Keywords: actin filament assembly and disassembly actin, formin, fascin, 𝛼-actinin, cofilin, filopodia, stress fibers, bilayer, microfluidics, fluorescence microscopy, fluorescence polarization microscopy, electron microscopy Jahnavi C -doctoral thesis actine, formine, fascin, 𝛼-actinine, cofiline, filopodia, fibres de stress, bicouche, microfluidique, microscopie de fluorescence, microscopie de polarisation de fluorescence, microscopie électronique Jahnavi

en français

Dans les cellules, le cytosquelette, composé de filaments d'actine, de microtubules et des filaments intermédiaires, joue un rôle pour déformer la cellule, lui permettre de transmettre les contraintes mécaniques venant de l'extérieur.

L'actine est l'une des protéines les plus abondantes dans les cellules. En fonction des stimuli dans les cellules, les monomères d'actine s'assemblent en filaments hélicoïdaux de manière très dynamique. Les filaments d'actine peuvent former des réseaux en s'interconnectant. Selon le contexte, différentes architectures d'actine sont assemblées telles que les lamellipodes, les filopodes, les fibres de stress,...Les filopodes sont des protubérances cellulaires en forme de doigts, constitués de filaments d'actine parallèles regroupés en faisceaux et capables d'exercer une force de poussée sur la membrane ; les fibres de stress sont des faisceaux d'actine de polarité mixte, qui peuvent être mis sous tension grâce à la présence de moteurs moléculaires appelés myosines.

L'interaction entre les signaux biochimiques et mécaniques orchestre l'assemblage ou le désassemblage rapide des filaments d'actine. Cette réorganisation des filaments s'effectue principalement à l'aide de protéines de liaison à l'actine (ABP). Des centaines d'ABP ont été découvertes à ce jour. La manière dont ces ABP interagissent et se régulent mutuellement dans l'espace et dans le temps au sein de différents réseaux est un champ de recherche très actif.

En tant que polymères semi-flexibles, ils peuvent résister à des forces de tension allant jusqu'à ~200 pN sans casser, mais flambent en compression à faible force. Cependant, lorsque les filaments sont interconnectés à l'aide crosslinkers, tels que la fascine, l'𝛼-actinine, la fimbrine ou l'espin, ils créent des faisceaux ou des réseaux plus rigides et résistent mieux à la contrainte.

La manière dont l'activité des protéines régulatrices peut être affectée par l'interconnexion des filaments dans un réseau n'est pas entièrement comprise et reste un défi à étudier. Cette question peut être abordée de différentes manières : dans des cellules ou par la reconstitution in vitro à partir de protéines purifiées, chacun avec leurs avantages et inconvénients.

), j'ai pu étudier comment l'activité de la formines et de la cofiline sont affectées lorsqu'elles agissent sur des faisceaux induits par la fascine ou l'alpha-actinine. Fig 1. Représentation schématique des réseaux d'actine réticulés par les ABP. A) faisceaux réticulés par la fascine, allongés par des formines à ancrage lipidique B) désassemblage des faisceaux par la cofiline. Imposition de contraintes aux filaments et aux formins, avec réticulation par fascin et ancrage lipidique respectivement. Ces contraintes affectent l'activité des formines ABP et de la cofiline. Remarque: il s'agit d'esquisses simplifiées d'un réseau. Impact de l'architecture du réseau sur l'activité des formines Mon objectif est d'étudier comment l'activité de la formine est modifiée lorsque la formine est ancrée. La formine est une protéine dimérique qui se lie au bout barbé et qui, en présence de profiline, accélère sa vitesse d'allongement. Pour ce faire, la formine suit de manière processive l'extrémité barbée des filaments d'actine. J'ai employé différentes stratégies d'ancrage des formines afin de restreindre leur liberté de rotation. De plus, la restriction de la rotation des filaments par leur mise en faisceau par la fascine peut conduire à la génération d'un couple et entraîner une diminution de la vitesse d'élongation et de la processivité de la formine (Suzuki et al., 2020). Nous nous attendons à ce que ce comportement ne s'extrapole pas de manière simple pour des faisceaux de plus grande taille, car les filaments sont disposés selon les mailles d'un réseau hexagonal par la fascine, et sont connectés à plusieurs voisins. Dans ce cas, le "sur-enroulement" induit par la mise en faisceau pourrait avoir un impact sur l'activité de la formine. 1. Les filaments, ou les formines, à la périphérie ou au coeur du réseau pourraient être contraints différemment. 2. L'orientation de la formine/du faisceau par rapport à la surface pourrait également jouer un rôle important sur l'activité de la formine. 3. L'ancrage à une surface fluide, une bicouche lipidique, permet de fournir un réservoir de formines disponibles pour se lier aux extrémités barbées des filaments disponibles après le départ d'une formine. Notre objectif est donc d'étudier l'activité des formines en fonction de la densité de formines, la taille du faisceau, sa vitesse d'élongation, etc. Cette étude a été publiée dans (Suzuki et al., 2020). Nous avons observé que les vitesses d'allongement des filaments par des formines ancrées étaient proches des vitesses pour des formines non ancrées. De plus, les taux de détachement des formines n'ont pas été affectés, sauf dans la condition où les formines étaient ancrées par leur côté FH2 à une surface lipidique. Dans ce cas, nous observons une augmentation des taux de détachement 2,5 fois supérieures. Cette configuration correspond à la condition où la distance entre le FH2 et la surface est sensiblement plus courte que dans les autres cas. Notre interprétation est que ce lien plus court augmente la fréquence de contact de la formine avec la surface et favorise son détachement.

Pour étudier comment l'activité des formines sera affectée dans des faisceaux de fascines plus grands, nous avons adapté le type de motifs utilisés dans Suzuki et al, 2020 et nous les avons changés en cercles de 2 ou 5 µm de diamètre. Nous avons également utilisé des billes comme reconstituer les faisceaux d'actine qui supportent les filopodes ('fascin bundles'), ou les fibres de stress d'actine ('𝛼-actinin bundles'), nous avons étudié les détails moléculaires impliqués dans l'activité de la cofiline sur les faisceaux.

encouraging me to learn new things to try for the project, for your invaluable support, for sharing your extensive knowledge both scientific and experimental, and for criticizing the results to shape this project better. You were considerate and helped me to stay focused when the road got tougher during the times of pandemic. Thank you Guillaume also for your close supervision, for invaluable insights and comments throughout the project. Your scientific explanations always brought the clarity necessary for the project. It has been a fantastic experience being in the lab both professionally and personally and I am grateful for such warm and welcoming people.

Next, I would like to thank all the present and past members of the GRAJ lab. I am extremely grateful to Hugo and Emiko for their willingness and enthusiasm in sharing the knowledge when I started either the cofilin or formin projects. Thanks, Hugo for being my cofilin guru and my go-to person for all the questions related to the experiments or analysis. I am always thankful for your practical suggestions and enjoyed the music during the experiments. I am also more than thankful to Emiko for all her knowledge transfer when I first started in the lab and for the wonderful times both in and out of the lab. I am also grateful to Bérengère , Wendy, and Sandy for all the purified proteins throughout the years, for being kind and helping me with the protein labeling. I also like to thank Bérengère for the wonderful times in the lab, teaching me new French words, and the delicious cookies.

Especially, I am also thankful to Yan for being my go-to person for questions related to structures and proteins and for being a great friend. Thank you, Veronique, for the discussions related to filopodia and chocolates. Thank you, Zeineb, for all the formin-related discussion and for being very kind to me. Thank you Heliciane for your cheerful disposition and helping nature. Also, I very much appreciate Léana for your help with the experiments and Foad for keeping up scientific enthusiasm in the lab. I wish you both good luck with your thesis. I had the pleasure of sharing the office with Cécile and Quang. Thank you both for all the interesting discussions about science and encouragement during my thesis writing. Once again thank you all members for all the support and checking up on me during the pandemic.

My appreciation also goes to my family and for their support. Last, but not least I am also extremely grateful to Sudheer for being an incredible partner and for all the encouragement. support d'ancrage des lipides. Nous avons ensuite essayé de mieux orienter les filaments allongés par rapport à la surface lipidique afin qu'ils correspondent mieux à la situation physiologique. Pour ce faire, nous avons fabriqué les GUVs avec des lipides fonctionnels. Dans tous ces cas, il a été très difficile d'obtenir la bonne quantité de formines actives à la surface. De plus, des problèmes de stabilité des faisceaux au point aval de la bille dans nos expériences microfluidiques ont rendu les observations difficiles. Il est intéressant de noter que ces instabilités étaient provoquées par l'écoulement microfluidique qui est un écoulement laminaire.

Comment la cofiline désassemble les filaments en faisceaux

La désassemblage des filaments d'actine par la cofiline a été largement étudié depuis 20 ans.

Cependant, ces études n'ont été faites que sur des filaments individuels et isolés les uns des autres. Dans les cellules, l'actine s'assemble en réseaux et l'impact de l'architecture du réseau sur son désassemblage n'est pas bien compris.

La cofiline en se liant aux côtés des filaments d'actine, nucléée et allonge des domaines. Ces domaines peuvent induire la fragmentation des filaments d'actine, la cassure ayant lieu aux bords des domaines. Jusqu'à présent, une seule étude s'est penchée sur la question de savoir comment la présence de la fascine affecte l'activité de la cofiline : grâce à des approches de reconstitution in vitro, l'étude a montré que la cofiline avait une activité globale de liaison réduite aux filaments en faisceaux, mais que le désassemblage de l'actine était accéléré par rapport aux filaments individuels [START_REF] Breitsprecher | Cofilin cooperates with fascin to disassemble filopodial actin filaments[END_REF]. Une autre étude montre de manière intéressante que des filaments intermédiaires uniquement par la seule présence d'un 'crowding agent' qui induit des forces de déplétion en volume résistent à l'activité de fragmentation de la cofiline (Michelot et al., 2007).Ces deux études montrent des résultats qui ne sont pas faciles à réconcilier. Ceci nous a incité à faire des expériences pour étudier plus en profondeur le désassemblage des filaments en faisceaux par la cofiline et mieux déchiffrer les détails moléculaires sous-jacents.

Nous avons observé que l'activité de la cofiline est différente sur les filaments uniques en présence de différents crosslinker, la fascine ou l'𝛼-actinine. En présence de fascine, l'activité de la cofiline sur les filaments uniques n'est pas affectée. Cependant, ce n'est pas le cas en présence de 𝛼-actinine. La nucléation des domaines de cofiline, les vitesses de croissance et les taux de fragmentation des domaines étaient plus lents sur les filaments uniques en présence d'𝛼-actinine.

Cela pourrait être dû au fait que l'𝛼-actinine soit une protéine dimérique flexible qui lui permet de se lier aux filaments isolés uniques. Conformément aux rapports précédents, nous montrons que la 𝛼-actinine marquée se lie aux filaments isolés (Winkelman et al., 2014[START_REF] Hampton | Novel Structures for α-Actinin:F-Actin Interactions and their Implications for Actin-Membrane Attachment and Tension Sensing in the Cytoskeleton[END_REF].

Nous avons constaté que la capacité de la cofiline à nucléer un domaine sur des faisceaux de filaments induits par la fascine est plus lente que sur un filament individuel. Pour les faisceaux de deux filaments, le taux de nucléation des domaines est six fois plus lent. Plus largement, le taux de nucléation des domaines de cofiline sur les faisceaux dépend fortement du nombre de filaments formant le faisceau et de la concentration de fascine qui viennent saturer les sites de liaison à la surface des filaments. Ces résultats impliquent que plus le faisceau est grand, plus il est difficile pour la cofiline de nucléer des domaines. Ces résultats soutiennent la théorie selon laquelle les faisceaux sont protégés contre la fixation de la cofiline, précédemment proposée par des approches moins résolues [START_REF] Yang | Mammalian CARMIL Inhibits Actin Filament Capping by Capping Protein[END_REF]Michelot et al., 2007). Lorsque les filaments sont regroupés en faisceaux par l'𝛼-actinine, la distance inter filamentaire est plus importante que dans le cas de la fascine (environ 36 nm contre 8 nm seulement). Les filaments réticulés par l'alpha-actinine sont plus flexibles que ceux de la fascine, ce qui affecte différemment la capacité de liaison de la cofiline. Nos résultats montrent en effet que la nucléation des domaines de cofiline sur les faisceaux de 𝛼-actinine est moins diminuée par rapport aux faisceaux de fascine.

Pour les deux crosslinkers, nous observons que la vitesse de croissance des domaines de cofiline est diminuée par rapport à celle observée sur les filaments individuels, d'un facteur 2. De façon inédite, nous rapportons ici que la cofiline déplace la fascine des faisceaux et induit leur détricotage en portion de filaments individuels, localement. De manière tout aussi intéressante, nous avons constaté que la 𝛼-actinine n'est pas déplacée des faisceaux par la croissance des domaines de cofiline. Ces différentes observations impliquent que les faisceaux sont désassemblés par la cofiline par des mécanismes qui dépendent du crosslinker. À l'aide de l'intensité de fluorescence des domaines de cofiline, nous avons identifié la présence de deux domaines de cofiline se chevauchant sur les faisceaux avec deux filaments. En simulant, dans un modèle simple, l'apparition de ces domaines de cofiline qui se chevauchent, nous avons pu mesurer le taux de nucléation du second domaine de cofiline. Ce taux est fortement augmenté par rapport à la nucléation du premier domaine de cofiline. Cette augmentation peut provenir d'une sur-torsion du second filament induite par la croissance du premier domaine de cofiline.

Cela peut être suffisant pour conduire à un état de torsion du second filament qui augmente fortement l'affinité de la cofiline.

Nous avons pu également observer temporellement l'étape intermédiaire, pour 60% de nos observations, au cours de laquelle un domaine de cofiline fragmente un filament avant que le second domaine par fragmentation ne conduise à la fragmentation complète du faisceau. Ces observations nous permettent de mesurer le taux de fragmentation des domaines de cofiline et dire qu'il est du même ordre de grandeur que celui observé sur les filaments individuels. Cela semble indiquer que le départ de la fascine empêche toute accumulation de couple de torsion pour les filaments d'actine (Wioland et al., 2019b). Dans l'ensemble, pour les faisceaux de 2 filaments, même si la nucléation d'un deuxième domaine de cofiline sur le filament voisin est fortement accélérée, au moins deux événements de fragmentation du filament par la cofiline doivent se produire pour que le faisceau soit entièrement brisé en deux segments. Ceci est suffisant pour offrir une certaine protection au faisceau par rapport aux filaments uniques. Si l'on extrapole pour des faisceaux de taille plus importante, c'est-à-dire de 10 à 20 filaments, comme dans les filopodes, cette "protection" augmente considérablement, principalement en raison du taux de nucléation des domaines de cofiline qui décroît rapidement avec la taille du faisceau.

Nous nous sommes demandé si l'augmentation de l'hélicité des filaments lorsqu'un domaine de cofiline est nucléé sur un premier filament d'un faisceau de filaments pouvait induire une augmentation de l'hélicité locale du ou des filaments voisins. Nos résultats, obtenus par polarisation de fluorescence en molécule unique et par EM à coloration négative, soutiennent l'hypothèse d'une sur-torsion locale du faisceau par la cofiline. Avec nos études EM, nous avons observé que les plus petits faisceaux étaient tressés alors que des faisceaux plus gros étaient séparés en plus petits faisceaux (taille 2 à 4 filaments).

Les études relatives à la sur-torsion des faisceaux rapportés ci-dessus pour la fascine devront être approfondies pour les faisceaux d'𝛼-actinine. Nous avons eu des difficultés à reconstituer les plus grands faisceaux induits par l'𝛼-actinine, même avec des incubations de plusieurs heures.

Pour conclure, nos résultats montrent que les deux types de crosslinkers offrent une protection assez proche contre l'activité de désassemblage de la cofiline mais impliquent des mécanismes différents. l'alpha-actinine est malgré tout plus protectrice. Ici, avec notre système in vitro pour

INTRODUCTION

The Actin Cytoskeleton

Regulation of dierent actin networks

In cells, the cytoskeleton is an important feature providing internal support for the cell shape, by resisting stress and being able to transmit the forces across the cell. It consists of polymer networks with three different kinds: microtubules, intermediate filaments, and actin filaments.

Actin is one of the most abundant and ubiquitous proteins in cells. Based on the stimuli in cells, actin monomers are readily polymerized into helical filaments and depolymerized back into monomers. Actin filaments are assembled into networks by cross-linking as observed at the cell front, cell cortex, and attached to organelles. These networks provide a morphological framework for the cell and participate in regulating several functions in the cell. For example, motile or dividing cells require an active actin network reorganization able to exert forces to constrict the cell. Depending on the function to perform, different actin architectures are assembled such as lamellipodial, filopodia, stress fibers, invadopodia, podosomes, invadopodia, cytokinetic ring, microvilli, and actin blebs,... Three archetypal actin networks have been mostly studied: filopodia, lamellipodia, and stress fibers, important for cell motility. Filopodia are finger-like cell protrusions made up of parallel actin filaments to form bundles that can exert pushing force on the membrane; branched actin networks are seen in lamellipodia; and stress fibers are actin bundles of mixed polarity, which can be put under tension thanks to the presence of molecular motors called myosins.

The interplay between biochemical and mechanical cues orchestrates the quick assembly or disassembly of actin filaments. This reorganization of filaments is mostly carried out with the help of actin-binding proteins (ABPs). Hundreds of ABPs have been discovered thus far. The complex orchestration of the activity of ABPs organizes actin into specific structures required for specific functions. How these ABPs interact and regulate each other spatially and temporally in different networks is still unclear. For instance, in filopodia, at least three different ABPs (fascin, cofilin, and tropomyosin) bind to the side of actin filaments. Yet, it is unknown how they are regulated throughout the protrusion and retraction cycle of filopodia. In vitro studies that would reconstitute the basic features of a specific actin network, using a specific set of purified proteins Jahnavi C -doctoral thesis -2021 and controlling their relative concentrations (or stoichiometry), could help in understanding each protein's activities and role(s). This is relevant to understanding actin network dynamics in cells, where ABPs work together. Finally, this leads to an understanding of processes involving these structures, like cancer cell migration, wound healing and morphogenesis,.... During my PhD, I studied two main aspects of actin filament bundle dynamics: First, the regulation of mDia1 formin activity, a major actin filament elongator, when elongating filament that are in bundles; Second, the disassembly of actin filament bundles by proteins of the ADF/cofilin family.

I will introduce the rationale for these two studies more in detail in chapter 2. In this introduction chapter, I will present all the important aspects of actin assembly, disassembly, and their regulation by biochemical and mechanical factors.

Actin biochemistry

A) General Actin biochemistry

The actin monomer is a globular protein with a molecular weight of 42 kDa, with size along its long axis of 5.4 nm [START_REF] Dominguez | Actin Structure and Function[END_REF], 2011) . It is the basic unit of the actin filament.

The actin is an ATPase, where ATP hydrolysis occurs only when actin is in the filament. The actin filament can be described as a double-stranded right helix with a half-pitch of 36 nm, consisting of 13 actin subunits (figure 1.1C).

A single actin filament has a persistence length of around 10 µm, length below which it can be considered as a rigid rod. Its torsional rigidity is ~ 5.8 × 10 -26 N.m 2 [START_REF] Tsuda | Torsional rigidity of single actin filaments and actin-actin bond breaking force under torsion measured directly by in vitro micromanipulation[END_REF] . One essential aspect of helical polymers is that their bending and twisting mechanics are coupled (De La Cruz et al., 2010) .

The globular actin monomer (G-actin) has 4 subdomains (Fig 1 .1 A). An actin monomer has two important interfaces, the first one, called the 'barbed' face at the surface of subdomains 1,3 and a 'pointed' face from subdomains 2 and 4. Actin filament can elongate more from the' barbed end' (BE) compared to the 'pointed end' (PE) ( Fig 1.2A). A binding site for both nucleotide and Jahnavi C -doctoral thesis -2021 cations like Ca 2+ , Mg 2+ are located in the deep cleft in between subdomains 2 and 4. A loosely structured region called the DNase I binding loop ('D-loop'), located in subdomain 2 [START_REF] Kabsch | Atomic structure of the actin: DNase I complex[END_REF][START_REF] Oda | The nature of the globular-to fibrous-actin transition[END_REF] , plays an important role in stabilizing longitudinal monomer interactions in the filament. Its accessibility and post-translational modified state regulate the binding of several ABPs. Another important binding groove is present on the barbed face of the actin subunit, in between subdomains 1 and 3. Several ABPs, such as profilin, formin, gelsolin, and twinfilin, interact with this region of the barbed face.

In cells, actin exists in both monomeric (G-actin) and filamentous (F-actin) forms. The nucleation of actin filaments depends on the concentration of monomers available for pure actin.

The total concentration of actin in non-muscle cells is 100-200 µM [START_REF] Funk | Profilin and formin constitute a pacemaker system for robust actin filament growth[END_REF][START_REF] Pollard | Molecular Mechanisms Controlling Actin Filament Dynamics in Nonmuscle Cells[END_REF] . At this concentration, all the actin present in cells should be in the polymerized form but that is not the case, as a relatively large fraction (~ ⅓ ) is maintained in monomeric form. Some ABPs seem to play a major role in preventing actin filament nucleation.

The nucleation step requires the formation of the intermediate oligomers (dimers, trimers and tetramers) before filament elongation can proceed with the addition of monomers at the barbed and pointed ends. However, dimers and trimers are highly unstable with high dissociation rates (10 6 s -1 and 100 s -1 respectively) (Cooper et al., 1983;[START_REF] Frieden | Polymerization of actin: Mechanism of the Mg2+-induced process at pH 8 and 20 degrees C[END_REF] . A very recent article has been revisiting this dogma, using numerical simulations (Rosenbloom et al., 2021) . This study seems to indicate that the difficulty to nucleate a filament from actin monomers would indeed result from very low actin monomer association rates to form dimers or trimers than their large unstability. These low association rates are mainly caused by the rapid transition of the shape of the actin monomers between states where only one is favorable enough to lead to monomer-monomer association.

Once reaching the tetrameric form, the oligomers become more stable thanks to the higher number of intermolecular contacts between actin subunits. Here, the D-loop is involved in establishing longitudinal inter-subunit contacts in the filament [START_REF] Dominguez | Actin Structure and Function[END_REF] .

Jahnavi C -doctoral thesis -2021 When actin subunits get incorporated into filaments, their conformation becomes more flattened, by 20° compared with monomeric actin (Chou & Pollard, 2019;[START_REF] Oda | The nature of the globular-to fibrous-actin transition[END_REF] (Fig 1.1B). As monomers, actin is mostly bound to ATP (rather than ADP) in the presence of divalent cations in cells (Rosenblatt et al., 1995) . Due to the higher physiological concentration of Mg 2+ compared to Ca 2+ , the actin monomers are Mg-ATP bound and are assembled into actin filaments. (Pollard, 2016a) . Actin subunit incorporation at filament ends leads to the irreversible ATP hydrolysis at a rate of 0.3 s⁻¹ (Blanchoin et al., 2014;Carlier et al., 1988;[START_REF] Zsolnay | Structural basis for polarized elongation of actin filaments[END_REF] forming MgADP-Pi-F-actin subunits. The release of this inorganic phosphate is stochastic in the filament with a half time of around 102 seconds, independent of filament assembly from only actin or profilin-actin (I. [START_REF] Fujiwara | Polymerization kinetics of ADP-and ADP-Pi-actin determined by fluorescence microscopy[END_REF][START_REF] Jégou | Individual Actin Filaments in a Microfluidic Flow Reveal the Mechanism of ATP Hydrolysis and Give Insight Into the Properties of Profilin[END_REF] , which leads to more conformational changes that affect subunit dissociation when actin subunits reach filament pointed end (Chou & Jahnavi C -doctoral thesis -2021 Pollard, 2019) . The state of actin nucleotide has profound consequences on the binding of certain ABPs like ADF/cofilin as well as myosins.

Actin filaments are polar with different kinetics for monomer addition and removal at both ends (Fig 1 .2). The Mg-ATP-actin association/binding rate at the barbed end is higher than at the pointed end. The critical concentration for actin polymerization at the barbed end is ~ 0.1 µM and 0.6 µM at the pointed end [START_REF] Pollard | Molecular Mechanisms Controlling Actin Filament Dynamics in Nonmuscle Cells[END_REF] . The rates of actin monomer association and dissociation from each end are well documented [START_REF] Pollard | Actin and Actin-Binding Proteins[END_REF] . The dynamic behavior of the actin filament caused due to the difference in critical concentrations of monomers at both ends leads to the treadmilling of actin filaments: i.e. the co-existence of filaments of stable length along with the monomers in solution at a steady state. Here, ATP-actin at the barbed end dissociates more slowly than ADP-actin at the pointed end. At steady-state, the disassembly of filament at the pointed end by the loss of ADP-actin is equal to the assembly at the barbed end by the addition of ATP-actin (Neuhaus et al., 1983;[START_REF] Wegner | Head to tail polymerization of actin[END_REF] . Actin treadmilling is probably not taking place in cells, as actin dynamics is maintained out of equilibrium, with the help of several ABPs, tightly regulating actin polymerization and depolymerization. Affinities (K values, in µM) are the ratio of dissociation rate to association rate constants. The association rate constants, µM -1 s -1 ; unit of dissociation rate constants, s -1 (Pollard, 2016b) B) Actin Filament showing polymerized subunits with nucleotides at different states, showing ATP rich region at the barbed end, and exponential decay of the ADP-Pi content within the filament from the barbed end to the pointed end.

Jahnavi C -doctoral thesis -2021

The helicity of an actin filament is one of the important aspects in regulating the actin dynamics.

Several ABPs are able to sense the conformation and relative orientation of actin subunits within the filaments. The helicity of actin filament could be modified by interaction with ABPs. Also, the filament being polar and helical, is a chiral object. This asymmetry is translated to the higher scale, first at the scale of networks. In turn, it has profound consequences on cellular processes and tissue-level organization. For example, zebrafish melanophores exhibit intrinsic chirality regulated by the actin cytoskeleton [START_REF] Yamanaka | Rotating pigment cells exhibit an intrinsic chirality[END_REF] . In isotropically cultured fibroblasts, the cross-linking activity of 𝛼-actinin was shown to be the main factor for the establishment of chiral pattern from the symmetric pattern of actin organization [START_REF] Tee | Cellular chirality arising from the self-organization of the actin cytoskeleton[END_REF][START_REF] Tee | Actin polymerization and crosslinking drive left-right asymmetry in single cell and cell collectives[END_REF] . The details of how filament helicity regulates the binding of several ABPs in actin networks and how this could break asymmetry in cells during development are not understood (Jegou & Romet-Lemonne, 2020) .

B) Actin isoforms

There are six mammalian actin isoforms, four muscle, and two non-muscle cell actins: Three 𝛼-actin (skeletal, cardiac, and vascular actins), one β-cytoplasmic actin, and two 𝛾-cytoplasmic and smooth muscle isoforms. They are encoded by different genes. The difference in the sequences of β and 𝛾 actin is only at the N-terminal end (Müller et al., 2013) . They differ by 4 amino acids where the aspartate acid and valine of β actin are replaced with glutamic acid and isoleucine in 𝛾 actin respectively. The 𝛼-skeletal and 𝛼-cardiac actins are 99% identical. These isoforms differ from one another in exchange for two amino acids aspartate and glutamate in positions 2 and 3 at the N-terminal [START_REF] Perrin | The actin gene family: Function follows isoform[END_REF][START_REF] Vandekerckhove | Simultaneous expression of skeletal muscle and heart actin proteins in various striated muscle tissues and cells. A quantitative determination of the two actin isoforms[END_REF] . In spite of the similar sequences, actin isoforms are differentially expressed and segregate into different networks.

β and 𝛾-cytoplasmic actins are widely expressed isoforms. The occurrence of these isoforms depends on cell types (Khaitlina, 2001) . In the late metaphase-1 of the maturing oocyte, 𝛾-isoform was preferentially localized to the cortex whereas β-isoform was more present during the cytokinesis at the contractile structures and the cell-cell contact region. Moreover, the importance and major role of 𝛾-isoform actin role in asymmetry in meiosis-1 was also shown [START_REF] Brockmann | Beta-and gamma-cytoplasmic actins are required for meiosis in mouse oocytes[END_REF] .

Jahnavi C -doctoral thesis -2021

Studies in microvascular pericytes, endothelial monolayers, differentiating neurons show that cytoplasmic ꞵ-actin is more specifically present at the plasma membrane ruffles, filopodia, pseudopodia, and in the growth cones. Cytoplasmic ꞵ-actin is always associated with the actively growing structures at the membrane interface where the 𝛾 isoform is mostly present in stress fibers (Hoock et al., 1991;Micheva et al., 1998) . In most cells, the isoforms ꞵ:𝛾 coexist in a 2:1 ratio and this specific ratio is maintained across different cell types: myoblasts and fibroblasts (Hill & Gunning, 1993;[START_REF] Leavitt | Expression of transfected mutant beta-actin genes: Alterations of cell morphology and evidence for autoregulation in actin pools[END_REF] .

Depending on their distinct functions, the actin isoforms are segregated or localized to different networks implying that their roles can be either different or overlapping.

How ABPs interact with different actin isoforms has yet to be explored in more detail. For example, profilin is known to have 100 times more affinity for non-muscle actin than skeletal muscle actin [START_REF] Larsson | The effect of divalent cations on the interaction between calf spleen profilin and different actins[END_REF] . Cofilin also binds to actin in an isoform-dependent manner. Cofilin binding dynamics were shown to be dependent on the actin isoform [START_REF] Prochniewicz | Cofilin Increases the Torsional Flexibility and Dynamics of Actin Filaments[END_REF][START_REF] Wioland | ADF/Cofilin Accelerates Actin Dynamics by Severing Filaments and Promoting Their Depolymerization at Both Ends[END_REF] . On the contrary, some studies have shown that non-isoform specific binding of actin to cross-linking protein fascin-2 in mouse stereocilia with both ꞵ and 𝛾 actin isoforms [START_REF] Perrin | β-Actin and Fascin-2 Cooperate to Maintain Stereocilia Length[END_REF] . Another ABP, tropomyosin, expressed as 40 isoforms in mammals can differentiate different actin structures in cells, raising the hypothesis that it may recognize filaments made of a specific composition of actin isoforms.

Different actin isoforms along with the ABPs isoforms, lead to the complex regulation of actin networks spatially and temporally. Recent studies on yeast actin isoforms and their efficiencies in assembling either linear or branched actin networks have shown that certain isoforms are targeted to form specific networks (reviewed in [START_REF] Sanders | Specialization of actin isoforms derived from the loss of key interactions with regulatory factors[END_REF] .

C) Actin Post-translational Modifications

In addition to six different isoforms of actin, post-translational modifications (PTMs) can diversify the actin nature in cells. PTM involves the insertion or deletion of certain groups in the proteins that may affect the protein structurally and functionally. How these changes affect the conformation of actin subunits and their interaction with other ABPs, and whether these changes assist in the localization of actin needs to be addressed.

The first identified PTM of actin is the N-terminal residue acetylation of skeletal actin [START_REF] Gaetjens | N-acetylaspartic acid in G-actin[END_REF] . Till now, 140 different PTMs of actin have been identified on 94 different side chains of actin. However, acetylation, oxidation, and arginylation are thus far the most studied PTMs [START_REF] Varland | Actin Post-translational Modifications: The Cinderella of Cytoskeletal Control[END_REF] .

N-terminal (Nt) acetylation is one of the PTMs that proteins undergo in the cells that are catalyzed by Nt-acetyl transferases (NAA). In a recent study by Drazic et al, NAA80 has been shown to have substrate specificity for actin. This acetylation is shown to be very important in cell motility and morphology [START_REF] Drazic | NAA80 is actin's N-terminal acetyltransferase and regulates cytoskeleton assembly and cell motility[END_REF][START_REF] Goris | Structural determinants and cellular environment define processed actin as the sole substrate of the N-terminal acetyltransferase NAA80[END_REF][START_REF] Rebowski | Mechanism of actin N-terminal acetylation[END_REF] . Also, the lysine acetylation in actin has been shown to be involved, in complex with the protein CAP, in the inhibition of formin inverted formin 2 (INF2) activity (A et al., 2019, 2020) .

The N-terminal end of actin undergoes a series of residue processing, starting with Nt-acetylation. A small fraction of total cytoplasmic actin methionine residue is removed, rendering this end target for arginylation. In the study by Karakozova et al, it has been shown that ꞵ-actin is arginylated in-vivo . This PTM is shown to be very important for preventing F-actin aggregation, lamellipodia formation, and ꞵ-actin localization in cells [START_REF] Karakozova | Arginylation of b-Actin Regulates Actin Cytoskeleton and Cell Motility[END_REF] . An interesting feature of this PTM is only arginylated ꞵ-actin is stable in-vivo, as opposed to 𝛾-actin (Kashina, 2006;[START_REF] Zhang | Differential Arginylation of Actin Isoforms Is Regulated by Coding Sequence-Dependent Degradation[END_REF] .

Mical, a redox enzyme is known to oxidize methionines 44 and 47 in the D-loop of subdomain 2 of actin. This protein transiently binds to filamentous actin and with the help of nicotinamide adenine dinucleotide phosphate (NADPH) drives the oxidation of methionines. This leads to structural changes in subdomain 2 that promote the disassembly of single filaments and actin bundles cross-linked by fascin [START_REF] Hung | Mical links semaphorins to F-actin disassembly[END_REF][START_REF] Hung | Direct Redox Regulation of F-Actin Assembly and Disassembly by Mical[END_REF] . A significant increase in the cofilin binding and severing rates has been observed when filaments are oxidized with Mical-1, such that even the inactive phosphomimetic mutant of cofilin can bind to the actin filament Jahnavi C -doctoral thesis -2021 [START_REF] Grintsevich | F-actin dismantling through a redox-driven synergy between Mical and cofilin[END_REF][START_REF] Wioland | Actin filament oxidation by MICAL1 suppresses protections from cofilin-induced disassembly[END_REF] . This PTM can be reversed by the action of SelR/MsrB2, a specific methionine reductase [START_REF] Bai | Actin reduction by MsrB2 is a key component of the cytokinetic abscission checkpoint and prevents tetraploidy[END_REF] . How these differences in actin isoforms and PTMs come into play in regulating actin dynamics within the cell is not fully understood so far and remains a challenge to study in detail. After these two factors, the third one can regulate actin dynamics and functions in the cells in the presence of actin-binding proteins (ABPs).

Actin Binding Proteins ABPs)

In cells actin filaments do not occur as a single entity, they are usually part of networks. ABPs play a crucial role in regulating the actin networks. There are around 10 different categories of ABPs in cells (fig 1.3). At a basic level, actin network dynamics rely upon A) assembly and B) disassembly of networks. Different ABPs are involved in those processes which are explained in detail here [START_REF] Pollard | Actin and Actin-Binding Proteins[END_REF] .

Jahnavi C -doctoral thesis -2021 Several elements are involved in the assembly of actin networks such as nucleation, elongation, and cross-linking.

Controlling actin dynamics

In cells, actin nucleation and elongation are regulated tightly by different stimuli and signaling pathways. Cells maintain high actin monomer concentrations despite the critical concentration of ATP-bound actin being ~ 0.1 µM at the barbed end, in vitro. Cells have control over this by sequestering actin monomers with proteins like profilin, thymosin-ꞵ4, and by blocking the filament barbed ends with proteins such as Capping Protein (CP).

A) Profilin and Thymosin-ꞵ4

In the cytoplasm, actin monomers exist in a complex with profilin or thymosin-ꞵ4. Both profilin and thymosin-ꞵ4 competes and bind to actin monomers stoichiometrically [START_REF] Pantaloni | How profilin promotes actin filament assembly in the presence of thymosin beta 4[END_REF] . Both profilin and thymosin-ꞵ4 bind ATP-actin with a higher affinity than ADP-actin.

Thymosin-ꞵ4 is a 5 kDa protein. In cells, the concentration of profilin and thymosin-ꞵ4 is 50-100 µM and 100-500 µM, respectively [START_REF] Funk | Profilin and formin constitute a pacemaker system for robust actin filament growth[END_REF][START_REF] Xue | Structural basis of thymosin-β4/profilin exchange leading to actin filament polymerization[END_REF] .

The affinity of profilin for the filament is very low as the binding site at the barbed end of actin is hidden inside the filament. Profilin is a 14 to 17 kDa protein, depending on the isoform, that regulates actin dynamics through different means [START_REF] Tilney | Actin from Thyone sperm assembles on only one end of an actin filament: A behavior regulated by profilin[END_REF]) : a) profilin can suppress the spontaneous nucleation of actin filaments [START_REF] Pollard | Quantitative analysis of the effect of Acanthamoeba profilin on actin filament nucleation and elongation[END_REF][START_REF] Schutt | The structure of crystalline profilin-p-actin[END_REF] ; b ) monomeric actin nucleotide exchange is enhanced by profilin [START_REF] Vinson | Interactions of Acanthamoeba Profilin with Actin and Nucleotides Bound to Actin[END_REF] ; c) profilin-actin cannot dimerize or bind to the pointed end of the filament; d) profilin promotes the elongation from the barbed end [START_REF] Pollard | Quantitative analysis of the effect of Acanthamoeba profilin on actin filament nucleation and elongation[END_REF]) ; e) profilin-actin directly interacts with formins (see below formins in actin nucleators section), an important ABPs implicated in the rapid polymerization of F-actin.

Profilin can either promote or inhibit actin polymerization at the barbed ends depending on its concentration. Similarly, many studies show that profilin affects formin FH1-mediated actin polymerization biphasically (Courtemanche & Pollard, 2012;Kovar et al., 2006;[START_REF] Pernier | Profilin Interaction with Actin Filament Barbed End Controls Dynamic Instability, Capping, Branching, and Motility[END_REF]Vavylonis et al., 2006) . The barbed end elongation rate of profilin-bound actin is the same as the free actin monomer. In a recent study, it has been shown that the step of profilin release Jahnavi C -doctoral thesis -2021 from the barbed end is the rate-limiting step in the formin mediated elongation [START_REF] Funk | Profilin and formin constitute a pacemaker system for robust actin filament growth[END_REF] . Profilin interacts with many ABPs containing proline-rich regions, such as formins, VASP, and N-WASP. Thus profilin plays a central role in the regulation of actin networks (Rotty et al., 2015;[START_REF] Skruber | Arp2/3 and Mena/VASP Require Profilin 1 for Actin Network Assembly at the Leading Edge[END_REF][START_REF] Suarez | Profilin regulates F-actin network homeostasis by favoring formin over Arp2/3 complex[END_REF] .

B) Actin nucleators

Several nucleation-promoting proteins control actin filament nucleation in cells: the Actin-related Protein 2/3 complex (Arp2/3), proteins from the formin family, Enabled/ vasodilator-stimulated phosphoprotein (Ena/VASP), and WH2-containing proteins see fig 1.4 for different nucleators.

Cells can tailor the actin networks with the help of actin nucleating proteins. For example, formin nucleates linear unbranched actin filaments, as seen in stereocilia, filopodia, drosophila bristles, and stress fibers. The Arp2/3 is the nucleator for the branched networks as observed in lamellipodia, phagocytic cups, vesicle formation, and actin comet tails of intracellular pathogen Listeria monocytogenes . Alone the Arp2/3 complex is inactive. It gets activated by the binding of one or two NPFs, like N-WASP, WHAMM, WASH, and JMY. These NPFs possess a 35 kDa WH2 domain that can bind actin monomers, and for some of them along with a proline-rich region that interacts with many ABPs, like profilin (Higgs & Pollard, 2001;[START_REF] Paunola | WH2 domain: A small, versatile adapter for actin monomers[END_REF] .

Recently, SPIN90 has been identified as a novel class of Arp2/3 activator: it interacts with the Arp2/3 in order to nucleate a new filament without the need of a pre-existing filament to bind to and its binding interface on Arp2/3 is different from the WASP-like binding interface. As a consequence, SPIN90 + Arp2/3 is able to nucleate filaments and generate actin networks with no branches (L. [START_REF] Cao | SPIN90 associates with mDia1 and the Arp2/3 complex to regulate cortical actin organization[END_REF][START_REF] Wagner | Dip1 defines a class of Arp2/3 complex activators that function without preformed actin filaments[END_REF] . 5 D). They observed that the pointed end of filaments is arranged at an 70 0 to the side of the pre-existing/mother filament so that the barbed ends of the filament are free to elongate unless capped by the CP (Mullins et al., 1998;Robinson et al., 2001) . Such branched actin networks are observed in lamellipodia, in the actin comet tails of Listeria , during endocytosis, and vesicle trafficking in cells [START_REF] Pollard | Actin, a Central Player in Cell Shape and Movement[END_REF] .

• Formins

Formin is a family of proteins that are important actin nucleators and elongators. They are highly conserved proteins from plants to vertebrates. In mammals, there are 15 different formin isoforms, the model plant Arabidopsis thaliana has 20 isoforms, Dictyostelium has 9 isoforms, fission yeast has 3 and budding yeast has 2 isoforms [START_REF] Blanchoin | Plant formins: Diverse isoforms and unique molecular mechanism[END_REF][START_REF] Higgs | Formin proteins: A domain-based approach[END_REF]Rivero et al., 2005) . This family of proteins has been named after the mouse limb deformity gene. They were shown to be involved in the formation of organ systems, where the disruption of formin encoding transcripts in mice resulted in the formation of severe limb defects [START_REF] Maas | Disruption of formin-encoding transcripts in two mutant limb deformity alleles[END_REF][START_REF] Woychik | Formins": Proteins deduced from the alternative transcripts of the limb deformity gene[END_REF] .

Formins are homodimeric multidomain proteins. They are defined by the presence of conserved Formin Homology domains 1 (FH1) & 2 (FH2). Actin regulation activity of these domains is well proven. Besides these domains, the other domains can vary among the isoforms and sub-families. Evolutionarily conserved, formins are shown to have a very important role in morphogenesis, cytokinesis, and polarity in flies and yeast (Castrillon & Wasserman, 1994;Kohno et al., 1996;[START_REF] Watanabe | MDia2 Induces the Actin Scaffold for the Contractile Ring and Stabilizes Its Position during Cytokinesis in NIH 3T3 Cells[END_REF] . Other than actin nucleation and elongation, some formins have other functions such as actin bundling (for example for Daam1), severing ( eg INF2), depolymerization, and microtubule-binding ( eg mDia1, mDia2 or INF2) (Chesarone et al., 2010;[START_REF] Goode | Mechanism and function of formins in the control of actin assembly[END_REF] .

Mammalian isoforms are categorized into 8 subfamilies based on the phylogenetic analysis: Dia (diaphanous), Daam (disheveled-associated activator of morphogenesis), FMNL (formin related gene in leukocytes), WHIF (WH2 domain-containing protein), INF (inverted formin), FHOD (formin homology domain-containing protein), Delphilin, and FMN (formin) [START_REF] Higgs | Formin proteins: A domain-based approach[END_REF] .

Here, I will mostly focus on diaphanous formins which I have worked with but the following details are characteristic enough for formins in general.

Different isoforms are localized to different actin structures in cells, with some overlap. For example, mouse mDia1 & mDia2 are shown to be localized both at the filopodial tips, as well as in lamellipodia, and are also involved in actin dynamics in contractile stress fibers (Hotulainen & Lappalainen, 2006;[START_REF] Riveline | Focal Contacts as Mechanosensors: Externally Applied Local Mechanical Force Induces Growth of Focal Contacts by an Mdia1-Dependent and Rock-Independent Mechanism[END_REF][START_REF] Tominaga | Diaphanous-Related Formins Bridge Rho GTPase and Src Tyrosine Kinase Signaling[END_REF][START_REF] Watanabe | P140mDia, a mammalian homolog of Drosophila diaphanous,is a target protein for Rho small GTPase and is a ligand for profilin[END_REF]C. Jahnavi C -doctoral thesis -2021[START_REF] Yang | Novel Roles of Formin mDia2 in Lamellipodia and Filopodia Formation in Motile Cells[END_REF] . Mammalian formin-1 is shown to have a role in assembling actin cables at cell-cell adhesion in epithelial cells in an 𝛼-catenin dependent manner (Kobielak et al., 2004) .

Diaphanous formins structure

Structurally the well-studied subset of formins is Diaphanous Related Formins (DRFs) that include Dia, Daam, and FMNL formins in mammals and yeast isoforms such as Bni1, Bnr1, and sepA. This subset of formins is known for their established interaction and activation by the Rho GTPases directly. This was first studied in mouse Dia1 (mDia1) [START_REF] Schönichen | Fifteen formins for an actin filament: A molecular view on the regulation of human formins[END_REF][START_REF] Watanabe | P140mDia, a mammalian homolog of Drosophila diaphanous,is a target protein for Rho small GTPase and is a ligand for profilin[END_REF] . Functionally, these DRFs are divided into C-terminal and N-terminal halves.

The C-terminal half consists of two highly conserved domains: 1) FH2 domain that homodimerizes head-to-tail in a donut shape (see fig 1.6 A). FH2 can bind actin monomers and alone is enough to nucleate actin filaments in vitro (F. [START_REF] Li | The Mouse Formin mDia1 Is a Potent Actin Nucleation Factor Regulated by Autoinhibition[END_REF][START_REF] Pruyne | Role of Formins in Actin Assembly: Nucleation and Barbed-End Association[END_REF] . One FH2 dimer can bind to the barbed end of actin filaments and partially cap the barbed end ('leaky capping' activity). It tracks the growing barbed end. Processivity is the ability of the formin to stay, track before dissociating from the barbed end, and control actin subunit incorporation [START_REF] Kovar | Insertional assembly of actin filament barbed ends in association with formins produces piconewton forces[END_REF][START_REF] Romero | Formin is a processive motor that requires profilin to accelerate actin assembly and associated ATP hydrolysis[END_REF] . 2) FH1 domain , is a proline-rich, disordered domain that can bind several profilins or profilin/actin complexes. FH1 is responsible for the enhancement of the actin elongation (see fig 1.6 B and Fig 1.7). The length and number of proline stretches of FH1 vary from 2 to 14 between formin isoforms. [START_REF] Horan | Computational modeling highlights the role of the disordered Formin Homology 1 domain in profilin-actin transfer[END_REF] . Profilin-actin complexes interact with these tracts. They are delivered to the barbed end rapidly and generate a closed ring. [START_REF] Courtemanche | Mechanisms of formin-mediated actin assembly and dynamics[END_REF][START_REF] Otomo | Crystal structure of the Formin mDia1 in autoinhibited conformation[END_REF] .

Finally, a diaphanous auto-regulatory domain (DAD) with 20-30 amino acids, C-terminal to the FH2 domain (Fig 1 .5 A) [START_REF] Alberts | Identification of a Carboxyl-terminal Diaphanous-related Formin Homology Protein Autoregulatory Domain*[END_REF] , mediates the auto-inhibition by interacting with the DID domain at the N-terminal. In addition, the DAD domain, being a WH2-like domain that can interact with G-actin, is shown to also have a role in actin nucleation properties [START_REF] Gould | The formin DAD domain plays dual roles in autoinhibition and actin nucleation[END_REF] . Lastly, the DAD domain, maybe by loosely interacting with the side of actin filament in the vicinity of barbed ends modulates formin processivity [START_REF] Vizcarra | The Role of Formin Tails in Actin Nucleation, Processive Elongation, and Filament Bundling *[END_REF] .

The N-terminal part of DRF formins is composed of a GTPase binding domain (GBD), followed by a diaphanous inhibitory domain (DID). Next, there is a dimerization domain and lastly, a coiled coin region participating in the localization of these formins (Kohno et al., 1996;[START_REF] Watanabe | P140mDia, a mammalian homolog of Drosophila diaphanous,is a target protein for Rho small GTPase and is a ligand for profilin[END_REF] (Figure 1.5A)

In the cytosol, Diaphanous formins exist in an autoinhibitory state due to the intramolecular interaction between the DID and DAD domains. In such an autoinhibited state, the C-terminus of formins is not available to interact with actin due to steric hindrance (A. Nezami et al., 2010;[START_REF] Otomo | Crystal structure of the Formin mDia1 in autoinhibited conformation[END_REF] . This autoinhibition is released, at least partially, by the interaction of formin's GBD domain with Rho GTPases (Breitsprecher & Goode, 2013;Rose et al., 2005; N. Jahnavi C -doctoral thesis -2021 [START_REF] Watanabe | Cooperation between mDia1 and ROCK in Rho-induced actin reorganization[END_REF] . They have also been involved in the localization of formin to different cellular localizations for generating distinct actin assemblies (Breitsprecher & Goode, 2013;[START_REF] Watanabe | P140mDia, a mammalian homolog of Drosophila diaphanous,is a target protein for Rho small GTPase and is a ligand for profilin[END_REF] .

FH2 domain structure

Several crystallographic studies were carried out to understand the structure of diaphanous-related formins. These studies resolved the structure of the FH2 domain in yeast formin Bni1p alone and in complex with actin. Since the FH2 domain is quite conserved through evolution, the homology of the Bni1p FH2 domain with the one of mouse mDia1 is relatively high and allows to match residues in interaction with actin for the latter [START_REF] Shimada | The Core FH2 Domain of Diaphanous-Related Formins Is an Elongated Actin Binding Protein that Inhibits Polymerization[END_REF][START_REF] Xu | Crystal Structures of a Formin Homology-2 Domain Reveal a Tethered Dimer Architecture[END_REF] . Each FH2 subunit in the dimer is rod-shaped and is further subdivided into a post, coiled-coil, and knob regions as shown in fig 1.5 (middle row). At the N-terminal of each half of the dimer, there is a closed-loop called the 'lasso', that can link with the 'post' protrusion from the other hemidimer and helps in the dimerization process (A. G. Nezami et al., 2006;[START_REF] Otomo | Structural basis of actin filament nucleation and processive capping by a formin homology 2 domain[END_REF][START_REF] Xu | Crystal Structures of a Formin Homology-2 Domain Reveal a Tethered Dimer Architecture[END_REF] .

Formin localization at the membrane

In cells, formins are often localized at the membrane. There are many ways a formin can interact with the membrane [START_REF] Bucki | Lateral distribution of phosphatidylinositol 4,5-bisphosphate in membranes regulates formin-and ARP2/3-mediated actin nucleation[END_REF]Cvrčková, 2013;[START_REF] Gorelik | Mechanisms of plasma membrane targeting of formin mDia2 through its amino terminal domains[END_REF][START_REF] Seth | Autoinhibition regulates cellular localization and actin assembly activity of the diaphanous-related formins FRLα and mDia1[END_REF] by interacting directly with some specific phospholipids [START_REF] Ramalingam | Phospholipids regulate localization and activity of mDia1 formin[END_REF] or by being recruited by Rho GTPases, I-Bar, or F-Bar domain-containing proteins (Cvrčková, 2013) . For example, mDia1 is shown to be localized at the phagocytic cup by IQGAP-1 and CLIP 170 [START_REF] Brandt | Dia1 and IQGAP1 interact in cell migration and phagocytic cup formation[END_REF][START_REF] Lewkowicz | The microtubule-binding protein CLIP-170 coordinates mDia1 and actin reorganization during CR3-mediated phagocytosis[END_REF] , whereas in stress fiber formation it interacts with the SH3 domain of IRSp53 protein (T. [START_REF] Fujiwara | Rho Small G-Protein-Dependent Binding of mDia to an Src Homology 3 Domain-Containing IRSp53/BAIAP2[END_REF][START_REF] Goh | MDia1 and WAVE2 Proteins Interact Directly with IRSp53 in Filopodia and Are Involved in Filopodium Formation[END_REF] . Finally, PTMs can help formins interact with the membrane, such as N-terminal myristoylation of FMNL1 [START_REF] Han | Formin-like 1 (FMNL1) Is Regulated by N-terminal Myristoylation and Induces Polarized Membrane Blebbing[END_REF] .

It is unclear how this interaction with membranes affects the activity of formins. Recently we studied how formin anchoring is important for its activity, by employing different anchoring strategies of single formins. We showed that formin's processivity decreased when anchored with their FH2 domain. In the same study, we also showed that formins activity is greatly affected when filaments, elongated from formins, are constrained by actin cross-linking protein fascin [START_REF] Suzuki | Geometrical Constraints Greatly Hinder Formin mDia1 Activity[END_REF] .

Jahnavi C -doctoral thesis -2021

Actin filament nucleation, elongation and capping activity of formins and the role of profilin

Formin-assisted actin assembling activity is lost in-vitro when point mutations in the yeast Bni1p formin FH2 domain are blocking their dimerization [START_REF] Xu | Crystal Structures of a Formin Homology-2 Domain Reveal a Tethered Dimer Architecture[END_REF] . So tethered dimers are really necessary for interaction with the actin barbed end and its processive activity at the barbed end. As revealed by structural data, the FH2 domain can bind simultaneously up to three actin monomers and thus promote filament nucleation [START_REF] Otomo | Structural basis of actin filament nucleation and processive capping by a formin homology 2 domain[END_REF] .

As proposed, but not directly observed by Otomo et al, the FH2 dimer can adopt two different conformations at the barbed ends which might explain how the FH2 dimer can track the BE.

Formin is a 'leaky' capper that can allow actin polymerization in contrast to the other capping proteins (Fig 1.8). Due to this 'leaky' capping, FH2 domains elongate the barbed ends but at a slower rate than free barbed ends [START_REF] Zigmond | Formin Leaky Cap Allows Elongation in the Presence of Tight Capping Proteins[END_REF] . In this model, called the 'stair-stepping' model, the FH2 dimer alternates between two conformations at the barbed end, the 'open' and 'closed' states. In the 'open' state, when elongating the filament, one-half of the FH2 dimer can unbind from the barbed end and allow the addition of an actin monomer while the other half is still bound to the barbed end [START_REF] Otomo | Structural basis of actin filament nucleation and processive capping by a formin homology 2 domain[END_REF] [START_REF] Jégou | Formin mDia1 senses and generates mechanical forces on actin filaments[END_REF][START_REF] Kubota | Biphasic Effect of Profilin Impacts the Formin mDia1 Force-Sensing Mechanism in Actin Polymerization[END_REF] .

Jahnavi C -doctoral thesis -2021

It is thought that the increase of the probability of the actin monomer encountering the barbed end in a conformation ready for polymerization is achieved for actin that are bound to profilin themselves bound to FH1 domains (M. [START_REF] Tanaka | Poly(l-proline)-binding proteins from chick embryos are a profilin and a profilactin[END_REF]Vavylonis et al., 2006) .

The increase in elongation rate depends upon the number of polyproline tracks in the FH1 domain in a non-monotonous way, where different polyproline tracks participate with a different efficiency to the increase in filament elongation (Courtemanche & Pollard, 2012) . In the presence of profilin, mDia1, which possesses 14 polyproline tracks, shows a five-fold increase in elongation rate compared to mDia2, having only two polyproline tracks. Jahnavi C -doctoral thesis -2021

An interesting study at physiological concentrations of profilin and actin (up to 200 µM) performed in vitro by Funk et al. recently showed that profilin dissociation after the successful transfer of an actin monomer to the barbed end is the rate-limiting step for the actin filament elongation. This rate is accelerated by formins in an FH1 length-dependent manner [START_REF] Funk | Profilin and formin constitute a pacemaker system for robust actin filament growth[END_REF] .

Formins are mechanosensitive

Formin's processivity has been shown to be decreasing for mDia1 and mDia2 with increasing ionic strength, actin concentration, and profilin concentrations in an in-vitro study (L. [START_REF] Cao | Modulation of formin processivity by profilin and mechanical tension[END_REF] . This study has shown that when piconewton pulling forces are applied to filaments, formin's detachment rate is increased and proposed a model (Fig 1.9) for formin dissociation, based on the stair-stepping model from Otomo et al [START_REF] Otomo | Structural basis of actin filament nucleation and processive capping by a formin homology 2 domain[END_REF] . In this model formin dissociation from the barbed end can originate from two different states. At 'low' force, formin dissociation occurs predominantly, when each time a new actin subunit is added at the barbed end, where the FH2 domain goes through a 'weak, dissociation-prone' conformation. At higher force, formins mostly dissociate in the open state (L. [START_REF] Cao | Modulation of formin processivity by profilin and mechanical tension[END_REF] . Moreover, formin remains processive even when the barbed end is depolymerizing (Jégou et al., 2013, p. 2;[START_REF] Kubota | Biphasic Effect of Profilin Impacts the Formin mDia1 Force-Sensing Mechanism in Actin Polymerization[END_REF][START_REF] Pernier | Profilin Interaction with Actin Filament Barbed End Controls Dynamic Instability, Capping, Branching, and Motility[END_REF] . Jahnavi C -doctoral thesis -2021

Several in vitro studies have shown that formin is a mechanosensitive protein. When pulling forces are applied on mDia1 formin through a fluid flow, a two-fold increase in elongation rate was observed [START_REF] Jégou | Formin mDia1 senses and generates mechanical forces on actin filaments[END_REF] . Surface anchored yeast Bni1p formin when subjected to tension by hydrodynamic flow under small forces showed an increase in formin mediated actin elongation in the presence of profilin and a decrease in the absence of profilin [START_REF] Courtemanche | Tension modulates actin filament polymerization mediated by formin and profilin[END_REF] . However, for mDia1 it has been shown that even in the absence of profilin, the elongation rates are enhanced when pulling forces are applied (L. [START_REF] Cao | Modulation of formin processivity by profilin and mechanical tension[END_REF][START_REF] Kubota | Biphasic Effect of Profilin Impacts the Formin mDia1 Force-Sensing Mechanism in Actin Polymerization[END_REF] . Another study using magnetic tweezers and also in the absence of profilin, has shown that formin can sense torque and the FH2 domain is promoted to open conformation upon pulling, increasing the rate of actin polymerization [START_REF] Yu | mDia1 senses both force and torque during Factin filament polymerization[END_REF] . Dramatic increases in elongation rates of >600 subunits per second at 0.5 µM G-actin and 2 µM profilin, with a pulling force of at 4 pN, was reported for rotationally unconstrained mDia1 formin in vitro in the presence of profilin [START_REF] Yu | Effects of Mechanical Stimuli on Profilin-and Formin-Mediated Actin Polymerization[END_REF] . This result largely exceeds reported rates by other groups and has not been reproduced yet.

In cells, several forces are acting upon the actin filaments. These involve binding of ABPs to actin filaments such as pulling forces due to the myosins, or actin depolymerization at the leading edges, pushing forces at the leading membrane edges in filopodia due to the actin polymerization and membrane resisting the deformation, or forces due to the external stress. In many of the situations above, formins are present at the barbed ends of the filament. Hence, formins force-mediated formin actin polymerization could be very important in regulating actin networks.

• Ena/VASP

Ena/VASP is another actin nucleator and elongator protein that have both F-actin and G-actin binding domains (Fig 1 .10 A). It is a tetrameric protein that can efficiently cap the barbed ends and protect from CP [START_REF] Barzik | Ena/VASP Proteins Enhance Actin Polymerization in the Presence of Barbed End Capping Proteins *[END_REF][START_REF] Pasic | Ena/VASP Proteins Capture Actin Filament Barbed Ends *[END_REF] . These proteins can remain bound processively to the barbed ends where they can collect and elongate multiple ends simultaneously [START_REF] Breitsprecher | Molecular mechanism of Ena/VASP-mediated actin-filament elongation[END_REF]Winkelman et al., 2014) . Ena has been

shown to have increased processivity on the barbed ends of trailing filaments in the fascin bundles than 𝛼-actinin or fimbrin bundles [START_REF] Harker | Ena/VASP processive elongation is modulated by avidity on actin filaments bundled by the filopodia cross-linker fascin[END_REF] . Ena/VASP along with formin Jahnavi C -doctoral thesis -2021 mDia2 is shown to regulate the filopodial length and dynamics in cells (Fig 1 .10 B) (Barzik et al., 2014) .

C) Actin stabilizing proteins

A) Capping Protein

Capping Protein (CP) is a 64 kDa heterodimer. It binds to the barbed end of the actin filaments and blocks the addition or release of actin subunits. It has a high affinity for the barbed end, K d ~1 nM [START_REF] Caldwell | Effects of CapZ, an actin-capping protein of muscle, on the polymerization of actin[END_REF] . In actin networks, such as lamellipodia, CP is necessary to limit the length of actin filaments and create short and stiff networks [START_REF] Pollard | Cellular Motility Driven by Assembly and Disassembly of Actin Filaments[END_REF] .

To release this inhibition, some proteins have been discovered to interact with CP while bound at the barbed end. For example, twinfilin, a protein that interacts with actin monomers as well as filament barbed ends, has been shown to be necessary to uncap the filament barbed ends and to regulate the localization and turnover of CP in mammalian cells [START_REF] Hakala | Twinfilin uncaps filament barbed ends to promote turnover of lamellipodial actin networks[END_REF] . Similarly, in yeast, Capping protein is necessary for the localization of twinfilin to carry out its function at the actin patches [START_REF] Palmgren | Interactions with PIP2, ADP-actin monomers, and capping protein regulate the activity and localization of yeast twinfilin[END_REF] . Gelsolin, espin8, and Hip1R are a few other proteins with barbed end capping activity [START_REF] Le Clainche | Regulation of Actin Assembly Associated With Protrusion and Adhesion in Cell Migration[END_REF] . It has both G-actin and F-actin binding sites in the EVH2 domain (adapted from [START_REF] Harker | Ena/VASP processive elongation is modulated by avidity on actin filaments bundled by the filopodia cross-linker fascin[END_REF] ). B) GFP-VASP is shown to localize at the filopodial tips of MV D7 cells [START_REF] Barzik | Ena/ VASP regulates mDia2-initiated filopodial length, dynamics, and function[END_REF] .

Jahnavi C -doctoral thesis -2021

Proteins like V1 (Myotrophin) and CARMIL have been shown to be direct regulators of CP.

They bind directly to CP, preventing its binding to the barbed end and increasing its dissociation rate [START_REF] Edwards | Capping protein regulators fine-tune actin assembly dynamics[END_REF][START_REF] Yang | Mammalian CARMIL Inhibits Actin Filament Capping by Capping Protein[END_REF] . However, the reverse role, ie., delivering CP to the barbed end, was also recently proposed for CARMIL [START_REF] Hakala | Twinfilin uncaps filament barbed ends to promote turnover of lamellipodial actin networks[END_REF] . Proteins like formins, tensin, and Ena/VASP are indirect regulators of CP by protecting the barbed end from CP [START_REF] Le Clainche | Regulation of Actin Assembly Associated With Protrusion and Adhesion in Cell Migration[END_REF][START_REF] Shekhar | Formin and capping protein together embrace the actin filament in a ménage à trois[END_REF]Winkelman et al., 2014) .

B) Tropomyosin

Tropomyosin (Tpm) is another family of actin-binding proteins that are involved in stabilizing the actin filament. It is a 33 kDa rod-like antiparallel dimer that binds along the side of actin filaments (Fig 1 .11 A) [START_REF] Perry | Vertebrate tropomyosin: Distribution, properties and function[END_REF] . So far more than 40 different tropomyosin isoforms have been identified in mammals that are developed from alternate splicing of four tropomyosin genes (P. [START_REF] Gunning | Tropomyosin-Based Regulation of the Actin Cytoskeleton in Time and Space[END_REF] .

The occurrence of tropomyosins in cells can be tissue-specific, cell-specific (cancer cells), or site-specific. In non-muscle cells, these 40 or more different isoforms of tropomyosin regulate ꞵ and 𝛾-actin isoforms as mentioned in section 1.

D) Actin Disassembly

Actin disassembly is an important feature of actin network regulation, as filaments in some networks are constantly turning over in order to adapt quickly to changing conditions. Related to actin network disassembly, the recycling of actin monomers from a least polymerization-competent state (ADP-G-actin) to a more polymerization-competent state (ATP-G-actin) is also important for this turnover. ABPs like capping protein, and profilin helps in accelerating the process of turnover. ADF/cofilin is a major player in actin filament disassembly. Its effect can be further amplified by other ABPs. The disassembling property of myosin is also emerging in the studies.

ADF/cofilin

ADF/cofilin is a family composed of three isoforms in mammals, namely Actin Depolymerising Factor (ADF), cofilin-1 and cofilin-2. ADF/cofilin is the most abundant ABP involved in actin filament disassembly in cells [START_REF] Poukkula | Actin-depolymerizing factor homology domain: A conserved fold performing diverse roles in cytoskeletal dynamics[END_REF] . A study in 2005 in mouse embryos showed that cofilin is very important for neural crest development, and lack of it is very lethal to embryos [START_REF] Gurniak | The actin depolymerizing factor n-cofilin is essential for neural tube morphogenesis and neural crest cell migration[END_REF] . In another study, it has been shown that deletion of the ADF gene has resulted in irregular corneal epithelium leading to blindness [START_REF] Ikeda | Aberrant actin cytoskeleton leads to accelerated proliferation of corneal epithelial cells in mice deficient for destrin (actin depolymerizing factor)[END_REF] .

ADF/cofilin's main disassembling activity is performed through the severing of actin filaments (J. R. [START_REF] Bamburg | Partial purification and characterization of an actin depolymerizing factor from brain[END_REF][START_REF] Lappalainen | Cofilin promotes rapid actin filament turnover in vivo[END_REF] . Cofilin is a 17 kDa protein, which can interact with both actin monomers and filaments through its ADF-homology (ADF-H) domain. It binds on the filament on the outer side of two longitudinal subunits interacting with subdomain 2 of the lower subunit and subdomain 1 and 3 of the upper subunit (J. R. [START_REF] Bamburg | Proteins of the ADF/Cofilin Family: Essential Regulators of Actin Dynamics[END_REF][START_REF] Poukkula | Actin-depolymerizing factor homology domain: A conserved fold performing diverse roles in cytoskeletal dynamics[END_REF]K. Tanaka et al., 2018) . ADF/cofilin binds cooperatively to the filament side to nucleate and grow domains (see fig 1 .12 A). Severing preferentially occurs at domain boundaries [START_REF] Prochniewicz | Cofilin Increases the Torsional Flexibility and Dynamics of Actin Filaments[END_REF][START_REF] Suarez | Cofilin Tunes the Nucleotide State of Actin Filaments and Severs at Bare and Decorated Segment Boundaries[END_REF][START_REF] Suarez | Cofilin Tunes the Nucleotide State of Actin Filaments and Severs at Bare and Decorated Segment Boundaries[END_REF]Wioland et al., 2019a) .

In lamellipodia and during endocytosis, actin networks are turning over quickly (typical timescale is 1-10 seconds). Hence filaments need to be disassembled at a similar rate (Rottner, 2008) . In vitro, spontaneous depolymerization of actin filaments from the pointed end occurs at ~ 5-10 subunits per second [START_REF] Pollard | Rate constants for the reactions of ATP-and ADP-actin with the ends of actin filaments[END_REF][START_REF] Wioland | ADF/Cofilin Accelerates Actin Dynamics by Severing Filaments and Promoting Their Depolymerization at Both Ends[END_REF] . Cofilin, and assisted by other Jahnavi C -doctoral thesis -2021 proteins (mainly Coronin and Aip1) are thought to be the main contributors to accelerate actin filament disassembly by fragmenting them. Moreover, it has been reported that cofilin, by saturating the filament up to the barbed end, efficiently prevents any resuming of the elongation at the barbed end [START_REF] Wioland | ADF/Cofilin Accelerates Actin Dynamics by Severing Filaments and Promoting Their Depolymerization at Both Ends[END_REF] . Recently, CAP (Cyclase-Associated Protein) along with cofilin was observed to accelerate the depolymerisation of the pointed end of actin filaments (Kotila et al., 2019;[START_REF] Shekhar | Synergy between Cyclase-associated protein and Cofilin accelerates actin filament depolymerization by two orders of magnitude[END_REF] ADF was first identified in chick embryo extracts and is known to bind with 1:1 stoichiometry with G-actin (Nishida et al., 1984) . In addition, it can also bind to filamentous actin and rapidly depolymerize them, hence the name ADF. It is shown to be ubiquitously present in the epithelial cell's cytoplasm, leading edges of membrane ruffles and growth cones (J. R. [START_REF] Bamburg | Distribution and cellular localization of actin depolymerizing factor[END_REF] . Next, the protein cofilin was named for its ability to co-sediment with F-actin. Cofilin-1 is present widely in all cells while cofilin-2 is found in muscles. Cofilin 1 and 2 isoforms are 80% identical with each other and 70% identical with ADF in their sequences. ADF/cofilin activity is regulated by the phosphorylation of serine 3 at its N-terminal by LIM-kinases (LIMKs), and testicular protein kinases (TESKs). Phosphorylated cofilin is inactive and cannot bind to actin.

Dephosphorylation of cofilin into its active form is carried out by the SSH (slingshot) family of phosphatases, chronophorin, protein phosphatases, and cathepsin D (Y.-J. [START_REF] Liu | The noncanonical role of the protease cathepsin D as a cofilin phosphatase[END_REF]K. Mizuno, 2013;Morgan et al., 1993;Moriyama et al., 1996) .

Cofilin preferentially binds ADP-actin, compared with ATP-or ADP-Pi-actin in the filaments [START_REF] Carlier | Actin Depolymerizing Factor (ADF/Cofilin) Enhances the Rate of Filament Turnover: Implication in Actin-based Motility[END_REF]De La Cruz, 2009;[START_REF] Suarez | Cofilin Tunes the Nucleotide State of Actin Filaments and Severs at Bare and Decorated Segment Boundaries[END_REF]Wioland et al., 2019a) . However, cofilin-2 isoform in sarcomeres can bind monomeric ADP-actin and ATP-actin with the same affinity (Kremneva et al., 2014) .

The initial binding of cofilin molecules to the actin filaments is termed nucleation. Once nucleation is achieved, a cofilin domain grows symmetrically towards both filament ends [START_REF] Wioland | ADF/Cofilin Accelerates Actin Dynamics by Severing Filaments and Promoting Their Depolymerization at Both Ends[END_REF] , thanks to the cooperative binding of cofilin molecules at the boundaries of the domain. [START_REF] Prochniewicz | Cofilin Increases the Torsional Flexibility and Dynamics of Actin Filaments[END_REF][START_REF] Hawkins | Human actin depolymerizing factor mediates a pH-sensitive destruction of actin filaments[END_REF][START_REF] Hayden | Analysis of the interactions of actin depolymerizing factor with G-and F-actin[END_REF] . Cofilin binding to actin subunits decreases the helical pitch of filaments (from 36 nm down to 27 nm), rotating each subunit by ~ 4-5 0 (Fig 1 .12 B).

Jahnavi C -doctoral thesis -2021

The severing of actin filaments by ADF/cofilin occurs at the boundaries of the cluster (shown in Fig 1 .12 A). The mismatch in filament twist between bare and cofilin-decorated filament segments leads to strain accumulation at the interface would induce filament severing at cofilin cluster boundaries (De La Cruz et al., 2015;[START_REF] Schramm | Actin Filament Strain Promotes Severing and Cofilin Dissociation[END_REF] .

Most of the cofilin-induced severing (83%) happens at the boundary towards the pointed end of the filaments (De La Cruz, 2009;[START_REF] Suarez | Cofilin Tunes the Nucleotide State of Actin Filaments and Severs at Bare and Decorated Segment Boundaries[END_REF][START_REF] Wioland | ADF/Cofilin Accelerates Actin Dynamics by Severing Filaments and Promoting Their Depolymerization at Both Ends[END_REF] . The global severing activity of activity depends on the concentration of cofilin: at low concentration, cofilin barely nucleates clusters; at intermediate concentration, cofilin nucleates few clusters that will eventually sever the filament; while in the high concentration regime, the filament is rapidly Jahnavi C -doctoral thesis -2021 saturated by cofilin and the only remaining cofilin cluster boundaries are the end of the filament, leading to no fragmentation and a stable cofilin-saturated filament [START_REF] Andrianantoandro | Mechanism of Actin Filament Turnover by Severing and Nucleation at Different Concentrations of ADF/Cofilin[END_REF] .

Filament ends saturated by cofilin depolymerize, more rapidly than a free end in the case of the pointed end (0.2 s -1 free end compared to 0.5 s -1 for cofilin-1), more slowly than a free end for the barbed end (7 s -1 free compared to 0.6 s -1 for cofilin-1). One interesting observation is that, even in the presence of actin in solution, barbed ends saturated by cofilin depolymerize for minutes, indicating a highly reduced monomer association rate for this type of barbed end [START_REF] Wioland | ADF/Cofilin Accelerates Actin Dynamics by Severing Filaments and Promoting Their Depolymerization at Both Ends[END_REF] .

pH is another factor that regulates the mammalian cofilin activity in cells. Several studies have shown that cofilin actin-binding and depolymerization are affected by pH [START_REF] Hawkins | Human actin depolymerizing factor mediates a pH-sensitive destruction of actin filaments[END_REF][START_REF] Maciver | The effect of two actin depolymerizing factors (ADF/cofilins) on actin filament turnover: PH sensitivity of F-actin binding by human ADF, but not of Acanthamoeba actophorin[END_REF][START_REF] Pope | Solution structure of human cofilin: Actin binding, pH sensitivity, and relationship to actin-depolymerizing factor[END_REF][START_REF] Yonezawa | PH control of actin polymerization by cofilin[END_REF] . In vitro, the severing rate per cofilin domain is not affected by pH whereas the assembly rate of cofilin domains decreases at higher pH [START_REF] Pavlov | Severing of F-actin by yeast cofilin is pH-independent[END_REF]Wioland et al., 2019a) .

In addition to the actin nucleotide state and pH, cofilin is also regulated by binding to phosphatidylinositol phosphate and 4,5-bisphosphate (PIP and PIP2) [START_REF] Frantz | Cofilin is a pH sensor for actin free barbed end formation: Role of phosphoinositide binding[END_REF][START_REF] Yonezawa | Inhibition of the interactions of cofilin, destrin, and deoxyribonuclease I with actin by phosphoinositides[END_REF] . Finally, there are several actin-binding proteins that complement the activity of cofilin in the cells to regulate actin assembly and disassembly. Proteins like Actin interacting protein 1 (Aip1) and coronin are shown to promote cofilin activity in vitro and in yeast cells (Kueh et al., 2008;[START_REF] Lin | Overlapping and distinct functions for cofilin, coronin and Aip1 in actin dynamics in vivo[END_REF][START_REF] Okada | Aip1 and cofilin promote rapid turnover of yeast actin patches and cables: A coordinated mechanism for severing and capping filaments[END_REF] .

Other disassembling factors

Another potent severing protein is gelsolin. An interesting point is that only one gelsolin molecule is able to induce filament severing, which contrasts with cofilin domain formation requiring at least a few tens of proteins [START_REF] Suarez | Cofilin Tunes the Nucleotide State of Actin Filaments and Severs at Bare and Decorated Segment Boundaries[END_REF][START_REF] Wioland | ADF/Cofilin Accelerates Actin Dynamics by Severing Filaments and Promoting Their Depolymerization at Both Ends[END_REF] . Strikingly, gelsolin can also nucleate actin filaments, by binding two actin simultaneously on their barbed face, as well as it caps already existing actin filaments. It uses Ca 2+ which binds to the gelsolin and releases the molecule from auto-inhibition so that it can bind to filamentous actin [START_REF] Pope | Probing the effects of calcium on gelsolin[END_REF] . Once gelsolin has severed a filament into two, gelsolin remains attached to the newly Jahnavi C -doctoral thesis -2021 formed barbed end and caps it. There is an overlap between binding sites of gelsolin and other binding proteins like myosin, scruin, tropomyosin, and cofilin (McGough et al., 1998) .

Myosin II mini filaments have also been observed to induce the fragmentation of F-actin. In filament networks, myosin can induce filament buckling, increasing filament curvature that leads to a mechanically induced severing (Murrell & Gardel, 2012) . Haviv et al have shown that myosin II can induce the unbundling and severing, at the ends of parallel fascin cross-linked actin bundles [START_REF] Haviv | A Cytoskeletal Demolition Worker: Myosin II Acts as an Actin Depolymerization Agent[END_REF] . Myosins II and VI have also been observed to promote the disassembly of anti-parallel bundles, but not parallel bundles. Moreover, the presence of cross-linker 𝜶-actinin impeded the disassembling activity of myosin VI [START_REF] Reymann | Actin Network Architecture Can Determine Myosin Motor Activity[END_REF] .

Myosin II has been shown to be involved in regulating actin bundle length in growth cones.

Myosin II inhibition resulted in decreased retrograde actin flow and long actin bundles due to decreased disassembly of actin networks at the transition zones towards the bundle pointed ends (Medeiros et al., 2006) .

Other than the above-mentioned proteins, Glial Maturation factor (GMF) [START_REF] Ydenberg | GMF severs actin-Arp2/3 complex branch junctions by a cofilin-like mechanism[END_REF] , Twinfilin [START_REF] Paavilainen | Structure of the actin-depolymerizing factor homology domain in complex with actin[END_REF] , and formins like FRL-𝛼 [START_REF] Harris | The mouse formin, FRLalpha, slows actin filament barbed end elongation, competes with capping protein, accelerates polymerization from monomers, and severs filaments[END_REF] , and INF-2 [START_REF] Gurel | INF2-Mediated Severing through Actin Filament Encirclement and Disruption[END_REF] are few other proteins that could sever actin filaments see [START_REF] Pollard | Actin and Actin-Binding Proteins[END_REF] for a review. However, recent studies in twinfilin have not shown the severing of actin filaments in vitro or in cells [START_REF] Hakala | Twinfilin uncaps filament barbed ends to promote turnover of lamellipodial actin networks[END_REF] .

Myosins

F-actin contraction by myosin motors is a major player in force generation in cells. Myosin is an actin-based motor and uses actin filaments as tracks transporting cargoes. In cells, myosins have diverse functions, in addition, to force production, regulating actin structures, or driving retrograde actin flow in neuronal growth cones (Houdusse & Titus, 2021; C. H. [START_REF] Lin | Myosin Drives Retrograde F-Actin Flow in Neuronal Growth Cones[END_REF] .

Myosin is a hexameric ATPase protein complex, composed of 2 heavy chains and four light chains, that quickly hydrolyses ATP to generate mechanical force. Structurally, myosins are composed of a head, i.e. the motor domain which binds ATP and produces a force on actin, a flexible neck domain, and a tail which binds to cargo and is specific depending on the motor functions [START_REF] Sweeney | Structural and Functional Insights into the Myosin Motor Mechanism[END_REF] . Except for Myosin-VI, myosin motors move towards Jahnavi C -doctoral thesis -2021 the barbed end (Robert-Paganin et al., 2020) . The localization and roles of some myosins will be discussed in section 1.4 on actin networks.

Cross-linking

Different architectures of actin networks are made possible due to the cross-linking proteins which help to organize the filaments into highly ordered complex structures. Filamin, fascin, fimbrin, 𝛼-actinin, dystrophin, and espin... are the actin cross-linkers in the cells.

A)Filamin

Filamin (FLN) is the first cross-linking protein identified in non-muscle cells [START_REF] Hartwig | Isolation and properties of actin, myosin, and a new actinbinding protein in rabbit alveolar macrophages[END_REF] . There are three isoforms in mammals (FLN A, B, and C). It is a highly flexible dimer with two 280 kDa subunits joined at one end forming a V Shape and a total length of 160 nm (see fig 1.13). The N-terminal part of the protein has spectrin related-actin binding site (sr-ABD) and the C-terminal part contains the dimerization domain (Nakamura et al., 2011) . Its N-terminal actin-binding domain is similar to the ABD domains of 𝛼-actinin, therefore composed of two Calponin Homology domains. FLN cross-links the actin filaments 'orthogonally' forming a network (gel-like) (Nakamura et al., 2007) . FLN induced networks are very important for cell migration [START_REF] Baldassarre | Filamins Regulate Cell Spreading and Initiation of Cell Migration[END_REF] . Importantly, mutations in the FLN gene could result in several conditions due to disrupted morphogenesis [START_REF] Feng | The many faces of filamin: A versatile molecular scaffold for cell motility and signalling[END_REF] .

B) Fascin

Fascin is an actin cross-linking protein that bundles actin filaments in parallel, i.e. all filaments having the same orientation (as opposed to anti-parallel) (see fig 1.14 C right). In cells, fascin is highly enriched in filopodia, where actin filaments are bundled with their barbed ends directed towards the tip of filopodia.

Historically, fascin has been first identified in sea urchin oocytes. In mammals, there are three fascin isoforms. While fascin is absent in epithelial cells in adults, fascin-1 is expressed in mesenchymal and nervous tissues, fascin-2 is found in retinal, and fascin-3 is found in the testis cells (Kureishy et al., 2002;[START_REF] Tubb | Testis Fascin (FSCN3): A Novel Paralog of the Actin-Bundling Protein Fascin Expressed Specifically in the Elongate Spermatid Head[END_REF][START_REF] Wada | Mutation of Human Retinal Fascin Gene (FSCN2) Causes Autosomal Dominant Retinitis Pigmentosa[END_REF] . Fascin is localized in filopodia, microspikes, stress fibers, invadopodia, and podosomes, hence having a strong role in cell motility, dendritic cell maturation, and cell adhesion [START_REF] Elkhatib | Fascin Plays a Role in Stress Fiber Organization and Focal Adhesion Disassembly[END_REF]A. Li et al., 2010;[START_REF] Van Audenhove | Fascin actin bundling controls podosome turnover and disassembly while cortactin is involved in podosome assembly by its SH3 domain in THP-1 macrophages and dendritic cells[END_REF][START_REF] Vignjevic | Role of fascin in filopodial protrusion[END_REF][START_REF] Yamakita | Fascin1 Promotes Cell Migration of Mature Dendritic Cells[END_REF]; Yamashiro-Matsumura & Jahnavi C -doctoral thesis -2021 Matsumura, 1986) . Overexpression of fascin has been observed in cancer cells escaping the tumor leading to recurrent carcinomas [START_REF] Hashimoto | Dual Actin-bundling and Protein Kinase C-binding Activities of Fascin Regulate Carcinoma Cell Migration Downstream of Rac and Contribute to Metastasis[END_REF] .

Fascin is a globular protein of ~5-6 nm in diameter and molecular weight of 55 kDa [START_REF] Yamashiro-Matsumura | Purification and characterization of an F-actin-bundling 55-kilodalton protein from HeLa cells[END_REF] . It has four ꞵ-trefoil domains with crucial actin-binding sites in domains 1 and 3. Unlike many other cross-linking proteins, like the ones of the 𝛼-actinin family, where actin cross-linking activity is achieved by protein dimerization, fascin is a monomer. Its subdomain arrangement appears as pseudo-two-fold symmetry [START_REF] Jansen | Mechanism of Actin Filament Bundling by Fascin *[END_REF][START_REF] Ono | Identification of an Actin Binding Region and a Protein Kinase C Phosphorylation Site on Human Fascin *[END_REF][START_REF] Sedeh | Structure, evolutionary conservation, and conformational dynamics of Homo sapiens fascin-1, an F-actin crosslinking protein[END_REF] . Fascin has been shown to have three different actin-binding sites (S. [START_REF] Yang | Molecular Mechanism of Fascin Function in Filopodial Formation[END_REF] (figure 1.14A). Actin binding site-1 includes residues from N and C terminal along with the cleft formed between ꞵ-trefoil domains 1 and 4, actin-binding site-2 includes residues from ꞵ-trefoil domains 1 and 2 opposite to binding site-1 [START_REF] Jansen | Mechanism of Actin Filament Bundling by Fascin *[END_REF]S. Yang et al., 2013) (see fig 1.14 (top)). The two actin-binding sites are ~5 nm apart, and the interfilament distance in bundles is around ~8-9 nm [START_REF] Ishikawa | Polarized actin bundles formed by human fascin-1: Their sliding and disassembly on myosin II and myosin V in vitro[END_REF] .

Finally, actin-binding site-3 is ꞵ-trefoil domain 3. Mutation in this domain leads to impaired actin-bundling activity making it the third binding site in fascin. In addition, ꞵ-trefoil domain 1 is also shown to be actin-binding indirectly by its interaction with fascin inhibitor macroketone (Chen et al., 2010) . Fascin is regulated by serine-39 phosphorylation by protein kinase C (PKC).

Similar to cofilin, fascin is also inactive in its phosphorylated form [START_REF] Yamakita | Phosphorylation of Human Fascin Inhibits Its Actin Binding and Bundling Activities ( * )[END_REF] . In addition, monoubiquitination of fascin at lysine residues in ꞵ-trefoil domain 2 also decreases the fascin bundling activity (S. [START_REF] Lin | Monoubiquitination Inhibits the Actin Bundling Activity of Fascin*[END_REF] . [START_REF] Jansen | Mechanism of Actin Filament Bundling by Fascin *[END_REF][START_REF] Winkelman | Fascin-and α-Actinin-Bundled Networks Contain Intrinsic Structural Features that Drive Protein Sorting[END_REF] FRAP studies on GFP-fascin in cells have shown that cross-linking of actin filaments by fascin is highly dynamic with a half time of recovery around 6 s [START_REF] Aratyn | Intrinsic Dynamic Behavior of Fascin in Filopodia□D[END_REF][START_REF] Vignjevic | Role of fascin in filopodial protrusion[END_REF] and has not seen binding to single filaments in vitro [START_REF] Winkelman | Fascin-and α-Actinin-Bundled Networks Contain Intrinsic Structural Features that Drive Protein Sorting[END_REF] . Several in vitro studies have shown that fascin bundling occurs in a cooperative fashion (see fig 1.14 C; left), when two actin filaments are closer and rapidly zippers the two filaments [START_REF] Breitsprecher | Molecular mechanism of Ena/VASP-mediated actin-filament elongation[END_REF][START_REF] Winkelman | Fascin-and α-Actinin-Bundled Networks Contain Intrinsic Structural Features that Drive Protein Sorting[END_REF] . The nature of fascin-actin interactions is dynamic and forms stiff bundles (see fig 1.14 C; right).

Small-angle X-ray scattering, as well as EM and cryo-ET studies, have shown that fascin can crosslink filaments in a hexagonal lattice and binds regularly every 36 nm, following F-actin half-pitch [START_REF] Aratyn | Intrinsic Dynamic Behavior of Fascin in Filopodia□D[END_REF]Claessens et al., 2008;[START_REF] Jansen | Mechanism of Actin Filament Bundling by Fascin *[END_REF] . Interestingly, the maximum size of fascin-induced filament bundles seems to be limited to ~ 20 filaments, as observed experimentally in vivo and in vitro [START_REF] Ishikawa | Polarized actin bundles formed by human fascin-1: Their sliding and disassembly on myosin II and myosin V in vitro[END_REF][START_REF] Jansen | Mechanism of Actin Filament Bundling by Fascin *[END_REF][START_REF] Lewis | Nerve growth cone lamellipodia contain two populations of actin filaments that differ in organization and polarity[END_REF]Medalia et al., 2007;[START_REF] Svitkina | Mechanism of filopodia initiation by reorganization of a dendritic network[END_REF] . This limitation seems to originate from fascin binding sites on neighboring filaments that are not perfectly aligned every 36 nm, so fascin cross-linking slightly under twists filaments (Shin et al., 2009) and creates a torque. This torque can be partially relaxed by the supercoiling of the whole bundle (see fig 1.15) (Claessens et al., 2008;[START_REF] Heussinger | Theory of crosslinked bundles of helical filaments: Intrinsic torques in self-limiting biopolymer assemblies[END_REF] . Torque imposed by cross-linking on filaments is proposed to be relaxed by supercoiling of the whole bundle adapted from [START_REF] Heussinger | Theory of crosslinked bundles of helical filaments: Intrinsic torques in self-limiting biopolymer assemblies[END_REF] .

Jahnavi C -doctoral thesis -2021

C) 𝛼-actinin

𝛼-actinin is another cross-linking protein that belongs to the spectrin superfamily with a molecular weight of 94-103 kDa [START_REF] Blanchard | The structure and function of α-actinin[END_REF] . Alternative splicing and duplication of genes resulted in 4 isoforms in humans: two muscle isoforms 𝛼-actinin 2 and 3 localized to z-disk of sarcomeres [START_REF] Langanger | The molecular organization of myosin in stress fibers of cultured cells[END_REF] , whereas 𝛼-actinin 1 and 4 are the nonmuscle isoforms seen in stress fibers and focal adhesions of migrating cells. [START_REF] Quick | α-Actinin 1 and α-actinin 4: Contrasting roles in the survival, motility, and RhoA signaling of astrocytoma cells[END_REF][START_REF] Shao | α-Actinin-4 Is Essential for Maintaining the Spreading, Motility and Contractility of Fibroblasts[END_REF][START_REF] Vallenius | CLP-36 PDZ-LIM Protein Associates with Nonmuscle α-Actinin-1 and α-Actinin-4 *[END_REF] .

𝛼-actinin is an antiparallel rod-shaped homodimer that can bind filaments in a both antiparallel and parallel manner. Monomers are composed of three domains: an N-terminal actin-binding domain (ABD) containing a pair of two calponin homology domains (McGough et al., 1994) , a

middle flexible region that has several spectrin repeats (Davison & Critchley, 1988;Djinović-Carugo et al., 1999) and finally a C-terminal calmodulin-like domain (see fig 1.16 left).

40 Jahnavi C -doctoral thesis -2021

A study by Burridge et al. has shown that cytoplasmic isoforms cannot bind to actin only in the presence of calcium whereas the muscle isoforms are insensitive to calcium-binding [START_REF] Beggs | Cloning and characterization of two human skeletal muscle alpha-actinin genes located on chromosomes 1 and 11[END_REF][START_REF] Burridge | Non-muscle α-actinins are calcium-sensitive actin-binding proteins[END_REF] . Studies have shown that 𝛼-actinin binds filament in a bundle with a large distribution of angles between the 𝛼-actinin and filament long axis [START_REF] Hampton | Novel Structures for α-Actinin:F-Actin Interactions and their Implications for Actin-Membrane Attachment and Tension Sensing in the Cytoskeleton[END_REF] , leading to an interfilament distance ranging from 17 to 25 nm [START_REF] Hampton | Novel Structures for α-Actinin:F-Actin Interactions and their Implications for Actin-Membrane Attachment and Tension Sensing in the Cytoskeleton[END_REF][START_REF] Winkelman | Fascin-and α-Actinin-Bundled Networks Contain Intrinsic Structural Features that Drive Protein Sorting[END_REF] . Interestingly in these bundles, some 𝛼-actinin was observed to bind to single filaments, with both ABDs bound to the sides of the same filament (see fig 1.16 right) [START_REF] Hampton | Novel Structures for α-Actinin:F-Actin Interactions and their Implications for Actin-Membrane Attachment and Tension Sensing in the Cytoskeleton[END_REF][START_REF] Winkelman | Fascin-and α-Actinin-Bundled Networks Contain Intrinsic Structural Features that Drive Protein Sorting[END_REF] . 𝛼-actinin binds to the subdomain 1 of the actin monomer whose binding site overlaps with fimbrin and gelsolin [START_REF] Lebart | Further characterization of the alpha-actinin-actin interface and comparison with filamin-binding sites on actin[END_REF][START_REF] Way | Evidence for functional homology in the F-actin binding domains of gelsolin and alpha-actinin: Implications for the requirements of severing and capping[END_REF] .

Similar to fascin, 𝛼-actinin also binds to filaments in a cooperative manner in vitro [START_REF] Winkelman | Fascin-and α-Actinin-Bundled Networks Contain Intrinsic Structural Features that Drive Protein Sorting[END_REF] . It is also dynamic with residence time similar to fascin (6s) in two filament bundles invitro [START_REF] Winkelman | Fascin-and α-Actinin-Bundled Networks Contain Intrinsic Structural Features that Drive Protein Sorting[END_REF] . Also, 𝛼-actinin is shown to be essential for contractility [START_REF] Goldmann | Analysis of filamin and α-actinin binding to actin by the stopped flow method[END_REF]Hotulainen & Lappalainen, 2006) . Both in muscle Z disks and non-muscle stress fibers 𝛼-actinin shows periodic distribution along with myosin II where they exclude each other and appear as a striated band in arrangement [START_REF] Langanger | The molecular organization of myosin in stress fibers of cultured cells[END_REF] .

𝛼-actinin is an important protein for focal adhesion maturation. It interacts with several other

ABPs like vinculin [START_REF] Bois | Structural Dynamics of α-Actinin-Vinculin Interactions[END_REF][START_REF] Le | Mechanotransmission and Mechanosensing of Human alpha-Actinin 1[END_REF] , zyxin to recruit it along stress fibers [START_REF] Reinhard | An α-Actinin Binding Site of Zyxin Is Essential for Subcellular Zyxin Localization and α-Actinin Recruitment*[END_REF] , and integrins to participate in the transmission of the force exerted by cells to the extracellular matrix (Roca-Cusachs et al., 2013;Sampath et al., 1998) . Its central role in stress fiber formation and mechanosensitivity has been proposed to be also key for the emergence of a chiral pattern of the actin cytoskeleton in surface-plated individual cells [START_REF] Tee | Cellular chirality arising from the self-organization of the actin cytoskeleton[END_REF][START_REF] Tee | Actin polymerization and crosslinking drive left-right asymmetry in single cell and cell collectives[END_REF] .

Cross-linkers like fascin, espin [START_REF] Bartles | Identification and characterization of espin, an actin-binding protein localized to the F-actin-rich junctional plaques of Sertoli cell ectoplasmic specializations[END_REF] , and fimbrin help in forming compact parallel bundles as seen in filopodia, stereocilia, and microvilli respectively whereas 𝛼-actinin and filamin bind filaments more loosely. When reconstituted in vitro fascin and 𝛼-actinin mutually exclude each other from the filament [START_REF] Winkelman | Fascin-and α-Actinin-Bundled Networks Contain Intrinsic Structural Features that Drive Protein Sorting[END_REF] , besides cross-linkers espin and fimbrin have been shown to have a higher affinity for fascin bundles than 𝛼-actinin networks [START_REF] Winkelman | Fascin-and α-Actinin-Bundled Networks Contain Intrinsic Structural Features that Drive Protein Sorting[END_REF] .

Jahnavi C -doctoral thesis -2021

It is not clear how the presence of a crosslinker could affect the binding properties of other ABPs and what's the physiological significance behind such kind of sorting within the networks.

Here in this chapter, although it is not an exhaustive list, I have explained different actin-binding proteins and their importance in regulating actin networks. Now, I will discuss further how specific kinds of networks in cells are assembled with a different set of ABPs. It is important for the ABPs to orchestrate together to tightly regulate these networks.

Actin Networks in cell migration

As I have mentioned earlier in section 1.1, the three main well-documented and archetypical actin networks involved in cell migration are lamellipodia, filopodia, and stress fibers (see fig 1.17). Branched actin networks as seen in lamellipodia, parallel actin bundles as seen in filopodia, and contractile actin networks with filaments cross-linked in both parallel and antiparallel directions [START_REF] Letort | Dynamic reorganization of the actin cytoskeleton[END_REF] .

Lamellipodia

Lamellipodia are thin (0.1-0.2 µm), wavy pattern dense branched actin networks observed at the migrating front of the cell [START_REF] Pollard | Cellular Motility Driven by Assembly and Disassembly of Actin Filaments[END_REF] . The Arp2/3 complex is involved in nucleating and initiating branches from the side of actin filaments leading to the formation of a dendritic network (Mullins et al., 1998) . Actin polymerization at the barbed ends in contact with the plasma membrane at the cell front provides the force required for cell migration, through a mechanism called the 'Brownian Ratchet'. Although formins have been known to be present in lamellipodia, it is only recently that formins have been identified to also actively participate in lamellipodia force production [START_REF] Kage | FMNL formins boost lamellipodial force generation[END_REF] . Apart from fomin and the Arp2/3 complex, other ABPs involved in regulating lamellipodial dynamics include nucleation promoting factors (NPFs), Ena/VASP, and disassembly proteins such as GMF, twinfilin and cofilin [START_REF] Gandhi | GMF Is a Cofilin Homolog that Binds Arp2/3 Complex to Stimulate Filament Debranching and Inhibit Actin Nucleation[END_REF] .

Although lamellipodia actin networks have their own specificity, branched actin networks with some level of similarity have also been observed during clathrin-mediated endocytosis (Mund et al., 2018;[START_REF] Weinberg | Clathrin-mediated endocytosis in budding yeast[END_REF] , oocyte spindle positioning [START_REF] Yi | Actin cytoskeleton in cell polarity and asymmetric division during mouse oocyte maturation[END_REF] , and in the comet tails of Listeria monocytogenes that drive the motility of these bacteria [START_REF] Cameron | Dendritic organization of actin comet tails[END_REF] .

Filopodia

Filopodia are thin finger-like projections with parallel actin bundles, of several microns up to 100 µm in length and 0.1-0.3 µm in diameter protruding from the plasma membrane (Mattila & Lappalainen, 2008) . A typical filopodial protrusion consists of 10-20 actin filaments cross-linked together [START_REF] Svitkina | Mechanism of filopodia initiation by reorganization of a dendritic network[END_REF] . Filopodia are highly dynamic and play an important role during cell migration, wound healing, cell signaling, and cell adhesion. They are one of the sensory and exploratory structures of the cell.

To date, the mechanisms and the complete set of proteins involved in the initiation protrusion and retraction of filopodia are not identified clearly. For instance, formin mDia2 [START_REF] Schirenbeck | The Diaphanous-related formin dDia2 is required for the formation and maintenance of filopodia[END_REF] , Ena/VASP (Dent et al., 2007;[START_REF] Schirenbeck | The bundling activity of vasodilator-stimulated phosphoprotein is required for filopodium formation[END_REF] , fascin (Yamashiro-Matsumura [START_REF] Yamashiro-Matsumura | Purification and characterization of an F-actin-bundling 55-kilodalton protein from HeLa cells[END_REF]& Matsumura, , 1986) ) , Capping Protein [START_REF] Sinnar | Capping protein is essential for cell migration in vivo and for filopodial morphology and dynamics[END_REF] , cofilin [START_REF] Gehler | Brain-Derived Neurotrophic Factor Regulation of Retinal Growth Cone Filopodial Dynamics Is Mediated through Actin Depolymerizing Factor/Cofilin[END_REF] , Jahnavi C -doctoral thesis -2021 and IRSp53 ( insulin receptor phosphotyrosine 53 kDa substrate) have a decisive role in filopodia formation and maintenance [START_REF] Ahmed | I-BAR domains, IRSp53 and filopodium formation[END_REF] . Myosin X, an unconventional myosin, has been reported to be required for filopodia initiation [START_REF] Tokuo | The motor activity of myosin-X promotes actin fiber convergence at the cell periphery to initiate filopodia formation[END_REF] . Myosin X has a cargo transport activity [START_REF] Bohil | Myosin-X is a molecular motor that functions in filopodia formation[END_REF][START_REF] Zhang | Myosin-X provides a motor-based link between integrins and the cytoskeleton[END_REF] delivering Mena/VASP [START_REF] Tokuo | Myosin X transports Mena/VASP to the tip of filopodia[END_REF] , and integrins [START_REF] Grabham | Nerve Growth Factor Stimulates the Accumulation of β1 Integrin at the Tips of Filopodia in the Growth Cones of Sympathetic Neurons[END_REF][START_REF] Zhang | Myosin-X provides a motor-based link between integrins and the cytoskeleton[END_REF]) at filopodium tip. ADF/cofilin and myosin II are involved in the severing of the filaments at the base of filopodia to control filopodia length [START_REF] Breitsprecher | Cofilin cooperates with fascin to disassemble filopodial actin filaments[END_REF]Medeiros et al., 2006) .

There are two important models explaining the formation of filopodia.

Convergent elongation model

The main idea behind this model is that filopodia can form from the reorganization of the dendritic/branched actin network (the actin cortex or a lamellipodium). Using EM to observe melanoma cells, Svitkina et al. showed filopodia emerging from lamellipodia (see fig 1.18) [START_REF] Svitkina | Mechanism of filopodia initiation by reorganization of a dendritic network[END_REF] . In this model, while most filament barbed ends in the branched network are eventually capped by CP, recruit formins, and Ena/VASP to the tips. This formin and Ena/VASP decorated filaments elongate rapidly, deforming the plasma membrane that will help them gather together. Now, this group of filaments can be cross-linked to form parallel unbranched bundles resulting in the formation of a filopodium [START_REF] Svitkina | Mechanism of filopodia initiation by reorganization of a dendritic network[END_REF] . Jahnavi C -doctoral thesis -2021

De Novo nucleation or Tip nucleation model

This model suggests that filopodia can be formed even in the absence of Arp2/3 complex as observed in Arp2/3 knock-out mouse melanoma cells where filopodia formation was not affected [START_REF] Steffen | Filopodia Formation in the Absence of Functional WAVE-and Arp2/3-Complexes[END_REF] .

In contrast to the convergent elongation model, where the existing filament ends are elongated by formins/Ena/VASP, here filaments are nucleated and elongated by mDia2 formin or

Ena/VASP at the plasma membrane. The barbed ends of these filaments are thus protected from capping by CP. Eventually, the elongated filaments are cross-linked with fascin to form a parallel bundle.

It was identified in the growth of neural growth cones that the protrusion of filopodia is due to actin polymerization at the barbed ends against the plasma membrane and retraction is due to the retrograde flow of actin [START_REF] Mallavarapu | Regulated Actin Cytoskeleton Assembly at Filopodium Tips Controls Their Extension and Retraction[END_REF] .

There are many unanswered questions about the composition, structure, and mechanism involving protrusion and retraction of filopodia like how cells regulate the number of filaments in the bundle? Do filopodia have a different set of ABPs depending on their function or cell type? Recently, it has been proposed that different stochastic combinations of the ABPs presented above can lead to filopodia formation (Dobramysl et al., 2021) . Why is there more than one actin elongating protein in the tip complex, and how are their activities regulated in the presence of one another still need to be addressed?

In my thesis, I will try to address how the different constraints on formins or bundle size affect the elongation of actin bundles in the presence of fascin. Moreover, I will also study how such bundles can be disassembled by cofilin.

Stress Fibers

Stress fibers are actomyosin structures. They have been first observed in cells grown in tissue culture [START_REF] Buckley | Cytoplasmic fibrils in living cultured cells: A light and electron microscope study[END_REF] . They interact with the Extracellular Matrix (ECM) through the focal adhesions. They are either anchored at one end or at both ends by focal adhesions. They are assembled as a response to the cell's biochemical and mechanical cues [START_REF] Pelham | Cell locomotion and focal adhesions are regulated by substrate flexibility[END_REF] .

Jahnavi C -doctoral thesis -2021

Each stress fiber is composed of largely distributed (~30-300) filaments cross-linked by 𝛼-actinin with mixed polarity (Cramer et al., 1997;[START_REF] Tojkander | Actin stress fibers -assembly, dynamics and biological roles[END_REF] . The mixed polarity is also important for the incorporation of myosin and thus the contractility. Many studies have shown the alternating localization of myosins and 𝛼-actinin along stress fibers, in a sarcomeric fashion, in non-muscle cells [START_REF] Gordon | Immunofluorescent and ultrastructural studies of "sarcomeric" units in stress fibers of cultured non-muscle cells[END_REF][START_REF] Langanger | The molecular organization of myosin in stress fibers of cultured cells[END_REF] . Myosin II is recruited to stress fibers in a tropomyosin isoform-dependent specific way [START_REF] Tojkander | A Molecular Pathway for Myosin II Recruitment to Stress Fibers[END_REF] . Another actin-binding protein involved in cross-linking at the stress fibers termini is fascin [START_REF] Elkhatib | Fascin Plays a Role in Stress Fiber Organization and Focal Adhesion Disassembly[END_REF] .

Depending on their organization in cells and interaction with focal adhesions, there are four different kinds of stress fibers observed in U2OS cells: A) Dorsal stress fibers assembled from formin driven actin polymerization at focal adhesion and they are non-contractile [START_REF] Tojkander | A Molecular Pathway for Myosin II Recruitment to Stress Fibers[END_REF] ; B) Transverse arcs assembly depends on myosin and integration of short actin bundles from lamellipodia. Transverse arcs are curved bundles connecting the dorsal stress fibers to transmit the contractile force to the neighboring fibers. These arcs have the ability to move from the leading front to the center of the cell [START_REF] Heath | Behaviour and structure of the leading lamella in moving fibroblasts. I. Occurrence and centripetal movement of arc-shaped microfilament bundles beneath the dorsal cell surface[END_REF] . C) Ventral stress fibers, which emerge from dorsal stress fibers and transverse arcs (Hotulainen & Lappalainen, 2006;[START_REF] Small | Assembling an actin cytoskeleton for cell attachment and movement[END_REF] . A recent study has shown that the ventral stress fibers can also arise spontaneously from the actin cortex without any pre-existing actin bundles [START_REF] Lehtimäki | Generation of stress fibers through myosin-driven reorganization of the actin cortex[END_REF] . The fourth kind is around the nucleus: D) perinuclear actin caps governing the shape of the nucleus (Khatau et al., 2009;[START_REF] Lehtimäki | Generation of stress fibers through myosin-driven reorganization of the actin cortex[END_REF] .

Stress fibers contractility is important for cellular force generation, producing tension for several cellular processes such as migration, morphogenesis, wound healing (Hinz et al., 2001;[START_REF] Pellegrin | Actin stress fibres[END_REF][START_REF] Tomasek | Myofibroblasts and mechano-regulation of connective tissue remodelling[END_REF] . Proteins like zyxin help in the strengthening of the stress fibers when there is mechanical force exertion on cells by activating formins, and myosin assembly and inhibiting disassembly by cofilin [START_REF] Smith | A zyxin-mediated mechanism for actin stress fiber maintenance and repair[END_REF] . Stress fibers in cells like vascular endothelium [START_REF] Franke | Induction of human vascular endothelial stress fibres by fluid shear stress[END_REF] constantly experience mechanical stress, hence constantly requiring the stress fibers to reorganize, remodel and reorient themselves all the time.

Stress fiber disassembly is not well studied. A study in extracted stress fibers has shown that the myosin is involved in the disassembly at Mg-ATP concentrations higher than the physiological conditions [START_REF] Matsui | Non-muscle myosin II induces disassembly of actin stress fibres independently of myosin light chain dephosphorylation[END_REF] . Here, with a minimal reconstitution of 𝛼-actinin-1 actin bundles and no myosins, I will address in my thesis how these structures are targeted by cofilin for disassembly.

Motivation

General Question:

Actin filaments can withstand a lot of mechanical stress and strain, generated in motile or dividing cells, by assembling into networks. As semiflexible polymers, actin filaments' mechanical properties allow force transmission over microns especially when subjected to tension (can resist forces up to ~200 pN). However, they will buckle easily under compression.

In turn, when filaments are interconnected with the help of cross-linkers like fascin, 𝛼-actinin, fimbrin, and espin (mentioned in section 1.3.3), they create bundles that are more rigid and resist bending compared to their single filament counterparts. Another important aspect is that the twists of actin filaments are constrained due to cross-linking. The mechanical properties of these networks depend upon the cross-linker type: more flexible structures are obtained with cross-linkers like 𝛼-actinin or filamin, or more rigid when filaments are more tightly bundled by fascin or espin.

In cells, bundle networks can be highly dynamic as the components of the network such as actin ABPs regulate the networks could be challenging. In vitro experiments using purified proteins can offer some biochemical control and thus provide useful insights into these mechanisms.

Filopodia actin network as the model system:

The actin network within filopodia can be a good model system to reconstitute and study these questions (See section 1.4.2 for filopodia), as the reconstitution of minimal bundle configuration similar to one seen in filopodium is simple and the geometric constraints are clear. It is very important to understand to what extent those different constraints affect the activity of ABPs.

Jahnavi C -doctoral thesis -2021

In filopodia, 10-20 filaments cross-linked together by fascin, counter the resisting force of tensed plasma membranes, and are able to grow under compression to extend filopodia over microns.

Filaments are in continuous assembly (formins) and disassembly (cofilin), which affects the mechanical properties of the network. Moreover, the constant flux of ABPs in the network, their binding and unbinding, probably also impacts the network's stiffness. Those two features are at play in filopodia, as filopodia grow and shrink, sometimes displaying local kinks. In addition how these proteins diffuse and how they are supplied in these networks is not well understood.

These questions are not addressed here in the thesis and I will focus on the impact of bundling on the function of ABPs.

In my thesis, I am interested in

How cross-linking affects formin activity:

Formins in cells do not actively elongate filaments in the cytoplasm, but are mostly seen to be anchored to membranes through a variety of intermediates (see section 1.3.1-B) or could be part of complexes where multiple formins are interconnected. Formins have been shown to perform helical rotation when processively elongating actin filament barbed ends (H. [START_REF] Mizuno | Rotational movement of the formin mDia1 along the double helical strand of an actin filament[END_REF] . Depending on the degree of freedom of the formin and the actin filament, some mechanical torque may be accumulating which has to be relaxed at some point, as proposed by Shemesh et al. [START_REF] Shemesh | A novel mechanism of actin filament processive capping by formin: Solution of the rotation paradox[END_REF] . How this mechanical torque could affect the formin 52 Jahnavi C -doctoral thesis -2021 activity is not known. This force could provoke the formin to detach or formin to remain bound to the barbed end, hindering or even stalling filament elongation.

Formins are anchored to the membrane and localized at the leading edge of filopodia (see section 1.3.1-B). As a consequence, the rotation of each individual formin might be partially restricted.

In this situation, for formin processive elongation to proceed, the relative rotation between the formin and the actin filament would have to be achieved by the actin filament. But the filaments are constrained by cross-linking in networks, making it difficult or even impossible for them to rotate. How such rotational and geometric constraints affect the activity of formins is intriguing and has never been studied and quantified so far.

By employing different anchoring strategies for formins to restrict their rotation, my aim is to study how formin's activity is affected when either the formin is anchored (single filaments) or when filaments are geometrically constrained by fascin. Such restrictions in filament rotation can lead to the generation of torque and result in a decrease in formin's elongation rate and processivity in two-to three-filament fascin bundles [START_REF] Suzuki | Geometrical Constraints Greatly Hinder Formin mDia1 Activity[END_REF] . I have contributed to this study and I will discuss this later in the results section 4.1.

This study was carried out on bundles of 2-3 filaments, which is significantly less than the 10-20 filaments observed in filopodia. Our goal is to extend these results to bigger bundles, moving closer to the physiological context. The molecular arrangement of the physiological context is summarized in figure 2.2. We expect the behavior to not scale to bigger bundles as the filaments are expected to be arranged in a hexagonal lattice by fascin cross-linking, filaments are connected to several neighbors and bundle supercoiling might impact formin activity. 1.

Filaments (or formins) in the periphery or in the core of the network could be constrained differently. 2. The orientation of the formin/ bundle relative to the lipid bilayer surface might also play an important role in formin activity 3. The lipid bilayer is a reservoir of formins that are available to bind barbed ends upon a formin detachment event; therefore we can study, as a function of formin density, the elongation rate of the whole bundle.

How cross-linking affects cofilin activity:

The cofilin-induced severing of single actin filaments has been extensively studied by bulk assays and more recently using live single filament studies. It is now much more well understood (see section 1.3.1 D) compared to the severing of bundles. However, in cells, actin assembles into different networks and the impact of network architecture on its disassembly is not well understood. This is important to be understood as the disassembly of networks is required for the actin turnover in cells.

A recent study from our lab has shown that cofilin binding generates torsional strain on filaments that are permanently anchored to a surface and thus increases cofilin mediated severing up to 100 -fold (Wioland et al., 2019b) . So far only two studies addressed the question of how the presence of crosslinker fascin affects cofilin activity: with in vitro reconstitution assays, cofilin was shown to have reduced binding activity to filaments to fascin-induced bundles compared to single 54 Jahnavi C -doctoral thesis -2021 filaments. Surprisingly, overall, actin disassembly by cofilin was enhanced for fascin-induced filament bundles [START_REF] Breitsprecher | Cofilin cooperates with fascin to disassemble filopodial actin filaments[END_REF] . Schmoller et al., have shown that actin depolymerization decreases in a cross-linker concentration-dependent manner in their in vitro studies [START_REF] Schmoller | Slow down of actin depolymerization by cross-linking molecules[END_REF] . Though this study reports disassembly over the course of hours, which is very slow compared to what could be physiologically relevant for cell processes.

Interestingly, filaments that were bundled with no cross-linkers, but by the sole presence of a crowding agent, methylcellulose, have been shown to resist cofilin severing activity in bead motility assays (Michelot et al., 2007) . This study observed the fluctuations in the filaments length due to burst of cofilin disassembly at filament pointed ends, which is an indirect observation of bundle severing. Hence, those two studies, with diverging observations prompted us to do experiments to further investigate whether the presence of fascin and the twist constraints imposed by fascin bundling affect cofilin activity. Moreover, these studies in bundles did not fully decipher the underlying molecular details and associated reaction rates of how cofilin targets fascin bundles.

We are also interested in studying how several ABPs are regulated in such tight spatial conformations in networks like in filopodia. It is not so clear how several actin side-binding proteins like fascin, cofilin, and tropomyosins work together in the networks and influence each other's activity. For example, a recent study showed that cofilin has a lower affinity for filaments elongated by mDia1: on twist-constrained filaments, cofilin and mDia1 exert the torque in opposite direction (H. [START_REF] Mizuno | Helical rotation of the diaphanous-related formin mDia1 generates actin filaments resistant to cofilin[END_REF] .

Cofilin has been shown to make filaments more flexible upon binding (McCullough et al., 2008;[START_REF] Prochniewicz | Cofilin Increases the Torsional Flexibility and Dynamics of Actin Filaments[END_REF] , But the effect on cofilin binding, when filaments are under tension, is still a matter of debate, as two publications have shown opposite results. A study, using optical tweezers, has observed that filaments under tension have less cofilin binding than when they are at rest [START_REF] Hayakawa | Actin filaments function as a tension sensor by tension-dependent binding of cofilin to the filament[END_REF] , whereas the study from our lab, using microfluidics to apply tension on filaments, has shown that the tension has very limited on cofilin binding (Wioland et al., 2019b) .

Jahnavi C -doctoral thesis -2021

One major aim of my PhD is to understand how cofilin fragments actin bundles, with precise molecular details: cofilin domain nucleation rate, domain growth, and severing rates.

To study how geometrical constraints on filaments due to fascin cross-linking affect formin and cofilin activity (see fig 2 .3), I have been focusing on the following two questions during my thesis.

1)

How is formin activity affected in bundles larger than 3 filaments?

2)

How does filament bundling affect cofilin activity?

Experimental strategy:

I reconstituted actin bundles in vitro using purified proteins (actin, profilin, formin mDia1, human fascin-1, human cofilin-1) as shown in fig 2 .3, using a microfluidic assay that offers good control of the biochemical conditions during the experiments.

Here, I have employed different strategies to reconstitute large fascin-cross-linked bundles polymerized from formins: 1) lipid micropatterns on a flat surface, 2) beads covered with lipid bilayers, and 3) giant unilamellar vesicles (GUVs): to mimic physiological conditions with formins anchored to the membrane. Jahnavi C -doctoral thesis -2021

For the study of disassembly of actin networks, cross-linked with fascin, I reconstituted networks of interconnected filaments by fascin in a chamber where the network is constrained in two dimensions, and small filament bundles of 2 to 10 filaments in microfluidics. We directly observed the fluorescence of labeled cofilin to study the domain nucleation, domain growth and severing. We employed different imaging techniques such as epifluorescence, Total Internal Reflection Fluorescence (TIRF) microscopy, fluorescence polarization, and electron microscopy to understand the series of events involved in the disassembly and address how the bundle size and fascin concentration affect cofilin activity.

Further, my study was also extended to another crosslinker, 𝛼-actinin, to quantify how differently cofilin disassembles networks made from different cross-linkers. Such study is important as the two crosslinker-generated networks are very different in terms of rigidity and interfilament spacing

MATERIALS AND METHODS

• Human 𝛼-actinin-1 was purified with a GST tag at the N-terminal based on the protocol mentioned in Ciobanasu et al 2014 (Ciobanasu et al., 2015) . For experiments with labeled 𝛼-actinin, purified 𝛼-actinin was labeled on cysteine residues with alexa-568 maleimide (~ 1.8 labeled cysteines per 𝛼-actinin).

• Human profilin-1 was purified according to the procedure from Gieselmann et al. 1995 and is described in [START_REF] Suzuki | Geometrical Constraints Greatly Hinder Formin mDia1 Activity[END_REF][START_REF] Gieselmann | Distinct biochemical characteristics of the two human profilin isoforms[END_REF][START_REF] Suzuki | Geometrical Constraints Greatly Hinder Formin mDia1 Activity[END_REF] • Two different mouse formin mDia1 constructs with various tags at N-or C-terminals on the protein were used to investigate the effect of anchoring on formin activity. These constructs were purified according to the protocol mentioned in [START_REF] Romero | Formin is a processive motor that requires profilin to accelerate actin assembly and associated ATP hydrolysis[END_REF][START_REF] Suzuki | Geometrical Constraints Greatly Hinder Formin mDia1 Activity[END_REF] . The two constructs are homodimers (FH1-FH2 DAD, 552-1255 aa, Uniprot:008808).

The construct for FH1 anchoring has a 6xHistidine tag at the N-terminus and a Strep-Tag II at the C-terminus. The FH2 anchoring construct has the 6xHis tag at the C-terminus and a SNAP-tag at the N-terminus.

• Mouse Capping Protein heterodimer 𝛼1𝛽2 with a histidine tag at the N-terminal was purified according to the procedure described in [START_REF] Wioland | ADF/Cofilin Accelerates Actin Dynamics by Severing Filaments and Promoting Their Depolymerization at Both Ends[END_REF] .

See fig 3.1 for the SDS-PAGE gels to assess the purity of proteins mDia1, fascin, mCherrycofilin-1, and 𝛼-actinin-1. Jahnavi C -doctoral thesis -2021

Studying actin dynamics using microfluidics assisted microscopy

A) Microfluidics

Microfluidics is the discipline where fluids can be manipulated and precisely controlled fluids, in the microlitres to nanolitres range, and in channels with a typical size of tens to several hundreds of micrometers.

In our lab, we mainly use microfluidic chambers consisting of a molded PDMS (Poly-Dimethyl-Siloxane) chamber attached to a glass coverslip by permanent covalent bonding, by exposing them to deep UV for 4 min. To ensure proper bonding, the chamber was then heated on a hotplate at 100℃ for 5 min. Previously, glass coverslips (22x40 mm, #1.5) were cleaned in bath sonication following several steps in the following order: 2% Hellmanex for 30 min at 35℃, 2M potassium hydroxide (KOH) for 20 min at room temperature, and for 30 min in absolute ethanol. Coverslips were washed thoroughly with milli-Q water in between these steps.

Finally, coverslips were stored in absolute ethanol until used for up to 2 weeks.

The PDMS chamber forms the flow cell of the experiment and consists of typically 3 inlets and one outlet. The channels of the chamber were cross-shaped. Chambers of different heights 20, 40, or 60 µm, and different widths of 800 or 1600 µm were used for different experiments, mostly to apply low or high friction forces to the actin filaments anchored to the glass coverslip.

The chamber was connected to the MCFS-EZ Fluigent flow control system (Fluigent), and filled with a buffer. The system was then handled to achieve different biochemical conditions depending on the experiment. The chamber was mounted on a fluorescent microscope (TIRF and/or epifluorescence).

Microfluidics is a powerful and versatile technique. It has been used for studying actin dynamics for the first time in our lab, but now over the past 10 years it is being used by more labs (L. [START_REF] Cao | Modulation of formin processivity by profilin and mechanical tension[END_REF][START_REF] Courtemanche | Tension modulates actin filament polymerization mediated by formin and profilin[END_REF][START_REF] Jégou | Individual Actin Filaments in a Microfluidic Flow Reveal the Mechanism of ATP Hydrolysis and Give Insight Into the Properties of Profilin[END_REF][START_REF] Shekhar | Twinfilin bypasses assembly conditions and actin filament aging to drive barbed end depolymerization[END_REF]Wioland et al., 2019b[START_REF] Wioland | The advantages of microfluidics to study actin biochemistry and biomechanics[END_REF] .

Compared to the more classical open chamber assay which appeared in the '90s to monitor the (Howard, 2001;[START_REF] Jégou | Formin mDia1 senses and generates mechanical forces on actin filaments[END_REF] . This feature offers an elegant way to exert pulling forces on tens of filaments in parallel. Such parallelization is very difficult to achieve with a conventional optical tweezer system. Though, the fluctuations of the applied pulling force are much more reduced when applied with an optical tweezers system (~5%) than with a microfluidics flow (~30%).

For some experiments involving the reconstitution of actin networks, we used open chambers (see fig 3.2 B). These chambers were assembled with cleaned glass coverslips and parafilm heated on the hotplate for <1 min at 60℃. The chamber volume is typically ~10 µL, which reduces the amount of proteins consumed compared to a microfluidics assay where protein solutions are constantly flowed in.

• Experiments were performed at room temperature (20-25°C), in F-buffer:

B) Microscopy

Microfluidic chambers were mounted on a Nikon Eclipse Ti inverted microscope with a 60X objective NA 1.49. Images were acquired mostly in epifluorescence or Total Internal Reflection Microscopy (TIRF) using the iLas system from Gataca-systems, using an sCMOS Orca-Flash4.0 camera (Hamamatsu) and controlled using the micromanager software.

Formin anchoring strategies

To investigate the effect of formin anchoring on its activity, I carried out experiments as follows.

Experiments were designed such that I could compare anchored formins (either FH1 side or FH2 side) directly with as reference condition, unanchored formins, within the same chamber. I took advantage of microfluidics to inject two different protein solutions at the same time. I expose them to the same biochemical condition to assess actin elongation and formin processivity.

Different linking strategies were employed to have interaction of formins with the surface, or with the lipids. For instance, histidine tag interaction with polyhistidine antibodies or Ni-NTA lipids. (see fig 4.1)

Anchoring seeds in a microfluidic chamber

To assess unanchored formin activity, actin filaments are elongated from surface anchored spectrin actin seeds (SAS/seeds) (see fig 3.3 top). Filaments were anchored at their pointed end, with their barbed end unanchored. This was achieved by following steps. Following the connection of the microfluidic chamber with the buffer, the glass surface was exposed to 2 pM SAS for exactly 4 min at a high flow rate in a chamber of 20 µm height, in order to get a reasonable seed density (~160 seeds per 100 x100 µm²). Then the surface was passivated using 5% Bovine Serum Albumin (BSA) for at least 5 minutes. After this, the experimental setup was ready to elongate actin filaments by exposing the SAS to actin.

Also, this is the same setup that I used to make bundles with fascin for cofilin experiments ( anchoring seeds to the surface).

Finally, the actin filaments were elongated to a certain length around 3-5 µm in length, exposed to 5 nM of formin mDia1 before exposing them to a specific elongating condition (see the Results section). This results in the majority of the barbed ends being formin-bound. The remaining free barbed ends are used as internal control, to assess elongation rate in the absence of formins.

Glass anchoring

The glass surface for formin anchoring was prepared as follows: chamber was connected with buffer (see fig 3.3 bottom). This was followed by an injection of 10 µg/mL of neutravidin in the F-buffer for 5 min. Here, neutravidin adsorbs to the glass non-specifically. Surface passivation was achieved by subsequently injecting a solution supplemented with 5% BSA for 5 min. Next, the surface was further functionalized by injecting 1 µg/mL biotinylated PentaHis antibody (Qiagen) in F-buffer for 5 min. Finally, the formins with His-tag (either at their FH1 side or FH2 side) were injected at 5 nM in F-buffer for 5 min.

Lipid anchoring

Different strategies were employed to have a reservoir of mDia1 formins freely diffusing on lipid bilayers: Supported lipid bilayers on glass coverslips or glass beads, or Giant Unilamellar Vesicles (GUVs).

In my experiments, injected formins can interact with the NTA lipids with the 6xHis tag through their FH1 or FH2 side. Short preformed actin filaments were injected into the microfluidic chamber. The filaments' barbed end was caught by the lipid anchored formins. Due to the flow, the formins with filaments slide to the edge of the patterns or are collected downstream to GUVs/bilayer coated with beads. When the desired number of filaments were collected by formins, single filaments were elongated with exposure to a mixture of actin/profilin. For the formation of bundles larger than 3 filaments, exposed to a mixture of actin/fascin/ profilin (see

fig 3.3 bottom).
Usual composition of liposomes for bilayers: DOPC complemented with DOGS Ni-NTA (1-4%), and with or without Rhodamine-PE 0.05%. For bilayer with biotin lipids, DSPE biotin lipids 0.1-1% were used in the place of Ni-NTA lipids.

• Supported lipid bilayers SLBs):

To study the formin activity in microfluidics on lipids, we need lipid boundaries. To achieve this, we used micropatterns on the glass surface to assemble the SLBs. The assembly of SLBs involves two components for the experimental setup i.e., a) preparation of liposomes b) preparation of PEG-silane passivated coverslips. Here the SLBs were formed with the vesicle fusion method on glass in patterns of different sizes burnt in PEG-silane passivated coverslips.

Liposome preparation: Our liposome preparation consists of 96% DOPC, 4% DGS-NTA, and Liss-Rhodamine PE lipids from Avanti polar lipids. All lipids were stored at -20°C in chloroform and brought to room temperature before liposome preparation. Required amounts of lipids (in chloroform) were added to a glass tube using only glass syringes. Then the lipids were dried using the flow of argon gas and further dried up by leaving the glass tube in a vacuum for 1 hr.

The dried lipids were resuspended in PBS in the same glass tube on a gentle vortex at room temperature for 30 min to form large multilamellar vesicles to achieve a 1 mg/mL lipid concentration. The aliquots of liposomes were subjected to 5 freeze-thaw cycles in liquid nitrogen to form small unilamellar vesicles. After this, liposomes are stored at -80°C until used.

On the day of experiments, liposomes were brought to room temperature and sonicated for 5 minutes (pulse on for 30s and off for 30s at 100% amplitude) using a tip sonicator. This step also • Beads coated with bilayers:

Glass beads were coated with bilayer following the protocol in (Hansen and Mullins 2015). 10 µL beads of 5 or 2 µm in diameter (stock at 10 %wt/vol) were washed with 1M KOH with sonication for 30 min. This was followed by a washing ( ie resuspension/centrifugation) step in the F-buffer, repeated three times. Next, the beads were incubated with the 20 µL liposome solution (1 mg/mL) along with 5 mM Calcium chloride. Beads along with the liposomes were left on a gentle vortex for 5 min. Excess liposomes solution was removed by washing/centrifugation in the F-buffer. Next, bilayer coated beads were passivated with 5% BSA followed by washing with F-buffer. Later, they were incubated with 5 nM formins for 5 min.

Finally, 40 µl formin-coated beads + 160 µl buffer was injected into the PDMS chamber with a glass coverslip and connected to the microfluidics with F-buffer (see fig 3.4 B).

• Giant Unilamellar Vesicles GUVs):

In collaboration with Stephanie Mangenot (Institut Curie), we successfully prepared GUVs with both biotin and NTA-containing lipids using the electroformation method. The aim is to have the GUVs anchored to the surface of the coverslips with neutravidin so that we can image the GUVs in microfluidics.

This technique involves the hydration of dried lipid film using an oscillating electric field. The required lipid solution was coated on ITO-coated slides on their conductive sides and dried in vacuum for 30 min. Slides were joined together to form a chamber using vitex paste. Before closing the chamber, it was filled with an inner buffer (100 mM sucrose and 25 mM Tris) and Jahnavi C -doctoral thesis -2021 closed with the vitrex paste. This chamber was connected to a generator with copper clips delivering 10 Hz and 1V for 1-2hr. GUVs were collected, stored at 4℃, and used within a week.

This technique generates GUVs of typical size 1 µm-100 µm in diameter which are mostly unilamellar. The F-buffer with 50 mM KCl was used as the outer buffer. The outer buffer osmolarity was adjusted to one of the inner sucrose solution, by adding a few microliters from 1M sucrose stock solution. Next, the KCl was added after the osmolarity of the buffer was adjusted.

For these experiments, it was very important to maintain the osmolarity of the buffers. Changes in the osmolarity of the buffer would result in the shrinking and swelling of the GUVs.

Eventually, the GUVs could collapse in the microfluidic flow due to hyper or hypotonic buffers.

So care was taken to prepare such that the buffer inside the GUVs and outside the GUVs does not deviate more than 10% in their osmolarity.

To Jahnavi C -doctoral thesis -2021

Analyzing formin activity

Elongation rates and detachment rates

To assess the formin activity, we measured actin filament elongation rates and formin detachment rates from barbed ends (processivity). Images were analyzed using the software Image J (NIH).

A region with at least 30 single filaments was selected. All the filaments were analyzed in this region. By looking at the kymographs for each filament, a kymograph is constructed and the elongation rate is derived by measuring its slope (see figure 3.6). Here, the presence of mDia1 formins at the barbed ends results in faster elongation of barbed ends than for free barbed ends.

A formin detachment event could be observed in kymographs as a sharp change in slope in the case of unanchored formins. In the case of glass anchored or lipid anchored formins, formin detachment from the barbed end could be easily seen, as the filament disappears from the field of view. The time at which those events occurred were tracked in order to build the survival fraction of formins that has not detached yet, using the Kaplan-Meier method [START_REF] Kaplan | Nonparametric Estimation from Incomplete Observations[END_REF] . Jahnavi C -doctoral thesis -2021

We excluded filaments that are stuck to the surface, severing of filament due to the light and stalling of anchored formins from our analysis.

3.4 Experimental setups for cofilin activity on bundles PLL-PEG polymer brush to passivate our surfaces, as it resulted, at least for those proteins, in better surface passivation than BSA. Prior to passivation, the chamber was exposed to 2 pM SAS for 5 min. A mixture of 20 µL PLL-PEG (1 mg/mL), 10 µL BSA (50 mg/mL), and 10 µL 𝜅-casein (1 mg/mL) was then injected into the chamber and incubated for at least 30 minutes at room temperature in a humidity chamber. After the incubation, the chamber is connected to the microfluidic device with an F-buffer.

Actin bundle formation and exposure to cofilin

For the actin bundle formation, the microfluidic chamber was prepared similar to the procedure described above for unanchored formins until the SAS elongated with actin as mentioned in section 3.3.1.

A. For bundles with two filaments

The filaments were elongated to typically around 5-10 µm in length by exposing them to 1 µM 10% Alexa-488 labeled actin. Next, the filaments were bundled and aged for 15 minutes (see section 5.1.2) by exposing them to 0.2 µM fascin + 0.13 µM labeled actin. Close enough filaments could zipper together forming fascin-induced bundles [START_REF] Breitsprecher | Molecular mechanism of Ena/VASP-mediated actin-filament elongation[END_REF][START_REF] Suzuki | Geometrical Constraints Greatly Hinder Formin mDia1 Activity[END_REF] . The SAS concentration was optimized so that we have both single filaments and 2-filament bundles in the same field of view. Having single filaments together with the bundles in the same field of view provides an important internal control for each experiment performed.

Cofilin-1 binds with a much higher affinity to ADP-F-actin than ADP-Pi-F-actin [START_REF] Carlier | Actin Depolymerizing Factor (ADF/Cofilin) Enhances the Rate of Filament Turnover: Implication in Actin-based Motility[END_REF] . The Pi release from actin subunits in a filament is a random process with a characteristic rate of 7•10 -3 s -1 (I. [START_REF] Fujiwara | Polymerization kinetics of ADP-and ADP-Pi-actin determined by fluorescence microscopy[END_REF][START_REF] Jégou | Individual Actin Filaments in a Microfluidic Flow Reveal the Mechanism of ATP Hydrolysis and Give Insight Into the Properties of Profilin[END_REF] . We aged the filaments for 15

Jahnavi C -doctoral thesis -2021 minutes in F-buffer so that they will be composed of >99% ADP-F-actin subunits after aging and cofilin should bind with the same rate throughout filament length. Since we are limited by the number of inlets available in our experiments, we age and bundle filaments together. We therefore also expose the filaments to 0.13 µM actin (slightly above the steady-state barbed end actin concentration), so that filaments will not shrink or grow during the 15 minutes aging process.

After aging, single filaments and bundles were typically exposed to 0.2 µM labeled mCherry-cofilin along with 0.2 µM fascin, and 0.13 µM actin, unless otherwise stated. Images

were acquired typically at a rate of 1 frame every 10 seconds.

To verify that fascin-induced bundling had no major impact on the Pi release in bundled filaments, we measured their depolymerization rate in the buffer (thus the bundles 'unbundled' back to single filaments, since there was no fascin) see fig 3.7. They depolymerized at a rate of ~11 subunits/s, similar to control filaments never exposed to fascin. This rate of polymerization is in agreement with the ADP-actin departure rate at 25°C in a pH 7.4 buffer (Wioland et al., 2019a) . Jahnavi C -doctoral thesis -2021

B. Forming bigger actin bundles on beads

Forming bigger bundles (>3 filaments) using seeds that are randomly distributed on the surface of the coverslip is very challenging and the relative position of the seeds along the bundle makes it difficult to control the bundle size (i.e. the number of filaments) along the bundle, as it will frequently change (see fig 3.8). To circumvent this difficulty, we have used 1 µm in diameter beads functionalized with seeds, anchored to the glass surface, to elongate filaments and form bigger bundles. As all filaments elongate synchronously and elongate from the bead surface, this ensures that along the bundle shaft the bundle size is constant prior to being exposed to cofilin.

Glass beads of 1 µm diameter, previously washed in 1 M KOH (sonication for 30 min and washed three times in FME buffer) were functionalized and incubated with > 1 nM SAS (100 -fold dilution for beads) for 5 min at room temperature. Then excess SAS were washed with an F-buffer. SAS coated beads (final dilution 270-fold) were manually injected using a micropipette Jahnavi C -doctoral thesis -2021 into the microfluidic chamber through the outlet and allowed to settle on the surface (typically 5 minutes). Then the rest of the inlets were connected to the chamber injecting F-buffer, and the experiment can proceed following the same steps as for the SAS/seeds experiments (see fig 3.9).

With this method, we achieved bigger bundles on the beads. Bundle sizes on the different beads were quantified looking at the actin fluorescence intensity. The distribution is shown in Fig 3 .10.

One downside of this approach though, was we could not know the exact filament arrangement in the bundles and whether we were looking at one or more bundles. Jahnavi C -doctoral thesis -2021

Analyzing cofilin activity in bundles

Disassembly of bundles by cofilin was analyzed by looking at the three following types of events: cofilin domain nucleation, cofilin domain growth, and cofilin domain boundary severing (or whole bundle severing). For each individual experiment (or dataset), these corresponding rates on bundles were compared to the one measured on single filaments. A field of view containing both single filaments and bundles was selected and analyzed. Systematic analysis of all filaments (or bundles) within a predefined area was performed to avoid any (human) bias.

Microsoft Excel and python/scipy were used for statistical tests.

As we could not perform three-color imaging to simultaneously observe actin, fascin, and cofilin to identify the number of actin filaments in a bundle or to see the effect of labeling on recruitment of cofilin (section 5.1 in results), we relied upon the actin fluorescence to make sure that we were analyzing the bundles. The actin fluorescence of bundles of two filaments is on average, double the fluorescence of single actin filaments (figure 3.11 B). We also determined the positions of the spectrin-actin seeds by taking a snapshot of the actin filaments at an early stage of the elongation step and used this to further confirm the number of filaments engaged in a bundle (figure 3.11 A). 1

Domain nucleation rate

Single filaments and bundles were divided into segments of 4.3 µm (= 20 pixels on our camera).

Filaments may not be completely bundled by fascin, either at the region closer to the anchoring point, due to the distance between the seeds, or at the end of the bundles (see Fig 3.11. B Right).

Those regions were excluded from our analysis. Moreover, cofilin nucleates domains much faster in sharply bent regions, which are encountered close to the seeds due to their random orientation on the surface (Wioland et al., 2019b) . Jahnavi C -doctoral thesis -2021

To derive cofilin nucleation rates per available cofilin binding site on the filaments, we took into account considering that all sites are available in the bundled filament that a bundle of twofilaments have twice more binding sites than a single filament. So we used segments that were half as long in bundles (2.15 µm or 10 pixels on our camera) to have the same total number of binding sites on single filament, except for large bundles where that would lead to analyzing very small segments, so instead we divided the measured rate by the number of filaments in the bundle.

The time at which a cofilin domain appeared on filament/bundle segments was used to construct the survival fraction of segments without any cofilin domain (see figure 5.7 for example of curves). Filaments lost due to severing occurring upstream a tracked segment were considered as censoring events, and the Kaplan Meier method was used to take them into account [START_REF] Kaplan | Nonparametric Estimation from Incomplete Observations[END_REF] . The survival fraction curve was constructed either using the excel or the 'lifelines' A cofilin domain grows symmetrically towards both ends on a single filament [START_REF] Wioland | ADF/Cofilin Accelerates Actin Dynamics by Severing Filaments and Promoting Their Depolymerization at Both Ends[END_REF] . Growth rates at each end of the domain were obtained by observing the domain fluorescence over time in kymographs. Average growth rates at each end were calculated.

Domain severing rate

A domain severing event on a single filament, either at the pointed or the barbed end of a domain, was counted when the downstream part of the actin filament was lost and flowed away with the flow in the chamber. Those events were recorded manually. The time difference between the appearance of a cofilin domain and this severing event was used to derive the cofilin severing rate in a specific experiment. Again, censoring events due to other types of events (filaments lost) preventing the observation of the outcome of a cofilin domain were taken into account and used to construct the survival fraction of cofilin domains that have not severed yet (see fig 5.9 A), using the Kaplan Meier method.

The severing of 2-filament bundles requires more than one single cofilin domain severing. There have to be two severing events, one on each of the filaments of the bundle, domains which should spatially overlap (see fig 3 .12; explained further in results section). Then this can lead to the loss of the downstream part of the bundle with the flow. However, it is harder to separate/distinguish between both events. One way is to look at the decrease in cofilin domain fluorescence intensity drops. This helped us to observe the events of domain severing on bundles.

Determination of actin filament rotation in a bundle upon cofilin binding

Coflin binding increases the helicity of actin filaments (change of 9° degrees per actin subunits along the long helical pitch [START_REF] Galkin | Remodeling of actin filaments by ADF/cofilin proteins[END_REF] ). This effect induces torsional stress on twist constrained filaments (Wioland et al., 2019b) . When filaments are bundled, each filament is paired to a neighboring filament. As a consequence, one might wonder whether a cofilin domain is able to induce the rotation of the segment of the bundle downstream the cofilin domain. We

A) Single-molecule fluorescence polarisation

Fluorescence polarisation is a technique that has proven to be powerful to study the rotational movement of proteins with a fluorescent probe. In particular, several studies have adapted and used this technique to study the actin filament orientation or rotation when interacting with some ABPs such as formin, myosin, fascin, and cofilin [START_REF] Mizuno | Rotational movement of the formin mDia1 along the double helical strand of an actin filament[END_REF][START_REF] Sase | Axial rotation of sliding actin filaments revealed by single-fluorophore imaging[END_REF]Suzuki et al. 2020;Wioland et al. 2019).

To probe actin bundle rotation when exposed to cofilin, in a microfluidic chamber, actin filaments were elongated from SAS, using both 5% alexa-488 labeled actin and 0. and sent to two separate areas of the camera detector (see fig 3.13 Right). This results in the proper alignment of the polarization of the emitted light with respect to the optical path, so that maximum emission can be collected for both FL V and FL H . In the end, the camera displays two images corresponding to the two polarization emissions of the fluorophore.

Actin filaments were elongated with a mixture of 0.5 µM 0.2 % labeled alexa-568 actin and 5% alexa-488 actin for 15 min, to slowly grow the filaments and partially age them so that cofilin can 'efficiently' bind to them. Next, the filaments were exposed to 0.2 µM unlabeled fascin for 1 minute to induce filament bundling. Finally, the bundles were exposed to 0.2 µM unlabeled fascin, and 0.2 µM cofilin. Images were captured in both channels with an acquisition interval of 2 seconds, exposure time of 50 ms for alexa-488, and 200 ms for alexa-568.

We could image both single filaments and two filaments actin bundles in the same field of view.

The control experiment of observing single filaments and bundles (no cofilin) in F-buffer, to record the fluorophore intensities due to fluctuations in filaments due to flow were also done.

For image processing, the speckles that were part of a single filament or bundle were identified in the pair of images. For each frame, the vertical and horizontal fluorescence polarizations were obtained by measuring the average intensity in a 5x5 pixels ROI minus the average background intensity in a region close to the ROI of interest. Finally, the fluorescence polarization (FL P ) was calculated using the formula.

FL P = (FL H -FL V )/(FL H + FL V ).

B) Transmission Electron Microscopy TEM imaging

Experiments with EM were conducted at the Imagoseine platform at Institut Jacques Monod.

Experiments were done on a Tecnai 12 microscope, equipped with a CCD camera, under the expertise of Remi le Borgne, member of the ImagoSeine imaging platform at the institute.

EM samples were prepared as follows: 10 µM actin was pre-polymerized in an eppendorf tube for at least 5 hours at room temperature in F-buffer. Just before depositing the sample on the EM grid, filaments were diluted to 1 µM and mixed with 0.2 or 1 µM fascin and 0.2-0.3 µM cofilin, or in the absence of both for the control condition, to a final volume of 20 µL. The plasma-activated copper grids (400 mesh). Freshly mixed samples were loaded on the copper mesh grids for 1 min and the excess sample was removed using a blotting paper. Next, the samples were stained with uranyl acetate for 1 min. Once positioned into the microscope, the samples were frozen and imaged at different magnifications.

RESULTS

Jahnavi C -doctoral thesis -2021

Geometric constraints hindering formin activity

Surface anchoring of formins weakly aects its activity

This study was published in [START_REF] Suzuki | Geometrical Constraints Greatly Hinder Formin mDia1 Activity[END_REF] . This study was mainly the work of a former PhD student Emiko Suzuki from our lab. I contributed to perform further additional control experiments on the effect of anchoring constraints on formin's activity.

For single filaments, either FH1 or FH2 anchored formins (for methods see 3.3), were elongated using 0.2 µM actin and 0.2 µM profilin. The elongation and processivity rates of formin were calculated as mentioned in section 3.3.4. The activity of anchored formins was compared to the activity of unanchored formins. Here, we observed that elongation rates of anchored formins were reduced slightly (by less than 20%) compared to the reference rate of unanchored formins present in the same chamber (Fig 4 .1.B). Moreover, the detachment rates of formins were not affected except for the condition of FH2 side-anchored formins, with an increase in the detachment rates of 2.5-fold on lipids. This is the condition where the FH2 to surface distance was the shortest ( see fig 4 .1 A right) and our interpretation was that this shorter link increases the frequency of the formin to contact the surface (in a region which contains the boundary between lipids and the PLL-PEG brush). Such contact events may affect the ability of formins to translocate at the barbed end, thus reducing formin processivity.

Activity of formins in bigger bundles

In physiological situations, filopodia are composed of bundles with more than three filaments.

Emiko Suzuki has observed that in fascin cross-linked actin bundles of two to three filaments, elongation rates, and detachment rates were greatly affected, in particular for trailing formins anchored to glass (see fig 4 .2). Formin's activity was improved when attached to lipids as formins being free to reposition themselves might help in reducing hindrance [START_REF] Suzuki | Geometrical Constraints Greatly Hinder Formin mDia1 Activity[END_REF] . Still those results may only partially explain how formins collectively work to elongate actin bundles made of 10 to 20 filaments in filopodia. How does the 'crowding' at the lipid/bundle interface impede or on the contrary favor the processivity of formins? Are formins by incorporating monomers can induce actin depletion which could slow down the overall elongation of the actin bundle? If there is a mismatch of formin elongation between formins involved in bundle elongation, this may cause mechanical pulling on some of them, which accelerates their detachment and lead to the reduction of bundle size as it elongates? These Jahnavi C -doctoral thesis -2021 questions require specific new in vitro assays that extend beyond what has been described above, in order to be addressed.

To study how formin activity will be affected in bigger bundles of fascin, we adapted the type of patterns used in Suzuki et al, 2020 and were changed to circles of diameter 2 or 5 µm. This could help us to have individual bundles in each pattern of different sizes in our field of view.

Hence, the edges of the patterns are not as crowded as with bigger, square patterns.

Next, Ni-NTA-containing SLBs were made in these patterns and exposed to His-tag formins.

When the surface was exposed to short preformed actin filaments, we observed that the formins that caught the barbed ends of filaments gathered at the downstream part of the patterns successfully. Then the filaments were exposed to actin, profilin, and fascin to elongate them and observe formin activity. We observed individual bundles on each pattern. However, the main difficulty appeared to be that the density of active formins remained low on the patterns, preventing the formation of bundles with enough filaments. When the bundle elongates, some formins are pushed upstream and reach the opposite edge of the pattern. Interestingly, once at the upstream edge, formins seems to rapidly unbind from the filament barbed ends. Those events indicated that, in this specific geometry, a pushing force originating mainly from actin polymerization, and is limited by the buckling force of a single actin filament (here, estimated ~ 0.2 pN), was sufficient to detach formin from the barbed end. Jahnavi C -doctoral thesis -2021

Next, we have used beads as support for lipid anchored formins. Beads were coated with a lipid bilayer, with 4% of Ni-NTA functionalized lipids headgroups. These beads were introduced into the microfluidics and allowed to settle down on the surface. Beads were then exposed to 80 nM formins for ~8 minutes. Next, 1-2 µM of short alexa-488 labeled preformed filaments (< 2 µm in length) were flowed into the chamber. Formins caught the barbed end of the filaments and, due to the flow, they gathered downstream of the beads. Using 0.5 µM actin and 2 µM profilin, filaments were elongated.

The fluidity of bilayer around the beads and the specificity of the protein anchoring via the NTA-lipids was confirmed by using 40 nM His-tag Capping protein (CP) (see fig 4.3). Here, the CP also caught the filaments by their barbed end when exposed to preformed short filaments. In contrast to formins, we observed that filaments gathered nicely downstream of the beads implying that the protein can freely diffuse around the bilayer. We interpreted that formins, having multiple domains, some being elongated disordered, some harboring different surfaces of with opposing net charges, represent a difficult challenge to control their anchorage on lipid surfaces, while ensuring that they do not form aggregates and remain active.

Our next attempt was to better orient the elongating filaments relative to the lipid surface so that they would better match the physiological situation. To do that we made the GUVs with both Ni-NTA and biotin lipids (see section 3.3.3 in methods). The GUVs with 4 % of Ni-NTA lipids 91 In either case, having the right amount of formins on the surface was very difficult. Moreover, either with the lipid-coated beads or the GUVs, we had difficulty in maintaining the bigger bundles downstream. Interestingly, we observed flow-dependent instabilities, like bundles rotating along with the GUVs. When the bundles were generated from lipid patterns, we observed that bundles would unzip (shown in Fig 4.5).

92 ABSTRACT: Formins are one of the central players in the assembly of most actin networks in cells. The sensitivity of these processive molecular machines to mechanical tension is now well established. However, how the activity of formins is affected by geometrical constraints related to network architecture, such as filament cross-linking and formin spatial confinement, remains largely unknown. Combining microfluidics and micropatterning, we reconstituted in vitro mDia1 formin-elongated filament bundles induced by fascin, with different geometrical constraints on the formins, and measured the impact of these constraints on formin elongation rate and processivity. When filaments are not bundled, the anchoring details of formins have only a mild impact on their processivity and do not affect their elongation rate.

When formins are unanchored, we show that filament bundling by fascin reduces both their elongation rate and their processivity. Strikingly, when filaments elongated by surface-anchored formins are cross-linked together, formin elongation rate immediately decreases and processivity is reduced up to 24-fold depending on the cumulative impact of formin rotational and translational freedom. Our results reveal an unexpected crosstalk between the constraints at the filament and the formin levels. We anticipate that in cells the molecular details of formin anchoring to the plasma membrane strongly modulate formin activity at actin filament barbed ends. KEYWORDS: Formin, actin, bundle, cytoskeleton, microfluidics, fluorescence polarization T o perform complex cellular functions and mechano- transduction at the micron scale, actin filaments assemble to create networks that vary in size, structure, and dynamics. Actin filaments are continuously generated, polymerized, crosslinked to each other, or attached to membranous cellular compartments. The intertwining of actin filament assembly and cross-linking is tightly regulated in space and time to shape the various cytoskeletal structures, such as the cell cortex, stress fibers, or transverse arcs. 1 Formins, together with Ena/VASPs, are actin binding proteins that have the unique ability to processively track actin filament barbed ends and increase their elongation rates. 2-5 Members of the formin family are head-to-tail homodimers with two functional formin homology domains, FH1 and FH2 (recently reviewed in 6 and 7). The FH2 homodimer interacts with the last subunits of the actin filament barbed end, adopts different conformations in rapid equilibrium, and gates actin monomer addition or removal from the barbed end. 8 The FH1 domains are disordered domains harboring multiple polyproline tracks to which profilin and profilin-actin complexes bind. These two functional domains work together to speed up actin filament barbed end elongation. 9,10 The mechanosensitivity of formins is now well established. Applying a pulling force on a formin bound to an actin filament led to an increase in barbed end elongation rate for mDia1, 11-14 mDia2, 15,16 and Bni1p, 17 whereas the opposite effect was observed for Cdc12 16 and for Bni1p in the absence of profilin. 17 The processivity of mDia1 and mDia2 formins was shown to depend on the efficiency of FH1 domains to bind, with the help of profilin, to the actin filament barbed end and to thereby increase the lifetime of the FH2 interaction with the barbed end. 15 Most importantly, formin mDia1 and mDia2 processivity was shown to be severely reduced when a pulling force was applied on those formins with a 3 pN pulling force increasing the formin dissociation rate more than 10fold. 15 Lastly, observations using magnetic tweezers to probe the increase in elongation rate with force revealed that mDia1 formins were also sensitive to torque. 13 These observations have provided novel insights into the molecular details of formin function and crucial evidence for the high sensitivity of formins to biochemical and mechanical conditions to which they are exposed. However, these insights were obtained for individual formins elongating single isolated actin filaments. This situation is rarely, if ever, encountered in cells where formins elongate filaments which are cross-linked together into various networks, such as the cell cortex, filopodia, and stress fibers. 18 Furthermore, in cells formins are specifically localized to membranes thanks mostly to interactions with other proteins like GTPases, IQGAP1, or IRSp53 (reviewed in refs 19 and 20). Formin localization is mediated by domains at the amino-terminus of the FH1 domain or by FH1 itself in the case of its interaction with IRSp53. It is thus necessary to study formins in a more physiological context, where formins are anchored and filaments are cross-linked, to better understand the impact of these constraints on their activity.

Here, using in vitro approaches, we investigated the activity of mDia1(FH1FH2DAD) formins (hereafter referred to as formins) in various geometrical configurations with the fascininduced bundle geometry as a case study. As readouts of formin activity, we monitored the elongation rate of filament barbed ends and the formin detachment rate. We first examined, separately, the consequences of geometrical constraints on formins (anchoring) and on filaments (bundling). Different anchoring conditions were tested, binding formins from either end (FH1 or FH2 side) on a solid or a fluid surface. None of these conditions had a significant impact on formin activity at the barbed ends of independent, individual filaments (Figure 1). When we bundled filaments elongating with free, unanchored formins, we found that bundling on its own slowed down elongation and enhanced formin detachment (Figure 2). We next combined filament bundling and formin anchoring and found that formin activity was affected further, in ways that depended on the anchoring features (Figures 345). These results show that details of formin anchoring, which appear inconsequential when elongating single filaments, become crucial when filaments are bundled together. We determined that in order to function efficiently when filaments are bundled, anchored formins must have both rotational freedom (Figure 4) and translational freedom (Figure 5).

Anchoring a Single Formin mDia1 Weakly Affects Its Activity. In cells, activated formins are bound to membranes compartments, via direct binding to lipids or through protein complexes. 21,22 To study the impact of formin anchoring, we used an in vitro microfluidics approach where we tested four different anchoring schemes and compared them to situations where the formins were not anchored; formins were anchored by either their N-terminus or their C-terminus and either to proteins adsorbed on glass (referred to as "FH1-anchored-toglass" and "FH2-anchored-to-glass" formins) or to a freely diffusing lipid bilayer bordered by a PEG brush (referred to as "FH1-anchored-to-lipids" and "FH2-anchored-to-lipids" formins) (see Figure 1A and Supporting Information Methods).

In all these configurations, individual anchored formins were probed in terms of elongation rate and processivity (Figure 1B,C, Supporting Information Figure 1A)a n dd i r e c t l y compared to unanchored formins within the same microfluidics chamber therefore exposed to the same biochemical conditions.

All anchored formins displayed slightly reduced elongation rates compared to unanchored formins, that did not exceed 20% in reduction. All anchored formins were as processive as unanchored formins except FH2-anchored-to-lipids formins, which were ∼3-fold less processive (Figure 1C). The fact that among all the anchoring configurations that we tested, FH2anchored-to-lipids corresponds to the shortest distance between the FH2 dimer and the underlying surface (Figure 1A, no antibody being used with lipids) already suggests that anchoring details may have important consequences.

To further characterize our different anchoring schemes, we looked at how anchoring formins either via their FH1 or via their FH2 side could affect their ability to freely rotate around their surface attachment point. This aspect is important because due to the helical structure of the actin filament, it appears that the formin needs to be able to rotate around the filament axis as it tracks the growing barbed end. 3,8,23 It has recently been reported that, for different surface-anchoring schemes, putting different constraints on formin rotation could affect their ability to elongate filaments. 13 Here, for FH1-side anchored formins, the FH1 domain can be considered as a flexible linker with a contour length of ∼40 nm, connecting the formin to the surface. 24 In contrast, when formins are anchored by their FH2 side, the DAD domain, which lies C-terminus of FH2 and is composed of a short α-helix followed by an unstructured region, can be considered as a linker of ∼10 nm in contour length. 20 FH2-anchoring thus constitutes a shorter tether than FH1-anchoring, and we anticipated that it would affect the formin's ability to rotate around its anchoring point as the tether length is similar to the FH2-bound actin filament barbed end diameter (∼8-10 nm). 8 In order to assess filament rotation around its main axis, we measured the polarization of the light emitted by a single fluorescently labeled actin subunit incorporated within the filament (Figure 1D). 23,25 This allowed us to determine the polarization index of this subunit, which varies over time as the filament rotates around its axis (which itself points in the fixed direction of the flow). If the filament cannot rotate around its axis, the polarization index remains constant (Supporting Information Figure 1). If the filament is anchored to the surface via a formin, we can expect two main outcomes depending on the formin's ability to rotate: (i) if the formin can rotate freely around its anchoring point, thermal fluctuations should cause the filament to twirl around its axis, and the polarization index is expected to vary rapidly and erratically over time; (ii) if the formin cannot rotate, then the filament should rotate steadily around its axis as it elongates, and the polarization index is expected to oscillate at a rate matching the elongation rate divided by the filament helicity. Individual single molecule fluorescence polarization traces lasted a few seconds before the fluorophore photobleached or the filament detached from anchored formins. Their visual inspection did not reveal any obvious switching between the erratic and steady rotation behaviors, thus indicating stable subpopulations at the time scale of a few seconds. The polarization traces were processed by fast Fourier transform in order to determine the main frequency of the signal. Filaments exhibiting an erratic rotation (i) were expected to have randomly distributed main frequencies, whereas filaments exhibiting a steady rotation (ii) were expected to have a main frequency imposed by the filament'sh e l i c i t ya n d elongation rate, thus following a normal distribution. Consistently, for each type of formin anchoring, the cumulative distributions of the main frequencies could be well fitted by the weighted sum of a random distribution and a normal distribution centered on a frequency which was compatible with the filament elongation rate (Figure 1E, rotation at 0.4 Hz would correspond to an elongation rate of ∼11 s -1 , consistent with our conditions). The relative weight of these two distributions thus allowed us to quantify the fraction of filaments in each category. Surprisingly, regardless of the solid (glass) or fluid (lipids) nature of the surface, we found that approximately 54% of filaments elongated by FH1-anchored formins were in situation (i) whereas this proportion was only 13% for FH2-anchored formin elongated filaments (Figure 1F). Therefore, as could be anticipated from the aforemen- tioned structural details of the physical link connecting formins to the surface, most FH1-anchored formins were able to rotate around their anchoring point, whereas the rotation of FH2anchored formins was mostly blocked.

Nano Letters

Our results thus far show that the anchored formin's ability to diffuse on the surface (lipid-versus glass-anchored) and its ability to rotate around its anchoring point (FH1-versus FH2anchoring) only mildly affect its ability to rapidly elongate individual actin filaments and only increased its detachment rate when the formin-to-surface distance is of the order of 10 nm (FH2-anchored-to-lipids).

In a Fascin-Induced Bundle, Unanchored Trailing Formins Are Slower and Less Processive. We next sought to investigate how filament cross-linking, on its own, could affect their elongation by unanchored formins. We used fascin as a way to cross-link filaments into parallel bundles (Figure 2A). First, we characterized the bundling activity of fascin, using fluorescently labeled fascin. We observed that fascin binds cooperatively to zipper two parallel actin filaments with an effective affinity constant of K d ∼ 75 nM (Supporting Information Figure 2A) which is in agreement with previous reports. 26,27 After two filaments were bundled together by exposure to 100 nM fascin, the bundle could be maintained by fascin concentrations as low as 10 nM, for durations exceeding tens of seconds, in a fascin concentration-dependent manner (Supporting Information Figure 2B,C). This result indicates that bundle maintenance is easier to achieve than its formation. On single filaments (not bundled), the presence of fascin in solution had no detectable impact on formin elongation rate or processivity, for fascin concentrations as high as 1 μM (Supporting Information Figure 2D).

Nano Letters

We then tested the impact of filament bundling on formininduced polymerization and depolymerization of filament barbed ends (Figure 2A). When filaments elongated by unanchored formins were bundled together by 100 nM fascin, we observed that the barbed end elongation of the leading filament was unaffected, i.e., consistent with single filament observations. In contrast, the elongation rates of the first and second trailing filaments were reduced by 18% and 30%, respectively (Figure 2B, Supporting Information Figure 2E). This decrease in elongation rate upon fascin-induced bundling is not specific to formins, because we also observed a similar reduction for trailing free barbed ends in bundles formed in the absence of formins (Supporting Information Figure 2F), as previously reported. 27 This effect could originate from monomer diffusion being partially hindered by the presence of neighboring filaments within the bundle, 8-12 nm away. 28-30 We tested this hypothesis by simulating monomer diffusion and barbed end binding on a 3D lattice (see Methods, Supporting Information Figure 2J-L). We found that in the presence of a neighboring filament 8 nm away from the barbed end, the polymerization rate dropped by less than 10% (Figure 2D). Thus, hindrance of monomer diffusion alone seems insufficient to explain the observed decrease in the elongation rate of trailing filament barbed ends both in the presence or absence of formins. One additional contribution could originate from the change in filament conformation induced by fascin bundling, 31 which could alter the barbed ends of trailing filaments and decrease their affinity for monomeric actin.

In the presence of 4 μM profilin and 100 nM fascin, the depolymerization of the leading barbed end was similar to that of single filaments. In contrast, the depolymerization of the trailing barbed end was reduced by 78% (Figure 2C), which is a much stronger effect than in the polymerization regime (Figure 2B). Remarkably, when the leading formin caught up with the trailing formin, both filament barbed ends depolymerized synchronously at an intermediate rate and remained in close proximity (Figure 2A,bottom). The observed slower trailing formin depolymerization may originate from the combined effect of barbed end conformational change already effective in the polymerization regime, and the stabilization of terminal actin subunits by fascin connections to neighboring filaments. A similar decrease in depolymerization rate and the ensuing barbed end synchronization were observed in the absence of formins (Supporting Information Figure 2G).

We next quantified the impact of bundling on the processivity of unanchored formins. In the presence of 100 nM fascin and various concentrations of profilin-actin, the detachment rate of the first and second trailing formins were increased ∼3-and 12-fold, respectively, relative to the leading formin, which is unaffected by fascin-induced bundling (Figure 2E, Supporting Information Figure 2H). To further quantify the impact of bundling on formin activity, we varied the fascin concentration between 50 and 500 nM. At 50 nM fascin, although the filaments visually appeared to be bundled together and trailing formin elongation rates were reduced compared to those of the leading one (Supporting Information Figure 2I), we found that, surprisingly, the detachment rate of the leading, first, and second trailing formins were all identical (Figure 2F). In the presence of 500 nM fascin, the detachment rates of trailing formins were increased to a similar extent as what is observed with 100 nM fascin (Figure 2F). Therefore, it appears that low fascin concentrations affect the elongation rate but not the processivity of the formins in the bundle.

Overall, these results indicate that formin elongation rate is affected by fascin-induced bundling, potentially originating from filament under-twisting 31 and monomer diffusion hindrance, which happens even at low fascin concentration, whereas formin processivity appears to be more sensitive to the efficient barbed end zippering occurring at higher fascin concentrations.

Anchoring Formins to a Solid Surface Further Hinders Their Activity in Filament Bundles. We next sought to investigate how formin anchoring may affect their activity when filaments' rotation is impaired by cross-linking. In the presence of profilin-actin and 100 nM fascin, as filaments elongate from glass-anchored formins, pairwise bundles form with random distances between the two formins, typically 1-20 μm( Figure 3A, Supporting Information Movie 1 and Movie 2). As a standard condition, we used low actin and profilin concentrations to elongate filaments from formins at a moderate rate (∼8 subunits/s) with the intent to keep filaments reasonably short (∼10-30 μm), in order to form mainly 2-filament bundles, but similar results were obtained for higher actin and profilin concentrations (see below, Figure 3K).

When bundling occurred, we observed that the elongation rates of both leading and trailing formins abruptly changed, dropping on average to 50% of the elongation rate before bundling. In bundles, both the FH1-anchored-to-glass and the FH2-anchored-to-glass formin elongation rates were distributed quite uniformly between almost zero and the elongation rate observed before bundling (Figure 3B,E). As filament elongation proceeded, two typical behaviors were observed (Figure 3G). Either the leading filament elongated faster than the trailing filament and buckled (35%, n = 8 out of 23) or the two filaments elongated synchronously (65%, n = 15 out of 23). In cases where the leading filament buckled between the leading and trailing formin attachment points, the buckling force was estimated to be lower than 0.15 pN (see Supporting Information Methods). For trailing formins, this force adds up to the minimal viscous pulling force applied to the trailing filament and is expected to accelerate elongation not slow it down. 11-13 We therefore concluded that the applied forces likely play no role in the slowing down of formin elongation rates.

In these bundles, we also quantified the rate at which filaments detached from the glass-anchored formins. We found that fascin-induced bundling strongly increased the detachment of formins (Figure 3C,F). The detachment rate in bundles was significantly higher for FH2-anchored-to-glass formins than for FH1-anchored-to-glass formins. Notably, we observed that the processivity of the leading formin was affected by fascin-induced bundling (Figure 3H). Leading formins dissociated from barbed ends before trailing formins in 35% of the cases, therefore more frequently than what we observed for unanchored formins (25%). This frequency was independent of the formin anchoring side (Figure 3H), of fascin concentration (Supporting Information Figure 3A,B), and of whether leading filaments buckled or not (Supporting Information Figure 3C). Bundled formin detachment rate was independent of formin elongation rate reduction induced by bundling (Figure 3I) and of the distance between the leading and trailing formins (when comparing two subpopulations of bundles with average distances of 2.7 ± 0.8 μm or 7.8 ± 3.3 μm between bundled formins) (Figure 3J). When varying profilin-actin concentrations, we observed that bundle formin detachment rates scaled with the single formin detachment rates (Figure 3K).

Nano Letters

Nano Letters

We also checked that applying a significant pulling force (by working with stronger microfluidics flow rates) increased formin bundle detachment rates but did not affect the amplitude of the increase due to bundling (Supporting Information Figure 3D). Formin detachment rate increase caused by fascin-induced bundling was significantly different depending on the anchoring side, thus on the anchoring details. To further investigate this aspect, we performed measurements with heterodimeric formin constructs, comprising the FH2 dimer, one FH1 domain, and only one anchoring point (located either on the FH1-side or the FH2-side, see Methods and Supporting Information Figure 3G). Each of these formin heterodimers could thus bind to the glass surface via a single anchoring point. Heterodimeric formin processivity was reduced to the same extent as for homodimeric formins (Supporting Information Figure 3E,F), suggesting that the observed processivity reduction for homodimeric formins cannot be attributed to a double anchoring of the formins on the surface, which would impede their rotation as filaments elongate.

Nano Letters

Overall, compared to single formins, the detachment rate of FH1-anchored-to-glass formins was increased 6-and 11-fold for leading and trailing formins, respectively, whereas for FH2anchored-to-glass formins this reduction was more pronounced, respectively by 13-and 24-fold (Figure 3H). Taken together, those results indicate that in the situation of bundles where formins are statically anchored to a substrate, the anchoring of formins amplifies the effect of fascin-induced bundling to reduce formin elongation rate and processivity.

Preventing the Rotation of a Single Filament Has the Same the Impact as Bundling on Anchored Formin Activity.

To test if the strong reduction in anchored formin activity requires the bundling of filaments by fascin, or if it can occur by only blocking filament rotation, we performed experiments where filaments elongating from glass-anchored formins were bound to inactivated glass-anchored NEM-myosins to prevent filament rotation (Figure 4A and Supporting Information Movie 3). Single formin elongation rates dropped and spread similarly to what we observed for glass-anchored formin elongating filaments bundled by fascin (Figure 4B). This observation is reminiscent of what has been observed by Mizuno and colleagues with formin mDia1 elongated filaments occasionally attaching to the surface through biotin-avidin interaction. 32 Formin detachment rate increased upon NEMmyosin binding, similarly to what was observed for leading glass-anchored formins in fascin bundles, with FH2-anchored-to-glass formins detaching faster than FH1-anchored-to-glass formins (Figure 4C,D). Using this assay, we thus showed that a single attachment point along the side of the filament is enough to account for most of the change in formin activity observed in fascin bundle experiments. This suggests that the dominant effect of fascin-induced bundling, regarding the activity of glass-anchored formin, is to block filament rotation.

Lipid-Anchored Formins Efficiently Elongate Actin Filament Bundles. In cells, formins are anchored to lipid membranes and can potentially move independently from each other. 33 We thus investigated the impact of filament bundling in the more physiological situation where formins are anchored to a lipid bilayer.

Filaments gathered at the edge of the lipid bilayer (Figure 5A and Supporting Information Movie 4) were bundled together by flowing in fascin in addition to profilin-actin (Figure 5B). Starting with a low density of single filaments allowed us to form mostly 2-filament bundles, whose elongation was then monitored. Here, the distance between bundled formins was much smaller than in the case of glassanchored formins and below the optical resolution of our TIRF microscope (∼200 nm). Therefore, we used fluorescently labeled fascin to monitor when the bundled region moved away from the lipid edge (Figure 5C), which we identified as formin dissociation events. In contrast to glass-anchored formins, lipid-anchored 2-filament bundles grew steadily, and the elongation rate was not reduced compared to single filaments (Figure 5D). For some bundles, we could observe leading formins moving upstream as they elongated filament barbed ends away from the lipid pattern edge and the trailing formin (Figure 5C, bottom), possibly indicating a slower elongation of the trailing formin, reminiscent of what we observed for unanchored trailing formins (Figure 2B). Interestingly, the detachment rate of lipid-anchored formins appeared similar to that of unanchored formins (Figure 5F). The ∼2-fold difference between FH1-anchored-to-glass and FH2-anchored-to-glass formins detachment rate (Figure 3H,K) was still present for lipid-anchored formins, indicating that the tether length still plays an important role even for lipid-anchored formins in a bundle. Overall, the results obtained from lipid-anchored formins show that (1) the translational freedom of formins thanks to the fluidity of the lipid bilayer seems to allow a smoother and more processive filament elongation by formins when filament rotation is blocked by fascin-induced bundling, whereas [START_REF] Hansen | VASP is a processive actin polymerase that requires monomeric actin for barbed end association[END_REF] this process is still dependent on the tether length connecting the formins to the surface.

Nano Letters

Discussion. In this work, we investigated the impact of geometrical constraints on the activity of formin mDia1, quantified by the rate at which it elongates barbed ends and by the rate at which it detaches from them, which we summarized in Figure 6. First, we showed that having a barbed end within a fascin-induced bundle slowed down its elongation and increased formin detachment rate (Figure 2). As revealed by numerical simulations, these effects, in part, can be attributed to the presence of the neighboring filament which acts as an obstacle hindering monomer diffusion. Formin steric hindrance as well as a barbed end conformational change may also contribute to these effects. We also observed that FH2anchored-to-lipids formins exhibit an increase of their detachment rate. This indicates that being very close to the surface can hinder formin activity. This observation is reminiscent of what was observed in a previous study, where Bni1p formin activity was affected by the height of the chromium barrier it was pushed against by a microfluidics flow. 17 These observations, together with the impact of fascin-induced bundling, indicate that formins are very sensitive to the proximity of other components (e.g., membrane-bound proteins).

More strikingly, we found that the application of constraints to both actin filaments (bundling) and formins (anchoring) had a significant impact on formin activity (Figures 3 and5). This unexpected cross-talk between constraints located micrometers apart is illustrated by our observation that formin anchoring details, which may play no role when elongating individual filaments (Figure 1), matter significantly as soon as filaments are bundled. In particular, constraints relative to formin's ability to rotate around its anchoring point appear to have a strong impact on formin activity when filaments are bundled. Remarkably, formins anchored to a lipid bilayer via their N-terminus, hence with minimal constraints, are able to elongate bundled filaments as efficiently as if they were not anchored (Figure 5). Notably, in the case of lipid surfaces where lipid diffusion may favor the double anchoring of formin dimers, such a situation still appears to allow formins to reorient and to function with minimal hindrance.

Interestingly, the issue of formin rotational freedom upon anchoring has recently been investigated in the context of pulling forces applied to single filaments by Yu and colleagues. 13 In this study, the authors used magnetic beads to pull on filaments and found that piconewton pulling forces applied to formins that were free to rotate allowed them to elongate filaments extremely rapidly, close to the theoretical diffusion limit in the presence of profilin-actin. 14 In contrast, when applying significant forces to our freely rotating formins, the elongation rates remained comparable to what we have reported earlier using microfluidics 11,15 and to what others have reported using optical traps 12 or myosins 16 to apply pulling forces. Control experiments in the latter study indicate that the effect they observe (on mDia2 and Cdc12 formins) can indeed be attributed to tension. Nonetheless, the contribution of active myosins to torsional constraints is not fully understood 34 and may be worth investigating further, following our results. Thanks to these earlier reports that used different means to apply mechanical tension to actin filaments, the fact that formins are sensitive to external forces is now well established. 7 Here, we show that formins are also sensitive to the geometrical organization of the filaments they elongate. When filaments are cross-linked and cannot rotate around their main axis, hindering the rotation of the anchored formin results in the generation of a mechanical torque as the filaments elongate, and, as a consequence, the formin's elongation rate is reduced and its off-rate is increased. This sensitivity to geometry, where mechanical stress is not applied from the outside but rather generated by the protein's activity in a specific context, is reminiscent of our recent work showing that cofilin binding applies a mechanical torque to cross-linked filaments, and thereby greatly enhances their severing. 25 Here, we focused on fascin-induced bundling as a means to cross-link filaments, a situation typically encountered in filopodia 35 and invadopodia. 36 More generally, most actin cross-linkers and network geometries are likely to also block filament rotation and to have a similar impact on formin activity, as exemplified by our experiments with NEM-myosins (Figure 4). As we show, the details of formin anchoring are of great importance in this context, and these can certainly take different forms in cells. The binding of Diaphanous-related formins directly to membranes or to membrane-bound proteins and activators via their N-terminal regions 37-39 likely allows them to maintain some rotational freedom while being anchored. This freedom may be tuned by a number of other factors, such as the membrane lipid composition or the presence of other proteins. In particular, in the context of filopodia, the presence of Ena/VASP and its potential interaction with formins 40,41 may alter formin's rotational freedom and thereby its ability to efficiently elongate barbed ends for significant durations. Future studies will certainly shed light on how the rotational freedom of membrane-anchored formins can be modulated and regulate the assembly dynamics of actin filaments in cells.

■ ASSOCIATED CONTENT

* S Supporting Information

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.nanolett.9b02241. . Schematic summary of filament bundling and formin anchoring impact on formin activity.Depending on filaments being bundled by fascin or not, and whether formin translational or rotational freedom are blocked or not, formin-induced actin filament elongation and formin detachment rate are differently affected. Top, left: a single filament elongated by an unanchored formin is chosen as the reference for the comparison of elongation rates (V elong ) and formin detachment rates (k off ). Bottom, left: when fascin bundles filaments, the activity of the formin elongating the leading filament is unaffected, whereas the elongation rate is reduced and the detachment rate is increased for formins elongating trailing filaments. Top, right: the activity of surface-anchored formins elongating individual filaments is not affected by anchoring, except in the case of a short formin-to-surface distance. Bottom, right: Simultaneously blocking filament rotation by fascin-induced bundling and formin rotational or translational freedom, strongly impacts both formin elongation rate and detachment rate, for both leading and trailing filaments.

Nano Letters

Letter DOI: 10.1021/acs.nanolett.9b02241

Nano Lett. 2020, 20, 22-32

Eect of filament cross-linking on cofilin activity

5.1 Cofilin activity on 2D fascin-induced filament networks

It has been shown previously that, compared to single filaments, actin filaments that have been bundled solely by the presence of a crowding agent, but without any specific cross-linkers, were resistant to cofilin-induced severing (Michelot et al., 2007) . The authors interpreted their observations as cofilin having difficulty accessing and binding to the filaments in the 'core' of bundles. The mechanical properties of bundles, being stiffer than single filaments, was also raised by the authors as a parameter that could reduce cofilin activity, compared to single filaments.

The presence of cross-linkers, such as fascin, could affect this reported behaviour in a way that is hard to predict in the light of the recent results on twist-constrained filaments (Wioland et al., 2019b) . To observe cofilin activity on fascin cross-linked actin filaments, I reconstituted actin networks in open chambers (Methods and materials section 3.2 and 3.4.1 for surface passivation). We used two-color TIRF microscopy to observe the Alexa-568 labeled fascin cross-linked bundles and eGFP-cofilin.

Filaments were elongated from surface-anchored seeds with 1 µM labeled or unlabeled actin.

Subsequently, filaments were bundled using Alexa-568-labeled fascin, along with 0.13 µM of unlabeled actin to age them for 30 minutes. A solution containing 200 nM Alexa-568 labeled fascin, 0.13 µM unlabeled actin and 75 nM eGFP-cofilin is rapidly flowed in and then the acquisition is started as soon as possible (~ 30 seconds after the beginning of the protein solution injection).

As a control, we first exposed the single filaments in the absence of fascin to cofilin. Next, we repeated the same assay but this time exposed the filaments to cofilin in the presence of fascin (either 0.2 µM or 1 µM fascin). We observed the presence of more cofilactin segments in the single filaments due to the severing. Overall, we noticed that cofilin severed cross-linked fascin bundles slower than single filaments (fig 5.1 and 5.2). Here, we noticed that the fluorescent Quantification of cofilin intensity recruited to the single filaments and filament bundles with 0.2 µM, and 1µM fascin. Both single filaments and bundles were exposed to 75 nM cofilin. For each assay, cofilin intensity is divided by the filament density to take into account variation in filament density in the chamber between the three assays. Jahnavi C -doctoral thesis -2021

Again, as for the effect observed for actin, further reducing the amount of light used to observe fascin reduced the binding of cofilin on the network.

The effect of fascin labeling and its illumination was somehow unexpected since fascin molecules turnover quickly (t 1/2 ~ 6s, [START_REF] Aratyn | Intrinsic Dynamic Behavior of Fascin in Filopodia□D[END_REF] and do not recruit cofilin molecules on filaments. Reactive oxygen species created by Alexa dyes upon illumination accelerate cofilin recruitment as well, it may also ease cofilin severing activity, in an unknown precise mechanism. • cofilin domains bound to filament bundles did not readily lead to bundle fragmentation.

• Bundle disassembly is further decreased in the presence of higher fascin concentration.

• Cofilin activity is sensitive to illumination of labeled actin and fascin.

We report here only the global severing activity of cofilin on fascin cross-linked networks. By using the microfluidic assays, I will study further the molecular details involved in the disassembly of fascin induced bundles. Since the cofilin activity is sensitive to labeled actin, care was taken in the microfluidic experiments not to image the filaments/bundles often, before exposure to the cofilin.

Molecular details of cofilin activity on fascin-induced bundles

Impact of fascin on single filaments exposed to cofilin

Fascin binds to the single filaments transiently so it is important to investigate the effect of the presence of fascin on cofilin activity on single filaments. We carried out most of the experiments at 0.2 µM fascin, which is the typical fascin concentration we use to make filament bundles.

Impact of fascin on cofilin domain nucleation on single filaments:

We asked whether the presence of fascin has any impact on cofilin domain nucleation on single filaments. To investigate this, using microfluidics, we exposed single filaments to cofilin, in the presence or absence of fascin. First, filaments were elongated from surface-anchored spectrin-actin seeds. Since we are limited by the inlets of the microfluidic chamber, filaments age as they are elongated. So to have enough ADP-actin in the filaments for the cofilin binding, we elongate the seeds with 0.5 µM alexa-488 labeled actin for 15 minutes. Then, in order to accurately measure the impact of fascin, one half of the microfluidic chamber was exposed to 0.2 µM fascin and 0.2 µM mCherry-labeled cofilin, and 0.13 µM actin, while the other half was exposed to cofilin and actin in the absence of fascin (see fig 5.6). We observed that exposing filament to 0.2 µM fascin did not impede cofilin binding to the single filaments.(see fig 5.7) Jahnavi C -doctoral thesis -2021 Summary:

• As a control, a pre-requisite for the results on fascin-induced bundles in the next sections, we show that the presence of fascin does not impact the cofilin activity (nucleation of domains, growth of domains, and severing at domain boundaries) on single filaments.

Global severing of fascin bundles

We now ask how the bundles are severed by cofilin compared to the single filaments. To investigate this, we looked at two-filament bundles and single filaments in the same field of view. Actin filaments were elongated from the seeds in a microfluidic chamber. Filaments were then aged for 15 minutes while also being bundled by fascin, prior to being exposed to 0.2 µM cofilin as mentioned in section 3.4.2.

We quantified the occurrence of cofilin severing of 5 µm segments of fascin-induced two-filament bundles compared to segments of single filaments of similar length. Here, we observed that the two filament fascin bundles survived for much longer (Fig 5.10). Severing a 2-filament bundle involves severing the two filaments and has several individual molecular details that can be altered due to bundling compared to the single filaments. At the cofilin concentration I've used in these assays, on single filaments, the majority of cofilin nucleated domains did sever the filaments before cofilin domains could fuse together, or saturate the filament.

As a partial conclusion, this first observation seems to contradict what was previously reported by Breitsprecher et al, 2011, where the authors argued that cofilin activity was enhanced by fascin bundling.

Thanks to our experimental set up, we could look more closely at the level of individual cofilin domains and quantify the details such as the rates of nucleation, growth and severing on bundles. A) Filaments elongated from seeds were bundled with 0.2 µM unlabeled fascin, and simultaneously exposed to 0.13 µM unlabeled actin to maintain their length constant. Also, the actin fluorescence intensity is used to differentiate single filaments (SF) from a bundle with two filaments (bundle). Actin

Jahnavi C -doctoral thesis -2021

Impact of fascin concentration on cofilin domain nucleation:

To investigate the impact of fascin concentration on the ability of the cofilin domain to nucleate, two-filament bundles were formed and exposed to cofilin alongside different fascin concentrations. The elongated filaments were first exposed to different fascin concentrations (0.1 µM, 0.2 µM and 0.5 µM) in order to bundle them, as they were aged to become ADP-actin filaments. Then, the bundled filaments were exposed to 0.2 µM mCherry-cofilin, 0.13 µM unlabeled actin, and the same fascin concentration that was used to bundle the filaments in the first place. We tested 0.1 µM, 0.2 µM and 0.5 µM fascin, a set of concentration where, experimentally, fascin efficiently bundles filaments in microfluidics but with different saturation levels of the available fascin binding sites along actin filament side (Kd ~ 200-300 nM according to [START_REF] Winkelman | Fascin-and α-Actinin-Bundled Networks Contain Intrinsic Structural Features that Drive Protein Sorting[END_REF][START_REF] Suzuki | Geometrical Constraints Greatly Hinder Formin mDia1 Activity[END_REF].

We observed that the cofilin domain nucleation was slower as the fascin concentration was increased in the experiments, as shown in Fig 5 .12.

This dose-dependence indicates that, within this concentration range, filament bundles are not saturated by fascin, and that cofilin nucleation is more difficult when filaments are more tightly bundled by fascin.

is in yellow and cofilin is in blue. When exposed to 0.2 µM mCherry-cofilin, nucleated domains can be observed as shown here in the boxes. It can be seen here that the SF have more domains compared to bundles. Jahnavi C -doctoral thesis -2021 Summary:

B)

• With the reconstitution of fascin bundles in microfluidics, we quantified the cofilin domain nucleation rate successfully.

122 The rates we compare here correspond to the results of the exponential fits from the figure above (A) divided by the number of filaments in the bundle, in order to compare nucleation rates on equal number of actin subunits. Jahnavi C -doctoral thesis -2021

In the hypothesis that a cofilin domain grows normally in between two fascin sites (every 13 subunits; site occupancy ~ 0.5 at 200 nM fascin) at a rate of 1.5 subunits/s, and that cofilin has to wait for a fascin to depart from its binding site at a rate of 0.11 s -1 [START_REF] Suzuki | Geometrical Constraints Greatly Hinder Formin mDia1 Activity[END_REF][START_REF] Aratyn | Intrinsic Dynamic Behavior of Fascin in Filopodia□D[END_REF] independently of cofilin presence, then the resulting cofilin domain growth rate would be 0.99 s -1 , close to the experimentally measured value (average of 1.04 sub/s over the 3 repeats) Jahnavi C -doctoral thesis -2021

Using alexa-568-fascin was another means to ensure that we were looking at filament bundles in microfluidics experiments. We used 5% alexa-488 labeled actin to elongate filaments from the seeds. The filaments were aged and bundled using 0.2 µM 100% alexa-568 labeled fascin and 0.13 µM unlabeled actin. Finally, we exposed the fascin bundles to 0.1 µM eGFP-cofilin, 0.2 µM 100% alexa-568-labeled fascin, and 0.13 µM unlabeled actin. We observed that eGFP-cofilin nucleated domains very efficiently displaced fascin from filaments (Fig 5.16). We The direct consequence of this effect is that the filament segments where the fascin has departed are not cross-linked anymore. Even if the exact binding interface of fascin on the actin filament side has not been properly determined, according to available Electron Tomography data for fascin (Aramaki et al, 2016), a steric clash between fascin and cofilin on filament sides is probably the cause of this displacement. Furthermore, we cannot directly conclude from the kymographs that the growth of a single cofilin domain on one of the two filaments is enough to displace fascin. Though, it is highly probable that one cofilin domain is enough, as fascin has a very low affinity on single filaments and requires two 'facing' binding site to be fluorescently imaged in microscopy assays.

126

Impact of fascin concentration on cofilin domain growth

Next, we investigated if the cofilin domain growth rates could be affected by the different fascin concentrations when bundles are exposed to cofilin. We exposed bundles, along with cofilin, to 0.2 , 0.5, and 1 µM fascin and looked at the cofilin domain growth rates on the bundles. We observed that cofilin domain growth rates were not significantly affected by an increase in fascin concentration in the experiments (Fig 5.17). Given the dispersion of our data points, it was hard to assess a change of cofilin domain growth rate due a change of fascin binding site occupancy from 0.6 to 1, roughly expected for an increase in fascin concentration from 200 nM to 1 µM [START_REF] Suzuki | Geometrical Constraints Greatly Hinder Formin mDia1 Activity[END_REF] .

Impact of bundle size on cofilin domain growth

We questioned if bundle size has an impact on cofilin domain growth rate. Bundles reconstituted on beads were observed for this study. Here the bundles on beads were of different sizes (see section 3.7). We noticed that growth rates of the cofilin domain decreased as the bundle size increased (see fig 5.18).

127 Jahnavi C -doctoral thesis -2021 Summary:

• Cofilin domain growth on fascin 2-filament bundles decreased 1.5-fold compared to single filaments.

• Cofilin domain displaces fascin from bundles.

• Any increase in fascin concentration does not significantly affect the domain growth on bundles.

• An increase in bundle size slows down the cofilin activity on bundles.

128 Jahnavi C -doctoral thesis -2021

Cofilin domain severing in bundles

The main contribution of cofilin in actin disassembly is probably thanks to its ability to sever filaments.

As mentioned in section 3.4.3, severing a two-filament bundle implies two severing events, one on each filament. But in the kymograph of (figure 5.19 B), we observed a severing event that appears similar to the one seen for single filaments (Fig 5 .19 A and 5.20 A for sketch). However, they are not similar events but only appear to be due to our limited resolution in space and time. Jahnavi C -doctoral thesis -2021 al, 2019). However, compared to the previous study, although fascin crosslinks filaments together, the geometrical context of fascin-induced bundles is different. First, fascin cross-linking is dynamic, and we showed that cofilin prevents fascin rebinding, so the length over which helicity frustration accumulates and converts into torsional stress increases over time.

Second, and probably more importantly, the bundle is not twist-constrained as a whole in our assay, as the downstream part of the bundle is not anchored to the surface of the experimental chamber, offering thus the possibility for the part downstream of where a cofilin domain has nucleated and is growing to rotate.

Our results suggest that there is no drastic increase in severing rates. We hypothesize that the part of the bundle that is downstream of the cofilin domain rotates as the cofilin domain grows to relax the stress (Fig 5.25). One interesting consequence of the bundle rotation is that it could induce a change of helicity for the region of the second filament facing the (first) cofilin domain.

In turn, this might favor the nucleation of a cofilin domain on the second filament in this region.

This proposed mechanism would favor situations where 2 cofilin domains overlap on 2-filament bundles, and explain why we often see the nucleation of a second cofilin domain in the same region as the first. on bigger bundles too. For these bigger bundles (average of 6 filaments with bundle size of 3-14 filaments) we could record 'total bundle fragmentation' events. Upon construction of the survival fraction of unsevered domains with respect to time, we observed that 'total bundle fragmentation' events on bigger bundles happened slower compared to the two filament bundles as shown in fig 5.27 B. One could expect a higher cofilin-induced severing rate on bigger bundles because cofilin would be unable to twist/rotate stiffer bundles (as more filaments are cross-linked by fascin) and severing would be accelerated due to torque accumulation. This effect, if happening, does not seem to compensate for the higher number of filaments to sever in one region for the whole bundle to be fragmented. B) The survival fraction of unsevered bundles decays more slowly for >3-filament bundles than for 2-filament bundles.On average the bundle size was around 6 filaments. N = 31, and 34 domains analyzed on two filaments and >3-filament bundles, respectively.

Jahnavi C -doctoral thesis -2021

• Using a simple model for cofilin disassembling 2-filament bundles, we could derive the nucleation rate of the second domain.

• Finally, we hypothesize that the bundle has to relax the torsional stress generated by the first cofilin domain on the bundle. We propose that the bundles relax the stress by turning into a supercoiled conformation. This conformation might favor the nucleation of the second cofilin domain on the bundle.

Bundles supercoiling induced by cofilin binding

To test our hypothesis of bundle supercoiling upon cofilin binding, we used two different techniques: single-molecule fluorescence polarization microscopy and negative staining EM (section 3.4.4). As a control, we probed the rotation of single filaments and 2-filament bundles in the absence of cofilin (see fig 5.30 and fig 5.32 respectively). Both single filaments and bundles in my experiment setup were elongated from seeds, so they cannot rotate around the filament long axis.

Single-molecule fluorescence polarization microscopy

The polarisation index values from the actin subunits on these two cases was constant, an indication that filaments (and bundles) are rigid enough to infer some rotational movement if any,see fig 5.31 and Fig 5.33 for single filaments and bundles, respectively).

In experiments using eGFP-cofilin, we looked at the single labeled actin molecules downstream of a cofilin domain. We saw that polarisation index was oscillating and changing sign, indicating the rotation of the subunit around the main axis (6 out of 12 observed actin subunits for fascin cross-linked bundles), see fig 5.31 and 5.33 for representative examples of single filament and bundle traces, respectively. Jahnavi C -doctoral thesis -2021

Transmission Electron Microscopy TEM imaging

For direct visualization of the structural details of filament organization in bundles exposed to cofilin, we used TEM imaging. 1 µM F-actin was incubated with 0.2 µM or 1 µM fascin, prior to being exposed to 0.3 µM cofilin for 1 minute, and then deposited on the copper grids for staining and EM imaging (see methods 3.4.4 (B)).

In the absence of cofilin, filaments and bundles appear straight (fig 5.34). In contrast to this, bundles exposed to cofilin appeared highly braided (fig We observe that filaments appear to be disjoined at the end of the bundles consistent with our observation that cofilin displaces fascin. This feature was particularly visible on larger bundles with more than 3-filaments. [START_REF] Winkelman | Fascin-and α-Actinin-Bundled Networks Contain Intrinsic Structural Features that Drive Protein Sorting[END_REF] . So, we wondered how cofilin disassembles a network made with a different crosslinker, 𝛼-actinin-1.

𝛼-actinin-induced bundles are less compact compared to the ones formed with fascin. We hypothesized that the larger filament spacing (~35 nm) in 𝛼-actinin bundles compared to fascin bundles (8 nm) could affect the cofilin activity very differently (see fig 5.38). Even though 𝛼-actinin can form bundles with parallel or antiparallel filaments (J. [START_REF] Liu | A 3-D Reconstruction of Smooth Muscle α-Actinin by CryoEm Reveals Two Different Conformations at the Actin-binding Region[END_REF][START_REF] Taylor | Isoforms of α-Actinin from Cardiac, Smooth, and Skeletal Muscle Form Polar Arrays of Actin Filaments[END_REF] , we only made 𝛼-actinin bundles with parallel filaments in our microfluidics assay. Jahnavi C -doctoral thesis -2021 𝛼-actinin bundles were generated in a similar way as fascin bundles: fluorescently labeled filaments were elongated from surface-anchored spectrin-actin seeds, and then were aged for 15 minutes in the presence of 0.2 µM 𝛼-actinin in order to bundle them. Then they were exposed to 0.2 µM mCherry-cofilin1 in the presence of 0.2 µM unlabeled 𝛼-actinin and 0.13 µM unlabeled actin. Similar to the experiments with fascin, 𝛼-actinin was present in solution to maintain the filaments as bundles owing to its turnover rate (see section 1.3.3).

Before presenting results on 𝛼-actinin bundles (section 5.4.2) I will present results on single filaments exposed to 𝛼-actinin.

Impact of 𝛼-actinin on cofilin activity on single filaments

𝛼-actinin binding to the single filaments

Prior to assessing the impact of 𝛼-actinin presence on cofilin activity on single filaments, we looked for 𝛼-actinin's ability to bind single filaments. Since single filaments exposed to 𝛼-actinin are targeted differently by cofilin, we investigated 𝛼-actinin's ability to bind to them.

When single filaments were exposed to the 200 nM alexa-568-labeled 𝛼-actinin, we observed Jahnavi C -doctoral thesis -2021

Impact of 𝛼-actinin on cofilin domain nucleation on single filaments

We asked whether cofilin's ability to nucleate domains on single filaments would be affected by the presence of 𝛼-actinin that is able to bind single filaments. The experimental setup was similar to the procedure mentioned in section 5. We observed that the rate of cofilin domain nucleation on 𝛼-actinin bundles or single filaments (which are also exposed to 𝛼-actinin) were similar (Fig 5.44 C and D). These observations, when compared to the single filament in the absence of 𝛼-actinin, indicate that the presence of 𝛼-actinin molecules bound to filaments, whether they are single filaments or bundled filaments, is sufficient to already impact cofilin domain nucleation. This observation seems to indicate that no additional change in the filament conformation between the single filament and 𝛼-actinin bundles would induce a different cofilin binding between those two species.

Although it is hard to compare the effect for 𝛼-actinin and fascin, due to their apparent difference in binding affinity for actin filaments, it appears that at a similar concentration (200 nM, for 15 minutes), fascin-induced bundles are less prone to cofilin domain nucleation, than their 𝛼-actinin counterparts. C) Computed cofilin domain survival fractions of 'domain severing event' and 'total bundle fragmentation' on two filament 𝛼-actinin bundles with the proposed model (in orange and red) compared to the experimental curves of the respective events. D) Cofilin domain nucleation rates (in /subunit/s) of the second and first domain nucleation on two filament bundles compared to single filaments.

Discussion and perspectives

My PhD aimed at understanding how actin filament bundles that are present in filopodia, are assembled by formins and disassembled by cofilin. During the course of this study, similar bundles were reconstituted to get molecular insights on the impact of filament cross-linking on the activity of regulatory proteins. This study mainly investigated how the bundled geometry and the presence of cross-linkers affect the activity of cofilin. Our work aimed to address the lesser studied part of actin network regulation: the disassembly of the bundles. Also, we studied how the geometrical constraints on formins (mimicking membrane anchoring in cells) affected its activity on single filaments and attempted to form fascin bundles larger than 3 filaments.

Discussion

A) Surface anchoring of formin aects its rotational freedom:

In our study [START_REF] Suzuki | Geometrical Constraints Greatly Hinder Formin mDia1 Activity[END_REF] , we showed that geometric constraints affect formin activity in single filaments and bundles. For this study, formin activity was assessed by the following readouts: elongation rates and formin detachment rates. When both the formins (by surface anchoring) and filaments (by cross-linking) were constrained, we observed that formin activity was affected. In particular, the detachment rate of formin was increased 24-fold.

For single filaments, for all configurations, anchoring formins from either side (FH1-or FH2-side) and on either type of surface (on glass or lipids), formin elongation rates were mildly affected. In the case of formins anchored by their FH2-side on lipids, their detachment rate was significantly increased. Our interpretation is that the length of the leash would cause the formin to be in contact with the surface more often than in the other anchoring situations. A previous study, using Bni1p formin from yeast, showed that a chromium barrier affected formin activity when exposed to a microfluidic flow to exert a pulling force [START_REF] Courtemanche | Tension modulates actin filament polymerization mediated by formin and profilin[END_REF] . Still, in our assay, only formin processivity was affected, as the elongation rate was comparable to one of the unanchored formins. In both studies, a minimal force (estimated to be ~ 0.1 pN) was applied by the flow to the formins. Those two studies both highlight the sensitivity of formins to the presence of a surface/obstacle which impedes their activity, although not observing the same behaviors.

Jahnavi C -doctoral thesis -2021

To address the impact of a more physiologically relevant context on formin activity (type of surface, formin/filament orientation, collective effect, actin monomer depletion effects, …), we have designed several in vitro assays to reconstitute formin-elongating bundles, cross-linked by fascin, involving more filaments (typically aiming at 5-15 filaments). We employed different techniques like SLBs, lipid-coated beads, and GUVs in the course of this study. But, several challenges have arisen that were difficult to circumvent: 1) difficulty to get a satisfying density of active formins on the surface; 2) difficulty to have diffusing formins on the surface, in the case of lipid-coated beads and 3) instabilities in maintaining the bundles as one entity ( e.g.

unzippering).

B) cross-linkers aect cofilin activity in bundles

When we investigated how the presence of cross-linkers affects bundle disassembly by cofilin,

extending beyond what can be obtained with the bulk assays, we were able to quantify the underlying molecular reactions, such as cofilin domain nucleation rate, domain growth rate, and domain severing rate on bundles.

We found that the ability of cofilin to nucleate a domain on fascin cross-linked filaments is slower than a single isolated filament. For two filament bundles, the domain nucleation rate is at least six-fold slower compared to single filaments, and can be further decreased by fully saturating all the fascin binding sites on bundles. Different factors affect cofilin domain nucleation rates on bundles: number of filaments per bundle and fascin concentration. Here, we observe that the number of filaments in the bundle has more impact compared to the fascin concentration. There is up to a 10-fold decrease difference in cofilin domain nucleation rate on bundles of six or more filaments compared to two-filament bundles. These results imply that the bigger the bundle, the more difficult for the cofilin it is to nucleate domains even though, if one considers filaments to arrange in a hexagonal lattice, there are more available actin binding subunits at the surface of bigger bundles. These results are in agreement with previous observations which, without deciphering the molecular events of cofilin activity, observed that bundles were protected against cofilin disassembly activity ( [START_REF] Yang | Mammalian CARMIL Inhibits Actin Filament Capping by Capping Protein[END_REF] .

The decrease in cofilin domain nucleation rate cannot be caused solely by the presence of fascin molecules every 13 actin subunits along the filaments of the bundle. It can also be due to the compactness in the arrangements of filaments in the bundle [START_REF] Schmoller | Slow down of actin depolymerization by cross-linking molecules[END_REF] . In fascin bundles, filaments are arranged in a hexagonal lattice and the inter-filament distance is 8 nm [START_REF] Ishikawa | Polarized actin bundles formed by human fascin-1: Their sliding and disassembly on myosin II and myosin V in vitro[END_REF][START_REF] Jansen | Mechanism of Actin Filament Bundling by Fascin *[END_REF]. This may partially decrease cofilin binding to the filament side for filament regions that are 'buried' into the bundle, through partial hindered diffusion. (W. [START_REF] Cao | Energetics and Kinetics of Cooperative Cofilin-Actin Filament Interactions[END_REF] suggested that the cooperative binding of cofilin may be decreased compared to single filaments when the actin filaments are cross-linked: their reasoning is that bundling would affect the accessible filament conformations that a single, unconstrained filament usually explores, changing the modes of fluctuations of actin filaments ('filaments' breathing'). This idea was also invoked for the reduction in filament branching rate by the Arp2/3 complex at the surface of curved filaments [START_REF] Risca | Actin filament curvature biases branching direction[END_REF] . Here, some specific conformations, which would favor cofilin binding, become less frequently accessible. A coflin domain grows through cooperative binding. Its growth rate, though roughly twice slower than on single filaments, appears less affected than the initial cofilin binding required for nucleating a domain, and is compatible with cofilin molecules to wait for the closest fascin-bound molecule to spontaneously depart to bind and make the domain grow by one more cofilin unit.

When filaments are bundled by 𝛼-actinin, the inter filament distance was more compared to the fascin (around 36 nm). Different cross-linkers may constrain filaments differently, thus reducing the range of accessible conformations to a different subset. 𝛼-actinin cross-linked filament bundles are more flexible than fascin ones, at least for bundles of >~5 filaments (Claessens et al., 2006) . Indeed, what we observed for cofilin domain nucleation on 𝛼-actinin-crosslinked bundles seems more to originate from the presence of the 𝛼-actinin itself than the actual stiffness of the bundle, since the decrease in cofilin domain nucleation rate is already observed on 𝛼-actinin-bound single filaments.

We observed that the cofilin domain grows symmetrically towards both ends of the filaments in a bundle, similarly to what is observed on single filaments (my own observations and [START_REF] Wioland | ADF/Cofilin Accelerates Actin Dynamics by Severing Filaments and Promoting Their Depolymerization at Both Ends[END_REF] ). Our data indicates that cofilin domain growth rate is decreased due to the presence of cross-linkers. Cofilin domain growth rates are twice slower on 2-filament bundles, either with fascin or 𝛼-actinin, in comparison to single filaments. Here, fascin is present at regular intervals of 36 nm in the bundle i.e., every 13 actin subunits. This means that cofilin encounters a fascin subunit once for its 13 available binding sites. Interestingly, we report here that cofilin displaces fascin from the bundles. This observation was not reported before. This result was somehow expected since a cofilin domain saturates all available binding sites along a filament. So far there is no precise map of the binding of fascin onto F-actin. We therefore cannot directly exclude that cofilin and fascin binding interfaces on actin filaments overlap. This could be the reason for the difficulty of the cofilin domain to grow on the bundled filaments, as it has to displace fascin (or at least wait for fascin departure) from the bundles. This result is in line with the cofilin localization at the shafts of retracting filopodia concomitantly with the decrease of the fascin intensity in the study by Breitsprecher et al [START_REF] Breitsprecher | Cofilin cooperates with fascin to disassemble filopodial actin filaments[END_REF] . Our result provides new insights in the relationship between the existence of fascin and cofilin in actin structures like filopodia. Do cofilin domains occupy the binding sites of fascin when it dissociates or do cofilin binding generate a change in twist of filament conformation that could result in the unbinding of fascin?

One important observation is that the bigger the bundle size, the slower the domain growth rates of cofilin on bundles. This observation seems to indicate a bigger change of filament conformation imposed by fascin bundling as bundle size grows, where not only filaments long-pitch helicity is further decreased by fascin cross-linking, but the bundle itself is supercoiled (Claessens et al., 2008;[START_REF] Heussinger | Theory of crosslinked bundles of helical filaments: Intrinsic torques in self-limiting biopolymer assemblies[END_REF]Shin et al., 2009) .

Our preliminary data show that 𝛼-actinin is not displaced from the bundles. But this needs to be investigated further, because 𝛼-actinin and cofilin binding sites overlap on the F-actin [START_REF] Galkin | Opening of tandem calponin homology domains regulates their affinity for F-actin[END_REF][START_REF] Galkin | Remodeling of actin filaments by ADF/cofilin proteins[END_REF] . Next, the domain growth rates on 𝛼-actinin bundles was 2-fold slower compared to single filaments (not exposed to 𝛼-actinin) in our studies. We wondered if the 𝛼-actinin binding to the single filaments, unlike fascin, could impede the domain growth on bundles. Supporting this notion, we show that presence of 𝛼-actinin also impeded the cofilin domain growth rates on single filaments compared to single filaments in the absence of 𝛼-actinin. On the other hand, the presence of fascin does not affect the cofilin domain growth rates on single filaments. These results imply that bundles with different cross-linkers are disassembled by cofilin by different mechanisms.

With the help of cofilin domain fluorescence intensity curves, we identified the presence of two overlapping cofilin domains on bundles with two filaments. By computing the outcome of bundle severing due to the presence of 2 overlapping cofilin domains, we could derive the rate of the nucleation of the second cofilin domain using a simple model. This rate is strongly enhanced compared to the nucleation of the first cofilin domain. This enhancement may originate from an overtwisting of the second filament induced by the growth of the first cofilin domain on the first filament. This may be enough to lead to a twisted state of the second filament that strongly increases cofilin affinity locally on the second filament.

Furthermore, looking at the cofilin domain fluorescence, we report the signature for the cofilin to fully fragment a 2-filament bundle: we were able to resolve the intermediate step , where one cofilin domain severing first before the second domain severs, leading to full bundle fragmentation. We report that cofilin 'domain severing' occurs at the same rate on 2-filament bundles and single filaments. Moreover, fascin departure upon cofilin domain growth appears to be enough to allow cofilin-dependent local filament twisting, therefore preventing any torque accumulation as opposed to the situation where single actin filaments are twist-constrained by being permanently anchored to a surface (Wioland et al., 2019b) . The direct consequence of coflin-induced twisting is the enhancement of cofilin domain nucleation on the neighboring filament. On bigger bundles (~ 3-10 filaments), we also observed overlapping cofilin domain nucleation, which look similar to what we characterized more in depth for 2-filament bundles.

Next, our data demonstrated that bigger bundles survived to cofilin fragmentation longer than two filament bundles.

Overall, for 2-filament bundles, even though the nucleation of a second cofilin domain on the neighboring filament is highly accelerated, the nucleation of the first domain is hindered, and at least two cofilin severing events need to occur for the bundle to be fully broken into two segments. This is enough to offer some protection to bundles in comparison to single filaments.

Extrapolating to bundles of higher size, i.e. 10 to 20 filaments, as in filopodia, this 'protection'

increases substantially, at least thanks to cofilin domain nucleation which decay rapidly with increasing bundle size.

A previous study by Breitsprecher et al has proposed that the fascin cross-linked bundles severed more compared to single filaments in in vitro experiments [START_REF] Breitsprecher | Cofilin cooperates with fascin to disassemble filopodial actin filaments[END_REF] .

In this study, they assess cofilin activity rather indirectly, by recording the increase of bundle size with time in the presence of cofilin through bundle reorganization, in a TIRF microscopy assay.

Their interpretation is that cofilin, by inducing severing, allows filament fragments to join pre-existing bundles and thus the bundle size to increase. From our point of view, this assay makes it hard to make a direct comparison with the level of coflin-induced severing between single filaments and fascin-crosslinked bundles.

Our results, by directly visualizing cofilin domains with fluorescence, demonstrate that global cofilin severing of bundles is slower compared to single filaments, owing mostly to the slower domain nucleation rates on the bundles. Study by Elkhatib et al in cells looked at the role of fascin in focal adhesion (FA) disassembly. Our results seem to agree with their observation in cells, where fascin has to depart from stress fibers termini 'before' cofilin disassemble stress fibers at this location [START_REF] Elkhatib | Fascin Plays a Role in Stress Fiber Organization and Focal Adhesion Disassembly[END_REF] .

We wondered whether the increase in filament helicity when a cofilin domain nucleated and grew on a single filament of a filament bundle could induce a filament helicity increase on neighboring filaments of the bundle. Our results, obtained by single-molecule fluorescence polarisation and negative staining EM, support the hypothesis of bundles being overtwisted by cofilin (fig 5.16). With our EM studies, we observed that smaller bundles were braided due to the overtwisting whereas the bigger bundles were separated into smaller bundles (2-4 filaments).

However, it is not clear whether the bigger bundles are unbundled again due to the over twisting.

Importantly, these findings imply that the cofilin can twist the bundles of low torsional rigidity to grow the cofilin domains and induce the severing of individual filaments leading to disassembly of bundles.

Bundle over twisting were extensively done for fascin bundles and should be further investigated for 𝛼-actinin bundles. Also, we had difficulties in reconstituting the bigger bundles induced by 𝛼-actinin in microfluidics to observe the individual molecular events of cofilin activity in disassembling bigger bundles.

Jahnavi C -doctoral thesis -2021

Our results show that both fascin and 𝛼-actinin crosslinkers offer some level of protection from cofilin activity but involves different mechanisms, with 𝛼-actinin being overall more protective.

Cofilin domain nucleation rates on fascin bundles were slower compared to nucleation rate on 𝛼-actinin bundles, while severing is slower on 𝛼-actinin bundles. Moreover, both domain nucleation and growth appears to be reduced by the presence of 𝛼-actinin, even on single filaments.

Here, with our simplified system to reconstitute actin bundles that support filopodia ('fascin bundles'), or actin stress fibres ('𝛼-actinin bundles'), we have studied the molecular details involved in the cofilin activity on bundles. We propose a new mechanism for the cofilin severing on the bundles. Our study showed that the presence of a crosslinker partially protects the filaments from cofilin disassembly. Together, our results show that different networks in the cells like filopodia and stress fibers, could be disassembled by different mechanisms.

Perspectives

Open questions:

This Phd work, by providing more details at the molecular scale, for both assembly and disassembly of actin filament bundles, gives us a new perspectives on bundle dynamics and

prompt for new open questions: for cofilin displacing the crosslinker fascin, is the change of cofilin-induced helicity accelerates fascin departure? A very recent study, available on the bioRxiv preprint server, in rat hippocampal neuronal growth cones using both fluorescence microscopy and Cryo-ET, has shown the presence of a fascin-excluded cofilactin region at the base or at specific regions along the filopodia and its shaft as shown in fig 6 [START_REF] Hylton | Cofilin Regulates Filopodial Structure and Flexibility in Neuronal Growth Cones[END_REF] . These findings are in line with our results of cofilin displacing fascin from the two filament bundles. Structural details of fascin and cofilin interacting with actin might help to understand this area.

An interesting way to challenge our proposed model for bundle severing is to anchor the bundles close to the barbed end on the surface, so that bundles could no longer rotate upon cofilin binding. In such a case, we could see an enhancement in first cofilin domain severing on the bundles and second domain nucleation rates not faster than on a single filament.

Another interesting question to explore further is why 𝛼-actinin is not displaced by cofilin? Is it because 𝛼-actinin is a long flexible dimer, offering it the possibility to reattach to a filament ?

Our studies with 𝛼-actinin bundles were done with filaments arranged in parallel, but 𝛼-actinin can also bundle anti parallel filaments. Then the question arises whether this difference in filament orientation affects the cofilin activity? One might expect that filament helicity (right handedness is preserved in both directions) and the symmetrical growth of cofilin domains to not modify our observations. Jahnavi C -doctoral thesis -2021

Future studies involving additional proteins : tropomyosins, myosins, formin generated actin filaments fascin bundles disassembly.

Physiologically actin structures, such as the one found in filopodia and stress fibers, are more complex than the simplified bundle architectures we have reconstituted. There are several other proteins that can regulate the activity of cross-linkers and cofilin in cells.

The open question to ask is how the formin-generated filaments are disassembled by cofilin. A study by Mizuno et al in 2018 both in vivo and in vitro, has shown that mDia1 generated filaments are resistant to cofilin activity (H. [START_REF] Mizuno | Helical rotation of the diaphanous-related formin mDia1 generates actin filaments resistant to cofilin[END_REF] . Their interpretation is that formin would induce filament under twisting that would diminish cofilin activity. How the formin generated actin filaments when bundled by fascin (similar to filopodia situation) are disassembled by cofilin?

Tropomyosins are interesting proteins that are known for their protection and stabilisation of actin proteins in the cells. The biochemical study by Matsumura et al, has shown that different tropomyosin isoforms can regulate the fascin binding to the actin filaments differently (Matsumura & Yamashiro-Matsumura, 1986) . But this study was done in bulk assays, the molecular details involved in the interaction of these proteins are yet to be studied. Moreover, tropomyosins are also known as competitors of cofilin for actin filament binding. Tpm 1.8 was shown to decrease cofilin binding and severing to the actin filaments [START_REF] Wioland | Actin filament oxidation by MICAL1 suppresses protections from cofilin-induced disassembly[END_REF] .

Different isoforms of tropomyosins protect the actin filaments from cofilin activity differently [START_REF] Gateva | Tropomyosin Isoforms Specify Functionally Distinct Actin Filament Populations In Vitro[END_REF]Kuhn & Bamburg, 2008) . Hence it would be worth exploring how the presence of tropomyosin changes the activity of fascin bundling, and in a subsequent step, how it affects cofilin on those bundles?

Finally, another interesting area to explore would be how cofilin activity will be affected in the presence of myosins. For example, myosin II was shown to be involved in actin bundle disassembly [START_REF] Haviv | A Cytoskeletal Demolition Worker: Myosin II Acts as an Actin Depolymerization Agent[END_REF] . As several recent studies are showing the myosin-induced actin disassembling property, it is interesting to study the interaction between cofilin and myosins in the presence of cross-linkers in the bundles [START_REF] Wilson | Myosin II contributes to cell-scale actin network treadmilling via network disassembly[END_REF] . • Howard, J. (2001). Mechanics of Motor Proteins and the Cytoskeleton (New édition).

OUP USA.

• Huang, S., Robinson, R. C., Gao, L. Y., Matsumoto, T., Brunet, A., Blanchoin, L., & Staiger, C. J. (2005). Arabidopsis VILLIN1 Generates Actin Filament Cables That Are Resistant to Depolymerization. The Plant Cell , j'ai pu étudier comment l'activité de la formines et de la cofiline sont affectées lorsqu'elles agissent sur des faisceaux induits par la fascine ou l'alpha-actinine.

209 Nous avons observé que l'activité de la cofiline est différente sur les filaments uniques en présence de différents crosslinker, la fascine ou l'𝛼-actinine. En présence de fascine, l'activité de la cofiline sur les filaments uniques n'est pas affectée. Cependant, ce n'est pas le cas en présence de 𝛼-actinine. La nucléation des domaines de cofiline, les vitesses de croissance et les taux de fragmentation des domaines étaient plus lents sur les filaments uniques en présence d'𝛼-actinine.

Cela pourrait être dû au fait que l'𝛼-actinine soit une protéine dimérique flexible qui lui permet de se lier aux filaments isolés uniques. Conformément aux rapports précédents, nous montrons que la 𝛼-actinine marquée se lie aux filaments isolés (Winkelman et al., 2014[START_REF] Hampton | Novel Structures for α-Actinin:F-Actin Interactions and their Implications for Actin-Membrane Attachment and Tension Sensing in the Cytoskeleton[END_REF].

Nous avons constaté que la capacité de la cofiline à nucléer un domaine sur des faisceaux de filaments induits par la fascine est plus lente que sur un filament individuel. Pour les faisceaux de deux filaments, le taux de nucléation des domaines est six fois plus lent. Plus largement, le taux de nucléation des domaines de cofiline sur les faisceaux dépend fortement du nombre de filaments formant le faisceau et de la concentration de fascine qui viennent saturer les sites de liaison à la surface des filaments. Ces résultats impliquent que plus le faisceau est grand, plus il est difficile pour la cofiline de nucléer des domaines. Ces résultats soutiennent la théorie selon laquelle les faisceaux sont protégés contre la fixation de la cofiline, précédemment proposée par des approches moins résolues [START_REF] Yang | Mammalian CARMIL Inhibits Actin Filament Capping by Capping Protein[END_REF]Michelot et al., 2007). Lorsque les filaments sont regroupés en faisceaux par l'𝛼-actinine, la distance inter filamentaire est plus importante que dans le cas de la fascine (environ 36 nm contre 8 nm seulement). Les filaments réticulés par l'alpha-actinine sont plus flexibles que ceux de la fascine, ce qui affecte différemment la capacité de liaison de la cofiline. Nos résultats montrent en effet que la nucléation des domaines de cofiline sur les faisceaux de 𝛼-actinine est moins diminuée par rapport aux faisceaux de fascine. À l'aide de l'intensité de fluorescence des domaines de cofiline, nous avons identifié la présence de deux domaines de cofiline se chevauchant sur les faisceaux avec deux filaments. En simulant, dans un modèle simple, l'apparition de ces domaines de cofiline qui se chevauchent, nous avons pu mesurer le taux de nucléation du second domaine de cofiline. Ce taux est fortement augmenté par rapport à la nucléation du premier domaine de cofiline. Cette augmentation peut provenir d'une sur-torsion du second filament induite par la croissance du premier domaine de cofiline.

Cela peut être suffisant pour conduire à un état de torsion du second filament qui augmente fortement l'affinité de la cofiline.

Nous avons pu également observer temporellement l'étape intermédiaire, pour 60% de nos observations, au cours de laquelle un domaine de cofiline fragmente un filament avant que le second domaine par fragmentation ne conduise à la fragmentation complète du faisceau. Ces observations nous permettent de mesurer le taux de fragmentation des domaines de cofiline et dire qu'il est du même ordre de grandeur que celui observé sur les filaments individuels. Cela semble indiquer que le départ de la fascine empêche toute accumulation de couple de torsion pour les filaments d'actine (Wioland et al., 2019b). Les études relatives à la sur-torsion des faisceaux rapportés ci-dessus pour la fascine devront être approfondies pour les faisceaux d'𝛼-actinine. Nous avons eu des difficultés à reconstituer les plus grands faisceaux induits par l'𝛼-actinine, même avec des incubations de plusieurs heures.

Pour conclure, nos résultats montrent que les deux types de crosslinkers offrent une protection assez proche contre l'activité de désassemblage de la cofiline mais impliquent des mécanismes différents. l'alpha-actinine est malgré tout plus protectrice. Ici, avec notre système in vitro pour reconstituer les faisceaux d'actine qui supportent les filopodes ('fascin bundles'), ou les fibres de stress d'actine ('𝛼-actinin bundles'), nous avons étudié les détails moléculaires impliqués dans l'activité de la cofiline sur les faisceaux.

Fig 1 . 1 .

 11 Fig 1.1. Structure of actin monomer and filament. A) Actin monomer with four subdomains colored differently. A DNAse-I binding domain is shown in subdomain 2 and the nucleotide-binding domain is shown in between the domains (Otterbein et al., 2001) B) Conformational changes in actin monomer structure in G-actin and F-actin. During this transition, the actin subunit is flattened by 20° (Dominguez & Holmes, 2011) C) Actin filament with right-handed helix with crossover length of 72 nm and diameter 8 nm. The actin monomer has a diameter of 5.4 nm.

Fig 1 . 2 .

 12 Fig 1.2. Actin assembly rates and nucleotide states : A) rate constants of association and dissociation of actin monomers, at the pointed and barbed ends of the actin filament, are shown in this figure. Affinities (K values, in µM) are the ratio of dissociation rate to association rate constants. The association rate constants, µM -1 s -1 ; unit of dissociation rate constants, s -1 (Pollard, 2016b) B) Actin Filament showing polymerized subunits with nucleotides at different states, showing ATP rich region at the barbed end, and exponential decay of the ADP-Pi content within the filament from the barbed end to the pointed end.

Fig 1 . 3 .

 13 Fig 1.3. Different families of ABPs: ABPs regulating actin networks such as monomer binding, elongation, capping, severing, cross-linking, and branching of filaments with few examples of proteins are shown in the image. Tropomyosins and Myosins are also other ABPs that are not depicted here in side binding proteins[START_REF] Pollard | Actin and Actin-Binding Proteins[END_REF] .

Fig 1 . 4 .• Arp2/ 3 Arp2/ 3

 1433 Fig 1.4. Summary of different actin nucleators : A) Arp2/3 complex with class I NPFs, B) or with DIP/SPIN90, C) formin D) Ena/VASP E) proteins containing one or several WH2 domains (Siton-Mendelson & Bernheim-Groswasser, 2017)

  Jahnavi C -doctoral thesis -2021 A dendritic nucleation model was proposed by Mullins et al. to show the assembly of actin filaments at the leading edge of the cells by Arp2/3 (Fig 1.

Fig 1 . 5 .

 15 Fig 1.5. Arp2/3: nucleator of dendritic networks. A) Dendritic networks as seen in fish keratinocytes. Scale bar: 50 nm adapted from[START_REF] Svitkina | Analysis of the Actin-Myosin II System in Fish Epidermal Keratocytes: Mechanism of Cell Body Translocation[END_REF]) B) 'branch' from the actin filament using purified Arp2/3 complex adapted from (Mullins et al., 1998) C) Seven subunits of Arp2/3 complex D) proposed branching reaction: Inactive Arp2/3 is activated by binding of the VCA [Verprolin (V), Central and Acidic] region and ATP-actin subunit forming a complex. This complex can bind to the mother filament. VCA is dissociated, and the daughter filament is nucleated. Mother and daughter filaments are elongated. Adapted from[START_REF] Espinoza-Sanchez | Conformational changes in Arp2/3 complex induced by ATP, WASp-VCA, and actin filaments[END_REF] .

Fig 1 . 6 .

 16 Fig 1.6. Formin structure and actin polymerization: A) Different domains of formins such as GTPase, profilin, and actin-binding domains were shown at the top. At the bottom, dimerization of the N-terminus and FH2 domain is shown. Here, the individual domains of the FH2 domain such as a knob, linker, lasso, and post are indicated. B) FH1 mediated actin polymerization is depicted here. The flexible FH1 domain has several polyproline tracks (could be ranging from 2-14[START_REF] Horan | Computational modeling highlights the role of the disordered Formin Homology 1 domain in profilin-actin transfer[END_REF] . Profilin-actin complexes interact with these tracts. They are delivered to the barbed end rapidly and generate a closed ring.[START_REF] Courtemanche | Mechanisms of formin-mediated actin assembly and dynamics[END_REF][START_REF] Otomo | Crystal structure of the Formin mDia1 in autoinhibited conformation[END_REF] .

Fig 1 . 7 .

 17 Fig 1.7. Formin activity measured by elongation and detachment rates: Formin can bind and track growing barbed ends. They can enhance the actin elongation rate and are processive at the barbed end. Profilin-actin complexes interact with FH1 domains of formins and enhance the rate of actin elongation. By measuring the detachment rate (K off ) of formin from the barbed end, one can estimate how processive the formin was.

Fig 1 . 8 .

 18 Fig 1.8. Actin filament elongation with FH2 domain . Actin subunit in yellow, two monomers of the FH2 domain were depicted in red and blue. Monomer addition to the barbed end by the FH2 domain with the help of the flexible linker. Adapted from[START_REF] Pollard | Actin and Actin-Binding Proteins[END_REF]

Fig 1 . 9 .

 19 Fig 1.9. Formin is in rapid equilibrium between open and closed states in the absence of profilin (Top). Actin monomer can be added only in the open state. After the subunit addition, formin rapidly adapts to a transition state of open-closed rapid equilibrium at low force, whereas at high force FH2 domain detaches from the barbed end (L.[START_REF] Cao | Modulation of formin processivity by profilin and mechanical tension[END_REF]

Fig 1 . 10 .

 110 Fig 1.10. Structure of Ena/VASP and its localization A) Ena/VASP is a tetramer with multi-domains.It has both G-actin and F-actin binding sites in the EVH2 domain (adapted from[START_REF] Harker | Ena/VASP processive elongation is modulated by avidity on actin filaments bundled by the filopodia cross-linker fascin[END_REF] ). B) GFP-VASP is shown to localize at the filopodial tips of MV D7 cells[START_REF] Barzik | Ena/ VASP regulates mDia2-initiated filopodial length, dynamics, and function[END_REF] .

  2 B. A very interesting feature of tropomyosins is that they control the binding of other actin side binding proteins like myosins, formin, cofilin, and fascin (Fig 1.11 B) (P. Gunning et al., 2008; P. W. Gunning et al., 2015; Wawro et al., 2007) . Christensen et al. have shown that the binding of yeast fimbrin Fim1 promotes the dissociation of yeast Tropomyosin Cdc8 and leads to the subsequent binding of ADF/cofilin (Christensen et al., 2017) .

Fig 1 . 11 .

 111 Fig 1.11. Tpm regulating the ABPs binding to the actin filaments: A) Tpm binding to the side of the actin filament. B) Depending on the Tpm isoform, some ABPs are binding to the actin filament and some don't.

Fig 1 . 12 .

 112 Fig 1.12. Cofilin dynamics on actin filament: A) 1) initial cofilin binding to the actin filament nucleates a domain; 2) the cofilin domain grows symmetrically towards both the BE and PE; 3) cofilin severs the filament at the boundary of the domain B) cofilin induces changes in a twist where the helical pitch gets shorter while filament length is not changed. Adapted from(Jegou & Romet-Lemonne, 2020) .

Fig 1 . 13 .

 113 Fig 1.13. Filamin structure: homodimer with multi-domains such as actin-binding domains at the N-terminal and Ca 2+ sensitive calpain sites and flexible hinge regions along with dimerization domains at the C-terminal. adapted from[START_REF] Stossel | Filamins as integrators of cell mechanics and signalling[END_REF]

Fig 1 . 14 .

 114 Fig 1.14. Fascin structure, its binding sites, and binding affinity: A) Fascin monomer with four subdomains (left) and two actin-binding sites for fascin along with a third actin-binding site (right) adapted from (Chen et al., 2010; S. Yang et al., 2013) . B) two binding sites of fascin proposed by model from (Aramaki et al., 2016) C) Fascin bundling affinity of actin filaments with increasing fascin concentration reaches a saturation around 600 nM (left) and (right) EM images showing the parallel actin filaments bundled by fascin. adapted from[START_REF] Jansen | Mechanism of Actin Filament Bundling by Fascin *[END_REF][START_REF] Winkelman | Fascin-and α-Actinin-Bundled Networks Contain Intrinsic Structural Features that Drive Protein Sorting[END_REF]

Fig 1 . 15 .

 115 Fig 1.15. Supercoiling of the bundle due to filament-crosslinking: The binding sites for cross-linker is distributed on the helical structure of actin filament are shown in the figure in black. Individual twists of filaments are shown as ⲫ' and bundle twist is shown as 𝛀.Torque imposed by cross-linking on filaments is proposed to be relaxed by supercoiling of the whole bundle adapted from[START_REF] Heussinger | Theory of crosslinked bundles of helical filaments: Intrinsic torques in self-limiting biopolymer assemblies[END_REF] .

Fig 1 . 16 .

 116 Fig 1.16. Structure of 𝛼-actinin monomer and 𝛼-actinin bundles: (Bottom) EM image of 𝛼-actinin bundling actin filaments. White arrows represent the 𝛼-actinin binding to the side of the single filaments in the bundles. (Top) Rod-shaped 𝛼-actinin monomers as an anti-parallel dimer adapted from[START_REF] Hampton | Novel Structures for α-Actinin:F-Actin Interactions and their Implications for Actin-Membrane Attachment and Tension Sensing in the Cytoskeleton[END_REF][START_REF] Jahed | Chapter Five-Mechanotransduction Pathways Linking the Extracellular Matrix to the Nucleus[END_REF]

Fig 1 . 17 .

 117 Fig 1.17. Different actin networks involved in cell migration.Branched actin networks as seen in lamellipodia, parallel actin bundles as seen in filopodia, and contractile actin networks with filaments cross-linked in both parallel and antiparallel directions[START_REF] Letort | Dynamic reorganization of the actin cytoskeleton[END_REF] .

Fig 1 . 18 .

 118 Fig 1.18. Platinum replica EM showing filopodia. filopodia emerging front the actin cortex adapted from[START_REF] Svitkina | Mechanism of filopodia initiation by reorganization of a dendritic network[END_REF]

  monomers and regulating ABPs are in constant flux(fig 2.1). Indeed, ABPs activity could be affected by filament cross-linking and the way mechanical stresses are transmitted across the filaments. This complex interplay is not fully understood and remains a challenge to study. It is therefore important to address how the architecture of networks could affect the activity of ABPs. This can be addressed in different ways: in cells or by in vitro reconstitution of systems with different complexities. To study in cells the molecular details involved in how individual

  studying how the activity of ABPs formin and cofilin is affected, when filaments arranged in parallel are cross-linked by fascin, as seen in filopodia, using purified proteins and in vitro reconstituted systems (Fig 2.1).

Fig 2 . 1 .

 21 Fig 2.1. Schematic representation of cross-linked actin networks with ABPs. A) fascin cross-linked bundles elongated by lipid anchored formins B) Bundle disassembly by cofilin. Imposing constraints on filaments and formins, with cross-linking by fascin and lipid anchoring respectively. These constraints affect the activity of ABPs formins and cofilin. Note: These are simplified sketches of a network. For sketch (A) more details about anchoring are shown in Fig 2.3.

Fig 2 . 2 .

 22 Fig 2.2. Schematic representations of lipid-anchored formin elongated filaments. (A) on Giant Unilamellar Vesicle (GUV) and (B) on micropatterned lipid islands, show the difference in filament orientation relative to the anchoring surface between the two cases. GUVs appear more suitable to obtain a more physiological filament orientation relative to the lipid bilayer. C) Sketch to represent the filaments in hexagonal lattice when cross-linked by fascin.

Fig 2 . 3 .

 23 Fig 2.3. In vitro reconstitution of fascin-cross-linked actin filaments to study ABPs (formin and cofilin) activity affected by geometrical constraints: A) lipid anchored formin-elongated actin bundles larger than 3 filaments ( formin anchored to the GUVs) B) Disassembly of actin bundles by cofilin .

Fig 3 . 1 .

 31 Fig 3.1. SDS-PAGE gels of purified proteins: fascin, mCherry-cofilin-1, mDia1and 𝛼-actinin-1 to show the purity of proteins. Molecular weights of respective proteins were also mentioned. Gel images showing different steps of the purification of proteins. M: represents the well of marker; P: represents the well that has final protein output. The 'Red rectangle' shows the pooled fractions of purified proteins.

Fig 3 . 2 .

 32 Fig 3.2. Experimental setup in microfluidics and open chambers: A) microfluidic chamber connected to the pressure controller and used to inject the different ABPs required for the particular experiment adapted from (Wioland et al., 2020) b) typical open chamber prepared with two glass coverslips and parafilm making channels. A mix of required ABPs is injected from one side and aspirated from the other side (top). Different channels in the chamber are used for different conditions of the experiment (In figure: with and without cofilin) (bottom)

Fig 3 . 3 .

 33 Fig 3.3. Microfluidics setup with two different anchoring situations : to study the activity of unanchored (Top), lipid, or glass anchored formins (Bottom) along with the images. Filaments caught by the formins slide to the edge of the lipid bilayer (200 x 200 µm square patterns) due to the flow (Bottom image).Scale bar: 10 µm

Fig 3 . 4 .

 34 Fig 3.4. Different lipid surfaces used in the microfluidics experiments A) Bilayer in 2 µm diameter circular patterns with 20 µm distance in between. B) Actin filaments around lipid-coated on glass beads C) GUVs settled on the surface with neutravidin on the surface in microfluidics. Scale bar: 10 µm.

Fig 3 . 5 .

 35 Fig 3.5. Sketch representing the GUVs reconstitution in microfluidics . GUVs stick to the neutravidin with the help of biotin lipids. So, the GUVs do not flow away in the experiments.

Fig 3 . 6 .

 36 Fig 3.6. Kymograph showing the elongation of an actin filament by an anchored formin mDia1: filament elongated from the formin in the presence of 0.2 µM 6% alexa-488-labelled actin and 0.2 µM profilin. Elongation rate was measured from the slope (green dashed line) and formin detachment from the barbed end was made visible by the departure of the filament from the surface (or field of view) (white arrow).

3. 4 . 1

 41 Surface passivation For experiments where filaments are exposed to labeled fascin and cofilin, such as the open chambers (see fig 3.2 B) and fluorescence polarization assays (see section 3.4.4), we used

Fig 3 . 7 .

 37 Fig 3.7. Pi release is not affected by fascin-induced bundling of actin filaments . Each small circle represents individual depolymerization rates from the three individual experiments. Each big circle represents the averages of these measurements. N > 30 measurements for each condition. P = 0.152 (paired t -test).

Fig 3 . 8 .

 38 Fig 3.8. Forming bigger bundles from regularly localized anchored seeds is challenging:Reconstituting bigger bundles from seeds on the surface is challenging as the number of filaments could be varying from one place to the other.Arrows pointing different anchoring points of a bundle.

Fig 3 . 9 .

 39 Fig 3.9.Reconstituting bigger bundles on glass beads: A) Beads coated with seeds were introduced into the microfluidic chamber. Filaments were elongated from the beads using 10% alexa-4888 labeled actin. B) Elongated filaments on the beads were aged and bundled using unlabeled fascin + unlabeled actin. C) Bigger bundles on beads were then exposed to cofilin along with fascin and actin. Scale bar: 5 µm.

Fig 3 . 10 .

 310 Fig 3.10. Bundles of varying sizes are formed on the beads: Distribution of sizes of the bundles on beads estimated from the actin fluorescence. N=179 bundles.

Fig 3 . 11 .

 311 Fig 3.11. Strategies to identify the bundle size in the experiments. A) looking at the seed positions (left) and estimating the number of filaments in the bundle (right) or Quantifying the fluorescence intensity of labeled actin for a single filament or bundle. B) Left: Fluorescence intensity of actin for single filament and bundles. The intensity of bundles is twice compared to a single filament implying the presence of two actin filaments. Scale bar: 10 µm. Right: Sketch showing the single filament region at the base and end of the bundle in a fascin-crosslinked bundle.

  package in python. The following equation was used to fit experimental data and derive k on with the single exponential curve in excel f surv = exp(-t.l.k on,domain ), Where t=time, l = segment length in actin monomers, k on,domain = domain nucleation rate /subunit/s 2 Domain growth rate

Fig 3 . 12 .

 312 Fig 3.12. Two severing events have to occur to sever the two filaments in the bundle. The severing of two filament bundles involves the severing of the two filaments individually by the cofilin domains.

  2-0.3% alexa-568 labeled (see fig 3.13 A). This low labeling fraction ensures enough spacing between single alexa-568 fluorophores along the filaments to record the fluorescence polarization of the light emitted by those probes. The alexa-488 labeling helps to identify single filaments and bundles in the field of view (see fig 313 B left). The fluorophore was excited with epifluorescence. The emitted light from the fluorophores passes through a polarizing beam splitter (Optosplit II ByPass, Cairn Research) and the vertically polarized fluorescence (FL V ) and horizontally polarized fluorescence (FL H ) is sent on the two halves of the sCMOS camera.

Fig 3 . 13 .

 313 Fig 3.13. Experimental setup for single-molecule fluorescence polarization microscopy: A) Sketch representing actin bundles and single filaments in microfluidics for single-molecule fluorescence polarisation assays. B) Single-molecule fluorescence polarisation on single filaments as an example here.Single filaments with sparsely labeled Alexa-568 actin exposed to buffer (Top, left) and to cofilin (Bottom, left). Alexa-568 dye emission moment was split into vertically polarized moment (FL V ) and horizontally polarized moment (FL H ) (Right). When exposed to just a buffer, the filament, FL V and FL H remain constant and alternate in phase when exposed to cofilin as the filament rotates to relax the stress caused due to the cofilin binding.

Fig 4 . 1 .

 41 Fig 4.1. Elongation rates were not affected by the rotational constraints of the formin. A) Sketches showing the different side anchoring (FH1and FH2) and surface anchoring (glass or lipids) of formins in the microfluidics The distance between the surface and formin in each case of anchoring was shown here. B) Normalised elongation rates and processivity rates of formins in each condition. Adapted from[START_REF] Suzuki | Geometrical Constraints Greatly Hinder Formin mDia1 Activity[END_REF]

Fig 4 . 2 .

 42 Fig 4.2. Sketch depicting the leading and trailing formins in a fascin cross-linked bundle when formins are FH1-anchored side anchored to glass.

Fig 4 . 3 .

 43 Fig 4.3. Time-lapse images showing the fluidity of the bilayer around the lipid-coated beads. On the bilayer, His-tag containing CP caught preformed filaments by their barbed end. Filaments are arranged in the direction of flow implying that CP can freely diffuse around the bilayer on beads. Scale bar: 10 µm

Fig 4 . 4 .

 44 Fig 4.4. Time-lapse images showing the fluidity of bilayer (A, B and C) . Filaments around the GUVs arrange in the direction of flow. This implies the free translational movement of FH1 anchored formins around the GUVs. D) Bundle on GUV elongated using 0.2 µM actin/ 0.2 µM profilin /0.1 µM fascin. E) Kymograph showing elongation of a bundle by formins. Scale bar: 5 µm.

Fig 4 . 5 .

 45 Fig 4.5. Instabilities observed for bundles on GUVs and patterns. (Top) Rotation of the bundle from one anchored point to the opposite side on GUVs. (Bottom) Unzippering of actin filaments from the bundle on patterns as they elongate. Dotted circles represent the patterns.

  Letter DOI: 10.1021/acs.nanolett.9b02241 Nano Lett. 2020, 20, 22-32

Figure 1 .

 1 Figure 1. Formin anchoring may impact its rotational freedom but does not affect single actin filament elongation rates. (A) In a microfluidics chamber, shown in upper left, formin-induced actin filament elongation is monitored for unanchored formins (bottom left) or for formins specifically anchored to either glass or a lipid bilayer (right) by a 6× Histidine tag located either at their N-or C-terminus. Typical fields of view showing alexa488-labeled actin filaments aligned by the microfluidics flow. (B) Formin-induced actin filament mean elongation rate in the presence of 0.2 μM 7% alexa488-labeled actin and 2 μM profilin, as a function of formin anchoring (error bar is sample standard deviation) (see Supporting Information Figure 1A). (C) Formin detachment rate as a function of formin anchoring in the presence of 0.2 μM 7% alexa488-labeled actin and 2 μM profilin (error bar is standard error, see Supporting Information Methods and Supporting Information Figure 1A). (D) The polarization of the emitted light indicates the orientation of a single fluorescently labeled actin subunit. The polarization index P =( I +4 5 -I -45 )/(I +45 + I -45 )i s determined by measuring the emitted intensity through two orthogonal polarization filters (I +4 5 and I -45 ). Depending on the rotation constraints at the anchoring point, an actin filament elongated by an anchored formin will exhibit either an erratic variation of polarization (left) or a steady oscillation of the polarization signal (right). For each sketched situation, a typical experimental data curve is shown as an example. (E) Cumulative distributions of the main frequency of the polarization signal for filaments elongated by (left) FH1-anchored formins or (right) FH2-anchored formins, anchored either on glass or lipids, in the presence of 1 μM unlabeled actin. Experimental data are fitted by the weighted sum of the cumulative distribution functions of a normal distribution (the mean frequency, f norm , is indicated for each case) and a random distribution. (F) The fraction of formins identified as rotationally constrained or rotationally unconstrained was determined by fitting the cumulative distributions, as shown in panel E.

  Letter DOI: 10.1021/acs.nanolett.9b02241 Nano Lett. 2020, 20, 22-32

  Letter DOI: 10.1021/acs.nanolett.9b02241 Nano Lett. 2020, 20, 22-32

Figure 2 .

 2 Figure 2. Fascin-induced bundling slows down trailing actin filament barbed end elongation and increases trailing formin detachment rate. (A) Sketch depicting a fascin-induced bundle where barbed ends are elongated by unanchored formins, identified as "leading", "trailing #1", and "trailing #2" depending on the relative barbed end positions The kymographs show either the elongation of bundled filaments by formins, in the presence of 0.2 μM actin, 2 μM profilin, and 100 nM fascin, for leading (green dashed line), trailing #1 (orange dashed line), and trailing #2 (yellow dashed line) formins or the depolymerization of bundled filaments by formins in the presence of 4 μM profilin and 100 nM fascin, for leading formin (green dashed line), trailing #1 formin (orange dashed line), and "synchronized" leading and trailing formins (white dashed line). Abrupt drops in the filament elongation rate were interpreted as formin-barbed end detachment events. (B) Mean filament elongation rate for leading (n = 52), trailing #1( n = 21), or trailing #2( n = 5) unanchored formins in conditions shown in panel A middle. Error bar is sample standard deviation. (C) Mean filament depolymerization rate for leading (n = 20), trailing (n = 15), and synchronized (n = 25) unanchored formins in conditions shown in panel A bottom. Error bar is sample standard deviation. (D) (Left) sketch representing a three-dimensional numerical simulation of actin monomer diffusion and a leading and a trailing filament separated by a distance, d, between their main axis. simulation mesh size = 2.7 nm (see Supporting Information Methods). (right) Comparison between simulated and experimental measurements of the leading/trailing elongation rate ratio, as a function of the distance d. (E) Survival fraction of formin-bound barbed ends as a function of time for single filaments (gray, n = 80) or bundled filaments whose barbed end is leading (green, n = 34), trailing #1 (orange, n = 28), and trailing #2 (yellow, n = 8), fitted by a monoexponential decay function. (F) Normalized detachment rate of trailing formins, relative to leading formin detachment rate, as a function of fascin concentration. (error bar is standard error of the fit).

Figure 3 .

 3 Figure 3. Fascin-induced bundling affects glass-anchored formin elongation and detachment rates. (A,D) Sketches of a 2-filament bundle elongated by (A) FH1-anchored-to-glass or (D) FH2-anchored-to-glass formins, and respective typical fields of view showing alexa488-labeled actin filaments bundling together. Filament unbinding from the formin-decorated surface is interpreted as a formin-barbed end detachment event and used to quantify formin off rate k off . (B) Barbed end elongation rate distribution for single (n = 48) or bundled (n = 48) filaments elongated by FH1anchored-to-glass formins in the presence of 0.2 μM actin, 2 μM profilin, and 100 nM fascin. (C) Survival fractions of FH1-anchored-to-glass single (n = 51) or bundled filaments (n = 22), in the presence of 0.2 μM actin, 2 μM profilin, and 100 nM fascin. (E) Barbed end elongation rate distribution of single (n = 29) or bundled (n = 32) filaments elongated by FH2-anchored-to-glass formins in the presence of 0.2 μM actin, 2 μM profilin, and 100 nM fascin. (F) Survival fractions of FH2-anchored-to-glass single (n = 46) or bundled filaments ( n = 85), in the presence of 0.2 μM actin, 2 μM profilin, and 100 nM fascin. (G) Typical images and corresponding kymographs of 2-filament bundles where bundling leads to either (top) "synchronized" elongation of the two filaments, or (bottom) "buckling" of the leading filament. Pairwise elongation rates for trailing and leading filaments in 2-filament bundles for FH1-anchored-to-glass formins, before (orange) or during (blue) bundle elongation, in the presence of 0.2 μM actin, 2 μM profilin, and 100 nM fascin. (H) Normalized detachment rate of the leading and trailing FH1-anchored-to-glass or FH2anchored-to-glass formins, relative to the detachment rate of single formins (error bars are standard error of the fit). (I) Survival fractions of FH1anchored-to-glass formin-bound bundled filaments for three populations where the normalized elongation rate, relative to the elongation rate before bundling, is higher than 0.8, lower than 0.5 or in between (n = 11, 20, and 7 bundles respectively; log-rank test p-value = 0.31, 0.28, 0.34 between subset pairs). (J) Survival fractions of FH1-anchored-to-glass formin-bound bundled filaments for two populations where the forminformin distance is 2.7 ± 0.8 and 7.8 ± 3.3 μm (average ± standard deviation, n = 16 and 27 bundles, respectively; log-rank test p-value = 0.193). (K) Bundle detachment rate as a function of single formin detachment rate at 100 nM fascin obtained by varying actin and profilin concentrations, for FH1-anchored-to-glass or FH2-anchored-to-glass formins (error bars are standard errors).

  Letter DOI: 10.1021/acs.nanolett.9b02241 Nano Lett. 2020, 20, 22-32

Figure 4 .

 4 Figure 4. Single surface attachment of the filaments reduces single formin elongation and processivity. (A) (top) Sketch of a glass-anchored formin elongating a single filament whose rotation is blocked by surface attachment upon binding of a NEM-myosin to the filament side. (bottom) Kymograph showing an actin filament elongated by a FH1-anchored-to-glass formin, whose elongation is slowed down upon filament binding to a surface-bound NEM-myosin, until the filament unbinds from the surface-anchored formin (arrow). Filament unbinding from the formin-decorated surface is interpreted as a formin-barbed end detachment event and used to quantify formin off rates k off . (B) Distribution of elongation rates of individual actin filaments, elongated by FH1-anchored-to-glass formins, bound or not to NEM-myosins attached to the glass surface (n = 48 for both conditions; Student's t test p-value <0.001). (C) Survival fractions of formin-bound single filaments attached to the surface via a NEMmyosin or not, for FH1-anchored-to-glass (n = 78 for NEM-myosin-bound and 35 for single filaments) or FH2-anchored-to-glass formins (n =53 for NEM-myosin-bound and 76 for single filaments) in the presence of 0.2 μM actin and 2 μM profilin. (D) Normalized formin detachment rates for either FH1-anchored-to-glass or FH2-anchored-to-glass individual formins, whose elongating filaments are rotationally blocked by a surfaceattached NEM-myosin, relative to glass-anchored formins elongating rotationally unconstrained single filaments.

  Letter DOI: 10.1021/acs.nanolett.9b02241 Nano Lett. 2020, 20, 22-32

Figure 5 .

 5 Figure 5. Fascin-induced bundling moderately affects lipid-anchored formin detachment rate but not elongation rate. (A) Sketch of a fascininduced 2-filament bundle elongated by lipid-anchored formins in a microfluidics flow. (B) Typical field of view of filament bundles elongated by FH1-anchored-to-lipids formins at the edge of a lipid square pattern, in the presence of 0.2 μM 15% alexa488-labeled actin, 2 μM profilin, and 100 nM fascin, in a microfluidics flow. (C) (Top) Raw data of a 2-filament bundle imaged with both 15% alexa488-labeled actin and 100% alexa568labeled fascin; (bottom) Kymograph of a 2-filament bundle where a leading filament moves upstream as its elongation rate is higher than the elongation rate of the trailing filament. Filament unbinding from the formin-decorated surface is interpreted as a formin-barbed end detachment event and used to quantify formin off rates, k off . (D) Elongation rate distributions of single filaments (n = 18) or 2-filament bundles (n = 18) elongated by FH2-anchored-to-lipids formins (Student's t test p-value = 0.34). (E) Survival fractions of lipid-anchored formin-bound single filaments or 2-filament bundles for FH1-anchored-to-lipids (n = 15 and 22 filaments, for single filaments and 2-filament bundles respectively) or FH2-anchored-to-lipids formins (n = 35 and 25 filaments, for single filaments and 2-filament bundles respectively) in the presence of 0.2 μM actin, 2 μM profilin, and 100 nM fascin. (F) Normalized individual formin detachment rates for either FH1-anchored-to-lipids or FH2-anchored-to-lipids individual formins elongating 2-filament bundles, relative to the detachment rate of formins elongating single, unbundled filaments (orange bar). For comparison, the average detachment rate of both leading and trailing unanchored formins is shown (light blue bar). (Error bars are standard errors.)

Figure 6

 6 Figure 6. Schematic summary of filament bundling and formin anchoring impact on formin activity.Depending on filaments being bundled by fascin or not, and whether formin translational or rotational freedom are blocked or not, formin-induced actin filament elongation and formin detachment rate are differently affected. Top, left: a single filament elongated by an unanchored formin is chosen as the reference for the comparison of elongation rates (V elong ) and formin detachment rates (k off ). Bottom, left: when fascin bundles filaments, the activity of the formin elongating the leading filament is unaffected, whereas the elongation rate is reduced and the detachment rate is increased for formins elongating trailing filaments. Top, right: the activity of surface-anchored formins elongating individual filaments is not affected by anchoring, except in the case of a short formin-to-surface distance. Bottom, right: Simultaneously blocking filament rotation by fascin-induced bundling and formin rotational or translational freedom, strongly impacts both formin elongation rate and detachment rate, for both leading and trailing filaments.

Fig 5 . 1 .

 51 Fig 5.1. Cofilin activity on reconstituted fascin cross-linked actin bundles. Time-lapse micrographs of 75 nM cofilin activity on single filaments (top), 0.2 µM fascin cross-linked filaments (middle), 1 µM fascin cross-linked filaments (bottom). At t= 450 s, single filaments were severed by cofilin whereas the fascin cross-linked filaments were still intact. Scale bar = 10 µm. Here actin and cofilin are in the same color, but the low labeling fraction of actin makes it possible to observe the cofilin domains.

Fig 5 . 2 .

 52 Fig 5.2. Less cofilin was recruited onto the bundles compared to the single filaments .Quantification of cofilin intensity recruited to the single filaments and filament bundles with 0.2 µM, and 1µM fascin. Both single filaments and bundles were exposed to 75 nM cofilin. For each assay, cofilin intensity is divided by the filament density to take into account variation in filament density in the chamber between the three assays.

Fig 5 . 3 .

 53 Fig 5.3. Actin labeling affects cofilin activity: Time-lapse micrographs of 0.2 µM fascin cross-linked networks with (A) 5% labeled actin, or (B) unlabeled actin. These networks were exposed to 0.1 µM cofilin. When the actin was labeled, the network disassembled faster and it was difficult to observe individual cofilin domains (top). Scale bar : 10 µm. Here actin (labeled) and cofilin are in the same color, but the low labeling fraction of actin makes it possible to observe the cofilin domains.

Fig 5 . 4 .•Fig 5 . 5 .

 5455 Fig 5.4. Fascin labeling affects the cofilin activity: Decreased fascin labeling from (A) 100% to (B) 5% leads to uniform disassembly of the network. 0.2 µM labeled fascin cross-linked network was

Fig 5 . 6 .Fig 5 . 7 .

 5657 Fig 5.6. Sketch representing the microfluidic setup to observe cofilin activity on the single filaments in the presence (A) and absence of fascin (B) respectively. Seeds elongated with 0.5 µM labeled actin. Filaments were then exposed to 0.2 µM mCherry-cofilin, with and without 0.2 µM unlabeled fascin. Cofilin domain nucleation was then quantified for both conditions. (Right) single filaments with cofilin domains aligned in microfluidic flow. Actin is in yellow and cofilin is in blue. Scale bar: 5 µm

Fig 5 . 9 .

 59 Fig 5.9. Fascin presence does not affect the cofilin domain severing in single filaments. A) Fraction of unsevered cofilin domains on single filaments exposed to no fascin compared to single filaments exposed to fascin. N > 50 cofilin domains for each curve. Shaded regions represent 95% confidence intervals (Log-rank test) P = 0.915, 0.521 (this data set), and 0.688 (for data points shown in B). Dashed lines are exponential fits. B) Cofilin domain severing rates are not affected on single filaments when exposed to fascin. Paired experiments from the same assay are connected by a straight line. P = 0.549 (paired t -test). Error bars represent the values obtained by fitting the borders of the 95% confidence interval.

Fig 5 . 10 .

 510 Fig 5.10. Bundles cross-linked with fascin were severed slower than single filaments. A) Single filaments (SF) and fascin induced two-filament bundle (bundle) aligned by the microfluidic flow. Actin is in yellow and cofilin is in blue. B) Fraction of unsevered segments (5µm length) on single filaments and two filament bundles cross-linked by fascin. N > 20 cofilin domains for each curve. Dashed lines are exponential fits. Shaded

Fig 5 . 11 .

 511 Fig 5.11. Cofilin nucleates domains slower on bundles compared to single filaments.A) Filaments elongated from seeds were bundled with 0.2 µM unlabeled fascin, and simultaneously exposed to 0.13 µM unlabeled actin to maintain their length constant. Also, the actin fluorescence intensity is used to differentiate single filaments (SF) from a bundle with two filaments (bundle). Actin

  Left: Nucleation of first cofilin domain onto segments containing 4.3 µm of F-actin for both single filaments and bundles from the same experiment. Time t = 0 corresponds to the beginning of exposure to cofilin. N = 61 segments for single filaments and N = 41 segments for bundles respectively. Shaded regions represent 95% confidence intervals (Log-rank test) P <0.001 for 6 repeated experiments. Dashed lines are exponential fits. Right: comparison of cofilin domain nucleation rates (/subunit/sec) in between single filaments and two-filament fascin bundles. Paired experiments from the same assay are connected by a straight line. C) Cumulative distribution of the location of cofilin domains along the 6 µm long two-filament fascin bundles (performed at 200 nM fascin) for n = 32 cofilin domains analyzed.

Fig 5 . 12

 512 Fig 5.12 Cofilin domain nucleation is decreased by fascin cross-linking in a concentration dependent manner. Normalized cofilin domain nucleation on bundles is decreased upon increase in fascin concentration (100 nM, 200 nM, and 500 nM). Each circle represents a different experiment with N > 20 4.3 µm segments of F-actin for single filaments and two filament bundles .

Fig 5 . 13

 513 Fig 5.13 Cofilin domain nucleation is decreased by the increase in bundle size. A) Nucleation of the first cofilin domain onto 3 µm long segments of single filaments and bundles of different sizes from the same experiment. They correspond to the points in the graph below. Time t = 0 corresponds to the beginning of exposure to cofilin. Dashed lines are exponential fits. B) Cofilin domain nucleation rate is decreased with increase in the number of filaments per bundle.The rates we compare here correspond to the results of the exponential fits from the figure above (A) divided by the number of filaments in the bundle, in order to compare nucleation rates on equal number of actin subunits.

Fig 5 . 14

 514 Fig 5.14 Cofilin domain growth rates are slower on fascin cross-linked bundles compared to single filaments. A) sketches showing the cofilin domain growth on single filaments and fascin cross-linked two-filament bundles. B) Kymographs showing cofilin domains growing symmetrically on both sides, on single filaments and bundles. C) Growth rates of individual mCherry cofilin domains on single filaments and bundles when exposed to 0.2 µM cofilin and 0.2 µM fascin ( N =3 repeats).Small circles represent individual measurements from three repeats and bigger circles represent the average of these measurements. P = 0.031 (paired t -test)

(see fig 5 . 125 Fig 5 . 15

 5125515 Fig 5.15 Cofilin domain intensities on bundles: A) Cofilin encounters fascin every 13 subunits when expanding the domain B) Cofilin domain intensity on two filament bundles is twice as high compared to single filaments .

  have characterized the impact of labeled fascin on cofilin recruitment in open chamber assays in section 5.1 B. Here our observations were limited to observing the fascin displacement by cofilin, but no rates were quantified from these experiments.

Fig 5 . 16

 516 Fig 5.16 Cofilin displaces fascin in bundles. Kymographs showing cofilin domains appearing and growing on a fascin two-filament bundle. (Left) Merge of eGFP cofilin domains (right, blue) growing on the filaments cross-linked with the alexa-568 fascin (middle, pink). The gaps left in the fascin fluorescence where the cofilin domains are present can be seen in the middle image.

Fig 5 . 17

 517 Fig 5.17 Cofilin domain growth rates on fascin-induced bundles are unaffected by fascin concentration. Growth rates of individual mCherry-cofilin domains on bundles when exposed to 0.2 µM cofilin and different fascin concentrations. Each point is the measurement for an individual cofilin domain.

Fig 5 . 18

 518 Fig 5.18 Cofilin domain growth rates slowed as the number of filaments in the bundle were increased . Growth rates of individual mCherry cofilin domains on single filaments and bundles at 0.2 µM cofilin and 0.1 µM fascin concentration.

Fig 5 . 19

 519 Fig 5.19 Cofilin severing bundles is seen as a single event in kymograph . (Top) Images of a single actin filament (A) and bundle (B) with cofilin domains (in blue) and their respective kymographs (below). White arrowheads point to the severing events.

Fig 5 . 20

 520 Fig 5.20 Model for bundle disassembly by cofilin. (A) Sketches to show cofilin domain severing single filaments. It is the most frequent case (~80%) that severing occurs towards the Pointed end (PE) (Wioland et al., 2017) . (B) Sketch showing and cofilin domain nucleation, growth, and severing on bundles with two filaments.

Fig 5 . 21

 521 Fig 5.21 Two different cases were observed for cofilin domain severing on bundles . A) Intact bundle after one of the filaments is severed in the bundle. The white arrowhead indicates the cofilin domain that severs and disappears. B) downstream part of the bundle lost after domain severing. The severing event is indicated by the white arrowhead.

Fig 5 . 22

 522 Fig 5.22 Bundle severing observed from cofilin domain intensity. A) Cofilin domain intensity analysis on a bundle with two filaments with the ROIs showing two different cofilin domains (here the size of ROI is 7x5 pixels (height and width respectively). B) Plot showing the fluorescence intensity of cofilin over time, in the right ROI of panel A. The first drop in intensity is the severing of one of the filaments, called 'domain severing' . The second drop in intensity is caused by the bundle being severed due to the second cofilin domain severing the filament called 'total bundle fragmentation' .

Fig 5 . 24

 524 Fig 5.24 Cofilin severing at the PE side of a domain is detectable in the absence of actin. A kymograph showing the depolymerization due to the cofilin domain severing towards the PE side. Actin is yellow and cofilin is blue. Red dotted line shows the depolymerization. Domains to observe are pointed with white stars. A) A second cofilin domain remains after one has severed and a barbed end is seen depolymerizing. B) Cofilin domain severed before the nucleation of the second domain.

Fig 5 . 25

 525 Fig 5.25 Cofilin binding induces stress on bundles: Fascin cross-linked bundles attain a supercoiled conformation to relax the torsional stress due to binding of cofilin to the filaments.

Fig 5 .

 5 Fig 5.26 The 'Second' cofilin domain nucleation on bundles is faster on bundles than cofilin nucleation on single filaments. A) Computed cofilin 'domain severing' and 'total bundle fragmentation' survival fractions for fascin-induced two-filament bundles with the proposed model shown figure 5.23 (in orange and red) compared to the experimental curves. B) Cofilin domain nucleation rates (in /subunit/s) of second and first domain nucleation on two-filament bundles compared to single filaments. Second cofilin domain nucleation on two-filament bundles: values were computed from the model and fitting the curves in A, and are on average 10 times faster compared to the nucleation of the first cofilin domain.

Fig 5 . 27

 527 Fig 5.27 Second domain nucleation is observed in bundles of >3-filament bundles. A) Cofilin domain fluorescence intensity on a 7-filament bundle showing multiple drops in intensities implying that more than one cofilin domain has nucleated in the same region of the bundle.B) The survival fraction of unsevered bundles decays more slowly for >3-filament bundles than for 2-filament bundles.On average the bundle size was around 6 filaments. N = 31, and 34 domains analyzed on two filaments and >3-filament bundles, respectively.

  By monitoring the polarised light emitted by single alexa-568-labeled actin subunits incorporated in actin bundles (fig 5.28), we quantified the rotation of fascin cross-linked bundles upon cofilin binding, in microfluidics. Subunit rotation seen as the alternating fluorescence signal for vertically or horizontally polarized photons is shown in fig 5.29.

Fig 5 . 28 .

 528 Fig 5.28. Sketch representing experimental setup for the single-molecule fluorescence polarization microscopy A) bundles B) single filaments. In microfluidics, sparsely 0.1-0.5 % alexa-568 labeled actin is incorporated into bundles/single filaments that were exposed to 0.3 µM unlabeled cofilin. Cofilin binding to the constrained bundle/single filaments could lead to rotating the bundle as a whole or the single filaments. Emission moment of fluorescent dye alexa-568 on a single actin subunit was captured for analysis.

Fig 5 . 29 .Fig 5 . 30 .

 529530 Fig 5.29. Bundles rotate upon cofilin binding: Example of vertically and horizontally split images from single-molecule fluorescence polarization experimental setup. (Top) Single filaments (SF) and bundles could be analyzed from the same field of view. (Bottom) Time-lapse images of vertically and horizontally split polarised light emissions from a single alexa-568 labeled actin subunit (white squares) of a bundle upon exposure to 0.3 µM unlabeled cofilin

Fig 5 . 31 .

 531 Fig 5.31. Single filaments rotate upon cofilin binding. Intensity values (left) FL V and FL H and (right) fluorescence polarisation index (FL P ) of single filaments with cofilin respectively display some oscillation.

Fig 5 . 32 .

 532 Fig 5.32. Bundles exposed to buffer only do not rotate . (A) Intensity values (FL V and FL H ) and (B) fluorescence polarisation index (FL P ) of bundles without cofilin .

Fig 5 . 33 .

 533 Fig 5.33. Pointed end anchored bundles rotates after cofilin binding . (Left) Intensity values (FL V and FL H ) and (Right) fluorescence polarisation index (FL P ) for 3 different bundles.

Fig 5 . 34 Fig 5 . 35 Fig 5 . 36

 534535536 Fig 5.34 Filaments appear straighter in the bundles not exposed to cofilin . The area in the black box is zoomed into, in figure 5.36. Scale bar: 50 nm

Fig 5 .

 5 Fig 5.37 (A) Filaments in the bundles exposed to cofilin separated into smaller bundles. Disassembly is observed at the filament ends separating the bundles. Scale bar: 50 nm

Fig 5 . 38

 538 Fig 5.38 Sketch showing the interfilament distance between the two filaments bundled by fascin and 𝛼-actinin. Fascin bundles are more compact compared to 𝛼-actinin bundles.

  𝛼-actinin bound to single filaments (see fig 5.41). Our results confirm the previous observations made by Winkelman et al., with fluorescence microscopy and Hampton et al.,with the EM studies (Hampton et al., 2007; Winkelman et al., 2016) . Hampton et al., suggested that 𝛼-actinin dimers probably have enough flexibility to bind twice on the same filament.

Fig. 5 .

 5 Fig. 5.39 0.2 µM-Alexa-568 labeled 𝛼-actinin binding to the single actin filaments.

  2.1. -see fig 5.40 A for the sketch of the setup. We observed a trend where the cofilin domain nucleation on single filaments in the presence of 𝛼-actinin was 2.5-fold slower than in the absence of 𝛼-actinin (Fig 5.40 B and C). According to Winkelman et al, the number 𝛼-actinin of per actin subunits bound to bundled filaments is of the order of ~ 1 to 25 at 200 nM alpha-actinin. Simple steric hindrance between 𝛼-actinin and cofilin competing for binding to the filament side would be insufficient to account for the effect reported here on cofilin domain nucleation. It rather seems to suggest a change of filament conformation upon alpha-actinin binding, that needs further investigation.

Fig 5 . 40

 540 Fig 5.40 The presence of 𝛼-actinin affects cofilin domain nucleation on single filaments. A) Sketch representing the microfluidic setup used to observe cofilin activity on single filaments in the

Fig 5 . 41

 541 Fig 5.41 Cofilin domain growth on single filaments is slower in the presence of 𝛼-actinin. A) Kymographs showing the cofilin domain growth on single filaments in the presence (right) and absence of 𝛼-actinin (left). Dotted lines show the boundaries of one cofilin domain, over time. B) Superplot of the growth rates of individual mCherry-cofilin domains on single filaments exposed to 0.2 µM mCherry-cofilin and either 0 or 0.2 µM 𝛼-actinin. Small dots represent the individual measurements and the big circles are the averages of these measurements, for each experiment. Paired experiments are in the same colours. For single filament without 𝛼-actinin N = 52, 36, and 47 domains; for single filament with 𝛼-actinin N = 51, 20, and 19 domains. P = 0.046 (paired t -test).

Fig 5 .

 5 Fig 5.42 Presence of 𝛼-actinin on single filaments slowers the domain severing rate. A) Fraction of unsevered cofilin domains on single filaments exposed to 200 nM cofilin in the presence or absence of 0.2 µM 𝛼-actinin. N > 30 cofilin domains for each curve. Shaded regions represent 95% confidence interval. (Log-rank test) P = 0.044 (this data set), 0.060, and 0.457 (values for three data pairs shown at the bottom). Dashed lines are exponential fits. B) Cofilin domain severing rates were 2.5-fold slower on single filaments in presence of 𝛼-actinin to single filaments with no 𝛼-actinin (control). Paired experiments from the same assay are connected by a straight line. For single filament without 𝛼-actinin N = 53, 44, and 68 domains; for single filament with 𝛼-actinin N = 53, 45, and 29 domains. P =0.214 (paired t -test). Error bars represent the values obtained by fitting the borders of the 95% confidence interval.

Fig 5 .

 5 Fig 5.43 Global severing rate of 𝛼-actinin bundles is slower compared to single filaments. A) fraction of unsevered segments on two-filament 𝛼-actinin bundles compared to single filaments. Segment length = 5 µm. Shaded regions represent 95% confidence intervals (Log-rank test) P = 0.0004 (this data set), 0.127, and 0.0006 (values for three data pairs shown at the bottom). Dashed lines are exponential fits. B) Severing rates of 5 µm segments in single filaments and two-filament bundles (/s). Error bars represent the values obtained by fitting the borders of the 95% confidence interval, as shown in panel A. Paired experiments from the same assay are connected by a straight line. Each circle is an individual experiment. For single filaments N = 26, 27, 53 and bundles N = 15, 21,and 28 segments analyzed, respectively. P = 0.218 (paired t -test).

Fig 5 .

 5 Fig 5.44 Cofilin domain nucleation is similar on single filaments and bundles in the presence of 𝛼-actinin. A) Sketch representing cofilin activity on 𝛼-actinin cross-linked bundles. B) Actin filaments elongated from the seeds were bundled with 0.2 µM 𝛼-actinin, aged for 15 min and exposed to 0.2 µM mCherry-cofilin. Actin is in yellow, cofilin is in blue. C) Nucleation of the first cofilin domain onto 4.3 µm long segments of single filaments and bundles from t = 0 s. N = 40 for single filaments and N = 45 for bundles. Shaded regions represent 95% confidence intervals (Log-rank test) P = 0.495 (this data set), 0.439, and 0.001 (values for three data pairs shown on the right). Dashed lines are exponential fits. D) Comparison of cofilin domain nucleation rates (/subunit/s) in between single filaments and two filament 𝛼-actinin bundles ( N =3 different repeats). Paired experiments from the same assay are connected by a straight line.(paired t -test) P = 0.312. Error bars represent the values obtained by fitting the borders of the 95% confidence interval.

Fig 5 .Fig 5 .

 55 Fig 5.46 Cofilin domain growth rates are not affected on 𝛼-actinin cross-linked bundles compared to single filaments . Growth rates of individual mCherry-cofilin domains on single filaments and two-filament 𝛼-actinin bundles exposed to 0.2 µM mCherry-cofilin and 0.2 µM 𝛼-actinin. ( N =3 repeats) Small circles represent individual measurements from three repeats and bigger circles represent the average of these measurements. P = 0.926 (paired t -test)

Fig 6 .

 6 Fig 6. Cofilin displaces fascin in neuronal cells. Fascin-excluded cofilactin region at the base of filopodia in rat hippocampal neurons shown at the top. Fluorescence intensities of the cofilin and fascin along the filopodia shown at the bottom adapted from (Hylton et al., 2021) .

Fig 1 .

 1 Fig 1. Représentation schématique des réseaux d'actine réticulés par les ABP. A) faisceaux réticulés par la fascine, allongés par des formines à ancrage lipidique B) désassemblage des faisceaux par la cofiline. Imposition de contraintes aux filaments et aux formins, avec réticulation par fascin et ancrage lipidique respectivement. Ces contraintes affectent l'activité des formines ABP et de la cofiline. Remarque: il s'agit d'esquisses simplifiées d'un réseau.

  Pour les deux crosslinkers, nous observons que la vitesse de croissance des domaines de cofiline est diminuée par rapport à celle observée sur les filaments individuels, d'un facteur 2. De façon inédite, nous rapportons ici que la cofiline déplace la fascine des faisceaux et induit leur détricotage en portion de filaments individuels, localement. De manière tout aussi intéressante, nous avons constaté que la 𝛼-actinine n'est pas déplacée des faisceaux par la croissance des domaines de cofiline. Ces différentes observations impliquent que les faisceaux sont désassemblés par la cofiline par des mécanismes qui dépendent du crosslinker.

  Dans l'ensemble, pour les faisceaux de 2 filaments, même si la nucléation d'un deuxième domaine de cofiline sur le filament voisin est fortement accélérée, au moins deux événements de fragmentation du filament par la cofiline doivent se produire pour que le faisceau soit entièrement brisé en deux segments. Ceci est suffisant pour offrir une certaine protection au faisceau par rapport aux filaments uniques. Si l'on extrapole pour des faisceaux de taille plus importante, c'est-à-dire de 10 à 20 filaments, comme dans les filopodes, cette "protection" augmente considérablement, principalement en raison du taux de nucléation des domaines de cofiline qui décroît rapidement avec la taille du faisceau.Nous nous sommes demandé si l'augmentation de l'hélicité des filaments lorsqu'un domaine de cofiline est nucléé sur un premier filament d'un faisceau de filaments pouvait induire une augmentation de l'hélicité locale du ou des filaments voisins. Nos résultats, obtenus par polarisation de fluorescence en molécule unique et par EM à coloration négative, soutiennent l'hypothèse d'une sur-torsion locale du faisceau par la cofiline. Avec nos études EM, nous avons observé que les plus petits faisceaux étaient tressés alors que des faisceaux plus gros étaient séparés en plus petits faisceaux (taille 2 à 4 filaments).

  studying the interactions of ABPs with actin filaments and bundles. Biochemical concentrations are well controlled with microfluidics as, by constantly flowing protein solutions from the inlets, protein concentrations in the region of interest can be maintained at the desired level in most cases (i.e. no global protein depletion) (see fig 3.2 A). In addition, many individual actin filaments (or actin bundles) can be monitored in parallel, to offer a good statistical sample size to quantify reaction rates. It is also very helpful to study the protein dynamics on filaments/bundles: filaments/bundles are anchored at single/multiple anchoring points and align with the flow. Hence the fluorescent image analysis is much easier as they appear straight due to reduced lateral filament fluctuations. Moreover, the viscous drag applied by the flow allows applying pulling forces, up to a few tens of piconewton, depending on the local flow velocity, filament length, and fluid viscosity

F-actin in real time, microfluidics presents several advantages for observing single actin filament dynamics and

  5.35 & fig 5.36 (bottom)). These observations, though purely qualitative, are in agreement with our hypothesis that filaments in the bundles get twisted by cofilin. Interestingly, we could observe that bigger bundles were not braided, but separated into smaller bundles of 2-4 filaments that are braided (fig5.37 A and B).

•

  Higgs, H. N., & Pollard, T. D. (2001). Regulation of Actin Filament Network Formation Through ARP2/3 Complex: Activation by a Diverse Array of Proteins. Annual Review of Biochemistry , 70 (1), 649-676. https://doi.org/10.1146/annurev.biochem.70.1.649 • Hill, M.,& Gunning, P. (1993). Beta and gamma actin mRNAs are differentially located within myoblasts. ://doi.org/10.1083/jcb.122.4.825 • Hinz, B., Celetta, G., Tomasek, J. J., Gabbiani, G., & Chaponnier, C. (2001). Alpha-Smooth Muscle Actin Expression Upregulates Fibroblast Contractile Activity. Molecular Biology of the Cell , 12 (9), 2730-2741. https://doi.org/10.1091/mbc.12.9.2730 • Hoock, T. C., Newcomb, P. M., & Herman, I. M. (1991). Beta actin and its mRNA are localized at the plasma membrane and the regions of moving cytoplasm during the cellular response to injury. Journal of Cell Biology , 112 (4), 653-664. https://doi.org/10.1083/jcb.112.4.653 • Horan, B. G., Zerze, G. H., Kim, Y. C., Vavylonis, D., & Mittal, J. (2018). Computational modeling highlights the role of the disordered Formin Homology 1 domain in profilin-actin transfer. ://doi.org/10.1002/1873-3468.13088 • Hotulainen, P., & Lappalainen, P. (2006). Stress fibers are generated by two distinct actin assembly mechanisms in motile cells. Journal of Cell Biology , 173 (3), 383-394. https://doi.org/10.1083/jcb.200511093 • Houdusse, A., & Titus, M. A. (2021). The many roles of myosins in filopodia, microvilli and stereocilia.

	Journal	of	Cell	Biology ,	122 (4),	825-832.
		FEBS	Letters ,	592 (11),	1804-1816.
	Current https://doi.org/10.1016/j.cub.2021.04.005	Biology ,		31 (10),	R586-R602.

httpshttps

This is an open access article published under a Creative Commons Non-Commercial No Derivative Works (CC-BY-NC-ND) Attribution License, which permits copying and redistribution of the article, and creation of adaptations, all for non-commercial purposes.Downloaded via BIU SANTE on October 14, 2021 at 12:09:52 (UTC).See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles.

ACKNOWLEDGEMENTS

I am utmost grateful to my wonderful supervisors Antoine Jegou and Guillaume Romet-Lemonne for giving me this opportunity. Thank you, Antoine, for your patience and

■ ACKNOWLEDGMENTS

We thank all members of the G.R.-L./A.J. laboratory for their help, especially Hugo Wioland for help in the fluorescence polarization analysis and Sandy Jouet for protein purifications. We acknowledge funding from the French ANR (Grants "MuscActin" and "Conformin" to G.R.-L.) and the European Research Council (Grant StG-679116 to A.J.).

Materials and methods

In this chapter, I will first detail the protocols and procedures to produce and purify the different proteins used in our reconstitution assays in section 3.1. This is followed by a description of the microfluidic setup and microscopic imaging along with the open chamber assay in section 3.2.

Next, I will describe the steps involved in reconstituting actin bundles for disassembly by cofilin in section 3.4. Finally, I will explain the different strategies involved in reconstituting formin generated, and fascin cross-linked actin bundles in section 3.3.

Proteins and buers

Proteins were purified by research engineers in the lab, Bérengère Guichard , Sandy Jouet, and Wendy Auchère .

• Alpha skeletal actin was purified from rabbit muscle acetone powder following the protocol by [START_REF] Spudich | The Regulation of Rabbit Skeletal Muscle Contraction[END_REF] as described in detail in [START_REF] Wioland | ADF/Cofilin Accelerates Actin Dynamics by Severing Filaments and Promoting Their Depolymerization at Both Ends[END_REF] [START_REF] Spudich | The Regulation of Rabbit Skeletal Muscle Contraction[END_REF][START_REF] Suzuki | Geometrical Constraints Greatly Hinder Formin mDia1 Activity[END_REF][START_REF] Wioland | ADF/Cofilin Accelerates Actin Dynamics by Severing Filaments and Promoting Their Depolymerization at Both Ends[END_REF] . Actin was labeled on surface lysines accessible when actin is polymerized, using alexa-488 or Alexa 594 succinimidyl esters. The standard actin labeling fraction was 10%, specified in the figure legend if different.

• Spectrin actin seeds were purified from human erythrocytes according to the protocol from Casella et al. 1986 and described in detail in [START_REF] Wioland | ADF/Cofilin Accelerates Actin Dynamics by Severing Filaments and Promoting Their Depolymerization at Both Ends[END_REF](Casella et al., 1986;[START_REF] Wioland | ADF/Cofilin Accelerates Actin Dynamics by Severing Filaments and Promoting Their Depolymerization at Both Ends[END_REF] • Human fascin-1 was purified with a GST tag at the N-terminal following the protocol by [START_REF] Vignjevic | Formation of filopodia-like bundles in vitro from a dendritic network[END_REF] [START_REF] Vignjevic | Formation of filopodia-like bundles in vitro from a dendritic network[END_REF] . Purified fascin was labeled on cysteine residues with alexa-568 maleimide (~ 1.8 labeled cysteines per fascin). Uniprot: Q16658.

• The purification of mouse cofilin-1, either unlabelled or fusion proteins with mCherry or eGFP at the N-terminal, was based on the protocol from Kremneva et al. and detailed in Wioland et al. 2017 (Uniprot: P18760) (Kremneva et al., 2014;[START_REF] Wioland | ADF/Cofilin Accelerates Actin Dynamics by Severing Filaments and Promoting Their Depolymerization at Both Ends[END_REF] .

Jahnavi C -doctoral thesis -2021

The direction of the polarization of the emitted light by the alexa dye is at 45° relative to the long axis of the filament [START_REF] Sase | Axial rotation of sliding actin filaments revealed by single-fluorophore imaging[END_REF] , so in our experiments a microfluidic chamber was placed diagonally on the stage. Emitted photons can be separated by a polarizing beamsplitter

PUBLISHED MANUSCRIPT

Methods; three figures showing the supplementary data of formin activity in bundles; one table summarizing the population sample sizes and statistical significance tests for the data presented in the main figures (PDF) Supplementary movie #1: Randomly spaced FH1anchored-to-glass formins elongate filaments in the presence of 0.2 μM 15% alexa488-labeled actin, 2 μM profilin and 100 nM fascin. As the filaments elongate they encounter and bundle with other filaments due to fascin crosslinking. Scale bar, 10 μm. Flow direction: right (AVI) Supplementary movie #2: Annotated sub-region of supplementary movie #1. Numbers (either '2' or '3') indicate the size of a bundle; 'up. detach.' (respectively 'down. detach.') indicates that the upstream (resp. downstream) filament detaches from the 'leading' (resp. 'trailing') formin of a 2-filament bundle (AVI) Supplementary movie #3: Randomly spaced FH1anchored-to-glass formins elongate filaments in the presence of 0.2 μM 15% alexa488-labeled actin and 2 μM profilin. Filaments may attach to randomly spaced NEM-myosins non-specifically adsorbed to the glass surface. Scale bar, 10 μm. Flow direction: right (AVI) Supplementary movie #4: FH1-anchored-to-lipid formins that have collected at the lipid/PEG brush boundary elongate filaments in the presence of 0.5 μM actin, 2 μM profilin and 100 nM fascin. Green: alexa488labeled actin; Red: alexa568-labeled fascin. Scale bar, 10 μm. Flow direction: right (AVI)

■ AUTHOR INFORMATION

Corresponding Authors *E-mail: antoine.jegou@ijm.fr. *E-mail: romet@ijm.fr.

ORCID

Guillaume Romet-Lemonne: 0000-0002-4938-1065 Antoine Jeǵou: 0000-0003-0356-3127

Notes

The authors declare no competing financial interest.

Jahnavi C -doctoral thesis -2021 labeling of actin and/or fascin had a strong impact on cofilin activity. These observations are presented in more detail in the following paragraphs.

A) Eect of actin labeling on cofilin activity

First, we investigated the impact of actin labeling on cofilin activity, by using either 5% Alexa-488-actin or unlabelled actin in the assay. We observed that, in TIRF, cofilin recruitment on actin filament bundles was stronger for 5% labeled actin than with unlabeled actin (Fig 5.3).

The difference between those two conditions could be reduced by diminishing the amount of light to observe actin (either by reducing the laser power or with a lower acquisition frame rate) (Fig 5 .3).

B) Eect of fascin labeling on cofilin domain nucleation

We next focus on the impact of fascin labeling. Using unlabeled actin, we could still notice that the network disassembled more where we imaged fascin than away from it (Fig 5.4 (A)). This observed difference of cofilin-induced network disassembly between illuminating or not illuminated regions of the network was decreased by decreasing the fascin labeling from 100% to 5% (Fig 5.4 (B)).

Impact of fascin on cofilin domain severing on single filaments:

Finally, can the presence of fascin have an effect on cofilin domain severing, on single filaments? For this, we looked at the domain severing on single filaments in the presence and 114 Similar results were obtained at higher fascin concentrations (0.5 µM and 1 µM). We thus concluded that fascin, up to 1 µM, has no effect on cofilin domain nucleation on single filaments. This is to be expected because fascin binds to the single filaments with a low affinity, so the presence of fascin in solution should not be affecting the cofilin ability to bind on single filaments.

Impact of fascin on cofilin domain growth on single filaments: Further, we asked if domain growth on single filaments could be affected due to the presence of fascin. Domains nucleated on single filaments, in the presence and absence of fascin, were observed for the domain growth rates.We found that the cofilin domain growth rates were not

Summary:

• We noticed that the fascin-induced bundles were severed slower compared to the single filaments by observing the fraction of unsevered segments (5 µm length).

Cofilin domain nucleation on bundles

To investigate how cofilin activity is affected by fascin bundling, we looked at the cofilin domain nucleation on two-filament bundles and single filaments. Single filaments were distinguished from two-filament bundles with the help of the seed positions and the intensity of actin fluorescence (see section 3.4.3). We analyzed the cofilin domain nucleation on single filaments and 2-filament bundles as mentioned in 3.4.3. We measured that cofilin domain nucleation on bundles is around 6-fold slower than on single filaments (see fig 5.11). We verified the nucleation events were homogeneously distributed over the length of the bundles (see fig 5.11 C) Impact of bundle size on cofilin domain nucleation:

Next, we asked if the cofilin domain nucleation is affected by bundle size. To generate bundles of different sizes in a more controlled way, we reconstituted fascin-induced bundles of filaments emerging from glass beads (see section 3.4.2 b). The elongated filaments on the beads were aged and bundled using 0.1 µM unlabeled fascin and 0.13 µM unlabeled actin. Depending on the seeds concentration on the individual beads, bundles of different sizes could be observed (see fig 3.10 for size distribution). We observed that, cofilin domain nucleation rate strongly decreased with bundle size, by up to more than a 100-fold (Fig 5.13). Very strikingly, the reduction of cofilin domain nucleation rate is already very strong between 2-and 3-filament bundles, while the accessibility of filaments for cofilin in those two populations is not very different. This seems to indicate that as filaments get more and more crosslinked between each other by fascin, there would be a change of filament conformation, unfavorable to cofilin binding.

• We found that the ability of cofilin to nucleate domains on two-filament bundles was six-fold slower than on single filaments, at 200 nM fascin.

• We also studied the impact of bundle size and fascin concentration on cofilin activity, showing that the cofilin nucleation rate reduction can be very strong for tightly or densely cross-linked filaments.

Cofilin domain growth on bundles

Next, we investigated whether the presence of fascin affects the growth of cofilin domains on bundles (Fig 5 .14 A). We measured the individual growth rate of the cofilin domain on fascin cross-linked bundles.

The individual domain growths appear symmetrical on the kymograph towards both ends on both single filaments and fascin cross-linked bundles (Fig. 5.14 B). We found that, on average, the cofilin domain growth rate on fascin-induced 2-filament bundles is slightly reduced, by 1. ' domain severing ' event = one cofilin domain out of the two is fully severed (i.e. on both sides of the cofilin domain) and is flowed away. This type of event is seen in 60% of the cofilin domains analyzed ( n = 49 out of 83). Please note that when a domain fragmentation occurs towards the pointed end side first, the cofilactin segment is probably highly curved by the flow. We never observed highly curved cofilin domains (which would appear as a downstream shift of the cofilin fluorescent signal), probably because curvature strongly enhances the severing rate at the other remaining boundary, as previously reported (Wioland et al., 2019b) . The whole cofiliactin segment fully detaches from the bundle without us being able to image the intermediate step of the process.

2. ' total bundle fragmentation ' event = the bundle is fully fragmented at the location where the cofilin intensity is being measured, i.e. both filaments have been severed.

We recorded the occurrence of these two types of individual events and plotted the survival fraction of unsevered cofilin domains against time. Depending on image acquisition rate and the rate of those events, we may observe a decrease in fluorescence intensity in two steps ('domain severing' followed by 'total bundle fragmentation') or not (only the 'total bundle fragmentation' is observed, directly)In cases where the bundle fragmented without detecting a 'domain severing' event, the time at which this bundle fragmentation occurred was counted both as an event of 'domain severing' and 'total bundle fragmentation' event. Obviously, the 'total bundle fragmentation' survival curve decays slower than the survival curve of cofilin domain severing on single filaments. In this model, the 'one cofilin domain' state can be left following two possible paths, at a rate which is the sum of the two independent rates of the two paths, (k sev + k' nuc ) shown in fig 5.23. We have measured the rate at which one cofilin domain can sever before a second cofilin domain is nucleated, k sev , by performing a dedicated experiment where cofilin activity is measured in the 133 In the first path, the nucleated cofilin domain severs one of the filaments in the bundle, at rate k sev . The cofilactin segment leaves the bundle. However the bundle is not fragmented because the second filament is still intact. A second cofilin domain can subsequently nucleate on the bare, single-filament region within the bundle. (Right): In the second path, a second cofilin domain is nucleated on the other filament in a region adjacent to the first cofilin domain, at a rate k' nuc . As the two coflin domains overlap, their sequential severing leads to the fragmentation of the bundle. We assume that the severing rate is the same for each domain, and the first severing event occurs with rate 2*k sev because there are 2 domains available for severing. B) Time evolution of the survival fraction of unsevered cofilin domains (domain severing and total bundle fragmentation) on 2-filament bundles and on the single filaments. N =88 and 31 cofilin domains for single filaments and fascin cross-linked bundles, respectively. Time t =0 corresponds to the appearance of the cofilin domain.

Jahnavi C -doctoral thesis -2021 absence of actin, but the filaments' barbed ends were previously capped by exposing them to 1 nM CP along with fascin during the 15 minutes aging phase.

In this dedicated experiment, we could detect cofilin domain severing events occurring at the pointed end (PE) side by observing the depolymerization of the new barbed end created upon filament severing, thanks to the absence of actin (see fig 5.24). We measured the corresponding rate, k sev + k' nuc = 6.5•10 -3 s -1 . We also noted that only 28% ( n = 7 out of 25 events) of the cofilin domains severed before a second cofilin domain was nucleated, meaning, since reactions following path #1 occurs with a probability k sev /(k sev + k' nuc ), that k sev = 1.8•10 -3 and therefore k' nuc = 4.7•10 -3 s -1 . First, we also note that the 'apparent' first cofilin domain severing rate on a 2-filament bundle is close to the severing rate of a single coflin domain on a single filament (at the PE side) 2.1•10 -3 s -1 , determined for single filaments in the same chamber. Second, the derived k' nuc is an effective rate, expressed in s -1 (i.e. not normalized by the number of available actin subunits).

We have previously shown that, for twist-constrained filaments, cofilin-induced change of helicity creates some torsional stress, accelerating filament severing up to 100-fold (Wioland et Jahnavi C -doctoral thesis -2021 To quantify the actual nucleation rate of the second cofilin domain, we computed the survival fractions for 'domain severing' and 'total bundle fragmentation' based on our model in figure 5. [START_REF] Mizuno | Rotational movement of the formin mDia1 along the double helical strand of an actin filament[END_REF], where we took into account the number of available sites for nucleation on the second filament as the first domain grows. As shown on figure 5.26 left, this simple model seems to be able to reproduce our observation satisfactorily. The rate k' nuc was the only free parameter when fitting the two curves simultaneously (fig 5.23). Interestingly, this fit leads to a second domain nucleation rate 10-fold higher than the first cofilin domain nucleation rate on two filament bundles (see fig 5.26 right). Strikingly, this second cofilin domain nucleation rate is even faster than the nucleation rate measured on single filaments. This result is consistent with the view that the cofilin-induced change in helicity of the first filament propagates to the adjacent, bare region of the other filament, thereby favoring the binding of cofilin.

Summary:

• We identified the signature of the cofilin domain severing the bundles by looking at the cofilin domain fluorescence intensity. We used the simpler case of fascin bundles with two filaments for our study.

• Based on the the analysis the fluorescence intensity of cofilin domains on the bundle, we showed that two overlapping cofilin domains are frequently observed, and that cofilin disassembling/fragmenting a bundle involves two steps: 1) Domain severing 2) total bundle fragmentation.

• We observed that >3-filament bundles were severed more slowly compared to two filament bundles.

• We saw that, once a first domain has been nucleated on a 2-filament bundle, a second domain is 'rapidly' nucleated on the 2nd filament in the region facing the first cofilin domain, at a rate higher than the one observed on individual filaments.

Jahnavi C -doctoral thesis -2021 Though, these observations cannot be considered as a conclusive proof of bundle twisting upon cofilin binding: 2-filament bundles are anchored twice to the glass by the seeds. There always exists some portion of the filaments, located upstream the bundled segment, where the two filaments are not bundled and which are more prone to cofilin targeting and severing. If one filament is severed in these regions, the bundle is only anchored by one anchoring point to the surface. Then, the observed bundle twisting could result from a cofilin domain twisting a single filament segment upstream a bundled region, and not inside it.

Summary:

• We carried out studies with two different techniques: single-molecule fluorescence polarisation and negative staining EM, which both seem to confirm that the bundles over twist upon cofilin exposure.

Impact of 𝛼-actinin on cofilin domain severing on single filaments

Next, we looked at how cofilin domains sever single filaments in the presence or absence of 𝛼-actinin. For each experiment, we systematically observed domain severing being slower on single filaments in the presence of 𝛼-actinin compared to in the absence of 𝛼-actinin. In average, the rate at which the single filaments were severed in the presence of 0.2 µM 𝛼-actinin was 2.5 -fold slower than in the absence of 𝛼-actinin, as shown in fig 5.42 Summary:

• We confirm that 𝛼-actinin binds to the single filaments in our assays as previously reported [START_REF] Hampton | Novel Structures for α-Actinin:F-Actin Interactions and their Implications for Actin-Membrane Attachment and Tension Sensing in the Cytoskeleton[END_REF][START_REF] Winkelman | Fascin-and α-Actinin-Bundled Networks Contain Intrinsic Structural Features that Drive Protein Sorting[END_REF] , for protein concentrations where fascin binding is not detected by fluorescence microscopy.

Jahnavi C -doctoral thesis -2021

• We observed that the presence of 𝛼-actinin affects the cofilin binding, domain growth rates, and domain severing on single filaments. These observations on single filaments are in contrast to what we report for fascin.

• The domain nucleation rates were 2.5-fold slower, domain growth rates were 2.2-fold slower, and domain severing rates were 2.5-fold slower on single filaments in the presence of 200 nM 𝛼-actinin compared to single filaments in the absence of 𝛼-actinin.

Impact of 𝛼-actinin on cofilin activity on two-filament bundles

Global severing of 𝛼-actinin bundles

We asked how the global severing of 𝛼-actinin bundles compares to that of single filaments.

Here, an important difference with the assays performed with fascin is that 𝛼-actinin affinity allows significant binding to single filaments. We roughly quantified the rate at which 5-µm-segments of 𝛼-actinin bundles were severed, compared to the single filaments, by fitting the survival fractions of unsevered 5µm-long filament segments by a simple exponential decay function. We observed that the bundles were severed 3. • In conclusion, we find that the 𝛼-actinin presence has no additional impact on the nucleation of cofilin domains on two-filament bundles compared to 𝛼-actinin-bound single filaments.

Cofilin domain growth

The interfilament spacing, and affinity for single filaments was different for 𝛼-actinin compared to fascin (see section 1.3.3). 𝛼-actinin can bind to the sides of individual actin filaments even when not cross-linked. How could this affect the activity of cofilin domain growth? The growing domain could encounter 𝛼-actinin molecules on filaments rather than at regular intervals of half pitch of actin filament (36 nm).

We wondered whether the cofilin domain can displace 𝛼-actinin from cross-linked bundles (on single filaments as well). To carry out this we elongated seeds with alexa-488 labeled actin.

Next, the filaments were aged and bundled with alexa-568 labeled 𝛼-actinin and 0.13 µM unlabeled actin. Finally the bundles were exposed to 0.2 µM eGFP-cofilin, 0.2 µM alexa-568 labeled 𝛼-actinin, and 0.13 µM unlabeled actin. We did not observe any displacement of the fluorescent 𝛼-actinin from bundles unlike what we observed for fascin (Fig 5.45). These surprising but preliminary observations will need to be reproduced to be further confirmed.

Besides, bundles eventually get fully fragmented (see next section), which is difficult to understand if alpha-actinin molecules keep on crosslinking severed segments of filaments together.

162 Jahnavi C -doctoral thesis -2021 Next, to quantify the domain growth rates, we measured the growth rate of each domain towards both pointed and barbed ends following the spatial expansion of cofilin fluorescence of domains over time in kymographs. (See section 3.4.3 analysis similar to the method mentioned with fascin bundles). We found that the cofilin domain growth rates were similar on single filaments and bundles, both exposed to 𝛼-actinin, even though the distribution of rates seems larger for bundles (Fig 5.46).

Summary:

• We quantified the cofilin domain growth rates on 𝛼-actinin two-filament bundles. We noticed that the rate of domain growth is two-fold slower on bundles compared to single filaments devoid of any 𝛼-actinin bound to their side.

• Preliminary observations indicate that, in contrast to fascin, 𝛼-actinin is not displaced by cofilin domain growth.

Cofilin domain severing

So far, we have observed that different cross-linkers affect the ability of cofilin to nucleate domains and grow the domains differently. Next, we observed how cofilin domain severing of 𝛼-actinin cross-linked bundles. We followed the fluorescence intensity of mCherry-cofilin domains on alexa-488 labeled actin filaments cross-linked by unlabeled 𝛼-actinin. (see section 5.2.5 for more details about following the fluorescence intensity of domains). Similarly to what we observed in the case of fascin bundles, we report on 𝛼-actinin induced bundles, cofilin intensities compatible with two overlapping cofilin domains. As shown in figure 5.47.A we also recorded a drop in cofilin intensities, referred to as 'cofilin domain severing', which we attributed to the departure of one of the two cofilin domains.

We observed that the rates of both the domain severing and total bundle fragmentation were slower compared to the rate of cofilin domain severing on single filaments (Fig 5 .47 B).

Using the model proposed in section 5.

Summary:

• We observed the cofilin domain severing on two filament bundles of 𝛼-actinin by looking at the cofilin domain intensities similar to fascin bundles.

• We saw that two cofilin domains nucleated closer to each other in 𝛼-actinin bundles.

• We could fit our experimental data with the model proposed in section 5.2.5 to derive (k' nuc ) second cofilin domain nucleation rate on bundles and saw that this rate was faster compared to the domain nucleation rates on single filaments and first domain nucleation on bundles. • Nishida, E., Maekawa, S., & Sakai, H. (1984). Cofilin, a protein in porcine brain that binds to actin filaments and inhibits their interactions with myosin and tropomyosin.

DISCUSSION

Comment la cofiline désassemble les filaments en faisceaux

La désassemblage des filaments d'actine par la cofiline a été largement étudié depuis 20 ans.

Cependant, ces études n'ont été faites que sur des filaments individuels et isolés les uns des autres. Dans les cellules, l'actine s'assemble en réseaux et l'impact de l'architecture du réseau sur son désassemblage n'est pas bien compris.

La cofiline en se liant aux côtés des filaments d'actine, nucléée et allonge des domaines. Ces domaines peuvent induire la fragmentation des filaments d'actine, la cassure ayant lieu aux bords des domaines. Jusqu'à présent, une seule étude s'est penchée sur la question de savoir comment la présence de la fascine affecte l'activité de la cofiline : grâce à des approches de reconstitution in vitro, l'étude a montré que la cofiline avait une activité globale de liaison réduite aux filaments en faisceaux, mais que le désassemblage de l'actine était accéléré par rapport aux filaments individuels [START_REF] Breitsprecher | Cofilin cooperates with fascin to disassemble filopodial actin filaments[END_REF]. Une autre étude montre de manière intéressante que des filaments intermédiaires uniquement par la seule présence d'un 'crowding agent' qui induit des forces de déplétion en volume résistent à l'activité de fragmentation de la cofiline (Michelot et al., 2007).Ces deux études montrent des résultats qui ne sont pas faciles à réconcilier. Ceci nous a incité à faire des expériences pour étudier plus en profondeur le désassemblage des filaments en faisceaux par la cofiline et mieux déchiffrer les détails moléculaires sous-jacents.