTs at AJs and patterns MTbased forces across a tissue via polarized transcellular stability. These results provide a physical basis to explain how global patterning of MTs controls cell mechanics to coordinate collective cell behavior during tissue remodeling [START_REF] Singh | Polarized microtubule dynamics directs cell mechanics and coordinates forces during epithelial morphogenesis[END_REF].

Despite of their obvious importance, there is still a lot left to understand about the role of MTs at the level of complex epithelial behavior, which serves as an interesting future research direction in cell biology.

I.2.3.3. Intermediate filaments (IFs)

Unlike actin and tubulin, IFs are not present in all eukaryotic cells. In the most exposed epithelia, such as the skin, and the cells undertaking mechanical stress, IFs are chemically modified and fill the cell in a massive amount. This implies that IFs endure mechanical tension, provide mechanical stability to the cells and tissues and maintain their integrity [START_REF] Kolega | Effects of mechanical tension on protrusive activity and microfilament and intermediate filament organization in an epidermal epithelium moving in culture[END_REF][START_REF] Loranger | Simple epithelium keratins are required for maintenance of hepatocyte integrity[END_REF][START_REF] Hesse | Targeted deletion of keratins 18 and 19 leads to trophoblast fragility and early embryonic lethality[END_REF]Fisher and Fowler, 2015). IFs are flexible and extensible structures. Most types of IFs (like neurofilaments, keratins or desmins) are cytoplasmic but nuclear IFs (lamins) also exist. They assemble into filaments of 812nm in diameter. These filaments assemble in antiparallel tetramers, combination of two dimers with a tripartite structure: flexible N and Cterminal domains that flank a central coiled coil domain. The functions of IFs include organizing the internal structure of epithelial cells and maintaining the cell shape by bearing mechanical tensions [START_REF] Kolega | Effects of mechanical tension on protrusive activity and microfilament and intermediate filament organization in an epidermal epithelium moving in culture[END_REF][START_REF] Bornslaeger | Breaking the connection: displacement of the desmosomal plaque protein desmoplakin from cellcell interfaces disrupts anchorage of intermediate filament bundles and alters intercellular junction assembly[END_REF]. They are proposed to be able to resist a significantly higher level of longitudinal strain than actin or MTs [START_REF] Kreplak | Biomechanical properties of intermediate filaments: from tissues to single filaments and back[END_REF]. Their ability to rapidly change their organization in response to injury is a crucial part in tissue repair. Instead of treadmilling like actin and MTs, their dynamic structural changes are achieved through posttranslational modifications, like phosphorylation or sumoylation [START_REF] Depianto | Intermediate filaments and tissue repair[END_REF][START_REF] Pásti | Epithelial junctions, cytoskeleton, and polarity[END_REF]. As mentioned in the paragraph about junctions, IFs also take part in cellcell desmosomes and cell matrix HDs. Therefore, they also play a role in tension transmission between epithelial cells and contribute to shear stress resistance [START_REF] Hahn | Tissue integrity: Hemidesmosomes and resistance to stress[END_REF]. They are important during development as well: in the elongating C. elegans embryo their phosphorylation is at the final step of a mechanotransduction pathway and it leads to HDs remodeling, needed for the proper completion of the C. elegans embryonic development (Zhang et al., 2011).

In this section, I reviewed the general characteristics and structure of the epithelia. Epithelial cells by their own are already very smartly designed small entities, possessing a series of useful molecular features that help their cellular functions, enable selforganization and a dynamic crosstalk with their environment. These functions and crosstalk imply to a large extent mechanical forces that can already drive cell shape changes in a single cell. But if cells cope up at a higher level through tissue interplay, it can lead to morphological changes that are crucial in development and in various other biological processes. The upcoming section aims to summarize the mechanisms underlying cell shape changes and epithelial morphogenesis, with an outlook on mechanotransduction as it is a key mechanism in this PhD work.

II. Epithelia remodeling during morphogenesis

Tissue organization arises from cells showing a set of welldefined morphogenetic behaviors that include movement, shape change, differential growth, and apoptosis. Morphogenetic events extend from the organization of subcellular structures through migration of single cells to the coordinated activity of the thousands of cells that achieves the complex folding. Collective and coordinated epithelial cell shape changes have been reported in numerous biological processes. The classical examples are crucial developmental processes like gastrulation (studied extensively in Ascidians, Drosophila, zebrafish or Xenopus), primitive gut tube formation in Xenopus formation [START_REF] Reed | Morphogenesis of the primitive gut tube is generated by Rho/ROCK/myosin IImediated endoderm rearrangements[END_REF] and several organogenetic aspects (neural tube formation, mammary gland, kidney or lung tubulogenesis) [START_REF] Colas | Towards a cellular and molecular understanding of neurulation[END_REF][START_REF] Rogers | The Rho family of small GTPases is involved in epithelial cystogenesis and tubulogenesis[END_REF][START_REF] Ewald | Collective epithelial migration and cell rearrangements drive mammary branching morphogenesis[END_REF][START_REF] Davidson | No strings attached: new insights into epithelial morphogenesis[END_REF]. Recent research also explores new models, where not the entire organ, but some parts of it have an epithelial origin and therefore contribute to morphogenesis. Such systems are for instance teeth morphogenesis in zebrafish [START_REF] Verstraeten | Zebrafish teeth as a model for repetitive epithelial morphogenesis: dynamics of E cadherin expression[END_REF] or eye morphogenesis in mice [START_REF] Chauhan | Epithelial morphogenesis: the mouse eye as a model system[END_REF], but the impact of epithelial pouches and clefts that contribute to the patterning of the vertebrate face are also subjects of intense research [START_REF] Choe | Dynamic epithelia of the developing vertebrate face[END_REF].

At a tissue level, morphogenesis arises because of cellular proliferation and motility. Detailed analyses of morphogenetic events in a variety of animals suggests that most morphogenetic events are in fact driven by only few basic cellular mechanisms, used in different combinations and sequences. For example, cell proliferation is driven by cell division, giving rise to two daughter cells, while apoptosis results in the disappearance of the dying cell. Changes in cell position are brought about by either cell migration or cellular rearrangements, such as cell intercalations and neighbor exchanges. Tissue separation can also occur via more dramatic cellular differentiation events during which epithelial cells become mesenchymal. Mesenchymal cells typically leave the epithelial tissue because of changes in cell adhesive and contractile properties and migrate away from the epithelium to associate with other similar cells in a new location [START_REF] Yu | Homeostatic signaling by cellcell junctions and its dysregulation during cancer progression[END_REF]. Coordinated changes in position of individual cells can trigger tissue rotations, spatially controlled cell proliferation, cell division orientation and cell death within multicellular tissues can give rise to global changes in tissue shape [START_REF] Heisenberg | Forces in tissue morphogenesis and patterning[END_REF].

However there is another of central importance for tissue morphogenesis during development: shape changes. Cell shape is the product of a cell's material and active properties balanced by external forces. Control of cell shape, therefore, relies on both tight regulation of intracellular mechanics and the cell's physical interaction with its environment. Indeed, throughout the lifespan of an organism, shape changes are necessary for cells to carry out their essential functions. Nowhere is this more dramatic than embryonic development, when cell shape changes drive largescale rearrangements in tissue architecture to establish the body plan of the organism. A longstanding question for both cell and developmental biologists has been how are forces generated to change cell shape?

Increase in tension leads to an increase in adhesion

Two principal factors contribute to cellular deformation and mechanical stresses that are experienced by cells and influence cell behavior in early development-the mechanical stiffness of the local tissue environment (extrinsic force) and the contractile activity of the cells pulling on that environment (intrinsic force). Extrinsic forces are applied on cells by the neighboring tissues or by other external factors, often by force transmission through the ECM [START_REF] Engler | Matrix elasticity directs stem cell lineage specification[END_REF]. But epithelial cells are also able to deform autonomously, by intrinsic force generation through actomyosin contractility, without any application of external stress [START_REF] Murrell | Forcing cells into shape: the mechanics of actomyosin contractility[END_REF]. Cell deformation triggered by extrinsic forces is more like a passive response, while internal force generation can be considered as an active process. A proper balance between extrinsic and intrinsic forces is a key component of finely controlled cell shape changes and needs to be strictly regulated, both by cellular mechanical properties and by biochemical signaling [START_REF] Paluch | Biology and physics of cell shape changes in development[END_REF].

In development, understanding the interplay between cellular contractile activity, stiffness of surrounding tissues, and the resultant deformations and mechanical stresses is critical for refining model of embryogenesis (Fig. 6).

II.1. Contractility and intrinsic forces

Various internal forces also contribute to mechanical stresses during embryogenesis. These internal forces refer to contractile forces generated internally by the actomyosin cytoskeleton. There are several strategies to develop tissue dynamics. Such as cortical tension or basolateral protrusions, as reported in the case of gut organogenesis, notochord formation in ascidians, amphibians and fish, or dorsal intercalation in C. elegans embryos [START_REF] Pilot | Compartmentalized morphogenesis in epithelia: from cell to tissue shape[END_REF].

II.1.1. Apical constriction

In epithelial sheets, the mechanical coupling of cells via AJs allows individual cell behaviors to propagate change across the tissue, leading to tissue morphogenesis. A common epithelial cell shape change that participates in morphogenetic events throughout development is apical constriction [START_REF] Sawyer | Apical constriction: a cell shape change that can drive morphogenesis[END_REF][START_REF] Martin | Apical constriction: themes and variations on a cellular mechanism driving morphogenesis[END_REF][START_REF] An | Apical constriction is driven by a pulsatile apical myosin network in delaminating Drosophila neuroblasts[END_REF]. Apical constriction reduces the apical surface area of the epithelial cell, which contains AJs, and often expands at the basal end, transforming a columnarshaped cell to a wedge or cone shape (Fig. 7). Due to the symmetrical constriction of actomyosin, the apical side of epithelial cells contracts resulting in cells taking on a wedged shape [START_REF] Takeichi | Dynamic contacts: rearranging adherens junctions to drive epithelial remodelling[END_REF]. flows. Actinmyosin network coupling to apical junctions leads to myosin organizing into a supra cellular network that connects each cell to transmit forces across the tissue [START_REF] Martin | Integration of contractile forces during tissue invagination[END_REF][START_REF] Bosveld | Mechanical control of morphogenesis by Fat/Dachsous/Fourjointed planar cell polarity pathway[END_REF][START_REF] Heisenberg | Forces in tissue morphogenesis and patterning[END_REF].

Apical constriction and MyoII contraction in mesoderm cells are not continuous but occur as a series of constriction pulses that are often asynchronous in neighboring cells [START_REF] Martin | Pulsed contractions of an actin-myosin network drive apical constriction[END_REF].

Individual cells undergo three to five pulses before invagination that exhibit a periodicity of about 90 seconds. Importantly, mesoderm cells maintain their contracted state between contraction pulses, which allows these cells to rapidly (5-10 min) reduce their apical area by 75% in an incremental manner [START_REF] Mason | Tuning cell shape change with contractile ratchets[END_REF]. This stabilization of the contracted state between pulses occurs despite the fact that apical constriction generates levels of tension along the length of the furrow that are high enough to influence the directionality of the cell shape change [START_REF] Martin | Integration of contractile forces during tissue invagination[END_REF].

Thus, it appears that apical constriction also occurs in a ratchetlike manner: pulses of actomyosin contraction drive apical area reduction and cell shape is stabilized between pulses to prevent apical relaxation (Fig. 8). [START_REF] Mason | Tuning cell shape change with contractile ratchets[END_REF].

II.1.2. Cell migration

Cell migration is critical to the development of most animals, being responsible for the dispersal of cells from one place to others (eg cells originating in the neural crest that disperse to form melanocytes, some neural tissue and much of the face, or primordial germ cells that migrate to the developing gonads) and also being responsible for the extension of neural axons and dendrites to their targets. Cell migration is driven mainly by organization of a motile leading edge (lamellipodium) in one part of the cell, this leading edge being based on polymerization of Factin filaments, mostly oriented with their growing (plus or barbed) ends facing the plasma membrane [START_REF] Svitkina | Arp2/3 complex and actin depolymerizing factor/cofilin in dendritic organization and treadmilling of actin filament array in lamellipodia[END_REF][START_REF] Pollard | Cellular motility driven by assembly and disassembly of actin filaments[END_REF][START_REF] Ponti | Two distinct actin networks drive the protrusion of migrating cells[END_REF][START_REF] Koestler | Differentially oriented populations of actin filaments generated in lamellipodia collaborate in pushing and pausing at the cell front[END_REF]. They are controlled by ARP2/3 complexes themselves regulated, via proteins such as WASP, by small GTPases such as Rac and cdc42. Contractile forces are generated by a MyoIIcontaining network of longer oriented actin filaments behind the lamellipodium, called the lamella, and by actomyosin bundles called stress fibers (Verhovsky et al., 1995;[START_REF] Svitkina | Analysis of the actinmyosin II system in fish epidermal keratocytes: mechanism of cell body translocation[END_REF][START_REF] Koestler | Differentially oriented populations of actin filaments generated in lamellipodia collaborate in pushing and pausing at the cell front[END_REF][START_REF] Aratynschaus | Dynamic and structural signatures of lamellar actomyosin force generation[END_REF].

The range of the periodic contractions of MyoII can vary from about 25 seconds to several minutes [START_REF] Giannone | Periodic lamellipodial contractions correlate with rearward actin waves[END_REF][START_REF] Giannone | Lamellipodial actin mechanically links myosin activity with adhesionsite formation[END_REF][START_REF] Vicentemanzanares | Regulation of protrusion, adhesion dynamics, and polarity by myosins IIa and IIb in migrating cells[END_REF][START_REF] Meili | Myosin II is essential for the spatiotemporal organization of traction forces during cell motility[END_REF][START_REF] Burnette | A role for actin arcs in the leadingedge advance of migrating cells[END_REF].

Cell motility is possible because actin filaments are semiflexible polymers that, in conjunction with the molecular motor myosin, can act as biological active springs or "dashpots" able to exert or resist against force in a cellular environment [START_REF] Blanchoin | Actin dynamics, architecture, and mechanics in cell motility[END_REF]. To modulate their mechanical properties, actin filaments can organize into a variety of architectures generating a diversity of cellular organizations including branched or crosslinked networks in the lamellipodium, parallel bundles in filopodia, and antiparallel structures in contractile fibers. These different architectures can be envisioned as a series of interconnected active springs and dashpots that act as mechanical elements to drive cell shape changes and motility (Fig. 9) [START_REF] Blanchoin | Actin dynamics, architecture, and mechanics in cell motility[END_REF].

~

Signal transduction cascades can regulate the activity of these proteins allowing cells to be guided by gradients of attractive or repulsive extracellular molecules, in a process called chemotaxis.

The migration of cells can also be controlled by differences in substrate adhesion, generally choosing more adhesive surfaces when presented with a choice, for biophysical reasons [START_REF] Lautscham | Biomembranemimicking lipid bilayer system as a mechanically tunable cell substrate[END_REF][START_REF] Simsek | Substraterigidity dependent migration of an idealized twitching bacterium[END_REF]. Adhesion to substrates depends on the ECM molecules within the substrate and the repertoire of matrix receptors (for example, integrins) expressed by the cells themselves. Different cells express different combinations of integrins, and therefore can respond in a cell typespecific manner to the same ECM cues of a substrate. This coupling to the underlying substrate via adhesions allows the Factin network to adapt and modulate cell shape. It is locally regulated and has been characterized as a molecular 'clutch' [START_REF] Gardel | Mechanical integration of actin and adhesion dynamics in cell migration[END_REF][START_REF] Stricker | Mechanics of the Factin cytoskeleton[END_REF]. Indeed, on one hand MyoII contractile force causes the leading edge of the migrating cell to periodically retract, while on the other hand coupling of actin arcs with focal adhesions prevents further retraction by stopping the retrograde flow of actin arcs and functioning as the 'clutch' to anchor arcs relative to the substrate [START_REF] Burnette | A role for actin arcs in the leadingedge advance of migrating cells[END_REF]. The hypothesis is that leading edge advance acts in a cyclical and ratchetlike manner: membrane extension initiates new focal adhesions that engage actin arcs and establish a new base for membrane protrusion (Fig. 10). A proper balance between contractility and cellsubstrate adhesion is required for optimal cell migration. Indeed, cells require traction to move, but too much adhesion results in drag forces that resist actomyosin contraction [START_REF] Gupton | Spatiotemporal feedback between actomyosin and focaladhesion systems optimizes rapid cell migration[END_REF]WatermanStorer, 2006, Mason and[START_REF] Mason | Tuning cell shape change with contractile ratchets[END_REF].

II.1.3. Convergent extension

Convergent extension is a mechanism that allows a structure to become long and thin without any net increase in cell volume or number. This process plays a crucial role in shaping the body plan during embryogenesis and occurs during gastrulation, neurulation, axis elongation, and organogenesis in both vertebrate and invertebrate embryos [START_REF] Keller | The function and mechanism of convergent extension during gastrulation of Xenopus laevis[END_REF][START_REF] Shih | Patterns of cell motility in the organizer and dorsal mesoderm of Xenopus laevis[END_REF][START_REF] Topczewski | The zebrafish glypican knypek controls cell polarity during gastrulation movements of convergent extension[END_REF][START_REF] Keys | Control of intercalation is cellautonomous in the notochord of Ciona intestinalis[END_REF][START_REF] Munro | Polarized basolateral cell motility underlies invagination and convergent extension of the ascidian notochord[END_REF][START_REF] Williams | Distinct apical and basolateral mechanisms drive planar cell polaritydependent convergent extension of the mouse neural plate[END_REF][START_REF] Shindo | Models of convergent extension during morphogenesis[END_REF]. Xenopus gastrulation serves as an excellent example of the role of convergent extension in embryogenesis. The driving force of convergent extension is the morphogenic activity of the presumptive dorsal mesodermal cells [START_REF] Keller | The forces that shape embryos: physical aspects of convergent extension by cell intercalation[END_REF]. If the convergent extension is interrupted or incomplete, the resulting organism will have a short anteroposterior axis, wide notochord, and broad, open neural tube [START_REF] Wallingford | Neural tube closure requires dishevelleddependent convergent extension of the midline[END_REF].

In Drosophila, after the initial infolding of gastrulation, the ventral region of the embryo undergoes a rapid elongation called germband extension. This elongation is produced by intercalation of the more lateral cells as they move toward the ventral midline (Fig. 11). The cells achieve convergent extension movements by treating their boundaries differently. Boundaries that lie within the plane of the epithelium but perpendicular to the axis of elongation shorten, under the action of actomyosin contraction. In many respects, the process is very similar to the convergent extension, which occurs during amphibian gastrulation [START_REF] Wieschaus | Convergence and Extension during Germband Elongation in Drosophila Embryos[END_REF][START_REF] Irvine | Cell intercalation during Drosophila germband extension and its regulation by pairrule segmentation genes[END_REF][START_REF] Da Silva | Oriented cell divisions in the extending germband of Drosophila[END_REF]Collinet et al., 2017;[START_REF] Kong | Forces directing germband extension in Drosophila embryos[END_REF][START_REF] Siang | Modeling cell intercalation during Drosophila germband extension[END_REF]. Although anisotropic tension itself could explain cell rearrangements observed during germband extension [START_REF] Rauzi | Nature and anisotropy of cortical forces orienting Drosophila tissue morphogenesis[END_REF], live imaging of MyoII revealed that pulsatile contractions are also present in the medial network spanning the apical surface [START_REF] Rauzi | Planar polarized actomyosin contractile flows control epithelial junction remodelling[END_REF]Fernandez Gonzalez and Zallen, 2011;[START_REF] Sawyer | A contractile actomyosin network linked to adherens junctions by canoe/afadin helps drive convergent extension[END_REF]. The shrinkage of dorsalventraloriented junctions during germband extension is known to require planar polarized junctional contractility by Myosin II [START_REF] Bertet | Myosindependent junction remodelling controls planar cell intercalation and axis elongation[END_REF][START_REF] Blankenship | Multicellular rosette formation links planar cell polarity to tissue morphogenesis[END_REF][START_REF] Rauzi | Nature and anisotropy of cortical forces orienting Drosophila tissue morphogenesis[END_REF]FernandezGonzales et al., 2009).

However, junctional Myosin II itself does not produce this shrinkage, but the polarized flow of medial actomyosin pulses towards vertical junctions does. Therefore, the proposed mechanism is the following: the MyoII cable along interfaces serves as the 'catch' in a ratchetlike mechanism that incrementally shrinks interfaces of a given orientation, resulting in cell rearrangements (Fig. 12).

Importantly, tension promotes the formation of multicellular MyoII cables during rosette formation, suggesting that mechanical feedback regulates this activity to coordinate cellular behavior and generate tissuelevel forces (FernandezGonzalez et al., 2009, Mason and[START_REF] Mason | Tuning cell shape change with contractile ratchets[END_REF]. The conservation of the ratchetlike behavior observed during cell migration, constriction and intercalation establishes the importance of this molecular machine. However, many questions still remain about this mechanism. While it is clear that dynamic and stable actomyosin networks are important for inducing and sustaining cell shape change, the connections between these distinct types of networks is still unclear.

II.2. Extrinsic forces -Mechanotransduction

As living organisms, we interact with our world through our senses. We are continuously exposed to mechanical cues and so are our cells. 3) transfer of a signal from sensor to effector cells, and (4) the effector cell response.

Mechanosensitivity in one form or another appears to be a property shared by all cells of the body and by all phyla from mammals to bacteria.

II.2.1. Matrix control of stem cell fate

Mechanotransduction has been found to occur in all corners of the biological realm and with an extremely rich and diverse set of mechanisms [START_REF] Jansen | A guide to mechanobiology: Where biology and physics meet[END_REF]. Some of these mechanisms are very similar across all domains of life, as in the case of the mechanosensitive channels that allow physical stimuli on or across membranes to control the flow of molecules across these membranes:

flow that can in turn release osmotic pressure or trigger another signaling pathway [START_REF] Kloda | Mechanosensitive channels in archaea[END_REF][START_REF] Martinac | Ion channels in microbes[END_REF]. Some are more specific to a given subset of cells, like the response of mammalian cells' cytoskeletons.

Mechanotransduction is intimately associated to cell adhesion processes targeting primarily cellmatrix and cellcell contacts. The traction forces developed and transmitted via integrins by cells toward the extracellular matrix and substratum have high incidence on cell shape, migration and differentiation. A very wellstudied example is the variable differentiation of mesenchymal stem cells (MSCs). Young MSCs differentiate in response to the stiffness of the underlying matrix. Softer matrices lead to the differentiation of MSC's into neuronal cells, i.e. brain, and are neurogenic, stiffer matrices that mimic muscles lead the MSC's to differentiate into muscles and are therefore myogenic, whereas rigid matrices that mimic bones differentiate the MSC's into osteocytes and are eventually osteogenic. [START_REF] Flanagan | Neurite branching on deformable substrates[END_REF][START_REF] Neuhuber | Reevaluation of in vitro differentiation protocols for bone marrow stromal cells: disruption of actin cytoskeleton induces rapid morphological changes and mimics neuronal phenotype[END_REF][START_REF] Garcia | Bioadhesive surfaces to promote osteoblast differentiation and bone formation[END_REF][START_REF] Engler | Matrix elasticity directs stem cell lineage specification[END_REF] (Fig. 13). Other work also showed that decreasing substrate stiffness appears to dramatically alter cell structure in many cell types, reducing cell spreading against the substrate, the formation of focal adhesions, and stress fibers [START_REF] Pelham | Cell locomotion and focal adhesions are regulated by substrate flexibility[END_REF]. Indeed, cytoskeletal filaments can propagate stresses over long distances [START_REF] Ingber | Mechanical control of tissue growth: function follows form[END_REF][START_REF] Wang | Longdistance propagation of forces in a cell[END_REF], while structures such as focal adhesions, desmosomes and junctions provide both tensile strength and effective transmission of stress.

II.2.2. Role of cytoskeleton in mechanotransduction

The role of the mammalian cell cytoskeleton in responding to physical cues such as the rigidity of its environment is one of the most studied examples of mechanotransduction (Johnson et al., 2007). Thanks to their cytoskeleton, mammalian cells can easily exert forces in the nanoNewton range on their surroundings and sense the mechanics of cells or substrates around them [START_REF] Du Roure | Force mapping in epithelial cell migration[END_REF]. For mammalian cells, physical forces play a direct role in important biological choices such as stem cell differentiation, motility or tumor formation [START_REF] Weaver | Reversion of the malignant phenotype of human breast cells in threedimensional culture and in vivo by integrin blocking antibodies[END_REF][START_REF] Engler | Matrix elasticity directs stem cell lineage specification[END_REF][START_REF] Vogel | Cell fate regulation by coupling mechanical cycles to biochemical signaling pathways[END_REF]Sheetz, 2009, Paluch et al., 2015).

Cytoskeletal filaments are proposed as a means to focus force upon molecules that can transmit mechanotransduction [START_REF] Chen | Mechanotransduction a field pulling together?[END_REF]). The way mechanical stimuli are transmitted into the cell depends on the coordinated activity of mechanosensors, influenced by resting tension levels within the cell, which are set by the cytoskeletal system [START_REF] Chen | Cell shape provides global control of focal adhesion assembly[END_REF][START_REF] Polte | Extracellular matrix controls myosin light chain phosphorylation and cell contractility through modulation of cell shape and cytoskeletal prestress[END_REF][START_REF] Ingber | Cellular mechanotransduction: putting all the pieces together again[END_REF]. The adaptive cytoskeleton deforms through assembly and disassemby of its filaments in response to an applied force. ABPs also help to dynamically organize Factin into many different structural forms such as lamellipodia, stress fibers, filopodia, podosomes, actin asters, vortices, and stars (Fritzche et al., 2017;[START_REF] Wang | Review of cellular mechanotransduction[END_REF][START_REF] Harris | Mechanotransduction by the actin cytoskeleton: Converting mechanical stimuli into biochemicals signals[END_REF]. These different architectures serve specialized roles in the cell's multiplex response to mechanical stimulation. FRET, AFM microscopy and optical traps experiments revealed that actin filaments in the various actinbased structures bear a mechanical load (per filament) [START_REF] Wang | Threedimensional super resolution microscopy of Factin filaments by interferometric photoactivated localization microscopy (iPALM)[END_REF][START_REF] Wang | Review of cellular mechanotransduction[END_REF]. These different actin structures are associated with specific mechanical loading that are optimized for the structure's specialized cellular functions. Mechanical loading (increased tension) of filaments alters their conformation [START_REF] Shimozawa | Mechanical distortion of single actin filaments induced by external force: detection by fluorescence imaging[END_REF], and how ABPs bind and affect filaments [START_REF] Harris | Mechanotransduction by the actin cytoskeleton: Converting mechanical stimuli into biochemicals signals[END_REF] (Fig. 14).

In the case of cofilin, a Factin severing protein, changes in filament length affect its binding and function. Tensile forces that stretch a cell correspondingly increase the length of filaments parallel to the direction of the stretch. Under these conditions, the binding affinity of cofilin is reduced and that of myosin II is increased [START_REF] Hayakawa | Actin filaments function as a tension sensor by tensiondependent binding of cofilin to the filament[END_REF][START_REF] Uyeda | Stretching actin filaments within cells enhances their affinity for the myosin II motor domain[END_REF][START_REF] Hayakawa | Singlemolecule imaging and kinetic analysis of cooperative cofilinactin filament interactions[END_REF]. This mechanicalinduced change in Factin length and binding partners results in stabilized F actin which can more easily form stress fibers, an essential part of a cell's mechanotransduction processes [START_REF] Mcgough | Cofilin changes the twist of Factin: implications for actin filament dynamics and cellular function[END_REF][START_REF] Hayakawa | Actin filaments function as a tension sensor by tensiondependent binding of cofilin to the filament[END_REF][START_REF] Uyeda | Stretching actin filaments within cells enhances their affinity for the myosin II motor domain[END_REF][START_REF] Hayakawa | Singlemolecule imaging and kinetic analysis of cooperative cofilinactin filament interactions[END_REF][START_REF] Ohashi | Roles of the cytoskeleton, cell adhesion and rho signaling in mechanosensing and mechanotransduction[END_REF] (Fig. 14). Tensioninduced changes in actin structural dynamics also affect the binding of actinnucleating proteins such as Arp2/320 [START_REF] Risca | Actin filament curvature biases branching direction[END_REF]. Mechanically induced changes in actinbased structures can also affect gene expression in at least some cell types. As more stress fibers form during mechanical stimulation, the transcriptional coactivator YAP translocates to the nucleus where it is activated. YAP is integral in Hippo signaling and mediates increased expression of genes involved in cell proliferation and differentiation. Thus, the response of the actin cytoskeleton to extracellular mechanical forces can result in processes that have both physiological and pathophysiological relevance [START_REF] Dupont | Role of YAP/TAZ in mechanotransduction[END_REF][START_REF] Halder | Transduction of mechanical and cytoskeletal cues by YAP and TAZ[END_REF][START_REF] Ohashi | Roles of the cytoskeleton, cell adhesion and rho signaling in mechanosensing and mechanotransduction[END_REF].

II.2.3. Protein unfolding under force: in vitro example, spectrin

Similar to Factin, ABPs and other actinassociated proteins directly respond to mechanical stresses. Common responses include conformational changes, which expose previously concealed protein binding sites. Indeed, in many contexts, mechanosensory molecules have a broad set of structural regions or motifs that can be altered over a range of mechanical forces [START_REF] Weaver | Reversion of the malignant phenotype of human breast cells in threedimensional culture and in vivo by integrin blocking antibodies[END_REF]Maritnac et al., 2008;[START_REF] Vogel | Cell fate regulation by coupling mechanical cycles to biochemical signaling pathways[END_REF]. Such proteins link the integrins or IFs of the structure to cytoskeleton. These proteins consist of tandemrepeat sequences such as spectrinfamily members (αactinin, dystrophin), talin, titin, fibronectin and cadherins. Forces can either unravel a domain or hinder the movement of a specific domain, both resulting in change of the ligand binding topology [START_REF] Rohs | Unraveling proteins: a molecular mechanics study[END_REF][START_REF] Adhikari | Unraveling the mechanism of the cadherincateninactin catch bond[END_REF].

How proteins sense forces and cellular geometry to create the correct morphology is not understood in detail but protein unfolding appears to be a major component in force and displacement sensing. Thus, the crystallographic structure of a protein domain provides only a starting point to then analyze what will be the effects of physiological forces through domain unfolding or catchbond formation [START_REF] Yan | Crystal structure of the repetitive segments of spectrin[END_REF][START_REF] Anthis | The structure of an integrin/talin complex reveals the basis of insideout signal transduction[END_REF][START_REF] Elliott | The Structure of the talin head reveals a novel extended conformation of the FERM domain[END_REF]Yogesha.et al., 2012). Mechanical unfolding of a doublerepeat b spectrin from human erythrocytes (adapted from [START_REF] Paramore | Examining the influence of linkers and tertiary structure in the forced unfolding of multiplerepeat spectrin molecules[END_REF]. Each spectrin repeat (labeled 8 and 9) is made of three αhelices denoted as A, B, and C. The unfolding sequence shows how the linker region unfolds first. (Inset) Force extension curves for a βbeta spectrin repeat construct (adapted from [START_REF] Law | Cooperativity in forced unfolding of tandem spectrin repeats[END_REF]. The bottom trace shows cooperative unfolding. Mutations weakening the linker region of spectrin have been shown to cause hereditary spherocytosis (Johnson et al., 2007). Adapted from [START_REF] Sotomayor | Singlemolecule experiments in vitro and in silico[END_REF] A wellknown example is the spectrin. The erythrocytes are able to rapidly adapt to wide arteries and narrow capillaries thanks to their discoidal shape and mechanical properties. Diseases, such as hereditary spherocytosis and elliptocytosis, causing hemolytic anemia are associated with a lack of an elastic, adaptable shape are caused by mutations affecting the red blood cell cytoskeletal network made of spectrin, ankyrin, and associated proteins [START_REF] Bennett | Spectrin and ankyrinbased pathways: metazoan inventions for integrating cells into tissues[END_REF]Discher and 9.9 11.6 13.1 15.5 18.7 20.9 24.8 , 2001;Johnson et al., 2007). Crystal structures of spectrin revealed building blocks made of threehelix bundles repeated in series and forming part of heterotetrameric assemblies arranged in elongated filaments [START_REF] Bennett | Spectrin and ankyrinbased pathways: metazoan inventions for integrating cells into tissues[END_REF][START_REF] Kusunoki | Structural insights into the stability and flexibility of unusual erythroid spectrin repeats[END_REF]. The structures also revealed an αhelical linker. Moreover, AFM experiments suggested that spectrin repeats mechanically unfold predominantly one by one in an independent, allornone fashion [START_REF] Rief | Single molecule force spectroscopy of spectrin repeats: low unfolding forces in helix bundles[END_REF] (Fig. 15). Force peaks were found to be substantially smaller than those observed for other proteins made of β strands instead of α helices.

Carl

Further AFM experiments confirmed the relative weakness of spectrin and the onebyone unfolding pathway but also revealed that different sets of spectrin repeats may exhibit intermediates and cooperative unfolding events involving more than one repeat [START_REF] Altmann | Pathways and intermediates in forced unfolding of spectrin repeats[END_REF][START_REF] Law | Cooperativity in forced unfolding of tandem spectrin repeats[END_REF]Randles et al. 2007) (Fig. 14, inset). In addition, recent work identified mutations at the linker regions of spectrin causing disease, thereby corroborating the relevance of linkers in the mechanical response of this protein as indicated by simulations (Johnson et al., 2007).

Singlemolecule force experiments in vitro enable the characterization of the mechanical response of biological matter at the nanometer scale but they do not reveal the molecular mechanisms underlying mechanical function. in silico experiments, despite their limitations, have resolved the molecular mechanisms underlying the elastic response of biomolecules. However, as force sensing and generation at the tissue and cellular scale is central to many biological events, there is a growing interest in modern cell biology for methods enabling force measurements in vivo.

Fortunately, the development of new single molecule and superresolution imaging methods enable the analysis of single molecule mechanics in physiologically relevant conditions [START_REF] Jun | Calibration of optical tweezers for in vivo force measurements: how do different approaches compare?[END_REF][START_REF] Backholm | Micropipette force sensors for in vivo force measurements on single cells and multicellular microorganisms[END_REF].

II.2.4. Protein unfolding under force: in vivo example, talin

In the few cases where single molecule mechanics are studied under physiological conditions such, as titin and talin, there are rapid cycles of stretchrelaxation that produce mechanosensing signals. Talin is one of the beststudied FA adaptor proteins. In addition to FAs, talin has been reported in podosomes, invasive structures, immunological synapses, cytotoxic synapses and so forth [START_REF] Nolz | WAVE2 regulates highaffinity integrin binding by recruiting vinculin and talin to the immunological synapse[END_REF][START_REF] Ham | Dedicator of cytokinesis 8 interacts with talin and WiskottAldrich syndrome protein to regulate NK cell cytotoxicity[END_REF]. In FAs, talin is under tension and work as direct bridges between actin and integrin and as recruiters for other FA proteins [START_REF] Kumar | Talin tension sensor reveals novel features of focal adhesion force transmission and mechanosensitivity[END_REF]. It is composed of an N terminal globular head, a flexible rod domain and Cterminal helices [START_REF] Martino | Cellular Mechanotransduction: From Tension to Function[END_REF] (Fig. 16a). Talin rod contains an additional binding site for integrin, and two sites for actin, as well as several binding sites for vinculin, its main partner at the FA site [START_REF] Gingras | Mapping and consensus sequence identification for multiple vinculin binding sites within the talin rod[END_REF][START_REF] Gingras | Structural determinants of integrin binding to the talin rod[END_REF]. When forces are applied to talin, it unfolds to expose cryptic hydrophobic binding sites to host vinculin head [START_REF] Del Rio | Stretching single talin rod molecules activates vinculin binding[END_REF][START_REF] Hirata | Forcedependent vinculin binding to talin in live cells: a crucial step in anchoring the actin cytoskeleton to focal adhesions[END_REF][START_REF] Maki | Nanomechanical characterization of tensionsensitive helix bundles in talin rod[END_REF][START_REF] Rahikainen | Mechanical stability of talin rod controls cell migration and substrate sensing[END_REF]. Talin has been shown to displays stepwise unfolding dynamics due to the characteristic transition kinetics of its mechanosensitive rod subdomains. In the absence of force, talin rod remains fully structured, and no vinculin binding sites (VBS) are available. Under lowforce regimes, only the weakest bundle unfolds revealing its VBS. This activates one vinculin molecule, releasing it from its autoinhibited state. As the force applied to talin increases, more bundles are unfolded, revealing more VBSs and thus activating an increasing number of vinculin molecules [START_REF] Haining | All subdomains of the talin rod are mechanically vulnerable and may contribute to cellular mechanosensing[END_REF]. Moreover, FRET experiments have shown the increase of tension on talin by vinculin depends mainly on actinbinding site 2 (ABS2) within the middle of the rod domain, rather than ABS3 at the far C terminus [START_REF] Kumar | Talin tension sensor reveals novel features of focal adhesion force transmission and mechanosensitivity[END_REF]. This process is called talinvinculin mechanosensitivity (Fig. 16b). The successful binding of vinculin to talin is considered essential to stabilize talinFactin interaction and thus transfer the mechanical signal inward [START_REF] Humphries | Vinculin controls focal adhesion formation by direct interactions with talin and actin[END_REF].

II.2.5. The plasma membrane as a tension sensor

The physical tension of the plasma membrane can also play a role as an orchestrator of many cellular events. By forming a physical boundary between cells and their environment that is also a biochemical platform, the plasma membrane is a key interface mediating both cellular response to mechanical stimuli, and subsequent biochemical responses. Its physical state and integrity are crucial for cell survival, and one of its major functions is to preserve its integrity and enable changes in cell shape. These changes occur in response not only to cell processes such as division, migration or spreading, but also to the constant external mechanical forces present in physiological scenarios. In this context, the membrane constitutes a crucial interface, since mechanical forces will result in a change of its state. Accordingly, extensive work has addressed how membrane tension interplays with the actin cytoskeleton to regulate cell shape [START_REF] Chugh | Actin cortex architecture regulates cell surface tension[END_REF]Pontes et al., 2017;[START_REF] Simon | Interplay between membrane tension and the actin cytoskeleton determines shape changes[END_REF], motility [START_REF] Gauthier | Temporary increase in plasma membrane tension coordinates the activation of exocytosis and contraction during cell spreading[END_REF][START_REF] Lieber | Membrane tension in rapidly moving cells is determined by cytoskeletal forces[END_REF][START_REF] Lieber | Fronttorear membrane tension gradient in rapidly moving cells[END_REF][START_REF] Hetmanski | Membrane tension orchestrates rear retraction in matrix directed cell migration[END_REF] and polarity [START_REF] Houk | Membrane tension maintains cell polarity by confining signals to the leading edge during neutrophil migration[END_REF][START_REF] Tsujita | Feedback regulation between plasma membrane tension and membranebending proteins organizes cell polarity during leading edge formation[END_REF], as well as the feedback between membrane mechanical properties, cytoskeleton organization and cell dynamics [START_REF] Keren | Cell motility: the integrating role of the plasma membrane[END_REF][START_REF] Gauthier | Mechanical feedback between membrane tension and dynamics[END_REF][START_REF] Dizmuñoz | Use the force: membrane tension as an organizer of cell shape and motility[END_REF]Calrk et al., 2014;[START_REF] Sens | Membrane tension and cytoskeleton organization in cell motility[END_REF]Pontes et al., 2017;Diz Muñoz et al., 2018;[START_REF] Saha | Joining forces: crosstalk between biochemical signalling and physical forces orchestrates cellular polarity and dynamics[END_REF].

For example, fibroblasts employ membrane tension as a global master regulator of overall shape by 'sensing' tension changes and adjusting the actomyosin cytoskeleton and membrane trafficking accordingly [START_REF] Parton | The multiple faces of caveolae[END_REF][START_REF] Gauthier | Temporary increase in plasma membrane tension coordinates the activation of exocytosis and contraction during cell spreading[END_REF][START_REF] Hamada | Lateral phase separation in tense membranes[END_REF][START_REF] Simon | Interplay between membrane tension and the actin cytoskeleton determines shape changes[END_REF] (Fig. 17). Considering a cell contacting a new substrate, first, the rounded up cell shows weak cell-substrate attachment but higher membrane tension than interphase cell (Fig. 17a). Then the cell goes through a rapid and noncontractile phase of spreading. In this phase, membrane tension is at a high but constant level compared with the interphase cell (Fig. 17b). Once the membrane reservoirs of the cell are totally unfolded, it give rise to an increase in membrane tension due to area limitation. This is followed almost immediately by activation of exocytosis and myosin II mediated contraction. The cell enters the contractile spreading phase (Fig 17c). As the cell spread, the leading edge becomes more heterogeneous with alternating protrusive and retractile regions along the boundary. Activation of contraction enables stable adhesions to mature and global remodeling of the cytoskeleton with formation of actin bundles. The cell starts to exert strong forces onto the substrate at this point. As a consequence of exocytosis and further spreading, the membrane area progressively increases whereas membrane tension progressively decreases (Fig. 17d). When the cell is fully spread, alternating protrusive and retractile activities reduce drastically.

Meanwhile actin bundles have matured into strong and clearly identifiable stress fibers linking focal adhesions. Endocytosis and exocytosis balance maintains a constant membrane area. The membrane tension is now at its low resting level (Fig. 17e). Finally, the cell polarizes. Lamellipodia protrude on one side of the cell, whereas the other side of the cell shrinks. Due to protrusion, membrane tension increases and the higher tension seems to help to maintain polarity (Fig. 17f). When encountering a new substrate, the cell will go from round shape with weak cell-substrate attachment to a polarized shape in several steps. It will increase tension on the substrate, as it membrane sense and adapt to the substrate, while cytoskeleton remodel. Adapted from [START_REF] Gauthier | Mechanical feedback between membrane tension and dynamics[END_REF].

II.2.6. Importance of stiffness during morphogenesis

Mechanotransduction has been extensively studied in cells and tissues in culture but it has also become increasingly clear that mechanosensation and transduction play important roles in many developmental and diseaserelated processes, such as embryo morphogenesis and cell spreading during metastasis [START_REF] Jaalouk | Mechanotransduction gone awry[END_REF][START_REF] Chanet | Mechanical force sensing in tissues[END_REF].

In vivo there is also evidence that stiffness is important during embryogenesis. For example, during Xenopus laevis gastrulation, convergence and extension movements can only occur if the mesoderm and notochord remain stiff enough to resist buckling [START_REF] Adams | The mechanics of notochord elongation, straightening and stiffening in the embryo of Xenopus laevis[END_REF][START_REF] Keller | Xenopus Gastrulation without a blastocoel roof[END_REF]. In addition, during this same process, the involuting marginal zone actively stiffens so that this tissue does not collapse or deform during gastrulation [START_REF] Moore | The dorsal involuting marginal zone stiffens anisotropically during its convergent extension in the gastrula of Xenopus laevis[END_REF]. Tissue stiffness may arise from several different factors such as the stiffness of the cells, usually regulated by the cytoskeleton [START_REF] Pasternak | Capping of surface receptors and concomitant cortical tension are generated by conventional myosin[END_REF], the strength of cellECM or cellcell contacts, the biochemical identity of ECM proteins, and ECM organization and maturation. It is proposed that during convergence and extension movements in X. laevis, stiffness arises primarily from changes in the cytoskeleton and the ECM [START_REF] Moore | The dorsal involuting marginal zone stiffens anisotropically during its convergent extension in the gastrula of Xenopus laevis[END_REF]. Considering the dramatic changes in cellcell and cell matrix adhesion occurring during this complex rearrangement of cells, it is likely that changes in adhesion also contribute to tissue stiffness.

However, because experiments targeting either cytoskeleton, cell adhesions, or ECM often affect all three, it has been difficult to develop an appropriate in vivo model for how these numerous factors independently contribute to a tissue's stiffness. Similarly, because of the technical challenges of accurately measuring mechanical parameters in vivo, only a few studies have directly measured embryo stiffness (VuongBrender et al., 2017). Nevertheless, laser ablations are a good technique to give insight into the forces required for embryogenesis (Priess and Hirsh, 1986;[START_REF] Hardin | The role of secondary mesenchyme cells during sea urchin gastrulation studied by laser ablation[END_REF][START_REF] Williamsmasson | An actinmediated twostep mechanism is required for ventral enclosure of the C. elegans hypodermis[END_REF][START_REF] Kiehart | Multiple forces contribute to cell sheet morphogenesis for dorsal closure in Drosophila[END_REF][START_REF] Hutson | Forces for morphogenesis investigated with laser microsurgery and quantitative modeling[END_REF][START_REF] Davidson | Measuring mechanical properties of embryos and embryonic tissues[END_REF][START_REF] Peralta | Upregulation of forces and morphogenic asymmetries in dorsal closure during Drosophila development[END_REF]. In C. elegans and Drosophila melanogaster, it helped reporting changes in global movements that are too fast to be explained by signal transduction cascades, suggesting such movements are mechanical in nature [START_REF] Hardin | The role of secondary mesenchyme cells during sea urchin gastrulation studied by laser ablation[END_REF]Suppato et al., 2005;[START_REF] Peralta | Upregulation of forces and morphogenic asymmetries in dorsal closure during Drosophila development[END_REF].

For example, recent work from our lab showed that myosinIIdependent force anisotropy within the lateral epidermis of C. elegans embryos, and stiffness anisotropy within the fiber reinforced dorsoventral (D/V) epidermis are critical in driving their elongation. By measuring the opening shape of the epidermal actin cortex after laser nanoablation, we assessed the spatiotemporal changes of actomyosindependent force and stiffness along the anteroposterior and D/V axis. We proved that the actomyosin cortex preferentially squeezes the embryo circumferentially, and that the stress anisotropy is tightly linked to the geometry of the embryo (VuongBrender et al., 2017). This work showed that tissue elongation relies on two fundamental physical quantities (mechanical stress and tissue stiffness), and provided the most advanced mesoscopic understanding to date of the mechanics at work during the first steps of C. elegans embryonic elongation (Fig. 18). Epithelial tissues define the boundary that separates our bodies from of our world. They protect us from microbial pathogens and secrete proteins that help to digest our food and feed our young. Epithelia absorb nutrients from what we consume and excrete waste to detoxify our bloodstream. Therefore, epithelial cells are one of the most important cell types in organ and body.

The reshape and rearrangement of epithelial cells at the cellscale and the tissuescale drive the process of morphogenesis. Cellular components such as the cytoskeleton and the adhesion complex can trigger and regulate the morphogenetic process by generating intercellular forces and transmitting them among cells. Actomyosin contractions at tissuescale morphogenetic processes are complex, characterized by pulses and flows. Certainly, if a contractile system would only pulse back and forth, no developmental progress could be achieved. To progress in development cell shape also needs to be maintained between consecutive contractile cycles. Such questions around cell shape maintenance allowed the discovery of morphogenetic ratchet mechanisms that are interesting new research perspectives in developmental biology and biophysics. Moreover, it is now well established that mechanical cues-either extrinsic from the cell environment or intrinsic from cellular structures-can also be control cell and tissue migration, proliferation, differentiation, homeostasis and by extend play important roles in many developmental processes, such as embryo morphogenesis. Overall, understanding how mechanical forces remodel epithelia, as well as how they contribute to largescale tissue shape change are essential to understand embryonic morphogenesis in development.

To tackle such questions during my PhD, I focused on a specific step of C. elegans morphogenesis, its embryonic elongation. But before describing the details of this process, I will first introduce C. elegans as a model system in biology.

III. Introduction to our model: the nematode Caenorhabditis elegans

C. elegans is small freeliving soil nematode. In 1963, Sydney Brenner proposed research into C. elegans primarily in neuronal development. In 1974, he began research into the molecular and developmental biology of C. elegans, which has since been extensively used as a model organism (Brenner, 1974). This pioneer work has been rewarded by two Nobel Prizes in physiology and processes (metabolism, organelle structure and function, gene regulation) can be studied in these little roundworms. They are easy to handle and breed under laboratory conditions. They easily grow on NGM (nematode growth media) plates, fed with Escherichia coli -OP50 (Brenner, 1974). Their growth can be controlled, either by incubating it at 12 or 15°C which slows the development or accelerating the growth at 25°C. In the lack of food, larvae can get arrested in development and enter in a protective state (called dauer), which enables them to survive even for several months.

The L1 larvae of the organism can be frozen, just like bacteria at 80°C and stored for longterm (Brenner, 1974). It is possible to synchronize the animals and grow them in bulk in liquid medium, which enables largescale biochemistry and screenings. They also have a large brood size, and a rapid development. In favorable environments, C. elegans undergoes reproductive development and progresses rapidly from embryo to adult in 3-5 days (15°C-20°C). The embryogenesis takes about 16

hours and the embryo grows from a comma stage to 2fold and then 4fold before hatching (see Fig. 28, will be detailed later). The newly hatched larva develops through four larval stages (L1L4). Adults then live another 2-3 weeks. Moreover, their transparent body that eases in vivo microscopy with little dissection.

54

C. elegans was the first multicellular organism to have its whole genome sequenced, allowing genetic manipulations and offering a wide array of mutants, and as of 2012, is the only organism to have its connectome completed [START_REF] White | The structure of the nervous system of the nematode Caenorhabditis elegans[END_REF][START_REF] White | Getting into the mind of a worm a personal view[END_REF][START_REF] Cook | Wholeanimal connectomes of both Caenorhabditis elegans sexes[END_REF]. It is also reassuring that C. elegans, unlike several other Nematodes, is benign to humans and no C. elegans related allergic reactions have been documented. Another advantage is that adult worms are self fertilizing hermaphrodites, but males also occur naturally in 0.10.2% of the total progeny. Strains can be kept as hermaphrodites but building new strains through genetic crossing is also possible. C.

elegans strains follow the Mendelian segregation rules. The developmental fate of every single somatic cell (959 in the adult hermaphrodite; 1031 in the adult male) has been mapped [START_REF] Sulston | Postembryonic cell lineages of the nematode, Caenorhabditis elegans[END_REF][START_REF] Kimble | The postembryonic cell lineages of the hermaphrodite and male gonads in Caenorhabditis elegans[END_REF]Hirsh, 1979, Long et al., 2009;Giurumescu and Chisholm, 2015). These patterns of cell lineage are invariant between individuals, whereas in mammals, cell development is more dependent on cellular cues from the embryo. C. elegans has five pairs of autosomes and one pair of sex chromosomes. The worms display sexual dimorphism and X0 sex determination: self fertilizing hermaphrodites, which are XX and males, which are X0. Males are rare and only 0.10.2 % of the progeny, which is a result of a rare meiotic nondisjunction of the X chromosome (Hodgkin et al., 1978). The percentage of males can be increased by starving the plates or by temperature shock.

As all systems, C. elegans also has its drawbacks: some experiments can be challenging due to its small size, not all metazoan genes are present in C. elegans and few cell culture lines are available.

III.1. C. elegans general anatomy

C. elegans is an unsegmented roundworm and bilaterally symmetrical that belongs to the Nematoda phylum, a phylogenic group assembling early evolved and simple metazoans. Despite its simplicity, C. elegans has almost all the main tissues that higher multicellular organisms have. It has a cuticle (a tough outer covering, as an exoskeleton), an epidermis secreting the cuticle (also called hypodermis), four rows of muscle cells, and a fluidfilled pseudocoelom (body cavity). It also has some of the same organ systems as larger animals. Its basic anatomy includes a mouth, pharynx, intestine, gonad, and collagenous cuticle. Like all nematodes, they have neither a circulatory nor a respiratory system. The four bands of muscles that run the length of the body are connected to a small but complex neural system that allows the muscles to move the animal's body only as dorsal bending or ventral bending, but not left or right, except for the head, where the four muscle quadrants are wired independently from one another [START_REF] Corsi | A Transparent Window into Biology: A Primer on Caenorhabditis elegans[END_REF] (Fig. 19). In the following sections, I will first describe in more details the internal organization of the embryo, the different tissues and the molecular players involved, with a special focus on the cytoskeleton as it will be of main interest in the results. Then I will discuss the different step of C. elegans embryonic elongation.

III.2. C. elegans muscles

As found in most of the animals, muscles exist in the simple invertebrate C. elegans. Its 95 somatic muscle cells are particular, they are striated but mononucleated, having multiple sarcomeres per cell [START_REF] Sulston | Postembryonic cell lineages of the nematode, Caenorhabditis elegans[END_REF]Waterston, 1988, Bird and[START_REF] Bird | The structure of nematodes[END_REF]. The most abundant are the body wall muscles that are responsible for locomotion and contribute to a fully accomplished embryonic elongation. They are arranged in four quadrants, two dorsally and two ventrally, beneath the D/V epidermal cells, along the full length of the body. Each quadrant is a double row of muscle cells [START_REF] Moerman | Muscle: Structure, function and development[END_REF]. Muscle cells in each longitudinal quadrant are separated from epidermal cells by a basal lamina. Their innervation is peculiar, it plays a role only during the postembryonic life, since mutations affecting neuronal function do not affect muscles during embryogenesis [START_REF] Saifee | The Caenorhabditis elegans unc64 locus encodes a syntaxin that interacts genetically with synaptobrevin[END_REF]. The muscle fibers consist of myofibrils that primarily contain actin filaments and myosin. They generate contractions that may change their length or/and their shape or maintain their shapes against extrinsic tensions. To establish coordinated movements in the full body, the force generated by muscle contractions must be transmitted both between the neighboring muscle cells and between the muscle and the epidermis. The musclemuscle adhesion plaques link the neighboring cells together [START_REF] Francis | Muscle cell attachment in Caenorhabditis elegans[END_REF]Coutu Hresko et al., 1994).

Two muscleepidermal structures, the dense bodies and the Mlines, connect the actin filaments and myosin filaments, respectively, to the epidermis through the muscle plasma membrane and then the basal lamina to transmit the contractile forces out from muscle cells [START_REF] Barstead | Cloning, sequencing, and mapping of an alphaactinin gene from the nematode Caenorhabditis elegans[END_REF]. The force passes first from the actin filaments of the dense bodies, through cytoskeletal adaptor proteins into extracellular receptors, PAT2/PAT3 integrins [START_REF] Gettner | Characterization of beta pat3 heterodimers, a family of essential integrin receptors in C. elegans[END_REF], which then transmit the force into the ECM between the muscles and the epidermis. The complex of UNC112/Kindlin, PAT4/ILK and PAT6/actopaxin is another important component of the muscle attachment assembly, as it bridges the muscular actin filaments with the PAT3 integrin: the lack of any of these proteins prevents the proper recruitment of actin to the muscle membrane [START_REF] Rogalski | The UNC-112 gene in Caenorhabditis elegans encodes a novel component of cell-matrix adhesion structures required for integrin localization in the muscle cell membrane[END_REF][START_REF] Mackinnon | elegans PAT4/ILK functions as an adaptor protein within integrin adhesion complexes[END_REF][START_REF] Lin | elegans PAT6/actopaxin plays a critical role in the assembly of integrin adhesion complexes in vivo[END_REF]. Muscle membranes connect to the cuticle through the epidermis via cell basement membrane junction called fibrous organelle (FO) (Waterston, 1988;[START_REF] Francis | Muscle cell attachment in Caenorhabditis elegans[END_REF][START_REF] Moerman | Muscle: Structure, function and development[END_REF]Coutu Hresko et al., 1999;[START_REF] Hahn | Tissue integrity: Hemidesmosomes and resistance to stress[END_REF][START_REF] Cox | Sticky worms: adhesion complexes in C. elegans[END_REF].

Myoblasts are born after the end of gastrulation. At this stage, muscle cells lie in two lateral rows next to the seam cells, and some muscle cells have not yet undergone their terminal divisions.

Around 1.5fold stage, they migrate dorsally and ventrally to contact the ventral and dorsal epidermis. All muscle cells finish their divisions before assuming their final positions. Around the 2 fold stage they become flattened and their attachment to the epidermis begins [START_REF] Hresko | Assembly of body wall muscle and muscle cell attachment structures in Caenorhabditis elegans[END_REF]Williams and Waterston, 1994;[START_REF] Moerman | Sarcomere assembly in C. elegans muscle[END_REF]. Therefore, the alternated contractions and relaxations of the opposing dorsal and ventral muscle quadrants can start. This contraction pattern provides the sinusoidal movement of the worms after hatching.

III.3. C. elegans epidermis

The morphogenesis of the C. elegans embryo is controlled by the development of the epidermis (also known as the hypodermis) a single epithelial layer that surrounds the animal. In wild type embryos, epidermal cells are generated on the dorsal side of the embryo [START_REF] Chisholm | Epidermal morphogenesis[END_REF]. A hierarchy of transcription factors regulates specification of epidermal fate. After specification, dorsal epidermal cells rearrange, a process known as dorsal intercalation [START_REF] Sulston | The embryonic cell lineage of the nematode Caenorhabditis elegans[END_REF][START_REF] Williamsmasson | The cellular mechanism of epithelial rearrangement during morphogenesis of the Caenorhabditis elegans dorsal hypodermis[END_REF]. Then ventral epidermis undergoes epiboly to enclose the rest of the embryo in a process known as ventral enclosure. Following enclosure, the epidermis elongates, and most epidermal cells fuse to generate a multinucleated syncytial tissue, consisting of polarized epithelial cells [START_REF] Podbilewicz | The C. elegans Research Community[END_REF]. It enables communication with the external environment and bridges the cuticle (that the epidermis secretes apically to serve for protection and as an exoskeleton) and the muscles. The epidermis and the muscles are tightly coupled, though separated by the basal lamina, secreted also by the epidermis [START_REF] Francis | Muscle cell attachment in Caenorhabditis elegans[END_REF][START_REF] Hresko | Assembly of body wall muscle and muscle cell attachment structures in Caenorhabditis elegans[END_REF]. Morphogenesis of the epidermis involves both autonomously generated changes in epidermal cell shape and position, and interactions with internal tissues, including the developing nervous system and body wall muscles. Molecules required for epidermal morphogenesis thus include components of the epidermal cytoskeleton, MTs, IFs, epidermal cellular junctions, cell signaling pathways running between the epidermal cells and underlying tissues, and of the ECM (Priess and Hirsh, 1986;Costa et al., 1997;[START_REF] Costa | A putative catenincadherin system mediates morphogenesis of the Caenorhabditis elegans embryo[END_REF][START_REF] Williamsmasson | An actinmediated twostep mechanism is required for ventral enclosure of the C. elegans hypodermis[END_REF][START_REF] Williamsmasson | The cellular mechanism of epithelial rearrangement during morphogenesis of the Caenorhabditis elegans dorsal hypodermis[END_REF][START_REF] Antoshechkin | elegans evl20 gene is a homolog of the small GTPase ARL2 and regulates cytoskeleton dynamics during cytokinesis and morphogenesis[END_REF].

III.3.1. C. elegans Adherens Junctions (CeAJs)

Adherens junctions (AJs) in vertebrates and invertebrates are essential for cell adhesion. By the onset of embryonic elongation, the epidermis organizes into three zones: one dorsal cell row and one ventral cell raw, connected on both sides by one lateral cell rows, also called seam cells. These cells are connected to each other through AJlike, referred to as C. elegans apical junctions (CeAJs). C.

elegans epithelia only has this type of apical junction [START_REF] Podbilewicz | Cell fusions in the developing epithelial of C. elegans[END_REF][START_REF] Costa | A putative catenincadherin system mediates morphogenesis of the Caenorhabditis elegans embryo[END_REF][START_REF] Mohler | Dynamics and ultrastructure of developmental cell fusions in the Caenorhabditis elegans hypodermis[END_REF]Raich et al., 1999, Armenti and[START_REF] Armenti | Adherens junctions in C. elegans embryonic morphogenesis[END_REF]. They have been shown to be key components of the embryonic development from several aspects [START_REF] Hardin | Skin tight: cell adhesion in the epidermis of Caenorhabditis elegans[END_REF].

They not only seal the epidermal layer and maintain its integrity but also provide a mechanical link between cells. They help to transmit forces between the individual cells. Therefore, they orchestrate the epidermal morphogenetic movements. At the same time, they provide mechanical stability and resistance against forces, generated by actomyosin contractility, muscles or other factors, like hydrostatic pressure.

As in vertebrates and Drosophila, CeAJs contains two sets of proteins, the cadherin/catenin complex (CCC) [START_REF] Costa | A putative catenincadherin system mediates morphogenesis of the Caenorhabditis elegans embryo[END_REF] and the DLG1/AJM1 (DAC) complexe (Priess and Hirsh, 1986;[START_REF] Francis | Muscle cell attachment in Caenorhabditis elegans[END_REF][START_REF] Podbilewicz | Cell fusions in the developing epithelial of C. elegans[END_REF][START_REF] Mohler | Dynamics and ultrastructure of developmental cell fusions in the Caenorhabditis elegans hypodermis[END_REF]. They have been reported to localize to CeAJs, based on their subapical localization and analogy with other systems.

The apically localized polarity proteins PAR3 and PAR6 mediate formation and maturation of junctions, while the basolaterallylocalized regulator LET413/Scribble ensures that junctions remain apically positioned [START_REF] Legouis | LET413 is a basolateral protein required for the assembly of adherens junctions in Caenorhabditis elegans[END_REF][START_REF] Armenti | Adherens junctions in C. elegans embryonic morphogenesis[END_REF]. PAR6 is also essential for epithelial polarization (Von [START_REF] Stetina | PAR6, but not Ecadherin and βintegrin, is necessary for epithelial polarization in C. elegans[END_REF]. In contrast to vertebrates, CeAJ proteins are not essential for general cell adhesion or for epithelial cell polarization.

III.3.2. C. elegans hemidesmosomes (CeHDs)

The intraepidermal junctions are not the only epithelial attachments. Another key element of proper muscleepidermis attachment is the C. elegans hemidesmosomes (CeHD). They connect the dorsal and ventral (but not the lateral) epidermal cells to the underlying muscles basally and to the cuticular exoskeleton apically. The CeHDs are electron dense plaques that resemble ultra structurally, functionally and molecularly to vertebrate HDs, epidermisECM attachment structures [START_REF] Nievers | Biology and function of hemidesmosomes[END_REF][START_REF] Litjens | Current insights into the formation and breakdown of hemidesmosomes[END_REF]Zhang and Labouesse, 2010). They are also interconnected by the IFs, forming transepidermal attachment structures called fibrous organelles (FOs). FOs function as tendonlike structures, bridging between the muscles and the cuticle exoskeleton through the epidermis [START_REF] Cox | Sticky worms: adhesion complexes in C. elegans[END_REF]Hardin, 2004, Francis and[START_REF] Francis | Muscle organization in Caenorhabditis elegans: localization of proteins implicated in thin filament attachment and band organization[END_REF][START_REF] Francis | Muscle cell attachment in Caenorhabditis elegans[END_REF]. The IFs IFB1/IFA3 and IFB1/IFA2 are a principal component of the CeHD (Bosher at al., 2003;[START_REF] Sonnenberg | Plakins in development and disease[END_REF]. IFs provide extra strength to cells, which experience a lot of tension. They are predicted to be anchored to CeHDs through a core protein: VAB10A (Fig. 20). It is a plakin homologous to vertebrate plectin and BPAG1e. In its absence all the other components disperse, aggregate, detach or form ectopic bundles (Bosher et al., 2003;Zhang and Labouesse, 2010;Zhang et al., 2011). As it will be of importance in the results section, I will shortly discuss the spectraplakin in C. elegans.

Spectraplakins are enormous multidomain cytoskeletal proteins named after their features resembling both the spectrin and the plakin family. C. elegans possesses two categories of spectraplakin isoforms encoded by a single locus: vab10 (Variable ABnormal morphology) [START_REF] Roper | The 'spectraplakins': cytoskeletal giants with characteristics of both spectrin and plakin families[END_REF]Bosher et al., 2003;[START_REF] Suozzi | Spectraplakins: master orchestrators of cytoskeletal dynamics[END_REF]. VAB10A and VAB10B share a common region with a pair of calponinhomology (CH) domains and nine spectrin repeats (SRs) forming a plakin domain (Suman et al., BioRxiv). When fused to GFP, The Nterminal CHdomain region of VAB10 colocalizes nicely with actin filaments in vivo and can be used as a fluorescent probe to visualize actin organization (Gally et al., 2009). It means that the two CH domains serve as an actinbinding domain (ABD) in VAB10. The second CH domain expressed in epidermis also appears to be localized in the CeHDs [START_REF] Kim | Punctuated actin contractions during convergent extension and their permissive regulation by the noncanonical Wntsignaling pathway[END_REF]. Among these SRs, the SR5 of VAB10 contains a Src Homology 3 (SH3) domain like the SR5 of vertebrate plectin, which is a feature shared by all plakin members [START_REF] Sonnenberg | Plakins in development and disease[END_REF][START_REF] Ortega | The structure of the plakin domain of plectin reveals a noncanonical SH3 domain interacting with its fourth spectrin repeat[END_REF]Gally et al., 2016, Suman et al., BioRxiv). It was proposed that the accessibility of the SH3 embedded in a SR domain is determined by intramolecular interaction with other SR domains, indicating complex regulation of protein interactions within these domains (Hermann and Wiche, 1987;[START_REF] Ortega | The structure of the plakin domain of plectin reveals a noncanonical SH3 domain interacting with its fourth spectrin repeat[END_REF][START_REF] Valencia | Intermediate filamentassociated cytolinker plectin 1c destabilizes microtubules in keratinocytes[END_REF]. The VAB10Aspecific region contains sixteen plectin repeats (PRs) following a small coiledcoil domain (Bosher at al., 2003;[START_REF] Gally | Functional and genetic analysis of VAB-10 spectraplakin in Caenorhabditis elegans[END_REF]. The VAB10Bspecific domains contain 20 SRs, an EFHand domain and a MT-binding domain called Growtharrest specific protein 2 (GAS2)related homology (Fig. 20).

Therefore, the predicted function of VAB10A might be to crosslink actin and IFs cytoskeletons, while VAB10B might mediate interaction between actin and MTs. Along with VAB10A, a series of other adhesion molecules contribute to proper CeHD maintenance. Apically there are MUA3 and MUP4, two homologs, essential for embryonic epithelial morphogenesis and maintenance of muscle position [START_REF] Gatewood | The mup4 locus in Caenorhabditis elegans is essential for hypodermal integrity, organismal morphogenesis and embryonic body wall muscle position[END_REF][START_REF] Bercher | mua3, a gene required for mechanical tissue integrity in Caenorhabditis elegans, encodes a novel transmembrane protein of epithelial attachment complexes[END_REF], [START_REF] Hong | MUP4 is a novel transmembrane protein with functions in epithelial cell adhesion in Caenorhabditis elegans[END_REF]. mua3 shares high homology with human FBN1. It is predicted to have collagen binding activity and IF binding activity. Similarly, mup4, shares high homology with human MATN4 (matrilin 4), and encodes a transmembrane protein required for attachments between the apical epithelial surface and the cuticular matrix (Fig. 21). Basally, there is LET805/myotactin, a single transmembrane protein connecting the CeHDs to muscles and helping relay the contractile information of muscles to epidermis [START_REF] Hresko | Myotactin, a novel hypodermal protein involved in musclecell adhesion in Caenorhabditis elegans[END_REF][START_REF] Bercher | mua3, a gene required for mechanical tissue integrity in Caenorhabditis elegans, encodes a novel transmembrane protein of epithelial attachment complexes[END_REF][START_REF] Hong | MUP4 is a novel transmembrane protein with functions in epithelial cell adhesion in Caenorhabditis elegans[END_REF]. LET The CeHDs start to assemble as foci at the apical and basal membranes prior to elongation and progressively start to form circumferential bundles above the muscles during elongation. The process depends on the presence of the underlying muscle precursors, and muscles also play a significant role in their maturation during elongation. Indeed, muscle contractions induce a mechanotransduction pathway that triggers the phosphorylation of IFs and therefore promotes the further elongation of embryos beyond 2fold (Zhang et al., 2011).

III.3.3. C. elegans extracellular matrix

As muscle contractions are essential for the elongation, they need to be properly transmitted to the epidermis. This depends partially on the ECM, apically and basally, between the two tissues.

Therefore, the ECM can also affect elongation, especially through coordinating shape changes between the muscles and the epidermis [START_REF] Labouesse | Role of the extracellular matrix in epithelial morphogenesis: a view from C. elegans[END_REF]. Some ECM components influence elongation indirectly, through affecting muscle sarcomere assembly. Other act more directly: for instance, even a slight reduction of UNC52 perlecan, coupled to weakened CeHDs affects the fibrous organelle structure [START_REF] Zahreddine | CRT1/calreticulin and the E3 ligase EEL1/HUWE1 control hemidesmosome maturation in C. elegans development[END_REF]. To conduct a normal embryonic development, not only proper ECM composition is important, but also the proper attachment of the epidermis and the muscles to the ECM. The tissues connect to the basement membrane through ECM receptors, integrins. The musclespecific perlecan receptors presumed to be PAT2/PAT3 and their lack causes a pat phenotype. (In C. elegans, only two α (INA1, PAT2) and one βintegrin chain (PAT3) are present). The supposed epidermal perlecan receptor is LET805/myotactin, which can also severely compromise elongation, when disrupted (Williams and Waterston, 1994;[START_REF] Hresko | Assembly of body wall muscle and muscle cell attachment structures in Caenorhabditis elegans[END_REF][START_REF] Rogalski | Mutations in the unc52 gene responsible for body wall muscle defects in adult Caenorhabditis elegans are located in alternatively spliced exons[END_REF][START_REF] Hresko | Myotactin, a novel hypodermal protein involved in musclecell adhesion in Caenorhabditis elegans[END_REF][START_REF] Moerman | Sarcomere assembly in C. elegans muscle[END_REF][START_REF] Zahreddine | CRT1/calreticulin and the E3 ligase EEL1/HUWE1 control hemidesmosome maturation in C. elegans development[END_REF].

Recent work from our lab showed another key role of the apical ECM embryonic morphogenesis. It helps preserving the integrity of the embryos and distributes tension throughout the embryo during elongation. The leucinerich repeat (LRR) proteins SYM1, EGG6 and LET4, and the zona pellucida (ZP) domain protein FBN1/Fibrillin have already been proposed to be part of the embryonic sheath.

They line the outer part of the embryo and/or are secreted in the extraembryonic space. SYM1, EGG6 and LET4 were shown essential to organize the apical extracellular matrix and maintain epithelial junction integrity [START_REF] Mancuso | Extracellular leucinerich repeat proteins are required to organize the apical extracellular matrix and maintain epithelial junction integrity in C. elegans[END_REF]. In addition, FBN1 mediates pharynx attachment and resistance of the epidermis to mechanical deformation during C. elegans embryogenesis [START_REF] Kelley | FBN1, a fibrillinrelated protein, is required for resistance of the epidermis to mechanical deformation during C. elegans embryogenesis[END_REF]. SYM1 might also help attach muscles to the cuticle [START_REF] Davies | Functional overlap between the mec8 gene and five sym genes in Caenorhabditis elegans[END_REF]. Recently, along with these already described players, we identified two ZP proteins, NOAH1 and NOAH2, acting in the same pathway, and in parallel to SYM1, LET4 and FBN1/Fibrillin. NOAH1 and NOAH2 preserve the embryonic integrity together with the p21activated kinase PAK1 via maintaining and relaying the actomyosin contractile tension before muscle contraction. Also, during late elongation, these ECM proteins are essential for muscleepidermis anchorage and the input of muscle contraction transduction to epithelia (VuongBrender et al., 2017).

III.4. Cytoskeleton

C. elegans has all the main cytoskeletal networks (actin, MTs, IFs, spectrins) and junctional components that higher organisms have. IFs can be found at the level of CeHDs, establishing the transepithelial connection between the apical and the basolateral CeHDs structures. Actin forms a meshwork near the epidermal cortex that rearranges to form circumferential, parallel bundles first in the D/V cells, followed by its rearrangement in the lateral cells (Priess and Hirsh, 1986;Costa et al., 1997;[START_REF] Costa | A putative catenincadherin system mediates morphogenesis of the Caenorhabditis elegans embryo[END_REF]. As they will be of major interest in the results of this thesis, I will specify what is inferred by bundles. They correspond to the cortical actin filaments that bias the growth of the epithelial cell membranes and coincide with the pattern of circumferentially oriented, parallel furrows on the cuticle of the first larval stage (Costa et al., 1997). They are constituted of several actin filaments, as it will be discussed later.

The organization of MTs before, during and after elongation is very similar that of actin, they are even intermingled, though MTs are still a little less regular than actin bundles (Priess and Hirsh, 1986;[START_REF] Quintin | Noncentrosomal epidermal microtubules act in parallel to let502/rock to promote C. elegans elongation[END_REF]. The spectrin cytoskeleton attaches to the actin network and to the cell membrane, to which it is apically and basolaterally linked. It is this organization that we will depict in the following sections.

III.4.1. Actin

Actin is well conserved among different eukaryotes [START_REF] Elzinga | Complete aminoacid sequence of actin of rabbit skeletal muscle[END_REF]. Small differences in actin sequences can lead to changes in their function. The actin network consists of filamentous or Factin.

The actin filaments are righthanded helical polymers of the protein Gactin. The monomers of Gactin are 375amino acid polypeptides. They are single units allowing the formation of flexible structures of diameter 47nm that have the capacity to organize into anything from a simple filament to a 3 dimensional sheet [START_REF] Reisler | Actin molecular structure and function[END_REF][START_REF] Graceffa | Crystal structure of monomeric actin in the ATP state. Structural basis of nucleotidedependent actin dynamics[END_REF].

The Factin polymer has a structural polarity: the end that possesses an actin subunit that has its ATP binding site exposed is called the () end or pointed end, while the opposite end where the cleft is directed at a different adjacent monomer is called the (+) end or barbed end [START_REF] Lodish | [END_REF]. Although polymerization and depolymerization can also occur at both ends, in general there is a dynamic equilibrium between the two poles and the faster growing end is the barbed end, while the actin monomers can dissociate mostly at the pointed end in an ATPdependent manner [START_REF] Begg | The visualization of actin filament polarity in thin sections. Evidence for the uniform polarity of membraneassociated filaments[END_REF][START_REF] Hollenbeck | Intermediate filament collapse is an ATPdependent and actindependent process[END_REF]Jarhaus et al., 2001). Actin dynamics are influenced by the availability of actin monomers and remodeling proteins. This group contains various proteins such as nucleating factors which accelerate actin polymerization and are responsible for branched filaments, filament stabilizing proteins such as capping proteins, severing proteins such as gelsolin and depolymerization factors as cofilin (Kovar et al., 2005, Nomura and[START_REF] Nomura | ATPdependent regulation of actin monomerfilament equilibrium by cyclase associated protein and ADF/cofilin[END_REF]. Therefore, the structural organization of different actin networks such as bundles, dendritic networks and web like structures depends on specialized accessory proteins. These proteins also control the interactions of other proteins such as myosin with actin filaments. Some of these proteins will be discussed in the next paragraph. Due to its dynamics, actin becomes a central player in various biological processes related to dynamic cellular movements and shape changes: endocytosis, cytokinesis, organelle transport or cellular motility (e.g. filopodia at the leading edge of lamellipodia in migrating cells) [START_REF] Pollard | Actin, a central player in cell shape and movement[END_REF].

C. elegans has five closely related actins (ACT15). They contribute to an apically organized actin skeleton essential for cell shape changes and for shape maintenance during morphogenesis (Priess and Hirsh, 1986;Costa et al., 1997). The contribution of actin to embryonic morphogenesis has been reported from the end of gastrulation [START_REF] Marston | Actinbased forces driving embryonic morphogenesis in Caenorhabditis elegans[END_REF]. Starting at the 1.5 fold stage, the cortical actin network reorganizes dramatically and forms parallel bundles of 510 filaments [START_REF] Labouesse | Epithelial junctions and attachments[END_REF]. The bundles are present all over the embryonic epidermis, having a more regular organization in the D/V cells. They are associated with nonmuscle myosin II, closely attached to the membrane, below the furrows of the embryonic sheath and they have strong attachment to CeAJs in DV cells (Priess and Hirsh, 1986). The nonmuscle myosin II subunits include the heavy chains NMY1 and NMY2, the regulatory light chain MLC4 and the essential light chain MLC5 (Fyrberg, et al., 1994;[START_REF] Shelton | The nonmuscle myosin regulatory light chain gene mlc4 is required for cytokinesis, anterior posterior polarity, and body morphology during Caenorhabditis elegans embryogenesis[END_REF]Piekny, et al., 2003;Gally, et al., 2009). The phosphorylation of MLC4 S18 and MLC4 T19 control the activity of myosin II in epidermal cells of C.

elegans (Gally, et al., 2009). During elongation, the number of bundles does not change, but the spacing between them increases (Priess and Hirsh, 1986;Costa et al., 1997). Such an epidermal actin skeleton becomes the guiding structure of C. elegans early embryonic elongation, until the start of muscle contractions at midelongation, [START_REF] Shelton | The nonmuscle myosin regulatory light chain gene mlc4 is required for cytokinesis, anterior posterior polarity, and body morphology during Caenorhabditis elegans embryogenesis[END_REF]Piekny et al., 2003;Gally et al., 2009).

Though we increased greatly our knowledge about the role of the actin cytoskeleton and actomyosin contractility during C. elegans development, several poorly understood issues about the organization of this network remain. Within the dorsal and ventral epidermal cells, the specific molecular composition, the organization, and the polarity of filaments within bundles has not been established. It is not known whether actin polymerizes as long filaments running from one dorsal seam CeAJ to the other, whether they run from one CeAJ to a CeHDs, or whether they make several shortintermingled filaments of similar or opposite polarity. The occurrence of apparent actin bundle discontinuities at the level of CeHDs in some backgrounds could indicate that CeHDs represent an intermediate anchoring structure between CeAJs. Another important question is the nature of the cues that trigger the formation and orientation of these bundles. As they are present in the entire epidermis, their organizing factors must include common features in all epidermal cells. Both polarity and mechanical cues have been suspected to be such possible factors.

III.4.2. Actin remodeling proteins

Actin cytoskeleton is essential for a wide variety of cellular functions, such as cell motility, phagocytosis, cell division, and muscle contraction. A tremendous number of molecules regulate the function of actin cytoskeleton. Regulation of polymerization and depolymerization of actin is crucial for the function of the actin cytoskeleton.

III.4.2.1. Formin

Nucleation of actin is the ratelimiting step of actin filament assembly (Cherasone et al., 2010;[START_REF] Sit | Rho GTPases and their role in organizing the actin cytoskeleton[END_REF]). Members of the formin family nucleate unbranched microfilaments. Formins stabilize the first actin dimer, recruit profilin, an actin monomer binding protein and then remain bound to the growing (+) end of the filament and prevent capping proteins from terminating filament extension. The resultant long, unbranched actin filaments can be bundled into stress fibers [START_REF] Taniguchi | Mammalian formin fhod3 regulates actin assembly and sarcomere organization in striated muscles[END_REF][START_REF] Iskratsch | Formin follows function: a musclespecific isoform of FHOD3 is regulated by CK2 phosphorylation and promotes myofibril maintenance[END_REF][START_REF] Kano | Mammalian formin Fhod3 plays an essential role in cardiogenesis by organizing myofibrillogenesis[END_REF][START_REF] Breitsprecher | Formins at a glance[END_REF][START_REF] Bechtold | FHOD proteins in actin dynamicsa formin class of its own[END_REF]. Formins participate in multiple cellular processes [START_REF] Goode | Mechanism and function of formins in the control of actin assembly[END_REF]Cherasone et al., 2010) including cytokinesis, cell movement and changes in cell shape. The mammalian genome encodes fifteen formins while in C. elegans there are seven formins.

cyk1 acts during embryonic cytokinesis and in the excretory cell [START_REF] Severson | A Formin Homology Protein and a Profilin Are Required for Cytokinesis and Arp2/3 Independent Assembly of Cortical Microfilaments in C. elegans[END_REF][START_REF] Mimi | Zline formins promote contractile lattice growth and maintenance in striated muscles of C. elegans[END_REF][START_REF] Shaye | A network of conserved formins, regulated by the guanine exchange factor EXC5 and the GTPase CDC42, modulates tubulogenesis in vivo[END_REF]. daam1 and frl1 participate in Wntmediated cell polarity of the B cell [START_REF] Wu | A novel noncanonical Wnt pathway is involved in the regulation of the asymmetric B cell division in C. elegans[END_REF]. fozi1 encodes a divergent formin required in cell fate specification of muscles and neurons [START_REF] Johnston | An unusual Znfinger/FH2 domain protein controls a left/right asymmetric neuronal fate decision in C. elegans[END_REF][START_REF] Amin | A Znfinger/FH2domain containing protein, FOZI1, acts redundantly with CeMyoD to specify striated body wall muscle fates in the Caenorhabditis elegans postembryonic mesoderm[END_REF]. In addition to the spermatheca, exc6 functions in the excretory cell, as does the second inverted formin, inft2 [START_REF] Shaye | The DiseaseAssociated Formin INF2/EXC6 Organizes Lumen and Cell Outgrowth during Tubulogenesis by Regulating FActin and Microtubule Cytoskeletons[END_REF][START_REF] Hegsted | INF2 and FHOD related formins promote ovulation in the somatic gonad of C. elegans[END_REF][START_REF] Shaye | A network of conserved formins, regulated by the guanine exchange factor EXC5 and the GTPase CDC42, modulates tubulogenesis in vivo[END_REF]. And fhod1 encodes the only C. elegans member of the FHOD subfamily of formins and is related to the human and mouse FHOD1 and FHOD3 (MiMi et al., 2012;[START_REF] Pruyne | Revisiting the Phylogeny of the Animal Formins: Two New Subtypes, Relationships with Multiple Wing Hairs Proteins, and a Lost Human Formin[END_REF]. It has a characteristic prolinerich formin homology FH1 domain, recruiting profilinbound actin. The FH2 domain engages in formin dimerization, forming a ring that is involved in the nucleation/processive capping of actin. Like many formins, it is initially inactive due to an autoinhibitory interaction between the formin's Cterminal diaphanous autoregulatory domain (DAD) with the Nterminal diaphanous inhibitory domain (DID, sometimes referred to as FH3). FHOD1 also contains an Nterminal GTPasebinding domain (GBD). A coiledcoil domain is found between the FH1 and FH3 domains [START_REF] Vanneste | The role of the formin gene fhod-1 in C. elegans embryonic morphogenesis[END_REF] (Fig. 22). It can be activated by binding a Rac GTPase in a nucleotideindependent manner or by phosphorylation of the DAD domain by Rhobinding kinase, although the latter does not appear to be essential in C.

elegans [START_REF] Vanneste | The role of the formin gene fhod-1 in C. elegans embryonic morphogenesis[END_REF]. FHOD1 has nucleating (Patel et al., 2017) and bundling functions [START_REF] Schönichen | FHOD1 is a combined actin ilament capping and bundling factor that selectively associates with actin arcs and stress ibers[END_REF][START_REF] Kutscheidt | FHOD1 interaction with nesprin2G mediates TAN line formation and nuclear movement[END_REF] and may also contribute to lateral vs. dorsal/ventral differences. FHOD1 also functions in C. elegans muscle, where it is partially redundant with CYK1 for formation of striated body wall sarcomeres [START_REF] Mimi | Zline formins promote contractile lattice growth and maintenance in striated muscles of C. elegans[END_REF][START_REF] Mimi | Loss of Sarcomereassociated Formins Disrupts Zline Organization, but does not Prevent Thin Filament Assembly in Caenorhabditis elegans Muscle[END_REF]. FHOD1 is localized near the Z lines within the contractile lattice, and along the edges of growing body wall muscle cells. Actin thin filaments still form in fhod1 mutants, but muscles are narrower and further apart, and Z lines attachments are defective.

III.4.2.2. Gelsolin

Gelsolinrelated proteins and actin depolymerizing factor (ADF)2/cofilin are the two major classes of actin filamentsevering proteins that enhance actin filament turnover by severing and depolymerizing actin filaments and take part in several cell biological processes. The gelsolin family of proteins is a major class of actin regulatory proteins that sever, cap, and nucleate actin filaments in a calciumdependent manner [START_REF] Yu | Identification of a polyphosphoinositidebinding sequence in an actin monomer binding domain of gelsolin[END_REF] and are involved in various cellular processes [START_REF] Becker | Pulmonary vascular permeability and ischemic injury in gelsolindeficient mice[END_REF][START_REF] Feldt | Structure, regulation and related diseases of the actinbinding protein gelsolin[END_REF]. Typically, gelsolinrelated proteins exhibit three to six repeats of homologous domains of 100-120 amino acids, which are designated as gelsolinlike (G) domains and each domain plays a distinct role in severing, capping, and nucleation [START_REF] Sun | a multifunctional actin regulatory protein[END_REF][START_REF] Ghoshdastider | The expanding superfamily of gelsolin homology domain proteins[END_REF][START_REF] Feldt | Structure, regulation and related diseases of the actinbinding protein gelsolin[END_REF].

In C. elegans there are three genes encoding for gelsolinrelated proteins: gsnl1, fli1 and viln 1. fli1 encodes a homolog of Flightless1 [START_REF] Goshima | Characterization of a novel Rasbinding protein CeFLI1 comprising leucinerich repeats and gelsolinlike domains[END_REF]. FLI1 is widely expressed in many tissues, and fli1 mutations cause several developmental defects [START_REF] Deng | The Flightless I homolog, fli1, regulates anterior/posterior polarity, asymmetric cell division and ovulation during Caenorhabditis elegans development[END_REF]. Little is known about viln1.

gsnl1 (gelsolinlike protein1) encodes an unconventional gelsolinrelated protein. It is ortholog of several human genes including AVIL (advillin), GSN (gelsolin), and VIL1 (villin 1). It has four gelsolinlike (G) domains (G1G4), unlike typical gelsolinrelated proteins with three or six G domains. It has been shown that G1 and the linker between G1 and G2 were sufficient for actin filament severing, whereas G1 and G2 were required for barbed end capping. A PIP2sensitive domain was mapped to G1 and G2. At least two actinbinding sites were detected: a calcium dependent Gactinbinding site in G1 and a calciumindependent G and Factinbinding site in G3 and G4. [START_REF] Liu | Distinct roles of four gelsolinlike domains of Caenorhabditis elegans gelsolinlike protein1 in actin filament severing, barbed end capping, and phosphoinositide binding[END_REF] (Fig. 23). Sequence alignment suggests that GSNL1 lacks two G domains that are equivalent to fourth and fifth G domains of gelsolin. In vitro, GSNL1 severed actin filaments and capped the barbed end in a calciumdependent manner [START_REF] Pardee | Purification of muscle actin[END_REF][START_REF] Choe | The calcium activation of gelsolin: Insights from the 3A structure of the G4G6/actin complex[END_REF][START_REF] Klaavuniemi | Caenorhabditis elegans gelsolinlike protein 1 is a novel actin filamentsevering protein with four gelsolinlike repeats[END_REF], like gelsolin. However, unlike gelsolin, GSNL1 stays bound to the side of Factin with a submicromolar affinity and did not nucleate actin polymerization, although it bound to Gactin with high affinity [START_REF] Klaavuniemi | Caenorhabditis elegans gelsolinlike protein 1 is a novel actin filamentsevering protein with four gelsolinlike repeats[END_REF]. It localizes to the actin cytoskeleton and striated muscle dense body and is expressed in the epidermis. Gelsolinlike (G) domains are numbered from G1 to G6 in the order of appearance from the Ntermini but not necessarily representing sequence homology. Indeed, G4 of GSNL1 is most closely related to G6 of gelsolin. Functional domains of C. elegans GSNL1 were adapted from [START_REF] Klaavuniemi | Caenorhabditis elegans gelsolinlike protein 1 is a novel actin filamentsevering protein with four gelsolinlike repeats[END_REF][START_REF] Liu | Distinct roles of four gelsolinlike domains of Caenorhabditis elegans gelsolinlike protein1 in actin filament severing, barbed end capping, and phosphoinositide binding[END_REF] Functional domains of mammalian gelsolin were adapted by [START_REF] Liu | Distinct roles of four gelsolinlike domains of Caenorhabditis elegans gelsolinlike protein1 in actin filament severing, barbed end capping, and phosphoinositide binding[END_REF], from Sun et al., 1999, with modifications based on the following references: severing [START_REF] Kwiatkowski | Identification of critical functional and regulatory domains in gelsolin[END_REF], capping [START_REF] Weber | Role of the N and Cterminal actinbinding domains of gelsolin in barbed filament end capping[END_REF][START_REF] Sun | The actin sidebinding domain of gelsolin also caps actin filaments. Implications for actin filament severing[END_REF], PIP2 binding [START_REF] Janmey | Phosphoinositidebinding peptides derived from the sequences of gelsolin and villin[END_REF][START_REF] Yu | Identification of a polyphosphoinositidebinding sequence in an actin monomer binding domain of gelsolin[END_REF][START_REF] Feng | Fullcontact domain labeling: Identification of a novel phosphoinositide binding site on gelsolin that requires the complete protein[END_REF], calciumsensitive Gactin binding in G1 [START_REF] Way | Identification of a region in segment 1 of gelsolin critical for actin binding[END_REF], calciuminsensitive Factin binding in G2 [START_REF] Sun | The actin sidebinding domain of gelsolin also caps actin filaments. Implications for actin filament severing[END_REF], and calciumsensitive Gactin binding in G4 [START_REF] Pope | Localization of the calciumsensitive actin monomer binding site in gelsolin to segment 4 and identification of calcium binding sites[END_REF].

III.4.2.3. Vilin

viln1 is an ortholog of human SVIL (supervillin) [START_REF] Pope | Cloning, characterization, and chromosomal localization of human superillin (SVIL)[END_REF][START_REF] Liu | Distinct roles of four gelsolinlike domains of Caenorhabditis elegans gelsolinlike protein1 in actin filament severing, barbed end capping, and phosphoinositide binding[END_REF]. Supervillin is a 205kDa Factin binding protein, tightly associated with both actin filaments and plasma membranes, suggesting that it forms a highaffinity link between the actin cytoskeleton and the membrane [START_REF] Pestonjamasp | Supervillin (p205): A novel membraneassociated, Factinbinding protein in the villin/gelsolin superfamily[END_REF][START_REF] Ghoshdastider | The expanding superfamily of gelsolin homology domain proteins[END_REF]. C. elegans viln1 is predicted to also have actin filament binding activity. viln1 encodes a villinlike protein with six G domains and a Cterminal villin headpiece. It has a NH2terminal region with one putative nuclear targeting region, three potential protein kinase A phosphorylation sites. Its vilinlike conserved COOHterminal domain contains also one putative nuclear targeting region, three potential Factin binding sites and one potential tyrosine phosphorylation [START_REF] Pope | Cloning, characterization, and chromosomal localization of human superillin (SVIL)[END_REF][START_REF] Liu | Distinct roles of four gelsolinlike domains of Caenorhabditis elegans gelsolinlike protein1 in actin filament severing, barbed end capping, and phosphoinositide binding[END_REF] (Fig. 24). viln1 function is still unknown but at the adult stage, it is expressed in the head and the tail [START_REF] Mckay | Gene expression profiling of cells, tissues, and developmental stages of the nematode C. elegans[END_REF]Hunt Newbury et al., 2007).

III.4.3. Microtubules

MTs are known to form structures such as cilia and flagella, the motile and sensory whips, or sensory devices on the surface of the cell [START_REF] Haimo | flagella, and microtubules[END_REF][START_REF] Lodish | Cilia and Flagella: Structure and Movement[END_REF]. They can organize themselves as tracks for the transport of materials in the cell. They are long hollow cylinders made of protein tubulin. The outer diameter is 25 nm and these structures are rigid compared to actin microfilaments and are more complex than actin. MTs are long with often one end attached to a MTOC [START_REF] Desai | Microtubule polymerization dynamics[END_REF][START_REF] Marshall | Cell division: The renaissance of the centriole[END_REF]. The roles of MTs are diverse and comparatively more dynamic than actin.

The nematode C. elegans has 20 kinesins. Most kinesins walk towards the plus end of the MTs.

Some isoforms of kinesins walk towards minus end, while some do not move and depolymerize MTs [START_REF] Vale | Identification of a novel forcegenerating protein, kinesin, involved in microtubulebased motility[END_REF]. MTs are circumferentially oriented in D/V cells in epidermis. They have been proposed to provide a passive response to help elongation in the dorsal and ventral epidermis (Priess and Hirsch, 1986;[START_REF] Ciarletta | Continuum model of epithelial morphogenesis during Caenorhabditis elegans embryonic elongation[END_REF]. However, recent work has indicated that MTs are more likely to function as a transport key structure to favor the morphogenesis process (Quintin et al., 2006).

Before elongation, they are found in complex cytoplasmic networks in interphase cells or associated with the spindle apparatus in mitotic cells. In the DV cells, they undergo a remarkable transition in pattern at the start of elongation in C. elegans embryo and become circumferentially oriented (Priess and Hirsh, 1986). They might be intermingled with actin microfilament bundles. In the lateral epidermis, they remain less wellorganized during the whole elongation. In DV cells they appear to be attached to MTOC linked to membranes while the ones in seam cells are distributed throughout their cytoplasm [START_REF] Feldman | A role for the centrosome and PAR3 in the handoff of MTOC function during epithelial polarization[END_REF]. MTs function during embryogenesis and elongation was assessed using drugs preventing mitosis: colcemid and griseofulvin. These embryos developed abnormalities such as depressions and constrictions and could not elongate fully. The microfilament pattern was not affected (Priess and Hirsh, 1986). Recent data from our lab showed that during C. elegans embryogenesis, MTs promote elongation process in parallel to the actomyosin activation pathway LET502/ ROCK [START_REF] Quintin | Noncentrosomal epidermal microtubules act in parallel to let502/rock to promote C. elegans elongation[END_REF]. MTs are shown to be essential for elongation in a LET 502/ROCK partially impaired background. MTs promote the transport of Ecadherin and LET805 to CeAJs.

III.4.4. Spectrin cytoskeleton

Spectrin denotes the family of αhelical, high molecular weight, multifunctional ABPs, usually found in association with the plasma membrane of mature cells [START_REF] Marchesi | Selective solubilization of a protein component of the red cell membrane[END_REF][START_REF] Hartwig | Actinbinding proteins. 1: Spectrin super family[END_REF]. They are ubiquitous cytoskeletal proteins, forming two dimensional networks under the membrane as αβ heterotetramers (Isparo et al., 2010;[START_REF] Brown | The Physiological Molecular Shape of Spectrin: A Compact Supercoil Resembling a Chinese Finger Trap[END_REF]. They are part of the spectrin superfamily along with αactinin or dystrophin [START_REF] Broderick | Spectrin, alphaactinin, and dystrophin[END_REF]. The main characteristic they share is the presence of SRs. Some special domains allow to distinguish some of them such as actin binding CH domains, EF hand domains, SH3 domain or prolinerich regions, which are potential platforms for protein interactions [START_REF] Broderick | Spectrin, alphaactinin, and dystrophin[END_REF][START_REF] Gushchina | Highresolution crystal structure of spectrin SH3 domain fused with a prolinerich peptide[END_REF].

Spectrins have been first and so far, best described in red blood cells [START_REF] Stokke | Spectrin, human erythrocyte shapes, and mechanochemical properties[END_REF][START_REF] Greenquist | The spectrin phosphorylation reaction in human erythrocytes[END_REF][START_REF] Bodine | Spectrin deficient inherited hemolytic anemias in the mouse: characterization by spectrin synthesis and mRNA activity in reticulocytes[END_REF][START_REF] Bennett | Spectrin and ankyrinbased pathways: metazoan inventions for integrating cells into tissues[END_REF][START_REF] Lux | Anatomy of the red cell membrane skeleton: unanswered questions[END_REF]. They are concentrated just beneath the plasma membrane, forming a 2dimensional structure held together by actin filaments and interacting with several membranebound proteins. This network provides elasticity to the cell cortex and red blood cells can spring back to their original size after passing through a capillary.

However, for the past 1015 years, we have started to better understand their role in nonerythroid contexts as well. The function of spectrins in nonerythrocyte cells was unclear to a large extent for long, but recent research highlighted their many roles in various processes, like mitotic spindle orientation, DNA repair, cell signalling, or protein trafficking [START_REF] De Matteis | Spectrin tethers and mesh in the biosynthetic pathway[END_REF]Morrow, 2000, Phillips and[START_REF] Phillips | Brush border spectrin is required for early endosome recycling in Drosophila[END_REF][START_REF] Johansson | Activation of endosomal dynein motors by stepwise assembly of Rab7RILPp150Glued, ORP1L, and the receptor betalll spectrin[END_REF][START_REF] Kizhatil | AnkyrinG and beta2spectrin collaborate in biogenesis of lateral membrane of human bronchial epithelial cells[END_REF][START_REF] Machnicka | Spectrinbased skeleton as an actor in cell signaling[END_REF][START_REF] Fletcher | The Spectrin cytoskeleton regulates the Hippo signalling pathway[END_REF].

However, one of the most evident roles of spectrins is related to membrane organization and stabilizing membrane proteins at their right place. Spectrins are helping ion channel and cell adhesion molecule recruitment in the endoplasmic reticulum, in the cell, Golgi and muscle membrane or also in the nervous system. Defects in this membrane organization can lead to neurodegenerative diseases like spinocerebellar ataxia type 5 [START_REF] Lorenzo | Spectrin mutations that cause spinocerebellar ataxia type 5 impair axonal transport and induce neurodegeneration in Drosophila[END_REF][START_REF] Stankewich | Targeted deletion of betaIII spectrin impairs synaptogenesis and generates ataxic and seizure phenotypes[END_REF], hearing loss with mislocalized voltagegated channels at the Ranvier node in mice [START_REF] Parkinson | Mutant betaspectrin 4 causes auditory and motor neuropathies in quivering mice[END_REF][START_REF] Komada | Beta]IVspectrin regulates sodium channel clustering through ankyrinG at axon initial segments and nodes of Ranvier[END_REF] or loss of Na+ K+ATPase from the basolateral domain in Drosophila epithelium [START_REF] Dubreuil | Drosophila beta spectrin functions independently of alpha spectrin to polarize the Na,K ATPase in epithelial cells[END_REF].

The impact of spectrins in the mechanical stabilization of cells or tissues is also among their most important functions. This role is evident and pivotal in erythrocytes, but growing evidence shows that it is just as important in epithelia. For instance, mammalian βII spectrin is needed to maintain the proper separation between the apical and basolateral sides of epithelial cells [START_REF] Kizhatil | AnkyrinG and beta2spectrin collaborate in biogenesis of lateral membrane of human bronchial epithelial cells[END_REF]. In Drosophila βHspectrin contributes to eye morphogenesis through mediating the interaction between cadherin junctions and the cell adhesion molecule Roughest [START_REF] Lee | The cell adhesion molecule Roughest depends on beta(Heavy)spectrin during eye morphogenesis in Drosophila[END_REF].

Recent work showed that the scaffold big bang (Bbg) binds to βheavy-Spectrin/Karst subunit at the apical cortex and promotes Yorkie activity, Factin enrichment, and the phosphorylation of the myosin II regulatory light chain Spaghetti squash. They proposed a model in which the spectrin cytoskeleton recruits Bbg to the cortex, where Bbg promotes actomyosin contractility to regulate epithelial tissue growth of Drosophila wing discs [START_REF] Forest | The apical scaffold big bang binds to spectrins and regulates the growth of Drosophila melanogaster wing discs[END_REF]. Another example is the Drosophila photoreceptor morphogenesis, during which Spectrins are required to control the process through the modulations of cell membrane domains [START_REF] Chen | Membrane domain modulation by Spectrins in Drosophila photoreceptor morphogenesis[END_REF].

Finally, spectrins are also important during C. elegans embryonic morphogenesis and I will detail it in the following section.

C. elegans contains three spectrins, each of them encoded by a single gene: βGspectrin (unc 70), βHspectrin (sma1) and αspectrin (spc1). All these three spectrins have been shown to be essential for morphogenesis and/or muscular and neuron formation. βG and βHspectrin probably have distinct roles and can't substitute for each other's activity as neither their spatiotemporal expression, nor their subcellular localization overlap. However, the localization of αspectrin overlaps with both and they form αβ heterotetramers. SPC1 loss displays the strongest phenotype and it can be recapitulated by the joint loss of UNC70 and SMA1 (Norman and Moerman, 2002;[START_REF] Praitis | SMA-1 spectrin has essential roles in epithelial cell sheet morphogenesis in C. elegans[END_REF]. It suggests that SPC1 is present everywhere as a crucial element when UNC70 and SMA1

have different spatiotemporal functions. Yet, the presence of an intact αβspectrin heterotetramer skeleton, having all the three spectrins is necessary to accomplish its full function.

III.4.4.1. βGspectrin/UNC70

βGspectrin/UNC70 is a 262kDa protein, 54,2% identical to human SPTBN1. It is the C. elegans ortholog of the conventional nonerythrocyte βspectrin in vertebrates and in Drosophila [START_REF] Hu | Characterization of human brain cDNA encoding the general isoform of betaspectrin[END_REF][START_REF] Hammarlund | Mutations in betaspectrin disrupt axon outgrowth and sarcomere structure[END_REF]. UNC70 includes 17 SRs onsisting of 106 amino acids, a conserved region in the first two SRs (possible adducin and/or ankyrin binding motif), two Nterminal CH domains and a Cterminal plectrin homology (PH) domain [START_REF] Hammarlund | Mutations in betaspectrin disrupt axon outgrowth and sarcomere structure[END_REF][START_REF] Moorthy | Caenorhabditis elegans betaG spectrin is dispensable for establishment of epithelial polarity, but essential for muscular and neuronal function[END_REF] (Fig. 25). SRs are flexible rod domains consisting of triple αhelices (one parallel and two non parallels) that are attached through flexible linker regions. The helices are stabilized by interactions between hydrophobic residues and are folded in a coiled coil structure. They are supposed to be the key components in the molecular flexibility and elasticity within the entire spectrin superfamily and they have a special characteristic to fulfill this role. CHdomains are responsible for the actin binding ability of the protein. A PH domain allows the interaction with phospholipids; therefore, it provides a direct attachment to the cell membrane [START_REF] Broderick | Spectrin, alphaactinin, and dystrophin[END_REF].

UNC70 is expressed in all tissues, including the lateral membrane of the epidermis, starting in early embryos [START_REF] Moorthy | Caenorhabditis elegans betaG spectrin is dispensable for establishment of epithelial polarity, but essential for muscular and neuronal function[END_REF]. Strong unc70 mutants show that larvae cannot survive beyond the L1 stage and present an uncoordinated coiling, which severely harm the mobility of the larvae [START_REF] Hammarlund | Mutations in betaspectrin disrupt axon outgrowth and sarcomere structure[END_REF]. The defects of moving ability in unc70 larva are due to the progressive disorganization of myofilaments and the discontinuities in the dense bodies. In body wall muscles, a reduction or loss of the sarcoplasmic reticulum is also observed. unc70 larvae are lethal at the L1 stage, but the embryos complete the development process and hatch, meaning that UNC70 is dispensable for embryogenesis. UNC70 has also been shown important for neuron formation [START_REF] Sönnichsen | Fullgenome RNAi profiling of early embryogenesis in Caenorhabditis elegans[END_REF][START_REF] Hammarlund | Axons break in animals lacking betaspectrin[END_REF][START_REF] Schmitz | Axon guidance genes identified in a largescale RNAi screen using the RNAihypersensitive Caenorhabditis elegans strain nre1(hd20) lin15b(hd126)[END_REF]. Depletion of UNC70 in early larvae leads to multiple defects in nervous system. Abnormally enlarged neuronal bodies, apparent vacuolation in amphid neurons, abnormal axon outgrowth and ectopic displacement of neuronal bodies can be observed in these larvae [START_REF] Hammarlund | Axons break in animals lacking betaspectrin[END_REF]. unc70 mutants lose the ability to develop sensory neurons under stress in moving larvae. Atomic force spectroscopy experiments on isolated neurons, in vivo laser axotomy and fluorescence resonance energy transfer (FRET) imaging, showed that UNC70 is held under continuous tension, to transmit the prestress to touch receptor neurons. Genetic manipulations that decrease such spectrindependent tension also selectively impair touch sensation, suggesting that such pretension is essential for efficient responses to external mechanical stimuli [START_REF] Hammarlund | Mutations in betaspectrin disrupt axon outgrowth and sarcomere structure[END_REF][START_REF] Moorthy | Caenorhabditis elegans betaG spectrin is dispensable for establishment of epithelial polarity, but essential for muscular and neuronal function[END_REF][START_REF] Krieg | Mechanical control of the sense of touch by βspectrin[END_REF], Krieg et al., 2017).

III.4.4.2. βHspectrin/SMA1

βHspectrin/SMA1 is a 470kDa protein, C. elegans ortholog of Drosophila βHspectrin. SMA1 contains 30 SRs, two CH domains, a SH3 domain and a Cterminal PH domain [START_REF] Mckeown | sma1 encodes a betaHspectrin homolog required for Caenorhabditis elegans morphogenesis[END_REF] (Fig. 25). SH3 domains have been characterized in the protein Src and are widely known for their contribution to signal transduction and for acting as protein interaction platforms. The SH3 domain of SMA1 is buried within a loop between two αhelices of the SR and they acquire a folding transition state that can be switched when mechanical force is applied on it [START_REF] Martinez | The folding transition state between SH3 domains is conformationally restricted and evolutionarily conserved[END_REF][START_REF] Jagannathan | Direct observation of a forceinduced switch in the anisotropic mechanical unfolding pathway of a protein[END_REF]. SMA1 also shows an ankyrinbinding sequence present in βspectrin [START_REF] Dubreuil | A betaspectrin isoform from Drosophila (beta H) is similar in size to vertebrate dystrophin[END_REF]Thomas and Kiehart, 1997) and resembles more to Drosophila βHspectrin at the level of homology [START_REF] Mckeown | sma1 encodes a betaHspectrin homolog required for Caenorhabditis elegans morphogenesis[END_REF].

SMA1 has not been reported to impact on muscle structure or neuronal morphology. Its role is related to epithelial cell shape changes that the epidermis, gut, pharynx, pharyngeal gland and excretory canal cell undergo [START_REF] Mckeown | sma1 encodes a betaHspectrin homolog required for Caenorhabditis elegans morphogenesis[END_REF][START_REF] Buechner | Cystic canal mutants in Caenorhabditis elegans are defective in the apical membrane domain of the renal (excretory) cell[END_REF]Norman and Moerman, 2002;[START_REF] Praitis | SMA-1 spectrin has essential roles in epithelial cell sheet morphogenesis in C. elegans[END_REF][START_REF] Raharjo | Cell architecture: surrounding muscle cells shape gland cell morphology in the Caenorhabditis elegans pharynx[END_REF]. sma1(ru18) null mutants elongate at a lower rate resulting in shorter larva with round heads [START_REF] Mckeown | sma1 encodes a betaHspectrin homolog required for Caenorhabditis elegans morphogenesis[END_REF][START_REF] Praitis | SMA-1 spectrin has essential roles in epithelial cell sheet morphogenesis in C. elegans[END_REF]. SMA1 is expressed from the early embryos, at the apical part of epithelial tissues, and is required to determine cell shape in multiple epithelial tissues during morphogenesis [START_REF] Mckeown | sma1 encodes a betaHspectrin homolog required for Caenorhabditis elegans morphogenesis[END_REF].

SMA1 apical localization does not require the presence of its tetramerizing partner SPC1, though its organization becomes weaker and more punctate in spc1 mutants [START_REF] Praitis | SMA-1 spectrin has essential roles in epithelial cell sheet morphogenesis in C. elegans[END_REF]. As an actin binding cytoskeletal protein, SMA1 plays a role in actin organization: in its absence the actin remains intact at the cell boundaries and apically at the early embryonic stages but its association to the apical membrane gets disrupted during elongation [START_REF] Praitis | SMA-1 spectrin has essential roles in epithelial cell sheet morphogenesis in C. elegans[END_REF]. Another defect of sma1 mutants is the expanded distribution of muscle bands, basement membrane and CeHDs structures (Norman and Moerman 2002). Although sma1 is clearly required for normal morphogenesis, it is not an essential gene. It was hypothesized that SMA1 might be a downstream target of regulatory interactions affected by the muscleepidermis interaction or serve as a cytoskeletal binding site for signal transduction molecules [START_REF] Mckeown | sma1 encodes a betaHspectrin homolog required for Caenorhabditis elegans morphogenesis[END_REF].

III.4.4.3. αspectrin/SPC1

The single αspectrin in C. elegans is a 240kDa protein, SPC1. It shows 61% identity and 76% similarity to Drosophila αspectrin, while it is 57% identical and 72% similar to human nonerythroid αspectrin SPTAN (Norman and Moerman, 2002). SPC1 consists of 21 SRs, an SH3 domain and two C terminal EF hand domains, one domain being calciumdependent, the other one calcium independent (Fig. 25).

SPC1 is ubiquitously expressed all over the life cycle and it is recruited to the cell membrane.

Animals lacking functional spectrin do not complete embryonic elongation and die just after hatching. Proper differentiation of the body wall muscles is also affected, myofilaments of muscles are oriented abnormally from the longitudinal anterior/posterior (A/P) direction of the embryo, and the width of the CeHDs is increased (Norman and Moerman, 2002). During embryogenesis, SPC1 localizes to the cell membrane in most if not all cells, starting at the first cell stage. In epithelia, SPC1 is localized both apically like SMA1 and basolaterally, overlapping with UNC70. When SPC1 is absent, SMA1 localization itself is normal. On the other hand, SPC1 localization is dependent on UNC70 but not SMA1 (Norman and Moerman, 2002). spc1 mutants also have defects in the organization of the epidermal apical actin cytoskeleton that is needed for elongation. Therefore, it seems that the SPC1/SMA1 heterotetramers are required for a proper actin organization in the embryonic epidermis. Overall, these reports on the role of the spectrin skeleton in C. elegans embryonic elongation suggest that spectrins could have an important role in development, in the maintenance of cellular structures and probably such properties as elasticity in nonerythroid cells as well.

III.4.4.4. The spectrin heterotetramers

Spectrins do not fulfill their role as single molecules. They form αβ heterotetramers, assembling laterally aside each other to form a dimer first. This lateral association is highly conserved. The α and βspectrins show high affinity to each other and to date, no independently existing α or βspectrins have been reported yet. The head to head assembly occurs through the partial triplehelical repeats at the Cterminus of the βspectrin and the Nterminal part of the α spectrin, resembling to the assembly between triple helices within a SR. In this assembly, the EFhand domain of the αspectrin and the CHdomains of the βspectrin are juxtaposed to each other. Actin binding of the heterotetramers happens through βspectrins. No actin binding activity has been reported in αspectrins, though they are required to support their β partners, possibly to promote their proper activity (Norman and Moerman 2002). Such a heterotetramer is about 36nm in diameter, 5565nm at its resting length but it can reach 200260nm when stretched [START_REF] Bennett | Spectrin and ankyrinbased pathways: metazoan inventions for integrating cells into tissues[END_REF][START_REF] Machnicka | Spectrinbased skeleton as an actor in cell signaling[END_REF].

Recent work tried to answer how such a three to fivefold extension could be achieved with the maintenance of the heterotetramer's structural integrity. They modeled how the spectrin heterotetramer could function [START_REF] Brown | The Physiological Molecular Shape of Spectrin: A Compact Supercoil Resembling a Chinese Finger Trap[END_REF]. Their model has been based on recent knowledge on spectrin heterotetramers and proposes that it can undergo a seamless threefold extension under forces and can stay linear because it functions like a Chinese finger trap (Fig. 26). At its shorter "resting" state, the heterotetramer forms a hollow cylinder. During its extension in length, the pitch of the SRs increases and the internal diameter of the cylinder decreases [START_REF] Brown | The Physiological Molecular Shape of Spectrin: A Compact Supercoil Resembling a Chinese Finger Trap[END_REF]. Apart of modeling, the authors confirmed their hypothesis with experimentally supported data: by the crystal structure of chicken αspectrin tandem SRs, by structural mass spectroscopy and by electron micrographs of the full spectrin dimers and heterotetramers from erythrocytes [START_REF] Yan | Crystal structure of the repetitive segments of spectrin[END_REF]Pascual et al., 1997;Isparo et al., 2010;[START_REF] Mehboob | Crystal structure of the nonerythroid alphaspectrin tetramerization site reveals differences between erythroid and nonerythroid spectrin tetramer formation[END_REF]. Nevertheless, this model still leaves unanswered questions behind. For instance, it is not based on a native, full heterotetramer and it does not address either the alternative SRSH3 conformations in α or βH spectrins. However, it proposes an interesting alternative that could help to reach a more detailed understanding on the complexity of the spectrin skeleton.

III.5. C. elegans life cycle and its embryonic development

The life cycle of C. elegans consists of the embryonic stage, four larval stages (L1L4) and adulthood (Fig. 27). C. elegans embryogenesis takes places after ventral enclosure and lasts for 1216 hours at 20°C. The L1 larva hatches with 558 nuclei and many immature tissues [START_REF] Sulston | Postembryonic cell lineages of the nematode, Caenorhabditis elegans[END_REF]von Ehrenstein and Schierenberg, 1980;[START_REF] Sulston | The embryonic cell lineage of the nematode Caenorhabditis elegans[END_REF][START_REF] Bird | The structure of nematodes[END_REF]. At this point the L1 larva will begin postembryonic development where it will grow fivefold in length and tenfold in breadth before achieving adulthood [START_REF] Slack | Temporal pattern formation by heterochronic genes[END_REF]Ruvkun, 1997, Ambros, 2000). The L1 larval stage lasts for 16h, each of the following three stages (L2L4) last for 1012h. Each larval stage is separated by a molting event, where the larva forms a new cuticle (apolysis) and sheds the old cuticle (ecdysis). 12h after molting from L4, young adults start egg production that they continue for 23 days (until they run out of the selfproduced sperm). After their fertile period they can live for several more weeks before their senescence and death. In case of challenging conditions (crowd or starvation) C. elegans can activate an alternative life cycle: L2 molts into an alternative L3 larva called "dauer", that has a completely sealed cuticle with enhanced resistance against external perturbation until conditions get optimized [START_REF] Cassada | The dauer larva, a postembryonic developmental variant of the nematode Caenorhabditis elegans[END_REF]. Then they shed the dauer cuticle and continue as slightly different L4 larvae [START_REF] Corsi | A Transparent Window into Biology: A Primer on Caenorhabditis elegans[END_REF]. C. elegans embryogenesis is divided into, first, a proliferative phase (350 minutes), which covers formation of embryonic founder cells and gastrulation and second, the organogenesis/morphogenesis (490 minutes) during which the embryo gains a vermiform shape [START_REF] Schierenberg | Cell lineages and developmental defects of temperaturesensitive embryonic arrest mutants in Caenorhabditis elegans[END_REF][START_REF] Sulston | The embryonic cell lineage of the nematode Caenorhabditis elegans[END_REF]. I will first briefly describe the proliferative phase and then focus in more details on the elongation phase.

After fertilization, the single cell embryo begins a series of highly stereotyped cell divisions [START_REF] Sulston | The embryonic cell lineage of the nematode Caenorhabditis elegans[END_REF]. Proliferation events take place within the uterus and then continue in later stages, including gastrulation and morphogenesis after the embryo is laid. The C. elegans epidermis consists of 71 major and 11 minor epidermal cells, rising after the 9th and 10th round of cell divisions, respectively. Minor epidermal cells form the extreme head and tail epidermis; major ones form most of the epidermis [START_REF] Gendreau | The potential to differentiate epidermis is unequally distributed in the AB lineage during early embryonic development in C. elegans[END_REF][START_REF] Page | ELT1, a GATAlike transcription factor, is required for epidermal cell fates in Caenorhabditis elegans embryos[END_REF][START_REF] Page | The cuticle[END_REF]. Terminal divisions of the epidermis precursors lead to the following organization: dorsally two rows of ten cells, along the anteroposterior axis; flanking both sides of the dorsal cells one row of lateral or "seam" cells; and two rows of ventral epidermal cells at the very lateral edges. Only 10 minutes after these divisions of epidermal precursors, the two rows of dorsal epidermal cells also undergo a morphogenetic event, called dorsal intercalation, to line up in a single row. They develop pointed basolateral protrusions towards the midline, intercalate with their contralateral neighbors and elongate until they reach the seam cells of the opposite side [START_REF] Sulston | The embryonic cell lineage of the nematode Caenorhabditis elegans[END_REF][START_REF] Williamsmasson | The cellular mechanism of epithelial rearrangement during morphogenesis of the Caenorhabditis elegans dorsal hypodermis[END_REF]. Shortly after the beginning of dorsal intercalation, at the 30 cells stage, the ventral epidermal cells on both edges also start their morphogenetic process, called ventral enclosure. Ingressing cells become internalized and create a depression, called the ventral cleft that needs to disappear to enable further development. They migrate into the center of the embryonic mass to eventually create separate ectodermal, endodermal, and mesodermal compartments. Surrounding ventral neuroblasts move therefore towards the ventral midline after 230290 minutes after the first cleavage, to close the ventral cleft. About an hour following ventral cleft closure, early epidermal morphogenesis can start [START_REF] Chisholm | Epidermal morphogenesis[END_REF].

III.5.1. Overview of the embryonic elongation

The beginning of morphogenesis overlaps with the end of gastrulation, when most cells have ended proliferation and are joining tissue subgroups. Cells become structurally specialized to adopt shapes and cell contents that reflect their eventual cell fates within specialized tissue compartments [START_REF] Ding | The cytoskeleton and epidermal morphogenesis in C. elegans[END_REF][START_REF] Chisholm | Epidermal morphogenesis[END_REF]. Most epidermal cells begin to form multinucleated syncytia, with the disappearance of intervening cell membranes [START_REF] Podbilewicz | The C. elegans Research Community[END_REF]. Epidermal cell fusions normally follow a welldefined order and timing, though it can vary [START_REF] Mohler | Dynamics and ultrastructure of developmental cell fusions in the Caenorhabditis elegans hypodermis[END_REF].

Once the embryo's developing tissues begin to form a longer wormlike shape, they become folded within the eggshell. Early elongation events begin around 350 min after the first cleavage and involve both microfilaments and MTs. Moving through the comma, twofold and finally the threefold stage, the embryo increases its length along the A/P axis by four times and decreases its circumference by three times until it is ready for hatching (Fig. 28). During its embryonic elongation, the length of the embryo is multiplied by a factor 4 and its circumference is reduced by a factor 2.5. This 3hour process is affected only by cell shape changes and not by the division or intercalation of cells. The first phase (or early elongation) depends on a ROCKpromoted actomyosin force in seam cells (blue) and actinpromoted stiffness in D/V cells (yellow). The second phase then requires repeated muscle contractions (yellow arrow), which induce a PAK1dependent mechanotransduction pathway. A/P, Anterior/Posterior.

It is important to mention that, unlike in Drosophila and zebrafish embryonic development, there is no cell division, cell intercalation nor cell migration [START_REF] Sulston | The embryonic cell lineage of the nematode Caenorhabditis elegans[END_REF]) but only cell shape changes of the D/V and lateral epidermis. These changes are allowed by two main driving forces of C. elegans embryonic elongation: the epidermal actomyosin contractility in the lateral cells throughout the entire process and muscle activity beneath the epidermis observed at 475 min after fertilization (around 1.7fold stage) (Aridel et al., 2017;[START_REF] Gieseler | Development, structure, and maintenance of C. elegans body wall muscle[END_REF]. The elongation can thus be divided into two phases: the early elongation -before muscles become active and the late elongation -after muscles become active (Chisholm, 2015) (Fig. 28). Thus, it requires the interplay of not only epithelial cell groups, but also of different tissue layers. Terminal differentiation occurs without many additional cell divisions ( [START_REF] Sulston | The embryonic cell lineage of the nematode Caenorhabditis elegans[END_REF]. In rare cases, specific cells undergo a delayed apoptotic cell death in the embryo or in the L1 larva after fulfilling their role in tissue morphogenesis.

III.5.2. Early elongation

Early elongation refers to the period between comma and 2fold stages before muscles become active. During early elongation, the epidermis starts to go through shape changes, as can be most easily observed in the lateral epidermis: they shorten themselves along the dorsal/ventral (D/V) direction and lengthen themselves along the A/P direction. However, the perimeter of these lateral epidermal cells stays the same during early elongation (VuongBrender et al., 2017). Genetic and pharmacological studies have shown that epidermal actomyosin contractility is crucial for elongation since the beginning of this process. The actin filaments and the MTs start to organize into more and more regular, circumferential, parallel bundles in the DV cells, associated to the membrane (Priess and Hirsh, 1986;Costa et al., 1997;[START_REF] Williamsmasson | An actinmediated twostep mechanism is required for ventral enclosure of the C. elegans hypodermis[END_REF][START_REF] Costa | A putative catenincadherin system mediates morphogenesis of the Caenorhabditis elegans embryo[END_REF]). This organization also happens in the lateral cells but with a slight delay and to a less regular extent.

Interestingly, epidermal actomyosin contractility is mostly needed in the lateral cells, the DV cells seem to passively accommodate to the early embryonic lengthening [START_REF] Chisholm | Epidermal morphogenesis[END_REF]Diogon et al., 2007). Epidermal actomyosin contractility driving this first phase of elongation is regulated by the Rho kinase, LET502, and the serine/threonine p21 activated kinase PAK1. An evolutionary conserved, actin microfilament associated RhoGAP/RGA2 behaves as a negative regulator of LET502/ROCK. RGA2 is needed only in the D/V cells and colocalizes with the circumferential actin bundles. Its lack unleashes myosin contractions in the DV cells, which exert pulling forces on the circumferential bundles and indirectly on the CeAJs as well. This effect can be clearly seen on hypercontracted rga2 mutants. The small GTPase RHO1 is the preferred target of RGA2 in vitro, and acts between RGA2 and LET502 in vivo (Diogon et al., 2007). Moreover, the assembly of myosin II filaments, but not actin microfilaments, depends on the myosin regulatory light chain (MLC4) and essential light chain MLC5. Earlier work showed that phosphorylation of two evolutionary conserved MLC4 serine and threonine residues is important for myosin II activity and organization. Myosin II filaments can be inactivated through their dephosphorylation by the myosin phosphatase, MEL11. Additionally, the joint loss of ROCKPAK, or ROCKMRCK, completely prevented embryonic elongation. It suggests that ROCK and MRCK regulate MLC4 [START_REF] Wissmann | The Caenorhabditis elegans mel11 myosin phosphatase regulatory subunit affects tissue contraction in the somatic gonad and the embryonic epidermis and genetically interacts with the Rac signaling pathway[END_REF]Piekny et al., 2003;Gally et al., 2009). The presence of both these regulators is vital for proper elongation: let502 null mutants fail to elongate, while mel11 mutation causes a "hypercontracted" phenotype with bulges and rupture. On the other hand, simultaneous lack of let502 and mel11

suppress each other, showing that they are antagonists and argue, for the need for another kinase activity in parallel to ROCK [START_REF] Wissmann | Caenorhabditis elegans LET502 is related to Rhobinding kinases and human myotonic dystrophy kinase and interacts genetically with a homolog of the regulatory subunit of smooth muscle myosin phosphatase to affect cell shape[END_REF][START_REF] Wissmann | The Caenorhabditis elegans mel11 myosin phosphatase regulatory subunit affects tissue contraction in the somatic gonad and the embryonic epidermis and genetically interacts with the Rac signaling pathway[END_REF]. In vertebrate smooth muscle, this redundant pathway is activated by Calmodulin and myosin light chain kinase [START_REF] Somlyo | Signal transduction by Gproteins, rhokinase and protein phosphatase to smooth muscle and nonmuscle myosin II[END_REF]. However, in C. elegans, there is no obvious myosin light chain kinase homolog [START_REF] Batchelder | Cytokinesis is not controlled by calmodulin or myosin light chain kinase in the Caenorhabditis elegans early embryo[END_REF]. The C. elegans redundant also pathway includes FEM2 (PP2c phosphatase).

Indeed, fem2 mutations genetically enhance and suppress mutations of let502 and mel11, respectively. Although fem2 mutations alone show only weak elongation defects, no elongation occurs in let502; mel11; fem2 triple mutants because both redundant pathways are inactive [START_REF] Piekny | Embryonic morphogenesis in Caenorhabditis elegans integrates the activity of LET502 Rho binding kinase, MEL11 myosin phosphatase, DAF2 insulin receptor and FEM2 PP2c phosphatase[END_REF].

Overall, C. elegans embryonic epidermal cells to undergo a smooth musclelike actin/myosin based contraction redundantly controlled by LET 502/Rho kinase and MEL11/myosin phosphatase in one pathway and FEM2/PP2c phosphatase and PAK1/p21activated kinase in a parallel pathway(s). In addition, it has also been shown that early elongation can be regulated, not only through myosin, but also through the remodeling of actin filaments. Although actin microfilaments surround the embryo, the force for contraction is generated mainly in the lateral epidermal cells whose actin microfilaments appear qualitatively different from those in their dorsal/ventral neighbors. The actin nucleator FHOD1, a formin homologue, has been shown to be specifically involved in organizing actin filaments in the contractile lateral cells [START_REF] Vanneste | The role of the formin gene fhod-1 in C. elegans embryonic morphogenesis[END_REF][START_REF] Refai | TissueSpecific Functions of fem2/PP2c Phosphatase and fhod1/formin During Caenorhabditis elegans Embryonic Morphogenesis[END_REF]. Indeed, fhod1 mutants show microfilament defects in these cells. fhod1 also genetically interacts with let502, mel11, fem2 and pak1. However, fhod1 regulation of microfilaments preferentially acts with let502 and mel11, and in parallel to fem2 and pak1. Thus, FHOD1 may contribute to the qualitative differences in microfilaments found in the contractile lateral epidermal cells and their noncontractile dorsal and ventral neighbors [START_REF] Vanneste | The role of the formin gene fhod-1 in C. elegans embryonic morphogenesis[END_REF]. In mammalian systems, autoinhibition of FHOD1 is relieved by Rho kinase, after which the FHOD1nucleated actin filaments, in turn, respond to Rho kinasemediated contraction [START_REF] Gasteier | Activation of the Racbinding partner FHOD1 induces actin stress fibers via a ROCK dependent mechanism[END_REF][START_REF] Hannemann | The Diaphanousrelated Formin FHOD1 associates with ROCK1 and promotes Src dependent plasma membrane blebbing[END_REF][START_REF] Takeya | The mammalian formin FHOD1 is activated through phosphorylation by ROCK and mediates thrombininduced stress fibre formation in endothelial cells[END_REF][START_REF] Iskratsch | Two distinct phosphorylation events govern the function of muscle FHOD3[END_REF]. However, since fhod1like actin defects are absent in let502/Rho kinase mutants (Norman and Moerman, 2002;Piekny et al., 2003, Gally et al., 2009). C. elegans FHOD1 appears not to require Rho kinase activation during elongation.

III.5.3. Late elongation

When C. elegans embryos reach 1.7fold to 1.8fold, muscles located beneath the dorsal and ventral epidermis start to become active. The actomyosin contractility is still present but is thought to become less important for elongation (Diogon et al., 2007). The epidermis, the ECM and muscles

IV. Aim of this thesis

Our understanding of C. elegans embryonic elongation largely increased in the past twenty years. Muscle activity is a key player for C. elegans morphogenesis during late elongation, however how it promotes embryo elongation is not entirely understood yet. Our laboratory identified a mechanotransduction pathway downstream of muscle input but also investigated redundant signaling pathways that could contribute to late elongation. As PAK1, effector kinase, is an important regulator of both early and late elongation, it became the starting point of our interaction tests. The work of Gabriella Pasti, former PhD student, identified SPC1, the αspectrin as a strong interactor of PAK1. The joined loss of function of the two genes leads to a drastic phenotype of elongation failure that we qualified as « retraction ». Thus, this interaction became the starting point of my PhD project aiming to answer:

How do SPC1 and PAK1 interact to the "lock" the elongation?

Are there other players involved in this process?

As it is also well described that actin cytoskeleton plays a key role cell shape changes and that the ratchet mechanism emerged as a general feature of epithelial mechanics, we wondered if it could be applicable to our system. Therefore, I also tried to answer:

To which extend is the actin cytoskeleton important for elongation?

How do actin cables get remodeled over time?

Can we model the progressive elongation of the embryo to understand how the forces contribute to the remodeling of the actin?

Animal strains, conditions of maintenance

The list of strains used is presented in Table 5. Animals were propagated on NGM agar plates as described previously (Brenner, 1974). Animals were held at a standard 20°C temperature except for the measurements of hatchlings implicating sma1(ru18), in which case L4 animals were shifted to 15°C before egg laying and measures were performed on their offsprings. However, the growth curves of sma1(ru18) were performed at 20°C. The gsnl1(tm2730) and viln1(2413) were outcrossed three times.

Yeast Two Hybrid Screening

Yeast twohybrid screening was performed by Hybrygenics Services (Paris, France). The bait component was the Nterminal 294 amino acids of PAK1 (including the regulatory region of the protein) fused as a Cterminal fusion to LexA. The construct was used as a bait to screen at saturation a highly complex, randomprimed C.elegans embryo cDNA library (Gomes et al., 2013). Screening involved a mating approach on a medium lacking Trp, Leu and His, supplemented with 0.5 mM 3 aminotriazole (FromontRacine, Rain and Legrain, 1997). The strongest hits of the screen can be found in Supplementary Table 1. Reciprocal screens using the spectrin repeat #9 or the SH3 domains of SPC1 as baits identified PAK1 region 160206, and no other meaningful prey in the context of the present study.

RNAi screens

A RNAi screen was performed in the pak1(tm403) mutant along with a wildtype control. A collection of 356 essential genes from the Ahringer RNAi library (Kamath et al., 2003), including adhesion proteins, signaling proteins, phosphatases, kinases, cytoskeletonassociated proteins and proteins important in epithelial morphogenesis, was assembled (Table 1), based on a previous screen performed in the git1(tm1962) background (C. Gally and M. Labouesse, unpublished). The screen was performed in liquid culture on 96well plates and RNAi knockdown was induced by feeding as described (Gally, Zhang and Labouesse, 2015). The primary screen was based on enhanced lethality and body morphology defects; the secondary screen focused on very short larvae and elongation defects. Gabriella Pàsti, former PhD student, took DIC images for body length measurements and performed DIC timelapse imaging for the strongest candidates. She and I performed two additional RNAi screens. First, she used a spc1(ra409) mutant carrying an unstable extrachromosomal rescuing spc1::gfp marker to look for potential enhancers of the spc1(ra409) elongation defects. She selected for this enhancer screen genes that had given the strongest defects in the initial screen with 356 genes (Table 4). In both cases, young L1 hatchlings were inspected for the presence/absence of a fluoresent spc1::GFP signal and photographed using either a Leica DMI4000 (1 st screen) or Leica DM6000 (2 nd screen) microscope. Length of the young larvae was measured using the ImageJ software. Second, with the help of Flora Llense, associate professor in the team, I likewise used a spc1(ra409) pak1(tm403) strain carrying an unstable extrachromosomal rescuing spc 1::gfp marker to look for potential suppressors of the retraction phenotype. I selected 13 actin related proteins from the Ahringer RNAi library (Kamath et al., 2003), including that were recently reported to modulate actin remodelling in the early embryo (Naganathan et al., 2018) (Table 3). RNAi was induced by RNAi feeding on L4 larvae maintained at 20°C, and the progeny was analyzed 20h to 30h postfeeding; for early acting essential genes (cyk1, pfn1, unc60), animals were maintained at 15°C, and the progeny was analyzed 16h to 20h postfeeding still inducing more than 14% early embryonic defects.

For specific genes (spc1, pak1, fhod1, vab10b, unc112), RNAi was induced by injection after preparing the doublestranded RNA (dsRNA) with the Ambion mMessage mMachine ® Kit and purifying the dsRNA with the Qiagen RNeasy ® MinElute ® Cleanup Kit (Bosher et al., 2003). The al., 2008;[START_REF] Frøkjaerjensen | Random and targeted transgene insertion in C. elegans using a modified Mosl transposon[END_REF]. However I decided to use a more recent approch, derived from the classical CRISPRCas9 system, that allows to produce integrations from extra chromosomal arrays (Yoshina et al., 2015). The first injection mixture consisted of 10ng/µl of the template, 100ng/µl of pBSK, and 50ng/µL of pFR60 (dpy10 repair template, courtesy of the Robin Lab) and was injected into N2 hermaphrodites. After a few days, Flora proceeded to a second injection into the progeny deriving from the first injection. The second injection mixture consisted of 70ng/µl of pDD162, 100ng/µL of pFR61 (dpy10 sgRNA, courtesy of the Robin Lab) and 100ng/µl of pPRF4 (roller). Then she screened for roller worms and separated this F1 them in single plates. She finally screened the F2 for plates where Dpy/Roller worms could be spotted and single cultured these worms. We succesfully obatined the desired strain, unfortunately its level of expression turned out to be too low to be used.

ACT1::GFP overexpression

To build an extrachromosomal Pdpy7::ACT1::linker::GFP construct, I amplified multiple fragments separatly first and assembled them in two steps. First, pJET, Pdpy7, act1 and linker::GFP have been amplified by PCR respectively from pJET blunt (NEB), pML36, genomic DNA and the plasmid act1::linker::GFP (that will be described in the next paragraph). Then, pJET, Pdpy7 and act1

were assembled first and a second Gibson inserted linker ::GFP in the previously obtained plasmid.

All constructs were purified using Qiaprep® Spin Miniprep Kit. I chose to use a linker as it was shown that small flexible linker contribute not only to the expression efficiency of the protein, but also to the correct folding and corresponding biological activities, especially for polymerizing proteins such as actin [START_REF] Zhang | Design and optimization of a linker for fusion protein construction[END_REF][START_REF] Klein | Design and characterization of structured protein linkers with differing flexibilities[END_REF]. The small linker comes from the GFP::ACT1 from Erin's Cram lab [START_REF] Dixon | Muscle arm development in Caenorhabditis elegans[END_REF][START_REF] Wirshing | Spectrin regulates cell contractility through production and maintenance of actin bundles in the Caenorhabditis elegans spermatheca[END_REF]. This linker is 17 aa long and is about 50% GS. Gs and Ss are usually added to linker to give them better flexibility. The full construction was injected in the worms at a concentration of 10ng/µL with the coinjection markers PRF4 (roller) at 100ng/µl and pCFJ90 (red pharynx) at 2.5ng/µl. The strain obtained was viable but very difficult to work with due to the low transmission of the extrachromosomal array. It was again injected at a concentration of 1ng/µL but we were not able to amplify the strain.

Pdpy7::GFP overexpression

To build an extrachromosomal Pdpy7::GFP construct, I amplified the desired portion from Pdpy7::ACT1::linker::GFP described just above by using Q5 technique and Q5® SiteDirected Mutagenesis Kit. The construct has been purified using Qiaprep® Spin Miniprep Kit and its sequence verified by GATC sequencing. Then Flora injected it in the young hermaphrodites in the following concentrations: 5ng/µl of Pdpy7::GFP, 100ng/µl of pRF4 (roller) and 2.5ng/µl of pCFJ90 (red pharynx). We easily amplified the strain by picking the bright green worms at the fluorescent dissecting microscope.

CRISPR/Cas9 fluorescent knockin transgenic worm generation

For the following constructs, Saurabh designed some of the different templates needed.

Flora, cloned and injected for SMA1::GFP. And Loan Bourdon, technician of the lab, injected the mixes in the worms for the other constructs.

I followed the established protocols for genome editing by use of CRISPR/Cas9.

ACT1 / SMA1 / SPC1

I first used the method described in [START_REF] Dickinson | Engineering the Caenorhabditis elegans genome using cas9triggered homologous recombination[END_REF]. We used the Megawhop or

Gibson techniques [START_REF] Miyazaki | Creating random mutagenesis libraries using megaprimer pcr of whole plasmid[END_REF][START_REF] Gibson | Enzymatic assembly of DNA molecules up to several hundred kilobases[END_REF][START_REF] Gibson | Enzymatic assembly of overlapping DNA fragments[END_REF] plasmid and used the pDD162 expressing the Cas9. pML2840 was derived from PIK198 (from AddGene), Shashi Kumar Suman, a postdoc from the lab, modified it so it would be compatible to easily insert the sgRNA sequence by PCR. This second strategy allowed me tune the sgRNA concentration (especially decrease it when it seems that it is toxic) in the injection mix without changing the Cas9 concentration (Katic, Xu and Ciosk, 2015). All constructs were purified using Invitrogen Purelink™ Quick Plasmid miniprep Kit or Qiaprep® Spin Miniprep Kit. The injection mixture consisted of 50100ng/µl of the repair template, 2550ng/µl of the sgRNACas9, the injection markers 100ng/µl of pRF4 (roller) and 2.5ng/µl of pCFJ90 (red pharynx). When they were synthetized separated, the sgRNA was injected at 25ng/µL and the Cas9 at 50ng/µL. Young adults were then injected into both gonades with this mixture and kept at 20°C. The F1 progeny was screened for roller and/or red pharynx, which were separated and genotyped by PCR to look for positive insertions after egg laying. A positive hit was defined by the specific band amplified from a fluorescent marker internal primer and a primer outside of the repair template. GATC sequencing of the transgenic lines was performed to confirm the CRISPR events. The CRISPR generated strains were further tested for fluorescence using dissecting microscope.

Sequence of the linker: TGCCCGGGGGATCGGTGGAGCTCCACCGGTGGCGGCCGCTCTAGAACTAGT UNC70 I also used the method based on Selfexcising drug selection cassette [START_REF] Dickinson | Streamlined Genome Engineering with a SelfExcising Drug Selection Cassette[END_REF].

I

Fluorescence imaging

DIC images for timelapse videos were obtained using a Leica DM6000 microscope with a Leica LASAF software, using a Leica DMRXA2 upright microscope equipped with a Peltier platform.

Observations were done under a 40X oil immersion objective. Mothers were cut up to gain early staged embryos, which were then transferred onto thin 5% soft agarose pads in a drop of M9. Z stack image series with a 1,5 µm Z step distance were taken in every 5 minutes during 6 to 10 hours.

ImageJ software was used to quantify the embryonic length from the end of ventral enclosure/onset of elongation, by taking a "segmented line" through the midline of the embryos from head to tail. To image the coupling between actin bundles displacement in the epidermis and muscle contractions, Gabriella used a double reporter strain carrying the epidermal Pdpy7::LifeAct::GFP and muscle

Pmyo3::his24::mCherry transgenes (ML2113, see Table 5), and a spinningdisk DMI6000 Leica microscope equipped with an Andor software (experiments for Fig. 1). Series of five Z planes (1 epidermal + 4 muscle) were imaged continuously for 5 min, with 0,5 µm Z steps and no averaging.

The time interval between two Z series was 360 ms. I measured the actin displacement according to the same strategy, using a CSUX1A1 spinningdisk mounted on a Zeiss Axio Observer Z1 inverted stage; spc1(RNAi) pak1(tm403) embryos were aged between 2fold and 3fold equivalent for a control embryo. TIRFSIM images (Gustafsson, 2000;[START_REF] Kner | Superresolution video microscopy of live cells by structured illumination[END_REF] were acquired on a DeltaVision OMX SR imaging system from GE Healthcare Life Sciences equipped with a 60× oil immersion objective from Olympus (PlanApo N 60x 1.42 NA). To minimize spherical aberrations, Pierre and I used Cargille labs immersion oil with a nD at 25°C (5893 Å) = 1.5140 ± 0.0002. Imaging was performed using the excitation at 488 nm with laser transmission ranging from 75 to 100% and integration time ranging from 2 to 3 ms. For each embryo, time series of 50 to 100 TIRFSIM images of 256 x 256 pixels (pixel size of 80 nm) were acquired. Each TIRFSIM image corresponds to a set of 9 images (3 phases at 3 angles) acquired within 90.6 to 99.6 ms. Reconstruction of TIRFSIM images (final pixel size after reconstruction is 40nm) were performed with the softWoRx software (Applied Precision, Inc) which in turn enables a resolution enhancement by a factor of 2 leading to a final lateral resolution in the order of 100 nm.

Image analysis and quantification of actin filament contraction, continuity and orientation

The analysis of mechanical displacement in the epidermis was performed on the movies of the dorsoventral actin layer by measuring the distance over time between two landmarks across the region of contraction. The landmarks were set manually on a frame showing relaxed tissue and tracked all over the contraction till the subsequent relaxed state. Landmarks tracking was performed using a statistical template matching approach (Mathhews, Ishikawa and Baker, 2004). The method was implemented as an ImageJ plugin (http://sites.imagej.net/Julienpontabry/), giving as output the landmarks locations, their distance across time and the Kymographs. The curves show a pre contraction state, a minimum (the maximal contraction point) and an ending part where the distance progressively increases again (see Fig. 1B'' and Fig. S9). After a smoothing and interpolation of the curves, the starting, ending and maximal contraction points were extracted by studying the time derivative of the distance and by setting a threshold on the distance itself. Finally the contraction time was computed as the difference between the ending time and the initial time. The quantification of bending angles was done using a similar strategy; the angles were measured on single bundles at the frame of maximal deformation in a contraction cycle (see figure S5). The analysis of the curves and statistics were done using a MATLAB script. All images were analysed using the ImageJ (FiJi) software (NIH, Bethesda, Maryland, USA; http://rsb.info.nih.gov/ij/) and MATLAB R2015b (The MathWorks Inc., Natick, MA). To study the features of actin pattern, I imaged embryos that were put to sleep by oxygen deprivation through a high concentration of bacteria with the Zeiss/Roper spinningdisk using a 100X oil immersion objective. For each experiments, a Zstack of 16

focal planes with 0,2 µm step size was acquired. On the original maximum z projection created by imageJ, a manual Region of Interest (ROI) was defined on the dorsoventral cells (Fig. 2 and Fig. S3) from which a high pass filter in the Fourier space was applied to select only structures smaller than 10 pixel of diameter (Fig. 2 and Fig. S3).

Continuity:

The filtered ROIs were binarized by setting to one all the pixels with a value bigger then zero and setting to zero all the other pixels. The resulting structures were then fitted by ellipses from which the length of the Major axis was extracted as a measure of the length of the actin filament.

The longer actin filaments are those presenting a more uniform fluorescence along their length (showing higher continuity). By contrast, short segments result from discontinuity in the fluorescence signal. To avoid noise only segments longer than 4 pixels have been considered for the analysis.

Anisotropy of the orientation:

The same filtered ROI used for continuity measurements were used to measure the distribution of cable orientation. Fast Fourier Transform (FFT) of these ROIs was computed in order to work in the frequency domain and more easily identify repetitive patterns. The resulting power spectrum of the ROIs was represented in polar coordinates in order to extract the distribution of angles of ROI pattern (Gonzalez and Woods, 2006). The method was implemented in an ImageJ plugin (http://sites.imagej.net/Julienpontabry/), giving as output the angular distribution.

In order to compare the distributions coming from different images the distributions were normalized by their integral (Fig. 2 and Fig. S3). The more the pattern consists in structures oriented in a preferred direction (the more anisotropic), the highest is the peak of the distribution in that direction. In the case of an isotropic pattern, the angular distribution should show a flat behavior. As an estimate of the pattern anisotropy, the prominence of the highest peak of the angular distribution was considered (Fig. 2 and Fig. S4). The analysis of the angular distributions and statistics was performed by a MATLAB script. All images were analysed using the ImageJ (FiJi) software (NIH, Bethesda, Maryland, USA; http://rsb.info.nih.gov/ij/) and MATLAB R2015b (The MathWorks Inc., Natick, MA). All MATLAB scripts used for the present analysis are available upon request.

Straightness:

For each embryo Teresa Ferraro, engineer in the team, selected an ROI containing the region above the muscles based on a contraction pattern. She selected ROIs containing about ten actin bundles, and she segmented manually seven of them for each ROI (the number of bundles that were on average well resolved). For each bundle she computed the 'Straightness' as the ratio between the length of the segmented bundle and the distance between the initial and final points of the bundle. This quantity has an upper limit equal to one for perfectly straight lines. The manual segmentation and 'Straightness' calculation were performed with a custom made MATLAB interface.

Bundle organization:

For each embryo, we measured the relative contrast in the image between the regions occupied by actin filaments and those inbetween as a proxy for bundle composition and organization. The reasoning was that in the extreme case where bundles defasciculate to generate individual filaments, each filament is likely to have a lower intensity than a bundle made of several filaments, and the contrast between filaments and the intervening space would be less sharp. This should result in a lower variance or standard deviation of the image intensity compared to a wild type bundle image. To do so we divided the standard deviation by the average intensity.

Statistical Analysis

For elongation curves, standard deviation was measured. For L1 length measurement and rescue experiments I perform unpaired ttest using GraphPad Prism 5.00 (San Diego, California, USA) and Excel. For contraction time, actin continuity and orientation, Teresa and I applied for all genotypes a paired ttest using MATLAB.

RESULTS

RESULTS

I. Introduction to the results

Morphogenesis is a process determining the shape, structure of tissues, organs and developing organisms. More specifically, embryonic morphogenesis refers to changes in the shape and position of cells within the embryo, especially in the epithelium. The importance of epithelial morphogenesis has been reported in crucial developmental processes like gastrulation or neural tube formation [START_REF] Chisholm | Epidermal morphogenesis[END_REF][START_REF] Colas | Towards a cellular and molecular understanding of neurulation[END_REF][START_REF] Davidson | No strings attached: new insights into epithelial morphogenesis[END_REF]. A primary component of morphogenesis is the actin cytoskeleton, which drives the cell shape changes, cell division or migration characterizing morphogenesis. Recent studies have emphasized the role of the mechanical forces powered by actomyosin contractility and of cortical tension in driving cell shape change [START_REF] Lecuit | Cell surface mechanics and the control of cell shape, tissue patterns and morphogenesis[END_REF][START_REF] Salbreux | Actin cortex mechanics and cellular morphogenesis[END_REF]. In other organisms, actin and myosin II filaments undergo rapid and dramatic apical flows in the minute range [START_REF] Martin | Pulsed contractions of an actin-myosin network drive apical constriction[END_REF][START_REF] Munro | Cortical lows powered by asymmetrical contraction transport PAR proteins to establish and maintain anterior-posterior polarity in the early C. elegans embryo[END_REF] and in different tissues [START_REF] He | Tissue elongation requires oscillating contractions of a basal actomyosin network[END_REF][START_REF] Kim | Punctuated actin contractions during convergent extension and their permissive regulation by the noncanonical Wntsignaling pathway[END_REF][START_REF] Munro | Cortical lows powered by asymmetrical contraction transport PAR proteins to establish and maintain anterior-posterior polarity in the early C. elegans embryo[END_REF][START_REF] Rauzi | Planar polarized actomyosin contractile flows control epithelial junction remodelling[END_REF]Roh Johnson et al., 2012;[START_REF] Solon | Pulsed forces timed by a ratchetlike mechanism drive directed tissue movement during dorsal closure[END_REF]. The pulsatile activity of myosin II induces cell deformations because they are interspersed with phases of cell shape stabilization, in a process analogous to a mechanical ratchet [START_REF] Martin | Pulsed contractions of an actin-myosin network drive apical constriction[END_REF][START_REF] Mason | Tuning cell shape change with contractile ratchets[END_REF]. However, C. elegans elongation does not involve myosin II pulsatile flows, but instead requires the input of muscle contractions providing the necessary mechanical force [START_REF] Waterston | The minor myosin heavy chain, mhcA, of Caenorhabditis elegans is necessary for the initiation of thick filament assembly[END_REF]Williams and Waterston, 1994). Moreover, C. elegans muscles contract every few seconds (Zhang et al., 2011), at a time scale where cells exhibit a mostly elastic behavior [START_REF] Salbreux | Actin cortex mechanics and cellular morphogenesis[END_REF] whereas in Drosophila the ratchet powered by actomyosin flows occurs every few minutes [START_REF] Martin | Pulsed contractions of an actin-myosin network drive apical constriction[END_REF][START_REF] Rauzi | Planar polarized actomyosin contractile flows control epithelial junction remodelling[END_REF][START_REF] Solon | Pulsed forces timed by a ratchetlike mechanism drive directed tissue movement during dorsal closure[END_REF] at a time scale where cells mainly exhibit a viscous behavior. Together, the fact that tension changes are causes by an extrinsic factor and are rapid could mean that the mechanism involved in stabilizing epidermal cells are different from those observed in Drosophila.

Therefore, C. elegans provides an anatomically simple and integrated model to study the cellular impact of mechanical forces, which does not depend on pulsatile actomyosin flows (Vuong Brender et al., 2017) as described in other cells [START_REF] Munro | Cortical lows powered by asymmetrical contraction transport PAR proteins to establish and maintain anterior-posterior polarity in the early C. elegans embryo[END_REF][START_REF] Martin | Pulsed contractions of an actin-myosin network drive apical constriction[END_REF][START_REF] Rauzi | Planar polarized actomyosin contractile flows control epithelial junction remodelling[END_REF][START_REF] Gilmour | From morphogen to morphogenesis and back[END_REF].

We investigated how the epidermis, an elastic material, acquires progressively its shape through cycles of muscle contractions, while extending only in the anteroposterior (A/P) direction.

More precisely, we characterized how cells adapt in response to mechanical input from muscles and how the cytoskeleton remodels during this process. Previous work of the lab had shown that these contractions promote the remodeling of the CeHDs (structures connecting the epidermis to the muscles) through a mechanotransduction pathway involving the kinase PAK1 (Zhang et al., 2011;[START_REF] Labouesse | Rac GTPase signaling in mechanotransduction during embryonic morphogenesis[END_REF]. Through genetic and molecular screens, we identified SPC1, the alphaspectrin, as a partner of PAK1 and showed that together they stabilize the shape of the full embryo by impacting on actin remodeling through several actinrelated proteins.

II. Previous work: molecular and functional screens identify SPC1 as a potential PAK1 partner

During C. elegans embryonic elongation, the length of the embryo increases while its circumference decreases. As we already discussed it in the introduction, muscular activity is crucial for the elongation to proceed beyond the 2fold stage. Because of their tight mechanical coupling to the epidermis through the hemidesmosomes (CeHD), muscle contractions mechanically impact on the epidermis. To prove it, a former PhD student of the lab, Gabriella Pàsti, manually tracked the displacement of both actin and muscle nuclei. She chose landmarks on the two tissues that she could track for a full cycle of contraction on short spinningdisk timelapses, at the 2fold stage of wildtype embryos. She developed a semiautomated analysis of the recordings to generate kymographs. From this tracking she extracted the distance between landmarks and normalized it to the maximal length (relaxation state). From the curves, she extracted the starting, ending and maximal contraction. She observed that the A/P displacement of circumferentially oriented epidermal actin filaments closely mirrors that of muscle nuclei (Fig. 1aa''). Importantly, all muscles do not contract simultaneously;

when some areas of the epidermis were longitudinally compressed (red line), others were stretched (green line) before eventually relaxing (Fig. 1bb"). The relaxation observed after each muscle contraction raises a conundrum: how can muscle activity power embryonic elongation from 100 µm to 200 µm within an hour if cell elasticity brings cells back to their initial length after each contraction. One simple hypothesis would be that some mechanism stabilizes the transient cell shape induced by muscle activity. For instance, during Drosophila gastrulation and germband extension actomyosin pulsatile flows are thought to modify junctions [START_REF] Rauzi | Planar polarized actomyosin contractile flows control epithelial junction remodelling[END_REF][START_REF] Simoes | Rho GTPase and Shroom direct planar polarized actomyosin contractility during convergent extension[END_REF][START_REF] Vasquez | Dynamic myosin phosphorylation regulates contractile pulses and tissue integrity during epithelial morphogenesis[END_REF].

II. 1. SPC1 and PAK1 loss leads to a retraction of the embryo

To uncover this mechanism, she focused on the kinase PAK1, which mediates mechanotransduction (Zhang et al., 2011) and regulates myosin II (Gally et al., 2009;VuongBrender et al., 2017;[START_REF] Campbell | PAK2 links cell survival to mechanotransduction and metabolism[END_REF]. Two screens were performed: a feeding RNAi screen in a strong pak1 yet viable mutant, looking for enhanced embryonic lethality (Fig. 2a) and a yeasttwo hybrid screen taking the Nterminal domain of PAK1 as a bait (Fig. 2b). The RNAi screen identified the gene spc1 encoding αspectrin as a strong pak1 genetic enhancer. Indeed, spc1 pak1 embryos elongate up to 1.5 fold and then retract to 1fold. These short hatchlings (~58 µm) were significantly shorter than pak1(tm403) (~178 µm) or spc1(RNAi) (~91 µm) hatchlings (Fig. 2c, Table 1). The yeast two hybrid screen identified the central Src Homology 3 domain (SH3) of SPC1, embedded within the large, 9th spectrin repeat domain (SR9), as an interactor of the Nterminal domain of PAK1 (Fig. 2b, Table 2). Together, both screens pointed to a functional interaction between SPC1 and PAK1 during axis elongation. To understand why pak1(tm403) spc1(RNAi) embryos are shorter than spc1(RNAi) embryos, she examined their elongation rate using DIC microscopy. Wildtype and pak1(tm403) embryos initially elongated at the same rate, while spc1 defective embryos elongated slower and stopped around the 2fold stage as previously described (Norman and Moerman, 2002) (Fig. 2d). By contrast, spc1(ra409) pak1(tm403) and spc1(RNAi) pak1(tm403) embryos reached ≈65 µm at a slow rate, but then could not maintain their shape, retracting back to ≈50 µm, which neither spc1(ra409) nor pak1(tm403) embryos did (Fig. 2d,h, Movie 1). (a) RNAi screen in a pak1 mutant identified spc1 as an enhancer (Table 1). (b) A yeast twohybrid screen using the PAK1 Nterm domain as a bait identified the SPC1 SH3 domain as a prey (orange background) (Table 2). As mentioned earlier, muscle tension is important for embryonic elongation (Williams and Waterston, 1994;Zhang et al., 2011). When muscle activity is inhibited, elongation is halted, and embryos are paralyzed at 2fold stage. Muscle tension is responsible for compressing and squeezing the epidermis laterally. As a result, epidermis experiences a tension inducing the recruitment of GIT 1 and PIX1, acting upstream of PAK1, to the CeHDs. Therefore, CeHD remodel via PAK1 / PIX1 / GIT1 signaling promoting embryonic elongation. We could have expected mutants for these three genes to be arrested at 2fold. However, git1(tm1962), pix1(gk416) and pak 1(tm403) mutants are viable although shorter than wildtype at hatching (Fig. 2dg) suggesting the existence of at least a parallel pathway to the one described before (Zhang, Landmann et al. 2011). This idea was confirmed by spc1 knockdown in git1 or pix1 mutants, which induced retraction phenotype as the one just described in spc1 pak1 embryos (Fig. 2dj).

II. 2. This retraction phenotype depends on the muscle input

This last observation led her to think that the retraction phenotype could be linked to muscle activity. This idea was supported by the fact that spc1(RNAi) pak1(tm403) embryos started to retract at the onset of muscle contractions in control embryos (box in Fig. 2d). To directly prove this, she abrogated muscle function in spc1(ra409) pak1(tm403) embryos by knockingdown the kindlin homolog UNC112 [START_REF] Rogalski | The UNC-112 gene in Caenorhabditis elegans encodes a novel component of cell-matrix adhesion structures required for integrin localization in the muscle cell membrane[END_REF]. When UNC112 is absent in wildtype background, it leads to disruption of myofilament attachment structure, causing a 2fold arrest. Strikingly, spc1(ra409) pak1(tm403) embryos defective for unc112 no longer retracted (Fig. 3a,f ; Movie 2). In addition, I verified that the joint loss of SPC1 or PAK1 along with UNC122 would not lead to short embryos similar to a retraction phenotype due to the loss of muscle activity. Indeed, unc112(RNAi); pak 1(tm403) and unc112(RNAi) spc1(ra409) behaved very similarly to unc112(RNAi) (Fig. 3a,c,d);

supporting the rescue of the retraction by unc112(RNAi) in spc1 pak1 background. We conclude that the mechanical input provided by muscles to the epidermis induces the retraction phenotype observed in spc1 pak1 double mutants.

III. PAK, SPC1, SMA1 colocalize with actin near the epidermal cell membrane

III. 1. PAK1 and SPC1 localize along the actin filaments

A previously proposed role of SPC1 is the maintenance of proper actin distribution (Norman and Moerman, 2002). SPC1 is supposed to ensure this role through forming heterotetramers with β spectrins. In C. elegans embryos, the apical localization of βHspectrin and the lateral localization of βGspectrin both have been reported [START_REF] Praitis | SMA-1 spectrin has essential roles in epithelial cell sheet morphogenesis in C. elegans[END_REF][START_REF] Hammarlund | Mutations in betaspectrin disrupt axon outgrowth and sarcomere structure[END_REF]. To examine how SPC1/PAK1/actin physical interaction could occur in the epidermis, we first looked at the potential colocalization of these actors. New constructs of SPC1::GFP and PAK1::mKate have been developed by Gabriella. Her spinningdisk images of the new PAK1::mKate reporter allowed to see a more subtle, previously lessdescribed localization of PAK1 near the cortex in C. elegans embryos (Fig. 4a).

Image processing and computing the colocalization coefficient was done using the Volocity software. The XZ and YZ projections better highlighted these regions of colocalization at the level of the apical cortex. They showed a high level of in vivo colocalization at the uppermost apical region of the epidermis, near the cell membrane and at the level of junctions. This localization pattern was

unc-112(RNAi) unc-112(RNAi); pak-1(tm403) spc-1(ra409) unc-112(RNAi); spc-1(ra409) pak-1(tm403) spc-1(ra409 pak-1(tm403)

highly reminiscent to actin expression (Fig. 4a,c). As the interaction between the spectrin and actin cytoskeleton has been reported both in erythroid and nonerythroid cells, in several model organisms (including C. elegans embryos) [START_REF] Baines | Evolution of spectrin function in cytoskeletal and membrane networks[END_REF][START_REF] Bennett | Spectrin and ankyrinbased pathways: metazoan inventions for integrating cells into tissues[END_REF][START_REF] Korsgren | The carboxyterminal EF domain of erythroid alphaspectrin is necessary for optimal spectrinactin binding[END_REF][START_REF] Korsgren | The carboxyterminal EF domain of erythroid alphaspectrin is necessary for optimal spectrinactin binding[END_REF][START_REF] Machnicka | Spectrinbased skeleton as an actor in cell signaling[END_REF], it was reasonable to suspect that PAK1 and SPC1 also colocalize with actin. Therefore, under the same conditions just described, she performed an in vivo colocalization test between our SPC1::GFP and an ABDVAB10::mKate reporter. Although a strong intestinal and cytoplasmic expression of SPC1::GFP on maximal Zprojection images made it difficult to observe the most apical SPC1 localization, on the single Z merge images and on the co localization channel a clear colocalization can be detected between SPC1 and actin at the cortical regions, near the cell membrane and the junctions (Fig. 4b,d).

III. 2. Superresolution shows precise colocalization of actin and spectrin cytoskeletons

As it has also been shown that SMA1 maintains the association between actin and the apical membrane via interactions at its Nterminus [START_REF] Praitis | SMA-1 spectrin has essential roles in epithelial cell sheet morphogenesis in C. elegans[END_REF], I tried to probe it further thanks to Flora Llense, associate professor in the lab, who developed a SMA1 reporter using CRISPRCas9 technology. With this new reporter, I used SIMTIRF super resolution microscopy to unravel a more detailed organization of the spectrin/actin cytoskeletons. TIRF microscopy allowed us to illuminate our embryos only at the level of the epidermis and SIM microscopy uses spatially structured illumination light in three directions. The reconstruction of TIRFSIM images requires the acquisition of a minimum of three phase shifts per pattern rotation. Therefore, one final image corresponds to a set of 9 images (3 phases at 3 angles).

To perform the experiment I used a strain combining our SMA1::GFP to the ABDVAB10::mKate reporter described in the previous experiment. I acquired short movies of 50 to 100 TIRFSIM images (about 510 seconds) of embryos at the 2fold stage, when their muscles start to be active. The imaging revealed to be difficult as the embryo would often move faster than the temporal resolution of the microscope. Nevertheless, I could observe colocalization of SMA1 along actin cables, with a dotted pattern (Fig. 5b). Indeed SMA1 did not seem to form a continuous signal along the actin cables but rather a succession of small dots. Then, I also wondered if TIRFSIM microscopy could help refine the colocalization between actin and SPC1 compared to spinningdisk imaging. For this experiment, I used a CRISPR strain of SPC1 (SPC1::YFP, ordered from SunyBiotech) instead of the extrachromosomal overexpression strain Gabriella used before. Once again, I crossed this new reporter to ABDVAB10::mKate.

Unfortunately, the signal of SPC1::YFP appeared very fuzzy and was difficult to work with (Fig. 5a). It seemed that SPC1 still colocalized with actin but it did not significantly improve our knowledge compare to spinningdisk imaging.

By lack of time I could not perform a lot of acquisitions with these two strains, but I still want to better understand how spectrins and actin interact in vivo. Therefore, I am planning more acquisitions using a different approach. I would like to image anesthetized embryos by using sodium sulfite that mimics hypoxic stress [START_REF] Jiang | Sodium sulfite is a potential hypoxia inducer that mimics hypoxic stress in Caenorhabditis elegans[END_REF]. It would allow me to image the embryos with more ease and at later stages of development (3fold), when the actin and spectrins pattern will be sharper. I am also planning to work with other reporters. I am currently crossing another SPC1 CRISPR strain (SPC1::mKate, courtesy of Erin Cram's lab) to SMA1::GFP and to LifeAct::GFP (another actin reporter that will extensively be discussed in the following results). By changing the reporters, I hope to obtain a better signal and maybe access to the localization of the two spectrins in respect to each other. SMA1 appears as a succession of dots along the cables and it would be interesting to see if SPC1 intercalate in between or if it perfectly colocalizes with SMA1. Overall it would give us a clearer picture of the two spectrins localize and interact with actin during C. elegans elongation.

III. 3. Other tools have been developed to investigate actin dynamics

To better understand the interaction between actin and the spectrin cytoskeletons, I examined their localization and dynamics by in vivo imaging and super resolution microscopy as presented above. However, the original goal was even more ambitious: further elaborate the internal organization of these actin cables and their precise interaction with the spectrin cytoskeleton. Indeed, the circumferential actin bundles are formed of 510 individual filaments of about 7nm each (Priess and Hirsh, 1986;[START_REF] Pásti | Epithelial junctions, cytoskeleton, and polarity[END_REF]. However, nothing is known about the length of the individual filaments and their orientation inside the bundle. Considering data collected from in vitro experiments and other systems [START_REF] Burlacu | Distribution of actin filament lengths measured by fluorescence microscopy[END_REF]EdelsteinKeshet and Ermentrout, 1998;[START_REF] Cooper | The Cell: A Molecular Approach[END_REF]Haine et al., 2015), it seems unlikely that actin filaments could run uninterrupted from one side of the DV cell to the other. Therefore, we can imagine several scenarios raising the following questions (Fig. 6):

Are they all orientated in the same direction (either from the junction to the CeHD or the contrary)?

Are they organized as antiparallel filaments?

Can the filaments run uninterrupted from the junction to the CeHD or is the bundle subdivided in more minifilaments? I tried to build fluorescent marker knockin of actin and spectrins using CRISPR Cas9 genome editing strategy. In C. elegans, there are five genes encoding for actin: act1, act2, act3 (redundant, controlling cytoplasmic microfilament function in the early embryo, expressed in the epidermis), act 4 (expressed in body wall and vulval muscles and the spermatheca), act5 (expressed only in intestinal cells and in the excretory cell). Since I am interested in the localization and organization of actin in the epidermis through the embryonic elongation of the worm, I chose to work with ACT1 to design 8 different constructions, with the help of Saurabh Tak. I started to couple ACT1 either to GFP or to mMaple3 (photoconvertible protein) at Cterminus or at Nterminus. Once I obtained the four possible combinations, I inserted a linker between ACT1 and the fluorescent reporter. This linker has been shown to ease the interaction of the tagged proteins as actin forms polymers [START_REF] Dixon | Muscle arm development in Caenorhabditis elegans[END_REF][START_REF] Zhang | Design and optimization of a linker for fusion protein construction[END_REF][START_REF] Klein | Design and characterization of structured protein linkers with differing flexibilities[END_REF][START_REF] Wirshing | Spectrin regulates cell contractility through production and maintenance of actin bundles in the Caenorhabditis elegans spermatheca[END_REF]. Then, with the help of the technician of the lab, Loan Bourdon, I proceeded to injections to obtain CRISPR events in worms. We tried various injections mixes and although we did not get insertions for all the constructs, we did obtain many CRISPR events visible by genotyping. Unfortunately, I have never been able to spot fluorescence of the constructs in the embryos by spinningdisk imaging. I never obtained a functional tagged protein expression, probably due to the redundancy of the act genes. In parallel, I also worked on developing an extrachromosomal ACT1::GFP construct, that has been successfully injected in the worms at a concentration of 10ng. The strain obtained was viable but very difficult to work with due to the low transmission of the extrachromosomal array. Therefore, with the help of Flora, we tried to generate another strain injected at a lower concentration of 1ng and this time we failed to amplify a viable strain. By lack of time I did not pursue in that direction. However, it could still be interesting to try injections again at different concentrations to generate a viable strain.

Similarly, for the actin CRISPR, I did not have enough time to troubleshoot and develop alternative constructs, maybe with other types of linkers or other locations of insertions.

I also worked on building an alternative LifeAct reporter, in case no viable CRISPR strain could be generated for actin. I combined LifeAct to mMaple3, a photoconvertible protein, which turns to red from green on being illuminated by UV light (Wang, Moffitt et al. 2014). The goal was to use it for FRAP analysis using spinning microscopy, to get an idea of the dynamics of actin in our system. To generate this strain, with the help of Flora, we used a locusspecific integration of extrachromosomal transgene based on the CRISPR/Cas9 system (Yoshina et al., 2015). We successfully obtained the strain; however, the expression level was not sufficient to perform the experiment we had planned.

In parallel, we used the same CRISPR technology with the three spectrins: the αspectrin SPC1

(required for body morphogenesis, formation of body wall muscles, locomotion, and larval development), the ßGspectrin UNC70 (required for normal body curvature and shape, normal movement, and correct localization of the αspectrin SPC1) and the ßHspectrin SMA1 (required for a normal rate of elongation and thus, for a wildtype body length upon hatching). As mentioned above, thanks to Flora, we easily obtained a functional SMA1::GFP, that could be used for super resolution. For UNC70::mCherry the cloning has been done and the plasmids are ready to be injected, if needed in the future. For SPC1::wrmScarlet, I did obtain a viable strain nicely expressing the tagged SPC1, but I was really disappointed to realize that wrmScarlet, although extremely bright in the larvae [START_REF] El Mouridi | Reliable CRISPR/Cas9 Genome Engineering in Caenorhabditis elegans Using a Single Efficient sgRNA and an Easily Recognizable Phenotype[END_REF], is not expressed at all in the embryo. Since this strain turned out to be useless, the cloning for alternative SPC1::mCherry and SPC1::GFP constructs has been completed, but again by lack of time, they have not been injected in the worms and we requested the SPC1::mKate2 strain developed by Erin Cram's lab [START_REF] Wirshing | Spectrin regulates cell contractility through production and maintenance of actin bundles in the Caenorhabditis elegans spermatheca[END_REF], as mentioned earlier.

Overall, I tried to develop new reporters for actin and spectrin visualization. Unfortunately, most of them were unsuccessful and by lack of time I could not try other strategies. Therefore, all the work that will be discussed later, have been performed using our already existing dpy7::LifeAct::GFP construct.

IV. Genetic interactions of pak1, sma1, unc70, vab10b affects elongation

In most systems, spectrins can fulfill their role only if they form αβ heterotetramers.

Therefore it was important to address if, similarly to spc1, C. elegans βspectrin coding genes, sma1

(encoding for βHspectrin, the apical partner of αspectrin) and unc70 (encoding for βGspectrin, the lateral partner of αspectrin) could be involved in a genetic interaction with pak1.

As reported previously, the loss of unc70 does not affect embryonic elongation; L1 larvae look almost normal (Fig. 7b). The serious larval defects due to the absence of unc70 develop gradually during the larval life caused by neuronal problems, adults get paralyzed and dumpy [START_REF] Hammarlund | Mutations in betaspectrin disrupt axon outgrowth and sarcomere structure[END_REF]. unc70(RNAi); pak1(tm403) double mutants were similar to pak1 single mutants (Fig.

7c,e). Similarly, to unc70, sma1(ru18) L1 show a 2.5fold arrest but are viable (Fig. 7d). When unc70 is simultaneously downregulated with sma1, they recapitulate, but do not enhance the ~1.72fold embryonic elongation arrest of spc1 single deficient embryos (Norman and Moerman 2002). And when sma1 and spc1 are both downregulated, the result is not significantly different from spc1 single mutants. Therefore, I wondered if I could recapitulate the retraction phenotype with ßsubunit mutants. But even the triple deficient unc70(RNAi) sma1(ru18); pak1(tm403) arrested around the 2fold stage and never showed a retracted phenotype as spc1(RNAi) pak1(tm403) does (Fig. 7fk).

Hence, in the absence of PAK1, the knockdown of each ßsubunit had a milder phenotype than in the absence of SPC1, even though the ßHspectrin SMA1 appeared more important than the ßG spectrin UNC70. It suggested that SPC1 functions in interaction with PAK1 to stabilize embryonic shape independently of ßspectrin subunits. However, one of the isoforms of the spectraplakin VAB10 showed a genetic interaction with both SPC1 and SMA1. Indeed, as seen in the introduction, vab10 generates isoforms related either to plectin (VAB10A) or to microtubule actin crosslinking factor (VAB10B) and have been reported

to have specific localizations and functions in the epidermis (Bosher et al., 2003). The loss of VAB10A impairs the integrity of FOs, leading to epidermal detachment from the cuticle and muscles, while VAB10B loss increases epidermal thickness during embryonic morphogenesis when epidermal cells change shape, suggesting that it protects cells against tension that builds up within the epidermis.

I focused on VAB10B and I examined elongation rate of different genotypes using DIC microscopy. As previously described, sma1(ru18) elongated until 2.5fold and survived after hatching (Fig. 8a,b). vab10b(mc44) also elongated but were slightly shorter and stopped around 2.3 fold (Fig. 8a,c). However, vab10b(RNAi); sma1(ru18) showed a 2fold arrest quite similar to spc 1( 409) embryos (Fig. 8a,d, Movie 3). In addition, vab10b(mc44); spc1(RNAi) showed two different behaviors. About 60% of the embryos were shorter than spc1(ra409) and stopped their elongation around 1.7fold (Fig. 8a,e, Movie 3). The 40% others first elongated and could not maintain their shape when muscles started to contract. They retracted in a very similar fashion to that of spc 1(ra409) pak1(RNAi) (Fig. 8a,f,g, Movie 3). These results suggested that VAB10B may also play a role in stabilizing the shape of the embryos during elongation. Recent work from our lab showed that VAB10 acts as a CeHDs mechanosensor and could be the molecular component that induces the recruitment of GIT1, therefore the activation of the mechanotransduction pathway downstream of muscles (Suman et al., BioRxiv). I also mentioned that although muscle defective mutants show a strong phenotype (2fold arrest), git1, pix1 and pak1 mutants are viable, suggesting the existence of parallel pathways for this regulation. The retraction of spc1 pak1, git1; spc1 and pix1; spc1 embryos confirmed this idea. The enhanced phenotypes of vab10b combined to either sma1 or spc1 strengthened it even more. In more details, at 1.7fold -thus before muscles start to contract -the actin is still organized as a meshwork for all genotypes. At 2fold the actin cable anisotropy has decreased and circumferential parallel actin bundles run through the DV cells from one DV/ lateral cell junction to the other. Later, this pattern becomes even sharper and all genotypes get more organized with time, differences among them become less significant (Figs. 1011). Overall pak1 and unc112 display similar organization through time. spc1 and spc1 pak1 are constantly less organized than wildtype but the difference between themselves tends to disappear with time. Quantification of actin filament continuity ; the graph represents the length (in pixels) along the circumferential axis of actin filaments in early, mid and late (corresponding to 1.7fold, 2fold and 3fold equivalent stages in a wildtype embryo, respectively) embryos of wildtype (early n=12, mid n=19, late n=16), pak1(tm403) (early n=16, mid n=21, late n=16), spc1(RNAi) (early n=15, mid n=21, late n=20), spc1(RNAi) pak1(tm403) (early n=12, mid n=17, late n=26), unc112(RNAi) (early n=8, mid n=13, late n=12), spc1(ra409) pak1(tm403) (mid n=14, late n=20) and unc112(RNAi) ; spc1(ra409) pak1(tm403) (early n=8, mid n=15, late n=19) genotypes. Graphs represent median values, 25th and 75th percentiles; whiskers extend to the most extreme data points not considered outliers. Twosided paired ttest. Pvalues: *<0,05; **<0,001; ***<0,0001; ns, not significant. As we showed that spc1(ra409) pak1(tm403) embryos also defective for unc112 no longer retracted I wondered whether the abnormalities in filament organization observed in the spc 1(RNAi); pak1(tm403) embryos only appear in the presence of muscle activity. This experiment turned out to be technically challenging. I started again by isolating a new spc1(ra409) pak1(tm403) strain maintained by an extrachromosomal spc1(+)::GFP construct marked by a red pharynx marker (Pmyo2::mCherry), which I then crossed with our integrated LifeAct::GFP construct, hoping that the new combination would be less stable. I succeeded and recovered about 20% embryos after segregation of the spc1(+)::GFP construct tracked by loss of the red pharynx marker and absence of SPC1::GFP fluorescence (which is significantly different from that of LifeAct). The quantifications showed that the actin defects in unc112(RNAi); spc1(ra409) pak1(tm403) embryos were statistically comparable to those of spc1(ra409) pak1(tm403) embryos, although the bundles seemed less damaged by eye. From this experiment it is very difficult to conclude weather the actin disorganization of spc1 pak1 embryos depend on muscle input or not. Most probably, we reached the limit of our analysis and we are limited by the resolution of the pictures we can obtain with spinningdisk imaging.

V. 2. Enhanced visualization of actin filament abnormalities in spc1 pak1 defective embryos

As the embryo elongates, its circumference decreases, implying that the length of actin filaments in D/V cells should decrease and therefore the actin cables should remodel. To understand how this remodeling could happen, I tried to catch it live by again using TIRFSIM superresolution microscopy of the same LifeAct::GFP probe, focusing only on wildtype and spc1 pak1 genotypes.

As mentioned earlier, this approach allowed me to illuminate only the cortex of the embryos and I tried to follow the actin reorganization upon muscles contractions. Although it is a significant improvement in spatial resolution compared to spinningdisk microscopy, TIRFSIM stays challenging once the embryo starts to move as it often moves faster than the temporal resolution of the microscope. Nevertheless, superresolution confirmed our first observations according to which actin filaments in spc1 pak1 double mutants are more interrupted and do not show the same degree of anisotropy as control embryos. TIRFSIM superresolution images of actin filaments (Pdpy7::LifeAct::GFP reporter). (aa'') Wildtype and (bb") spc1(RNAi) pak1(tm403) embryos at the 2fold stage or equivalent. Grey and orange rectangles, region of interest (ROI) above muscles (area of higher bending in timelapse images); black and bordeaux rectangles, ROI taken elsewhere. Scale bar: 5 µm. (c) Actin continuity estimated as the segment length in binarised ROI images, and (d) peak value of the angular coefficient calculated after Fast Fourier Transformation as a proxy for actin bundle anisotropy. Defects are significantly more pronounced above muscles. (e) Coefficient of variation (SD/mean) of the fluorescence signal in ROIs above muscles as a proxy for actin bundle organization. (f) Actin bundle straightness (f) calculated as the ratio between the actual length of a bundle (black line in f') and the shortest distance between its endpoints (red line in f'). Graphs represent median values, 25th and 75th percentiles; whiskers extend to the most extreme data points not considered outliers. Twosided paired ttest. Pvalues: *<0,05; **<0,001; ***<0,0001; ns, not significant. Thanks to the increased spatial resolution, we slightly adapted our earlier analysis. We distinguished two different types of ROI on the actin pattern: ROIs above muscles (area of higher bending in timelapse images) (Fig. 12a'',b''; grey and orange rectangles) and ROIs closer to the DV/lateral cell junction (Fig. 12a',b'; black and bordeaux rectangles). It revealed that the defects are more prominent in the area that is over the muscles (putative CeHDs, Fig. 12ad, 13a,b), which I could not detect with spinningdisk microscopy. The actin appears even more fragmented (Fig. 12c) and more disorientated (Fig. 12d) in the areas submitted to a more direct stress from muscles underneath. Moreover, by performing a linescan intensity profile on the ROIs above muscles, the signal intensity between adjacent actin bundles appeared less sharp in spc1 pak1 deficient embryos (Fig. 12e) and they were more often bent (Fig. 12f), indicating that the bundles might have partially defasciculated from the main bundle (Fig. 13a,b). Importantly these phenotypes became apparent once muscles became active, suggesting that muscle contractions contribute to actin remodeling. Unfortunately, I could not use TIRFSIM microscopy to examine more precisely the defects in unc112(RNAi); spc1(ra409) pak1( tm403) and check if the nonsignificance of the analysis with the spinningdisk could be due to a lack of resolution. In fact, the spontaneous segregation of the extrachromosomal spc1(+)::GFP was low (20%) making useful embryos difficult to spot. Another limitation in our experiment was the fact that the SIMTIRF setup offered by the Beaurepaire laboratory does not come with a low magnification objective to first find embryos. These two problems combined made the experiment nearly impossible to perform, or it would have taken too much time.

a b wild-type spc-1(RNAi) pak-1(tm403)
Yet, we infer that after strong bending some circumferential actin filaments within bundles get severed, then probably partially depolymerized upon severing and rebundled. Indeed, we assume that crisscrossed and curved filaments observed in spc1 pak1 defective embryos, but not in control embryos, could correspond to severed filaments that did not get repaired/stabilized. However, I am remaining careful on that statement, because even TIRFSIM did not resolve how shortening events occurred. Indeed, the LifeAct::GFP signal, although very stable at the spinningdisk, bleached very fast due to the very high laser power used. Hence the movies acquired are short (10 seconds max).

Combined with the fact that the embryo often moves faster than the temporal resolution of the microscope, very few contractions could be fully captured, and it did not allow me to clearly see live remodeling events.

V. 3. The intensity of actin varies over time in spc1 pak1 defective embryos

From the spinningdisk and superresolution microscopy results, I concluded that the disorganization of actin observed in spc1 pak1 embryos could be due to the severing of filaments that did not get repaired properly. Therefore, it would mean that actin polymerization may be defective in these embryos. To investigate this hypothesis, I followed over time the intensity of actin.

With the help of Teresa, we made global measurements of Pdpy7::LifeAct::GFP fluorescence intensity from the spinningdisk images shown earlier. We found that whether measured on the entire embryo (Fig. 14a) or along the filaments in a small ROI (Figs. 1213), the fluorescence in spc1 pak1 defective embryos was lower than in control embryos (Fig. 14c). To ensure that this does not reflect a lower efficiency of the dpy7 promoter used to drive LifeAct::GFP in mutants, we generated transgenic lines carrying a Pdpy7::GFP construct showing fluorescence in the cytoplasm and nucleus (Fig. 14b). We observed that the average fluorescence of the reporter was very similar in both genotypes over time (Fig. 14d). Comparing the intensity ratio of Pdpy7::GFP to Pdpy7::LifeAct::GFP fluorescence clearly indicates that the activity of the Pdpy7 promoter is not affected in mutants, and that the LifeAct signal was significantly lower in spc1 pak1 compared to control embryos (Fig. 14e).

While we know that LifeAct provides only an indirect measure to actin polymerization, we showed that the intensity variation we observed in our double mutants does not depend on the epidermal promotor, or on the stage of the embryos. Therefore, it suggests that in spc1 pak1 double mutants the balance between polymerization and depolymerization is significantly tilted in favor of depolymerization.

VI. The embryo diameter decreases during elongation

By using the same spinningdisk anesthetized embryos as for the texture analysis, with the help of Teresa, we also observed that as wildtype embryos lengthen, their circumference decreases by roughly 20% due to embryo volume conservation (Fig. 15a,c,d), implying that the length of actin filaments in D/V cells should decrease and therefore that the cables should remodel. In spc1(RNAi) pak1(tm403) embryos, the trend is opposite; the circumference tends to increase by about 10%, leading to longer actin cables (Fig. 15bd). Interestingly, in unc112(RNAi); spc1(ra409) pak1(tm403)

the lateral seam cells did not become circumferentially as narrow. In this respect they behaved more like unc112 single mutants than spc1 pak1. Thus, although the spinningdisk quantification of the actin defects in unc112(RNAi); spc1(ra409) pak1(tm403) did not suggest a statistical difference compared to the spc1(ra409) pak1(tm403) embryos, this result lead us to believe that their actin filaments were less damaged and significantly stiffer than in spc1(ra409) pak1(tm403) embryos. Altogether, we suggest that the circumferential actin bundles remain damaged when muscle activity is prevented in spc1 pak1 double mutants due to the absence of SPC1 and PAK1, but less than in spc1 pak1 mutants alone.

VII. Muscle contractions bend actin filaments leading to the recruitment of severing proteins

VII. 1. Actin filaments are bend at very sharp angles upon muscle input

In wildtype embryos, muscle contractions promote embryonic elongation from the 2fold to the final 4fold stage. During this time, junctions must lengthen along the A/P direction, while the length of the stress fiberlike actin bundles present in dorsal and ventral cells must get shorter as the embryo diameter gets reduced. The next step I took was to further understand how this remodeling of the actin cables could happen in wildtype condition and how it is impaired in spc1 pak1 mutants. To do so, I acquired short spinningdisk timelapses. With Teresa, we examined the behavior of actin filaments upon muscle contractions. Strikingly, live imaging revealed that muscle contractions are strong enough to locally bend actin bundles with an angle greater than 57° (Fig. 16a,c), which has been reported to induce actin filament severing in vitro (McCullough et al., 2011).

To be more specific, when muscles locally contract, we observed that they locally squeeze the embryo along the A/P axis producing an increased circumferential stress due to volume conservation. Moreover, during these contraction phases, the actin bundles get bent to angles that match the local extent of muscle contractions. This could lead to a local severing of the cables and help their shortening through the elongation in wildtype condition. Interestingly, we observed similar bending of the actin cables in the spc1 pak1 embryos with angles in the same range as the wildtype (Fig. 16b,d).

This last result supports the hypothesis developed after the actin pattern analysis presented earlier. Both in control and in spc1 pak1 muscles can mechanically affect the epidermis and eventually promote actin severing. In control embryos, this severing would be quickly stabilized and would help the cables shorten through elongation as its circumference decreases. In spc1 pak1 embryos, the crisscrossed and curved filaments observed would be severed filaments that did not get stabilized.

VII. 2. GSNL1 and VILN1 are involved in the remodeling of actin in our system

Because muscles are strong enough to bend the actin cables at high angles, leading to a local severing of the cables, I investigated which proteins could be involved in this process. Therefore, I reasoned that compromising severing genetically might partially rescue the retraction of spc1 pak1 defective embryos. With the help of Flora, we performed a RNAi screen using the same spc1(ra409) pak1(tm403), spc1(+)::GFP strain as described earlier, and focused on actinbinding proteins known to modulate actin remodeling in early C. elegans embryos (Fig 17a). Remarkably, among thirteen genes tested (Table 3), the screen identified two proteins whose vertebrate homologs have known actinsevering activity, gelsolin and villin (Fig. 17b, Movie 4). The partial rescues observed by using gelsolin and villin RNAi were confirmed with gelsolin and villin mutation (Figs. 17b,18ag). As for spc1 pak1 when we first observed the retraction phenotype, we examined the elongation rate of the triple deficient embryos gsnl1(tm2730); spc 1(ra409) pak1(tm403) and viln1(ok2413); spc1(ra409) pak1(tm403) using DIC microscopy. They initially elongated at the same rate as spc1(RNAi) pak1( tm403), but once muscles started to be active, they could maintain their shape compared to the retracting embryos (Fig. 18ag). The finding that depleting GLSN1 and VLN1 can partially rescue elongation in spc1; pak1 mutants was intriguing. Until now, I addressed their role in mediating a loss of network integrity in the absence of SPC1/PAK1 function, but I did not address their other possible role in the cycle of filament bending, disassembly and network remodeling that leads to shortening of circumferential filament bundles. If VLN1 and GLSN1 had key roles in the disassembly step, then one would predict that depleting VLN1 and GLSN1 or perhaps both together, in wildtype embryos, would affect elongation. To do so, we requested single and double gsnl1 and viln1 very strong or null mutations, previously characterized by Shoichiro Ono and his colleagues. I found that gsnl1 and viln1 single mutants and gsnl1; viln1 embryos had an almost normal elongation, although their final length was slightly and significantly shorter than that of control embryos (Fig. 18c,d,h). Removing pak1 or spc 1 in addition did not significantly modify their length compared to single pak1 or single spc1 embryos (Fig. 18c,d,h), although gsnl1(tm2730); pak1(tm403) and viln1(ok2413); pak1(tm403) did displayed a lower rate elongation compared to pak1(tm403) (Fig. 18a). I concluded that the reason wildtype embryos are not more severely affected by the loss of zygotic GSNL1 and VILN1 activity could be that they rely on more than one process to remodel actin.

I also considered to test whether the retraction rescue provided by viln1 or gsnl1 would modify actin filament damage in gsnl1 or viln1; spc1(RNAi) pak1( tm403) triple deficient embryos.

Unfortunately, the viln1; Pepid::LifeAct::GFP; pak 1(tm403) combination was not viable for reasons that I did not explore, while the gsnl1 locus falls at about the same position as the LifeAct::GFP insertion point making a double recombination difficult to obtain.

Although spinningdisk microscopy did not reveal the precise remodeling mechanism, it suggests that muscle contractions induce actin filament bending and hence, direct or indirect stimulation of severing protein activity. Furthermore, we propose that this process goes uncontrolled in the absence of SPC1 and PAK1. The severing activity mediated by villin and gelsolin might act in parallel to some other process since villin gelsolin double deficient embryos show only minor elongation defects (Fig. 17h).

VIII. A KelvinVoigt model recapitulates the elongation of the embryos of various phenotypes

To rationalize the role of muscles in epidermal remodeling, we decided to use a mathematical model. The aim was to give a mesoscopic physical description and interpretation of embryo elongation, rather than a detailed mechanistic formulation. Thus, we described the C. elegans embryo under elongation as a viscoelastic body: a solid that deforms permanently when it is submitted to mechanical stress. The model that will be described now has been fully implemented by

Teresa. The model is considering:

the elongation profiles described in this work, the results of our previously published laser ablation experiments (VuongBrender et al, 2017), the data on the organization of the actin cytoskeleton described in this work as an indirect measure of its stiffness, the duration of muscle contractions described in this work.

Our model is summarized in four main equations (Fig. 19). Even if the scheme is very simple, the parameters have a strong connection with biological entities. The parameters playing a fundamental role in the equations that account for the elongation curves are:

αDV, which is positively related to actomyosin stiffness in the D/V cells;

β, which expresses the global activity of the remodeling factors SPC1, PAK1 and FHOD1;

γ, which represents the accumulation of cytoskeleton damage.

{

We chose to use a KelvinVoigt system represented by a spring in parallel to a dashpot, subject to two main active forces (Fig. 20). First, the epidermal force Fepid is a continuous positive force, allowing the embryo to elongate. The elongation will stop when the resistance of the spring will equalize the intensity of Fepid. Since muscledefective mutants cannot elongate beyond 2fold the presence of Fepid is tuned can capture the first phase of elongation. Second, the muscle force Fmuscles is a pulsatile force since muscles alternatively contract and relax, starting from the 1.7fold stage. We want to stress out that while the embryo extends along its A/P axis, actin bundles shorten along the DV axis due to volume conservation. We chose to model with a resting length increase only for positive rates for two reasons: 1) it is simple in terms of modeling; 2) it captures the mechanism we hypothesize for actin shortening. The model has free parameters, but we constrained the parameter space by using the experimental observations of the different phenotypes. Based on the mechanism of elongation that we hypothesized, a resting length that responds to stretching ensures elongation.

To simplify its comprehension, it will now be developed step by step.

We started with the simplest version of the model represented by a regular spring and a dashpot, only submitted to the force from the epidermis Fepid (Fig. 20a). In terms of physics, we represented the KelvinVoigt viscoelastic model in the first equation where k is the body stiffness, λ is the spring resting length and η is the coefficient of viscosity (Fig. 19a). It captures the behavior of viscoelastic solids under stress. Fepid is the result of an active force in the lateral epidermis (also called seam cells), and a passive force exerted by the dorsal and ventral epidermal cells (called DV cells) adjacent to the seam cells. The seam cells have a high concentration of nonmuscle myosin II, which has a nonpolarized distribution and does not display pulsatile flow [START_REF] Vuongbrender | elegans Embryonic Morphogenesis[END_REF]VuongBrender et al., 2017). Therefore, the stress generated by the seam cells is anisotropic and globally oriented along the DV axis. On the other hand, the DV epidermal cells do not contribute to generate active stress, as their myosin II is kept mostly silent through the activity of the RhoGAP RGA2 [START_REF] Vuongbrender | elegans Embryonic Morphogenesis[END_REF]VuongBrender et al., 2017;Diogon et al., 2007), but the presence of circumferential Factin filament bundles creates a global stiffness anisotropy. Thus, we described, in a second equation, Fepid as the product of an active force, Fseam, and a passive component, DV, resulting from actin bundle stiffness (Fig. 19b). It recapitulates the first phase of elongation before reaching a plateau that depends on DV (Fig. 20a'). The parameter αDV is positively related to the stiffness of the cytoskeleton in the D/V cells, with its initial value, αDV being the one set at the 2fold stage. In our model αDV can evolve in time by decreasing if there is tearing.

We constrained αDV to be constant for wildtype embryos, since we observed that their actin cytoskeleton integrity and straightness is maintained over time. Likewise, we assume that αDV is constant in the muscledefective unc112 background, since muscles do not exert any stress. By contrast, we allowed αDV to change for spc1 single and spc1 pak1 double mutants, considering that their cytoskeleton is less organized and more compliant to stress. Moreover, based on our measurements we constrained αDV (0) for all the genotypes to be inferior to the one obtained for wildtype. We would like to point out that when fitting the parameters in absence of this constraint we obtained the same results.

The second step was to introduce the force from the muscles into the system (Fig. 20b). As the muscles allow the elongation beyond the 2fold stage, we represented Fmuscles stronger than Fepid. The muscles contract in a cyclic manner, so the force they deploy oscillates between positive and negative values (Fig. 20b', blue rectangle). Because of this behavior, the net contribution to elongation is null; the simulated curve obtained is very similar to the first situation, except constant oscillations when the plateau is reached. and(b') predicted elongation change using Fepid=0.85 and ⃗ with an amplitude equal to 1 and the behavior depicted in the blueboxed inset. For simplicity, we will refer to the amplitude of ⃗ by Fmuscles. As the pulsatile force induces both compression and stretching (see Fig. 1c), its net input on elongation is transient and the system oscillates around the maximal value reached without ⃗ . In all other panels (except in a), ⃗ was set as a periodic function with positive and negative steps of duration 6 seconds modulated by a cosine function, alternating with periods of null value of duration 15 seconds (b'inset). In (ab') the elastic constant of the spring is k=1, the initial resting length has the value λ(t=0)=1, and the viscosity value is η=10. Despite having introduced the two forces submitting our system to stress, yet we could not recapitulate the elongation of the wildtype embryos as the curves rapidly reached a plateau. Thus, to introduce a positive contribution to embryo lengthening, we allowed some plasticity, in the physical sense, or ability of the system to get reorganized. In terms of biology, it corresponds to a permanent rearrangement as it has been already observed and modeled in systems undergoing stresses (Doubrovinski et al., 2017;Munoz and Albo, 2013). In terms of modeling, it means adding a "plasticity factor" β to the spring and a ratchet in the system, which can be done by a simple mathematical solution: having an adjustable resting length λ described in a third equation (Figs. 19c,21a). The simulated curves displayed an increase of the length with time. The speed of the growth (angle of the curve) can be adapted either by modulating either β or Fmuscles (Fig. 21a',a''). The "plasticity factor" β is constrained between 0 and 1, 0 corresponding to no plasticity, therefore no elongation beyond the 2fold stage. We chose the tearing factor, β, to be null in control embryos as a mean to simplify the equations and to avoid adding a positive polymerization factor. We view the "plasticity factor" as an indirect measure of actin bundle shortening, thus of stiffness maintenance, as they are related. Our measurements show that the circumferential length of dorsalventral cells in spc1 pak1 defective embryos is almost unchanged during the first elongation phase and increases during the second phase of elongation. We interpret this as evidence that spc1 pak1 defective embryos are unable to remodel their cytoskeleton at the level of D/V cells in order to reduce the length of actin bundles and to resist the tension created by actomyosin in lateral cells. The moderate gain in length of the embryo during the first elongation phase is only due to myosin II acting in the seam epidermal cells to reduce their circumferential dimension. The result of the fit is coherent with this picture since we found the plasticity factor to be close to zero. From a cellular standpoint, having a changing resting length at each cycle of contractions means that body elasticity does not bring the embryo back to its initial shape upon muscle relaxation, enabling progressive lengthening.

Regarding the force produced by muscles, which is essential for elongation, the growth rate is predicted to be an increasing function of Fmuscles. We could not directly test the behavior of an intermediate muscle force, since the available muscle mutants totally suppress muscle activity and show a Pat phenotype. To highlight the predicted effect of increasing Fmuscles, we considered the length of the embryo as increasing function of the intensity of the muscle force Fmuscles. To link muscles activity and cytoskeleton remodeling, we showed that they locally squeeze the embryo along the A/P axis producing an increased circumferential stress due to volume conservation. And, during these contraction phases, the actin bundles get bent to angles that match the local extent of muscle contractions. It has been demonstrated by in vitro experiments that actin can get severed when bent at an angle distributed around 57° (McCullough et al, 2011). Interestingly, we frequently observed that muscle contractions resulted in actin bending at angles greater than 57°. Result of the fit for the following genotypes: wt, unc112 alone spc1 alone, spc1 pak1 double, unc112; spc1 pak according to Eqs. [START_REF] Gilmour | From morphogen to morphogenesis and back[END_REF][START_REF] Collinet | Local and tissue-scale forces drive oriented junction growth during tissue extension[END_REF]911). The values of the parameters are specified in paragraphs 1.5 and 1.6. The shallow decrease in length for the curve of unc112; spc1 pak1 after 150 minutes is due to a deformation of the embryos under the effect of unc112 knockdown but not to retraction, which is why the fit has been evaluated on the first 150 minutes of the curve. After modeling the wildtype elongation, we wondered how we could reproduce the retraction of the double spc1 pak1 mutant embryos. We showed that the loss of SPC1 and PAK1, affects the integrity of the actin cables in the DV cells, which provide stiffness and define αDV (Figs 813). Thus, we defined a "tearing factor" γ as described in the fourth equation (Fig. 19d). When γ is equal to 0, it corresponds to an absence of tearing, as in wildtype embryos. It leads to a decrease of DV over time (Fig. 21b' blue rectangle) and therefore a similar decrease of Fepid. All these characteristics combined with a "plasticity factor" β equal to 0 generate a simulated curve that first grows and rapidly decreases; mimicking the retraction phenotype observed in the embryos.

To also further constrain the model by additional measurements we tried to follow over time the intensity of actin and its organization. Using TIRFSIM superresolution imaging, we could clearly observe crisscrossing occurrences in spc1 pak1 deficient embryos right above muscles.

Furthermore, by performing a linescan intensity profile of adjacent actin filaments, we observed that their intensity was more irregular in those double mutants consistent with some individual filaments defasciculating from the main bundles we are remaining careful on that statement, because even TIRFSIM did not resolve shortening events. Accordingly, we infer that after strong bending some circumferential actin filaments within bundles get severed, then probably partially depolymerized upon severing and rebundled. Furthermore, it suggests that the crisscrossing plus potential defasciculation of individual actin filaments in spc1 pak1 defective embryos, but not in control embryos, could correspond to severed filaments that did not get repaired/stabilized.

Thanks to the developed model, we could accurately predict the elongation pattern of wild type embryos but also of several mutant conditions, notably the retraction pattern of spc1 pak1

and the triple deficient unc112 spc1 pak1 (Fig. 21c). Note that for this last mutant, the simulated curve is less accurate, mostly due to the collapsing of the worms as the muscle input is removed and their epidermis is damaged / weaker. Nevertheless, the predictions of our model are strongly connected with some experimental findings. Fitting the parameters predicts a value close to zero for the plasticity factor of spc1 pak1 mutants associated with a tearing factor different from zero. It means that spc1 pak1 mutants are unable to remodel their cytoskeleton to reduce the circumferential size of the actin filaments in the D/V epidermal cells. Consistent with this view, we showed that the circumferential size of spc1 pak1 defective embryos increases once muscles become active, showing that the actin filaments did not shorten. The model also predicts a small plasticity factor but with a low tearing factor for single spc1 mutants. These mutants can slightly decrease their circumference, meaning that their actin filaments have a small ability to remodel.

To conclude on this part, we propose that SPC1/αspectrin and PAK1 regulate a cellular process of mechanical plasticity. When muscles contract, they locally squeeze the embryo along the AP axis, which generates an increased circumferential stress due to volume conservation. As shown before, circumferential actin cables become bent (Fig. 16), which certainly introduces a state of increased stress along their length and induce their severing (Figs. 1718). Overall it creates the conditions for actin filament remodeling toward filament shortening, as the embryo elongates and its circumference decreases. In spc1 pak1 defective embryos, the continuing stress on weakened actin filaments leads to their disorganization and reduces their stiffness. The remodeling process becomes less efficient and does not allow the embryo to stabilize their shape.

IX. Combined loss of FHOD1 and SPC1 leads to the same retraction phenotype

IX. 1. fhod1 spc1 retracts and their actin show the same abnormalities as spc1 pak1

Next, we wanted to mechanistically define how cell shapes are maintained at the molecular level when cells are exposed to repeated mechanical strain and further define the molecular basis of viscoplasticity. Thus, Gabriella searched for gene knockdowns inducing retraction of spc1( ra409) embryos (Fig. 22a; Table 4). The screen was limited to ninety essential genes, among phosphatases, cytoskeleton/cell cortexrelated and junctional/attachmentrelated genes, shortlisted from the initial enhancer screen mentioned earlier. It identified the atypical formin FHOD1 (Fig. 22a,b; Movie 5), which has previously been linked to actin dynamics in the epidermis [START_REF] Vanneste | The role of the formin gene fhod-1 in C. elegans embryonic morphogenesis[END_REF]. I confirmed that fhod1(tm2363); spc1(RNAi) embryos also showed a penetrant retraction phenotype (Fig. 22j). Then, with Teresa, we performed the same texture analysis as described before. Again, I acquired pictures of anesthetized embryos at different stages (1.7fold, 2fold and 3fold) by spinningdisk imaging (Fig. 23). Segmentation analysis of the fluorescence signal associated with actin filaments in the D/V epidermis revealed more discontinuity in fhod1; spc1 double deficient embryos compared to wild type embryos, with no significant difference from spc1 pak1 embryos (Fig. 24). Moreover, like in spc1 pak1 again, Fourier transform analysis showed that the degree of anisotropy relative to the circumferential axis of fhod1; spc1 was abnormal (Fig. 25).

Both parameters followed the same trend over time, as described earlier. Actin cable anisotropy decreases with time and at 2fold, the difference between the different genotypes reaches its maximum. As the embryos elongate, differences among them become less significant (Figs. 2425). Nevertheless, spc1 pak1 and fhod1; spc1 show similar defects over time and are constantly less organized than wildtype. Quantification of actin filament continuity ; the graph represents the length (in pixels) along the circumferential axis of actin filaments in early, mid and late (corresponding to 1.7fold, 2fold and 3fold equivalent stages in a wildtype embryo, respectively) embryos of wildtype (early n=12, mid n=19, late n=16), spc1(RNAi) (early n=15, mid n=21, late n=20), spc1(RNAi) pak1(tm403) (early n=12, mid n=17, late n=26), fhod1(tm2363) (early n=12, mid n=14, late n=10), fhod1(tm2363); spc1(RNAi) (early n=7, mid n=11, late n=8) genotypes. Graphs represent median values, 25th and 75th percentiles; whiskers extend to the most extreme data points not considered outliers. Twosided paired ttest. Pvalues: *<0,05; **<0,001; ***<0,0001; ns, not significant.

IX. 2. FHOD1 bundling activity is important for the remodeling

FHOD1 identification was intriguing as, in addition to nucleation, vertebrate FHOD1 promotes actin capping and bundling [START_REF] Schonichen | FHOD1 is a combined actin filament capping and bundling factor that selectively associates with actin arcs and stress fibers[END_REF]. This raised the tantalizing possibility that FHOD 1 activity stabilizes the actin cytoskeleton after severing. Furthermore, the genetic interaction suggested that FHOD1 acts with SPC1 and PAK1.

To examine this possibility, Flora built several constructions of FHOD1 based on what was known from the literature. Indeed it has been shown that the formin FHOD1 is initially inactive due to an autoinhibitory interaction between its Cterminal diaphanous autoregulatory domain (DAD) with the Nterminal diaphanous inhibitory domain (DID) 29 . By deleting the DAD domain, the autoinhibition is removed and was shown to generate a constitutively active form of the protein in vertebrate tissue cells. I wanted to test if a similar approach would work in our system and whether FHOD1 derivatives removing the Cterminal DAD domain could rescue the retraction phenotype of spc1 pak1 deficient embryos. Pdpy7 driven epidermis expression of truncated FHOD1 variants and terminal body length at hatching: spc 1(RNAi)(n=26); spc1(RNAi) pak1(tm403) with no transgene (n=36), with FHOD1(full length) (n=16), FHOD 1(ΔDAD) (n=17), FHOD1(ΔFH2DAD) (n=38) transgenes or nontransgenic siblings (n=78), FHOD1(ΔFH1FH2 DAD) transgene (n=18). Data represent mean values ± SD. Twosided paired ttest. Pvalues: *<0,05; **<0,001; ***<0,0001; ns, not significant. Strikingly, after epidermisspecific expression of a form lacking the FH2 and DAD domains, transgenic spc1(RNAi) pak1(tm403) embryos reached the length of spc1 single mutants without retracting; rescue was better than with the fulllength protein. By contrast, the DAD deleted construct failed to rescue, while deletion of the FH1FH2DAD domains and other forms marginally rescued retraction (Fig. 26), arguing that the FH2 Factin nucleation domain is dispensable for rescue while the FH1 is not. Importantly, a mammalian FHOD1 lacking the FH2DAD domains can still bundle actin [START_REF] Schonichen | FHOD1 is a combined actin filament capping and bundling factor that selectively associates with actin arcs and stress fibers[END_REF], thereby emphasizing that FHOD1 bundling activity matters. It further suggests that he atypical forminhomologue responsible for actin capping and bundling is involved in the same regulatory pathway as PAK1. The retraction of spc1 pak1 deficient embryos could mainly result from a lack of FHOD1 activation downstream of the muscleinduced mechanotransduction pathway. This result raises the possibility that this direct activation could be mediated by a phosphorylation of FHOD1 by PAK1. In conclusion, I suggest that the actin filament severing initiated by muscle contractions (Figs. 1718) followed by FHOD1dependent bundling or capping (Fig. 26) represent a ratchetlike mechanism, providing a molecular basis for viscoplasticity. These results strongly suggest that FHOD1, the atypical formin, responsible for actin capping and bundling, is involved in the same regulatory pathway as PAK1 and SPC1 during the embryonic developmental process we characterized and SPC1 could help recruit these proteins.

spc-1(RNAi) pak-1(tm403) spc-1(RNAi) pak-1(tm403); FHOD-1(Full Length) spc-1(RNAi) pak-1(tm403); FHOD-1(ΔDAD) spc-1(RNAi) pak-1(tm403); FHOD-1(ΔFH2/DAD) spc-1(RNAi) pak-1(tm403); FHOD-1(ΔFH1-DAD) Length (
Second, by using the short spinningdisk timelapses and tracking landmarks on the actin as described at the beginning, I found that muscle contractions in spc1(RNAi) pak1(tm403) embryos were almost twice as short as those in pak1(tm403) and wildtype controls (3 sec against 5.7 sec; Fig. 28, Movie 6). Although, muscles can strongly bend actin cables even in spc1 pak1, as shown earlier, such shorter contractions might not give enough time for FHOD1 to stabilize actin filaments. To conclude, we uncovered a novel machinery involving αspectrin/SPC1, the kinase PAK1 and several actin remodeling proteins involved in stabilizing cell shapes in a system submitted to repeated external mechanical stress. When SPC1 and PAK1 are both absent, the embryo starts to elongate then retracts to its initial length, A key aspect of our results is that embryonic retraction is triggered only when muscles start to contract, exposing the overlying epidermis to changes in tension every few seconds. In wildtype embryos, muscle contractions promote embryonic elongation from the 2fold to the final 4fold stage. As the embryo elongates and its diameter reduces, actin bundles present in D/V cells must shorten. Our data show that the molecular machinery enabling actin filament remodeling is at the heart of the defects observed in spc1 pak1

deficient embryos. We propose that the progressive shortening of actin filaments under the control of these factors mediates a cellular viscoplastic process promoting axis elongation. A similar viscoplastic process might operate in vertebrate tissues comprising an epithelial layer surrounded by a contractile layer, such as our internal organs.

DISCUSSION AND PERSPECTIVES

To study mechanotransduction and its importance in morphogenesis at the scale of an organism, I worked with a simple model, the nematode C. elegans. My thesis aimed to give a better understanding of the role of the actin cytoskeleton and its remodeling during C. elegans elongation as it would provide finer details of how cells adapt and respond to mechanical input. The work presented here is mostly included in a letter published in Nature. The full version of the paper including all the supplementary information is available in the annex of the thesis.

The focus of this work was directed to the second phase of C. elegans embryonic elongation.

This process does not involve cell divisions or rearrangements and relies entirely on epidermal cell shape changes. The second phase of elongation starts at the onset of muscle contractions: from this point the epidermal cells are submitted to regular cycles of intense mechanical input. The epidermis needs to meet two requirements for the maintenance of a proper embryonic development. On the one hand, it must be able to mechanically resist to this force input that exerts cyclic physical stress on the epidermis. On the other hand, this input provides a crucial development signal at the same time: it induces a biochemical signaling pathway that promotes hemidesmosome remodeling and further elongation through a tensioninduced mechanotransduction pathway. The molecular components of the epidermis need to be able to properly sense and translate this signal and execute the necessary developmental changes.

In the frame of this thesis project we extended our understanding on the molecular landscape around that complex process. We identified a novel morphogenetic ratchet mechanism that is responsible for the stabilization and remodeling not only of the epidermal cells, but also, of the entire embryonic body under cyclic stress from the second elongation phase. We equally identified the main molecular players of this morphogenetic ratchet through the interaction of PAK1, p21 activated kinase and SPC1, a cytoskeletal component, important for the maintenance of cellular mechanical properties.

Through genetic and reciprocal molecular screens, we established both an in vivo genetic and in vivo physical interaction between these two players. The combined loss of SPC1 and PAK1 lead the embryos to first elongate and then retract to their initial shape. We considered that together SPC1 and PAK1 function as a locking mechanism of the elongation. When they are absent, the system is not locked and goes awry. We provided evidence that this interaction takes place in the epidermis. To characterize the defects underlying the retraction, we developed a novel approach for the dynamic and simultaneous acquisitions of epidermal actin filaments and the underlying muscles.

We developed a corresponding novel approach for image analysis and quantification of this coupling.

This way we were able to establish that the two neighboring tissues, epidermis and muscles, are properly coupled, even in the spc1 pak1 deficient embryos. Using different translational reporters, colocalization tests and superresolution microscopy we showed that the physical interaction might take place between these players also in vivo as we established a colocalization of a PAK1/SPC 1/actin network at the epidermal cell cortex at the level of cell junctions and the circumferential actin bundles. We also know that, at the level of the epidermal components, the retraction process does not affect the proper recruitment and localization neither of the adherens junctions nor the microtubules (data not shown, Gabriella Pasti's thesis). A key aspect of our results is that embryonic retraction is triggered only when muscles start to contract, exposing the overlying epidermis to changes in tension every few seconds. The mechanical properties of a biological material are dominated by an elastic behavior at low timescales (seconds), which allows the propagation of tension between the cells in a tissue. Hence, the retraction phenotype most likely relies on the elastic properties of the epidermis. That is why we focused our attention to the actin cytoskeleton. Indeed, we observed a muscle dependent disorganization of the actin filaments in the combined loss of PAK and SPC1. Superresolution microscopy showed that epidermis circumferential actin filament bundles are discontinuous and not fully oriented perpendicular to adherens junctions in spc1() pak 1() embryos. The actin defects could be best observed in the region that overlaps with the muscle attachment zone. Additionally, spinningdisk microscopy revealed that muscle contractions are strong enough to locally bend actin bundles at great angles, which has been reported to induce actin filament severing in vitro (McCullough et al., 2011). We observed this strong bending of the actin cables both in spc1 pak1 and wildtype embryos.

Strikingly, Priess & Hirsh (1986) found that actin depolymerization induces embryo retraction, suggesting that actin rearrangement could account for the lock counteracting elasticity. In wildtype embryos, muscle contractions promote embryonic elongation from the 2fold to the final 4fold stage. During this time, since the embryo diameter gets reduced, the actin bundles present in dorsal and ventral cells must get shorter, hence they need to remodel. Therefore, we reasoned that on one hand severing proteins might help breaking the actin cables, on the other hand, capping proteins should help stabilizing the cables. Two additional RNAi screens were then performed to identify which severing and capping proteins could be involved in our system. We first looked for players that might partially rescue the retraction of spc1 pak1 defective embryos. Remarkably, among thirteen actin binding genes tested, the screen identified homologs of two actinsevering proteins, gelsolin and villin. Mutations in villin and to a lesser degree gelsolin confirmed this partial rescue. Second, we searched for gene knockdowns inducing retraction of spc1() embryos. This screen identified the atypical formin FHOD1, which has previously been linked to actin dynamics in the epidermis. We confirmed that fhod1(); spc1() embryos also showed a penetrant retraction phenotype with damaged actin. Furthermore, overexpressing in the epidermis a Cterminally truncated FHOD 1(ΔFH2/DAD) construct, predicted from vertebrate studies to only bundle actin, partially rescued the spc1() pak1() retraction phenotype. We thus suggest the following scenario in normal embryos:

(1) muscle activity bends at a sharp angle actin bundles which with the help of severing proteins could break them, ( 2) the formin FHOD1 with actin bundling properties blocks further actin depolymerization until the next cycle of muscle activity (Fig. 1a). We propose this goes uncontrolled in spc1 pak1 double mutants (Fig. 1b). A possible molecular mechanism could be that upon the muscleinduced epidermal cell deformation SPC1 somehow activates PAK1 kinase activity, which in turn modulates the remodeling of actin filaments via bundling and severing proteins. To back our results with theory, we modeled the embryo as a KelvinVoigt material experiencing actomyosin force from the epidermis plus muscle tension. We could predict embryo lengthening by introducing a viscoplastic component in the system, which we propose corresponds to actin shortening.

Altogether, we uncovered a novel machinery involving the αspectrin SPC1, the kinase PAK1, an atypical formin FHOD1 and two actin severing proteins, GSNL1 and VILN1, which confers mechanical plasticity to stabilize cell shapes during a ratchet morphogenetic process.

I. Identification of a novel morphogenetic ratchet

Based on our results we propose a novel morphogenetic ratchet mechanism, relying on PAK 1/spectrin/actin/actinremodeling system that is different from previously known molecular ratchet of three reasons.

First, previously described ratchets stabilize cell shape against internally generated forces, originating from epithelial actomyosin contractions. For example, mesoderm invagination during Drosophila gastrulation does require a wholebody coordination of the mechanics of tissue behavior but cell shape changes of cells belonging to different tissues is driven by their apical actomyosin contractility [START_REF] Rauzi | Planar polarized actomyosin contractile flows control epithelial junction remodelling[END_REF]. Similarly, the Drosophila dorsal closure is influenced by forces generated by two different embryonic tissues: the dorsally positioned amnioserosa and the lateral epidermis [START_REF] Kiehart | Multiple forces contribute to cell sheet morphogenesis for dorsal closure in Drosophila[END_REF][START_REF] Hutson | Forces for morphogenesis investigated with laser microsurgery and quantitative modeling[END_REF], Sawyer et al., 2010). Cells at the leading edge of the dorsally migrating epidermis assemble an actomyosin cable at the interface between these two tissues, exhibiting tension perpendicular to the direction of movement [START_REF] Young | Dynamic changes in the distribution of cytoplasmic myosin during Drosophila embryogenesis[END_REF][START_REF] Kiehart | Multiple forces contribute to cell sheet morphogenesis for dorsal closure in Drosophila[END_REF][START_REF] Hutson | Forces for morphogenesis investigated with laser microsurgery and quantitative modeling[END_REF]. Thus, contractile activity of the actinmyosin cable of the epidermis could function like a supracellular pursestring that helps pull the epidermis dorsally [START_REF] Edwards | An activitydependent network of interactions links the Rel protein Dorsal with its cytoplasmic regulators[END_REF]Franke et al., 2005, Martin and[START_REF] Martin | Apical constriction: themes and variations on a cellular mechanism driving morphogenesis[END_REF]. During C. elegans elongation, actomyosin contractility is present in lateral cells and drives the first phase of elongation until muscle become active. The mechanism we describe in this work is a stabilization occurring to answer an extrinsic force, provided by the cyclic contractility of the underlying muscle tissue.

Second, the timescale of stabilization is different. In already described ratchets in Drosophila, the frequency occurs in minutes. For example, prior to dorsal closure, actinmyosin networks undergo cell shape fluctuations with large amplitudes and a periodicity of about 4 min [START_REF] Blanchard | Cytoskeletal dynamics and supracellular organisation of cell shape fluctuations during dorsal closure[END_REF][START_REF] Sokolow | Cell ingression and apical shape oscillations during dorsal closure in Drosophila[END_REF][START_REF] Hayes | Drosophila dorsal closure: An orchestra of forces to zip shut the embryo[END_REF]. During dorsal closure, cell shape fluctuations become more frequent with a smaller amplitude. This transition is associated with increased apical myosin levels and a transition from cycles of actinmyosin network assembly and disassembly to more persistent apical actinmyosin networks [START_REF] Blanchard | Cytoskeletal dynamics and supracellular organisation of cell shape fluctuations during dorsal closure[END_REF][START_REF] David | The PAR complex regulates pulsed actomyosin contractions during amnioserosa apical constriction in Drosophila[END_REF][START_REF] David | Bazooka inhibits aPKC to limit antagonism of actomyosin networks during amnioserosa apical constriction[END_REF]. In the process we described, the frequency is considered at the scale of seconds. Indeed, we showed that wildtype embryos contract with an average timing of 6 seconds and a considerable proportion of their contractions are even shorter. In the scenario we proposed muscle activity bends at a sharp angle actin bundles which with the help of GSNL1 and VILN1 could break them and FHOD1 blocks further actin depolymerization until the next cycle of muscle activity. It means that the stabilization mechanism happens at each contraction, in a narrow time window.

Finally, the previously described ratchets used different stabilization mechanisms. For instance, during Drosophila embryonic germband extension, tissue elongation is driven by cell intercalation, requiring the shrinkage of dorsalventraloriented junctions during this process. The polarized flow of medial actomyosin pulsing towards junctions allows the irreversible and planar polarized remodelling of epithelial cell junctions [START_REF] Rauzi | Planar polarized actomyosin contractile flows control epithelial junction remodelling[END_REF][START_REF] Munjal | A selforganized biomechanical network drives shape changes during tissue morphogenesis[END_REF]. At the beginning of Drosophila dorsal closure, a supracellular actin cable that surrounds the opening provides the contractile force. Amnioserosa cells that fill the opening produce an additional critical force pulling on the surrounding epidermal tissue. As we already mentioned, this force is not gradual but pulsed and occurs long before dorsal closure starts. The actin cable function as a ratchet to counteract ventralward epidermis relaxation after force pulses. The dorsal closure proceeds thanks to the interplay of pulsatile actomyosin flows in one tissue and a continuous purse string constriction in the surrounding tissue [START_REF] Solon | Pulsed forces timed by a ratchetlike mechanism drive directed tissue movement during dorsal closure[END_REF]. During Drosophila gastrulation, cycles of MyoII and apical Rok pulses are associated with apical constriction. The dynamic coupling of MyoII phosphorylation to upstream signals organizes contractile MyoII pulses in both space and time. This pulsatile nature of apical constriction is required for the stable transmission of intercellular forces during tissue morphogenesis. Additionally, the polarized localization of Rok to medioapical foci results in the persistence of medioapical actomyosin fibers stabilizing cell shape between pulses [START_REF] Vasquez | Dynamic myosin phosphorylation regulates contractile pulses and tissue integrity during epithelial morphogenesis[END_REF].

Here, we propose that SPC1/αspectrin and PAK1 regulate a cellular process of mechanical plasticity. When muscles contract, they generate a stress. Circumferential actin cables are bent which induce their severing. It creates the conditions for actin filament remodeling toward filament shortening, as the embryo elongates and its circumference decreases. This actin filament severing initiated by muscle contractions followed by FHOD1dependent bundling or capping represent a ratchetlike mechanism, providing a molecular basis for viscoplasticity.

II. Modelization of our ratchet mechanism

The model developed by Teresa aims to describe the embryo under elongation as a solid that deforms permanently when it is submitted to mechanical stress. It gives a mesoscopic physical description and interpretation of embryo elongation, rather than a detailed mechanistic formulation.

We choose to describe the C. elegans embryo under elongation as a viscoelastic body: a solid that deforms permanently when it is submitted to mechanical stress. We took in account our previous and already published work, data on the organization of the actin cytoskeleton described in this work and the duration of muscle contractions also described in this work. There are three main parameters: αDV positively related to actomyosin stiffness in the D/V cells, β expressing the global activity of the remodeling factors SPC1, PAK1 and FHOD1, and γ, which representing the accumulation of cytoskeleton damage.

Because the model we proposed has several free parameters, we tried to narrow it down as possible. To do so, we extracted some of them from experimental data. For example, for Fmuscles, we specified its details on the basis of the measured contraction durations for embryos at the 2fold stage. For wildtype embryos, the duration of positive and negative periods has been set to 6

seconds while for spc1 mutants and spc1 pak1 double mutants the duration of nonnull activity has been set to 3 seconds. And the muscle force amplitude for spc1 and spc1 pak1 mutants has been set to 50% of the wildtype intensity according to our experimental observations. However, it was more difficult for αDV which is related to the stiffness in the D/V cells. As mentioned in the introduction, accessing the stiffness of a tissue in vivo is challenging. Laser ablation experiments could have been an added value to measure the relative stress and/or stiffness in our system.

However, as we model the elongation of the embryo, process enabled by muscle contractions, it would have been interesting to access the stiffness of the epidermis at 2fold and beyond.

Unfortunately performing laser ablation in a moving embryo is in our experience extremely challenging, because the embryo rotates once muscles start to twitch and reacts to the laser by stronger contractions, making it almost impossible to track the recoil process. Therefore, we used our previous work showing that prior to muscle contractions, actin bundles in D/V cells provide stiffness due to their high anisotropy in the circumferential direction, by using laser ablation (Vuong Brender et al, 2017). It allowed us to constrain the time behavior of Fepid (the epidermal force introduced by the shrinking of the seam cells).

We are also aware that the general form we propose is one of some other possibilities to capture the phenomenology of the process. We know that our model leads to nontrivial consequences about the speed of the applied deformation: fastapplied deformations will induce strong plastic response and very slow deformations will leave the system almost elastic. Indeed, we did not apply our model to a large range of deformation speeds, because the average speed of deformation is of the order of ~1 µm/s for all genotypes, making the value of the deformation speed uniform across our genotypes and not crucial for their description. Nevertheless, we investigated other possibilities to verify that the model we propose is the best to describe our system. A more standard way to introduce plasticity would be trough the following equation:

dλ dl dt dt = β (l -λ) H(αDV) if > 0 l -λ > Fc k and 154
Using different values of Fmuscles, the yield stress Fc and β, we observed a regime of elongation with some parameters (Fig. 2df), but it remains that elongation is predicted to occur when Fmuscles=0 irrespective of the parameters (Fig. 2ac), which is contradictory with the fact that Pat mutants (which have no muscle force) fail to elongate beyond the 2fold stage. Furthermore, some curves are predicting a poor relationship between the level of Fmuscles and the speed of elongation (Fig. 2ac), whereas some of our ongoing work point towards a direct relationship.

Overall this alternative is contradictory with the phenomenology observed in our data. In order to respect the biological phenomenology, the muscle force needs to contribute positively to elongation and elongation needs to arrest in the absence of this force even if the epidermal force is still present. On the other hand, our model properly recapitulates the elongation arrest in the absence of muscle activity. However, we do not pretend that it is easy to generalize it to other contexts, and that we are not aware of other work where it has been used. In principle, this model could be useful in a framework that requires a plastic deformation that saturates. We find it useful to rationalize a complex biological process such as the elongation of an embryo under the influence of two cooperating tissues. We think that our choice is appropriate to describe the phenomenology of the process, although we do recognize some of its limitations.

III. Unraveling the internal organization of actin

In the work, we describe a morphogenetic racthet in which actin bundles counteract the elasticity of the cells. As mentioned in the results, these circumferential actin bundles are formed of 510 individual filaments [START_REF] Pásti | Epithelial junctions, cytoskeleton, and polarity[END_REF]. But nothing is known about the length of the individual filaments and their orientation inside the bundle. It does not seem too risky to rule out that they would run uninterrupted from one side of the DV cell to the other. Moreover, super resolution revealed that the actin organization defects observed in spc1 pak1 were more prominent in the area over the muscles, most probably where hemidesmosomes are located. This trend was also verified in wildtype embryos where the wellorganized pattern seemed less sharp in the areas submitted to a more direct stress from muscles underneath. These results may point to an important role for CeHDs probably in anchoring the actin filaments, as relay in the DV cells. However, even super resolution and the potential defasciculation of individual actin filaments in spc1 pak1 defective embryos did not tell us anything about the internal organization of actin bundles.

As described in the figure 6 of the results section, we could image different scenarios.

Bundles could be formed of filaments running uninterrupted from the junction to the CeHD or could be subdivided in more minifilaments. Their orientation is also a pending question. I started to tackle this by developing new reporter tools to look at actin. I tried to obtain ACT1 CRISPR reporters, in C ter and Nter, with and without linker. I also created an extrachromosomal ACT1::GFP construct, that was viable but very difficult to work with due to the low transmission of the extrachromosomal array. And I built an alternative LifeAct::mMaple3, for FRAP analysis using spinning microscopy, which expression level was not sufficient to perform the experiment we had planned. All these approaches were focused on actin. However, to answer this big question, we could also focus on actin related proteins with specific binding to the filaments.

For example, we could imagine tagging a processive myosin motor that walk along the filament. Knowing that myosins move along the actin filament in the direction of the plus end, it would give us insight on the orientation of the filaments inside the bundle. TIRF imaging would help follow the displacement of the myosin and if the myosin stops and detach from the filament, its disappearance could indicate where the end of the filament stands. Therefore, at single molecule level, we may be able to track both the direction of the displacement and the length of the mini filaments.

Another way to do it could be to use an optogenetic tool as it is already has been extensively used for neurobiology [START_REF] Husson | Optogenetic manipulation of neural activity in C. elegans: from synapse to circuits and behaviour[END_REF][START_REF] Fangyen | Illuminating neural circuits and behaviour in Caenorhabditis elegans with optogenetics[END_REF][START_REF] Bergs | Rhodopsin optogenetic toolbox v2.0 for lightsensitive excitation and inhibition in Caenorhabditis elegans[END_REF]. We could even combine it to a new approach, the use of unnatural amino acids [START_REF] Greiss | Expanding the genetic code of an animal[END_REF][START_REF] Bianco | Expanding the genetic code of Drosophila melanogaster[END_REF][START_REF] Elliott | Proteome labeling and protein identification in specific tissues and at specific developmental stages in an animal[END_REF][START_REF] Han | Expanding the genetic code of Mus musculus[END_REF][START_REF] Italia | Expanding the genetic code of mammalian cells[END_REF][START_REF] Vinson | Expanding the genetic code in vertebrates[END_REF]). The use of unnatural amino acids had been limited to single celled systems until very recently, when it has been extended to C. elegans [START_REF] Davis | Genetic Encoding of Unnatural Amino Acids in C. elegans[END_REF]2018). There are photocaged amino acids already available for the design of lightactivatable proteins. As actin is incredibly challenging to tag, we would imagine targeting actin related proteins. This would allow us to dissect their dynamic inside living cells with great precision and great temporal resolution.

IV. Interaction of actin and spectrin cytoskeleton

To better understand the interaction between actin and spectrin cytoskeletons, I examined their localization and dynamics by in vivo imaging and super resolution microscopy. I used CRISPR strains for SMA1 and SPC1 both combined to our well characterized ABDVAB10::mKate reporter. SMA1 was present along actin cables, with a dotted pattern, while SPC1::YFP reporter turned out to be difficult to work with. Therefore, as I already briefly mentioned in the results, I propose an alternative imaging strategy. First, I am crossing a SPC1::mKate reporter to SMA1::GFP and to LifeAct::GFP. Second, with these two new strains, I would image anesthetized embryos by using sodium sulfite that mimics hypoxic stress [START_REF] Jiang | Sodium sulfite is a potential hypoxia inducer that mimics hypoxic stress in Caenorhabditis elegans[END_REF]. Indeed, I cannot use the same strategy as for spinningdisk imaging, put to sleep the embryos by oxygen deprivation through a high concentration of bacteria. The bacteria produce a strong autofluorescence that would interfere with the signal I would like to acquire, as with TIRFSIM we only illuminate the plans very close to the cover slip. However, anesthetizing the embryos seem a good option because it would allow me to image the embryos with more ease and at later stages of development (3fold), when the actin and spectrins pattern will be sharper.

Indeed, it would be interesting to see if SPC1 intercalate in between SMA1 or if it perfectly colocalizes with SMA1. It has been shown that the interaction between SMA1, actin, and the apical membrane is independent of SPC1 [START_REF] Praitis | SMA-1 spectrin has essential roles in epithelial cell sheet morphogenesis in C. elegans[END_REF]. As actin reorganizes into parallel bundles during morphogenesis, SMA1 is required to maintain the localization of actin at the apical membrane. When the embryo elongates, the SMA1 network stretches to accommodate changes in cell shape. To stabilize these changes, it dynamically reorganizes, returning to its relaxed state.

Therefore, the authors propose the following model. At the beginning of cell elongation, SMA1 interacts with SPC1 forming a tetrameric network that crosslinks actin to the apical membrane.

When cells elongate, the actin bundles move apart from each other (Costa et al., 1997), causing the associated SMA1 network to shift from a relaxed to a stretched state. Because SMA1 tetramer is not sufficiently long to accommodate the maximum distance between the actin fibers (Costa et al., 1997[START_REF] Dubreuil | A betaspectrin isoform from Drosophila (beta H) is similar in size to vertebrate dystrophin[END_REF], SMA1 tetramer would dissociate from the apical membrane and returns to a relaxed state. This association between the spectrin tetramer and the apical membrane may require SPC1. Following this hypothesis, by super resolution microscopy, I would expect at least a partial colocalization of SPC1 and SMA1 along the actin bundles but also in the interspace between the bundles.

V. SPC1 as a major player in a mechanotransduction pathway

As a crucial component of our morphogenetic locking mechanism, the spectrin cytoskeleton could play a major role in sensing the force exerted by muscles on the epidermis. It forms a ubiquitous 2D network, crosslinking the cell membrane, actin filaments and membraneassociated proteins. The contribution of spectrins to cellular mechanical properties, more precisely to cellular elasticity gained wide acceptance in multiple tissues. Recent studies showed that spectrins play a crucial role in cell morphology, protein localization, cellular motility and in the mechanical stabilization of both erythroid and nonerythroid tissues (like epithelia, neurons or other tissues exposed to mechanical stress and deformation). In this work, we provided evidence that C. elegans alphaspectrin SPC1 contributes to the elasticity of the cells during embryonic elongation. However, we did not investigate its behavior under force exertion. Special conformational changes are also in the focus of our interest as we suspect them to be important in the establishment of a PAK1 SPC1 interaction.

Spectrins have been shown to form functional units only as alphaß heterotetramers and as such they attach to the membrane and to the actin filaments. The alpha and ßspectrins show high affinity to each other and their lateral association is highly conserved. The heterotetramers are around 60nm at their resting length but they can reach up to a threetofivefold extension [START_REF] Sotomayor | Singlemolecule experiments in vitro and in silico[END_REF][START_REF] Mehboob | Crystal structure of the nonerythroid alphaspectrin tetramerization site reveals differences between erythroid and nonerythroid spectrin tetramer formation[END_REF][START_REF] Brown | The Physiological Molecular Shape of Spectrin: A Compact Supercoil Resembling a Chinese Finger Trap[END_REF].

A recent model (relying on crystal structures, electron micrographs, mass spectroscopy results and modeling approaches) proposes that the heterotetramers behave like Chinese finger traps that form a hollow cylinder at their resting length and during their extension the pitch of the spectrin repeats increases while the cylinder's internal diameter decreases. This way the heterotetramers can remain linear and maintain their structural integrity. Moreover, αspectrin and ßspectrin heterotetramers are modular proteins including several so called spectrinrepeats (SR), which can unfold under tension [START_REF] Rief | The mechanical stability of immunoglobulin and fibronectin III domains in the muscle protein titin measured by atomic force microscopy[END_REF]. Interestingly, they both possess an unconventional spectrin repeat domain that includes an alternative Srchomology domain3 (SH3). Our work highlighted that this domain is a crucial element of the morphogenetic locking process we revealed. Based on our reciprocal yeast twohybrid screens, the SH3 domain is the predicted interaction site between PAK1 and SPC1. It is a part of an evolutionary conserved site, located between the B and C helices of the unusually large triple αhelical SR9 spectrin repeat.

Previous work performed by Gabriella Pàsti examined whether the SH3 or the SR9 could be critical for the interaction between SPC1 and PAK1. In addition, she wondered whether the SH3 domain was easily accessible to interact with PAK1, or whether it required SR9 to unfold under mechanical stress, as many spectrin repeats can do. To test these possibilities, she used spc1(ra409) transgenic animals expressing alternative SPC1::GFP constructs with either the SH3 domain alone or the SR9 domain alone. She found that the SPC1(∆SH3)::GFP transgene failed to rescue the elongation defects of spc1(ra409) mutants. When pak1 was knocked down in these transgenic spc 1(ra409) embryos, they retracted nearly to their initial length. By contrast, the SPC1(∆SR9)::GFP transgene, could rescue the elongation of spc1(ra409). When combined with pak1(RNAi), these embryos did not retract. Instead, they arrested at 2fold, resembling to spc1 single mutant animals.

These results could indicate that SPC1 might interact through its SH3 domain not only with PAK1, but possibly with other molecular players in a molecular locking mechanism that relies behind the retraction. Therefore, the SH3 domain of SPC1 possibly serves as an interaction site for SPC1 binding partners and it is crucial for αspectrin function, including the maintenance of the embryonic shape, when challenged by repeated mechanical stress. This idea is supported by numerous studies that already proved the importance of the SH3 domain in interacting with signaling proteins [START_REF] Bialkowska | 3 domain of spectrin participates in the activation of Rac in specialized calpaininduced integrin signaling complexes[END_REF][START_REF] Bournier | Spectrin interacts with EVL (Enabled/vasodilatorstimulated phosphoproteinlike protein), a protein involved in actin polymerization[END_REF]Machkina et al., 2014;[START_REF] Desrochers | Molecular basis of interactions between SH3 domaincontaining proteins and the proline rich region of the ubiquitin ligase Itch[END_REF]. Indeed, they participate in the regulation of important cellular pathways, such as cell proliferation, migration and cytoskeletal modifications. For example, Human proteome contains ∼300 different SH3 domains and many more SH3 ligand proteins, creating an enormous number of theoretically possible SH3 interactions. Therefore, knowing which of these interactions actually take place and are biologically meaningful would greatly increase our understanding about the signaling networks that regulate normal cellular behavior and become deregulated in many important diseases [START_REF] Kazlauskas | LargeScale Screening of Preferred Interactions of Human Src Homology3 (SH3) Domains Using Native Target Proteins as Affinity Ligands[END_REF]. Moreover, recognition of polyproline and a number of noncanonical sequences by SH3 domains has been extensively studied by crystallography, nuclear magnetic resonance, and other methods. Highaffinity peptides that bind SH3 domains are used in drug development as candidates for anticancer treatment [START_REF] Kurochkina | 3 domains: modules of proteinprotein interactions[END_REF].

To probe further this hypothesis and to assess the cortical tension experienced by the epidermis once muscles are active, we developed a FRET tension sensor inserted within SPC1. Based on the recent use of TSMod within the linker separating SR8 and SR9 of the neuronal C. elegans ß spectrin UNC70, which is neutral for function and provides a good tension sensor [START_REF] Krieg | Mechanical control of the sense of touch by βspectrin[END_REF], the TSMod have been inserted at the linker regions separating adjacent SRs. Four regions have been chosen, two before the SR9 and two after, plus one in C terminal as a negative control. More specifically, we chose the linkers located around the SR9 of SPC1 because some of our previous data showed that the SH3 domain of SPC1 is essential for elongation, but not the surrounding SR9. Furthermore, as SPC1 and PAK1 cooperate to maintain embryo shape during elongation, it raises the possibility that the SPC1 SH3 domain defines a mechanotransduction pathway. Therefore, we started to work with this SPC1 FRET strain. First, we obviously need to image it alone to verify that the sensor works. Then, it would be of interest to introduce it in different mutant backgrounds such as sma1 or vab10b, to see how the cortical tension is affected.

Additionally to our first yeast two hybrid screen showing that PAK1 interacts with the conserved SH3 embedded within the central SR domain of SPC1 (SR9), another one showed that FHOD1 interacts with that of the ßspectrin SMA1 embedded within its SR4. Furthermore, we found that epidermis expression of a truncated derivative of FHOD1 predicted to be constitutively active fully rescues the retraction phenotype observed in defective spc1 pak1 mutants, raising the possibility that FHOD1 is the terminal player in a mechanotransduction pathway induced by muscles to bring actin remodeling. Hence, we could test whether PAK1 phosphorylates FHOD1 to activate it, and/or if the protein becomes properly localized by SPC1 and PAK1, and whether it depends on the muscle input as we previously did for CeHDs remodeling (Zhang et al., 2011). SPC1 might also act redundantly with another component during this process, as spc1 single mutant embryos do not retract. Such possible partners could be for instance SMA1 or also VAB10, with which one of our Y2H screen also yielded as a result. We started to investigate both of these possibilities.

VI. Identification of other players that could also be involved

Finally, it is important to underline that there must be several aspects that avoided our attention. It is also possible that there exist other molecular elements of the ratchet mechanism.

Several lines of evidence indicate that the actin cytoskeleton is an important component of cell shape maintenance. For example, in erythrocytes the actinspectrinbased membrane skeleton is responsible for the shape maintenance of the red blood cells. Spectrins link short actin filaments in a polygonal network to the membrane [START_REF] Bennett | The spectrinactin junction of erythrocyte membrane skeletons[END_REF][START_REF] Pan | SuperResolution Microscopy Reveals the Native Ultrastructure of the Erythrocyte Cytoskeleton[END_REF]. Besides the attachment of the actin filaments, their stabilization is just as important. In this role adducin helps by capping the fast growing end of actin and helps its association with spectrins. Nonmuscle tropomyosin sets the length of the actin filaments within the meshwork and tropomodulin caps the slowgrowing actin end to optimize actin dissociation [START_REF] Bennett | Spectrin and ankyrinbased pathways: metazoan inventions for integrating cells into tissues[END_REF]. This actinspectrin membrane skeleton is crucially needed in erythrocytes to ensure their flexible mechanical support in the bloodstream.

Insufficient lateral association of the spectrinactin system, disruption of the tetramers or improper support of the membrane bilayer leads to diseases [START_REF] Zhang | Spectrin: structure, function and disease[END_REF][START_REF] Smith | Dysfunction in the βII spectrindependent cytoskeleton underlies human arrhythmia[END_REF].

In C. elegans, it has been shown that actin capping by tropomodulin, UNC94, is important in the epithelial and intestinal lumen morphogenesis. In epithelia, UNC94 is enriched within a HMP1 dependent junctional actin network at epidermal adherens junctions subject to stress during morphogenesis. Loss of UNC94 leads to discontinuity of this network, and hmp1; unc94 embryos present large junctional displacements. In vitro, UNC94 acts in combination with HMP1, leading to longer actin bundles than with HMP1 alone. It suggests that tropomodulin protect actin filaments recruited by αcatenin from minusend subunit loss, enabling them to withstand the stresses of morphogenesis [START_REF] Coxpaulson | Tropomodulin protects αcatenindependent junctionalactin networks under stress during epithelial morphogenesis[END_REF]. In the intestine, UNC94, localizes at the Factin rich terminal web at the intestinal apical membrane, along with nonmuscle NMY1. In the lack of UNC94 the Factin amount is reduced, and the intestinal lumen is flatter, but this phenotype can be rescued by increased actomyosin contractility. This work points out that actin capping coupled to actomyosin contractility at the level of the apical cytoskeleton can influence epithelial morphogenesis and lumen shape maintenance in the C. elegans intestine (CoxPaulson et al. 2014).

In our system, we showed that actin cables are important to stabilize cell shape changes but the mechanism of formation of actin cables during C. elegans embryonic elongation is still unknown.

We wanted to probe it further and examined the contribution of other predicted C. elegans actin binding proteins (formins, filamins, tropomodulin …) as described in the examples above. We used a candidategene approach screening for retraction phenotype and/or actin organization defects, in single pak1(), spc1() and fhod1() backgrounds. We tested thirtythree actinbinding candidates [START_REF] Nishikawa | Controlling contractile instabilities in the actomyosin cortex[END_REF]. Only seven gave phenotypes different from the wildtype (ANI1, CYK1, INFT1, FLN1, DGN1, TMY1 and UNC60), and only two (DGN1 and CYK1) showed high embryonic lethality (greater than 20%) in a pak1() and fhod1() backgrounds. They are promising considering their function. CYK1 is a formin essential for cytokinesis embryonic and cortical assembly of actin filaments independent of the Arp2/3 complex. DGN1 is involved in the dystroglycan complex located at the cell membrane, allowing interactions between cellular components like actin filaments and extracellular matrix via laminins. Further quantification of these potential interactions would be needed. However, this screen has not been performed following a robust protocol and would need to be repeated.

To conclude, my four years of PhD lead to the identification of several proteins involved in stabilizing cell shapes in a system submitted to repeated external mechanical stress. We propose that the progressive shortening of actin filaments under the control of these factors mediates a cellular viscoplastic process promoting axis elongation. We described this ratchet mechanism both at the cellular/molecular level and in term of physics.

CAPTIONS FOR MOVIES

Movie 1: Embryonic elongation and retraction profiles. Combined DIC timelapse movie. Image acquisition was every 5 minutes in wildtype, pak1(tm403), spc 1(RNAi), spc1(RNAi) pak1(tm403) embryos. Scale bar: 10 µm. Table 1: Primary enhancer RNAi screen in pak-1(-) background. RNAi screen was performed in the pak1(tm403) mutant along with a wild type control, testing a collection of 356 essential genes from the Ahringer RNAi library. The table recapitulates all the genes tested and the score of their interactions for the strongest. Yeast twohybrid screening performed by Hybrygenics Services (Paris, France) using the Nterminus of PAK1 up to the kinase domain as a bait (Primary Screen), or two different regions of the SPC1 protein spanning the SH3 domain (Secondary Screens). The table recapitulates the strongest interactions.

CAPTIONS FOR TABLES

Table 3: Secondary RNAi screen in spc-1(ra409) pak-1(tm403) mutants.

Additional RNAi screen in a spc1(ra409) pak1(tm403) mutant maintained by an exctrachromosomal spc 1(+)::GFP transgene of 13 actin related proteins from the Ahringer RNAi library that were recently reported to modulate actin remodeling in the early embryo (see text).

Table 4: Secondary enhancer RNAi screen in spc-1(ra409) mutants.

Additional RNAi screen in a spc1(ra409) mutant maintained by an exctrachromosomal spc1(+)::GFP transgene. Genes that gave the strongest defects in the initial RNAi screen (Supplementary Table 1) were tested again. C. elegans provides an anatomically simple and integrated model to study the cellular effect of mechanical forces; however, unlike other such models, morphogenesis in C. elegans is not dependent on pulsatile actomyosin flows 1-3,10,11 . Because the muscles are tightly mechanically coupled to the epidermis through epidermal hemidesmosomes 12 (Fig. 1a, Supplementary Information), their contractions also displace the epidermis. Indeed, the anterior-posterior displacement of circumferentially oriented epidermal actin filaments closely mirrors that of muscle nuclei (Fig. 1b). Notably, the muscles do not all contract simultaneously; when some areas of the epidermis were longitudinally compressed (red line in Fig. 1c), others were stretched (green line) before eventually relaxing. The relaxation that follows each muscle contraction raises the conundrum of how muscle activity can power embryonic elongation from 100 µm to 200 µm if cell elasticity brings cells back to their initial length during relaxation. A simple hypothesis would be that some mechanism stabilizes the transient cell shapes induced by muscle activity. For instance, during Drosophila gastrulation and germband extension, actomyosin pulsatile flows are thought to progressively modify junctions 3,13,14 . To uncover such a mechanism, we focused on the kinase PAK-1, which mediates mechanotransduction 7 and regulates myosin II 15,16 . We first performed a feeding RNA-mediated interference (RNAi) screen in a strong but viable pak-1 mutant, looking for enhanced embryonic lethality (Extended Data Fig. 1a). The gene spc-1which encodes α-spectrin-behaved as a strong genetic enhancer of pak-1, producing short hatchlings (approximately 58 µm long), significantly shorter than pak-1(tm403) (approximately 178 µm long) or spc-1(RNAi) (approximately 91 µm long) hatchlings (Extended Data Fig. 1b, Supplementary Table 1). Moreover, a yeast two-hybrid screen identified the central Src homology 3 domain (SH3) of SPC-1 as an interactor with the PAK-1 N terminus (Extended Data Fig. 1c, Supplementary Table 2). Thus, both screens indicate a functional interaction between SPC-1 and PAK-1 during axis elongation.

Next, differential interference contrast (DIC) video microscopy showed that spc-1(ra409) pak-1(tm403) and spc-1(RNAi) pak-1(tm403) embryos could reach about 65 µm at a slow rate, but then failed to maintain their shape and retracted back to about 50 µm (Figs 1d-h, Extended Data Fig. 1d-j, Supplementary Video 1). Two observations suggest that muscle activity accounts for this phenotype. First, spc-1 knockdown in git-1 or pix-1 mutants, which act upstream of pak-1 in mediating mechanotransduction 7 , also induced retraction (Extended Data Fig. 1d-j). Second, spc-1(RNAi) pak-1(tm403) embryos started to retract at the onset of muscle contractions in control embryos (Fig. 1d, Extended Data Fig. 1d). We abrogated muscle function in spc-1(ra409) pak-1(tm403) embryos by knocking down the kindlin homologue UNC-112 17 ; the spc-1(ra409) pak-1(tm403) embryos defective for unc-112 no longer retracted (Fig. 1d-n, Supplementary Video 2). Therefore, we conclude that the mechanical input provided by muscles to the epidermis induces the retraction phenotype observed in spc-1 pak-1 double mutants.

The simplest interpretation of this retraction phenotype is that a cellular structure that maintains embryo shape fails to emerge or collapses when muscles contract. Two arguments suggest that this structure corresponds to the bundles of 3-5 actin filaments present in the dorsoventral epidermis 18,19 . First, SPC-1 and its binding partner SMA-1 (β-spectrin) form an actin-binding heterotetramer, colocalizing with actin 20 and partially with PAK-1 in epidermal cells (Extended Data Fig. 2). Second, treating C. elegans embryos with the actin-depolymerizing drug cytochalasin D induces a retraction phenotype very similar to the one described above 19 . We therefore characterized actin filaments using super-resolution microscopy of a LifeAct::GFP probe 10 . Segmentation analysis of the resulting images in the dorsoventral epidermis (Fig. 2a,b) revealed more discontinuity in spc-1 pak-1 double-deficient embryos compared with control genotypes, particularly over the area in which muscles contract (putative hemidesmosomes) (Fig. 2c, Extended Data Fig. 3). Fourier transform analysis indicated that their degree of anisotropy relative to the circumferential axis was abnormal (Fig. 2d, Extended Data Fig. 3). Moreover, the signal intensity between adjacent actin bundles was less sharp in spc-1 pak-1 deficient embryos and they were more frequently bent (Fig. 2e-h), indicating that the bundles might have partially defasciculated. Of note, these phenotypes became apparent once muscles became active (Extended Data Fig. 3), which suggests that muscle contractions contribute to actin remodelling.

To further investigate this phenomenon, we examined actin filaments during muscle contraction. As wild-type embryos lengthen, their circumference decreases by roughly 20% owing to embryo-volume conservation (Extended Data Fig. 4); thus, the length of actin filaments in dorsoventral cells would be expected to decrease. Spinning-disc microscopy revealed that muscle contractions are strong enough to locally bend actin bundles with an angle greater than 54° (Fig. 3a-d, Extended Data Fig. 5a,b), which has previously been reported to induce severing of actin filaments in vitro 21 . Therefore, we reasoned that compromising severing genetically might partially rescue the retraction of defective spc-1 pak-1 embryos (Extended Data Fig. 5c,d). Among 13 genes tested (Supplementary Table 3), our screen identified homologues of 2 actin-severing proteins, gelsolin and villin (Fig. 3e). Mutations in villin and, to a lesser degree, gelsolin confirmed this partial rescue (Fig. 3e, Extended Data Fig. 5d-l). Together, these data suggest that muscle contractions induce actin-filament bending, and directly or indirectly stimulate the activity of severing proteins. We propose that this is uncontrolled in spc-1 pak-1 double mutants (Fig. 3f,g). This model predicts that preventing muscle activity should improve actin organization in spc-1 pak-1 mutants, and that viln-1; gsnl-1 double mutants should exhibit defective elongation. First, we found that actin filaments in spc-1 pak-1 mutants were probably stiffer when muscles were inactive, as lateral cells were wider (Extended Data Fig. 4c,d)although continuity defects remained (Extended Data Fig. 3b,c). Second, villin-gelsolin double-deficient embryos showed only minor elongation defects (Extended Data Fig. 5l), which suggests that additional parallel processes might contribute to actin remodelling.

To rationalize the role of muscles in remodelling, we described the C. elegans embryo as a Kelvin-Voigt material (a spring in parallel with a dashpot) submitted to forces acting in the epidermis and muscles (F epidermis and F muscles , respectively) (equations ( 1) and ( 2); see Supplementary Information for details).

η λ = --+ + l t k l F F d d ( ) (1)
epidermis muscles

α = F F (2) epidermis seam DV
Note that F epidermis is written as the product of an active force, F seam , which corresponds to the contractile force produced by myosin-2 in 5). Scale bar, 10 µm. e, Elongation profiles of spc-1(RNAi) (n = 8 embryos), spc-1(RNAi) pak-1(tm403) (n = 9 embryos), viln-1(ok2413); spc-1 (RNAi) pak-1(tm403) (n = 11 embryos) and gsnl-1(tm2370); spc-1(RNAi) pak-1(tm403) (n = 5 embryos). Pink box, period of muscle activity. Data are mean ± s.e.m. f, g, Cellular model of embryo elongation based on volume conservation in normal embryos, in which an increase in axial length implies a decrease in circumferential length. f, Proposed model. In control embryos, muscle contractions (red arrows) induce actin-filament bending and their severing, followed by SPC-1-PAK-1-dependent stabilization; whether spectrin is found along or between actin filaments is unknown. g, In spc-1 pak-1 deficient embryos, actin remodelling is uncontrolled.

Letter reSeArCH seam epidermal cells, and a passive component, α DV , which results from actin-bundle stiffness in dorsal and ventral epidermal cells 10 . F epidermis can extend embryo length only up to twofold, as muscle-defective mutants cannot elongate more than this (Extended Data Fig. 6a, a´). The force F muscles should not trigger any further extension, because it oscillates between a positive and a negative input (Fig. 1b,c, Extended Data Fig. 6b,b´).

Several studies have suggested that systems exposed to a mechanical stress can undergo a permanent rearrangement that can be described as a plastic deformation 22 or as a change in the spring resting length 23,24 . Accordingly, we imposed the condition that the spring resting length λ in equation ( 1) changes linearly with positive elongation rates (equation ( 3), Fig. 4a).

λ β α λ β λ =                > ≤ < -> t l t H l t l F k d d d d ( )Hill( ) if d d 0 0 1 (3) C DV
Conversely, in spc-1 pak-1 defective embryos, the continuing damage to actin filaments should reduce their stiffness (component α DV in equation ( 2)). We accounted for this by including a tearing factor γ in the equation for stiffness (equation ( 4), Fig. 4b).

α γ α = < > t l t l t d d d d if d d 0 and 0 ( 4
)
DV DV

Using equations ( 1) to ( 4), we could accurately predict both the elongation pattern of wild-type embryos and the retraction pattern of spc-1 pak-1 embryos (Fig. 4c, Extended Data Fig. 6d,e). Further, the model predicts that the plasticity factor of the spc-1 pak-1 embryos is zero (Supplementary information). We propose that SPC-1 and PAK-1 regulate a cellular process of mechanical plasticity. From a cellular perspective, we suggest that elasticity does not fully bring the embryo back to its initial shape on muscle relaxation, enabling progressive lengthening.

To further define the molecular basis of viscoplasticity, we searched for gene knockdowns that induced retraction of spc-1(ra409) embryos (Extended Data Fig. 7a, Supplementary Table 4). This screen identified the atypical formin FHOD-1 (Fig. 4d, Extended Data Fig. 7, Supplementary Video 3), which has been linked to actin dynamics in the epidermis 25 . We confirmed that fhod-1(tm2363) spc-1(RNAi) embryos also showed a penetrant retraction phenotype with damaged actin (Fig. 4d,Extended Data Figs. 3,[START_REF] Zhang | A tension-induced mechanotransduction pathway promotes epithelial morphogenesis[END_REF]. Of note, vertebrate FHOD1 promotes actin capping, bundling and nucleation 26 , raising the possibility that FHOD-1 activity stabilizes the actin cytoskeleton after actin severing (Fig. 3). Furthermore, the genetic interaction suggests that FHOD-1 acts with SPC-1 and PAK-1. To investigate this possibility, we tested whether FHOD-1 derivatives that lack the C-terminal diaphanous autoregulatory domain (DAD), predicted to release the autoinhibition characteristic of formins 27 , could rescue the retraction phenotype of spc-1 pak-1 deficient embryos. After epidermis-specific expression of a form that lacks the FH2 and DAD domains, transgenic spc-1(RNAi) pak-1(tm403) embryos reached 90 µm in length without retracting; this was longer than embryos that express the full-length protein. By contrast, longer FHOD-1 forms that include the FH2 domain rescued

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poorly or not at all (Fig. 4e), which suggests that the FH2 F-actin nucleation domain is dispensable for the rescue. Of note, a mammalian FHOD1 lacking the FH2 and DAD domains can still bundle actin 26 . Collectively, our data underline that FHOD-1 bundling activity is key, and that the retraction phenotype mainly results from a lack of FHOD-1 activation downstream of the muscle-induced mechanotransduction pathway. We conclude that actin-filament severing initiated by muscle contractions (Fig. 3) followed by FHOD-1-dependent bundling or capping (Fig. 4) represents a ratchet-like mechanism, providing a molecular basis for viscoplasticity. Several factors could contribute to alter PAK-1 and FHOD-1 activity. First, SPC-1 could help recruit these proteins, as FHOD-1-GFP and PAK-1-GFP formed small aggregates in SPC-1 defective embryos (Extended Data Fig. 8). Second, muscle contractions in spc-1(RNAi) pak-1(tm403) embryos were decreased in duration by almost half compared with pak-1(tm403) or wild-type control embryos (3 s against 5.7 s) (Extended Data Fig. 9, Supplementary Video 4). These shorter contractions may mean that there is insufficient time for FHOD-1 to stabilize actin filaments.

In sum, our results identify several proteins that are involved in stabilizing cell shapes in a system subjected to repeated external mechanical stress. We propose that the progressive shortening of actin filaments under the control of these factors mediates a cellular viscoplastic process that promotes axis elongation. A similar viscoplastic process might operate in vertebrate tissues comprising an epithelial layer surrounded by a contractile layer, such as the internal organs in humans. Notably, high FHOD1 expression correlates with poor prognosis of patients with breast cancer 28 . Such a process might therefore also influence the metastatic properties of tumour cells juxtaposed with contractile cells.

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Any methods, additional references, Nature Research reporting summaries, source data, extended data, supplementary information, acknowledgements, peer review information; details of author contributions and competing interests; and statements of data and code availability are available at https://doi.org/10.1038/ s41586-019-1509-4.

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Methods

No statistical methods were used to predetermine sample size. The experiments were not randomized. The investigators were not blinded to allocation during experiments and outcome assessment. Worm strains and conditions of maintenance. The list of strains used is presented in Supplementary Table 5. Worms were propagated on NGM agar plates as previously described 29 , maintained at a standard 20 °C. The gsnl-1(tm2730) and viln-1(2413) worms were outcrossed three times. Yeast two-hybrid screening. Yeast two-hybrid screening was performed by Hybrygenics Services. The bait component was the N-terminal 294 amino acids of PAK-1 (including the regulatory region of the protein) fused as a C-terminal fusion to LexA. The construct was used as a bait to screen at saturation a highly complex, random-primed C. elegans embryo cDNA library 30 . Screening involved a mating approach on a medium lacking Trp, Leu and His, supplemented with 0.5 mM 3-aminotriazole 31 . The strongest hits of the screen can be found in Supplementary Table 2. Reciprocal screens using the spectrin repeat no. 9 or the SH3 domains of SPC-1 as baits identified PAK-1 region 160-206, and no other meaningful prey in the context of the present study. RNAi screens. A RNAi screen was performed in the pak-1(tm403) mutant along with a wild-type control. A collection of 356 essential genes from the Ahringer RNAi library 32 -including adhesion proteins, signalling proteins, phosphatases, kinases, cytoskeleton-associated proteins and proteins important in epithelial morphogenesis-was assembled (Supplementary Table 1), based on a previous screen performed in the git-1(tm1962) background (C.G. and M.L., unpublished). The screen was performed in liquid culture on 96-well plates and RNAi knockdown was induced by feeding as previously described 33 . The primary screen was based on enhanced lethality and body morphology defects; the secondary screen focused on very short larvae and elongation defects. We took DIC images for body-length measurements and performed DIC time-lapse imaging for the strongest candidates. We performed two additional RNAi screens. First, we used a spc-1(ra409) pak-1(tm403) strain carrying an unstable extrachromosomal rescuing spc-1::gfp marker to look for potential suppressors of the retraction phenotype. We selected 13 actin-related proteins from the Ahringer RNAi library 32 that were recently reported to modulate actin remodelling in the early embryo 34 (Supplementary Table 3). RNAi was induced by RNAi feeding on L4 larvae maintained at 20 °C, and the progeny was analysed 20 h to 30 h after feeding; for early-acting essential genes (cyk-1, pfn-1, unc-60), worms were maintained at 15 °C, and the progeny was analysed 16 h to 20 h after feeding still inducing more than 14% early embryonic defects. Second, we likewise used a spc-1(ra409) mutant carrying an unstable extrachromosomal rescuing spc-1::gfp marker to look for potential enhancers of the spc-1(ra409) elongation defects. We selected for this enhancer screen genes that had given the strongest defects in the initial screen with 356 genes (Supplementary Table 4). In both cases, young L1 hatchlings were inspected for the presence or absence of a fluoresent spc-1::GFP signal and photographed using either a Leica DMI4000 (first screen) or Leica DM6000 (second screen) microscope. Length of the young larvae was measured using ImageJ software.

For specific genes (spc-1, pak-1, fhod-1 and unc-112), RNAi was induced by injection after preparing the double-stranded RNA (dsRNA) with the Ambion mMessage mMachine kit and purifying the dsRNA with the Qiagen RNeasy MinElute Cleanup kit 35 . The embryos were analysed from 24 h to 48 h after injection. In one case, experiments involving the strain spc-1(ra409) pak-1(tm403); mcEx1016[spc-1(+)::GFP; Pmyo-2::RFP] (shown in Extended Data Figs. 3,4), RNAi against unc-112 was induced by feeding because the strain barely survived the regular microinjection procedure. Fluorescent translational reporter constructs. A 12,633-bp genomic sequence including the spc-1 coding sequence and a 3-kb promoter was inserted in frame with the GFP coding sequence present in the pPD95.75 vector (Addgene). To create the Ppak-1::pak-1::mKate reporter construct, first an mKate-containing backbone was created by exchanging the GFP-coding sequence of the pML1572, Plin-26::vab-10(ABD)::GFP plasmid 15 . In a following cloning step, a 8,204-bp genomic sequence, including the pak-1 coding sequence and a 4.5-kb promoter were inserted in frame with the mKate coding sequence present in the vector.

To test whether SPC-1::GFP could rescue the function of SPC-1, we first crossed the different transgenic worms of a wild-type background with mnDp33; spc-1(ra409) worms (strain DM3409), and F1 transgenic males again with DM3409 to establish mnDp33; spc-1(ra409); Ex[spc-1::GFP. Rescuing transgenes were recognized because all viable progeny was GFP-positive and all (or most) non-viable progeny was GFP-negative, reflecting the loss of the mnDp33 balancer. To attempt mnDp33 segregation, we repeatedly transferred single GFP-positive mothers over four generations and examined their progeny, starting from at least two independent extrachromosomal arrays per construct. Thereby, we successfully obtained viable spc-1(ra409); Ex[Pspc-1::spc-1(+)::gfp worms, and then viable spc-1(ra409) pak-1(tm403); Ex[Pspc-1 1 ::spc-1(+)::gfp worms through crossing and meiotic recombination, which segregated very short retracted GFP-negative embryos. For the FHOD-1 constituvely active construct, a 8,283-bp genomic sequence of fhod-1 (gift from D. Pruyne 36 ) deleted for part of the FH2 domain and the DAD domain was inserted under the control of the epidermis-specific 432-bp dpy-7 promoter. Deletion of the DAD alone was obtained by inserting back the FH2 domain in the FH2/DAD deleted construct using Hifi DNA assembly cloning kit (New England Biolabs); the FH1/FH2 deleted construct was obtained by deleting the FH1 domain using the Q5 site directed mutagenesis kit protocol (New England Biolabs). All cloning steps relied on the use of the Phusion High-Fidelity DNA Polymerase reaction kit (Fisher Thermo Scientific); the constructs were subsequently verified by sequencing. The constructs were injected at 10 ng µl -1 plasmid construct, with 150 ng µl -1 pBSK + 5 ng µl -1 pCFJ90 (P myo-2 ::mcherry) as co-injection markers for the spc-1::gfp constructs, or 100 ng µl -1 pRF4 (rol) co-injection marker for pak-1::mKate. Fluorescence imaging. DIC images for time-lapse videos were obtained using a Leica DM6000 microscope with Leica LAS-AF software. Observations were done under a 40× oil immersion objective. Mothers were cut up to gain early-staged embryos, which were then transferred onto thin 5% soft agarose pads in a drop of M9. Z-stack image series with a 1.5-µm Z-step distance were taken in every 5 min during 6 to 10 h. ImageJ software was used to quantify the embryonic length from the end of ventral enclosure/onset of elongation, by taking a segmented line through the midline of the embryos from head to tail. To image the coupling between actin-bundle displacement in the epidermis and muscle contractions, we used a double reporter strain carrying the epidermal Pdpy-7::LifeAct::GFP and muscle Pmyo-3::his-24::mCherry transgenes (ML2113, Supplementary Table 5), and a spinning-disc DMI6000 Leica microscope equipped with an Andor software (experiments for Fig. 1). Series of five Z planes (1 epidermal + 4 muscle) were imaged continuously for 5 min, with 0.5-µm Z steps and no averaging. The time interval between two Z series was 360 ms. The measurement of actin displacement was done according to the same strategy, and was done using a CSUX1-A1 spinning disc mounted on a Zeiss Axio Observer Z1 inverted microscope with a Roper Evolve camera controlled by the Metamorph software, and a 100× oil immersion objective (experiments for Extended Data Fig. 9). A Z stack of 4 focal planes with 0.5-µm step size was acquired using a streaming acquisition mode. The time between two acquisitions was 0.41 s during 300 time frames. To synchronize embryos, mothers were put on an empty NGM agar plate to lay eggs for a short time window, and embryos were left to develop until the stage of interest. For the analysis of the contraction see 'Image analysis and quantification of actin filament contraction, continuity and orientation' . To analyse the in vivo co-localization between PAK-1::mKate, ABD::mcherry and SPC-1::GFP, we used the Zeiss-Roper spinning-disc microscope under a 100× oil immersion objective, keeping the laser intensity at a constant level throughout the experiments. Image processing and computing the co-localization coefficient was done using the Volocity software. TIRF-SIM. Embryos were mounted between 22-mm square cover glasses (thickness of 0.170 ± 05 µm, Carl Zeiss Microscopy) and 25 × 75-mm teflon-coated glass slides with three depression wells. Embryos were embedded in 2 µl water containing Polybeads acrylate microspheres of 15.4 ± 1.43-µm diameter (Polysciences). Wild-type embryos were at 1.8-to 2-fold stage; spc-1(RNAi) pak-1(tm403) embryos were aged between twofold and threefold equivalent for a control embryo. TIRF-SIM images 37,38 were acquired on a DeltaVision OMX SR imaging system from GE Healthcare Life Sciences equipped with a 60 × oil immersion objective from Olympus (PlanApo N 60× 1.42 NA). To minimize spherical aberrations, we used Cargille labs immersion oil with a n D at 25 °C (5893 Å) = 1.5140 ± 0.0002. Imaging was performed using the excitation at 488 nm with laser transmission ranging from 75 to 100% and integration time ranging from 2 to 3 ms. For each embryo, time series of 50 to 100 TIRF-SIM images of 256 × 256 pixels (pixel size of 80 nm) were acquired. Each TIRF-SIM image corresponds to a set of 9 images (3 phases at 3 angles) acquired withing 90.6 to 99.6 ms. Reconstruction of TIRF-SIM images (final pixel size after reconstruction is 40 nm) were performed with the softWoRx software (Applied Precision), which in turn enables a resolution enhancement by a factor of 2 that leads to a final lateral resolution in the order of 100 nm. Image analysis and quantification of actin-filament contraction, continuity and orientation. The analysis of mechanical displacement in the epidermis was performed on the videos of the dorsoventral actin layer by measuring the distance over time between two landmarks across the region of contraction. The landmarks were set manually on a frame showing relaxed tissue and tracked all over the contraction till the subsequent relaxed state. Landmarks tracking was performed using a statistical template matching approach 39 . The method was implemented as an ImageJ plugin (http://sites.imagej.net/Julienpontabry/), giving as output the landmarks locations, their distance across time and the kymographs. The curves show a pre-contraction state, a minimum (the maximal contraction point) and an ending part where the distance progressively increases again (Fig. 1b, bottom, Extended Data Fig. 9). After a smoothing and interpolation of the curves, the starting, ending and maximal contraction points were extracted by studying the time derivative of the distance and by setting a threshold on the distance itself.

Finally the contraction time was computed as the difference between the ending time and the initial time. The quantification of bending angles was done using a similar strategy; the angles were measured on single bundles at the frame of maximal deformation in a contraction cycle (Extended Data Fig. 5). The analysis of the curves and statistics were done using a MATLAB script. All images were analysed using the ImageJ (FIJI) software (NIH; http://rsb.info.nih.gov/ij/) and MATLAB R2015b (MathWorks). To study the features of actin pattern, we imaged embryos that were put to sleep by oxygen deprivation through a high concentration of bacteria with the Zeiss-Roper spinning-disc using a 100× oil immersion objective. For each experiments, a Z-stack of 16 focal planes with 0.2-µm step size was acquired. On the original maximum Z projection created by imageJ, a manual ROI was defined on the dorsoventral cells (Fig. 2, Extended Data Fig. 3), from which a high-pass filter in the Fourier space was applied to select only structures smaller than 10 pixels in diameter (Fig. 2, Extended Data Fig. 3). Continuity. The filtered ROIs were binarized by setting to one all the pixels with a value higher than zero, and setting to zero all the other pixels. The resulting structures were then fitted by ellipses from which the length of the major axis was extracted as a measure of the length of the actin filament. The longer actin filaments are those presenting a more-uniform fluorescence along their length (showing higher continuity). By contrast, short segments result from discontinuity in the fluorescence signal. To avoid noise, only segments longer than four pixels have been considered for the analysis. Anisotropy of the orientation. The same filtered ROI used for continuity measurements was used to measure the distribution of bundle orientation. Fast Fourier transform (FFT) of these ROIs was computed to work in the frequency domain and more-easily identify repetitive patterns. The resulting power spectrum of the ROIs was represented in polar coordinates to extract the distribution of angles of ROI pattern 40 . The method was implemented in an ImageJ plugin (http://sites. imagej.net/Julienpontabry/), giving as output the angular distribution. To compare the distributions coming from different images the distributions were normalized by their integral (Fig. 2, Extended Data Fig. 3). The more the pattern consists in structures oriented in a preferred direction (the more anisotropic), the highest is the peak of the distribution in that direction. In the case of an isotropic pattern, the angular distribution should show a flat behaviour. As an estimate of the pattern anisotropy, the prominence of the highest peak of the angular distribution was considered (Fig. 2, Extended Data Fig. 4). The analysis of the angular distributions and statistics was performed by a MATLAB script. All images were analysed using the ImageJ (FIJI) software and MATLAB R2015b (MathWorks).

Straightness. For each embryo, we selected an ROI containing the region above the muscles based on a contraction pattern. We selected ROIs containing about ten actin bundles, and we segmented manually seven of them for each ROI (the number of bundles that were on average well-resolved). For each bundle we computed the straightness as the ratio between the length of the segmented bundle and the distance between the initial and final points of the bundle. This quantity has an upper limit equal to one for perfectly straight lines. The manual segmentation and straightness calculation were performed with a custom MATLAB interface.

Bundle organization. For each embryo, we measured the relative contrast in the image between the regions occupied by actin filaments and those in between the filaments as a proxy for bundle composition and organization. The reasoning was that in the extreme case in which bundles separate to generate individual filaments, each filament is likely to have a lower intensity than a bundle made of several filaments, and the contrast between filaments and the intervening space would be less sharp. This should result in a lower variance or standard deviation of the image intensity compared to a wild-type bundle image. To do so we divided the standard deviation by the average intensity. Statistical analysis. For elongation curves, s.e.m. was measured. For L1 length measurement and rescue experiments we performed paired t-test using Prism v.5.00 (GraphPad) and Excel. For contraction time, actin continuity and orientation, we applied for all genotypes a paired t-test using MATLAB. Reporting Summary. Further information on research design is available in the Nature Research Reporting Summary linked to this article. tm403) embryos is that the circumferential dimension of the seam cells decreased much more than that of their dorsoventral cells, which most probably reflects the actin-filament integrity defects combined with a F seam force largely unchanged.

Extended Data

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Extended Data Fig. 5 | Bending and severing of actin bundles during muscle contractions. a, b, Kymographs of the regions boxed in yellow in Fig. 3a, b after spinning-disc time-lapse imaging of epidermal actin filaments (Pdpy-7::LifeAct::GFP reporter) in wild-type (a) and spc-1(RNAi) pak-1(tm403) (b) embryos at mid-elongation (twofold equivalent) stage. Scale bar, 5 µm. c, Principle of the RNAi screen performed to identify proteins mediating actin remodelling; the recipient strain carried a rescuing, but frequently lost, spc-1(+) transgene (green). d, Quantification of L1 hatchling length after downregulation or mutation of the indicated genes; the presence of the spc-1::gfp transgene is denoted +. Control worms fed on L4440 bacteria. e-k, Elongation curves (e) and DIC images showing the terminal phenotypes of pak-1(tm403) (f; n = 11 embryos), gsnl-1(tm2730); pak-1(tm403) (g; n = 9 embryos), viln-1(ok2413); pak-1(tm403) (h; n = 9 embryos), gsnl-1(tm2730); spc-1(RNAi) pak-1 (tm403) (i; n = 5 embryos), viln-1(ok2413); spc-1(RNAi) pak-1(tm403) (j; n = 11 embryos) and spc-1(RNAi) pak-1(tm403) (k; n = 9 embryos). Pink box in e, period of muscle activity. Data represent mean ± s.e.m. Scale bar, 25 µm. l, Quantification of the L1 hatchling body length of wild type (n = 65 hatchlings), gsnl-1(tm2730) (n = 52 hatchlings), viln-1 (ok2413) (n = 43 hatchlings), viln-1(ok2413); gsnl-1(tm2730) (n = 41 hatchlings), pak-1(tm403) (n = 47 hatchlings), gsnl-1(tm2730); pak-1 (tm403) (n = 51 hatchlings), viln-1(ok2413); pak-1(tm403) (n = 70 hatchlings), viln-1(ok2413); gsnl-1(tm2730); pak-1(RNAi) (n = 35), spc-1(RNAi) (n = 27 hatchlings) and viln-1(ok2413); gsnl-1(tm2730); spc-1(RNAi) (n = 41 hatchlings). Data represent mean ± s.d. Two side paired t-test. *P < 0.05; **P < 0.001; ***P < 0.0001; n.s, not significant.

Letter reSeArCH

Extended Data Fig. 6 | Time-dependent length of a Kelvin-Voigt model in different conditions. a, A generic Kelvin-Voigt system exposed to a constant force F epid , and its predicted elongation change for F seam = 0.85 and four different values of α DV based on the equation α = F F epid seam DV . b, A similar system exposed to two forces, F epid and an oscillating force F muscles , and predicted elongation change using F epid = 0.85 and F muscles with an amplitude equal to 1 and the behaviour depicted in the blue-boxed inset. For simplicity, we will refer to the amplitude of F muscles as F muscles . As the pulsatile force induces both compression and stretching (see Fig. 1c), its net input on elongation is transient and the system oscillates around the maximal value reached without F muscles . In all other panels (except in a), F muscles was set as a periodic function with positive and negative steps of duration 6 s modulated by a cosine function, alternating with periods of null value of duration 15 s (b, inset). c, A Kelvin-Voigt system with mechanical plasticity introduced according to equations ( 1), ( 4), ( 6) and [START_REF] Zhang | A tension-induced mechanotransduction pathway promotes epithelial morphogenesis[END_REF] in the Supplementary Information, and predicted elongation change using F epid = 0.85, F c = 0, F muscles = 3 and four distinct values of the plasticity factor β, or using F epid = 0.85, F c = 0, β = 0.10 and four distinct values of F muscles . d, A Kelvin-Voigt system in which the plasticity is defective (β = 0), and in which there is actin tearing according to equation [START_REF] Zhang | A tension-induced mechanotransduction pathway promotes epithelial morphogenesis[END_REF] in the Supplementary Information, inducing a progressive reduction of F epid , and predicted elongation change with an initial value of F epid = 0.85, the tearing factor γ = 0.15 and F muscles = 3; the inset outlined in blue shows the behaviour of α DV (t) over time. In a-d, the elastic constant of the spring is k = 1, the initial resting length has the value λ(t = 0) = 1, and the viscosity is η = 10. e, Result of the fit for the following genotypes: WT, unc-112(-) alone spc-1(-) alone, spc-1(-) pak-1(-) double, unc-112(-); spc-1(-) pak(-) according to equations ( 1), ( 4), ( 9) to [START_REF] Munro | Cortical lows powered by asymmetrical contraction transport PAR proteins to establish and maintain anterior-posterior polarity in the early C. elegans embryo[END_REF] in the Supplementary Information. The values of the parameters are specified in paragraphs 1.5 and 1.6 in the Supplementary Information. The shallow decrease in length for the curve of unc-112(-); spc-1(-) pak-1(-) after 150 min is due to a deformation of the embryos under the effect of unc-112 knockdown but not to retraction, which is why the fit has been evaluated on the first 150 min of the curve.

Statistical parameters

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Only common tests should be described solely by name; describe more complex techniques in the Methods section.

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State explicitly what error bars represent (e.g. SD, SE, CI) Our web collection on statistics for biologists may be useful.

Software and code

Policy information about availability of computer code Data collection DIC images for time-lapse videos were obtained using a Leica DM6000 microscope 360 with a Leica LAS-AF software and with an inverted DMI 4000 microscope (Leica) equipped with a Coolsnap fx (Photometrix) digital camera controlled by micromanager software. Fluorescent images were acquired with a spinning-disk DM 6000 Leica microscope equipped 371 with an Andor software, a CSUX1-A1 spinning-disk controlled by the Metamorph software and a DeltaVision OMX SR imaging system from GE Healthcare Life Sciences. Reconstruction of TIRF-SIM images were performed with the softWoRx software (Applied Precision, Inc).

Data analysis

All images were analysed using the 405 ImageJ (FiJi) software (NIH, Bethesda, Maryland, USA; http://rsb.info.nih.gov/ij/) and 406 MATLAB R2015b (The MathWorks Inc., Natick, MA).

For manuscripts utilizing custom algorithms or software that are central to the research but not yet described in published literature, software must be made available to editors/reviewers upon request. We strongly encourage code deposition in a community repository (e.g. GitHub). See the Nature Research guidelines for submitting code & software for further information.

SUPPLEMENTARY MATERIAL An actin-based viscoplastic lock ensures progressive body axis elongation

Alic ia Lardennois 1 *, Gabriella Pásti 2 *, Teresa Ferraro 1 , Flora Llense 1 , Pierre Mahou 3 , J ulien Pontabry 2,4 , David Rodriguez 2 , Samantha Kim 2 , Shoic hiro Ono 5 , Emmanuel Beaurepaire 3 , C hristelle Gally 2 , Mic hel Labouesse 1,2 # CONTENT 1-Supplementary Mec hanical Modeling 2-Supplementary Referenc es 1-Supplementary Mechanical Modeling 1.1 Background information. During its morphogenesis, the C . elegans embryo undergoes a proc ess of elongation whereby it bec omes four times as long as the eggshell long axis (50 µm). C ell proliferation and cell intercalation are absent, therefore the proc ess of axis elongation relies only on the ability of the embryo to extend in the anterior-posterior direc tion. The outer epithelium (epidermis) plays an essential role in this process.

C hanging the status of any physic al entity requires the involvement of a forc e (mec hanical or c hemical), and the C . elegans embryo is no exception to this rule of physics. During the first phase of elongation and until musc les bec ome ac tive, the mac hinery driving elongation involves an ac tive forc e in the lateral epidermis (also c alled seam cells), and a passive force exerted by the dorsal and ventral epidermal c ells (c alled DV c ells) adjac ent to the seam c ells (Fig. 1a). Seam c ells have a high c onc entration of non-muscle myosin II, whic h has a non-polarized distribution and does not display pulsatile flows 41,42 , as observed for instance during Drosophila germband elongation 43 . Nevertheless, the stress generated by the seam c ells is anisotropic and globally oriented along the DV axis (see c yan box in Fig. 1a) 42 . The stress anisotropy results mainly from the presenc e of circ umferential F-ac tin filament bundles in DV epidermal c ells, whic h c reate a global stiffness anisotropy (see yellow box in Fig. 1a). Elec tron microsc opy suggests that these bundles are made of three to five ac tin filaments 44,45 .

The DV epidermal c ells do not c ontribute to generate ac tive stress (Fig. 1a), as their myosin II is kept mostly silent through the ac tivity of the RhoGAP RG A-2 41,42,46 . The interplay between stress anisotropy in seam c ells, stiffness anisotropy from the DV epidermis, and hydrostatic pressure resulting from the reduc tion of embryo diameter, induces a forc e oriented along the AP direc tion that is sufficient to extend the embryo until it reac hes the 2-fold stage 42 . Note that here as well as in the main text we refer to eac h elongation phase based on the ratio between the ac tual embryo length and that of the eggshell long axis (50 µm), i.e. 1.7-fold or 2-fold means that the embryo has reac hed roughly 85 µm or 100 µm, respec tively. Importantly, in mutant embryos whic h extend slower, we refer to embryo stages based on the length that a wild-type embryo would reac h after the same time duration, with t0 corresponding to the beginning of elongation (see extension curves in Fig. 2d).

During embryogenesis, muscles organize and assemble in four rows loc ated under the epidermis (Fig. 1a). Muscles are attac hed to the extrac ellular matrix that separates them from the epidermis, and that in turn serves to anc hor the epidermis through hemidesmosome-like junc tions 41 . Muscle organization and maturation is a progressive proc ess, suc h that muscle ac tivity starts with small c ontrac tions at the 1.7-fold, whic h progressively bec ome more robust. The mec hanic al ac tivity of muscles c an be summarized as an alternation of c ontrac tions followed by relaxation. Sinc e muscles are tightly c onnec ted to the epidermis, their c ontrac tions loc ally and repeatedly induc e an anterior-posterior c ompression and extension of the epidermis, which c an be visualized through the displac ement of the ac tin c ables (Fig. 1b-c , Extended Data Fig. 7). The stress exerted by muscle contrac tions on the epidermis induces a mec hanotransduc tion pathway (2 nd yellow box in Fig. 1a), which is essential to promote hemidesmosome maturation and embryo elongation 47 . Of note, when embryos reac h the 3.5-fold stage, they start sec reting a c ollagenous cuticle ac ting as a rigid exoskeleton that limits further muscle-driven elongation.

1.2 Viscoplastic model. For simplicity, let us c all the net forc e in the AP direc tion produced by the epidermis the epidermal c ell force (Fepid). This forc e is not enough to explain the elongation up to the 4-fold stage, since genetic analysis has established that embryos with non-func tional muscles do not elongate beyond the 2-fold stage (Fig. 2b) 48 . Therefore, musc les provide a sec ond ac tive force driving elongation beyond the 2-fold stage, whic h we will call Fmuscles.

The C . elegans epidermis c an be modelled as a visc o-elastic body, more specifically as a Kelvin-Voigt system with a spring and dashpot in parallel, subject to two main ac tive forces: the epidermal force Fepid, whic h is a continous positive forc e, and the muscle force Fmuscles, whic h is a pulsatile force sinc e musc les alternatively c ontrac t and relax. The first force is present sinc e the beginning of elongation, whereas the sec ond forc e starts only after the 1.7-fold stage. The elastic reac tion of the epidermis to ac tive forc es c an be c aptured by Hooke's law; the damped nature of the reac tion can be expressed by a visc ous term. Overall the length of the embryo over time l(t) c an be c aptured by the equation:

= -( -) + + ( 1
)
where k is the body stiffness, λ is the worm resting length and η is the c oefficient of visc osity. Inertia has been neglec ted given the low Reynolds number of the system. Eq.

(1) c orresponds to the so-c alled Kelvin-Voigt visc oelastic model 49,50 that c aptures the behavior of visc oelastic solids under stress or deformation. For c onstant forc es, the solution of Eq. ( 1) is given by:

() = + ( 1
- - � ) + (2)
meaning that the length of the system relaxes to the plateau value + + in a relaxation time of = /.

Fepid c an promote elongation until the 2-fold stage (Extended Data Fig. 6a'). Beyond, the pulsatile forc e originating from muscles, Fmuscles, alternates periods of positive, negative or null c ontribution, so that its temporal average < > is null:

< > = 1 ∫ () 0 = 0, for = ( 3
)
where θ is the integration period, T is the period and n is a positive integer. As a c onsequenc e, on average, Fmuscles will not c ontribute to the steady state length ( ) of the embryo (see Extended Data Fig. 6a-a') that is set by = + .

A way to introduc e a positive c ontribution to embryo lengthening is to allow some plasticity, in the physical sense, or ability of the system to get reorganized. For example, let c onsider a stretc hing pulse due to muscle ac tivity during whic h the embryo inc reases its length l(t) with an inc rement dl, suc h that the embryo will be temporarily l(t)+dl long at the end of the pulse. During the subsequent relaxation phase, due to elastic ity in the system, the embryo should return to the initial length l(t) it had before muscles had loc ally extended it. However, if it undergoes a permanent plastic deformation, then the body will permanently keep a portion of the stretc hed length. This situation c orresponds to a permanent rearrangement, and it has been observed and modeled in biological systems undergoing stresses 51,52 . In biological terms we imagine the rearrangement proc ess as follows: during the c ompression phases, musc le c ontrac tions locally squeeze the embryo along the AP axis, whic h generates an inc reased circ umferential stress due to volume c onservation. In partic ular, c ircumferential ac tin cables bec ome bent, which c ertainly introduces a state of inc reased stress along their length. As argued in the main text, our new results (Figs 2 and3), together with published results on the effec t of ac tin filament bending 53 , suggest that the c ompression phases will induc e ac tin filament severing. Thus, muscle c ontrac tions c reate the c onditions for ac tin filament remodeling in the subsequent relaxation and stretc hing phases toward filament shortening, hence they c reate the c onditions for plasticity.

Similarly to 52 , a simple mathematical solution to introduc e plasticity c onsists in having an adjustable resting length λ. We impose that λ(t) evolves with the same law as the length l(t) ac c ording to:

= H( ) if > 0 and -> � ( 4
)
where 0≤β<1 is a proportionality fac tor called 'plasticity fac tor'; the c ase of β =0 c orresponds to an absence of plastic ity. The c ondition > 0 ensures that there is rearrangement only during the extension phases; the c ondition -> � means that the rearrangement takes place only if the applied force exc eeds a c ritic al forc e . The term H( ) is the Haeviside step func tion, which expresses that dorso-ventral rearrangement is possible only in presence of resistance. For the desc ription of the term, see next paragraph. Given the form of Eq. 4, the resting length will not increase indefinitely for an applied c onstant positive force sinc e it is proportional to the derivative of , whic h evolves as a spring. This equation also implies that the ability to remodel to an applied force is finite, whic h is the case for natural systems. Indeed Eq. ( 4) is equivalent to = (0) (1 -) + assuming that (0) is the length and the resting length at time 0 , = 0 and > 0. With these c hoic es and with a c onstant positive forc e F, Eq. ( 1) has the following solution:

() = 1 (1-) (1 - -(1-) � ) + (0) (5)
Henc e, the plasticity c ondition effec tively reduces the body stiffness to (1 -) enabling the system to reac h a longer final size c ompared to the one allowed by the Kelvin-Voigt system alone, and inc reasing the relaxation time. By introducing a plasticity fac tor like in Eq. ( 4), the body progressively gains length at eac h stretc hing phase . Indeed, the length () is an inc reasing func tion of the plastic ity fac tor (Extended Data Fig. 6c').

We are aware that the general form of Eq. 4 is one of some other possibilities to c apture the phenomenology of the proc ess. It potentially implies an important plasticity response for very fast-applied deformations and an almost elastic behavior for very slowly applied deformation. We did not explore a large range of deformation speeds in our system since it was in the ~1 μm/s range for all of the mutants we examined (Extended Figure 9). Thus deformation speed does not disc riminate any mutant.

There are other options to express the equation giving the deformation of a Kelvin-Voigt material under stress than our c hoic e for Eq. 4. Indeed, acc ording to the c lassical formulation of plasticity reported in our ref. 24 (Munoz and Albo, PRE 88, 012708)} , the resting length c ould evolve proportionally to the deformation acc ording to:

= ( -)H( ) if > 0 and -> � (4 bis) For Fc bigger than a limit value and for large values of Fmuscles, this equation acc ounts for elongation and positive dependenc y on Fmuscles; for example by posing Fc≥1 Fmuscles>10 with all parameters set to = 10, = 1, = 0.85, and (0) = (0) = 1. On the other hand, for smaller values of Fc and , elongation takes place also in absence of Fmuscles. whic h is c ontradic tory with the experimental data. Therefore, we decided to privilege the Eq. 4 for plasticity (see above), sinc e its qualitative behavior rec apitulates the experimental phenomenology in a parameter independent manner. We disc uss the linear version of Eq. 4bis in sec tion 1.8.

1.3

The consequences of actin stability defects. As reminded above, the intensity of Fepid relies on two c omponents: the c onstant c ontrac tility of the seam cell ac tomyosin network, and the stiffness of the ac tin c ables in DV c ells. We c an then represent it like:

= (6)
where the forc e represents the ac tive force generated by myosin II in the lateral c ells and is the passive c omponent given by the presenc e of ac tin filament bundles in the DV c ells. The biomec hanic al significanc e of equation ( 6) is that both and positively c ontribute to Fepid , and that if one is absent Fepid=0. This c aptures the fac t that in the absence of myosin II there will be no pulling forc e because the ac tive c omponent is absent, and that if actin c ables are lost myosin II is missing the resistanc e struc ture onto whic h it c an pull, resulting in a null epidermis AP forc e. From Eq. 2 the size of sets the maximal elongation that the embryo c an ac hieve in the absenc e of muscle ac tivity (Extended Data Fig. 6a-a').

As shown in the main text (Fig. 3), the absenc e of SPC -1 and PAK-1, c ombined with the mec hanic al input from muscles, induces ac tin integrity defec ts in DV c ells. To translate this situation in mathematic al terms, we c hose to write the passive c omponent as follows:

= < 0 and ≥ 0 [START_REF] Zhang | A tension-induced mechanotransduction pathway promotes epithelial morphogenesis[END_REF] where γ≥0 is a proportionality fac tor defined as a 'tearing fac tor'. The c ondition () < 0

implies that decreases at eac h c yc le of muscle ac tivity (a c yc le is a sequence of positive and negative net forc e). In addition, we are imposing that γ=0 c orresponds to an absence of tearing, as in wild-type embryos. The biologic al significance of this c hoice is the following (see sec tion 1.2 for further details). When musc les c ontrac t and loc ally squeeze the embryo along the A/P axis (Extended Data Fig. 4, Video 1), they bend ac tin filaments (Fig. 3) and produc e an inc reased c ircumferential stress. As a c onsequenc e, their integrity in response to the stress originating from muscle ac tivity is not maintained in spc -1 pak-1 double mutants (see Fig. 3). For this reason, should progressively dec rease at eac h c yc le. The condition ≥ 0 prevents from assuming negative values. Thus with decreasing, Fepid will progressively decrease, and as c onsequence the system length will shorten (see Extended Data Fig. 5e and Fig. 4e).

Equations summary.

In summary, we describe the embryo body as a plastic Kelvin-Voigt solid ac c ording to the following system of equations:

-Kelvin-Voigt with adjusting resting length subjec t to Fepid+Fmuscles = as desc ribed in Eq. ( 6).

We assume that γ=0 for wild-type, meaning that the resistance of dorso-ventral ac tin filament bundles remains unaffec ted by the body length c hanges c aused by muscle ac tivity, and that γ=0 for unc-112 defec tive embryos, whic h are musc le-defec tive.

The equations ( 1), ( 4), ( 5), ( 6) and ( 7) have seven parameters: η, k, Fseam, (0), Fmuscles, β and γ. In order to reduc e the parameter spac e we fixed some of them:

-for simplic ity we set k=1; -from the laser ablation experiments performed in reference 42 , the relaxation time of epidermal ac tin filaments following the laser c ut is in the order of a few sec onds.

Being the relaxation time in a Kelvin-Voigt system given by = /, we set η=3 so that the relaxation time is 3 sec onds. -Fepid is the multiplic ation of two parameters, and thus from the parameter point of view can be c onsidered as a single parameter that we formally set to Fseam=1 letting (0) as a free parameter. -The size of the c ritical force has been c hosen to be half Fseam ( = . ). Thereby, we c onsider that low intensity forces cannot trigger a plastic response. -Regarding Fmuscles, we spec ified its details on the basis of the measured c ontrac tion durations for embryos between 1.7 and 2-fold stages (Extended Data Fig. 7). For wild-type embryos, the duration of positive and negative periods has been set to 6 sec onds and the period of null c ontribution has been set to 15 sec onds, whereas for spc-1 mutants and spc -1 pak-1 double mutants the duration of non-null ac tivity has been set to 3 sec onds and the duration of null c ontribution is set to 15 sec onds.

In wild-type embryos, the intensity of Fmuscles has been left as a fit parameter together with , β and γ in order to be determined by c omparing with the data. The musc le force amplitude for spc -1 and spc -1 pak-1 mutants has been set to 50% of the wt intensity ac c ording to our experimental observations. In our model, the length of the embryo is an increasing func tion of the intensity of the muscle force Fmuscles, (Extended Data Fig. 6c '').

To better adapt to the experimental observations, both Fseam and Fmuscles have been modified by introducing an initial transient that sets their behavior from zero to the regime of maximal intensity; the detailed form of these transients are reported in the paragraph 'Refining model details'.

1.5 Fitting procedure. In order to determine the remaining four free parameters: intensity of Fmuscles, (0) (the initial value of ac tin strength), β (the plasticity factor) and γ (the tearing fac tor) we fitted different genotypes. We started with musc le-defec tive unc-112 and wild-type embryos. As shown in Figs. 2 andS3, their elongation rate is quite similar until the 2-fold stage, at which point unc-112 embryos have no muscle forc e (Fmuscles=0), and they both have an identic al ac tin pattern (γ=0). Therefore, we fitted together the two elongation c urves to find the values of the three parameters (0), β and Fmuscles that c apture the main features of the two genotypes; we then refined the minor differences by allowing a 20% toleranc e with respec t to the parameters values determined through the c ommon fit. To estimate the value of Fmuscles intensity in spc-1 and spc -1 pak-1 embryos, we c onsidered that it was half the wild-type value, based on the observation that the muscle c ontrac tion/relaxation c yc les were roughly twice shorter in these embryos (Extended Data Fig. 7). The notion that Fmuscles is lower in spc-1 mutant embryos is c onsistent with the observation that musc les make an angle of 20° with the anteriorposterior axis, instead of 6° in wild-type embryos, predic ting that their input should be reduc ed 54 . The wild-type value of the plasticity fac tor was used as the upper limit for the variability range of β for spc-1 and spc -1 pak-1 embryos. We then proc eeded by fitting the spc -1 and spc-1 pak-1 elongation c urves to determine the values of (0), β and the tearing fac tor γ (see below for the method).

The best fit parameters were determined by minimalizing the following c ost func tion: In the Supplementary Table 7, we report the values of the fitted parameters for the different genotypes presented in the Fig. 1d and Extended Data Fig. 6e. Errors have been obtained by fitting the mean c urves plus and minus their standard errors respec tively and by taking the maximal deviation from the parameters obtained from the mean.

= ∑ ∑ [( () -()) 2 ] (8
1.6 Refining model details. Ablation experiments in seam cells 42 have shown that the c ircumferential stress is not c onstant during development but inc reases from the 1.3-fold to 1.7-fold stages. To better adapt our model to this observation, we introduc ed a time dependent func tion for Fepid that saturates to a plateau value within a time τs :

() = (1 -exp �- �) ℎ (9)
where hs is an exponent that sets the steepness of the func tion in reaching the plateau and is the plateau value. We set τs=50 min and hs=4, since this c hoic e produc es slow elongation for the first 50 minutes, as was observed for all the genotypes (see Fig. 2). Muc h like the epidermis force, the muscle force Fmuscles also starts at a small amplitude, then progressively evolves with a behavior similar to equation ( 8):

() = � () �1 -exp �- (-) �� ℎ > 0 0 ℎ ( 10
)
where A is the maximum amplitude, Θ(t) is the periodic func tion made of a c omposition of c osines desc ribed in Extended Data Fig. 5c ; hm sets the steepness of the func tion to reac h the plateau; t0 is the time at whic h muscles get ac tive and τm is the time nec essary for the func tion to reac h its plateau.

We started to measure the elongation c urves immediately before the c omma stage, whic h represents our initial time. We set tinit=90 min, sinc e around this point of elongation wild type embryos are 1.7-fold long and they start to c ontrac t muscles; we also assume that after the 2-fold stage the musc le force has reac hed its maximum amplitude, whic h is why we fixed τm=15 min (the time nec essary for a wild type embryo to go from 1.7 to 2 fold; hm has been arbitrarely set to 1).

The model summarized in Eqs. ( 5) and ( 9) has no plateau; however C . elegans embryos extend up to 4-fold whithin ≤150 minutes, then stay at this length for ~100 additional minutes before hatc hing. We do not know why the body length stops at 4-fold and this issue is not the foc us of this work. We c an spec ulate that the ability of the body to remodel is not illimited and may also be restric ted by c uticle sec retion. In this framework, we c an modify Eq.( 5) by introducing a multiplicative term under the form of a Hill func tion to ac c ount for the saturation of the elongation: [START_REF] Munro | Cortical lows powered by asymmetrical contraction transport PAR proteins to establish and maintain anterior-posterior polarity in the early C. elegans embryo[END_REF] where () = + , with L upper threshold for the resting length and d an exponent 56 . We set L=3.2 and d=15 to acc ount for a rapid saturation of elongation after the 3.2-fold stage, since the wild type embryos show, after this length, a rapid reduc tion of the elongation rate. By introduc ing these aditional func tions, we can improve the agrement between the data and the model results (Fig. 4j). The Equations presented above have been solved numerically by the Euler method implemented in a MATLAB sc ript, with the c hoice of intitial length (0) = (0) = 1.

= H( )() if > 0 , 0 ≤ β < 1 and -> � (
The Supplementary Table 8 is a summary of the parameter values that we fixed on the basis of experimental observations and therefore were not used as free parameters.

1.7 Predictive value of the model. The aim of the model is to give a mesosc opic physical desc ription and interpretation of embryo elongation, rather than a detailed mec hanistic formulation. Nevertheless its predic tions are strongly c onnec ted with some experimental findings.

Fitting the parameters as desc ribed in sec tion 1.5 predic ts a value c lose to zero for the plasticity fac tor of spc -1 pak-1 mutants assoc iated with a tearing fac tor different from zero (see Table 1). It means that spc-1 pak-1 mutants are unable to remodel their c ytoskeleton to reduce the c irc umferential size of the ac tin filaments in the dorso-ventral epidermal cells. C onsistent with this view, Extended Data Fig. 4 shows that the c ircumferential size of spc-1 pak-1 defec tive embryos ac tually inc reases onc e muscles bec ome ac tive, showing that the ac tin filaments did not shorten. The model also predic ts a very small plasticity fac tor but with a low tearing fac tor for single spc -1 mutants. These mutants can slightly decrease their c irc umferenc e (Extended Data Fig. 4), meaning that their ac tin filaments have a small ability to remodel. Finally, we note that equations ( 1) and ( 7) predic t that there should be no retrac tion if Fmuscles equals zero, whic h is what we observed for spc-1 pak-1 embryos in which muscle ac tivity is c ompromised by knoc king-down unc-112 (Fig. 1). In those embryos, fitting the unc -112; spc-1 pak-1 elongation curve gives a value of = 0.66 ± 0.01, whic h is very similar to that predic ted for spc-1 pak-1 double mutants.

1.8 Kelvin-Voigt-type model versus other models. In the present work we decided to model the C . elegans embryo as a visc oelastic solid with the ability to rearrange its resting length during elongation, and using this model we show that c hanging the behavior of the epidermal forc e c an acc ount both for elongation and retrac tion. The Maxwell model 50 , as a dashpot and a spring in series, would also acc ount for elongation when the system is under a positive force. The solution for the length () would be of the form 52 : () = 0 (1 + �1 + �), with 0 initial length, F a c onstant force, the elastic c onstant of the spring and the visc osity of the dashpot. A Maxwell-type material would keep extending over time as soon as a positive force ac ts on it; suc h a behavior would not ac c ount for the elongation arrest of muscle-defec tive embryos. We have also c onsidered an alternative model suggested in refs 51,52 , in whic h the rate of c hange of resting length is proportional to the difference between the length and the resting length. The dynamic system would obey the following equations:

= -( -) + (12)
(same type as our Eq. 1)

= ( -) (13) (instead of our Eq. 4)

where is a positive constant and (0) = (0) = 0 . The solution of this system has the following form:

() = 0 + (( (
When time tends to ∞, the forms of equations ( 14) and ( 15) imply a linear inc rease for both ()and (). Again, this behavior c annot account for the musc le-defec tive arrest of elongation, unless = 0. Supplementary Table 1 | Enhancer RNAi screen in a pak-1(-) mutant RNAi screen was performed in the pak-1(tm403) mutant along with a wild type control, testing a collection of 356 essential genes from the Ahringer RNAi library. The table recapitulates all the genes tested and the score of their interactions for the strongest.

2-Supplementary references

* Defect refers to lethality and body morphology defects

Supplementary

  forces intrinsèques et extrinsèques aux cellules. Comprendre comment les forces mécaniques influencent la morphogenèse au niveau cellulaire et moléculaire reste un défi majeur. Pour étudier la mécanotransduction et son importance dans la morphogenèse à l'échelle d'un organisme, nous travaillons avec un modèle simple, le nématode C. elegans. Depuis son introduction, par Sydney Brenner, dans les laboratoires à la fin des années 1960, C. elegans est utilisé comme organisme modèle en biologie du développement, génétique et biologie moléculaire grâce à sa progéniture abondante, son développement rapide, son corps transparent et son génome complètement séquencé. Son épiderme est un épithélium à monocouche séparé des muscles par une mince membrane au niveau basal. Les muscles sont disposés en quatre rangées, deux attachées à l'épiderme dorsal et deux à l'épiderme ventral via les hémidesmosomes, rendant l'épiderme sensible au stress mécanique résultant de leurs cycles de contraction. Au cours de son élongation embryonnaire, le nématode C. elegans voit sa longueur multipliée par un facteur 4 et sa circonférence réduite par un facteur 2,5. Il s'agit d'un processus rapide (trois heures environ) qui a lieu sans réarrangement ni division cellulaire, seulement permis par la déformation des cellules latérales et dorsoventrales de son épiderme. Cette élongation est initialement activée par la contractilité de l'actomyosine dans les cellules latérales, via la régulation de la Rho kinase. A partir du stade « 2fold », la tension fournie par les contractions musculaires permet le recrutement de la protéine adaptatrice GIT1 aux hémidesmosomes, permettant la seconde phase de l'élongation notamment via activation de la kinase PAK1. Lorsque l'activité musculaire est inhibée, les embryons sont paralysés à un stade « 2fold » et GIT1 n'est plus recrutée. Pourtant les mutants git1 et pak1 sont viables, suggérant qu'une autre voie agit en parallèle. Par ailleurs, chez C. elegans, la contribution du cytosquelette d'actine à la morphogenèse embryonnaire a été rapportée depuis la fin de la gastrulation. Au début, l'actine forme un maillage près du cortex épidermique, et au fur et à mesure elle se réorganise pour former des faisceaux circonférentiels et parallèles d'abord dans les cellules dorsoventrales, puis dans les cellules latérales. Une fois l'élongation embryonnaire terminée, les faisceaux se désassemblent. Dans ce contexte, l'objectif de mon projet de thèse a été de caractériser de manière plus détaillée l'apport du cytosquelette d'actine pendant l'élongation embryonnaire de C. elegans et la façon dont les câbles d'actine sont remodelés au cours de ce processus. De précédents travaux de l'équipe ont montré que PAK1 fait partie d'une voie de mécanotransduction induisant le remodelage des hémidesmosomes, structures de couplage entre les muscles et l'épiderme susjacent. Deux cribles ont alors été réalisés en fond sensible pak1() pour rechercher de potentiels partenaires de PAK1 et l'αspectrine SPC1 s'est révélée être un fort candidat. Les spectrines ont été décrites pour la première fois dans les érythrocytes en 1968 par Marchesi et Steers. Elles sont un des composants majeurs du cytosquelette de la membrane cellulaire et sont responsables des propriétés mécaniques (stabilité, plasticité et déformabilité) de celleci.

  En plus de contracter plus rapidement, les embryons spc1() pak1() présentent également des défauts d'organisation de l'actine : les câbles d'actine ne sont plus complètement parallèles, ils se regroupent et semblent parfois discontinus. Pour mieux caractériser ces défauts observés avec un microscope « spinningdisk », j'ai effectué une analyse de texture développée dans l'équipe avec l'aide de notre ingénieure, Teresa Ferraro. Nous avons analysé des images d'embryons anesthésiés à différents stades («1,7fold», «2fold» et «3fold») pour obtenir une résolution plus élevée de l'actine. L'analyse du signal de fluorescence associé aux filaments d'actine dans l'épiderme dorso ventral a révélé davantage de discontinuité dans les embryons spc1() pak1() par rapport aux témoins ; de plus, leur degré d'anisotropie par rapport à l'axe circonférentiel était anormal. Avant que les muscles commencent à se contracter, aucune différence significative n'est visible. Dès que l'activité musculaire est établie, l'organisation de l'actine devient significativement différente entre les contrôles et les spc1() pak1() mais également entre spc1(ARNi) et spc1() pak1(). Dans un second temps, j'ai utilisé la microscopie à super résolution pour affiner ces observations et éventuellement accéder à des évènements de remodelage en temps réel. L'analyse de segmentation du signal de fluorescence associé aux filaments d'actine a été confirmée et même améliorée puisque nous avons pu faire une différence entre la zone de l'épiderme située juste audessus des muscles et celle située à côté : les défauts d'organisation sont plus prononcés au niveau des muscles, là où la tension est plus forte. Par ailleurs, l'intensité du signal entre les faisceaux d'actine adjacents était également moins nette chez les embryons spc1() pak1() et ils étaient plus souvent courbés, indiquant que les faisceaux pourraient s'être partiellement défasciculés. Ces phénotypes apparaissent une fois que les muscles entament leur activité suggérant que les contractions musculaires contribuent au remodelage de l'actine. Pour étudier plus en détail leur rôle dans ce processus, nous avons examiné les filaments d'actine spécifiquement lors de la contraction des muscles. De manière frappante, la microscopie « spinningdisk » a révélé que les contractions musculaires sont suffisamment fortes pour courber localement des faisceaux d'actine avec un angle moyen de 57 °, ce qui induirait une cassure du filament d'actine d'après des analyses réalisées in vitro. Les cycles répétés d'activité musculaire pourraient avoir pour effet d'induire localement la rupture du filament d'actine épidermique, suivie de leur stabilisation. Dans les doubles mutants spc 1() pak1(), des contractions musculaires plus courtes pourraient faire pencher la balance entre rupture et stabilisation conduisant ainsi à leur désorganisation.

  induisent une possible rupture du filament d'actine et donc une stimulation directe ou indirecte de l'activité des protéines. Pour aller plus loin dans cette caractérisation moléculaire, Gabriella a effectué un dernier crible ARNi en fond sensible spc1() pour trouver d'autres partenaires potentiels permettant de reproduire le phénotype de rétraction. Nous avons identifié une protéine de « câblage », la formine atypique FHOD1. Pour évaluer le lien entre PAK1, SPC1 et FHOD1 dans le phénotype de rétraction, Flora a cloné plusieurs constructions de FHOD1 basées sur la littérature existante. Il a en effet été démontré que FHOD1 est initialement inactive en raison d'une interaction autoinhibitrice entre son domaine autorégulateur en Cterminal et son domaine inhibiteur en Nterminal (DID). Des expériences in vitro ont montré qu'en supprimant le domaine DAD, l'autoinhibition est levée et conduit à une forme constitutivement active de la protéine. L'objectif était de savoir si je pouvais sauver le phénotype de rétraction d'embryons spc1() pak1() en surexprimant FHOD1.

  modèle physique prédictif. Changer le statut d'une entité physique nécessite l'intervention d'une force (mécanique ou chimique) et l'embryon de C. elegans n'échappe pas à cette règle de la physique. Pendant la première phase d'élongation et jusqu'à ce que les muscles deviennent actifs, l'élongation est permise par une force active dans l'épiderme latéral et par une force passive exercée par les cellules épidermiques dorsales et ventrales suffisante pour allonger l'embryon jusqu'au stade « 2fold ». Cependant, cette force n'est pas suffisante pour expliquer l'allongement jusqu'au stade « 4fold », puisque les embryons avec des muscles non fonctionnels ne s'allongent pas audelà du stade « 2fold ». Par conséquent, les muscles fournissent une deuxième force motrice d'allongement.

Figure 1 :

 1 Figure 1: Morphological and functional diversity of epithelia. Epithelial cells can form tissues of very different shapes and functions within the same organism. Nevertheless, their apicobasal polarization is required for morphogenesis to take place. Adapted from Kévin Sollier's thesis.

Figure 2 :

 2 Figure 2: Features of the polarized epithelial phenotype.A typical vertebrate epithelial cell is shown with components of the polarized vesicle sorting machinery and the apical junctional complex depicted. Note that invertebrate (for example in Drosophila) epithelial cells lack primary cilia and the junctional complex is organized differently with adherens junctions (AJs) located more apically than the sealing junction (named septate junction instead of tight junction). In C. elegans, AJs and sealing junctions are combined into a single structure. Adapted from RodriguezBoulan and Macara, 2014.

Figure 4 :

 4 Figure 4: The dynamic steady state of actin. The minimal steps needed to reach a dynamic steady state of different actin architectures are illustrated. Sequestered and polymerizable actin represent the pool of actin monomers. Nucleation is the formation of actin dimers or trimers. Elongation and capping modulate controlled growth of the different forms of actin organization (branched networks that are generated by the Arp2/3 complex or bundles generated by formins). Disassembly and depolymerization results in the breakdown of actin structures to monomer subunits. Recycling renews the pool of actin monomers that are charged with ATP. The different nucleotide states of actin barbed and pointed ends and different proteins, or complexes are represented by the indicated symbols. The arrows at barbed (B) and pointed (P) ends indicate depolymerization, with larger arrows representing faster dissociation. Adapted from Plastino and Blanchoin, 2018.

Figure 5 :

 5 Figure 5: Domain structure of NM II.(a) The subunit and domain structure of NM II forms a dimer through interactions between the αhelical coiled coil rod domains. The globular head domain contains the actinbinding regions and the enzymatic Mg 2+ ATPase motor domains. The ELCs and the RLCs bind to the heavy chains at the lever arms that link the head and rod domains. In the absence of RLC phosphorylation, NM II forms a compact molecule through a head to tail interaction. This results in an assembly in competent form (10S; left) that is unable to associate with other NM II dimers. On RLC phosphorylation, the 10S structure unfolds and becomes an assemblycompetent form (6S). S1 is a fragment of NM II that contains the motor domain and neck but lacks the rod domain and is unable to dimerize. Heavy meromyosin (HMM) is a fragment that contains the motor domain, neck and enough of the rod to effect dimerization. (b) NM II molecules assemble into bipolar filaments through interactions between their rod domains. These filaments bind to actin through their head domains and the ATPase activity of the head enables a conformational change that moves actin filaments in an antiparallel manner. Bipolar myosin filaments link actin filaments together in thick bundles that form cellular structures such as stress fibers. Adapted from[START_REF] Vicentemanzanares | Nonmuscle myosin II takes centre stage in cell adhesion and migration[END_REF]

Figure 6 :

 6 Figure 6: Regulation of cell shape. (a) Cell shape is the result of the mechanical forces exerted on the cell surface. These forces can also be described by a set of interrelated physical properties, which include cellular adhesion, cortical tension and the cell's rheological properties. Physical properties are regulated at the protein level and are likely to feedback on protein activity and/or gene expression. (b) Example of the interaction between cortical tension and cellular adhesion during the formation of cell-cell contacts. Red lines, cortical cytoskeleton; black lines, plasma membrane; purple rods, adhesion sites; arrows, direction of forces. Adapted from Paluch and Heisenberg, 2009.

Figure 7 :

 7 Figure 7: Steady state control of contractility during Drosophila epithelial morphogenesis. Schematic of Drosophila mesoderm cells undergoing apical constriction and the pathway regulating RhoGEF2 delivery at the medial apical site of the cell. Adapted from Levayer and Lecuit, 2012.

Figure 8 :

 8 Figure 8: Ratchet mechanism and MyoII pulses during apical constriction of epithelial cells.Top view of an epithelial cell undergoing apical constriction. The accumulation of MyoII pulls on actin filaments (centripetal red arrow) and constricts the cell apical surface (black arrows). Contraction is either stabilized (further MyoII pulses lead to an incremental decrease of cell surface) or unstabilized (the cell returns to its initial conformation). Adapted from[START_REF] Levayer | Biomechanical regulation of contractility: spatial control and dynamics[END_REF]

Figure 9 :

 9 Figure 9: Schematic representation of mechanical elements driving cell shape changes.Overlay of the actin architecture and its mechanical profile. The red rectangles are the shock absorbers (dashpots) that represent the actin network, while the green circles are active springs due to myosin motor activity. Adapted from[START_REF] Blanchoin | Actin dynamics, architecture, and mechanics in cell motility[END_REF]

Figure 10 :

 10 Figure 10: Oscillatory behavior of the cell leading edge and ratchetlike movement.The leading edge alternates between phases of protrusion(3-4-1) and retraction[START_REF] Martin | Pulsed contractions of an actin-myosin network drive apical constriction[END_REF][START_REF] Rauzi | Planar polarized actomyosin contractile lows control epithelial junction remodelling[END_REF]. Phase 1: polymerization of actin generates the pushing force (red arrow) that drives leadingedge progression (grey arrow). At the same time, MyoII is progressively recruited in the mesh concomitantly with new focal adhesion point creation. Phase 2: backwardpulling forces, generated by MyoII and its anchorage to distal focal adhesions, progressively increase (green spring) while the actin polymerization rate decreases. Once the backwardpulling force overtakes the polymerization pushing force, the cell edge starts to retract (grey arrow). Phase 3: retraction is limited by focal adhesions (ratchetlike mechanism). Concomitantly, the high pullingforce breaks the actin mesh-cellfront connection. This could be reinforced by MyoIIinduced actin depolymerization. Phase 4: actin mesh-cellfront detachment leaves space for a new wave of actin polymerization. The backwardpulling force is close to zero. (Bottom graph) Progression of the leading edge over time. Displacement is higher during protrusion phases compared to retraction phases, hence allowing net movement of the cell. Adapted from[START_REF] Levayer | Biomechanical regulation of contractility: spatial control and dynamics[END_REF]

Figure 11 :

 11 Figure 11: Drosophila germ band extension. (Top) Schematic view of an early Drosophila embryo during germ band extension. The germ band (orange) elongates by convergent extension (black arrows). A, anterior; P, posterior; D, dorsal; V, ventral. (Middle)Convergent extension is induced by cell-cell intercalation along the dorsoventral (D/V) axis. Blue labeled cells will form new contacts with pink labeled cells, whereas the number of junctions shared by yellow cells will be reduced. Green lines symbolize the polarized enrichment of MyoII and the resulting high contractility. (Bottom) Cell-cell intercalation is driven by polarized junction remodeling, including T1 transitions (left) and rosette formation (right). D/V junctions (green) shrink, give rise to fourway vertices (yellow) and resolve irreversibly into a new AP junction (red). Rosette formation is induced by the shrinkage of multiple DV junctions. Adapted from[START_REF] Levayer | Biomechanical regulation of contractility: spatial control and dynamics[END_REF]

Figure 12 :

 12 Figure 12: Cell-cell intercalation and junction remodeling induced by polarized MyoII flow and stabilization of junction shrinkage.Ratchet model for cell interaction. Actomyosin contractions on the medial apical surface reduce apical area and shrink vertical interfaces (red edges). Flow of MyoII into the vertical junctions increases MyoII intensity in the junctional cable. This stabilizes the interface by preventing it from lengthening. The process repeats to incrementally bring cells closer along the dorsal-ventral axis. Adapted from[START_REF] Mason | Tuning cell shape change with contractile ratchets[END_REF]

Figure 13 :

 13 Figure 13: Tissue elasticity and differentiation of naive MSCs. (a) Solid tissues exhibit a range of stiffness, as measured by the elastic modulus, E. (b)The in vitro gel system allows for control of E through crosslinking, control of cell adhesion by covalent attachment of collagenI, and control of thickness, h. Naive MSCs of a standard expression phenotype are initially small and round but develop increasingly branched, spindle, or polygonal shapes when grown on matrices respectively in the range typical of Ebrain (0.1-1 kPa), Emuscle[START_REF] Behrndt | Forces driving epithelial spreading in zebraish gastrulation[END_REF][START_REF] Dierkes | Spontaneous oscillations of elastic contractile materials with turnover[END_REF][START_REF] Vuong-Brender | The interplay of stifness and force anisotropies drives embryo elongation[END_REF][START_REF] Munro | Cortical lows powered by asymmetrical contraction transport PAR proteins to establish and maintain anterior-posterior polarity in the early C. elegans embryo[END_REF][START_REF] Vuong-Brender | elegans embryonic morphogenesis[END_REF][START_REF] Simões | Rho GTPase and Shroom direct planar polarized actomyosin contractility during convergent extension[END_REF][START_REF] Vasquez | Dynamic myosin phosphorylation regulates contractile pulses and tissue integrity during epithelial morphogenesis[END_REF][START_REF] Gally | Myosin II regulation during C. elegans embryonic elongation: LET-502/ROCK, MRCK-1 and PAK-1, three kinases with diferent roles[END_REF][START_REF] Vuong-Brender | The apical ECM preserves embryonic integrity and distributes mechanical stress during morphogenesis[END_REF][START_REF] Rogalski | The UNC-112 gene in Caenorhabditis elegans encodes a novel component of cell-matrix adhesion structures required for integrin localization in the muscle cell membrane[END_REF], or stiff crosslinkedcollagen matrices[START_REF] Vanneste | The role of the formin gene fhod-1 in C. elegans embryonic morphogenesis[END_REF][START_REF] Schönichen | FHOD1 is a combined actin ilament capping and bundling factor that selectively associates with actin arcs and stress ibers[END_REF][START_REF] Kühn | Formins as efector proteins of Rho GTPases[END_REF][START_REF] Jurmeister | MicroRNA-200c represses migration and invasion of breast cancer cells by targeting actin-regulatory proteins FHOD1 and PPM1F[END_REF][START_REF] Brenner | The genetics of Caenorhabditis elegans[END_REF][START_REF] Gomes | Microtubule severing by the katanin complex is activated by PPFR-1-dependent MEI-1 dephosphorylation[END_REF][START_REF] Fromont-Racine | Toward a functional analysis of the yeast genome through exhaustive two-hybrid screens[END_REF][START_REF] Kamath | Systematic functional analysis of the Caenorhabditis elegans genome using RNAi[END_REF][START_REF] Gally | Functional and genetic analysis of VAB-10 spectraplakin in Caenorhabditis elegans[END_REF][START_REF] Naganathan | Morphogenetic degeneracies in the actomyosin cortex[END_REF][START_REF] Bosher | The Caenorhabditis elegans vab-10 spectraplakin isoforms protect the epidermis against internal and external forces[END_REF][START_REF] Mi-Mi | Z-line formins promote contractile lattice growth and maintenance in striated muscles of C. elegans[END_REF][START_REF] Gustafsson | Surpassing the lateral resolution limit by a factor of two using structured illumination microscopy[END_REF][START_REF] Kner | Superresolution video microscopy of live cells by structured illumination[END_REF][START_REF] Matthews | The template update problem[END_REF][START_REF] Gonzalez | Digital Image Processing 3rd edn[END_REF]. Scale bar, 20mm. Adapted from[START_REF] Engler | Matrix elasticity directs stem cell lineage specification[END_REF]

Figure 14 :

 14 Figure 14: Actin cytoskeleton and transduction of mechanical forces. Mechanical loads induce a: 1. Conformational change in Factin (left schematic); 2. Conformational change in ABPs that uncovers previously concealed binding sites (middle schematic); and 3. Alterations in ABPmediated actin polymerization dynamics (right schematic). Adapted from Cytoskeleton Newsletter, News from Cytoskeleton inc., 2018.

Figure 15 :

 15 Figure 15: Linkermediated elasticity of spectrin.Mechanical unfolding of a doublerepeat b spectrin from human erythrocytes (adapted from[START_REF] Paramore | Examining the influence of linkers and tertiary structure in the forced unfolding of multiplerepeat spectrin molecules[END_REF]. Each spectrin repeat (labeled 8 and 9) is made of three αhelices denoted as A, B, and C. The unfolding sequence shows how the linker region unfolds first. (Inset) Force extension curves for a βbeta spectrin repeat construct (adapted from[START_REF] Law | Cooperativity in forced unfolding of tandem spectrin repeats[END_REF]. The bottom trace shows cooperative unfolding. Mutations weakening the linker region of spectrin have been shown to cause hereditary spherocytosis(Johnson et al., 2007). Adapted from[START_REF] Sotomayor | Singlemolecule experiments in vitro and in silico[END_REF]

Figure 16 :

 16 Figure 16: Talinvinculin mechanosensitivity. (a) Illustration of the domain structure of fulllength talin. The talin head domain contains a FERM domain, followed by a flexible "neck" which connects the head domain to its Cterminal rod domain. The rod domain contains 11 cryptic VBS (drawn in blue). The dimerization domain is a single helix that sits at the end of the rod. (b) Schematics of the talin structure and interaction of the talin dimer with vinculin in cells. (left) In the initial stage of FA formation, the talin dimer binds to actin and integrin. At this stage, the cryptic VBSs remain buried among the αhelical bundles. (right) As the actin filament starts to pull on talin, the formerly buried VBS are revealed to allow vinculin binding and cause more actin filament recruitment. Adapted from Hu et al., 2017.

Figure 17 :

 17 Figure 17: Model of cell spreading and polarization.When encountering a new substrate, the cell will go from round shape with weak cell-substrate attachment to a polarized shape in several steps. It will increase tension on the substrate, as it membrane sense and adapt to the substrate, while cytoskeleton remodel. Adapted from[START_REF] Gauthier | Mechanical feedback between membrane tension and dynamics[END_REF]

Figure 18 :

 18 Figure 18: Actin filament organization correlation with stress and stiffness anisotropy pattern. (Left) The anisotropy of mechanical stress generated by the polarized actomyosin network and medial myosin pulses promote Drosophila germband extension. (Right) The interplay of stress anisotropy (generated in seam cells red) and stiffness anisotropy (DV cells -white) promote C. elegans embryo elongation. Note that, although myosin II does not display a polarized distribution within individual C. elegans epidermal cells as it does in Drosophila germband epithelial cells, its enrichment in seam cells along the circumference is reminiscent of the localized myosin II enrichment at vertical junctions in Drosophila. A, anterior; P, posterior. Adapted from VuongBrender et al., 2017.

  medicine. The first was awarded to Sydney Brenner, John Sulston and Robert Horvitz for genetics and organ development and programmed cell death, in 2002. The second went to Craig Mello and Andrew Fire for describing the mechanism of RNA interference, in 2006. A Nobel Prize in chemistry for discovery and development of green fluorescent protein is also associated to C. elegans -one of the laureates, Martin Chalfie, used C. elegans to conduct his research. Since then C. elegans became one of the most popular model organisms in the field of genetics, cell and developmental biology, hostparasitic interactions, evolution, and ageing. C. elegans worms are multicellular eukaryotic organisms, that have a quick generation time including embryonic development, four larval stages and adulthood. Newly hatched larvae are 0.25 mm long and adults are 1 mm long. Numerous evolutionary conserved cellular and molecular

Figure 19 :

 19 Figure 19: Schematic representation of the 2fold embryoOn the left: 2fold embryo represented from a side view. The red dotted rectangle represents the transversal cut through the embryo. On the right: open section of the embryo. In yellow, D/V epidermis. In blue, lateral cells also called seam cells. In pink are represented the four quadrants of muscles tightly connected to the D/V epidermis through the C. elegans hemidesmosomes (CeHDs), in dark blue. Running from one lateral junction to the other, the actin bundles are represented in green. A/P, Anterior/Posterior.

Figure 20 :

 20 Figure 20: Schematic diagrams of C. elegans VAB10 isoforms. VAB10A and VAB10B each possesses a pair of calponin homology domains (CH1 and CH2) specialized for actin binding. Recent work from our lab updated the number of spectrins domains in C. elegans VAB10 by homology to Human plectin plakin domain (Suman et al., BioRxiv). They are situated right after the CH domains (two light purple domains). Therefore, VAB10A and VAB10B share a plakin domain including nine SRs (SR18), among which the fifth SR also contains a SH3 domain. The PR 11-15 of VAB10A is predicted for IFs binding. The GAS2 related homology domain of VAB10B binds to MTs. Adapted from Fu et al., 2017.

  805 is functional anal, although molecularly different, to the mammalian α6β4integrin. Muscle detachment is observed in myotactin mutants, once muscles become active. Other associated molecules are found around the CeHDs, like the nematodespecific coiledcoil protein PAT12A, which might contribute to the apical stabilization of IFs and VAB10A(Hetherington et al., 2010), or tumor suppressor Kankhomolog VAB19, which contains Cterminal ankyrin repeats. vab19 mutants show muscle detachment and display aberrant actin organization. Lastly, GIT1, a scaffolding and GTPase associated protein (GAP), recruits other proteins such as PAK1 and PIX1. It is maintained at the level of CeHDs once muscles become active(Zhang et al., 2011). The initial recruitment of these CeHD components happens independently from each other, but they help each other in their fine patterning at the muscle epidermis interface(Zhang and Labouesse, 2010).

Figure 21 :

 21 Figure 21: Schematic representation of the C. elegans hemidesmosomes (CeHDs) On the left: open section of the embryo. The red rectangle highlights two CeHDs, one on the apical side and one on the basal side. On the right: structure of the CeHDs connecting muscles to epidermis. NOAH1 and NOAH2 are proteins of the embryonic sheath that will become the cuticule in the larva. MUA3 and MUP4 are at the apical side of the CeHD. VAB10 and VAB19 are present at both apical and basal sides, while IFs hold the structure. LET805 is localized at the basal side. A/P, Anterior/Posterior. Adapted from Zahreddine et al., 2010 and Saurabh Tak's thesis.

Figure 22 :

 22 Figure 22: Schematic diagram of C. elegans FHOD1. Domain assignments are based on those of Schulte et al., 2008, for human FHOD1. Amino acid similarities to corresponding domains of human FHOD1 are indicated. Adapted from Vanneste et al., 2013.

Figure 23 :

 23 Figure 23: Schematic diagrams of C. elegans GSNL1 and mammalian gelsolin.Gelsolinlike (G) domains are numbered from G1 to G6 in the order of appearance from the Ntermini but not necessarily representing sequence homology. Indeed, G4 of GSNL1 is most closely related to G6 of gelsolin. Functional domains of C. elegans GSNL1 were adapted from[START_REF] Klaavuniemi | Caenorhabditis elegans gelsolinlike protein 1 is a novel actin filamentsevering protein with four gelsolinlike repeats[END_REF][START_REF] Liu | Distinct roles of four gelsolinlike domains of Caenorhabditis elegans gelsolinlike protein1 in actin filament severing, barbed end capping, and phosphoinositide binding[END_REF] Functional domains of mammalian gelsolin were adapted by[START_REF] Liu | Distinct roles of four gelsolinlike domains of Caenorhabditis elegans gelsolinlike protein1 in actin filament severing, barbed end capping, and phosphoinositide binding[END_REF], from Sun et al., 1999, with modifications based on the following references: severing[START_REF] Kwiatkowski | Identification of critical functional and regulatory domains in gelsolin[END_REF], capping[START_REF] Weber | Role of the N and Cterminal actinbinding domains of gelsolin in barbed filament end capping[END_REF][START_REF] Sun | The actin sidebinding domain of gelsolin also caps actin filaments. Implications for actin filament severing[END_REF], PIP2 binding[START_REF] Janmey | Phosphoinositidebinding peptides derived from the sequences of gelsolin and villin[END_REF][START_REF] Yu | Identification of a polyphosphoinositidebinding sequence in an actin monomer binding domain of gelsolin[END_REF][START_REF] Feng | Fullcontact domain labeling: Identification of a novel phosphoinositide binding site on gelsolin that requires the complete protein[END_REF], calciumsensitive Gactin binding in G1[START_REF] Way | Identification of a region in segment 1 of gelsolin critical for actin binding[END_REF], calciuminsensitive Factin binding in G2[START_REF] Sun | The actin sidebinding domain of gelsolin also caps actin filaments. Implications for actin filament severing[END_REF], and calciumsensitive Gactin binding in G4[START_REF] Pope | Localization of the calciumsensitive actin monomer binding site in gelsolin to segment 4 and identification of calcium binding sites[END_REF].

  site potential protein kinase A phosphorylation site vilin-like conserved COOH-terminal domain potential F-actin binding site

Figure 25 :

 25 Figure 25: Schematic diagrams of the three C. elegans spectrins. Domain structure of UNC70, SMA1 and SPC1. Adapted from SMART (a Simple Modular Architecture Research Tool, http://smart.emblheidelberg.de/) website.

Figure 26 :

 26 Figure 26: The "Chinese Finger Trap" model of spectrin. Cartoon representation depicting the domain organization of (a) erythroid and (b) nonerythroid spectrin tetramers (αspectrin-brown SRs; βspectrin-yellow SRs). The pink pentagons labeled CH are the actin binding domains other known spectrin domains are labeled EF, SH3 and PH. (c) End and side views of the SRs that comprise each tetramer are arranged in a similar fashion to the geometry reported by McGough & Josephs, 1990. (d) The proposed mechanism by which spectrin can undergo a threefold extension, while remaining a linear filamentous polymer. Adapted from Brown et al., 2015.

Figure 27 :

 27 Figure 27: Schematic representation of the life cycle of C. elegans at 20°C. C. elegans life cycle starts with fertilization and numerous cell divisions. First cleavage occurs at about 40 min. postfertilization. Eggs are laid outside at about 150 min postfertilization and during the gastrula stage. The embryonic elongation is highlighted in green, as it will be of main interest for the following work. After hatching, the larva goes through four larval stages before becoming an adult. Numbers in blue along the arrows indicate the length of time the animal spends at a certain stage. Adapted from WormAtlas (wormatlas.org).

Figure 28 :

 28 Figure 28: Schematic representation of the embryonic elongation of C. elegans.During its embryonic elongation, the length of the embryo is multiplied by a factor 4 and its circumference is reduced by a factor 2.5. This 3hour process is affected only by cell shape changes and not by the division or intercalation of cells. The first phase (or early elongation) depends on a ROCKpromoted actomyosin force in seam cells (blue) and actinpromoted stiffness in D/V cells (yellow). The second phase then requires repeated muscle contractions (yellow arrow), which induce a PAK1dependent mechanotransduction pathway. A/P, Anterior/Posterior.

  form a feedback network that controls embryonic elongation. In this network CeHDs are well positioned to integrate multiple signals and influence other cellular processes. Previous work from our laboratory unraveled a mechanotransduction pathway in which muscle contractions indeed trigger the elongation beyond the 2fold stage. It transforms the mechanical input, provided by muscle contractions into a biochemical signaling pathway acting in the D/V epidermis that leads to CeHD remodeling(Zhang et al., 2011). Muscles strongly contract and stretch the epidermis, exerting longitudinal stress upon it. In turn, the epidermis senses this mechanical input by a yet unidentified molecular component that induces the recruitment of GIT1 adaptor protein, which in turn activates its binding partner guaninenucleotide exchange factor PIX1, CED10 and PAK1 to the CeHDs. As a result, PAK1, as a terminal effector of the pathway phosphorylates the IFs, which promotes CeHD remodeling. PAK1 is a particularly important player in our system. It is one of the three PAK proteins found in C. elegans that are CePAK1 (PAK1, related to the mammalian group I PAKs), CePAK2 (PAK2, related to the mammalian group II PAKs) and MAX2 (related to Drosophila DPAK3). Among them PAK1 is the best studied. It has a highly conserved, catalytic Cterminal kinase domain and a prolin rich Nterminal regulatory domain, also called GTPasebinding CRIB domain or p21binding domain (PBD). As already mentioned, PAK1 forms a signaling module along with PIX1 (PAK interacting exchange factor) and GIT1 (G proteincoupled receptor kinase interactor). Within this complex, PAK 1 is most commonly activated in a GTPasedependent way by CED10 (C. elegans RAC1 homolog) and CDC42. Its localization near the junctions and the muscle attachment sites positions PAK1 at the very center of force transmission within the C. elegans embryonic epidermis, where this highly conserved kinase functions as a terminal effector of elongation in multiple pathways(Gally et al. 2009; Zhang et al. 2011). As it regulates embryonic elongation relying both on chemical and physical signals, PAK1 is an ideal starting point to understand the interplay of epithelial morphogenesis and mechanotransduction in development. Therefore, the idea to gain a better view on the molecular landscape around PAK1 during C. elegans embryonic elongation became the initial motivation of this project. Indeed, while muscle defective mutants with no effective tension on the epidermis arrest midway through elongation at the twofold stage (paralyzed at twofold stage or Pat phenotype), git 1, pix1 and pak1 mutants are viable, suggesting that parallel pathways must also exist for this regulation. It is these parallel pathways that I investigated during my PhD.

  embryos were analyzed from 24h to 48h postinjection. In one case, experiments involving the strain spc1(ra409) pak1(tm403); mcEx1016[spc1(+)::GFP; Pmyo2::RFP] (displayed in Figs. ), RNAi against unc112 was induced by feeding because the strain barely survived the regular microinjection procedure.Fluorescent translational reporter constructsSPC1::GFP and PAK1::mKate A 12633 bp genomic sequence including the spc1 coding sequence and a 3 kb promoter was inserted in frame with the GFP coding sequence present in the pPD95.75 vector (Addgene, Cambridge USA). To create the Ppak1::pak1::mKate reporter construct, first an mKatecontaining backbone was created by exchanging the GFPcoding sequence of the pML1572, Plin26::vab 10(ABD)::GFP plasmid(Gally et al., 2009). In a following cloning step a 8204 bp genomic sequence, including the pak1 coding sequence and a 4.5 kb promoter was inserted in frame with the mKate coding sequence present in the vector.To test if SPC1::GFP could rescue the function of SPC1, Gabriella and I first crossed the different transgenic animals of a wildtype background with mnDp33; spc1(ra409) animals (strain DM3409), and F1 transgenic males again with DM3409 to establish mnDp33; spc1(ra409);Ex[spc1::GFP].Rescuing transgenes were recognized because all viable progeny was GFPpositive and all (or most) nonviable progeny was GFPnegative, reflecting the loss of the mnDp33 balancer. To attempt mnDp33 segregation, she repeatedly transferred single GFPpositive mothers over four generations and examined their progeny, starting from at least two independent extrachromosomal arrays per construct. Thereby, she successfully obtained viable spc1(ra409); Ex[Pspc1::spc1(+)::gfp] animals, and then viable spc1(ra409) pak1(tm403); Ex[Pspc11::spc1(+)::gfp] animals through crossing and meiotic recombination, which segregated very short retracted GFPnegative embryos.FHOD1 full length and alternative constructsFor the FHOD1 constitutively active construct, Flora deleted part of the FH2 domain and the DAD domain of a 8283 bp genomic sequence of fhod1 (gift fromDavid Pruyne, (MiMi et al., 2012)) and inserted it under the control of the epidermisspecific 432 bp dpy7 promoter. Deletion of the DAD alone was obtained by inserting back the FH2 domain in the FH2/DAD deleted construct using Hifi DNA assembly cloning Kit (New England Biolabs); the FH1/FH2 deleted construct was obtained by deleting the FH1 domain using the Q5 ® site directed mutagenesis Kit protocol (New England Biolabs).All cloning steps relied on the use of the Phusion HighFidelity DNA Polymerase reaction Kit (Fisher ThermoScientific); the constructs were subsequently verified by sequencing. The constructs were injected at 10 ng/µl plasmid construct, with 150 ng/µl pBSK + 5 ng/µl pCFJ90 (Pmyo2::mcherry) as co injection markers for the spc1::gfp constructs, or 100 ng/µl pRF4 (rol) coinjection marker for pak 1::mKate.LifeAct::mMaple3 photoconvertible construct For LifeAct::mMaple3, I amplified LifeAct from the pML36 plasmid (Pdpy7::LifeAct::GFP generated by a previous postdoc of the lab, Thanh VuongBrender) and mMaple3 from the pCU97 plasmid (which was codon optimized for C. elegans by Saurabh Tak, a former PhD student of the lab).Both fragments were assembled by Gibson technique[START_REF] Gibson | Enzymatic assembly of DNA molecules up to several hundred kilobases[END_REF][START_REF] Gibson | Enzymatic assembly of overlapping DNA fragments[END_REF] using the NEBuilder® HiFi DNA Assembly Gibson Cloning Kit and then were purified using Qiaprep® Spin Miniprep Kit. The sequence was verified by GATC sequencing. First I wanted to use this construct to generate a transgenic line by mos1mediated Single Copy Insertion (mosSCI), a method to insert a single copy of a transgene into a welldefined location in the C. elegans genome. (FrøkjaerJensen et

  to build the homology repair template. I first amplified a 2 kb segment on the Carboxyterminus or the Amino terminus of the target gene from genomic DNA and cloned it into the pJET1.2 vector (from Thermo Fisher Scientific). I then inserted the fluorescent tag sequence (GFP, mMaple, mCherry or wrmScarlet) in a way that 1500 bp are before it and 500 bp are after it for a construction in C terminal or the reverse for a construction in Nterminal. These 1500 bp and 500 bp segments function as homology arms. Additionally, I inserted the same small linker as mentioned above between the target gene sequence and the fluorescent tag sequence for ACT1 and SPC1. The small linker was amplified from the GFP::ACT1 from Erin's Cram lab[START_REF] Dixon | Muscle arm development in Caenorhabditis elegans[END_REF][START_REF] Wirshing | Spectrin regulates cell contractility through production and maintenance of actin bundles in the Caenorhabditis elegans spermatheca[END_REF] and then was cloned into the repair template plasmids by Gibson with the NEBuilder® HiFi DNA Assembly Gibson Cloning Kit. As the linker was extremely small (51bp) compared to the plasmid (between 5.5kb and 8kb) I tried to insert it into; I had to adjust several times the Gibson mix. I used www.crispr.mit.edu to select a Protospacer Adjacent Motif (PAM) site. PAM site in the template was mutated (without changing the protein sequence) to prevent the plasmid and the repaired genomic locus from being cleaved by Cas9. For the synthesis of single guide RNA (sgRNA), two strategies were used. Either I cloned the sgRNA sequence in pDD162 plasmid (that also encodes Cas9 under a germline promoter) by Gibson cloning. Or I cloned the sgRNA sequence in the pML2840

  amplified 700 bp arms flanking the site of insertion from genomic DNA by using Thermo Scientific Phusion HighFidelity DNA polymerase. The plasmids pJJR82 and pJJR83 were predigested with AvrII and SpeI for Carboxy terminal insertion and with ClaI and SpeI for Amino terminal insertion. The left and right arm were assembled with the digested plasmid by using NEBuilder® HiFi DNA Assembly Gibson Cloning Kit. As for the first strategy, I used www.crispr.mit.edu to select a PAM site and then mutate it. I synthetized the sgRNA by cloning its sequence into the pDD162 plasmid. The resulting plasmids were then injected in the gonads of young adult worms. The F1 progeny was screened specifically for rollers with no red pharynx. Screening in the F2 generation allowed to separate the homozygotes rollers. They were then given a temperature shock at 32°C for 45 hours to excise the cassette. The insertion of the fluorescent tag was confirmed by GATC sequencing.

  microscope with a Roper Evolve camera controlled by the Metamorph software, and a 100x oil immersion objective (experiments for Fig.S9). A Zstack of 4 focal planes with 0,5 µm step size was acquired using a streaming acquisition mode. The time between two acquisitions was 0.41 second during 300 time frames. To synchronize embryos, mothers were put on an empty NGM agar plate to lay eggs for a short time window, and embryos were left to develop until the stage of interest. (For the analyse of the contraction see next section on Image analysis. To analyse the in vivo o localisation between PAK1::mKate, ABD::mcherry and SPC1::GFP, Gabriella used the Zeiss/Roper spinningdisk microscope under a 100X oil immersion objective, keeping the laser intensity at a constant level throughout the experiments. Image processing and computing the colocalisation coefficient was done using the Volocity software.TIRFSIM imagingEmbryos were mounted between 22 mm square cover glasses (thickness of 0.170±05 µm, Carl Zeiss Microscopy GmbH, Jena, Germany) and 25×75 mm tefloncoated glass slides with three depression wells. Embryos were embedded in 2 µl water containing Polybeads® acrylate microspheres of15.4±1.43 µm diameter (Polysciences, Inc). Wildtype embryos were at 1.8 to 2fold

Figure 1 :

 1 Figure 1: Muscle contractions deform the epidermis due to their mechanical coupling. (aa''') Spinningdisk micrograph of epidermis actin filaments (green) and muscle nuclei (red) in a wildtype 2 fold embryo. Scale bar: 10 µm. (a') Kymographs (yellow rectangle area in a) illustrate the concurrent displacement of epidermal actin and muscle nuclei. (a'') Quantification of the area below the resulting displacement curves (pink box) (n=11, contractions=33). (bb'') A muscle contraction/relaxation cycle illustrating its local impact on epidermal actin filaments in a wildtype 2fold embryo (timing above). Yellow (relaxation), red (compression), green (stretching) distances between four landmarks (denoted 14): (b) [12], 7.8 μm; [23], 19.8 μm; [34], 24.6 μm. (b') [12], 9.4 μm; [23], 13.6 μm; [34], 26.2 μm. (b'') [12], 8.0 μm; [2 3], 19.2 μm; [34], 25.0 μm.

Figure 2 :

 2 Figure 2: Combined loss of PAK1 and SPC1 triggers embryo retraction.(a) RNAi screen in a pak1 mutant identified spc1 as an enhancer (Table1). (b) A yeast twohybrid screen using the PAK1 Nterm domain as a bait identified the SPC1 SH3 domain as a prey (orange background) (Table2). (c) DIC pictures and quantification of newly hatched wildtype body length (n=38), pak1(tm403) (n=32), spc 1(RNAi) (n=26) and spc1(RNAi) pak1(tm403) (n=36). Scale bar: 25 µm (wt and pak1), 10 µm (spc1 and spc1 pak1). Data represent mean values ± SD. Twosided paired ttest. (dj) Loss of the proteins GIT1 and PIX1, acting upstream of PAK1 in the mechanotransduction pathway promoted by muscle contractions, in the absence of spc1 also triggers a retraction phenotype. (d) Elongation curves and (ej) terminal phenotypes of wildtype (n=12), (e) pak1(tm403) (n=11),(f) git1(tm1962) (n=10), (g) pix1(gk416) (n=10), spc1(RNAi) (n=8), (h) spc1(RNAi) pak1(tm403) (n=9), (i) spc1(RNAi) git1(tm1962) (n=11), (j) spc1(RNAi) pix1(tm416) (n=8). Pink box, period of muscle activity. Scale bar: 17 µm. Data represent mean values ± SEM.

  Figure 2: Combined loss of PAK1 and SPC1 triggers embryo retraction.(a) RNAi screen in a pak1 mutant identified spc1 as an enhancer (Table1). (b) A yeast twohybrid screen using the PAK1 Nterm domain as a bait identified the SPC1 SH3 domain as a prey (orange background) (Table2). (c) DIC pictures and quantification of newly hatched wildtype body length (n=38), pak1(tm403) (n=32), spc 1(RNAi) (n=26) and spc1(RNAi) pak1(tm403) (n=36). Scale bar: 25 µm (wt and pak1), 10 µm (spc1 and spc1 pak1). Data represent mean values ± SD. Twosided paired ttest. (dj) Loss of the proteins GIT1 and PIX1, acting upstream of PAK1 in the mechanotransduction pathway promoted by muscle contractions, in the absence of spc1 also triggers a retraction phenotype. (d) Elongation curves and (ej) terminal phenotypes of wildtype (n=12), (e) pak1(tm403) (n=11),(f) git1(tm1962) (n=10), (g) pix1(gk416) (n=10), spc1(RNAi) (n=8), (h) spc1(RNAi) pak1(tm403) (n=9), (i) spc1(RNAi) git1(tm1962) (n=11), (j) spc1(RNAi) pix1(tm416) (n=8). Pink box, period of muscle activity. Scale bar: 17 µm. Data represent mean values ± SEM.

Figure 3 :

 3 Figure 3: spc1 pak1 retraction is muscle dependent. (a) Elongation curves and (bg) DIC pictures showing the terminal phenotypes of (b) unc112(RNAi) (n=14), (c) unc112(RNAi); pak1(tm403) (n=8), (d) unc112(RNAi); spc1(ra409) (n=4), (e) spc1(ra409) (n=8), (f) unc 112(RNAi); pak1(tm403) spc1(ra409) (n=7), (g) spc1(ra409) pak1(tm403) (n=8). Pink box, period of muscle activity; bracket, extent of retraction. (d) Terminal phenotype of unc112(RNAi); spc1(ra409) obtained by inducing unc112(RNAi) in the strain ML2436 bearing a rescuing extrachromosomal spc1::gfp array and looking for embryos having lost the array; we could only obtain a few embryos of the desired phenotype despite numerous repeats (n=4), which all had the phenotype illustrated here and is similar to that of spc1(ra409) alone. Scale bar: 17 µm. Data represent mean values ± SEM.

Figure 4 :

 4 Figure 4: PAK1 and SPC1 colocalize with actin filaments. (ab) Distribution of (a) PAK1::mKate (n=20) and (b) SPC1::GFP (n=13) in a late embryo. Enlarged pictures of PAK1 and SPC1 showing a filamentous distribution in the dorsoventral (D/V) epidermis similar to actin filaments. Scale bar: 10 µm. (c) Fluorescence pictures of PAK1::mKate (red) and SPC1::GFP (green) (n= 20): the panel shows the colocalization image for the most apical focal planes (top image), and full XZ (green panel) and YZ (red panel) projections. The level of colocalization is high based on Pearson's correlation coefficient (0.7 0.9, n=20). The highest level of colocalization is detected at the apical cortex. (d) Fluorescence pictures of Plin 26::VAB10(ABD)::mKate (red) and SPC1::GFP (green) (n=8): the panel shows the colocalization image for the most apical focal planes (top image), and full XZ (green panel) and YZ (red panel) projections. The level of co localization is high based on Pearson's correlation coefficient (0.70.9, n=8). The colocalization is almost exclusively detected at the apical cortex. The gene lin26 drives expression in the epidermis; VAB10(ABD) corresponds to the two actinbinding domains (calponin homology) of the protein VAB10. Scale bar: 10 µm.

Figure 5 :

 5 Figure 5: SPC1 and SMA1 colocalization with actin filaments is highlighted by TIRFSIM microscopy. (ab) TIRFSIM snapshots of grouped Z movies to emphasize the colocalization of (a) SMA1 (SMA1::GFP) (n=20) and (b) SPC1 (SPC1::YFP) (n=6) with actin bundles (ABDVAB10::mKate). Scale bar: 2 µm.

Figure 6 :

 6 Figure 6: Schematic representations of the different hypothesis about actin organization inside a bundle. Hypothesis 1 and 2: actin bundles are constituted of long filaments going from one DV/lateral cell junction to the CeHDs. Hypothesis 3 and 4: actin bundles are constituted of several smaller filaments all orientated in the same direction. Hypothesis 5: actin bundles are constituted of several smaller filaments in antiparallel disposition.

Figure 7 :

 7 Figure 7: Genetic interactions of pak1, spc1, sma1 and unc70 affect elongation. (a) Quantification of L1 hatchling length and DIC pictures showing the terminal phenotypes of wildtype (n=65), unc70(RNAi) (n=23) (b), pak1(tm403) (n=47) (c), sma1(ru18) (n=28) (d), unc70(RNAi) ; pak1(tm403) (n=16) (e), sma1(ru18) ; pak1(tm403) (n=52) (f), unc70(RNAi) sma1(ru18) (n=33) (g), unc70(RNAi) sma1(ru18) ; pak1(tm403) (n=26) (h), spc1(RNAi) (n=27) (i), sma1(ru18); spc1(RNAi) (n=28) (j), spc1(RNAi) pak1(tm403) (n=) (k),. Scale bar: 25 µm. Data represent mean values ± SD. Twosided paired ttest. Pvalues: *<0,05; **<0,001; ***<0,0001; ns, not significant.

Figure 8 :

 8 Figure 8: Combined loss of SPC1 and VAB10B also triggers embryo retraction. (a) Elongation curves and (bg) DIC pictures showing the terminal phenotypes of (b) sma1(ru18) (n=8), (c) vab 10b(mc44) (n=6), (d) vab10b(mc44); sma1(ru18) (n=10), spc1(RNAi) (n=8), (e) vab10b(mc44); spc1(RNAi) (n=11) that do not retract, (f) vab10b(mc44); spc1(RNAi) (n=8) that retract and (g) spc1(RNAi) pak1(tm403) (n=8). Pink box, period of muscle activity. Scale bar: 17 µm. Data represent mean values ± SEM.

  (mc44); spc-1(RNAi) vab-10b(mc44); spc-1(RNAi)

Figure 9 :

 9 Figure 9: Actin filaments show organization defects in spc1 pak1 defective embryos. (ae) Epidermal actin filaments visualized with the Pdpy7::LifeAct::GFP reporter construct in wildtype (aa'), pak1(tm403) (bb'), unc112(RNAi) (cc'), spc1(RNAi) (dd'), spc1(RNAi) pak1(tm403) (ee') (at mid elongation (2fold equivalent) stage. Yellow rectangle, region of interest (ROI). (a'e') ROI after binarisation (green) and major axis detection (red), based on (a''') three steps of image treatment for continuity and orientation analysis. (a'') Actin continuity: distribution of actin segments based on their length. Scale bar: 10 µm (ae). Scale bar: 1 µm (a'e').

Figure 10 :

 10 Figure 10: Actin filament continuity varies during development.Quantification of actin filament continuity ; the graph represents the length (in pixels) along the circumferential axis of actin filaments in early, mid and late (corresponding to 1.7fold, 2fold and 3fold equivalent stages in a wildtype embryo, respectively) embryos of wildtype (early n=12, mid n=19, late n=16), pak1(tm403) (early n=16, mid n=21, late n=16), spc1(RNAi) (early n=15, mid n=21, late n=20), spc1(RNAi) pak1(tm403) (early n=12, mid n=17, late n=26), unc112(RNAi) (early n=8, mid n=13, late n=12), spc1(ra409) pak1(tm403) (mid n=14, late n=20) and unc112(RNAi) ; spc1(ra409) pak1(tm403) (early n=8, mid n=15, late n=19) genotypes. Graphs represent median values, 25th and 75th percentiles; whiskers extend to the most extreme data points not considered outliers. Twosided paired ttest. Pvalues: *<0,05; **<0,001; ***<0,0001; ns, not significant.

Figure 11 :

 11 Figure 11: Actin filament orientation varies during development. Actin filament orientation based on Fast Fourier Transform and binarisation. Wildtype (early n=12, mid n=18, late n=14), pak1(tm403) (early n=16, mid n=20, late n=16), spc1(RNAi) (early n=14, mid n=18, late n=18), spc 1(RNAi) pak1(tm403) (early n=12, mid n=18, late n=21), unc112(RNAi) (early n=8, mid n=13, late n=12), spc 1(ra409) pak1(tm403) (mid n=14, late n=19) and unc112(RNAi) ; spc1(ra409) pak1(tm403) (early n=8, mid n=15, late n=19) genotypes. Note that the characteristics of actin filaments in spc1(RNAi) pak1(tm403) embryos differ mostly at the equivalent of the twofold stage when muscles become active. At ealier and later stages, spc1(RNAi) embryos and spc1(RNAi) pak1(tm403) embryos become similar. Graphs represent median values, 25th and 75th percentiles; whiskers extend to the most extreme data points not considered outliers. Twosided paired ttest. Pvalues: *<0,05; **<0,001; ***<0,0001; ns, not significant.

Figure 12 :

 12 Figure 12: Actin filament abnormalities are highlighted by TIRFSIM microscopy in spc1 pak1 embryos.TIRFSIM superresolution images of actin filaments (Pdpy7::LifeAct::GFP reporter). (aa'') Wildtype and (bb") spc1(RNAi) pak1(tm403) embryos at the 2fold stage or equivalent. Grey and orange rectangles, region of interest (ROI) above muscles (area of higher bending in timelapse images); black and bordeaux rectangles, ROI taken elsewhere. Scale bar: 5 µm. (c) Actin continuity estimated as the segment length in binarised ROI images, and (d) peak value of the angular coefficient calculated after Fast Fourier Transformation as a proxy for actin bundle anisotropy. Defects are significantly more pronounced above muscles. (e) Coefficient of variation (SD/mean) of the fluorescence signal in ROIs above muscles as a proxy for actin bundle organization. (f) Actin bundle straightness (f) calculated as the ratio between the actual length of a bundle (black line in f') and the shortest distance between its endpoints (red line in f'). Graphs represent median values, 25th and 75th percentiles; whiskers extend to the most extreme data points not considered outliers. Twosided paired ttest. Pvalues: *<0,05; **<0,001; ***<0,0001; ns, not significant.

Figure 13 :

 13 Figure 13: Actin filament abnormalities are highlighted by TIRFSIM microscopy in spc1 pak1 embryos. (ab) TIRFSIM snapshots of grouped Z movies with Fire LUT to emphasize the actin bundle defects of spc 1(RNAi) pak1(tm403) embryos compared to wildtype. Pvalues: *<0,05; **<0,001; ***<0,0001; ns, not significant.

Figure 14 :

 14 Figure 14: Variation of actin intensity over time in wildtype and spc1 pak1 embryos (ab) Spinningdisk images of wildtype embryos expressing the Pdpy7::Lifeact::GFP (a) and the Pdpy7::GFP (b) contsructs in the epidermis at the 2fold stage. Scale bar: 10µm. (cd) Quantifications of the Pdpy 7::LifeAct::GFP (c) and the Pdpy7::GFP (d) intensity in the entire embryo (ROI in yellow on the images) at threes stages early, middle and late (corresponding to 1.7fold, 2fold and 3fold equivalent stages in a wild type embryo, respectively) in wildtype and spc1(RNAi) pak1(tm403) embryos. Graphs represent median values, 25th and 75th percentiles; whiskers extend to the most extreme data points not considered outliers. (e) Ratio between the signal in spc1(RNAi) pak1(tm403) and wildtype embryos for the Pdpy7::Lifeact::GFP and the Pdpy7::GFP constructs at threes stages. Data represent mean values and SD. (ce) Twosided paired ttest. Pvalues: *<0,05; **<0,001; ***<0,0001; ns, not significant.

Figure 15 :

 15 Figure 15: Embryo diameter varies during elongation.(ab'') Spinningdisk images of embryos expressing the Pepid::Lifeact::GFP construct in the epidermis at three elongation stages early, middle and late (corresponding to 1.7fold, 2fold and 3fold equivalent stages in a wildtype embryo, respectively) for wildtype (aa'') and spc1(RNAi) pak1(tm403) embryos (bb''). Scale bar: 10 µm. The Pepid promoter corresponds to Pdpy7. The yellow lines correspond to the segments used to measure the D/V width of the V1 seam cell. (c) Quantification of the average V1 cell circumferential width normalized to the initial width during elongation, and (d) of the average D/V circumferential width at the level of the V1 seam cell, which was calculated using the measured embryo length and V1 cell width, taking into consideration the conservation of the total embryo volume, in wildtype (early n=38, mid n=10, late n=14), pak 1(tm403) (early n=26, mid n=8, late n=20), spc1(RNAi) (early n=24, mid n=26, late n=18), spc1(RNAi) pak 1(tm403) (early n=22, mid n=30, late n=38), unc112(RNAi) (early n=8, mid n=9, late n=8), and unc112(RNAi) ; spc1(ra409) pak1(tm403) (early n=7, mid n=12, late n=17) genotypes. Error bars, SEM. A notable feature of spc1(RNAi) pak1(tm403) embryos is that the circumferential dimension of the seam cells decreased much more than that of their DV cell, which most likely reflects the actin filament integrity defects combined with a Fseam force largely unchanged.

Figure 16 :

 16 Figure 16: Actin bundles strongly bend during muscle contractions. (ad) Spinningdisk timelapse images of epidermal actin filaments (Pdpy7::LifeAct::GFP reporter) and quantification of their bending angles in wildtype (n=23, contractions=101) (a, c) and spc1(RNAi) pak 1(tm403) (n=134, contractions=131) (b, d) embryos at midelongation (2fold equivalent) stage; kymographs of the region boxed in yellow are displayed below. Scale bar: 10 µm.

Figure 17 :b

 17 Figure 17: Identification of two severing proteins rescuing the retraction phenotype.(a) Principle of the RNAi screen performed to identify proteins mediating actin remodeling; the recipient strain carried a rescuing but frequently lost spc1(+) transgene (noted +). (b) Quantification of L1 hatchling length after downregulation or mutation of the indicated genes. spc1(ra409) pak1(tm403) (n=92), spc1(ra409) pak 1(tm403); spc1::GFP (n=81), plst1(RNAi); spc1(ra409) pak1(tm403) (n=55), plst1(RNAi); spc1(ra409) pak 1(tm403); spc1::GFP (n=30), unc60(RNAi); spc1(ra409) pak1(tm403) (n=16), unc60(RNAi); spc1(ra409) pak 1(tm403); spc1::GFP (n=19), gsnl1(RNAi); spc1(ra409) pak1(tm403) (n=64), gsnl1(RNAi); spc1(ra409) pak 1(tm403); spc1::GFP (n=68), viln1(RNAi); spc1(ra409) pak1(tm403) (n=69), viln1(RNAi); spc1(ra409) pak 1(tm403); spc1::GFP (n=52), gsnl1(tm2730); spc1(RNAi) pak1(tm403) (n=57), viln1(ok2413); spc1(RNAi) pak1(tm403) (n=55). Control animals fed on L4440 bacteria. Data represent mean values ± SD. Twosided paired ttest. Pvalues: *<0,05; **<0,001; ***<0,0001; ns, not significant.

Figure 18 :

 18 Figure 18: Combined loss of severing proteins, SPC1 and PAK1 rescues the retraction phenotype. (ag) Elongation curves and DIC pictures showing the terminal phenotypes of (b) pak1(tm403) (n=11), (c) gsnl 1(tm2730); pak1(tm403) (n=9), (d) viln1(ok2413); pak1(tm403) (n=9), (e) gsnl1(tm2730); spc1(RNAi) pak 1(tm403) (n=5), (f) viln1(ok2413); spc1(RNAi) pak1(tm403) (n=11) and (g) spc1(RNAi) pak1(tm403) (n=9) (a). Pink box, period of muscle activity. Scale bar: 25 µm. Data represent mean values ± SEM. (h) Quantification of the L1 hatchling body length of wildtype (n=65), gsnl1(tm2730) (n=52), viln1(ok2413) (n=43), viln 1(ok2413); gsnl1(tm2730) (n=41), pak1(tm403) (n=47), gsnl1(tm2730); pak1(tm403) (n=51), viln1(ok2413); pak1(tm403) (n=70), viln1(ok2413); gsnl1(tm2730); pak1(RNAi) (n=35), spc1(RNAi) (n=27), and viln 1(ok2413); gsnl1(tm2730); spc1(RNAi) (n=41). Data represent mean values ± SD. Twosided paired ttest. P values: *<0,05; **<0,001; ***<0,0001; ns, not significant.

Figure 19 :

 19 Figure 19: Equations supporting the mechanical model. (a) System equations for the viscoplastic mechanical model of embryo elongation. The embryo is represented as a KelvinVoigt solid (spring stiffness k, resting length λ, viscosity η) submitted to forces Fepid and Fmuscle.

Figure 20 :

 20 Figure 20: Timedependent length of a KelvinVoigt model in different conditions.(aa') A generic KelvinVoigt system exposed to a constant force Fepid, and (a') its predicted elongation change for Fseam =0.85 and four different values of αDV based on the equation = . (bb') A similar system exposed to two forces, Fepid and an oscillating force ⃗ , and (b') predicted elongation change using Fepid=0.85 and ⃗ with an amplitude equal to 1 and the behavior depicted in the blueboxed inset. For simplicity, we will refer to the amplitude of ⃗ by Fmuscles. As the pulsatile force induces both compression and stretching (see Fig.1c), its net input on elongation is transient and the system oscillates around the maximal value reached without ⃗ . In all other panels (except in a), ⃗ was set as a periodic function with positive and negative steps of duration 6 seconds modulated by a cosine function, alternating with periods of null value of duration 15 seconds (b'inset). In (ab') the elastic constant of the spring is k=1, the initial resting length has the value λ(t=0)=1, and the viscosity value is η=10.

Figure 21 :

 21 Figure 21: Timedependent length of a KelvinVoigt model in different conditions.(aa'') A KelvinVoigt system with mechanical plasticity introduced according to Eqs.[START_REF] Gilmour | From morphogen to morphogenesis and back[END_REF][START_REF] Collinet | Local and tissue-scale forces drive oriented junction growth during tissue extension[END_REF][START_REF] Lye | Mechanical coupling between endoderm invagination and axis extension in Drosophila[END_REF][START_REF] Zhang | A tension-induced mechanotransduction pathway promotes epithelial morphogenesis[END_REF], and (a') predicted elongation change using Fepid=0.85, Fc=0, Fmuscles =3 and four distinct values of the plasticity factor β, or (a'') using Fepid=0.85, Fc=0, β =0.10 and four distinct values of Fmuscles. (bb') A KelvinVoigt system in which the plasticity is defective (β=0), and in which there is actin tearing according to Eq. (7) inducing a progressive reduction of Fepid, and (b') predicted elongation change with an initial value of Fepid=0.85, the tearing factor γ=0.15 and Fmuscles =3; the blueboxed inset (b') shows the behavior of DV(t) over time. In (ab'') the elastic constant of the spring is k=1, the initial resting length has the value λ(t=0)=1, and the viscosity value is η=10. (c) Result of the fit for the following genotypes: wt, unc112 alone spc1 alone, spc1 pak1 double, unc112; spc1 pak according to Eqs.[START_REF] Gilmour | From morphogen to morphogenesis and back[END_REF][START_REF] Collinet | Local and tissue-scale forces drive oriented junction growth during tissue extension[END_REF] 911). The values of the parameters are specified in paragraphs 1.5 and 1.6. The shallow decrease in length for the curve of unc112; spc1 pak1 after 150 minutes is due to a deformation of the embryos under the effect of unc112 knockdown but not to retraction, which is why the fit has been evaluated on the first 150 minutes of the curve.

  unc-112; spc-1(-)pak-1(-) unc-112; spc-1(-) pak-1(-)

Figure 22 :

 22 Figure 22: Combined loss of SPC1 and PAK1 or SPC1 and FHOD1 leads to comparable retraction phenotypes. (a) A retraction screen in a spc1 mutant identifies fhod1; (b) quantification of spc1(ra409) L1 hatchling body length after feeding on L4440 control (n=21) or fhod1(RNAi) (n=25) bacteria. Scale bar: 15 µm. Data represent mean values ± SD. Twosided paired ttest. Pvalues: *<0,05; **<0,001; ***<0,0001; ns, not significant. (c) Elongation curves and (dj) corresponding DIC pictures showing the terminal phenotypes at hatching of (d) wildtype (n=12), (e) fhod1(tm2363) (n=10), (f) fhod1(RNAi) (n=10), (g) pak1(tm403) (n=11), (h) fhod 1(RNAi); pak1(tm403) (n=10), (i) spc1(RNAi) pak1(tm403) (n=8), and (j) fhod1(tm2363); spc1(RNAi) (n=9). Pink box, period of muscle activity. Note that the elongations curves of spc1(RNAi) pak1(tm403) and fhod 1(tm2363); spc1(RNAi) completely overlap. Scale bar: 25 µm. Data represent mean values ± SEM.

Figure 23 :

 23 Figure 23: Actin filaments show organization defects in fhod1; spc1 defective embryos. (a,b) Epidermal actin filaments visualized with the Pdpy7::LifeAct::GFP reporter construct in fhod1 (aa'), and fhod1(tm2363) spc1(RNAi) (bb') at midelongation (2fold equivalent) stage. Yellow rectangle, region of interest (ROI). Scale bar: 10 µm. (a'b') ROI after binarisation (green) and major axis detection (red).

Figure 24 :

 24 Figure 24: Actin filaments show continuity defects in fhod1; spc1 defective embryos.Quantification of actin filament continuity ; the graph represents the length (in pixels) along the circumferential axis of actin filaments in early, mid and late (corresponding to 1.7fold, 2fold and 3fold equivalent stages in a wildtype embryo, respectively) embryos of wildtype (early n=12, mid n=19, late n=16), spc1(RNAi) (early n=15, mid n=21, late n=20), spc1(RNAi) pak1(tm403) (early n=12, mid n=17, late n=26), fhod1(tm2363) (early n=12, mid n=14, late n=10), fhod1(tm2363); spc1(RNAi) (early n=7, mid n=11, late n=8) genotypes. Graphs represent median values, 25th and 75th percentiles; whiskers extend to the most extreme data points not considered outliers. Twosided paired ttest. Pvalues: *<0,05; **<0,001; ***<0,0001; ns, not significant.

Figure 25 :

 25 Figure 25: Actin filaments show orientation defects in fhod1; spc1 defective embryos. Actin filament orientation based on Fast Fourier Transform and binarisation. Wildtype (early n=12, mid n=18, late n=14), spc1(RNAi) (early n=14, mid n=18, late n=18), spc1(RNAi) pak1(tm403) (early n=12, mid n=18, late n=21), fhod1(tm2363) (early n=12, mid n=14, late n=10), fhod1(tm2363); spc1(RNAi) (early n=7, mid n=11, late n=8) genotypes. Note that the characteristics of actin filaments in spc1(RNAi) pak1(tm403) embryos differ mostly at the equivalent of the twofold stage when muscles become active. At ealier and later stages, spc 1(RNAi) embryos and spc1(RNAi) pak1(tm403) embryos become similar. Graphs represent median values, 25th and 75th percentiles; whiskers extend to the most extreme data points not considered outliers. Twosided paired ttest. Pvalues: *<0,05; **<0,001; ***<0,0001; ns, not significant.

Figure 26 :

 26 Figure 26: FHOD1 construction lacking FH2 and DAD domains rescues the retraction phenotype.Pdpy7 driven epidermis expression of truncated FHOD1 variants and terminal body length at hatching: spc 1(RNAi)(n=26); spc1(RNAi) pak1(tm403) with no transgene (n=36), with FHOD1(full length) (n=16), FHOD 1(ΔDAD) (n=17), FHOD1(ΔFH2DAD) (n=38) transgenes or nontransgenic siblings (n=78), FHOD1(ΔFH1FH2 DAD) transgene (n=18). Data represent mean values ± SD. Twosided paired ttest. Pvalues: *<0,05; **<0,001; ***<0,0001; ns, not significant.

  RNAi) pak-1(tm403); FHOD-1(ΔFH2/DAD) (siblings not carrying the construction)

IX. 3 .

 3 FHOD1 and PAK1 localization are affected the same way by the lack of SPC1 Several factors could contribute to alter PAK1 and FHOD1 activity. First, Gabriella noticed that inducing spc1(RNAi) in embryos expressing PAK1::GFP, disturbed PAK1 localization and lead to the formation of ectopic PAK1 aggregates (Fig. 27a,a'). Interestingly Flora observed the same defect in FHOD1::GFP expressing embryos upon spc1(RNAi) downregulation (Fig. 27b,b'). Additionally, FHOD1 localizes at the same sites as PAK1, SPC1 and actin at the level or the epidermal cell cortex.

Figure 27 :

 27 Figure 27: PAK1 and FHOD1 form aggregates in spc1(RNAi) loss of function. (aa') PAK1::GFP localisation in wildtype and spc1(RNAi) embryos. Yellow box, area enlarged below the panel. Note the punctae in SPC1 deficient embryos. (bb') FHOD1 localization in wildtype and spc1(RNAi) embryos. Note the aggregates (arrowheads). Note also that FHOD1::GFP displayed a filamentous organization reminiscent of actin filaments. Scale bar: 10 µm.

Figure 28 :

 28 Figure 28: Tracking of the actin displacement reveals duration of the muscle contractions. (ad) Spinningdisk microscopy tracking of actin filaments visualized with a Pdpy7::Lifeact::GFP marker specifically expressed in the epidermis. Individual displacement tracks of wildtype (a), pak1(tm403) (b), spc 1(RNAi) (c) and spc1(RNAi) pak1(tm403) (d) embryos at a stage equivalent to 2fold in a wildtype embryo. Scale bar: 10 µm. (e) Typical kymographs of the Lifeact::GFP-labeled actin filaments in wildtype and spc 1(RNAi) pak1(tm403) embryos from which the tracks in ad were derived. Time interval between two images is 0.41 second. Yellow dots correspond to landmarks for quantitative analysis. (f) Quantification of the displacement duration in (N=embryo/ n=contraction): wildtype, N=11/n=51; pak1(tm403), N=11/n=26; spc 1(RNAi), N=11/n=73; spc1(RNAi) pak1(tm403), N=11/n=89. Graphs represent median values, 25th and 75th percentiles; whiskers extend to the most extreme data points not considered outliers. Twosided paired ttest. Pvalues: *<0,05; **<0,001; ***<0,0001; ns, not significant.

Figure 1 :

 1 Figure 1: Cellular model of embryo elongation.(ab') Cellular model of embryo elongation based on volume conservation in normal embryos, in which an increase in axial length implies a decrease in circumferential length. (aa') Proposed model: in control embryos, muscle contractions (red arrows) induce actin filament bending and their severing, followed by SPC1/PAK1 dependent stabilization; whether spectrin is found along (scenario 1) or between (scenario 2) actin filaments is unknown. (bb') In spc1 pak1 deficient embryos, actin remodeling goes uncontrolled. AP, AnteriorPosterior.

Figure 2 :

 2 Figure 2: Timedependent length of a KelvinVoigt model in different conditions. (ae) A KelvinVoigt system with mechanical plasticity introduced according to Eqs. (1, 4 discussed here, 6, 7), and predicted elongation change (ac) using Fc=0.7, three distinct values of β, and three disctint values of Fmuscles for each β, or (df) three distinct values of β, and three disctint values of Fmuscles for each β.

Movie 2 :Movie 3 :Movie 4 :Movie 7 :

 2347 Muscledependence of the retraction profile. Combined DIC timelapse movie of unc112(RNAi) and unc112(RNAi); spc1(RNAi) pak1(tm403) embryos. Scale bar: 10 µm. Elongation profile of vab-10b; sma-1 defective embryos. Combined DIC timelapse movies of vab10b(mc44); sma1(ru18) embryos. Scale bar: 10 µm. Elongation profile of vab-10b; spc-1 defective embryos. Combined DIC timelapse movies of the two populations of vab10b(mc44); spc1(RNAi) embryos. Scale bar: 10 µm. Movie 5: Severing proteins rescuing the retraction profile. Combined DIC timelapse movies of gsnl1(tm2730); spc1(RNAi) pak1(tm403) and viln1(ok2413); spc1(RNAi) pak1(tm403) embryos. Scale bar: 10 µm. Movie 6: Retraction profile of fhod-1; spc-1 defective embryos. Combined DIC timelapse movies of spc1(ra409) and fhod1(RNAi); spc1(ra409) embryos. Scale bar: 10 µm. Epithelial actin displacement in mutants. Fluorescence movie showing the displacement of actin filaments labelled with Pdpy7::lifeact::GFP in the epidermis in wildtype, pak1(tm403), spc1(RNAi) and spc1(RNAi) pak1(tm403) embryos. Time interval: 0.41s. Scale bar: 10 µm.

1

 1 Puatative β-tubulin folding cofactor D C (I) usp-5 Ortholog of human USP5 and USP13 C (II) Y19D2B.1 Structural constituent of cytoskeleton C Reproducible 50-100% enhanced defect* compared to wild-type Reproducible 20-50% enhanced defect* compared to wild-type Reproducible 5-20% enhanced defect* compared to wild-type

  † † † † † † † ‡ ‡ ‡ ‡ ‡ ‡ ‡ ‡ ‡ ‡ ‡ ‡ ‡* Positive controls (PAK-1 itself + its known interactors) Body-axis elongation constitutes a key step in animal development, laying out the final form of the entire animal. It relies on the interplay between intrinsic forces generated by molecular motors1-3 , extrinsic forces exerted by adjacent cells4-7 and mechanical resistance forces due to tissue elasticity or friction8-10 . Understanding how mechanical forces influence morphogenesis at the cellular and molecular level remains a challenge 1 . Recent work has outlined how small incremental steps power cell-autonomous epithelial shape changes1-3 , which suggests the existence of specific mechanisms that stabilize cell shapes and counteract cell elasticity. Beyond the twofold stage, embryonic elongation in Caenorhabditis elegans is dependent on both muscle activity 7 and the epidermis; the tension generated by muscle activity triggers a mechanotransduction pathway in the epidermis that promotes axis elongation7 . Here we identify a network that stabilizes cell shapes in C. elegans embryos at a stage that involves non-autonomous mechanical interactions between epithelia and contractile cells. We searched for factors genetically or molecularly interacting with the p21-activating kinase homologue PAK-1 and acting in this pathway, thereby identifying the α-spectrin SPC-1. Combined absence of PAK-1 and SPC-1 induced complete axis retraction, owing to defective epidermal actin stress fibre. Modelling predicts that a mechanical viscoplastic deformation process can account for embryo shape stabilization. Molecular analysis suggests that the cellular basis for viscoplasticity originates from progressive shortening of epidermal microfilaments that are induced by muscle contractions relayed by actin-severing proteins and from formin homology 2 domain-containing protein 1 (FHOD-1) formin bundling. Our work thus identifies an essential molecular lock acting in a developmental ratchet-like process.

Fig. 1 |Fig. 2 |

 12 Fig. 1 | Combined loss of PAK-1 and SPC-1 triggers muscle-dependent embryo retraction. a, C. elegans embryonic elongation requires a ROCK-dependent actomyosin force in lateral cells (blue) and actin-promoted stiffness in dorsoventral cells (yellow), followed by repeated muscle contractions (red flash), which induce a PAK-1-dependent mechanotransduction pathway. Open sections (bottom), muscle positions; A-P, anterior-posterior. b, Spinningdisc micrograph (top left) and kymographs (top right; yellow rectangle area from top left) of epidermis actin filaments (green) and muscle nuclei (red) in a wild-type twofold embryo, showing their concurrent displacement. Scale bar, 10 µm. Bottom, quantification of the area below the resulting displacement curves (pink box) (n = 11 embryos, 33 contractions). c, Local effect of a muscle contraction-relaxation cycle on epidermal actin filaments in a wild-type twofold embryo (timing shown above each panel). Yellow (relaxation), red (compression) and green (stretching) distances were measured between four landmarks (denoted 1-4). Left, 7.8 µm (1-2), 19.8 µm (2-3), 24.6 µm (3-4); middle, 9.4 µm (1-2), 13.6 µm (2-3), 26.2 µm (3-4); right, 8.0 µm (1-2), 19.2 µm (2-3), 25.0 µm (3-4). In b, c, the Pepidermis promoter is Pdpy-7. d-h, Elongation profiles (d) and DIC images showing the terminal phenotypes of unc-112 (RNAi) (e; n = 14 embryos), spc-1(ra409) (f; n = 8 embryos), spc-1(ra409) pak-1(tm403) (g; n = 8 embryos) and unc-112(RNAi) spc-1(ra409) pak-1(tm403) (h; n = 7 embryos). Scale bar, 17 μm. Colours in d correspond to genotypes in f-h. Pink box, period of muscle activity; bracket, extent of retraction. Data are mean ± s.e.m.

Fig. 3 |

 3 Fig. 3 | Muscle contractions are linked to severing of epidermal actin filaments. a-d, Spinning-disc images of epidermal actin filaments (Pdpy-7::LifeAct::GFP reporter) and quantification of bending angles in wild-type (n = 23 embryos, 101 contractions)(a, c) and spc-1(RNAi) pak-1(tm403) (n = 14 embryos, 131 contractions) (b, d) embryos at twofold-stage equivalent (kymographs in Extended Data Fig.5). Scale bar, 10 µm. e, Elongation profiles of spc-1(RNAi) (n = 8 embryos), spc-1(RNAi) pak-1(tm403) (n = 9 embryos), viln-1(ok2413); spc-1 (RNAi) pak-1(tm403) (n = 11 embryos) and gsnl-1(tm2370); spc-1(RNAi)

Fig. 4 |

 4 Fig. 4 | An actin-remodelling network providing mechanical plasticity ensures embryo elongation. a-c, Viscoplastic mechanical model of embryo elongation. The embryo is represented as a Kelvin-Voigt solid with spring stiffness k, resting length λ, viscosity η, submitted to forces F epidermis and F muscle , defined by equations (1) to (4). a, Wild-type case. An increasing resting length during stretching phases imparts mechanical plasticity. b, spc-1 pak-1 mutants. F epidermis progressively decreases. c, Comparison of experimental and predicted elongation curves using the constitutive equations (1) to (4). d, DIC snapshots at three time points of spc-1 deficient

Fig. 2 | 4 |

 24 PAK-1and SPC-1 colocalize with actin filaments. a, b, Distribution of PAK-1::mKate (a; n = 20 embryos) and SPC-1::GFP (b; n = 13 embryos) in a late embryo. Enlarged images of PAK-1 and SPC-1 showing a filamentous distribution in the dorsoventral epidermis similar to actin filaments. c, Fluorescence images of PAK-1::mKate (red) and SPC-1::GFP (green) (n = 20 embryos). The panel shows the colocalization image for the most-apical focal planes (top image), and full XZ (green panel) and YZ (red panel) projections. The level of co-localization is high based on Pearson's correlation coefficient (0.7-0.9, n = 20 embryos). The highest level of colocalization is detected at the apical cortex. d, Fluorescence images of Plin-26::VAB-10(ABD)::mKate (red) and SPC-1::GFP (green) (n = 8 embryos). The panel shows the colocalization image for the most-apical focal planes (top image), and full XZ (green panel) and YZ (red panel) projections. The level of colocalization is high based on Pearson's correlation coefficient (0.7-0.9, n = 8 embryos). The colocalization is detected almost exclusively at the apical cortex. The gene lin-26 drives expression in the epidermis; VAB-10(ABD) corresponds to the two actin-binding domains (calponin homology) of the protein VAB-10. Scale bar, 10 µm. Extended Data Fig. Changes in embryo diameter during elongation. a, b, Fluorescence micrographs of embryos expressing the Pepid::Lifeact::GFP construct in the epidermis at three elongation stages early, middle and late (corresponding to 1.7-fold, 2-fold and 3-fold equivalent stages in a wild-type embryo, respectively) for wild-type (a) and spc-1(RNAi) pak-1(tm403) embryos (b). Scale bar, 10 µm. The Pepid promoter corresponds to Pdpy-7. The yellow lines correspond to the segments used to measure the dorsoventral width of the V1 seam cell. c, d, Quantification of the average V1 cell circumferential width normalized to the initial width during elongation (c), and of the average dorsoventral circumferential width at the level of the V1 seam cell (d), which was calculated using the measured embryo length and V1 cell width, taking into consideration the conservation of the total embryo volume, in wild-type (early n = 38, mid n = 10, late n = 14), pak-1(tm403) (early n = 26, mid n = 8, late n = 20), spc-1(RNAi) (early n = 24, mid n = 26, late n = 18), spc-1(RNAi) pak-1(tm403) (early n = 22, mid n = 30, late n = 38), unc-112(RNAi) (early n = 8, mid n = 9, late n = 8), and unc-112(RNAi) spc-1(ra409) pak-1(tm403) (early n = 7, mid n = 12, late n = 17) embryos. Error bars, s.e.m. A notable feature of spc-1(RNAi) pak-1(

Extended Data Fig. 7 |

 7 Comparable retraction phenotypes after the combined loss of SPC-1 and PAK-1 or SPC-1 and FHOD-1. a, Principle of the retraction screen in a spc-1 mutant that identified fhod-1. b, DIC image of spc-1 deficient embryos after feeding on L4440 control (n = 21 hatchlings) or fhod-1(RNAi) (n = 25 hatchlings) bacteria, and quantification of spc-1(ra409) L1 hatchling body length after feeding. Data represent mean ± s.d. Two-sided paired t-test. c-j, Elongation curves and (d) corresponding DIC images showing the terminal phenotypes at hatching of wild type (d; n = 12 embryos), fhod-1(tm2363) (e; n = 10 embryos), fhod-1(RNAi) (f; n = 10 embryos), pak-1(tm403) (g; n = 11 embryos), fhod-1(RNAi) pak1(tm403) (h; n = 10 embryos), spc-1(RNAi) pak-1(tm403) (i; n = 8 embryos) and fhod-1(tm2363); spc-1(RNAi) (j; n = 9 embryos). Data in c represent mean ± s.e.m. Scale bar, 25 µm. Letter reSeArCH Extended Data Fig. 8 | PAK-1 and FHOD-1 form aggregates in spc-1(RNAi) loss of function. a, PAK-1::GFP localization in wild-type and spc-1(RNAi) embryos. Yellow box, area enlarged below the panel. Note the punctae in SPC-1 deficient embryos. b, FHOD-1 localization in wild-type and spc-1(RNAi) embryos. Note the aggregates (arrowheads). Note also that FHOD-1::GFP displayed a filamentous organization reminiscent of actin filaments. Scale bar, 10 µm.

-

  Equation of epidermal forc e

  ) where () is the value of the data elongation c urve at the time point i and () is the solution of the model interpolated at the time point i; g refers to the genotypes c onsidered for a fit. To minimize the c ost func tion, a C ovariance Matrix Adaptation Evolution Strategy (C MA-ES) algorithm was used 55 . The algorithm has an available MATLAB c ode at http://www.lri.fr/~hansen/c maes_inMATLAB.html.

(

  Subunit of the actin related protein of the conserved Arp2/3 complex C (III) arx-3 Subunit of the actin related protein of the conserved Arp2/3 complex C Novel protein that contains three divergent armadillo repeats C (II) spv-1 Ortholog of human GMIP C (I) tbcd-1 Puatative β-tubulin folding cofactor D C (I) usp-5 Ortholog of human USP5 and USP13 C (II) Y19D2B.1 Structural constituent of cytoskeleton C Reproducible 50-100% enhanced defect* compared to wild-type Reproducible 20-50% enhanced defect* compared to wild-type Reproducible 5-20% enhanced defect* compared to wild-type

Supplementary Table 7 |

 7 spc-1(-) pak-1(-) (no retraction phenotype) Not longer compared to spc-1(-) pak-1(-) (retraction phenotype) Results of model fit Values of the fitted parameters for the different genotypes

Most commonly mentioned genes in this work fhod1

	TIRFSIM	Total Internal Reflection Fluorescence Microscopy Structured Illumination
		Microscopy
	VBS	Vinculin Binding Site
	Y2H	Yeast Two Hybrid
	ZP	Zona Pellucida
	Common abbreviations for mutant phenotypes in C. elegans
	Dpy	Dumpy
	Let	Lethal
	Pat	Paralysed at twofold
	Sma	Small size
	CRISPR Unc	Clustered Regularly Interspaced Short Palindromic Repeats Uncoordinated movement
	DIC Vab	Differential Interference Contrast Variable abnormal Morphology
	DLG1	(Drosophila) DiscsLarge (homologue)1
	DNA	Deoxyribonucleic Acid
	D/V	Dorsal/Ventral
	ECM	Extracellular Matrix
	FA	Focal Adhesions
	FH	Formin Homology (domain)
	FRAP	Fluorescence Recovery After Photobleaching
	FRET	Förster Resonance Energy Transfer
	GAS2	GrowthArrestSpecific protein 2
	GBD	GTPase Binding Domain
	GFP GIT	Green Fluorescence Protein G proteincoupled receptor kinase InTeractor	..
	IF	Intermediate Filament
	L1L4	Larval stages of C. elegans development
	MHC	Myosin essential Heavy Chain
	MLC	Myosin essential Light Chain
	MSC	Mesenchymal Stem Cells
	MT	Microtubule
	MTOC	Microtubule Organizing Center
	NGM	Nematode Growth Medium
	NMYII	Nonmuscle MyosinII
	PAK	p21Activated Kinase
	PAM	Protospacer Adjacent Motif
	PCR	Polymerase Chain Reaction
	PH unc112	Plecktrin Homology (domain) encodes for a C. elegans dense body component, vertebrate kindlinhomologue
	PIP2	Phosphatidylinositol4,5bisphosphate mutants display a Pat phenotype: embryonic arrest due to muscle dysfunction and
	PIX	PAK interacting exchange factor paralyzation at the 2fold stage.
	PR	Plectin Repeat
	RLC vab10	Regulatory Light Chain (of nonmuscle myosinII) encodes for C. elegans spectraplakin.
	RNA	Ribonucleic Acid mutants have defects in embryonic elongation, body morphology, uterusvulva
	RNAi	RNA interference connection, and gonad arm migration, the animals have poor mating efficiency.
	ROCK	Rhoassociated Kinase
	ROI	Region Of Interest
	sgRNA	single guide RNA
	SH3	Src Homology (domain)
	SR	Spectrin Repeat (domain)

encodes for C. elegans formin. mutants are viable and fertile although they show some body wall muscle defects. gsnl1 encodes for C. elegans gelsolin. mutants are viable and fertile. pak1 encodes for C. elegans p21activated kinase1. mutants are viable and fertile, slight BMD (enlarged head) in L1 larvae. spc1 encodes for C. elegans αspectrin. mutants show embryonic lethality and fails to elongate beyond 2fold. sma1 encodes for C. elegans βHspectrin. mutants display a Sma phenotype with shortbody length. unc70 encodes for C. elegans βGspectrin. mutants are short and paralyzed; the defects develop gradually through the larval stages. However embryonic elongation is not affected. generates isoforms related either to plectin (VAB10A) or to microtubule actin cross linking factor plakins (VAB10B) that have distinct functions and localizations. viln1 encodes for C. elegans villin. mutants are viable and fertile.

Schematic diagrams of the villin superfamily.

  Representation of the domains structure for human supervillin, C. elegans VILN1, Dictyostelium protovillin, and mammalian villin and gelsolin. Adapted from[START_REF] Pope | Cloning, characterization, and chromosomal localization of human superillin (SVIL)[END_REF][START_REF] Liu | Distinct roles of four gelsolinlike domains of Caenorhabditis elegans gelsolinlike protein1 in actin filament severing, barbed end capping, and phosphoinositide binding[END_REF]

	GSNL-1 (C. elegans)	G1	G2	G3	G4
	Severing
	Capping
	PIP2 binding
	Actin binding	Ca sensitive 2+		Ca insensitive 2+
		G-actin binding		G/F-actin binding
	Gelsolin (mammals)	G1	G2	G3	G4	G5	G6
	Severing Figure 24:
	Capping
	PIP2 binding
	Actin binding	Ca sensitive 2+	Ca insensitive 2+		Ca sensitive 2+
		G-actin binding	F-actin binding		G-actin binding

Table recapitulating the different strategies used

		CRISPR strategy	Repair template cloned successfully	sgRNA	Injected worms in the	CRISPRs events in worms
	ACT1::GFP	Homology directed repair	Yes	Yes, in pDD162	Yes	Yes but the worms never showed any fluorescence
	ACT1::linker::GFP	Homology directed repair	Yes	Yes, in pDD162	Yes	Yes but the worms never showed any fluorescence
	GFP::ACT1	Homology directed repair	No	Yes, in pDD162	No
	GFP::linker::ACT1	Homology directed repair	Yes	Yes, in pDD162 and pML2840	Yes	Yes but the worms never showed any fluorescence
	ACT1::mMaple3	Homology directed repair	Yes	Yes, in pDD162	Yes	No
	ACT1::linker::mMaple3	Homology directed repair	Yes	Yes, in pDD162	No
	mMaple3::ACT1	Homology directed repair	Yes	Yes, in pDD162	No
	mMaple3::linker::ACT1	Homology directed repair	Yes	Yes, in pDD162	No
	SMA1::GFP	Homology directed repair	Yes	Yes, in pDD162	Yes	Yes. Strain viable and working well
	SPC1::GFP	Homology directed repair	Yes	Yes, in pML2840	No
	SPC1::mCherry	Homology directed repair	Yes	Yes, in pML2840	No
	SPC1::wrmScarlet	Homology directed repair	Yes	Yes, in pML2840	Yes	Yes, but wrmScarlet is not fluorescent in the embryo
	UNC70::mCherry	Selfexcising drug selection cassette	Yes	Yes, in pDD162	Yes	No, due to screening errors

Table 2 : Primary and secondary Yeast TwoHybrid (Y2H) screens.

 2

Table 5 : List of strains used in this work.

 5

Table 6 : List of Extrachromosomal constructs and Insertions used in this work.

 6

Table 1 | Primary enhancer RNAi screen in pak-1(-) background

 1

	* Defect refers to lethality and body morphology defects

Table 1 | Primary enhancer RNAi screen in pak-1(-) background

 1

	* Defect refers to lethality and body morphology defects
	(I) afd-1	(II) aak-1	(III) abce-1	(IV) arp-11	(V) air-1	(X) aakb-1
	arx-7	arp-1	abi-1	ced-5	cct-7	aakg-2
	aspm-1	C27H5.4	arf-1.2	dli-1	F14H3.12	abl-1
	chs-1	cacn-1	cct-5	dnc-1	gck-2	dyn-1
	col-53	cal-2	cct-6	dyci-1	knl-3	efn-3
	cpn-1	ccm-3	cls-1	eps-8	mig-6	F20B6.1
	cutl-13	cct-1	cls-2	frk-1	noca-1	frm-9
	dhc-1	cct-2	col-94	gex-2	pak-2	hpk-1
	dlc-6	cct-4	col-97	gex-3	par-1	ifa-2
	eak-6	cdc-25.4	cra-1	klp-10	rbx-1	kin-29
	egg-5	cpn-2	cyk-4	klp-11	spas-1	lam-2
	egg-6	dep-1	daf-4	klp-5	sun-1	lin-18
	ekl-4	ebp-2	fem-2	let-60	syx-5	lpr-3
	erm-1	eff-1	frm-2	let-92	unc-112	nck-1
	fhod-1	egg-3	gei-4	M116.5	unc-70	pak-1
	gei-17	evl-20	gop-3	nsp-1		pfn-2
	gfi-2	F59A6.5	ina-1	par-5		pfn-3
	gsa-1	frm-5.2	inft-1	pfd-1		pqn-34
	gsk-3	glb-12	kin-18	pld-1		unc-97
	gsp-3	gpb-1	klp-6	pmk-2
	gsp-4	klp-1 / unc-104
	kca-1	klp-17
	lim-9	let-268
	mel-26	lrr-1
	mfap-1	max-2
	mom-5	mel-11
	nab-1	mig-5
	ned-8	mlt-8
	nkb-1	nsy-1
	nmy-2	pfd-2
	npp-4	pink-1
	ocrl-1	pir-1
	pes-7	ptc-3
	pfd-6	ptp-2
	ppk-1	ptp-3
	rga-2	saps-1
	rsa-1	scpl-2
	smgl-1	sds-22
	spd-1	spdl-1
	tba-2	tac-1
	ttx-7	tba-4
	unc-35	unc-52
	unc-59	vab-19
	unc-73	vab-9
	unc-94	vhp-1
	vab-10	vps-11
	viln-1	vps-32
	vps-20	W0761.1
	wve-1	zyg-9

Table 2 | Primary and secondary Y2H screens

 2

	Global Predicted Biological Score (categories computed and established by Hybrigenics, to assess the interaction reliability)
	D	Moderate confidence in the interaction
		(either due to false-positive interactions or due to interactions that are hardly detectable by the Y2H technique)
					Strongest candidates
					(Prey library: C. elegans embryo)
					Secondary Yeast Two Hybrid Screen
	(Bait: CePAK-1 N-terminal amino acids: 1-294)		† Bait I: CeSPC-1 SR8-10(aa:796-1243)
					‡ Bait II: CeSPC-1 SH3 (aa:986-1041)
					§ Common hits using Bait I and Bait II
	Interactor	Protein	Global	Interactor	Protein	Global
	candidate	Function	PBS	candidate	Function	PBS
	SPC-1	α-spectrin	A	PAK-1	p21-activated kinase
	F47B10.1	β-chain succinyl-co-A ligase		LIM-8	LIM domain muscle
						component
	CHW-1	RhoU homolog		F44.E2.3	ARGLU1 ortholog
	GCK-1	STE20-family kinase		CSN-5	COP9-subunit ortholog
						E3 ubiquitin ligase interactor
	NCK-1	NCK adaptor		DEB-1	Vinculin
	PIX-1 *	ARHGEF7 homolog β-Pix		DnaJ	DNAJ/ZRF1/MPP11 ortholog ribosome-associated chaperone
	CDC-42 *	Small GTPase		CYLD-1	Human CYLD1 ortholog
						NF-κβ signalling interactor
	PAK-1 *	P21-activated Ser/Tre kinase		VAB-3 /	Homeodomain protein PAX6
			(multiple hits through kinase domain)		VAR-1	ortholog
	CED-10 *	Rac-1 / Small GTPase		GRL-4	Hedgehog-like protein
	POD-2	Predicted acetyl-coA		UNC-34	Enabled/VASP homolog
			carboxylase
	Y39E4A.3	Transketolase		T04F8.6	Human ninein and ninein-like
						(GSK3B interactor) ortholog
	EEL-1	HECT-ubiquitin ligase		ALR-1	Human ARX (aristaless) ortholog
						homeodomain transcription factor
	NPP-21	Nuclear pore protein		ATN-1	α-actinin homolog
	TAG-143	Transcription factor		MMCM-1	Methylmalonyl-CoA mutase
	UNC-44	Ankyrin		UNC-70	βG-spectrin
	HIPR-1	SLA2 and Hip related		VAB-10	Spectraplakin
	T05C1.4	Conserved calmodulin-		F26A10.2	Zinc-finger containing protein
			binding TFs
	Y53F4B.13 RNA methyltransferase		F43C1.1	Human PHLPP1&PHLPP2 ortholog
	PTP-3	LAR-like receptor tyr-protein		ALP-1	Enigma family member ALP
			phosphatase			(α-actinin associated LIM Protein) ortholog
	COGC-6	Conserved Oligomeric Golgi		CIT-1.2	Cyclin T ortholog
			(COG) Component
	DAF-21	Hsp90 molecular chaperone		FLH-1	FLYWCH zinc finger
			family member			transcription factor homolog
	GCK-1	STE20-family kinase		SHW-1	Human KCNC3 voltage-gated
	variant				SHaW family potassium channel ortholog

Table 1 | Enhancer RNAi screen in a pak-1(-) mutant

 1

	* Defect refers to lethality and body morphology defects
	(I) afd-1	(II) aak-1	(III) abce-1	(IV) arp-11	(V) air-1	(X) aakb-1
	arx-7	arp-1	abi-1	ced-5	cct-7	aakg-2
	aspm-1	C27H5.4	arf-1.2	dli-1	F14H3.12	abl-1
	chs-1	cacn-1	cct-5	dnc-1	gck-2	dyn-1
	col-53	cal-2	cct-6	dyci-1	knl-3	efn-3
	cpn-1	ccm-3	cls-1	eps-8	mig-6	F20B6.1
	cutl-13	cct-1	cls-2	frk-1	noca-1	frm-9
	dhc-1	cct-2	col-94	gex-2	pak-2	hpk-1
	dlc-6	cct-4	col-97	gex-3	par-1	ifa-2
	eak-6	cdc-25.4	cra-1	klp-10	rbx-1	kin-29
	egg-5	cpn-2	cyk-4	klp-11	spas-1	lam-2
	egg-6	dep-1	daf-4	klp-5	sun-1	lin-18
	ekl-4	ebp-2	fem-2	let-60	syx-5	lpr-3
	erm-1	eff-1	frm-2	let-92	unc-112	nck-1
	fhod-1	egg-3	gei-4	M116.5	unc-70	pak-1
	gei-17	evl-20	gop-3	nsp-1		pfn-2
	gfi-2	F59A6.5	ina-1	par-5		pfn-3
	gsa-1	frm-5.2	inft-1	pfd-1		pqn-34
	gsk-3	glb-12	kin-18	pld-1		unc-97
	gsp-3	gpb-1	klp-6	pmk-2
	gsp-4	klp-1 / unc-104
	kca-1	klp-17
	lim-9	let-268
	mel-26	lrr-1
	mfap-1	max-2
	mom-5	mel-11
	nab-1	mig-5
	ned-8	mlt-8
	nkb-1	nsy-1
	nmy-2	pfd-2
	npp-4	pink-1
	ocrl-1	pir-1
	pes-7	ptc-3
	pfd-6	ptp-2
	ppk-1	ptp-3
	rga-2	saps-1
	rsa-1	scpl-2
	smgl-1	sds-22
	spd-1	spdl-1
	tba-2	tac-1
	ttx-7	tba-4
	unc-35	unc-52
	unc-59	vab-19
	unc-73	vab-9
	unc-94	vhp-1
	vab-10	vps-11
	viln-1	vps-32
	vps-20	W0761.1
	wve-1	zyg-9

Table 2 |

 2 Primary and secondary Y2H screens Yeast two-hybrid screening performed by Hybrygenics Services (Paris, France) using the N-terminus of PAK-1 up to the kinase domain as a bait (Primary Screen), or two different regions of the SPC-1 protein spanning the SH3 domain (Secondary Screens). The table recapitulates the strongest interactions.DModerate confidence in the interaction (either due to false-positive interactions or due to interactions that are hardly detectable by the Y2H technique)Global Predicted Biological Score (categories computed and established by Hybrigenics, to assess the interaction reliability)

				Strongest candidates
				(Prey library: C. elegans embryo)
				Secondary Yeast Two Hybrid Screen
	(Bait: CePAK-1 N-terminal amino acids: 1-294)		† Bait I: CeSPC-1 SR8-10(aa:796-1243)
				‡ Bait II: CeSPC-1 SH3 (aa:986-1041)
	* Positive controls (PAK-1 itself + its known interactors)	§ Common hits using Bait I and Bait II
	Interactor	Protein	Global	Interactor	Protein	Global
	candidate	Function	PBS	candidate	Function	PBS
	SPC-1	α-spectrin	A	PAK-1	p21-activated kinase
	F47B10.1	β-chain succinyl-co-A ligase		LIM-8	LIM domain muscle
					component
	CHW-1	RhoU homolog		F44.E2.3	ARGLU1 ortholog
	GCK-1	STE20-family kinase		CSN-5	COP9-subunit ortholog
					E3 ubiquitin ligase interactor
	NCK-1	NCK adaptor		DEB-1	Vinculin
	PIX-1 *	ARHGEF7 homolog β-Pix		DnaJ	DNAJ/ZRF1/MPP11 ortholog ribosome-associated chaperone
	CDC-42 *	Small GTPase		CYLD-1	Human CYLD1 ortholog
					NF-κβ signalling interactor
	PAK-1 *	P21-activated Ser/Tre kinase		VAB-3 /	Homeodomain protein PAX6
		(multiple hits through kinase domain)		VAR-1	ortholog
	CED-10 *	Rac-1 / Small GTPase		GRL-4	Hedgehog-like protein
	POD-2	Predicted acetyl-coA		UNC-34	Enabled/VASP homolog
		carboxylase
	Y39E4A.3	Transketolase		T04F8.6	Human ninein and ninein-like
					(GSK3B interactor) ortholog
	EEL-1	HECT-ubiquitin ligase		ALR-1	Human ARX (aristaless) ortholog
					homeodomain transcription factor
	NPP-21	Nuclear pore protein		ATN-1	α-actinin homolog
	TAG-143	Transcription factor		MMCM-1	Methylmalonyl-CoA mutase
	UNC-44	Ankyrin		UNC-70	βG-spectrin
	HIPR-1	SLA2 and Hip related		VAB-10	Spectraplakin
	T05C1.4	Conserved calmodulin-		F26A10.2	Zinc-finger containing protein
		binding TFs
	Y53F4B.13 RNA methyltransferase		F43C1.1	Human PHLPP1&PHLPP2 ortholog
	PTP-3	LAR-like receptor tyr-protein		ALP-1	Enigma family member ALP
		phosphatase			(α-actinin associated LIM Protein) ortholog
	COGC-6	Conserved Oligomeric Golgi		CIT-1.2	Cyclin T ortholog
		(COG) Component
	DAF-21	Hsp90 molecular chaperone		FLH-1	FLYWCH zinc finger
		family member			transcription factor homolog
	GCK-1	STE20-family kinase		SHW-1	Human KCNC3 voltage-gated
	variant				SHaW family potassium channel ortholog

N A t U r e | www.nature.com/nature

Acknowledgements

The authors thank A. Spang, S. Grill, Y. Bellaïche and R. Voituriez for critical comments on the manuscript and M. Gettings for improving the English. We also thank the Caenorhabditis Genetics Center (funded by the NIH Office of Research Infrastructure Programs P40 OD010440) and National BioResource Project at Tokyo Women's Medical University for strains, the IBPS Imaging Facility for advice. This work was supported by the Agence Nationale pour la Recherche, the European Research Council (grant no. 294744), Israel-France Maïmonide exchange program grants, and installation funds from the Centre National de la Recherche Scientifique (CNRS) and University Pierre et Marie Curie (UPMC) to M.L. A.L. was supported by a fellowship from the Fondation pour la Recherche Médicale (FDT201805005501). This work was also made possible by institutional funds from the CNRS, University of Strasbourg and UPMC, the grant ANR-10-LABX-0030-INRT, which is a French State fund managed by the Agence Nationale de la Recherche under the framework programme Investissements d'Avenir labelled ANR-10-IDEX-0002-02 to the IGBMC. The work of P.M. and E.B. was partly supported by the Agence Nationale de la Recherche (contract ANR-11-EQPX-0029 Morphoscope2), the work of S.O. was partly supported by the National Institutes of Health (grant AR048615).

Function Strength of interaction Shorter compared to spc-1(-) Not shorter compared to spc-1(-) Table 4 | Secondary enhancer RNAi screen in spc-1(ra409) background (I) fhod-1 (I) hmr-1 (I) hmp-2 (II) cdc-42 (II) spdl-1 (II) vps-11 (III) mtm-3 (III) mlc-5 (IV) dnc-1 (IV) epi-1 (I) goa-1 (I) kin-10 (I) mec-8 (I) nmy-2 (I) unc-94 (II) cap-2 (II) evl-20 (II) spv-1 (II) unc-52 (III) klp-7 (III) mup-4 (IV) cap-1 (IV) eps-8 (IV) frk-1

Data availability

Source Data for Figs. 1d, 4d, e and Extended Data Figs. 1b, d, k, 3b, c, 4c, d, 5d, e, l, 7a, b, 9f, as well as numbers of replicates and P values (where applicable) for all figures are provided in the online version of the paper.

Code availability

All MATLAB scripts used for the present analysis are available upon reasonable request.

V. The organization and remodeling of actin filaments is a key element of the retraction

V. 1. Spinningdisk characterization of the actin disorganization in spc1 pak1 embryos

The simplest interpretation of the retraction phenotype observed in spc1 pak1 embryos is that a cellular structure maintaining embryo shape fails to emerge or collapses in spc1 pak1 double mutants once muscles contract. Two arguments suggest that this structure corresponds to the bundles of 35 actin filaments present in the dorsoventral (D/V) epidermis (Costa et al., 1997;Priess and Hirsh, 1986). First, SPC1/αspectrin and its binding partner SMA1/ßHspectrin (apical) or UNC 70/ ßGspectrin (basolateral) form an actinbinding heterotetramer colocalizing with actin [START_REF] Praitis | SMA1 spectrin has essential roles in epithelial cell sheet morphogenesis in C. elegans[END_REF] and partially with PAK1 in epidermal cells (Fig. 4). Second and foremost, treating C. elegans embryos with the actindepolymerizing drug cytochalasinD induces a retraction phenotype very similar to that presented herein (Priess and Hirsh, 1986).

Thus, with the help of Teresa Ferraro, engineer in the lab, we characterized actin filaments organization, by imaging a LifeAct::GFP probe expressed specifically in the epidermis under the promotor dpy7. In C. elegans, the contribution of actin to embryonic morphogenesis has been reported from the end of gastrulation [START_REF] Marston | Actinbased forces driving embryonic morphogenesis in Caenorhabditis elegans[END_REF]. Actin forms a meshwork near the epidermal cortex but prior to embryonic elongation it rearranges to form circumferential, parallel bundles first in the D/V cells, followed by its rearrangement in the lateral cells. Once the embryonic elongation is completed, the circumferential bundles disassemble (Priess and Hirsh, 1986). Thus, we first performed some texture analysis (Fig. 9aa'') on spinningdisk images. We chose manually ROIs of a constant size in the D/V area for all genotypes. On these ROIs we performed a Fourier transform analysis with a high pass filter to select only small structures. After this treatment, the ROI were either binarized and fit by ellipses to extract the continuity of the actin filaments or directly used to measure the distribution of cable orientation (Fig. 9a'''). These analyses were done on anesthetized embryos (put to sleep by oxygen deprivation through a high concentration of bacteria) at different stages (1.7fold, 2fold and 3fold) to get higher resolution of the actin compared to live imaging.

Segmentation analysis of the fluorescence signal associated with actin filaments in the D/V epidermis revealed more discontinuity in spc1 pak1 double deficient embryos (Fig. 9dd''') compared to the control genotypes (Fig. 9ac'''). Moreover, Fourier transform analysis indicated that their degree of anisotropy relative to the circumferential axis was abnormal (Fig. 9d''d''').

APPENDIX I.

Captions for movies and tables

An actinbased viscoplastic lock ensures progressive body axis elongation

Author contributions M.L. conceived the project. A.L. performed most experiments with initial contributions from G.P. T.F. conceived the modelling, F.L. generated the FHOD-1 variants and the screen reported in Supplementary Table 3, P.M. and E.B. helped with TIRF-SIM imaging, T.F. and J.P. performed image analysis, C.G. shared data from a related screen, S.K. helped with the spc-1(ra409) mini-RNAi screen, D.R. provided technical assistance and S.O. provided the outcrossed gsnl-1 and viln-1 mutants. M.L. wrote the manuscript, and all authors commented and proofread it (except S.K., who was an intern), A.L. assembled figures, T.F. conceived and wrote the supplementary mathematical modelling material and F.L. prepared the Methods section.

Competing interests

The authors declare no competing interests.

Additional information

supplementary information is available for this paper at https://doi.org/ 10.1038/s41586-019-1509-4.

Correspondence and requests for materials should be addressed to M.L. Peer review information Nature thanks Edwin Munro, Bruce Vogel and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Reprints and permissions information is available at http://www.nature.com/ reprints.

Letter reSeArCH

Extended Data Fig. 1 | Genes required to maintain embryonic elongation. a, RNAi screen in a pak-1 mutant identified spc-1 as an enhancer (Supplementary Table

Letter reSeArCH

Extended Data Fig. 3 | Actin-filament continuity and orientation at three elongation stages. a, d-i, Epidermal actin filaments visualized with the Pdpy-7::LifeAct::GFP reporter construct in wild type (a), pak-1(tm403) (d), spc-1(RNAi) (e), spc-1(RNAi) pak-1(tm403) (f), unc-112(RNAi) (g), fhod-1(tm2363) (h) and fhod-1(tm2363) spc-1(RNAi) (i) at midelongation (twofold equivalent) stage. Yellow rectangle, ROI. Scale bar, 10 µm. ROI after binarization (green) and major axis detection (red) (a, top middle, d-i, bottom), based on three steps of image treatment for continuity and orientation analysis (a, right). Actin continuity: distribution of actin segments based on their length (a, bottom middle). b, Quantification of actin-filament continuity; the graph represents the length (in pixels) along the circumferential axis of actin filaments in early, mid and late (corresponding to 1.

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Sample size

Sample size was determined by checking the stability of the standard deviation.

Data exclusions For Figure 1, we excluded all embryos for which the simultaneous tracking of actin and muscles nuclei was not possible.

For Figure 2, we excluded out of focus embryos or blurred embryos due to their fast movements. For Extended data 3, 4, 5, 8 and 9, we excluded all the out of focus embryos. For Extended data 9, we excluded embryos for which we could not track a full cycle of contractions.

For others figures, nothing was excluded.

Replication

Data were replicated at least 3 independant times.

Randomization We did not use randomization.

Blinding

For Supplementary 3 and Supplementary In the format provided by the authors and unedited.

Supplementary Table 3 | Secondary RNAi screen in spc-1(ra409) pak-1(tm403) background Additional RNAi screen in a spc-1(ra409) pak-1(tm403) mutant maintained by an exctrachromosomal spc-1(+)::GFP transgene of 13 actin related proteins from the Ahringer RNAi library that were recently reported to modulate actin remodeling in the early embryo (see text).

(I) viln-1 Supplementary Table 4 | Secondary RNAi screen in spc-1(ra409) background Additional RNAi screen in a spc-1(ra409) mutant maintained by an exctrachromosomal spc-1(+)::GFP transgene. Genes that gave the strongest defects in the initial RNAi screen (Supplementary Table 1) were tested again.