Après trois ans de thèse le moment est venu de remercier toutes les personnes qui ont contribué à l'aboutissement de ce travail. J'ai bien conscience que cette thèse n'aurait pas été possible sans la participation, de près ou de loin, d'un très grand nombre d'entre vous. Je voudrais donc d'abord TOUS vous remercier pour votre contribution, votre aide, vos conseils, votre bonne humeur, votre efficacité qui ont rendu ces trois années plus légères et agréables et qui font de ce labo un lieu extrêmement convivial et motivant.

Je tiens tout d'abord à te remercier Olivier, pour m'avoir donné l'opportunité de faire, de construire, d'élaborer, et de penser ma thèse, merci pour la confiance et la liberté que tu m'as accordé. Il y a trois ans je commençais cette thèse, heureuse de t'avoir comme directeur : éternel optimiste, bienveillant, enthousiaste, (c)réactif, patient et passionné. Aujourd'hui je la termine, chanceuse d'avoir travaillé et échangé avec toi. Merci pour tes conseils et ton écoute, merci pour ta disponibilité (souvent mise à rude épreuve). Je remercie également Yvon, qui malgré une position parfois ambiguë (officieuse ou officielle), a également contribué à ce travail, m'a conseillé et guidé, et a été présent lorsque je me sentais un peu seule.

Je remercie ensuite les membres de mon comité de thèse, Emmanuelle Bayer et Stéphane Vincent, pour leurs bons conseils et leurs implications lors de ces réunions. Je remercie aussi les collaborateurs des différents projets, Satoru Tsugawa pour les analyses microtubules, Christophe Godin pour ta détermination dans l'élaboration du modèle, Virgil Viasnoff et Timothy Saunders, pour leurs retours sur le projet « proto », Antoine Chevallier pour avoir initié ce projet. Je remercie Mehdi, Marie-Cécile et Yvon de m'avoir donné l'opportunité de participer à leur super projet iDePP.

Je remercie aussi tous les membres (anciens et présents) de l'équipe MechanoDevo, pour leur aide, leur écoute et leurs conseils, mais aussi pour la joyeuse atmosphère qui règne dans cette équipe. Un énorme merci à Thomas, pour tout ce que tu m'as apporté et appris, avant et pendant la thèse. Merci de m'avoir montré les côtés positifs d'un tel projet, mais aussi de m'avoir appris à gérer le négatif. Merci pour ta confiance, patience, bonne humeur : merci pour ton humanité.

Je remercie également les membres de l'équipe SiCE, qui ont su m'adopter et m'apporter leur aide et leurs connaissances au moment où j'en avais le plus besoin. Un merci tout particulier à Vincent et Frédérique, sur qui j'ai pu compter. Merci pour votre disponibilité,

Un immense merci à la « team » du GN1 : Alice, Corentin, Julie, Matthieu, Florian et Anaïs qui ont ajouté une bonne dose d'humour et de rigolade à ma thèse. Merci de votre soutien dans les moments difficiles, mais aussi d'avoir partagé avec moi les moments de joie. Un merci spécial à Alexis, à qui j'ai pu confier mes doutes et mes craintes professionnels et personnels au cours de ces deux dernières années. Merci pour ton écoute, tes conseils, ton regard scientifique sur mon projet, ton amitié. J'ai toute confiance en ton avenir scientifique et je viendrai encore te demander ton avis. Je remercie également mon amie Amélie, qui a su être présente malgré la distance et qui a suivi toutes mes péripéties.

Enfin, je remercie mes parents, qui m'ont permis de suivre cette voie et qui m'ont toujours fait confiance. Merci de m'avoir soutenu, et de m'avoir toujours encouragé. Merci à Florian, pour ton soutien, ton écoute et ton optimisme. Merci d'être partant et motivé pour ma prochaine aventure : le postdoc ! Equipe MechanoDEVO (2021, Lyon)

Preamble

This manuscript is composed of three main parts: (i) general introduction, (ii) results and discussion, (iii) general discussion and perspectives.

The introduction contains two items from two review articles I contributed to, namely Table 1 (published in our team review in Current Biology, 2021) and a paragraph on the role of PI (4,5)P2 patterns during plant development (written with Yvon Jaillais and published in Current Opinion in Plant Biology, 2020).

The result part is subdivided in three sections, corresponding to the three main projects that I have conducted during my PhD. The two first projects, entitled "Contribution of PI (4,5)P2 phosphoinositide in SAM activities" and " Cortical tension overrides geometrical cues to orient microtubules in confined protoplasts", have led to scientific publications (as 2 nd and co-first author, respectively) that are included in this thesis manuscript. Each publication is preceded by one or two pages, which recapitulates the scientific question, the main results and my contribution.

The context of the last project, focusing on the role of the plasma membrane composition during cell wall synthesis, is rapidly introduced, and preliminary results are presented. The result part also includes discussions related to each project and addressing technical issues, new hypothesis and perspectives. This manuscript ends with a short general discussion on the role of mechanical forces in plant development, with new avenues on how to study that question in the future. In developmental biology, the shape is the external form, contours, or outline of a cell, tissue, organ, or organism. It is thus a purely geometrical entity. The diversity of shapes that exists for a given organ between the different plant species or within the same species has long retained the interest of biologists. For instance, the shape of flowers between two species can considerably vary, (e.g., between Petunia and Arabidopsis thaliana), but also within two close relative species (e.g., Brassica napus and Arabidopsis thaliana, both belonging to the Brassicaceae family) [START_REF] Moyroud | The Evolution of Diverse Floral Morphologies[END_REF] (Figure 1A). This diversity is not restricted to reproductive organs, and is even larger for vegetative organs, since their shapes highly depend on the environment [START_REF] Fritz | Mechanisms Underlying the Environmentally Induced Plasticity of Leaf Morphology[END_REF].

List of abbreviations

In living organisms, the shape of an organ is often tightly correlated with its function. For instance, the stigma increases the adhesive surface of the tip of the carpel, thereby increasing the probability to capture pollen grains. In the end, the shape of an organ is a result of a balance between the physiological function of this organ and environmental inputs, which largely contribute to the plasticity of the organ phenotype. For instance, the final surface area of leaves, is the result of trade-off between many parameters, including the maximization of (photonic) energy uptake and the reduction of water loss through transpiration. Several studies have investigated how the plant deals with these environmental inputs and convert them into adapted developmental responses, and thus give rise to variable phenotypes [START_REF] Fritz | Mechanisms Underlying the Environmentally Induced Plasticity of Leaf Morphology[END_REF]. In some cases, the final shape of the organ is the result of a long process of selection and of a coevolutive mechanism between two species. A good example of this, is the co-evolution between flower shape and pollinators. Indeed, morphological floral complexity correlates with a restricted number of visitors on the flower, thus filtering pollinators. This strategy has contributed to the specialization of pollinators, which in turn, improve plant fitness, notably by contributing to the targeted transport of pollen within the species [START_REF] Krishna | Morphological Complexity as a Floral Signal: From Perception by Insect Pollinators to Co-Evolutionary Implications[END_REF]. Overall, these data indicate that the shape of an organ undergoes a strong selective pressure (biotic or abiotic). Note that this selective pressure does not only apply to the final shape of the organ: it is also active during the whole development of the structure. It can be illustrated with the sepals in Arabidopsis thaliana: because they protect reproductive organs as they form in the flower, the sepal shape and size are tightly regulated to maintain a closed state (floral bud) thus matching the size of the flower as it grows.

Characterization of a shape requires morphometry and thus the use of quantitative parameters, i.e. shape descriptors (Figure 1B,C and D). Some of these descriptors can be quantified with absolute values (e.g. length of a stem) or relative values (e.g. angle of branch relative to the stem) (Figure 1B). These parameters can be normalized with a reference (e.g. angle of a stem relative to gravity vector, length of stem relative to the average stem length in a field).

Exceptions to this rule include the growing pollen tube, the abscission mechanism for fruits and leaves, and the invasive growth of fiber cells in wood. In contrast to animals, where cell division usually correlates with growth, in plants, this correlation is not obvious, mainly because most plant cells elongate through endoreduplication, i.e. without dividing. Last, while in animal programmed cell death is largely involved in embryo development, in plants, it is rather limited to specific cell types or certain differentiating tissues, and its contribution during the initial steps of organ shaping seems secondary. Therefore, plant cell growth can be recapitulated by monitoring the expansion of cells (or clones of cells), thus largely facilitating the analysis of the cellular bases of morphogenesis, when compared to animals.

Growth can be measured with three main parameters: growth rate, growth anisotropy and growth direction (Baskin, 2005;[START_REF] Coen | The genetics of geometry[END_REF]) (Figure 2A). Growth rate is the ratio between the volume increase between two time points (final volume minus initial volume), over initial volume. Growth rate can be measured in area and length too. When the expansion is at the same rate in all directions, i.e. growth rates are equal in all directions, growth is isotropic, whereas when the growth rate differs depending on direction, i.e. growth occurs preferentially in one direction, growth is anisotropic. The last parameter, growth direction, describes the angle of maximal growth rate [START_REF] Trinh | How Mechanical Forces Shape Plant Organs[END_REF].

Experimentally, growth rate can be estimated by tracking the positions of inks dots or natural landmarks present on a cell, tissue or organ over time [START_REF] Erickson | Modeling of Plant Growth[END_REF][START_REF] Gould | A kinematic analysis of tepal growth in Lilium longiflorum[END_REF]. This relates to kinematic analyses [START_REF] Bertels | leafkin -An R package for automated kinematic data analysis of monocot leaves[END_REF]. To integrate direction, growth rates are represented by vectors, forming velocity fields. The main limitation of these velocity fields is that they refer to a referential point, rather than regions, and considering the position where the referential point is taken, the field can look different. For these reasons, growth is more generally described in terms of local growth characterizing small regions [START_REF] Coen | The genetics of geometry[END_REF].

The growth of each regions can be described with the same three main parameters mentioned before: growth rate, growth anisotropy and growth direction. However, the number of parameters also depend on the dimensionality of the structure. Thus, for a 2D structure, only three parameters are required, while for a 3D structure, six parameters are needed to describe the growth (i.e., one parameter for growth rate in volume, two for the anisotropy, and three for direction). All these parameters can be grouped in a single measure, referred as "growth tensor" [START_REF] Coen | The genetics of geometry[END_REF]. Once known, all these parameters can be computed, allowing morphogenetic modeling.

Shape and growth are under genetic regulation

During the past few years, significant progress has been made regarding the establishment of gene expression patterns during development. However, how gene activity contributes to organ shaping is less understood. Investigating this question relies on the analysis of gene expression patterns in growing organs on the one hand, and on the quantification of growth in mutants or lines with altered genetic features.

The quantitative parameters to describe both shape and growth are not always easy to measure, and even more so, to correlate with gene expression. Nonetheless, several studies have addressed this question in plant leaves. Plant leaves represent an interesting system, since all leaves start to grow from almost similar primordia to reach a wide diversity of leaf shapes. Among this diversity, some leaves display a really simple shape (e.g., A. thaliana), while others exhibit complex geometry (e.g., C. hirsuta) [START_REF] Kierzkowski | A Growth-Based Framework for Leaf Shape Development and Diversity[END_REF] (Figure 2B). The establishment of complex shape has been correlated to the expression of homeobox genes, including KNOX (Knotted1-like homeobox) and RCO (REDUCED COMPLEXITY), which have been identified as important molecular regulator of leaf complexity [START_REF] Bharathan | Homologies in Leaf Form Inferred from KNOXI Gene Expression During Development[END_REF][START_REF] Hareven | The Making of a Compound Leaf: Genetic Manipulation of Leaf Architecture in Tomato[END_REF][START_REF] Hay | KNOX genes: versatile regulators of plant development and diversity[END_REF] (Figure 1B andC). Using multidisciplinary approaches (e.g., modelling, microscopy), Kierzkowski and collaborators identified differences in growth pattern, which could explain the differences between the complex geometry of C.hirsuta leaves and the simple shape of A. thaliana leaves. They found that the establishment of the complex shape of C.hirsuta leaves requires the expression of SHOOT MERISTEMLESS (STM) gene, belonging to the KNOX gene family, and is associated with a prolonged growth throughout the leaf primordium , allowing the formation of protrusions. In contrast, leaf shape of A. thaliana is correlated with local growth inhibition, mediated by the expression of RCO gene, which contribute to accentuate growth differences between the inhibited zones and the margin (Figure 2C) [START_REF] Kierzkowski | A Growth-Based Framework for Leaf Shape Development and Diversity[END_REF]. Besides these genes, many other components are involved in leaf development, such as miRNA, transcription factors, hormones for instance [START_REF] Ali | Molecular and Hormonal Regulation of Leaf Morphogenesis in Arabidopsis[END_REF]. Notably, the lamina growth and the final shape of margins are controlled by a complex molecular network. In Arabidopsis thaliana, the leaves constituting the rosette display less serration compared to leaves produced later. Leaf serration formation is controlled by several factors, including miRNAs, and gene expression [START_REF] Kong | IBR5 Regulates Leaf Serrations Development via Modulation of the Expression of PIN1[END_REF][START_REF] Nikovics | The Balance between the MIR164A and CUC2 Genes Controls Leaf Margin Serration in Arabidopsis[END_REF]. For instance, the expression of CUC (CUP-SHAPED COTYLEDON) genes is required for the separation of the two cotyledons, and plants mutated on these genes exhibit a cup-shaped fused cotyledon [START_REF] Aida | Genes involved in organ separation in Arabidopsis: an analysis of the cup-shaped cotyledon mutant[END_REF]. Thus, these examples illustrate that (complex) gene expression correlates with growth patterning, and thus final shapes. This also raises the question of the molecular coordination between the multitude of players involved.

Concentration gradients of signaling molecules contribute to growth patterning and development in animal. These signaling molecules, which can be distributed along a gradient and which provide positional information, have been called "morphogen" [START_REF] Wolpert | Positional information and the spatial pattern of cellular differentiation[END_REF].To be classified as a morphogen, the molecule has to function in concentration-dependent manner, and modifying this concentration gradient must affect the development of the targeted cells [START_REF] Bhalerao | The case for morphogens in plants[END_REF]. In plants, the identification of signaling molecules that could influence plant patterning through the formation of morphogen-like concentrations is still debated. To date, the most documented candidates to represent plant like morphogens are the phytohormones. As animal morphogens, these signaling molecules contribute to regulate plant cell responses in a dose-dependent manner. Among the phytohormones, auxin is probably the most promising plant equivalent of an animal morphogen [START_REF] Bhalerao | The case for morphogens in plants[END_REF]. Indeed, differential auxin concentrations along a gradient have been involved in several developmental processes.

For instance, different auxin concentrations have been measured in developing xylem, each concentration corresponding to a distinct zone of the developing vessel, displaying different stage of maturation [START_REF] Uggla | Auxin as a positional signal in pattern formation in plants[END_REF]. In addition, local application of auxin during vascular tissues differentiation results in different developmental responses according to the distance from the site of the application, highlighting the importance of auxin gradients during xylem formation [START_REF] Warren Wilson | Effects of auxin on the spatial distribution of cell division and xylogenesis in lettuce pith explants[END_REF]. Altogether, these results suggest that auxin may function as a morphogen, controlling the division, expansion and secondary wall formation in xylem developing cells. Differential auxin concentrations have also been measured in columella cells of the root apical meristem (RAM) in Arabidopsis. Modifications of auxin distribution in the RAM have been associated with changes in patterns and polarity [START_REF] Sabatini | An Auxin-Dependent Distal Organizer of Pattern and Polarity in the Arabidopsis Root[END_REF], also affecting the formation of lateral roots [START_REF] Casimiro | Auxin Transport Promotes Arabidopsis Lateral Root Initiation[END_REF]. The role of auxin has also been extensively investigated in the shoot apex, where auxin maxima control organ formation. This last point will be more detailed in the following part (part 1.2), which focus on the shoot apex.

Other phytohormones display a non-homogeneous distribution, and are directly involved in plant growth regulation. For instance, gibberellin (GA) are known as key regulators of plant growth, playing a crucial role in plant height control [START_REF] Wang | Gibberellin in plant height control: old player, new story[END_REF]. Modification of GA biosynthesis or of it signaling pathways directly impact plant height. The role of this phytohormone in many developmental processes, such as germination, leaf expansion, pollen maturation, stem elongation, has made it a prime target of crop breeding programs in the race to increase yields. Indeed, identification of genes involved in GA synthesis has allowed to genetically control plant size, producing semi dwarf plants, which are more resistant to environmental impacts, such as wind or rain for instance. This, has allowed the significant improvement of yields. Consistently, the overexpression of enzymes involved in the catabolism of GA also lead to a dwarf phenotype [START_REF] Gao | Gibberellin Metabolism and Signaling: Targets for Improving Agronomic Performance of Crops[END_REF] . Like auxin, GA affects plant growth through its accumulation concentration, leading to modification of plant stature, by affecting its growth. In the end, all hormones are impacting plant growth, and there is now accumulating evidence of multiple interplays between the genetic regulators of growth (e.g. transcription factors) and hormones. However, many other signaling molecules may play the role of morphogens. This is notably the case of miRNA, which the distribution in organs (like leaves) can form gradients and specify identities [START_REF] Skopelitis | Plant small RNAs as morphogens[END_REF]. Similarly, the likely most abundant signaling molecules in plants may be peptides, and there is growing evidence that they also play a key role in growth coordination [START_REF] Katsir | Peptide Signaling in Plant Development[END_REF].

In conclusion, shapes establishment is controlled by differential gene expression pattern or activity, which is coordinated by concentration gradients of signaling molecules (e.g., hormones, miRNA, peptides). This generates growth pattern, characterized by different growth rate, anisotropy and direction. The following part illustrate this point, by focusing on a welldescribed system: the shoot apical meristem.

Example: the shoot apical meristem of Arabidopsis thaliana

Description of the shoot apical meristem

Contrary to animals, plants continuously generate new organs during their entire lives. This activity is ensured by a specialized structure located at their growing tips: the shoot apical meristem (SAM) (Figure 3A). The SAM produces all aerial organs of the plant, but also determines their positions and their identities [START_REF] Clark | Organ Formation at the Vegetative Shoot Meristem[END_REF]. For these reasons, the SAM plays a key role during plant development. Characterization of the shoot apical meristem has been a gradual process dependent on the improvement of technological imaging methods. Organogenetic regions (corresponding to meristems) were formally identified for the first time in 1759 by Caspar Friedrich Wolff, but meristematic cells were only observed in 1858 by Karl Nageli. Since, a succession of histological analysis have highlighted the specific organization of the SAM. In 1868, Hanstein showed the organization in three distinct layers of the SAM, referred as L1 (epidermis), L2 (subepidermal layer) and L3 (Steeves and Sussex, 1989). Then, in 1924, Schmidt highlighted that these three layers can be characterized by different cell division patterns, with the L1 and L2 layers mostly dividing anticlinally (i.e., perpendicular to the surface of the meristem), and generating the epidermis and sub-epidermis of the SAM, while cells in the L3 layer dividing in all orientations, forming the internal tissues, including the vasculature [START_REF] Ha | Shoot Apical Meristem Form and Function[END_REF].

In 1950, markers of metabolic activity in the SAM revealed that the SAM is also characterized by different functional domains, on top of the organization in layers (Figure 3B). Although no physical boundaries separate these domains, the identification of differential cell division rate, and later on, differential gene expression patterns and signaling pathway have highlighted that each zones undergo distinct molecular and functional features [START_REF] Yadav | Gene expression map of the Arabidopsis shoot apical meristem stem cell niche[END_REF]. In the meristem center, at the top of the dome, the central zone (CZ) is characterized by a stem cell population, which is maintained by slowly dividing cells. These undifferentiated cells serve as a reservoir, allowing the meristem to constantly produce new organs. A tight control of the stem cell homeostasis is crucial to maintain a stable meristem size [START_REF] Shi | Patterning at the shoot apical meristem and phyllotaxis[END_REF]. Located under the CZ, the rib zone (RZ), provides cells which forms internal tissues. Between the RZ and CZ, a small group of cells is referred as the organizing center (OC). It plays a central role in the SAM, as it regulates the stem cell population located above it [START_REF] Aichinger | Plant Stem Cell Niches[END_REF][START_REF] Janocha | From signals to stem cells and back again[END_REF]. With cell divisions occurring in the CZ, some of the daughter cells enter the peripheral zone (PZ) surrounding the CZ. The PZ is constituted of cells which expand and divide rapidly, where young organs (called primordia) start to initiate. The different growth rates between the organ and PZ lead to tissues folding between these two zones and are called boundary regions. Interestingly, cells at the boundary grow slowly and exhibit a low division rate [START_REF] Breuil-Broyer | High-resolution boundary analysis during Arabidopsis thaliana flower development[END_REF][START_REF] Kwiatkowska | Growth and morphogenesis at the vegetative shoot apex of Anagallis arvensis L[END_REF].

The SAM changes its shape and identity during plant development. As mentioned above, the SAM first appear between the two pre-cotyledons, and only later on acquires its dome shape. During the vegetative phase of development, the above-ground organs can be divided into iterative modules, called phytomers. Each phytomer is composed of a leaf attached at a node, and an axillary meristem in the leaf axil. During this phase of vegetative growth, the SAM is referred as a vegetative meristem with an indeterminate activity, and forms stem tissues and leaves. Later, the SAM and each axillary meristem reach the floral transition stage, and turn into inflorescence meristems, bearing the reproductive organs (i.e., flowers) [START_REF] Carles | Shoot apical meristem maintenance: the art of a dynamic balance[END_REF][START_REF] Shi | Patterning at the shoot apical meristem and phyllotaxis[END_REF]. The dome of the inflorescence meristem is more pronounced than that of the vegetative meristem. Contrary to the vegetative meristem, the floral meristem (FM) displays a determined activity, producing a finite number of floral organs arranged in whorls.

Patterning at the shoot apical meristem: the case of phyllotaxy Organs are precisely positioned around the stem, highlighting a self-organized patterning in plants. This regular arrangement of above-ground organs is known as "phyllotaxis", whose term derives from ancient Greek, with phyllon for 'leaf' and taxis for 'arrangement' (Traas, 2013). Several phyllotactic patterns have been found in nature, such as the distichous (alternate), the decussate (opposite) and the spiral patterns (Figure 4A). The spiral phyllotactic pattern is the most widespread pattern, and it is also the one found in Arabidopsis [START_REF] Reinhardt | Phyllotaxisa new chapter in an old tale about beauty and magic numbers[END_REF]. The phyllotactic pattern is not determined, and sometimes it can shift from one to another during plant development (Traas, 2013). During the 1830's, mathematicians discovered that in the spiral phyllotactic pattern, the average divergence angles between two successive organs fits with the so-called 'golden-angle', (i.e., 137,5°) (Kuhlemeier, 2017) (Figure 4B and C). This famous angle is mathematically related to the Fibonacci sequence, and corresponds to 'the division of a circle by the value of the limit of the ratio between two consecutive numbers in the Fibonacci sequence' [START_REF] Shi | Patterning at the shoot apical meristem and phyllotaxis[END_REF].

Since then, numerous theoretical and experimental models have been proposed to understand how phyllotaxis is established and regulated, including purely geometrical models. Notably, in 1868, Hofmeister proposed a first model in which the new primordia appear periodically at the meristem periphery, in the first available space left by the existing primordia [START_REF] Hofmeister | Allgemeine morphologie der gewachse[END_REF]. Later, experimental approaches have suggested that phyllotaxis could be explained by the presence of an 'inhibitory field', created by chemical inhibitor, and secreted by the previously formed primordia, thus preventing the initiation of a new primordium in the same region (Figure 4D) (Shoute, 1913). Consistent with these observations, microsurgical experiments conducted on Lupinus albus meristems have shown that the position where the new primordium is initiated is influenced by the position of the closest previously formed primordia (Snow). Thus, the model proposed by Hofmeister was revised: the position of each new primordium would be determined by the first available space at a minimum distance from the meristem tip [START_REF] Snow | A theory of the regulation of phyllotaxis based on Lupinus albus[END_REF].

Behind the geometry, this equilibrium involves a signaling network, combining gene expression and specific plant hormone distributions, and allows the fascinating and highly regulated self-patterning observed in the SAM. In recent years, many studies have progressed on the understanding of the molecular mechanisms controlling SAM activities, and several detailed reviews have been done on this subject [START_REF] Clark | Organ Formation at the Vegetative Shoot Meristem[END_REF][START_REF] Ha | Shoot Apical Meristem Form and Function[END_REF][START_REF] Lopes | WUSCHEL in the shoot apical meristem: old player, new tricks[END_REF][START_REF] Shi | Patterning at the shoot apical meristem and phyllotaxis[END_REF][START_REF] Wang | Genetic Regulation of Shoot Architecture[END_REF]. I briefly illustrate this point, with the examples of stem cell maintenance and boundary definition at the SAM.

One of the key features of the SAM is the maintenance of a pool of undifferentiated cells in the CZ, which is regulated by a complex molecular network, controlling both the size and the position of the stem cell niche. One of the main actors of this regulation is the transcription factor gene WUSHEL (WUS). WUS is expressed in the OC of Arabidopsis, and it is required to maintain stem cell identity in the SAM [START_REF] Mayer | Role of WUSCHEL in Regulating Stem Cell Fate in the Arabidopsis Shoot Meristem[END_REF]. Ectopic expression of WUS is sufficient to induce shoot stem cells in other tissues [START_REF] Gallois | WUSCHEL induces shoot stem cell activity and developmental plasticity in the root meristem[END_REF]. The WUS protein is transported from the OC, toward the CZ, through plasmodesmata [START_REF] Daum | A mechanistic framework for noncell autonomous stem cell induction in Arabidopsis[END_REF], where it activates the expression of CLAVATA3 (CLV3) gene in stem cells. CLV3 belongs to the CLV3/EMBRYO SURROUNDING REGION (CLE) peptide family, and is involved in stem cell maintenance in the SAM [START_REF] Fletcher | Signaling of Cell Fate Decisions by CLAVATA3 in Arabidopsis Shoot Meristems[END_REF]. Once secreted, the CLV3 peptide is detected in the OC by the receptor-like kinase CLV1 to repress WUS activity [START_REF] Clark | The CLAVATA1Gene Encodes a Putative Receptor Kinase That Controls Shoot and Floral Meristem Size in Arabidopsis[END_REF][START_REF] Leyser | Characterisation of three shoot apical meristem mutants of Arabidopsis thaliana[END_REF]. The repression of WUS by CLV3 results in fewer stem cells being maintained. Consistently, both clv1 and clv3 mutants exhibit enlarged meristems, which has been correlated with a progressive accumulation of undifferentiated cells [START_REF] Clark | The CLAVATA1Gene Encodes a Putative Receptor Kinase That Controls Shoot and Floral Meristem Size in Arabidopsis[END_REF]. The double mutant clv1 clv3 displays identical phenotype to strong clv1 or clv3 single mutants, highlighting that these two genes are involved in the same pathway [START_REF] Running | Chapter 15 Confocal Microscopy of the Shoot Apex[END_REF]. Therefore, the duo WUS/CLV3 interacts in an autoregulatory negative feedback loop, contributing to the homeostasis of the stem cell niche in the SAM. New regulators have been identified, notably CLV co-receptors and HAM proteins, adding robustness to the CLV3-WUS loop [START_REF] Lopes | WUSCHEL in the shoot apical meristem: old player, new tricks[END_REF][START_REF] Zhou | HAIRY MERISTEM with WUSCHEL confines CLAVATA3 expression to the outer apical meristem layers[END_REF].

However, WUS expression is not sufficient to define meristematic cells. Meristems are usually defined by the expression of SHOOT MERISTEMLESS (STM) gene in Arabidopsis [START_REF] Long | A member of the KNOTTED class of homeodomain proteins encoded by the STM gene of Arabidopsis[END_REF]. The analysis of stm mutants have shown that these mutant fails to produce a SAM, indicating a role of STM protein in the maintenance of undifferentiated stem cells in the CZ [START_REF] Clark | Organ Formation at the Vegetative Shoot Meristem[END_REF]). Yet, STM expression is not homogeneously expressed in the SAM. In particular, several studies have reported that STM promoter is more active in boundary zones, i.e. where cells are slowing down their growth and division between the fast growing PZ and organ (Landrein et al., 2015a). In these regions, the STM proteins is required for organ separation, which is consistent with the phenotype of stm mutants, displaying fused cotyledons [START_REF] Long | A member of the KNOTTED class of homeodomain proteins encoded by the STM gene of Arabidopsis[END_REF]. The regulation of meristem cell differentiation by STM is not direct, and it occurs through the repression of the MYB-related gene ASYMETRIC LEAVES1 (AS1) [START_REF] Byrne | ASYMMETRIC LEAVES1 reveals knox gene redundancy in Arabidopsis[END_REF]. Moreover, other genes belonging the KNOX1 family, BREVIPEDICILLUS (BP), KNAT2 and KNAT6 genes acts redundantly with STM and participate to stem cell maintenance and organ separation [START_REF] Belles-Boix | KNAT6 : An Arabidopsis Homeobox Gene Involved in Meristem Activity and Organ Separation[END_REF].

WUS protein can inhibit the transcription of two type-A ARRs [START_REF] Leibfried | WUSCHEL controls meristem function by direct regulation of cytokinin-inducible response regulators[END_REF]. In turn, CKs can activate WUS expression, through a CLV-dependent and a CLV-independent pathways [START_REF] Gordon | Multiple feedback loops through cytokinin signaling control stem cell number within the Arabidopsis shoot meristem[END_REF]. In addition, CK signaling also contributes to positively regulate WUS, via the activation of the WUS-related homeobox gene STIMPY in the SAM [START_REF] Skylar | STIMPY mediates cytokinin signaling during shoot meristem establishment in Arabidopsis seedlings[END_REF]. Altogether, these results show that WUS and CK-signaling pathways are involved in common positive feedback loops, contributing to reinforce the stem cell niche maintenance mechanism. Interestingly, SAM geometry can play an instructive role here. Indeed, CK are mainly produced in the L1 layer, meaning that the gradient of CK would differ depending on SAM size. Such a geometrical feedback has been predicted in computational models, and validated in experiments [START_REF] Gruel | An epidermis-driven mechanism positions and scales stem cell niches in plants[END_REF]. CK biosynthesis is also mediated by KNOX1 genes. Indeed, the ISOPENTENYL TRANSFERASE (IPT) enzyme, catalyzing the first step of CK production, and several IPT genes are promoted by KNOX1 genes [START_REF] Sakakibara | CYTOKININS: Activity, Biosynthesis, and Translocation[END_REF] (Figure 5). Interestingly, the activation of IPT genes or the exogenous application of CK can partially rescue stm phenotype, suggesting that KNOX1 genes could contribute to sustain SAM activities through their action on CK-signaling pathway [START_REF] Jasinski | KNOX Action in Arabidopsis Is Mediated by Coordinate Regulation of Cytokinin and Gibberellin Activities[END_REF].

In contrast to CKs, which are mainly involved in stem cell maintenance in the CZ, auxin is largely involved in organogenesis, which starts in the PZ. The use of specific auxin biosensors [START_REF] Brunoud | A novel sensor to map auxin response and distribution at high spatio-temporal resolution[END_REF][START_REF] Liao | Reporters for sensitive and quantitative measurement of auxin response[END_REF] has revealed a non-homogeneous distribution of auxin in the SAM, with maxima of auxin concentration at the sites where primordia are initiated (Figure 6A) [START_REF] Petrasek | Auxin transport routes in plant development[END_REF][START_REF] Vernoux | The auxin signalling network translates dynamic input into robust patterning at the shoot apex[END_REF]. In tomato SAM, local applications of exogeneous auxin promote organ outgrowth, precisely at the site where auxin was added, indicating that auxin is sufficient to induce organ initiation (Reinhardt et al.). Auxin distribution is controlled by both efflux and influx carriers, which ensure a directional (i.e., polar) transport of auxin between cells. In the SAM, the PIN-FORMED1 (PIN1) efflux carrier is the primary contributor to auxin polar transport, and its regulation plays a key role in organogenesis [START_REF] Petrasek | Auxin transport routes in plant development[END_REF]. The importance of auxin transport during organogenesis is particularly well illustrated with the phenotype of pin1 mutants, which display naked meristems, i.e., no floral buds on their inflorescence meristem [START_REF] Galweiler | Regulation of Polar Auxin Transport by AtPIN1 in Arabidopsis Vascular Tissue[END_REF][START_REF] Okada | Requirement of the Auxin Polar Transport System in Early Stages of Arabidopsis Floral Bud Formation[END_REF] (Figure 6B). This phenotype is mimicked in plants treated with the N-1 napthtylphtalamic acid (NPA), an inhibitor of the auxin transport [START_REF] Okada | Requirement of the Auxin Polar Transport System in Early Stages of Arabidopsis Floral Bud Formation[END_REF] (Figure 6B). Immunodetection and live-imaging of PIN1 proteins have revealed that PIN1 are polarly distributed in cells of the L1, contributing to transport auxin towards discrete sites in the PZ, corresponding to future primordia. Conversely, developing organs acts as a sink that deplete auxin from the surrounding tissue. These observations are consistent with the model of an inhibitory field, controlling the phyllotactic pattern, and where the absence of auxin in tissues surrounding the developing organ prevents the initiation of another organ.

Interestingly, a geometrical feedback loop is also involved here. In particular, permutations are more likely to happen in larger meristems where shorter plastochrones are promoted, meaning that phyllotaxis is more robust when meristems are smaller (Landrein et al., 2015b).

Altogether, these results demonstrate that the shape of an organism is under the control of a complex regulatory network, involving biochemical factors (e.g., gene expression, hormone distribution), and a tight coordination between these factors at the tissue and organ levels are required for development. However, genetic regulation behind morphogenesis is not sufficient to understand how the final shape is achieved. Indeed, changing a shape is, by definition, changing a structure, and thus, it must involve the laws of mechanics. The idea that shapes of living organisms is a consequence of physics law was promoted by Thomas D'Arcy Thompson in "On growth and form" (D'Arcy [START_REF] Thompson | On Growth and Form[END_REF]. With recent developments in imaging, biophysics and computational modeling, it is now revisited with increasing momentum. In the following, I introduce the role of mechanics in plant development.

The mechanics behind shapes 2.1 Definitions

Force, stress, strain Mechanics can be defined as a branch of science that study how forces act on bodies, and how these bodies respond to these forces [START_REF] Bidhendi | Methods to quantify primary plant cell wall mechanics[END_REF]. Why should mechanical forces be considered in biology? How could mechanical properties contribute to plant development? During the past years, these questions have been extensively explored [START_REF] Echevin | Growth and biomechanics of shoot organs[END_REF][START_REF] Engler | Matrix Elasticity Directs Stem Cell Lineage Specification[END_REF][START_REF] Farge | Mechanical Induction of Twist in the Drosophila Foregut/Stomodeal Primordium[END_REF][START_REF] Mirabet | The Role of Mechanical Forces in Plant Morphogenesis[END_REF][START_REF] Robinson | Mechanical control of morphogenesis at the shoot apex[END_REF]Sampathkumar et al., 2014a) thanks to the development of new theoretically approaches and experimental tools. However, these questions are still largely opened since forces are in essence invisible, and thus, their presence, magnitude, or orientation can only be derived from deformation.

One of the main basis of plant morphogenesis is cell expansion, which relies on the mechanics of the plant cell itself. Therefore, understanding plant morphogenesis requires biophysical and mathematical description of cell growth, namely the biomechanical properties of the structure and the forces acting on that structure. This part aims to define the main biophysical parameters regulating plant cell growth (i.e., stress, strain, elasticity, plasticity), and the related biological responses will be extensively described in the following parts. More detailed definitions can be found in Karl Niklas' book (Niklas, 1992) and in [START_REF] Moulia | Plant biomechanics and mechanobiology are convergent paths to flourishing interdisciplinary research[END_REF]. Plant cells are characterized by a stiff exoskeleton: the cell wall. This cell wall is under tension, because of the presence of high turgor pressure in the cell. Thus, the mechanics of plant cell depends on mechanical properties (mainly, of the cell wall) and on forces (mainly, tension in the wall). At the single cell level, how forces drive cell expansion can be mathematically described.

Strain:

During cell expansion, a piece of cell wall of surface A (when viewed from top) and with a cross-section of area S is subjected to a pulling force F (tension). However, measuring the absolute deformation of the wall can be meaningless, since smaller walls are expected to deform less than larger walls (through allometry). Strain has been defined to normalize deformation according to original size of the object. The strain 𝜀 is a unitless assessment of deformation, which can be defined as the ratio of final size to initial size (i.e., (A-A0)/A0) (Figure 7A).

Stress:

Usually, the strain rate (dA/dt)/A is proportional to the force. However, one can intuitively realize that, assuming homogeneous properties, thicker walls would deform less than thinner walls. Stress has been defined to normalize force according to the geometry of the object. The stress σ is defined as the force per unit of area exerted on the cross-section. This means that in the cell wall, tensile stress is defined as σ = F/S. Elasticity: A material displaying elastic properties returns to its initial shape when forces are released. In Hooke's law, describing the deformation of an elastic string, there is a relation between force (F) and deformation (X) along the spring axis: F = kX, where k is the stiffness of the spring (Figure 7B). This definition for 1D elastic object can be extended to 3D objects as follows: σ = E 𝜀, where E is the apparent stiffness (also called Young's modulus) of the object (Figure 7C).

Plasticity:

Growth is irreversible, and thus cannot be reduced to an elastic behavior. To induce growth, the stress has to be larger than the yield threshold to induce a non-reversible expansion (i.e., plastic deformation) of the wall. Indeed, by definition, a material with a plastic behavior retains its deformed shape even after removing the forces. Because stress is not directly quantifiable, techniques measuring stress are based on the application of a known force and the measure of the resulted deformation or vice versa. While this is relatively easy to picture for large, man-made, materials, it can become much more challenging to estimate forces and mechanical properties in living matter, because of scale, complexity and temporal dynamics. In that respect, plant mechanics is relatively simpler (when compared to animal mechanics), because it is dominated the balance between cell wall and turgor pressure, as shown below.

Origin of mechanical stress

Beyond their biochemical nature, living organisms can also be considered as physical objects, experiencing physical constraints. At the whole plant scale, physical constraints can originate from the environment. Indeed, because plants are fixed in the soil, they are exposed to gravity, wind, neighboring living (trees in a forest) and non-living (e.g. wall) elements, rain impacts, osmotic changes (e.g. through drought). Although these factors are essential to understand the final shapes of plants, within the frame of this PhD, I focused on the internal cause of mechanical stress and its role in morphogenesis.

Regulation

Origin and regulation of turgor pressure

The cell wall is quite porous. Water is the most abundant element in primary cell walls, and the cell wall contains negligible amounts of osmolytes. This generates a difference in osmotic pressure between the apoplast and the protoplast (water tends to enter the cell). Turgor pressure is defined as a hydrostatic pressure from the cell wall onto the protoplast that counterbalances this osmotic pressure [START_REF] Schopfer | Biomechanics of plant growth[END_REF]. Turgor pressure was measured for the first time in the 1960s by Paul Green with a turgor pressure probe [START_REF] Green | Growth Phvsics in Nitella: a Method for Continuous in Vivo Analysis of Extensibility Based on a Micro-manometer Technique for Turgor Pressure[END_REF][START_REF] Green | Turgor pressure: direct manometric measurement in single cells of Nitella[END_REF]) (see in Table 1). This method consists in the insertion of a pipet full of liquid directly in the cell. The cell content pushes the liquid in the pipet, and the pressure requires to send it back to its initial position represents a measure of the turgor pressure. This technique was first applied to giant cells of Nitella, Chara and Acebularia [START_REF] Zimmermann | Direct turgor pressure measurements in individual leaf cells of Tradescantia virginiana[END_REF], and then later in stomatal guardian cells [START_REF] Franks | Use of the pressure probe in studies of stomatal function[END_REF]. Since then, other methods have been developed to measure more or less directly the turgor pressure at cellular, but also at tissue/organ levels [START_REF] Beauzamy | Flowers under pressure: ins and outs of turgor regulation in development[END_REF][START_REF] Forouzesh | In vivo extraction of Arabidopsis cell turgor pressure using nanoindentation in conjunction with finite element modeling[END_REF][START_REF] Hüsken | Pressure Probe Technique for Measuring Water Relations of Cells in Higher Plants[END_REF]. Turgor pressure is highly variable as it can be modified by every mechanism which allow water movements. First, modifications of the cytosolic and vacuolar concentrations of osmolytes, such as ions, carbohydrates and amino acids, directly affect turgor pressure [START_REF] Beauzamy | Flowers under pressure: ins and outs of turgor regulation in development[END_REF]. Then, water can also be transported through adjacent cells thanks to proteins called aquaporins, which mediate most of the water transport across the plasma membrane [START_REF] Maurel | Aquaporins in Plants[END_REF]. Finally, at the cell scale, water movements are also allowed through plasmodesmata, which are symplasmic channels linking two adjacent cells. Interestingly, it has been recently suggested, that plasmodesmata could be mechanosensitive [START_REF] Park | Controlling intercellular flow through mechanosensitive plasmodesmata nanopores[END_REF].

The regulation of turgor pressure is not cell autonomous. For instance, it has been demonstrated that tissue topology can affect turgor pressure. Indeed, a multicellular version of the Lockhart model can generate heterogeneous turgor pressure as an output from tissue topology, when uniform input parameters are considered. This output can be explained by differences in adjacent cell numbers, which generate irregularity in the tissue. This, involves an imbalance of tension at cell edges, and results in concave and convex curvatures in the walls through differences in turgor pressure. This phenomenon leads to a negative correlation between cell size and turgor pressure and has been experimentally validated by Atomic Force Microscopy (see Table1) in Arabidopsis thaliana SAM [START_REF] Long | Cellular Heterogeneity in Pressure and Growth Emerges from Tissue Topology and Geometry[END_REF].

Because the increase of cell volume is caused by the water uptake, turgor pressure is often considered as the motor of growth. However, turgor pressure exerts an isotropic pressure throughout the cell, and therefore, anisotropic cell expansion requires localized changes in cell wall properties to create the diversity of shapes observed in plants.

Cons:

Invasive method (reversibility is partial); formation of kink may affect the measurements.

Pressure probe

In a pressure probe, a pipette is filled with a liquid (e.g. silicon oil) and is inserted inside a cell. Because of turgor pressure, the cell content pushes against the liquid inside the pipette. The pressure required to send the content back into the cell is a measure of turgor pressure.

Pros: Direct measurement of turgor pressure Cons: invasive method; leaking can bias the measurement; only works with big cells.

Atomic force microscopy

Using an atomic force microscope, the surface of the sample is indented with a probe tip which is fixed to a flexible cantilever (of known stiffness) at a given force or displacement. The actual indentation depth is measured by the deformation of the cantilever, through laser deflection.

Pros: Non invasive, label-free method; diversity of tip shape and size can probe more or less superficial features for all cell size range; from stiffness, one can deduce other properties, such as wall tension or turgor pressure.

Cons: Indirect measurement; stiffness is measured orthogonal to the sample surface only.

Brillouin microscopy

Brillouin microscopy is based on the scattering of light when interacting with internal or simulated sound waves from the sample's molecules. Their collision results in a shift in the light frequency and direction. This shift is used to determine viscoelastic properties of the sample.

Pros: Non-invasive, label-free method; high spatial resolution; measurement of compressibility.

Cons: The relation with stiffness assessment is still debated; heterogeneity of biological material makes the interpretation complex.

This part aims to introduce some vocabulary used to describe cell wall properties, and briefly present techniques which are used to quantify these mechanical properties. The following list is therefore not exhaustive, and simply aims to give an overview of how technical approaches may help biologists to investigate the role of cell wall properties in plant morphogenesis.

The high stiffness of cell wall in plant cells hinders the use of available tools to study mechanical properties of animal cells, such as micropipette aspiration [START_REF] Hochmuth | Micropipette aspiration of living cells[END_REF], optical tweezers [START_REF] Hénon | A New Determination of the Shear Modulus of the Human Erythrocyte Membrane Using Optical Tweezers[END_REF] or magnetic rheometry beads. Indeed, these techniques display a force range limited to piconewtons, which is not sufficient to assess mechanical properties of walled plant cells [START_REF] Vogler | Measuring the Mechanical Properties of Plant Cell Walls[END_REF]. Other methods, notably indentation methods, have been developed to allow the quantification of material properties. This can be applied to wall properties as well as turgor pressure (depending on the depth of indentation). Indentation methods are based on the fact that the pressure can be deduced from the mechanical resistance to the indentation. Among these methods, the most resolutive one is probably atomic force microscopy (AFM), which can be used to measure either the turgor pressure (Beauzamy et al., 2015a), when using large indenter, or local cell wall properties by using small probes (10-40nm). Basically, AFM techniques use an indenter of known stiffness to induce a very local deformation or to apply a known force on the sample, and the resulted forces or deformations are then measured, from which material properties can be deduced [START_REF] Bidhendi | Methods to quantify primary plant cell wall mechanics[END_REF]. More precisely, the indenter is linked to a flexible cantilever, which reflects a laser differently according the sample's topography. Displacement curves are recorded and from their analysis with Hertzian (for spherical tip) or Sneddon (for pyramidal tip) model, together with finite element models of cell walls, wall properties can be extracted.

This technique has been used at both cells and tissues levels, and has highlighted heterogeneities in the cell wall properties across the SAM [START_REF] Milani | In vivo analysis of local wall stiffness at the shoot apical meristem in Arabidopsis using atomic force microscopy: Measuring wall stiffness in meristems with AFM[END_REF][START_REF] Milani | Matching Patterns of Gene Expression to Mechanical Stiffness at Cell Resolution through Quantitative Tandem Epifluorescence and Nanoindentation[END_REF]. It is important to note that AFM-results always should be interpreted with caution, as the probe and therefore the measures occur perpendicular to the direction of the deformation. Therefore, mechanical properties in the periclinal orientation are probably not well estimated. Furthermore, AFM only measures stiffness, which does not recapitulate all mechanical properties (e.g. plasticity). Interestingly, wall stiffness usually correlates very wall with growth in published reports, suggesting that the elastic component might still dominate. AFM methods remain limited to the outer layer, unless one uses much larger indenters to deduce the mechanics of inner cells indirectly (e.g. [START_REF] Peaucelle | Pectin-Induced Changes in Cell Wall Mechanics Underlie Organ Initiation in Arabidopsis[END_REF]. For larger scale assessments, an alternative is cellular force microscopy (CFM) [START_REF] Routier-Kierzkowska | Cellular Force Microscopy for in Vivo Measurements of Plant Tissue Mechanics[END_REF], which is based on similar principle as AFM, albeit using force sensors instead of a cantilever.

More recently, Brillouin scattering microscopy gained increased attention in cell mechanics studies. This acoustic related method is based on light scattering properties interacting with sound waves. Indeed, the collision between light and sound particles results in the scattering of light, with a shift in its frequency. This shift, between the incident and scattered light, is used to determine the viscoelasticity properties of the material [START_REF] Bidhendi | Methods to quantify primary plant cell wall mechanics[END_REF][START_REF] Prevedel | Brillouin microscopy: an emerging tool for mechanobiology[END_REF]. Some argue that this method truly determines material properties, as it does not involve a deformation of the material. Contrary to the indentation methods, the measurements obtained with the Brillouin methods result in a longitudinal modulus which could better represent the stiffness. However, Brillouin microscopy interpretation remains largely debated, notably for biological samples which display heterogeneous composition.

At even larger scale, other mechanical tests such as bending, tensile and compressive tests can be used to study mechanical forces at the organ level for instance. Tensile-compressive tests consist to compress or stretch or to apply a torsion to a stem and many features, such as stiffness or elastic modulus, can be calculated [START_REF] Shah | The strength of plants: theory and experimental methods to measure the mechanical properties of stems[END_REF]. Overall, these techniques allow the quantification, or at least the estimation of mechanical properties of the cell wall, and thus participate to the understanding of processes occurring during plant morphogenesis.

2.3 From mechanics to shape: focus on the shoot apical meristem

While understanding the molecular mechanism controlling SAM activities have seen a significant progress during the past few years, the role biomechanics in SAM functions remains poorly understood. Yet, increasing evidence indicate that the SAM displays a unique mechanical pattern contributing to organ formation and phyllotaxis. How biomechanics contribute to organ formation in the SAM is still largely investigated and several models have been proposed. One of these models has suggested that organ initiation can occur without modifications of cell wall mechanical properties, and that organ outgrowth can be explained by differential growth rates between the inner layers and outer layer, generating compressive stress in the outer layer, which is released by the formation of a bulge (i.e., the new organ) [START_REF] Dumais | New Evidence for the Role of Mechanical Forces in the Shoot Apical Meristem[END_REF]. Two other models assume that mechanical properties are modified at the site of the organ initiation. One of them suggests that inner tissues exert a pressure on outer tissue, due to an increased growth rates, and resulting in buckling [START_REF] Peaucelle | Pectin-Induced Changes in Cell Wall Mechanics Underlie Organ Initiation in Arabidopsis[END_REF]. Finally, the last model suggests that organ formation is triggered by a local increase in cell wall extensibility, which leads to the relaxation of tensile and compressive stress in the tissues [START_REF] Cosgrove | Plant cell wall extensibility: connecting plant cell growth with cell wall structure, mechanics, and the action of wall-modifying enzymes[END_REF][START_REF] Echevin | Growth and biomechanics of shoot organs[END_REF] (Figure 9A). All these models assume that the L1 layer is under tension, and that inner tissues are under compression.

The concept of tissue tension is not new, since it appears in the nineteenth century with Hofmeister, and then Sachs, who have shown that the outer layer of stem is under tension contributing to aerial organ shaping. Later, complementary experiments have provided evidence that the epidermis is under tension, notably in maize coleoptiles [START_REF] Kutschera | Cooperation of epidermis and inner tissues in auxin-mediated growth of maize coleoptiles[END_REF] or in sunflowers hypocotyls [START_REF] Peters | The Mechanic State of "Inner Tissue" in the Growing Zone of Sunflower Hypocotyls and the Regulation of Its Growth Rate Following Excision[END_REF]. In Arabidopsis mutants spontaneous cracks in the epidermis were notably observed in both hypocotyls (Bouton et al., 2002a) and stems [START_REF] Maeda | The Conflict Between Cell Proliferation and Expansion Primarily Affects Stem Organogenesis in Arabidopsis[END_REF], revealing the presence of a high tension in this tissue (Figure 9B). More recently, experiments on the SAM, using large indentation depth measurements combined with large tips, have revealed that the epidermis of the SAM is under tension, confirming a key role of the epidermis in organ shaping in the meristem (Figure 9C and D) [START_REF] Beauzamy | Mechanically, the Shoot Apical Meristem of Arabidopsis Behaves like a Shell Inflated by a Pressure of About 1 MPa[END_REF].

Plant cell walls can be classified into two distinct groups: primary and secondary walls. Primary walls are complex and highly heterogeneous structures, enable to resist to strong tensile stress generated by turgor pressure, while being stretchable to allow cell growth. Once the final cell size is reached, the secondary wall may be synthetized and deposited between the plasma membrane and the primary wall, mainly to strengthen cells and tissues. The secondary wall is not extensible and thus, preclude cell growth. During my PhD, I focused on the role of the primary cell wall in growing organs and meristems.

The molecular effectors of cellulose synthesis

Among cell wall components, cellulose microfibrils have received a particular interest, since they are usually considered as the main load-bearing components of the cell wall. Cellulose microfibrils can be described as a thin and strong ribbon around 4nm in diameter, which selfassembles into crystalline and inextensible microfibrils. Higher order of cellulose microfibrils and modification of its crystallinity have been correlated to wall stiffness [START_REF] Fujita | Cortical microtubules optimize cell-wall crystallinity to drive unidirectional growth in Arabidopsis: Microtubules and cell-wall crystallinity[END_REF].

Because they are fibrillar and stiff, cellulose microfibrils play a major role in growth anisotropy (Baskin, 2005): when the microfibrils are organized in a preferential orientation, cellular expansion, under the effect of turgor pressure, is reduced in that direction [START_REF] Bidhendi | Relating the mechanics of the primary plant cell wall to morphogenesis[END_REF].

Genetic studies have shown that alteration in cellulose microfibrils synthesis or regulation directly impair growth and morphogenesis. For instance, mutation of PROCUSTE1 gene, involved in the cellulose synthesis, is severely affected in cell elongation [START_REF] Fagard | PROCUSTE1 Encodes a Cellulose Synthase Required for Normal Cell Elongation Specifically in Roots and Dark-Grown Hypocotyls of Arabidopsis[END_REF]. Their synthesis is ensured by a large group of plasma membrane-localized proteins, called cellulose synthase (CESA) complexes (CSCs), that are organized as six-fold symmetrical rosettes (Figure 11A) [START_REF] Polko | The Regulation of Cellulose Biosynthesis in Plants[END_REF]. In Arabidopsis, CESA1, CESA3, and CESA6like proteins (e.g. CESA2, CESA5, CESA6 and CESA9) are involved in primary wall cellulose synthesis, whereas CESA4, CESA7, and CESA8 participate in secondary cell wall synthesis [START_REF] Desprez | Organization of cellulose synthase complexes involved in primary cell wall synthesis in Arabidopsis thaliana[END_REF][START_REF] Persson | Genetic evidence for three unique components in primary cell-wall cellulose synthase complexes in Arabidopsis[END_REF].

The delivery of CSCs to the plasma membrane plays a major role in the regulation of cellulose synthesis, and cytoskeleton components are critical for this regulation. Indeed, actin filaments are involved in the distribution of CSC secretory organelles throughout the cell cortex, notably during the primary cell wall synthesis [START_REF] Crowell | Pausing of Golgi Bodies on Microtubules Regulates Secretion of Cellulose Synthase Complexes in Arabidopsis[END_REF][START_REF] Gutierrez | Arabidopsis cortical microtubules position cellulose synthase delivery to the plasma membrane and interact with cellulose synthase trafficking compartments[END_REF].

Microtubules have also been involved in cellulose crystallinity, although the related mechanism remains mysterious [START_REF] Fujita | Cortical microtubules optimize cell-wall crystallinity to drive unidirectional growth in Arabidopsis: Microtubules and cell-wall crystallinity[END_REF]. Cortical microtubules actively participate to the regulation of CSCs trajectory. In 1963, Ledbetter and Porter observed a parallel alignment between cortical microtubules and cellulose microfibrils [START_REF] Ledbetter | A "MICROTUBULE" IN PLANT CELL FINE STRUCTURE[END_REF], rising the microtubule-microfibrils alignment hypothesis (Figure 11B). Since then, and thanks to live imaging, it has been demonstrated that CESA proteins are generally guided through the plasma membrane by cortical microtubules, allowing the deposition of new cellulose microfibrils in the cell wall (Paredez et al., 2006a) (Figure 11C).

One of these proteins is KORRIGAN1 (KOR1), a membrane-localized endo-β-1,4-glucanase, which has been shown to interact with the CSC complex, influencing the synthesis of cellulose, and increasing the amount of non-crystalline cellulose [START_REF] Lane | Temperature-Sensitive Alleles of RSW2 Link the KORRIGAN Endo-1,4-β-Glucanase to Cellulose Synthesis and Cytokinesis in Arabidopsis[END_REF][START_REF] Lei | The jiaoyao1 Mutant Is an Allele of korrigan1 That Abolishes Endoglucanase Activity and Affects the Organization of Both Cellulose Microfibrils and Microtubules in Arabidopsis[END_REF][START_REF] Nicol | A plasma membrane-bound putative endo-1,4-beta -D-glucanase is required for normal wall assembly and cell elongation in Arabidopsis[END_REF][START_REF] Takahashi | KORRIGAN1 and its Aspen Homolog PttCel9A1 Decrease Cellulose Crystallinity in Arabidopsis Stems[END_REF] (Figure 11C). Despite a large effort on this topic, the exact mechanism behind CSCs guidance remains largely unknown. Indeed, how CESA proteins are guided through the plasma membrane by the microtubules is still unclear, and several questions remain open. For instance, the contribution of the plasma membrane composition in this mechanism has not been explored so far. Yet, it has been shown that the lipid composition of the plasma membrane can modulate its biophysical and biochemical properties, and thus directly affect the protein recruitment (Simon et al., 2014). For instance, lipid composition of the PM could affect the recruitment of CSI1 proteins, which are known to have a C2 domain at their C terminal enable to bind the protein to phospholipids. Therefore, investigating the impact of modification of plasma membrane composition on CESA and CSI1 proteins dynamics seems to be relevant to decipher the mechanism of cellulose microfibrils deposition in the cell wall (see results part 3).

Although cellulose microfibrils are always described as the main load-bearing of the cell wall, they are also part of a more complex network of tethered molecules from the wall matrix, such as the pectin. These connections between cellulose microfibrils and other cell wall components allow the distribution of the load through all the cell wall networks, contribute to the dynamic remodeling of the wall and enable the cell to resist to pressure over time [START_REF] Dyson | A model of crosslink kinetics in the expanding plant cell wall: Yield stress and enzyme action[END_REF].

The molecular effector of matrix remodeling: the pectin case

Beyond pectins, the wall matrix contains hemicellulose and structural proteins. Here I only focus on pectins, to illustrate how a prominent component of the wall matrix is under genetic control and affects morphogenesis.

Pectins are major components of the cell wall, reaching up to 35% of the primary cell walls dry mass in dicotyledons and non-grass monocotyledons [START_REF] Mohnen | Pectin structure and biosynthesis[END_REF]. Pectins are synthetized in the Golgi apparatus and then inserted in the cell wall through vesicle-mediated exocytosis [START_REF] Zhang | Functional Compartmentation of the Golgi Apparatus of Plant Cells: Immunocytochemical Analysis of High-Pressure Frozen-and Freeze-Substituted Sycamore Maple Suspension Culture Cells[END_REF]. Pectins are complex polymers, enriched in galacturonic acid (GalA), that have the ability to form a gel-like configuration, connecting all the components of the cell wall [START_REF] Palin | The role of pectin in plant morphogenesis[END_REF]. Indeed, pectins form the middle lamella, which is an adhesive compartment localized between two neighboring cells [START_REF] Iwai | A pectin glucuronyltransferase gene is essential for intercellular attachment in the plant meristem[END_REF][START_REF] Verger | Cell adhesion in plants is under the control of putative O -fucosyltransferases[END_REF]. Moreover, pectins play an important role in the regulation of cell wall mechanical properties, directly affecting wall porosity and hydration, and probably regulating also the accessibility of wall-modifying enzymes to their substrates [START_REF] Willats | Pectin: cell biology and prospects for functional analysis[END_REF]. Pectins play a key role in the regulation of mechanical properties of the cell wall.

Among the large group of GalA, homogalacturonans (HGs), made of linear chains of galacturonic residues, have received more attention in developmental biology. Indeed, the carboxyl groups of HG chains can display different degree of methyl esterification, which modifies their ability to adopt a gel configuration upon addition of gelling agents, such as Ca 2+ (Figure 12A). Therefore, HGs can be found in two different forms in the cell wall, the methylesterified form (R-COOCH3) and the de-methyl-esterified form. Understanding how these two forms affects mechanical properties of the matrix is still largely investigated and discussed. In short, once de-methyl-esterified, HGs can become softer as they become the target of pectate lyases, or stiffer because they can generate calcium crosslinks. Patterned de-methylesterification of pectins also explains the mechanical polarity of hypocotyl cells (with softer, de-methyl-esterified, longitudinal walls), which precedes their anisotropic growth [START_REF] Peaucelle | The Control of Growth Symmetry Breaking in the Arabidopsis Hypocotyl[END_REF]. Conversely, in pollen tubes, pectin methyl-esterification has been associated with stiffer cell walls, through calcium crosslinking [START_REF] Bidhendi | Relating the mechanics of the primary plant cell wall to morphogenesis[END_REF]. However, these results should be viewed with caution, as other study in the pollen tube have associated methylesterified pectins with softer regions, whereas de-methyl-esterified pectins have been associated with stiffer regions [START_REF] Parre | Pectin and the role of the physical properties of the cell wall in pollen tube growth of Solanum chacoense[END_REF]. This, could be explained by the fact that pectin methyl-esterification decreases the ability of homogalacturonans to form crosslink with calcium ions, which bond pectin to each other, causing softening of the cell wall.

Conversely, de-methyl-esterification of pectins through PME activity, increases the capacity of homogalacturonans to form calcium bonds, causing wall stiffening and increasing cell adhesion [START_REF] Hocq | Connecting Homogalacturonan-Type Pectin Remodeling to Acid Growth[END_REF][START_REF] Virk | The role of wall calcium in the extension of cell walls of soybean hypocotyls[END_REF].

In conclusion, there are more and more evidence pointing at a primary role of pectins in regulating cell wall mechanical properties, however, further experiments are required to understand how pectin modifications could provide another mechanism for the control of the directional growth (Bou [START_REF] Bou Daher | Anisotropic growth is achieved through the additive mechanical effect of material anisotropy and elastic asymmetry[END_REF][START_REF] Peaucelle | The Control of Growth Symmetry Breaking in the Arabidopsis Hypocotyl[END_REF][START_REF] Saffer | Expanding roles for pectins in plant development[END_REF]. In this respect, investigating how pectin-modifying enzymes are regulated and how they affect pectin structure has become a hot topic in developmental biology.

These enzymes are known as homogalacturonan-modifying enzymes (HGMEs) and belong to large multigenic families. HGMEs can notably control both the degree of substitution (i.e. methylesterification and/or acetylation), and polymerization, which is regulated in part by PMEs for instance [START_REF] Sénéchal | Homogalacturonan-modifying enzymes: structure, expression, and roles in plants[END_REF]. PME are commonly found in plants, and although different isoforms have been identified, they all catalyze the specific hydrolysis of methylester bonds at C-6 from GalA residues, releasing free carboxyl groups. PME activity depends of a large range of different factors. For instance, several studies have reported the sensitivity of PMEs to pH changes; a low pH affecting their activity, while a slightly basic pH would help the release of carboxyl groups due to the electrostatic repulsion between the enzymes and the substrate [START_REF] Nari | Electrostatic effects and the dynamics of enzyme reactions at the surface of plant cells. 3. Interplay between limited cell-wall autolysis, pectin methyl esterase activity and electrostatic effects in soybean cell walls[END_REF]. It has also been established that the ionic environment is crucial for PME activity, and that cations affect PME catalysis. More detail on this are available in the following reviews [START_REF] Jolie | Pectin methylesterase and its proteinaceous inhibitor: a review[END_REF][START_REF] Sénéchal | Homogalacturonan-modifying enzymes: structure, expression, and roles in plants[END_REF].

Three distinct modes of action of PMEs have been described in plants. In short, in the first mechanism, PMEs remove all contiguous methylesters from a single chain of HG. The second mechanism is quite similar except that only a limited number of methylesters are removed from several chains of HG. These two mechanisms produce a similar demethylesterified HG. The last mechanism is rather attributed to acidic PMEs -PMEs activated in an acidic environment -where PMEs remove only one methylester before dissociating from GalA [START_REF] Sénéchal | Homogalacturonan-modifying enzymes: structure, expression, and roles in plants[END_REF]. These mechanisms generate different patterns of de-methyl-esterification, and thus differentially affect cell wall properties.

PMEs are also regulated through the inhibition of their activity. Protein inhibitor of plants PMEs (PMEIs) can form an inactive stoichiometric 1:1 complex, inhibiting PME activity [START_REF] Balestrieri | A glycoprotein inhibitor of pectin methylesterase in kiwi fruit (Actinidia chinensis)[END_REF]. This interaction in noncovalent and reversible. PMEI was first discovered in green kiwi fruit, where PMEI active form was only found in the fully mature stage [START_REF] Balestrieri | A glycoprotein inhibitor of pectin methylesterase in kiwi fruit (Actinidia chinensis)[END_REF]. Later, genes encoding PMEI were identified in other species, including in Arabidopsis [START_REF] Wolf | Identification of pollenexpressed pectin methylesterase inhibitors in Arabidopsis[END_REF]. Non-proteinaceous compounds have also been identified to inhibit PME activity. Among them, some detergents (e.g., SDS), sugars (e.g., sucrose and glucose), phenolic acids and iodine [START_REF] Jolie | Pectin methylesterase and its proteinaceous inhibitor: a review[END_REF].

Among HGMEs, other proteins such as pectate lyases (PLs), pectin acetylesterases (PAEs) or polygalacturonases (PGs) have been identified in plants, and are also able to modify pectin structure. While PLs cleave the ß (1)(2)(3)(4) bond between GalA units (Marin-Rodriguez, 2002; Uluisik and Seymour, 2020), PGs catalyze the hydrolysis of α(1-4) bonds linking Gal-A residues. Moreover, GalA from HG backbone can also be O-acetylated, and in this context, PAEs can act by specific hydrolysis of acetylester at O2 and/or O3 positions from GalA residues [START_REF] Sénéchal | Homogalacturonan-modifying enzymes: structure, expression, and roles in plants[END_REF]. Several studies have shown that the degree of pectin acetylation can affect cell wall properties, by modifying cell wall viscosity or improving gelation properties for instance [START_REF] Gou | Acetylesterase-Mediated Deacetylation of Pectin Impairs Cell Elongation, Pollen Germination, and Plant Reproduction[END_REF][START_REF] Ralet | Polyelectrolyte behaviour and calcium binding properties of sugar beet pectins differing in their degrees of methylation and acetylation[END_REF]. Overall, although PLs, PAEs and PGs catalyze different reactions, they all seem to preferentially target de-methyl-esterified substrates. For instance, in plants, PGs particularly preferentially targets HG with a chain region containing more than four de-methyl-esterified Gal-A residues between methyl-esterified Gal-A [START_REF] Clausen | Synthetic methyl hexagalacturonate hapten inhibitors of anti-homogalacturonan monoclonal antibodies LM7, JIM5 and JIM7[END_REF]. Likewise, optimal activities of PLs have often been quantified with nonmethylesterified substrates [START_REF] Chotigeat | Cloning and characterization of pectate lyase from Hevea brasiliensis[END_REF][START_REF] Tardy | Comparative analysis of the five major Erwinia chrysanthemi pectate lyases: enzyme characteristics and potential inhibitors[END_REF]. Consequently, these elements suggest that a prior action of PMEs seems to be required to allow the activities of these enzymes on HG. Like PMEs, the activity of these enzymes is highly sensitive to pH and to the ionic environment.

Over the past decades, several studies have highlighted the crucial role of HG in cell adhesion [START_REF] Daher | How to let go: pectin and plant cell adhesion[END_REF][START_REF] Jarvis | Intercellular adhesion and cell separation in plants: Intercellular adhesion and cell separation in plants[END_REF]. Indeed, a deficiency in pectin synthesis was previously correlated with a loss of cell adhesion (Bouton et al., 2002b;[START_REF] Mouille | Homogalacturonan synthesis in Arabidopsis thaliana requires a Golgi-localized protein with a putative methyltransferase domain: Homogalacturonan synthesis in Arabidopsis[END_REF]. Mutations in two genes, QUASIMODO1 and QUASIMODO2, encoding respectively a putative galacturonosyltransferase and a putative pectin methyltransferase, lead to a 50% reduction in HG content, and mutants display clear cell-detachment phenotype.

In conclusion, we have seen that numerous HGMEs modulate pectin status (e.g., degree of methylesterification and/or acetylation). Moreover, HGMEs should be considered, at least, as much as genes directly involved in pectin synthesis, since HG status directly affect cell wall mechanical properties (Figure 12B). Finally, HGMEs are regulated by a large variety of factors, such as the pH or the ionic environment, which can directly affect their activities. Interestingly, gene expression of many HGMEs has been shown to be modulated by hormones. For instance, it has been shown that auxin can specifically regulates the expression of PME, PAE,PG and PL genes during different events of plant development [START_REF] Goda | Comprehensive comparison of auxin-regulated and brassinosteroid-regulated genes in Arabidopsis[END_REF][START_REF] Quesada | Antisense Down-Regulation of the FaPG1 Gene Reveals an Unexpected Central Role for Polygalacturonase in Strawberry Fruit Softening[END_REF][START_REF] Vanneste | Cell Cycle Progression in the Pericycle Is Not Sufficient for SOLITARY ROOT/IAA14-Mediated Lateral Root Initiation in Arabidopsis thaliana[END_REF].

3.3 Linking auxin transduction, wall properties and organogenesis at the SAM Numerous studies have investigated how auxin contribute to cell wall expansion and how it affects cell wall properties. Auxin participates to the regulation of cell elongation through several pathways, involving gene expression regulation, pH modifications and cytoskeleton interactions for instance. This part will mainly focus on the effect of auxin on wall properties during cell elongation.

Auxin and cell expansion

To explore the role of auxin during cell elongation, dark-grown hypocotyls are useful model systems as most cells do not undergo cell division after germination. Transcriptomic analysis in this model system has notably highlighted 594 genes differentially regulated after 52hours in dark conditions (against only 66 differentially regulated genes between 45hours and 48hours after their transfer in dark conditions), suggesting that these genes are specifically related to cell elongation [START_REF] Pelletier | A role for pectin de-methylesterification in a developmentally regulated growth acceleration in dark-grown Arabidopsis hypocotyls[END_REF]. Moreover, transcriptomic analysis on seedling treated with exogeneous IAA have also revealed an important number, i.e., 790 genes, differentially expressed after the treatment, which include around 24 genes specifically related to cell walls [START_REF] Majda | The Role of Auxin in Cell Wall Expansion[END_REF]. Among these genes, 2 genes encode wall-loosening proteins [START_REF] Cosgrove | Loosening of plant cell walls by expansins[END_REF], 7 genes were more specifically related to pectin modifications [START_REF] Peaucelle | Pectin-Induced Changes in Cell Wall Mechanics Underlie Organ Initiation in Arabidopsis[END_REF][START_REF] Pelletier | A role for pectin de-methylesterification in a developmentally regulated growth acceleration in dark-grown Arabidopsis hypocotyls[END_REF], and 2 genes are cellulose-related genes [START_REF] Majda | The Role of Auxin in Cell Wall Expansion[END_REF]. Additionally, transcriptomic analysis after treatments with the synthetic auxin picloram (4-amino-3,5,6-trichloropicolinic acid), known to mimic auxin effect in planta and to induce hypocotyl elongation [START_REF] Savaldi-Goldstein | New auxin analogs with growth-promoting effects in intact plants reveal a chemical strategy to improve hormone delivery[END_REF], have revealed changes in the expression of 1193 auxin-responsive genes, in which, genes related to cell wall, cell expansion and hormone signaling are over-represented [START_REF] Majda | The Role of Auxin in Cell Wall Expansion[END_REF].

In addition, it has been shown that auxin induces the acidification of the apoplast, by stimulating the activity of plasma membrane H + -ATPase proton pumps [START_REF] Takahashi | Auxin Activates the Plasma Membrane H + -ATPase by Phosphorylation during Hypocotyl Elongation in Arabidopsis[END_REF]. During this process, potassium channels are activated, and potassium ions are pumped in the cytosol, which stimulates water uptake and thus, leads to an increase of tensile stress causing cell wall extension (Perrot-Rechenmann, 2010; Thiel and Weise). This phenomenon is called "acid growth" and is defined as the loosening of the walls linked to a low pH, inducing an increase in wall extensibility and promoting rapid cell elongation [START_REF] Rayle | The Acid Growth Theory of auxin-induced cell elongation is alive and well[END_REF].

Acidic environment also triggers the activation of wall-associated proteins, and it has been demonstrated that acid growth is mediated by EXPANSINs, which are non-enzymatic wallloosening proteins. These proteins are known to "unlock" the cell wall network by cutting and loosening the connections between cellulose microfibrils and non-cellulosic polysaccharide components constituting the cell wall [START_REF] Cosgrove | Loosening of plant cell walls by expansins[END_REF]. It results a cell wall loosening, as liaisons between cell wall constituents are broken, and a hydration, leading to a cell enlargement. EXPANSINs are not the only proteins to be activated by low pH values, and wall modifications are also mediated through the action of other protein families, such as CELLULASEs and xyloglucan endotransglucosylase (XTH) family members (Cosgrove, 2005). Interestingly, these proteins are also induced by auxin, and their activation results in wall loosening and increased in wall extensibility, promoting cell elongation [START_REF] Catala | Auxin regulation and spatial localization of an endo-1,4-beta-D-glucanase and a xyloglucan endotransglycosylase in expanding tomato hypocotyls[END_REF][START_REF] Mcdougall | Inhibition of auxin-stimulated growth of pea stem segments by a specific nonasaccharide of xyloglucan[END_REF]. In the SAM, although this is still debated today, the local application of expansins is sufficient to generate ectopic organogenesis [START_REF] Fleming | Induction of Leaf Primordia by the Cell Wall Protein Expansin[END_REF].

Linking auxin patterning and SAM organogenesis

We have seen above that organogenesis at the SAM relies on auxin peaks, where cell walls are softer. Immunochemistry experiments in the SAM have revealed that primordium formation is preceded by de-methyl-esterification of pectins [START_REF] Peaucelle | Arabidopsis Phyllotaxis Is Controlled by the Methyl-Esterification Status of Cell-Wall Pectins[END_REF]. In addition, microindentation results have shown that pectin de-methyl-esterification is associated with softer meristematic regions, and thus faster growth [START_REF] Peaucelle | Pectin-Induced Changes in Cell Wall Mechanics Underlie Organ Initiation in Arabidopsis[END_REF]. Although it has been shown that auxin reduces tissue stiffness locally in the SAM, and that this reduction requires pectin de-methyl-esterification [START_REF] Braybrook | Mechano-Chemical Aspects of Organ Formation in Arabidopsis thaliana: The Relationship between Auxin and Pectin[END_REF], how auxin affects pectin status in the SAM remains poorly described. Furthermore, it is unclear whether the softening of the cell wall occurs primarily in the L1 layer [START_REF] Fleming | Induction of Leaf Primordia by the Cell Wall Protein Expansin[END_REF][START_REF] Sassi | An Auxin-Mediated Shift toward Growth Isotropy Promotes Organ Formation at the Shoot Meristem in Arabidopsis[END_REF] and/or in the L2 layer [START_REF] Peaucelle | Pectin-Induced Changes in Cell Wall Mechanics Underlie Organ Initiation in Arabidopsis[END_REF]. Based on the transcriptomic analysis after auxin treatment in the hypocotyl described above, it has been hypothesized that auxin peaks in the SAM primarily activate genes regulating pectin status (e.g., PMEs, [START_REF] Braybrook | Mechano-Chemical Aspects of Organ Formation in Arabidopsis thaliana: The Relationship between Auxin and Pectin[END_REF].

Auxin also contributes to organogenesis at the SAM, by causing local changes in the direction of cell expansion [START_REF] Sassi | New insights in shoot apical meristem morphogenesis: Isotropy comes into play[END_REF]. Indeed, a study has provided evidence revealing that auxin directly interferes with wall anisotropy by modulating microtubule dynamics [START_REF] Sassi | An Auxin-Mediated Shift toward Growth Isotropy Promotes Organ Formation at the Shoot Meristem in Arabidopsis[END_REF]. At the tissue level, the degree of anisotropy is globally determined by a uniform microfibrils alignment in adjacent cells, which is itself highly dependent of microtubule orientation (Baskin, 2005;[START_REF] Paredez | Visualization of Cellulose Synthase Demonstrates Functional Association with Microtubules[END_REF]. Previous studies of cortical microtubule orientation in the SAM have shown that cortical microtubules display a specific circumferential orientation in the PZ, allowing cell growth along the vertical growth axis of the stem, and thus restricting lateral growth in the absence of auxin accumulation (Hamant et al., 2008). In their study, Sassi and collaborators, have shown that the presence auxin can disrupt this circumferential cortical microtubule organization (Figure 13A), thereby locally generating a zone an isotropic growth. The resulting conflict in directional growth is sufficient to trigger an initial bump, thus contributing to the first steps of organogenesis (Figure 13B andC) [START_REF] Sassi | New insights in shoot apical meristem morphogenesis: Isotropy comes into play[END_REF][START_REF] Sassi | An Auxin-Mediated Shift toward Growth Isotropy Promotes Organ Formation at the Shoot Meristem in Arabidopsis[END_REF].

Functional analysis of CELLULOSE SYNTHASE LIKE D (CSLD) genes have demonstrated that a subset of CSLD genes are involved in meristem maintenance, highlighting a key role of cell walls for meristem activity. More recently, the analysis of SAM morphology of the point mutants cev1 (for CESA3) and any1 (for CESA1) have shown that in these mutants, both meristem size and shape are altered. The reduced size of SAM in these mutants have been correlated with a fewer number of cells [START_REF] Sampathkumar | Primary wall cellulose synthase regulates shoot apical meristem mechanics and growth[END_REF]. However, whether this is due to cellulose defects in the SAM or related to cellulose defects in the vasculature (which is required to bring water and nutrients to the meristem) remains to be determined.

The wall properties can also be related to patterning at the SAM, notably through auxin distribution. The localization of PIN1 (pPIN1::PIN1-GFP) efflux carrier have also been monitored in the cev1 mutant. PIN1-GFP was still polarly localized at the plasma membrane, toward the domain of incipient primordia like is the WT. Interestingly, analysis of total fluorescent intensity in the central zone and the incipient primordia, have revealed a reduction of PIN1-GFP intensity in these regions in the cev1 mutant compared to the WT [START_REF] Sampathkumar | Primary wall cellulose synthase regulates shoot apical meristem mechanics and growth[END_REF]. Conversely, upon isoxaben treatment, PIN1 becomes hyper-polarized at the SAM [START_REF] Heisler | Alignment between PIN1 Polarity and Microtubule Orientation in the Shoot Apical Meristem Reveals a Tight Coupling between Morphogenesis and Auxin Transport[END_REF]. Altogether, these results suggest a role of CESA and cellulose microfibrils in the regulation of auxin in meristems, consistent with the reported link between cellulose and PIN1 [START_REF] Feraru | PIN Polarity Maintenance by the Cell Wall in Arabidopsis[END_REF].

Feedback from mechanics to genetics

Gene expression and the regulation of mechanical properties are tightly correlated. In previous parts, mechanics have been mainly defined as the result of variations of mechanical properties, generating different stiffness pattern in tissues, allowing differential growth pattern. However, this picture is not complete: when tissues are growing, or simply because they have a given shape and are pressurized, they constantly experience mechanical stress. In this part, we will analyze how such stress control cell behavior, i.e. consider forces as mechanical signals.

Definition: mechanical feedback

Plant cells in tissues not only experience a high turgor pressure as mentioned above, but they also undergo mechanical conflicts through their interaction with their neighbors. Indeed, because cells are glued together by their cell walls, differential growth can generate shear stress. This, and considering specific tissue shapes and differences in cell wall mechanical properties, intrinsic and complex mechanical stress pattern are generated through the tissue. This part focuses on how mechanical stress pattern triggers cellular responses, which in turn modulate cell growth, leading to tissue shape changes. In many cases, these changes alter the existing mechanical stress pattern in cells and tissues, thereby establishing a feedback loop [START_REF] Sampathkumar | Mechanical feedback-loop regulation of morphogenesis in plants[END_REF]. Understanding how this mechanical feedback loop controls plant morphogenesis and is involved in plant development remain opened questions. Many studies have tackled these questions, targeting different level of cellular response (e.g., molecular level (part4.2), cell level (part 4.3) and organ level (part 4.3 and 4.4)), and investigating the role of the mechanical feedback loop during different organ development.

Mechanical feedback on gene expression

Shape is achieved through a tight control between a specific genetic program and the remodeling of mechanical properties of cell walls. Indeed, although gene expression alone fails to explain how a shape is established, gene expression can lead to modification of cell wall mechanical properties, promoting cell expansion. Conversely, it has been shown that mechanical stimulations rapidly affect gene expression regulation. In total, more than 2.5% of Arabidopsis genes are significantly up-regulated after a transient touch. Many of these genes encode calcium-binding, cell wall modifying, defense, transcription factor and kinase proteins [START_REF] Braam | In touch: plant responses to mechanical stimuli: Tansley review[END_REF].

In Arabidopsis, a class of up-regulated genes after a mechanical perturbation were identified in 1990 and are known as TOUCH genes (TCH) [START_REF] Braam | Rain-, wind-, and touch-induced expression of calmodulin and calmodulin-related genes in Arabidopsis[END_REF]). Among TCH genes, TCH1 encodes one of the Arabidopsis calmodulins (CAM2) [START_REF] Braam | Rain-, wind-, and touch-induced expression of calmodulin and calmodulin-related genes in Arabidopsis[END_REF], TCH2 and TCH3 are coding CaM-like proteins (CMLs) [START_REF] Khan | Comparative modeling of the three-dimensional structure of the calmodulin-related TCH2 protein from arabidopsis[END_REF][START_REF] Sistrunk | Arabidopsis TCH3 encodes a novel Ca2+ binding protein and shows environmentally induced and tissuespecific regulation[END_REF] and

TCH4
is a xyloglucan endotransglucosylase [START_REF] Xu | Arabidopsis TCH4, regulated by hormones and the environment, encodes a xyloglucan endotransglycosylase[END_REF]. In their study, Lee and collaborators, have identified 589 genes that have a touch inducible expression, and 171 genes with decreased expression levels after touch [START_REF] Lee | Genome-wide identification of touch-and darkness-regulated Arabidopsis genes: a focus on calmodulin-like and XTH genes[END_REF]. They have also found that the expression of 12 CMLs and 4 XTHs are up-regulated by touch, while 3 XTHs displayed a reduced expression. Overall, identities of gene regulated by touch suggest that calcium and kinase signaling, but also wall modification and other downstream transcriptional responses may be affected by mechanical stimulations. Interestingly, TCH expression is also regulated by environmental, developmental and hormonal stimuli, whether these stimuli may cause mechanical perturbations that lead to activate TCH pathways remain to be defined [START_REF] Lee | Genome-wide identification of touch-and darkness-regulated Arabidopsis genes: a focus on calmodulin-like and XTH genes[END_REF].

Mechanosensitive genes were also identified in woody plants, where they can regulate growth in response to mechanical loading. For instance, application of known force on stems, leading to their bending, has been correlated with an arrest of diameter growth in tomato species and poplars [START_REF] Coutand | Biomechanical study of the effect of a controlled bending on tomato stem elongation: global mechanical analysis[END_REF]. In poplars, (populus tremula x populus alba), the gene PtaZF2, encoding a member of Cys2/His2 zinc finger protein (ZFP), is strongly expressed 5 min after bending, with a maximum level of expression 30 min later and then decreasing 1 h after bending [START_REF] Martin | Characterization and expression analysis under bending and other abiotic factors of PtaZFP2, a poplar gene encoding a Cys2/His2 zinc finger protein[END_REF]. Overexpression of PtaZF2 leads to longitudinal and cambial reductions together with modification of cell wall mechanical properties. Moreover, poplar overexpressing

PtaZF2 display a regulation level of mechanoresponsive genes weaker after stem bending compare to wild type poplar, highlighting that PtaZFP2 negatively regulates plant mechanical response [START_REF] Martin | The zinc finger protein PtaZFP2 negatively controls stem growth and gene expression responsiveness to external mechanical loads in poplar[END_REF]. Altogether, these results provide evidence that mechanical stimuli affect the regulation of mechanosensitive genes, which in turn affect cell growth.

How mechanical signals are transmitted through the cell until the nucleus and thus, affect gene expression regulation is still poorly understood, and these questions are investigated later in this introduction. However, in some cases, mechanical inputs can directly affect nucleus shape and modify nucleus mechanical properties. A recent study has shown that hyperosmotic stress decreases nuclear circularity and size and increases nuclear stiffness in root meristematic cells.

These changes have notably been accompanied by an increase of TCH gene expression [START_REF] Goswami | Mechanical Shielding in Plant Nuclei[END_REF]. Nuclear deformations have also been observed in organ-meristem boundary, where mechanical forces are supposed to be high due to the differential growth rate between the new organ and the meristem. In vivo imaging of the nuclear envelope reveals that nuclei are compressed in these regions, and for those which are the most deformed, the number of chromocenters is significantly reduced. Additionally, artificial compression could induce ectopic expression of linker histone H1.3. The methylation status of chromatin was also correlated to nucleus deformation, and such correlation was partially lost in h1.3 mutant [START_REF] Fal | Tissue folding at the organ-meristem boundary results in nuclear compression and chromatin compaction[END_REF]. These recent data provide new insights, highlighting that modulation of gene expression by mechanical forces might be directly due to both nucleus shape and mechanical properties of nucleus envelop.

Mechanical feedback on cell wall synthesis

Although the existence of a mechanical feedback on gene expression links pattern of stress with the genetic regulation of growth, it does not formally link mechanical forces to the effectors of growth, i.e. cell wall modifiers. This is the focus of this section.

Microtubule response to mechanical stress

At the cellular level, the microtubule cytoskeletal response to mechanical stress has raised major interests since their discovery in 1963, and even more in the last decades. Microtubules are key component of eukaryotic cells, constituted of polar polymers of a/ß tubulin heterodimers assembled into linear protofilaments. Usually 13 protofilaments are associated to form a rigid hollow cylinder of around 25nm in diameter. Microtubules are known as a highly dynamic structures, rapidly growing at their plus end extremity, and undergoing shrinking phases, which is also called 'dynamic instability' [START_REF] Pastuglia | Molecular encounters at microtubule ends in the plant cell cortex[END_REF]. In plant cells, microtubules are organized in four prominent microtubules arrays: cortical microtubules (CMTs), preprophase band (PPB), mitotic spindle and phragmoplast. While CMT arrays mainly regulate the direction of cell expansion, the three other microtubule arrays are involved in cell division, and intracellular trafficking of vesicles [START_REF] Hamada | Microtubule Organization and Microtubule-Associated Proteins in Plant Cells[END_REF]. Here I focus on CMTs.

By guiding CSCs through the plasma membrane, CMTs generally control the orientation of newly deposited cellulose microfibrils in the cell wall, and thus, indirectly contribute to the establishment of the cell shape. For these reasons, many studies have investigated how CMTs acquire their spatial information, and which parameters determine CMT orientation. Many studies have highlighted that CMT orientation depend on cell geometry (Ambrose et al., 2011a;[START_REF] Dixit | Encounters between Dynamic Cortical Microtubules Promote Ordering of the Cortical Array through Angle-Dependent Modifications of Microtubule Behavior[W][END_REF][START_REF] Durand-Smet | Cytoskeletal organization in isolated plant cells under geometry control[END_REF][START_REF] Lagomarsino | Microtubule Organization in Three-Dimensional Confined Geometries: Evaluating the Role of Elasticity Through a Combined In Vitro and Modeling Approach[END_REF][START_REF] Mirabet | The self-organization of plant microtubules inside the cell volume yields their cortical localization, stable alignment, and sensitivity to external cues[END_REF]). Yet, in several cases, geometry is not sufficient to predict CMT orientation. This is the case in Graptopetalum for instance, where CMTs are circumferentially oriented around the future site of organ emergence, independently from cell geometry [START_REF] Hardham | Reorganization of cortical microtubules and cellulose deposition during leaf formation in Graptopetalum paraguayense[END_REF]. In addition, CMT have been observed to reorient circumferentially in cells surrounding a wound in root of Pisum sativum (Hush and Hawes), indicating that other signals than geometrical cues can regulate CMT orientation.

This can also be illustrated with hypocotyl from dark-grown seedlings switching to light: in about 10 minutes, microtubules switch from transverse to longitudinal orientation, i.e. without any change in cell shape [START_REF] Fischer | Interaction of auxin, light, and mechanical stress in orienting microtubules in relation to tropic curvature in the epidermis of maize coleoptiles[END_REF][START_REF] Lindeboom | A Mechanism for Reorientation of Cortical Microtubule Arrays Driven by Microtubule Severing[END_REF]. Several studies have also shown a role of plant hormones in CMT organization [START_REF] Bouquin | The Arabidopsis lue1 mutant defines a katanin p60 ortholog involved in hormonal control of microtubule orientation during cell growth[END_REF][START_REF] Montesinos | Phytohormone cytokinin guides microtubule dynamics during cell progression from proliferative to differentiated stage[END_REF]. Among these cues, biophysical forces have been proposed to play a primary role in CMT orientation since the 1960s [START_REF] Williamson | Alignment of Cortical Microtubules by Anisotropic Wall Stresses[END_REF], and experimentally tested later on. Testing this hypothesis in planta has raised challenging issues, since cells experience their own endogenous mechanical stress, from their own turgor pressure and from mechanical conflicts with neighboring cells. Therefore, investigating the contribution of mechanical stress in a tissue/organ context is complex.

Several studies have taken advantage of single cell approaches to address this question. The analysis of CMT orientation in centrifuged wall-less plant cells (i.e., protoplast) have notably revealed that CMTs are oriented parallel to the centrifugal force vector, which can ultimately affect growth (Wymer and Cyr). Similar trend was observed in protoplasts embedded in agarose and then stretched, where CMT array and the axis of elongation were reoriented [START_REF] Fisher | Mechanical forces in plant growth and development[END_REF]. Using the same method, and assuming that cell division plane can be a proxy for interphasic CMT orientation, Lynch and Lintilhac have explored the impact of compression on cell division, and have highlighted that the cell division plane is determined by both geometrical and mechanical cues [START_REF] Lynch | Mechanical Signals in Plant Development: A New Method for Single Cell Studies[END_REF]. Overall, these data on single cell systems suggest a role of mechanical cues in the regulation of CMT orientation. However, the exact contribution of mechanical forces to CMT orientation has remained elusive. During my PhD, I investigated the contribution of both mechanical tension and cell geometry on CMT behavior in confined protoplasts. Taking advantage of that set-up, we found that CMTs reorient from curvature-derived geometric constraints to curvature-derived maximal tension upon pressurization (see Results Part 2).

Single cell systems represent a simpler model to determine the direction of the maximal mechanical stress, however, because cells are isolated, it does not reflect tissue context. Indeed, in tissues, many other signals have been shown to affect CMT behavior. The improvement and the combination of live imaging techniques and modeling approaches have allowed to assess both the theoretical mechanical stress pattern, and to visualize CMT organization in cells and tissues at higher spatial and temporal resolutions. Such strategy has allowed the prediction of the mechanical stress pattern at the SAM and in puzzle-shaped pavement cells of Arabidopsis cotyledons for instance, and have highlighted that CMTs align along the predicted maximal tensile stress direction in these cells (Figure 14A). Consistent with these results, CMTs usually align with the maximal tensile stress directions (Hamant et al., 2008;[START_REF] Robinson | Global Compression Reorients Cortical Microtubules in Arabidopsis Hypocotyl Epidermis and Promotes Growth[END_REF].

Experiments aiming to locally change the mechanical stress pattern in cells (e.g., tissue compression, cell ablations) indicate that CMTs reorient themselves in order to align with the new maximal tensile stress direction (Figure 14B) (Hamant et al., 2008;[START_REF] Hejnowicz | Tensile Tissue Stress Affects the Orientation of Cortical Microtubules in the Epidermis of Sunflower Hypocotyl[END_REF][START_REF] Sampathkumar | Subcellular and supracellular mechanical stress prescribes cytoskeleton behavior in Arabidopsis cotyledon pavement cells[END_REF]. These results suggest that supracellular mechanical cues can override the mechanical stress prescribed by the cell shape.

Mechanical forces regulate cell division plane orientation

When a cell divides, a new wall is installed, meaning that the tissue is mechanically reinforced in the direction of the wall locally. At a molecular level, orientation of cell division planes depends on the preprophase band (PPB), which consists of an agglomeration of CMTs forming a ring structure at the equatorial plan of the cell (Figure 15A). Interestingly, the PPB seems to indicate the position of the next division plane orientation [START_REF] Traas | Normal differentiation patterns in plants lacking microtubular preprophase bands[END_REF]. Therefore, and because the PPB largely depends of CMT orientation, it has been proposed that the impact of mechanical forces on cell division could be a mechanical stress-related CMT response.

Computational modeling and micromechanical experiments support this claim (Figure 15B and C) [START_REF] Louveaux | The mechanics behind cell division[END_REF].This conclusion also builds on a corpus of past studies [START_REF] Louveaux | The mechanics behind cell division[END_REF]. For instance, the bending of Helianthus tuberosus explants leads to more random cell division orientation [START_REF] Yeoman | Effects of Mechanical Stress on the Plane of Cell Division in Developing Callus Cultures[END_REF]. However, how mechanical forces control cell divisions is still not fully understood, and experiments conducted to investigate this question have often provided contradictory results. The compression of Coleus internodes of Nicotiana tabacum lead to cell division planes preferentially perpendicular to the compression, whereas compressing single cells from tobacco roots induce cell division planes parallel to the compression in most of the cases (Lintilhac andVesecky, 1981, 1984).

Similarly, how mechanical forces affect PPB formation and/or PPB positioning remains to be explored.

The question of cell division plane orientation is also an opportunity to discuss the relative contribution of geometry and mechanics as instructive developmental cues. The relationship between the orientation of cell division planes and cell geometry is established since a long time now, and many hypotheses explaining how cell division orientation is controlled by cell geometry have been elaborated since the end of the 19 th century. Indeed, Sachs observed that new cell walls were synthetized perpendicularly to the existing cell walls in symmetric divisions, later, Hofmeister suggested that cells divide perpendicularly to the cell's main growth axis. Finally, Errera proposed that cells behave like soap bubbles during division, in a way that they tend to minimize the area of the new cell wall between the two daughter cells (Errera, 1888). This observation was oversimplified and recapitulated in what it is called now the "Errera's rules" and, which argues that "cells divide along the shortest path". More recently, the Besson-Dumais hypothesis revisited the original Errera's analogy with soap bubbles and validated it (Figure 15D). In fact, cells do not divide along the minimum, but along one of the local minima of plane area, as prescribed by cell geometry [START_REF] Besson | Universal rule for the symmetric division of plant cells[END_REF]. Although these rules can globally describe the whole development of simple organism, such as

Coleochaete [START_REF] Dupuy | Coordination of plant cell division and expansion in a simple morphogenetic system[END_REF], they cannot be applied to all tissues. For instance, they do not reflect all cell division behavior in the cambium, where cells clearly divide along one of the longest path. Therefore, cell geometry is probably not the only one parameter involved in the control of cell division orientation.

One way to reconcile these different views is to note that for flat and/or isotropic tissues (like Coleochaete), tissues stress is isotropic. Thus, mechanical stress direction within a dividing cell would only depend on cell shape. For an elongated cell, the maximal tensile stress pattern in the wall is predicted to be circumferential. Therefore, the shortest path can also be the maximal tensile stress direction in this case. In other words, not only could mechanical stress explain exceptions to Errera's rule, but it could also explain Errera's rule itself. In fact, the analogy with soap bubbles already relies on surface tension.

The CMT mechanical feedback loop in morphogenesis

CMTs are thus in a mechanical feedback loop: CMT arrays are involved in the regulation of cell elongation, notably because CMTs usually guide the deposition of new cellulose microfibrils in cell walls. By indirectly contributing to the local reinforcing of the cell wall, CMT orientation prescribes a specific stiffness pattern, which constrains cell growth in one or another direction, and, in turn, influences the cell shape. Since a shape can be described as a 'diagram of forces' (D'Arcy [START_REF] Thompson | On Growth and Form[END_REF], CMTs in turn align to this mechanical stress pattern.

At first glance, the mechanical feedback loop mechanism seems conservative: it rather contributes to shape maintenance. For instance, for a growing cylindrical shape like a stem, maximal tensile stress direction is transverse, thus CMTs align transversely, growth occurs along the axis of the stem, and the cylindrical shape is maintained, further prescribing transverse tensile stress pattern (Figure 16A). Our recent review [START_REF] Trinh | How Mechanical Forces Shape Plant Organs[END_REF] has proposed that such a feedback could contribute to the elementary organ shapes namely spheres, cylinders and lamina. For instance, many plant organs display a flat shape, which can be easily assimilated to a lamina shape. This is the case for sepals, leaves or petals for instance. How these organs maintain their flatness remain an opened question. However, a recent study, in which experimental approaches were combined with computational modeling, has provided evidence that leaf shape depends on CMT mediated cellulose deposition along the main predicted stress orientations, in particular, along the adaxial-abaxial axis in internal tissues. These results suggest the presence of a mechanical feedback mediated through the CMT response, which could allow the maintenance, and even amplify the leave flatness (Figure 16B) [START_REF] Zhao | Microtubule-Mediated Wall Anisotropy Contributes to Leaf Blade Flattening[END_REF]. In that scenario, symmetry breaking, like the very first step of organogenesis would require additional biochemical triggers, leading to structural modifications (i.e., changes in cell wall mechanical properties). Symmetry breaking can be triggered by auxin-dependent acid growth or auxin-dependent CMT dynamics for instance [START_REF] Trinh | How Mechanical Forces Shape Plant Organs[END_REF]. Interestingly, it has been proposed that the katanin-dependent CMT response to stress maintains a basal level of growth heterogeneity in the SAM, and this could prime organogenesis, upstream of any hormonal input [START_REF] Uyttewaal | Mechanical Stress Acts via Katanin to Amplify Differences in Growth Rate between Adjacent Cells in Arabidopsis[END_REF]. Therefore, the CMT feedback loop may also have other roles in symmetry breaking too.

Mechanical feedback loop at the SAM

With its stereotypical morphology and well-documented gene expression pattern, growth and cell division pattern, the SAM can be viewed as an ideal site to investigate the contribution of mechanical feedback, and their synergy with the molecular effectors, in development.

Mechanical feedback on gene expression at the SAM

The SAM is a central driver of plant morphogenesis, producing new aerial organs during the whole plant life. However, understanding how mechanical forces impact this structure and modulate its functions remain challenging questions. Like all plant structures (i.e., leaf, sepal, part 4.3), the SAM also experiments mechanical stress. Because its shape and growth are so stereotypical, the associated mechanical stress pattern is also predictable. Note that the magnitude of external mechanical stress (like wind) are much lower in a protected structure like the SAM than in other tissues.

Here we thus focus on intrinsic mechanical stress, i.e. shape-and growth-derived stress. At the tissue scale, the mechanical stress pattern depend on local shape (e.g. local curvature) and on differential growth (e.g., mechanical conflicts between the inner and outer layer, or between two adjacent regions) [START_REF] Robinson | Mechanical control of morphogenesis at the shoot apex[END_REF]. To assess the mechanical stress pattern in the SAM, both experimental and computational approaches have been used. For instance, the analysis of the consequence of cuts, made on tissue surface, enables to determine whether the tissue surface in under tension or under compression. Such method was used in capitula (sunflower), and have shown that cuts in the dome tend to open, suggesting that the tissue is rather under tension, while cuts in the saddle shape regions tend to stay closed, suggesting that these parts are rather under compression [START_REF] Dumais | New Evidence for the Role of Mechanical Forces in the Shoot Apical Meristem[END_REF][START_REF] Hussey | Mechanical Stress in the Shoot Apices of Euphorbia, Lycopersicon, and Pisum under controlled Turgor[END_REF][START_REF] Snow | ON THE QUESTION OF TISSUE TENSIONS IN STEM APICES[END_REF]. This observation are consistent with AFM data on the CZ in Arabidopsis SAM, which confirm that the epidermis is under tension, and suggest that the meristematic dome behaves like a pressurized balloon [START_REF] Beauzamy | Mechanically, the Shoot Apical Meristem of Arabidopsis Behaves like a Shell Inflated by a Pressure of About 1 MPa[END_REF]. Considering only the shoot apex epidermis, computational modelling approaches have enabled to predict the expected pattern of stresses in outer cell walls of this tissue. In these cell walls, the tensile stress is predicted to be isotropic in the CZ, while the stresses might be anisotropic in the PZ, with the maximal tensile stress in a circumferential direction. Finally, boundary regions (i.e., zone between the dome apex and the new primordium), might undergo strong anisotropic stresses, with a tensile stress in the circumferential direction and even compressive stress in the radial direction (Figure 17A) (Hamant et al., 2008). Interestingly, boundary regions were quantitatively correlated with the activity of the promoter of several genes, such as STM or CUC3 genes (Figure 17B andD). The expression of these genes was also shown to be induced after micromechanical perturbations (Figure 17C) (Landrein et al., 2015a), suggesting that the mechanical stress in boundary regions contribute to the expression pattern of these genes. Interestingly, both STM and CUC3 are rather associated with reduced growth rate, which may further help the tissue fold at the boundary, and thus further consolidate the shape-derived stress pattern in a positive feedback loop (Landrein et al., 2015a). The fact that mechanical stresses can activate the expression of "mechanosensitive" genes in the shoot apex has been already suggested in the past.

Mechanical feedback on cell walls at the SAM

Morphogenesis requires directional cell growth, which is mainly dependent of anisotropic cell wall mechanical properties (see part2.2). Usually, cellulose microfibrils, embedded in the primary cell wall, are deposited perpendicularly to the direction of the maximal growth, and allow the local reinforcement of the cell wall. Since cellulose synthesis is closely related to CMT orientation, the organization and dynamics of CMTs at the surface of the SAM have been investigated in more details.

Studies have highlighted that CMTs display different behavior according to the region of the shoot apex (Figure 18) [START_REF] Burian | A correlative microscopy approach relates microtubule behaviour, local organ geometry, and cell growth at the Arabidopsis shoot apical meristem[END_REF]Hamant et al., 2008;[START_REF] Sakaguchi | Arrangement of cortical microtubules in the shoot apex of Vinca major L.: Observations by immunofluorescence microscopy[END_REF][START_REF] Uyttewaal | Mechanical Stress Acts via Katanin to Amplify Differences in Growth Rate between Adjacent Cells in Arabidopsis[END_REF], showing that CMTs anisotropy and organization is highly correlated with the mechanical stress pattern of the SAM. Thus, in the CZ, where the stress is mostly isotropic, CMTs look disordered and highly dynamics (i.e., in constant reorientation). Consistently, CMT anisotropy and organization increase in regions experiencing more anisotropic mechanical stress. Indeed, in PZ, CMTs display a circumferential orientation, and in boundary zones, where the stress is highly anisotropic, CMTs are aligned with the boundary (Figure 18) (Hamant et al., 2008). A careful analysis of curvature and CMT orientation in the same cells confirmed a positive correlation between isotropic curvature in the CZ on the one hand, and anisotropic curvature (even, negative curvature in the radial direction, positive curvature in the circumferential direction) and anisotropic CMT orientation in boundary on the other hand [START_REF] Burian | A correlative microscopy approach relates microtubule behaviour, local organ geometry, and cell growth at the Arabidopsis shoot apical meristem[END_REF]. However, in the PZ, the correlation is not as clear. It was proposed that the emergence of new organs, and the local growth heterogeneity may add noise. In fact, in the boundary, shape-and growth-derived stress acts synergistically to prescribe highly anisotropic tensile stress in that region, which may explain why the correlation is so strong in that domain [START_REF] Burian | A correlative microscopy approach relates microtubule behaviour, local organ geometry, and cell growth at the Arabidopsis shoot apical meristem[END_REF]. Mechanical stress is likely to influence other aspects of cell wall remodeling, although this remains to be investigated.

As mentioned before, Errera's rules are not sufficient to explain cell division behavior in the SAM, and only a restricted number of cells have been observed to follow this rule [START_REF] Shapiro | Analysis of cell division patterns in the Arabidopsis shoot apical meristem[END_REF]. More generally, only cells displaying a homogeneous growth and a local spherical shape seem to follow this rule. Therefore, in the SAM, only cells located in the CZ display cell division planes consistent with geometry rules, and the orientation of cell division planes in the saddle-shaped boundary region cannot be described with this rule. In these regions, cell division orientation planes closely correlates with a mechanical tension-based model (Figure 18) [START_REF] Louveaux | Cell division plane orientation based on tensile stress in Arabidopsis thaliana[END_REF]. Consistent with these results, it has also been shown that cell walls formed after cell ablation experiments are independent for cell geometry, and orient parallel to the direction of the stress [START_REF] Louveaux | Cell division plane orientation based on tensile stress in Arabidopsis thaliana[END_REF]. This theory, where mechanical stress pattern affects cell divisions, is consistent with the work of Linthillac and Vesecky, who have shown that compression of callus tissues led to a spatial ordering of cell division activity, establishing the new cell walls perpendicular to the compression [START_REF] Lintilhac | Stress-induced alignment of division plane in plant tissues grown in vitro[END_REF].

In particular, hypo-osmotic conditions would increase membrane tension, promote exocytosis, and thus maintain and increase PIN1 concentration at the plasma membrane [START_REF] Nakayama | Mechanical Regulation of Auxin-Mediated Growth[END_REF]. A local ablation could also modify PIN1 localization, so that PIN1 accumulate on the plasma membrane experiencing more tension (circumferential orientations) [START_REF] Heisler | Alignment between PIN1 Polarity and Microtubule Orientation in the Shoot Apical Meristem Reveals a Tight Coupling between Morphogenesis and Auxin Transport[END_REF]. Mechanistically, the exported auxin would acidify cell walls, leading to wall remodeling and softening, increased stress levels, and locally increasing membrane tension and further polarizing PIN1. Note however that mechanical perturbations have little impact on phyllotaxis, thus this mechanical feedback is likely secondary, e.g. when compared to the CMT and cell division response to stress.

Interestingly, both CMT orientation and PIN1 cellular localization respond to experimental mechanical perturbation, but one or the other is impaired (with oryzalin or NPA respectively), PIN1 or CMTs behave normally. This suggests that, while stress can act upstream of both targets, their response to stress can be uncoupled [START_REF] Heisler | Alignment between PIN1 Polarity and Microtubule Orientation in the Shoot Apical Meristem Reveals a Tight Coupling between Morphogenesis and Auxin Transport[END_REF]. This is consistent with previous works that showed that microtubules are not required for polar localization of PIN1, but actin is [START_REF] Boutte | The plasma membrane recycling pathway and cell polarity in plants: studies on PIN proteins[END_REF][START_REF] Geldner | Auxin transport inhibitors block PIN1 cycling and vesicle trafficking[END_REF]. The uncoupling between CMTs and PIN1 does not mean that they cannot act in synergy. In particular, auxin may trigger the disorganization of CMTs at site of incipient primordia. This would generate a zone of isotropic CMTs, and this is sufficient to promote the formation of an initial bulge [START_REF] Sassi | An Auxin-Mediated Shift toward Growth Isotropy Promotes Organ Formation at the Shoot Meristem in Arabidopsis[END_REF]. The coordination between CMT behavior and hormones is an avenue for future research at the SAM.

In conclusion, the existence of such mechanical feedback loops underlies that mechanical stress pattern is integrated by cells and tissues, and can be interpreted by the plant to modulate organogenesis. This, indicates that plant can sense and treat mechanical signals as developmental signals. However, the associated mechano-transduction pathways are not always well described. How can mechanical signals trigger the microtubule response? How is the mechanical environment of cells transduced into biochemical signals allowing cell adaptation? What are the structures involved in mechanical signaling pathway?

Mechano-sensing at the cell cortex

Since plants are able to respond to mechanical inputs, e.g. by reorienting their CMTs (Hamant et al., 2008;[START_REF] Sampathkumar | Subcellular and supracellular mechanical stress prescribes cytoskeleton behavior in Arabidopsis cotyledon pavement cells[END_REF] or by changing their gene expression [START_REF] Lee | Genome-wide identification of touch-and darkness-regulated Arabidopsis genes: a focus on calmodulin-like and XTH genes[END_REF], this implies that plants can sense mechanical signals. However, molecular mechanism through which plants perceive mechanical signals is still poorly understood and mechanotransduction pathways, allowing the transformation of the physical input in a chemical output triggering a response, remains largely unknown. Unlike animals, plants have not evolved a large array of specialized sensory cells or organs to perceive forces. Maybe the most famous mechanosensory cells are statocytes, which use the movement of statoliths (usually amyloplasts) to drive gravitropism [START_REF] Moulia | Posture control in land plants: growth, position sensing, proprioception, balance, and elasticity[END_REF]. However, these cells rather sense an external mechanical signal (gravity). Trichomes have also been proposed to amplify (external) mechanical signals [START_REF] Hamant | Life behind the wall: sensing mechanical cues in plants[END_REF].

More interesting for the question of the perception of intrinsic mechanical cues, i.e. shape-and growth-derived stress, the presence of actin cables in certain cell files, together with defects in posture in certain myosin mutant, suggest the existence of specialized cells able to perceive organ deformation, thereby contributing to proprioception. These cells have been coined "propriocytes", but their role is still debated [START_REF] Okamoto | Regulation of organ straightening and plant posture by an actinmyosin XI cytoskeleton[END_REF].

At the molecular scale, plants have developed strategies to detect mechanical signals, which is the focus of this section. More specifically, I will summarize what is known about cortical mechanical perception in plants, i.e. at the plasma membrane. The following reviews provide a more detailed synthesis of this subject [START_REF] Hamilton | United in Diversity: Mechanosensitive Ion Channels in Plants[END_REF][START_REF] Haswell | MscS-Like Proteins in Plants[END_REF][START_REF] Haswell | Mechanosensitive Channels: What Can They Do and How Do They Do It?[END_REF][START_REF] Monshausen | A force of nature: molecular mechanisms of mechanoperception in plants[END_REF][START_REF] Peyronnet | Mechanosensitive channels: feeling tension in a world under pressure[END_REF].

Mechanosensitive ion channels

Mechanosensitive (MS) ion channels are probably one of the most well-described mechanism for perceiving mechanical cues across kingdoms. Indeed, these proteins embedded in the plasma membrane, are able to convert (within milliseconds) mechanical stimuli, such as membrane tension or membrane curvature, into electrical or biochemical signals.

MS ion channels were first discovered in embryonic chick skeletal myocytes in 1984 [START_REF] Guharay | Stretch-activated single ion channel currents in tissuecultured embryonic chick skeletal muscle[END_REF], using the patch-clamp technique [START_REF] Hamill | Improved patchclamp techniques for high-resolution current recording from cells and cell-free membrane patches[END_REF]. This technique is largely used to characterize the activity of channels and consists to record the current across a patch of membrane, in which ion channels are embedded. To detect voltage-dependent channel activity, one modifies voltage at constant pressure; to detect mechanosensitive channels, a pressure clamp is used to apply a known hydrostatic pressure to the membrane of the patch, increasing the membrane tension and gating the MS channels present in this patch, at constant voltage [START_REF] Monshausen | A force of nature: molecular mechanisms of mechanoperception in plants[END_REF]. Later, MS ion channels have been identified in bacteria [START_REF] Martinac | Pressure-sensitive ion channel in Escherichia coli[END_REF], and finally they were found in plants [START_REF] Cosgrove | Stretch-activated chloride, potassium, and calcium channels coexisting in plasma membranes of guard cells of Vicia faba L[END_REF][START_REF] Falke | A stretch-activated anion channel in tobacco protoplasts[END_REF]. These channels are known to be involved in the perception of a large variety of mechanical signals, such as gravity, touch or osmotic homeostasis for instance. Moreover, although all ion channels, and more largely all proteins embedded in the plasma membrane, are ultimately sensitive to membrane tension and, therefore, mechanosensitive in a sense, MS ion channels are called mechanosensitive because they are primarily activated by increased tension at the plasma membrane. Indeed, tension at the plasma membrane can lead to its thinning, which modifies the environment and thus conformational state of MS channels, switching from a permissive form to non-permissive form or vice-versa.

In their review, Haswell and collaborators describe more precisely how MS channels function and how they allow the triggering of an adapted response [START_REF] Haswell | Mechanosensitive Channels: What Can They Do and How Do They Do It?[END_REF]. Briefly, two models have been proposed to explain how MS channels function: (i) the membrane-mediated mechanism and (ii) the trapdoor mechanism (Figure 19A).

In the first model, in the absence of tension, the channel is in a non-permissive form (i.e. closed state). This form corresponds to an equilibrium state. When a tension is applied, the equilibrium state is lost, and the protein conformation is changed leading to the perturbation of the interaction between the protein and the membrane. As a consequence, the channel functions can be modified, without the membrane pulling directly on the channel. The second model involves that tension and the channel are connected via an extramembrane component, such as the cytoskeleton for instance, which is attached to a trapdoor covering the channel. Without tension, the trapdoor remains closed and the channel is in a non-permissive form. When a tension is applied, the extramembrane component pulls on the trapdoor and the channel opens, switching to a permissive form. In plants, three distinct families of MS ion channels have been identified.

MscS-Like Channels

The probably most well-described family of MS ion channels correspond to the MscS-like (Mechanosensitive channel of Small conductance) and MscL-like (Mechanosensitive channel of Large conductance), which are homologs of the bacterial MS channel MscS. Ten MscSrelated proteins are present in the Arabidopsis genome [START_REF] Haswell | Mechanosensitive Channels: What Can They Do and How Do They Do It?[END_REF] and their expression pattern covers most plant tissues [START_REF] Haswell | MscS-Like Proteins in Plants[END_REF]. Furthermore, MS channels have been localized in diverse membrane types, such as membranes of plastids and mitochondria (consistent with their bacterial heritage) and the plasma membrane [START_REF] Haswell | MscS-Like Proteins in Plants[END_REF][START_REF] Haswell | MscS-like Proteins Control Plastid Size and Shape in Arabidopsis thaliana[END_REF]. Because mechanosensitive-like channels (MSL) channels have the ability to release osmolytes in response to membrane tension, MSL channels are generally associated to the regulation of osmotic forces, acting as pressure valves. For instance, MscSlike 8 (MSL8) has been identified and characterized during pollen hydration and germination, and is involved in the regulation of osmotic forces during pollen germination and pollen tube growth [START_REF] Hamilton | United in Diversity: Mechanosensitive Ion Channels in Plants[END_REF]. However, they have also been involved in more complex roles, participating to the regulation of cell death signaling [START_REF] Veley | Arabidopsis MSL10 Has a Regulated Cell Death Signaling Activity That Is Separable from Its Mechanosensitive Ion Channel Activity[END_REF], or maintaining the redox homeostasis in mitochondria during abiotic stress (Figure 19B) [START_REF] Lee | MSL1 is a mechanosensitive ion channel that dissipates mitochondrial membrane potential and maintains redox homeostasis in mitochondria during abiotic stress[END_REF].

Two-Pore Potassium channels

Plant MS ion channels also include several two-pore potassium (TPK) channels that can be mechanically gated during patch-clamp experiments [START_REF] Maathuis | Vacuolar two-pore K+ channels act as vacuolar osmosensors[END_REF]. As their name suggests, TPKs are K + selective and display two pore domains. Most of the TPK proteins are localized to the vacuolar membrane, and their activity has notably been characterized in guard cells [START_REF] Voelker | Roles of tandem-pore K+ channels in plants -a puzzle still to be solved*: Tandem-pore K+ channels[END_REF]. For instance, the AtTPK1, localized in the vacuolar membrane of Arabidopsis, is required for normal stomatal closure kinetics, K + homeostasis in several tissues types and it also plays a role during seed germination [START_REF] Gobert | The twopore channel TPK1 gene encodes the vacuolar K+ conductance and plays a role in K+ homeostasis[END_REF]. Interestingly, the expression of TPK proteins in Arabidopsis mesophyll protoplasts lacking two major vacuolar K+ channels, display an increase current in response to membrane tension and osmotic shock, indicating that TPKs are stretch-sensitive [START_REF] Maathuis | Vacuolar two-pore K+ channels act as vacuolar osmosensors[END_REF].

Calcium mechanosensitive channels

Calcium is a classic secondary messenger of mechanical deformations [START_REF] Knight | Calcium Signaling during Abiotic Stress in Plants[END_REF][START_REF] Monshausen | Ca2+ Regulates Reactive Oxygen Species Production and pH during Mechanosensing in Arabidopsis Roots[END_REF][START_REF] Toyota | Gravitropism and mechanical signaling in plants[END_REF]. Several calcium mechanosensitive channels or activities have been detected.

First, the Mid1-complementing activity (MCA) proteins, were discovered almost 20 years after the first recording of a plant MS channels because of their ability to rescue a yeast Δmid1 phenotype [START_REF] Nakagawa | Arabidopsis plasma membrane protein crucial for Ca2+ influx and touch sensing in roots[END_REF]. Interestingly, MCA proteins do not share clear sequence similarity with Mid1, and protein structural characterization has shown that MCA proteins do not resemble any other known ion channels or membrane-bound transporters [START_REF] Shigematsu | Structural Characterization of the Mechanosensitive Channel Candidate MCA2 from Arabidopsis thaliana[END_REF]. In contrast to the MSL channel family, which were essentially non-selective channels, MCA proteins appear to be Ca 2+ selective. Indeed, the overexpression of the homologues MCA1 and MCA2 proteins is correlated with an increase of Ca 2+ influx in response to hypo-osmotic stress or mechanical stimulus [START_REF] Kurusu | Plasma membrane protein OsMCA1 is involved in regulation of hypo-osmotic shock-induced Ca2+ influx and modulates generation of reactive oxygen species in cultured rice cells[END_REF][START_REF] Nakagawa | Arabidopsis plasma membrane protein crucial for Ca2+ influx and touch sensing in roots[END_REF][START_REF] Yamanaka | MCA1 and MCA2 That Mediate Ca 2+ Uptake Have Distinct and Overlapping Roles in Arabidopsis[END_REF]. Recent work has notably involved MCA channels in response to gravity signals in plants. For instance, MCA-overexpressing seedlings are hypersensitive to increased gravity, and the hypocotyl elongation growth is suppressed under hypergravity conditions, while these effects were reduced in hypocotyls of mca-null mutants [START_REF] Hattori | MCA1 and MCA2 Are Involved in the Response to Hypergravity in Arabidopsis Hypocotyls[END_REF]. Moreover, gravistimulation experimentsi.e., changes in the gravity vectorinduces a biphasic Ca 2+ concentration increase, characterized by a fast-transient Ca 2+ concentration increase followed by a slow one. Knockout mutation of MCA1 proteins strongly attenuates this second slow wave of Ca 2+ , involving MCA1 proteins in gravity sensing [START_REF] Nakano | The gravistimulationinduced very slow Ca2+ increase in Arabidopsis seedlings requires MCA1, a Ca2+-permeable mechanosensitive channel[END_REF]. Interestingly, MCA1 proteins have also been involved in cold-induced cytosolic Ca 2+ increase and in cold tolerance in Arabidopsis [START_REF] Mori | Ca2+-permeable mechanosensitive channels MCA1 and MCA2 mediate cold-induced cytosolic Ca2+ increase and cold tolerance in Arabidopsis[END_REF].

More generally, in plants, MCA1 and MCA2 proteins are mainly localized at the plasma membrane and in endomembrane of plant cells. Finally, in other studies, MCA1 protein was suggested to be involved in cell-wall damage signaling pathways. It has been notably proposed that MCA1 could play a role in sensing membrane tension changes caused by a reduction of the turgor pressure upon cell-wall loosening [START_REF] Hamann | Plant cell wall integrity maintenance as an essential component of biotic stress response mechanisms[END_REF].

Recent studies have identified two members of OSCA family, AtOSCA1.1 and AtOSCA3.1, as mechanosensitive channels gated during patch-clamp experiments (Zhang et al., 2018). Structural investigation by Cryo-EM techniques has revealed similarities with a protein membrane family (TMEM16) of which some members constitute a calcium-activated chloride channel [START_REF] Jojoa-Cruz | Cryo-EM structure of the mechanically activated ion channel OSCA1[END_REF]Zhang et al., 2018). Moreover, mutation of OSCA1 exhibit osmotic-stress related defects [START_REF] Yuan | OSCA1 mediates osmotic-stress-evoked Ca2+ increases vital for osmosensing in Arabidopsis[END_REF].

DEK1 proteins, which are crucial for epidermis specification and embryo development, have been associated with a mechanically activated CA 2+ current. Although the exact identity of the channel remains mysterious, the dek1 mutant shows an intriguing correlation between the lack of force perception and the lack of a true epidermis, in an organism where epidermis is under tension (Figure 19B) [START_REF] Tran | A mechanosensitive Ca2+ channel activity is dependent on the developmental regulator DEK1[END_REF].

PIEZO proteins are very large membrane proteins found in all kingdoms, including in plants.

Although the role of PIEZO proteins has been little investigated outside the animal kingdom, recent studies have progressed in the understanding of their functions in plants. For instance, recent work has shown that PIEZO proteins are expressed in the columella cells and at the root tip in Arabidopsis, and seems to be involved in root mechano-transduction. Indeed, PIEZO proteins are required for root penetration in solid medium, and piezo mutants exhibit diminished calcium transients in response to mechanical stimuli [START_REF] Mousavi | PIEZO ion channel is required for root mechanotransduction in Arabidopsis thaliana[END_REF]. These results are consistent with data recently obtained in moss, which show that PIEZO proteins allow the release of calcium from the vacuole towards the cytosol in response to hypoosmotic shock [START_REF] Radin | Regulation of Vacuole Morphology by PIEZO Channels in Spreading Earth Moss[END_REF]. Regarding plant cell mechanicsa large vacuole pressing both the cytoplasm and the plasma membrane against a stiff cell wallthese results confirm that PIEZO proteins could play an essential role in plant mechano-sensing (Figure 19B). Altogether, these elements provide interesting perspectives to investigate deeper the diversity of mechanosensing channels in plant membranes.

Cell wall sensors

Since the discovery that cell wall fragments released during a pathogen attack can serve as elicitors to trigger plant defense response, it clearly appears that the cell wall integrity (CWI) signaling is also a source of information for the plant [START_REF] Wolf | Growth Control and Cell Wall Signaling in Plants[END_REF]. Interestingly, it has been shown that chemical or genetic inhibition of cellulose synthesis leads to compensatory changes in plants, including ectopic lignification, enhanced callose deposition, modification of pectin methyl-esterification degree, increased of jasmonic acid level, increased production of reactive oxygen species (ROS) [START_REF] Hamann | Plant cell wall integrity maintenance as an essential component of biotic stress response mechanisms[END_REF]. Although exact pathways behind CWI signaling remain to be determined, a certain number of wall sensors, monitoring CWI, have been identified and major ones are described below. These sensors belong to the very large family of membrane-localized RECEPTOR-LIKE KINASE (RLKs), and more specifically to the subfamily CrRLK1L (Catharanthus roseus RLK family). This subfamily contains 17members and most of them are characterized by an extracellular malectin-like domain [START_REF] Lindner | CrRLK1L receptor-like kinases: not just another brick in the wall[END_REF].

Because in animals malectin domain can bind to dimeric and oligomeric glucose chains, it has been hypothesized, and in some cases shown, that the malectin-like domain of CrRLK1L family could bind wall components. This extracellular domain probably detects chemical signatures derived from the cell wall after mechanical inputs rather than directly sense mechanical cues.

CrRLKs family: sensors of cell wall integrity

The best-studied CrRLKs member is FERONIA, which is involved in wide range of pathways, such as pollen tube reception in the female gametophyte [START_REF] Liu | Pollen PCP-B peptides unlock a stigma peptide-receptor kinase gating mechanism for pollination[END_REF], root and root hair development, hormone signaling, and CWI [START_REF] Li | Extracellular matrix scaffolding guides lumen elongation by inducing anisotropic intercellular mechanical tension[END_REF]. FERONIA is binding pectins, and in vivo experiments have shown that FERONIA is required to maintain CWI during salt stress, notably through this interaction with pectins and also by inducing transient Ca 2+ bursts that are necessary for cell adaption to salt stress [START_REF] Feng | The FERONIA Receptor Kinase Maintains Cell-Wall Integrity during Salt Stress through Ca2+ Signaling[END_REF].

In their recent review, Anderson and Kieber [START_REF] Anderson | Dynamic Construction, Perception, and Remodeling of Plant Cell Walls[END_REF] describe the mechanism behind FERONIA signaling during root hair growth and in the female gametophyte post-pollination [START_REF] Duan | FERONIA receptor-like kinase regulates RHO GTPase signaling of root hair development[END_REF][START_REF] Duan | Reactive oxygen species mediate pollen tube rupture to release sperm for fertilization in Arabidopsis[END_REF]. This signaling pathway involves a large number of partners such as GEF proteins and GTPase proteins, which in turn regulate NADPH oxidasederived ROS species levels. Furthermore, loss of function of FERONIA leads to drastic growth defects and developmental phenotypes. For instance, fer mutants typically display bulging or bursting root hair cells [START_REF] Duan | FERONIA receptor-like kinase regulates RHO GTPase signaling of root hair development[END_REF][START_REF] Guo | Three related receptor-like kinases are required for optimal cell elongation in Arabidopsis thaliana[END_REF]. Interestingly, similar phenotype of bursting cells have been observed in anx1 anx2 double mutant, which are the closest homologues of FERONIA and expressed in the pollen tube [START_REF] Lindner | CrRLK1L receptor-like kinases: not just another brick in the wall[END_REF]. As for FERONIA, these two receptors display an extracellular malectin-like domain which may sense CWI [START_REF] Li | Extracellular matrix scaffolding guides lumen elongation by inducing anisotropic intercellular mechanical tension[END_REF]. Altogether these results suggest that FERONIA, ANXUR1 and ANXUR2 could sense changes in the mechanical equilibrium of cell walls, and could be involved in the initiation of compensatory processes to maintain CWI [START_REF] Monshausen | A force of nature: molecular mechanisms of mechanoperception in plants[END_REF]. However, the role of FERONIA in CWI mechano-sensing is still unclear and further experiments are required to determine whether it is a direct or an indirect role.

CrRLK1L family also includes THESEUS1, which was identified in a screen for suppressors of cellulose synthase 6-deficient mutant, called procuste1-1. Indeed, in their study, Hematy et al., have shown that THESEUS1 is expressed in elongating cells and mediates the response of growing plant cells to the perturbation of cellulose synthesis. These observations suggest that THESEUS1 may act as a CWI sensor, activated when cell wall properties are compromised [START_REF] Hématy | A Receptor-like Kinase Mediates the Response of Arabidopsis Cells to the Inhibition of Cellulose Synthesis[END_REF]. However, it has also been noticed that THESEUS1 is involved in the regulation of cell elongation, even in the absence of external stress. This last point highlights that stress responses and growth control probably share common signaling pathways.

Note that both FER and THE1 are binding RALF peptides (Figure 20). This suggests that either CWI integrity involves biochemical signals in addition to, or via, mechanical signals. This family of proteins may provide one of the best templates to analyze the possible synergy between biochemical and mechanical signals.

Wall-associated kinases (WAKs) are pectin receptors

The wall-associated kinases (WAKs) belong to a subfamily of RLKs and are constituted of 5 members. Although the characterization of WAKs functions have been largely hampered by a redundancy and clustered localization of the five WAK genes in a 30kb chromosomal region, making difficult to obtain double or triple mutants, it has become apparent that WAKs may act as wall sensors. First, WAKs are among the few RLKs for which the binding to pectin if formally established. More specifically, it has been shown that the N-terminal part of the extracellular domain of WAKs can bind both pectin and pectin-derived molecules [START_REF] Decreux | In vitro characterization of the homogalacturonan-binding domain of the wall-associated kinase WAK1 using site-directed mutagenesis[END_REF]. Second, WAKs are involved in plant defense, and can be activated by fragmented pectins, such as oligo-galacturonic acids produced during wounding (Kohorn and Kohorn, 2012). Interestingly, plants expressing a dominant allele of WAK2 (WAK2cTAP) exhibit lots of hallmarks of a pathogen effect, yet without the pathogen, which is consistent with the role of WAKs in pathogen response (Kohorn et al., 2012).

Cytoskeleton

On the inner side of the plasma membrane, and as in animal cells, the cytoskeleton can respond to mechanical stress in plant cells. Interestingly, in animal cells, it has been proposed that the actin cytoskeleton could even act as a mechanosensor. In vitro experiments have shown that actin depolymerization is significantly delayed in the presence of cofilin (i.e. actin depolymerization factor) when the actin filament is under tension. Moreover, tension in the actin filament reduces the cofilin binding and results in a decrease in its effective severing activity [START_REF] Hayakawa | Actin filaments function as a tension sensor by tension-dependent binding of cofilin to the filament[END_REF]. Altogether, these results show that tension prevents actin depolymerization by cofilin. In another study, it has been observed that bending of actin filament, when the cell is under compression, promotes actin branching [START_REF] Risca | Actin filament curvature biases branching direction[END_REF].

Plants affected in their actin cytoskeleton do not display strong phenotypes. This relates to the dominant role of microtubule in cellulose synthesis, and the more minor role of actin in wall synthesis, through vesicle trafficking.

Consistently, plant cells exhibit low density of actin at their cortex (when compared to animal cells). Yet, there is evidence that actin can respond to mechanical cues in plants too. For instance, in response to local ablation, actin filaments become circumferential around the wound [START_REF] Goodbody | Actin filaments line up acrossTradescantia epidermal cells, anticipating wound-induced divison planes[END_REF]. It must be noted that actin and microtubule have synergistic roles in the organization of their respective networks [START_REF] Sampathkumar | Live Cell Imaging Reveals Structural Associations between the Actin and Microtubule Cytoskeleton in Arabidopsis[END_REF].

It is however unclear whether actin respond before or after the microtubules. Whether actin can act as an autonomous mechanosensor in plant cells remains to be investigated.

There is more support for microtubules to be mechanosensors (Hamant et al., 2019a). The first argument relates to the microtubule structure, which seems to be adapted to sense mechanical cues at subcellular scale. Indeed, microtubules can be assimilated as thick and stiff tubes, which allow them to maintain their anisotropic shape, but also a given direction over a large part of the cell. Microtubules are also characterized by a high persistence length (around 5 200µm in vitro), which can be defined as a mechanical property quantifying the bending stiffness of a polymer, showing that microtubules are rigid structures over cellular dimensions [START_REF] Gittes | Flexural rigidity of microtubules and actin filaments measured from thermal fluctuations in shape[END_REF]. Moreover, in silico experiments have shown that cortical microtubules tend to spontaneously populate at the cell cortex, and to grow along the plasma membrane [START_REF] Mirabet | The self-organization of plant microtubules inside the cell volume yields their cortical localization, stable alignment, and sensitivity to external cues[END_REF]. This behavior is probably increased in vivo with the presence of anchoring proteins linking cortical microtubules to the plasma membrane. This position at the cell cortex makes microtubules particularly suited to respond to wall stress changes.

Furthermore, several in vitro studies have investigated the impact of tension on individual microtubule behavior. For instance, by combining gliding assays with stretchable PDMS substrate, microtubules, initially showing random movements, were observed aligning themselves along tension lines when substrate was stretched [START_REF] Inoue | Sensing surface mechanical deformation using active probes driven by motor proteins[END_REF]. In another study, Franck and collaborators [START_REF] Franck | Tension applied through the Dam1 complex promotes microtubule elongation providing a direct mechanism for length control in mitosis[END_REF] have taken advantage of optical tweezers to trap and then pulled a kinetochore protein (Dam1), itself attached to microtubule's end to test the effect of tension on microtubule dynamics (Figure 21C).

These experiments have shown that when microtubules are stretched, their shrinking rate is reduced to one third of its initial value, indicating that tension can reduce microtubule depolymerization. Moreover, the shrinking rate is immediately affected during rapid changes between the different force regimes, suggesting that microtubules can directly sense tension changes. Through its interaction with both the cell wall and the plasma membrane, microtubules are, therefore, an ideally candidate to sense, transduce and respond to mechanical stimuli. However concrete evidence still lacks to clearly determine this role and the impact of mechanical stress on microtubules.

One issue with the putative role of microtubules as mechanosensory in cellulo, is the relative contribution of cell geometry and mechanical stress in the final microtubule behavior. Several studies, including in silico, in vitro and in vivo experiments, have highlighted that cortical microtubules tend to align with the cell long axis, when cells stop growing, suggesting that cortical microtubules could be sensitive to cell geometry by default [START_REF] Durand-Smet | Cytoskeletal organization in isolated plant cells under geometry control[END_REF][START_REF] Lagomarsino | Microtubule Organization in Three-Dimensional Confined Geometries: Evaluating the Role of Elasticity Through a Combined In Vitro and Modeling Approach[END_REF][START_REF] Mirabet | The self-organization of plant microtubules inside the cell volume yields their cortical localization, stable alignment, and sensitivity to external cues[END_REF]. This orientation could be explained by the high persistence length of microtubules, which would make them avoid the curviest part of the cell, and thus align with the longest axis of the cell.

It has also been shown that microtubules depolymerize when they encounter sharp cell-edges head-on, while microtubules which are parallel to those sharp-edges remain. This phenomenon can be overcome by CLASP protein (i.e microtubule-associated protein) which accumulates at these specific cell edges. In other words, CLASP, and partners, would counterbalance the high persistence length of microtubules to allow them to curve without depolymerizing at cell edges (Ambrose et al., 2011b). However, the contribution of cell geometry on microtubule orientation has been tested independent of mechanical inputs. Computational simulations suggests that the geometrical bias is weak, and thus that mechanical inputs may override it above a small threshold (Figure 21D) [START_REF] Mirabet | The self-organization of plant microtubules inside the cell volume yields their cortical localization, stable alignment, and sensitivity to external cues[END_REF].

To conclude, the impact of geometry and mechanics on microtubule organization remains largely debated with evidence for both hypotheses and further experiments are required to determine clearly the contribution of each one. In our work, we have developed a system enable to test both the effect of cell geometry and mechanical constraints on the microtubule organization. By using single cell model (i.e. wall less plant cells), we were able to predict the mechanical stress pattern in confined protoplasts, and to apply different mechanical tension by adding adapted osmotic solutions, allowing the swelling or the plasmolysis of the cells (see result part 2).

6. Plasma membrane: more than a structural compartment, a critical checkpoint for the cell While other cell compartments and components, such as the cell wall or the cytoskeleton described above, have been the focus of many studies to understand how plant cells sense and respond to their mechanical environment, the plasma membrane has received much less attention. Yet, through its position at the interface of the cell wall and the cytosol and through its role as a host of many mechanosensors, the plasma membrane is likely a key mechanosensing player. The plasma membrane is also known as a highly dynamic structure, due to its lipid composition, regulating both cell trafficking (Noack and Jaillais, 2017) and cell signaling [START_REF] Colin | Phospholipids across scales: lipid patterns and plant development[END_REF][START_REF] Di Paolo | Phosphoinositides in cell regulation and membrane dynamics[END_REF]. Although many studies start to decipher the role of the plasma membrane in cell signaling, its contribution in mechanical signaling pathways remains largely unknown. The following part aims to describe briefly the plasma membrane composition and to open on how this complex compartment could contribute to mechano-transduction.

6.1 The lipid composition of the plasma membrane:

"Structural" lipids and "signaling" lipids

The plasma membrane is principally constituted of lipids (phospholipids an sterols), proteins, and carbohydrates groups, that are attached to some lipids or proteins. While proteins mainly help the cell to interact with its environment, lipids ensure both a structural and signaling role.

"Phospholipids, also known as glycerophospholipids, are a class of lipids whose structure is based on a glycerol backbone that connects a hydrophobic tail -consisting of two long-chain fatty acids linked at the sn-1 and sn-2 position (diacylglycerol) -and a hydrophilic head group. This specific structure provides them an amphiphilic nature, and therefore, phospholipids are key structural components of membrane bilayers, with the fatty acid chains aggregating together in the core of the bilayer and the hydrophilic heads on both sides" (Figure 22A) [START_REF] Colin | Phospholipids across scales: lipid patterns and plant development[END_REF]. Among the phospholipid class, two "categories" can be distinguished (i) 'structural' lipids and (ii) 'signaling' lipids.

The first group is constituted of abundant lipids, such as the phosphatidylcholine (PC) and phosphatitdylserine (PS), which are essential to establish a hydrophobic bilayer. Although they are considered as structural lipids, recent evidences have highlighted that these lipids can accumulate and form patterns, which have consequences on cell behavior and thus, could act also as signaling lipids [START_REF] Platre | Developmental control of plant Rho GTPase nano-organization by the lipid phosphatidylserine[END_REF]. The second group is rather constituted of low abundant lipids, involved in the regulation of membrane functions. This group includes phosphatidic acid (PA) and phosphatidyl-inositol-phosphates (PIPs). PIPs are minor phospholipids, which can be phosphorylated on the 3rd, 4th and/or 5th position of the inositol head group to generate up to seven PIP species, such as phosphatidylinositol-4-phosphate (PI4P) and phosphatidylinositol-4,5-bisphosphate (PI(4,5)P 2 ) (Figure 22B) [START_REF] Heilmann | Phosphoinositide signaling in plant development[END_REF].

Signaling lipid patterns contribute to plant development

Such lipid patterns at the plasma membrane have notably been observed for the PI(4,5)P2 and their contribution in Arabidopsis development have been recently in one of the reviews I contributed to write during my PhD [START_REF] Colin | Phospholipids across scales: lipid patterns and plant development[END_REF]. The main points are copied from the review below:

"Evidence for PI(4,5)P 2 patterning at the tissue scale comes from quantitative imaging studies of PI(4,5)P 2 sensors lines [8]. These transgenic lines stably express PI(4,5)P 2 binding domains fused to a fluorescent protein as an indirect way to localize this phospholipid [9][10][11][12]. Indeed, such fusion proteins are recruited to membranes that accumulate this lipid [12]. By contrast, in the absence of its target lipid, the sensor accumulates in the cytoplasm as a default localization [12]. In some cases, the chronic absence of the biosensor cognate lipid induces its subsequent destabilization and degradation. For example, the C2 domain of the bovine Lacthaderin protein

(C2 Lact
), a PS-binding domain, is unstable and degraded when expressed in a mutant background that lacks PS biosynthesis [START_REF] Burian | A correlative microscopy approach relates microtubule behaviour, local organ geometry, and cell growth at the Arabidopsis shoot apical meristem[END_REF]. Quantitative 3-D imaging revealed that the PI(4,5)P 2binding Plekstrin Homology (PH) domain of Phospholipase C (PH PLC ) accumulates to a low extent at the center of the shoot apical meristem in Arabidopsis, while it is stabilized in the boundary region (Figure 2a) [8]. By analogy to the C2 Lact sensor, one may speculate that destabilization of PH PLC occurs when PI(4,5)P 2 levels are low.

This hypothesis was recently substantiated in cotyledons, as PH PLC accumulates about fourfold when seedling are treated with a high concentration of NaCl (a condition known to induce PI(4,5)P 2 synthesis [10]) or U-73122 (which inhibits PI(4,5)P 2 hydrolysis by phosphoinositidespecific-PLC (PI-PLC) and thereby promotes its accumulation) [START_REF] Lindeboom | A mechanism for reorientation of cortical microtubule arrays driven by microtubule severing[END_REF]. Although the exact role of the PI(4,5)P 2 pattern in the shoot apical meristem needs to be defined, it could be involved in the two main functions of the meristem: stem cell maintenance and organogenesis. For instance, in the clv3-17 mutant, which displays a larger central zone with more stem cells, the PI(4,5)P 2 pattern tends to disappear, suggesting that destabilization of the PH PLC sensor correlates with stem cell maintenance [8]. The shoot apical meristem is also characterized by a typical mechanical stress pattern, with strong and highly anisotropic tensions in boundaries compared to the central zone (Figure 2a) [15]. A positive correlation between the accumulation of PI(4,5)P 2 sensors and mechanical stresses in the boundary zones suggests that the PI(4,5)P 2 pattern could be linked with tissue mechanics and mechanical signal transduction (Figure 23A) [8]. Future work will reveal how this PI(4,5)P 2 pattern is established and what its function is in shoot meristem biology. Lipid sensors are not the only clues pointing at the importance of specific PI(4,5)P 2 patterns at the tissue level. Indeed, PI4P 5-kinases (PIP5K), PI(4,5)P 2 5phosphatases, and PI-PLCs have tissue-specific expression patterns [16][17][18][19][20][21]. For example, PIP5K1, PIP5K2, PLC3, and PLC5 are expressed in the root meristem and in vascular tissues and PIP5K2 expression is regulated by the phytohormone auxin [16][17][18][19][20].

Furthermore, the plasma membrane-localized 5-phosphatase COTYLEDON VASCULAR PATTERN2 (CVP2) is expressed in developing vascular cells in various organs and displays exquisite expression specificity for the protophloem in the root [22,23,[START_REF] Molines | Physical properties of the cytoplasm modulate the rates of microtubule growth and shrinkage[END_REF][START_REF] Hejnowicz | Tensile tissue stress affects the orientation of cortical microtubules in the epidermis of sunflower hypocotyl[END_REF]. CVP2 and its homolog CVP2-LIKE1 (CVL1), as well as PIP5K1 and PIP5K2 are involved in venation pattern establishment in cotyledons (Figure 23B), while plc2, plc3, and plc5 mutants have root architecture phenotypes (Figure 23C) [17,19,20,22]. The cvp2 cvl1 double mutant root protophloem fails to fully differentiate, as revealed by the presence of undifferentiated 'gap' cells within protophloem strands (Figure 2b) [START_REF] Hejnowicz | Tensile tissue stress affects the orientation of cortical microtubules in the epidermis of sunflower hypocotyl[END_REF]. Surprisingly, CVP2 overexpression, which promotes PI(4,5)P 2 processing into PI4P, also induces protophloem gap cells and phenocopies the cvp2 cvl1 double mutant, which accumulates PI(4,5)P 2 (Figure 2b) [START_REF] Hejnowicz | Tensile tissue stress affects the orientation of cortical microtubules in the epidermis of sunflower hypocotyl[END_REF]. Further-more, inducible overexpression at the plasma membrane of a highly processive PIP5K, which boosts PI(4,5)P 2 production at the expense of the PI4P pool, also induces gap cells in developing protophloem (Figure 2b) [START_REF] Molines | Physical properties of the cytoplasm modulate the rates of microtubule growth and shrinkage[END_REF]. Therefore, it appears that the PI(4,5)P 2 /PI4P balance, specifically in protophloem cells, rather than the absolute amount of PI(4,5)P 2 is critical for the correct differentiation of this tissue (Figure 2b) (Figure 23D).

Cellular analyses revealed a correlation between increased vacuolar trafficking upon the alteration of the PI(4,5)P 2 /PI4P ratio and protophloem differentiation, suggesting that vacuole biogenesis and/or related endocytic trafficking regulated by these phosphoinositides could be linked with phloem development [START_REF] Molines | Physical properties of the cytoplasm modulate the rates of microtubule growth and shrinkage[END_REF]. Furthermore, PIP5K1 and PIP5K2 are not only localized at the plasma membrane but also in the nucleus [17,18]. Nuclear targeting is actively regulated, at least in the case of PIP5K2 [START_REF] Robinson | Global compression reorients cortical microtubules in Arabidopsis hypocotyl epidermis and promotes growth[END_REF]. These localizations suggest that PI(4,5)P 2 could also have a direct role in gene expression regulation, which has been reported in animal systems [START_REF] Franck | Tension applied through the Dam1 complex promotes microtubule elongation providing a direct mechanism for length control in mitosis[END_REF][START_REF] Celler | Microtubules in plant cells: Strategies and methods for immunofluorescence, transmission electron microscopy, and live cell imaging[END_REF].

Overall, these data indicate that the establishment of specific PI(4,5)P 2 accumulation pattern at the tissue level are hallmarks of tissue differentiation, at least in some cases. Some of the future challenges will be to sort which of the pleiotropic functions of this signaling lipids could be instrumental to regulate tissue differentiation."

The identification of a stereotypical PI(4,5)P2 pattern at the SAM raised questions about the potential role of this phosphoinositide in SAM activities. During my PhD, I investigated how these lipids could contribute to SAM functions. Because this specific pattern was found to correlate with the mechanical stress pattern at the SAM, I also tested the impact of mechanical stress pattern changes on PI(4,5)P2 dynamics (see part1 of the Results). More generally, how mechanical stress could affect plasma membrane composition or contribute to the generation of lipid patterns at the plasma membrane is still an open question.

Contribution of the plasma membrane to mechano-transduction

How is the plasma membrane involved in mechanical signaling pathways? More specifically, what is the role of the plasma membrane composition/regulation in mechano-transduction? Despite an increased interest for mechanobiology during the past years, these questions have been poorly investigated and remain largely open [START_REF] Ackermann | The Plasma Membrane-An Integrating Compartment for Mechano-Signaling[END_REF].

The plasma membrane is thought to be under tension because of the high turgor pressure in plant cells, and the indirect attachment of the plasma membrane to the cell wall and cortical cytoskeleton. This membrane tension is defined as the force per unit length acting on a crosssection of membrane, and directly affect the structure of the plasma membrane, by making it thinner when it is stretched for instance. Consequently, membrane tension directly modulates the events occurring at the plasma membrane, but it also impacts membrane-proteins interactions.

Membrane tension affects cell trafficking and membrane-protein interactions

One of the main effects of modification of membrane tension results in modifications of cell trafficking, including endocytosis and exocytosis. Indeed, exocytosis is promoted when plasma membrane tension increases, while the use of ethanol and dimethyl sulfoxide (DMSO), which are both known to decrease the plasma membrane rigidity and tension, enhance endocytosis (Figure 24A) [START_REF] Gurtovenko | Modulating the Structure and Properties of Cell Membranes: The Molecular Mechanism of Action of Dimethyl Sulfoxide[END_REF]. By affecting trafficking, membrane tension can also impact proteins localization and recycling. For instance, several studies indicate that PIN1 protein localization is sensitive to mechanical stress. Indeed, it has been shown that mechanical perturbations (e.g., osmotic treatments or tissue compression), leading to modification of membrane tension, affect the amount and intracellular localization of PIN1 in tomato shoot apex [START_REF] Nakayama | Mechanical Regulation of Auxin-Mediated Growth[END_REF]. Consistent with these results, it has also been shown that PIN1 distribution correlates with the principal direction of mechanical stress in Arabidopsis SAM, suggesting that auxin could be mechanically regulated (Figure 24B and C) [START_REF] Heisler | Alignment between PIN1 Polarity and Microtubule Orientation in the Shoot Apical Meristem Reveals a Tight Coupling between Morphogenesis and Auxin Transport[END_REF][START_REF] Murray | Systems Analysis of Shoot Apical Meristem Growth and Development: Integrating Hormonal and Mechanical Signaling[END_REF].

Furthermore, changes in membrane tension also impacts the function and distribution of proteins already present at the plasma membrane [START_REF] Andersen | Bilayer Thickness and Membrane Protein Function: An Energetic Perspective[END_REF][START_REF] Engelman | Membranes are more mosaic than fluid[END_REF]. Indeed, the application of tension to a membrane modifies its structure, e.g., increases its thickness or curvature, that can in turn alter the energetic balance of proteins, leading, for example, to the stabilization of the open state of channels. For instance, and as mentioned earlier, it has been shown that modification of membrane tensions are required to open or gate MscL mechanosensitive channels [START_REF] Perozo | Open channel structure of MscL and the gating mechanism of mechanosensitive channels[END_REF]. In their review, Haswell and collaborators precisely describe how the membrane tension can be transmitted to the channel (e.g., MscL channels), and thus lead to a conformational change, without a direct link between the channel itself and the surrounding membrane. In short, conformational changes of the channel result in membrane deformation that has a free energy cost. For instance, open channels have larger perimeter and thus induce a higher deformation in the surrounding membrane.

Signal transduction: plasma membrane and cytoskeleton are tightly associated

Since the plasma membrane faces the interior of the cell, it is closely linked to the cytoskeleton. This association is mediated through proteins. For instance, the CSI1 proteins physically bind CSCs and microtubules. Several proteins have been identified to link microtubules to the lipid bilayer, and could play a role in signal transduction from the plasma membrane to the cytoskeleton, or vice-versa. Among them, CLIP-associating proteins (CLASPs) were identified in plants, where they control microtubule dynamics and the organization of microtubule networks [START_REF] Ambrose | The Arabidopsis CLASP Gene Encodes a Microtubule-Associated Protein Involved in Cell Expansion and Division[END_REF]. Indeed, Clasp-1 mutants display a partial detachment of microtubules from the cortex, and detached microtubules undergo extensive waving, distortion and changes in orientation [START_REF] Ambrose | CLASP Modulates Microtubule-Cortex Interaction during Self-Organization of Acentrosomal Microtubules[END_REF]. Moreover, it has been demonstrated through live-imaging and computational modelling, that CLASP proteins, which accumulate at cell edges, overcome edge-induced microtubule depolymerization and enables microtubule growth around sharp edges. Overall, these data suggest that CLASP activity contribute to self-organization of cortical microtubules by governing microtubule-cortex attachment [START_REF] Ambrose | CLASP Modulates Microtubule-Cortex Interaction during Self-Organization of Acentrosomal Microtubules[END_REF]. Further studies are required to investigate the role of plasma membrane composition and/or tension in CLASP functions (Figure 25).

Interestingly, proteins involved in the regulation of plasma membrane composition have been proposed as potential microtubules-plasma membrane proteins linking. The most famous, and probably also the most contested, is the Phospholipase-D (PLD), involved in PA synthesis. This idea is mainly supported by one study, which show that a 90 kDa peptide (p90) in tobacco, sharing sequence similarity with Arabidopsis PLDδ, display a PLD activity and was associated with the plasma membrane and microtubules when transiently expressed in Bright Yellow2 (BY2) cells [START_REF] Gardiner | A 90-kD phospholipase D from tobacco binds to microtubules and the plasma membrane[END_REF]. This association would be mediated through the PH/PX or C2 membrane association domain [START_REF] Qin | The Arabidopsis Phospholipase D Family. Characterization of a Calcium-Independent and Phosphatidylcholine-Selective PLDζ1 with Distinct Regulatory Domains[END_REF]. However, the physical link between the PLD and plasma membrane remains largely discussed and deserves further investigations. Nonetheless, other data suggest that PLD could act on microtubules via its products (i.e. PA). Indeed, it has been shown that PA can interact with MICROTUBULE-ASSOCIATED PROTEINS (MAP65-1), inducing microtubule bundling. Accordingly, decreased PA levels in a pldα1 mutant resulted in microtubule depolymerization and salt sensitivity [START_REF] Zhang | Phosphatidic Acid Regulates Microtubule Organization by Interacting with MAP65-1 in Response to Salt Stress in Arabidopsis[END_REF] (Figure 25).

Rho-GTPases in plants (ROPs) have also been highlighted as interesting candidates to link microtubules and PM [START_REF] Zheng | The Rop GTPase: an emerging signaling switch in plants[END_REF]. ROPs are specifically addressed to the plasma membrane by lipid-based post-translational modifications [START_REF] Zheng | The Rop GTPase: an emerging signaling switch in plants[END_REF]. ROPs can both interact with the plasma membrane and other proteins, and are key player in the regulation of plant growth and development. Two ROPs, ROP2 and ROP6, together with their interactors, ROP-interactive CRIB motif-containing protein1 (RIC1), have been identified to mediate microtubule-plasma membrane association [START_REF] Wu | A genome-wide analysis of Arabidopsis Ropinteractive CRIB motif-containing proteins that act as Rop GTPase targets[END_REF]. RIC1 shows clear microtubule localization in pavement cells in vivo [START_REF] Fu | Arabidopsis Interdigitating Cell Growth Requires Two Antagonistic Pathways with Opposing Action on Cell Morphogenesis[END_REF]. Both in vitro and in vivo studies have shown that RIC physically interacts with KATANIN1 in Arabidopsis, promoting microtubulesevering [START_REF] Lin | Rho GTPase Signaling Activates Microtubule Severing to Promote Microtubule Ordering in Arabidopsis[END_REF]. The increased severing resulted in higher proportion of parallel microtubules and less lobes of Arabidopsis pavement cells [START_REF] Lin | Rho GTPase Signaling Activates Microtubule Severing to Promote Microtubule Ordering in Arabidopsis[END_REF].

Moreover, it has been reported that ROP2 and ROP6 antagonistically regulate the binding of RIC1 to microtubules. Indeed, while activated ROP2 binds to RIC1 and depletes RIC1 from microtubules, active ROP6 seems to promote the association of RIC1 with cortical microtubules [START_REF] Fu | Arabidopsis Interdigitating Cell Growth Requires Two Antagonistic Pathways with Opposing Action on Cell Morphogenesis[END_REF][START_REF] Fu | A ROP GTPase signaling pathway controls cortical microtubule ordering and cell expansion in Arabidopsis[END_REF]. These results illustrate that pavement cell shape is tightly controlled through a dynamic interplay of ROPs and their interactions with the plasma membrane and microtubules (Figure 25).

This list is not exhaustive, and other candidates have been identified as potential protein linker between microtubules and the plasma membrane in plants and are discussed in the following review [START_REF] Liu | The connection of cytoskeletal network with plasma membrane and the cell wall[END_REF]. Overall, this part highlights the central role of the plasma membrane in signaling, and thus potentially in mechano-transduction. Indeed, we have seen, that both biophysical and biochemical properties of the plasma membrane affect its behavior, and thereby its interactions with the other compartments of the cells (e.g., cell wall, cytoskeleton), through modification of protein localization or function. Besides its role of hydrophobic bilayer, the plasma membrane is crucial for signal transduction, and although its role in mechanotransduction remains largely unknown, many studies have demonstrated that membrane tension triggers cell responses. Similar studies have been conducted in animals, and sometimes knowledge is more advanced in animal cells, which could represent a good starting point for further studies in plants.

Highlights from cortical mechano-transduction in animal cells

In animals, mechano-sensitive responses have been involved in several major cellular processes (e.g., cell motility [START_REF] Keren | Cell motility: the integrating role of the plasma membrane[END_REF], cell polarity [START_REF] Asnacios | The mechanics behind cell polarity[END_REF][START_REF] Houk | Membrane Tension Maintains Cell Polarity by Confining Signals to the Leading Edge during Neutrophil Migration[END_REF], cell differentiation [START_REF] Engler | Matrix Elasticity Directs Stem Cell Lineage Specification[END_REF]. Mechano-sensing in animal cells is mainly ensured by transmembrane proteins, mechanosensitive channels and cytoskeletal and adhesion proteins.

Focal adhesion sites are multiprotein structures discovered in the 1970s, and identified as complex signaling hubs involved in mechano-transduction. Among all the proteins constituting focal adhesions, integrins are transmembrane proteins, which provide a physical link between the extracellular matrix (ECM) and the intracellular machinery, including the actin cytoskeleton. Mechanical signals trigger protein conformation change. For instance stretching of fibronectin, a major component of the ECM, triggers conformational changes of integrins, increasing their affinity for their ligands (e.g., talin) [START_REF] Asnacios | The mechanics behind cell polarity[END_REF]. The binding protein talin is also mechanosensitive, and the stretching of this protein by the actomyosin machinery enhances the exposition of crucial binding sites, facilitating its activation [START_REF] Goult | Talin as a mechanosensitive signaling hub[END_REF]. This ultimately leading to changes in actin cortex behavior.

A large number of studies has shown that the physical link between integrins and the actincytoskeleton machinery is critical for mechano-sensing, but also for cell motility. Cell motility process is the result of the constant polymerization of the actin cytoskeleton, located at the leading edge of the cell, into filamentous actin (F-actin). The force resulting from this polymerization generates a retrograde flow of actin, inducing the recruitment of integrins/Factin binding proteins.

The retrograde flow of actin can be then converted into a traction force, pulling on the ECM and allowing the formation of cellular protrusions (Figure 26A) [START_REF] Jansen | Mechanotransduction at the cell-matrix interface[END_REF][START_REF] Sun | Integrin-mediated mechanotransduction[END_REF]. This mechanism highlights that focal adhesions ensure bidirectional mechanotransduction pathways (i.e., from the ECM to intracellular compartment and reciprocally).

Interestingly, many studies have also shown that mechanical forces drastically affect focal adhesion formation, maturation and stability. The use of magnetic twisting device, allowing direct applications of mechanical forces on cell surface, has revealed that mechanical stimulation of the extracellular receptor integrin ß1 induces focal adhesion formation, leading to the increase of cytoskeleton stiffness [START_REF] Wang | Mechanotransduction across the cell surface and through the cytoskeleton[END_REF]. Consistently, several studies have shown that decrease mechanical stress can lead to the reduction of focal adhesion size, until their disassembly in absence of mechanical stimulation [START_REF] Balaban | Force and focal adhesion assembly: a close relationship studied using elastic micropatterned substrates[END_REF][START_REF] Chrzanowska-Wodnicka | Rho-stimulated contractility drives the formation of stress fibers and focal adhesions[END_REF], while mechanical stimulation promotes focal adhesion maturation (Figure 26B) [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].

In animal cells, the plasma membrane is directly in contact with the ECM, representing the main physical barrier between intracellular compartments and the environment. Many studies have provided evidence that the plasma membrane could directly act as a mechano-transducer compartment. In their review, Le Roux and colleagues, highlight how mechanical stress can trigger different membrane responses through the modification of membrane tension [START_REF] Le Roux | The plasma membrane as a mechanochemical transducer[END_REF]. For instance, tensile stress (e.g., hypoosmotic shocks, substrate stretching) induce an increase of membrane tension, which has been correlated with an increase of exocytosis [START_REF] Gauthier | Temporary increase in plasma membrane tension coordinates the activation of exocytosis and contraction during cell spreading[END_REF]. By contrast, compressive stress decrease membrane tension, and rather promote endocytosis. In addition, modification of membrane tension directly impacts plasma membrane organization and ordered (Figure 26C). This, can lead to an increase of lipids orders in the case of tensile stress, or conversely, to phosphoinositide clusters, membrane curvature or lipid packing defects under compressive stress [START_REF] Le Roux | The plasma membrane as a mechanochemical transducer[END_REF]. Formation of lipid raft domains and/or modification of membrane curvature can be recognized by specific proteins, which can subsequently activate different signaling pathways. Finally, membrane tension also contributes to conformational changes of mechanosensitive channels inserted into the plasma membrane, allowing their switch to an open state [START_REF] Haswell | Mechanosensitive Channels: What Can They Do and How Do They Do It?[END_REF][START_REF] Zhang | From membrane tension to channel gating: A principal energy transfer mechanism for mechanosensitive channels: Membrane Tension to Channel Gating[END_REF].

Altogether, these data provide some insights for putative transposition in plant cells. Note however that many of the focal adhesion proteins are not present in the plant genome. Yet, analogous structures may be found, such as Hechtian strands which could reflect local cell wall plasma membrane attachment points, possibly involving RGD-binding proteins [START_REF] Gouget | Lectin Receptor Kinases Participate in Protein-Protein Interactions to Mediate Plasma Membrane-Cell Wall Adhesions in Arabidopsis[END_REF]. This remains to be investigated. In particular, the RGD ligand in the cell wall is unknown.

Objectives:

In my PhD, I investigated how mechanical signals at the cell cortex contribute to plant development. I addressed this question focusing on the contribution of the plasma membrane, (both its composition and mechanical status), using a multiscale approach involving genetics, imaging and micromechanics.

Objective 1

To address the role of plasma membrane composition in development, one needs tools to target specific phospholipid for their synthesis, hydrolysis, or conversion. PI (4,5)

Objective 2

How orientation of CMTs is determined have been extensively debated. While many studies have reported that CMTs align with the cell geometry, other studies have shown that CMT array align with the maximal tensile stress direction, independently of cell shape. My second goal was to assess the relative role of tension and cell geometry on microtubule behavior, using a simpler single cell approach, consisting to confine wall-less plant cells (i.e., protoplast) in different sized and shaped microwells. This was also an opportunity to test the impact of different intensity of pressurization (different osmolarity) and for different times (dynamics).

Objective 3

Last, to address the contribution of plasma membrane in plant mechanics and morphogenesis, one can use a reverse genetics approach. Plant overexpressing the phospholipase PLAIIIß (p35S::PLAIIIß) display a global reduction of their lipid content, and are characterized by a reduced mechanical strength caused by a reduced cellulose content. My third goal was to use this line to investigate how cellulose biosynthesis process could be affected by PM lipid composition, and whether this could also affect the mechanical feedback on CMTs.

RESULTS

1-Contribution of PI(4,5)P 2 phosphoinositide in SAM activities

1-1 Summary

Phosphoinositides represent a small percentage of membrane lipids, yet, they ensure key regulatory functions involved in a large variety of signaling pathways [START_REF] Noack | Functions of Anionic Lipids in Plants[END_REF]. Previous studies have highlighted significant enrichments of some of these phosphoinositides at the cell, tissue and organ scales, sometimes establishing distinct patterns [START_REF] Colin | Phospholipids across scales: lipid patterns and plant development[END_REF][START_REF] Platre | Anionic lipids and the maintenance of membrane electrostatics in eukaryotes[END_REF]. Among these patterns, a stereotypical PI(4,5)P2 pattern has been previously identified at the SAM (Stanislas et al., 2018). The use of specific biosensor of PI(4,5)P2 (pPDF1::2xPH PLC -mCit) (Simon et al., 2014) suggests that the phosphoinositide is accumulating at organ-meristem boundary zones, while in the central zone of the meristem, the PI(4,5)P2 content is reduced (Stanislas et al., 2018). Organ-meristem boundary regions are crucial for organ separation, axillary meristem emergence and meristem self-maintenance. Interestingly, these regions are also zones of highly anisotropic tensile stress (Hamant et al., 2008), highlighting an eventual correlation between the PI(4,5)P2 pattern and the predicted mechanical stress pattern at the SAM (Stanislas et al., 2018). How such pattern is established and maintained, and whether it contributes to SAM functions remain open questions.

During my PhD, I investigated the role of the PI(4,5)P2 phosphoinositide in SAM activities. To address this question, I used a new genetically encoded and inducible system amenable to deplete specifically the PI(4,5)P2 at the plasma membrane, developed by Mehdi Doumane a previous PhD student in the Jaillais group. This system (also referred as iDePP: Inducible Depletion of PI(4,5)P2 in Plants) consists in fluorescently-labelled (mCherry) phosphatase domain (called dOCRL) fused to a myristoylation and palmitoylation (MAP) sequence to specifically and only target the PI(4,5)P2 located at the plasma membrane. This phosphatase domain converts the PI(4,5)P2 into PI4P, thus decreasing PI(4,5)P2 level at the plasma membrane. Because constitutive depletion of PI(4,5)P2 drastically affects germination and plant development, the expression of the enzyme is inducible, thanks to the dexamethasone-inducible GVG system (UBQ10pro:GVG:MAP-mCH-dOCRL). In parallel, two other versions of this tool were developed as negative controls, i.e. expressing a dead version of the phosphatase (UBQ10pro:GVG:MAP-mCH-dOCRL dead ) and a version in which the phosphatase domain is replaced by 3xmCherry (UBQ10pro:GVG:MAP-3xmCH) [START_REF] Doumane | Inducible depletion of PI(4,5)P2 by the synthetic iDePP system in Arabidopsis[END_REF].

I have first tested and confirmed the expression and the efficiency of the active version, and the non-efficiency for both negative controls in different aerial parts of Arabidopsis thaliana, such as cotyledons and dissected meristems. During this process, I observed that the active version of the phosphatase is homogeneously expressed in cotyledons after 16h on MS medium supplemented with 5µM of Dexamethasone (DEX). Consistently, upon dOCRL induction, a localization 'by default' in the cytoplasm of the PI(4,5)P2 biosensor is observed, suggesting that PI(4,5)P2 levels at the plasma membrane are decreased.

Quantification of the global content of PI(4,5)P2 (i.e., measurement of radiolabeled PI(4,5)P2 incorporation) before and after induction in the three lines showed that PI(4,5)P2 levels are decreased by 90% when the phosphatase is active, while PI(4,5)P2 levels were not affected in the negative control lines. In addition, similar quantifications confirmed that DEX induction did not affect the level the other classes of phospholipids. Altogether, these data confirm that this new tool correctly targets the PI(4,5)P2 phosphoinositide, and strongly affects the PI(4,5)P2 content at the plasma membrane. I also observed that the expression of the phosphatase in dissected meristems is not homogeneous. In particular, after 16h of induction, the expression of the dOCRL remained largely restricted to the boundary regions, which is consistent with the reported increased activity of the UBQ10 promoter in that domain (Figure 27A). Yet, prolonged exposure to DEX (e.g. after 4days on MS medium supplemented with Dex) could lead to a more homogeneous expression of the dOCRL in the SAM.

The principal function of the SAM is to ensure the production of all above-ground organs during the whole life-span of the plant. To test whether the PI(4,5)P2 could contribute to this function, seedlings expressing the inducible system were grown on MS medium supplemented with NPA.

NPA is an inhibitor of auxin transport and therefore, NPA-treated plants display naked stems and meristems (i.e., without any flowers). Organ initiation can be restored 4 days after the transfer of NPA-treated meristems toward a medium without NPA (figure). Interestingly, plants expressing the active form of the phosphatase displayed a clear-cut defect in organ initiation 4 days after their transferred in MS medium without NPA. By contrast, plants expressing the dead version of the phosphatase initiated new organs 4 days after their transfer. Altogether, these results suggest that PI(4,5)P2 plays a role in the organ initiation process.

In this study, my contribution was to perform the tests to validate the expression and the efficiency of the iDePP tool in different aerial parts of Arabidopsis thaliana, by testing several concentrations of DEX and comparing several times of induction. In parallel, I used this tool to investigate the role of the PI(4,5)P2 phosphoinositide in meristems (both dissected meristem and NPA-treated meristems).

1-3 Discussion

Investigating the role of the PI(4,5)P2 phosphoinositide in plants has remained challenging since phospholipid synthesis process is complex, and compensatory effects through rapid conversion of PI4P in PI(4,5)P2, or vice-versa, can rapidly occur. PI (4,5)P2 is produced by PI4P 5-kinases (PIP5K), however constitutive mutations on these enzymes often lead to drastic effects on seed germination and plant development. The use of drugs, such as PAO, does not directly target the PI(4,5)P2 and can induce unwanted and unexpected effects. Last, inducible tools were available in plants, but they were designed to increase PI(4,5)P2 levels, and not to decrease them. In this paper, we have developed a new inducible and genetically encoded system, iDePP, which specifically and rapidly (within 3hours) dephosphorylates PI(4,5)P2 at the plasma membrane.

Using this system, we have provided evidence that PI (4,5)P2 in involved in the regulation of several plant developmental processes, such as root elongation, root hair formation and organ initiation.

Here, by using the iDePP system in NPA-treated meristems, I have shown that decreased PI(4,5)P2 levels at the plasma membrane can prevent organ initiation in naked meristems. How PI(4,5)P2 affects organ initiation in NPA systems remains completely unknown. Interestingly, previous studies in roots have highlighted that the pip5k1 pip5k2 double mutant (also exhibiting reduced PI(4,5)P2 levels) is affected in auxin transport and displays abnormal localization of PIN1 and PIN2 auxin efflux carriers [START_REF] Ischebeck | Phosphatidylinositol 4,5-Bisphosphate Influences PIN Polarization by Controlling Clathrin-Mediated Membrane Trafficking in Arabidopsis[END_REF]. In addition, this double mutant also exhibits defects in clathrin-mediated endocytosis process, which is required for PIN cycling and polarization [START_REF] Ischebeck | Phosphatidylinositol 4,5-Bisphosphate Influences PIN Polarization by Controlling Clathrin-Mediated Membrane Trafficking in Arabidopsis[END_REF]. Altogether, these results suggest an important role of PI(4,5)P2 phosphoinositide in auxin distribution, notably through the regulation of PIN cycling. Further experiments should investigate whether auxin transport and/or distribution is affected at the SAM when PI(4,5)P2 levels are lower. Finally, and regarding the specific enrichment of PI(4,5)P2 at the organ-meristem boundary, we could also hypothesize that PI (4,5)P2 contribute to organ separation or to other boundary functions. Therefore, it would be interesting to analyze the expression of markers of organ separation (e.g., CUC, STM) and meristem maintenance (e.g., STM, WUS, CLV3).

To further investigate how the PI(4,5)P2 pattern contribute to SAM function, I used the iDePP system to perturb the PI(4,5)P2 pattern in dissected floral meristems. However, the dOCRL phosphatase signal in dissected floral meristems is restricted to the boundary regions. As mentioned in the introduction, this could be explained by the use of Ubiquitin10 promoter, which is known to be more active in boundary zones of meristems. To be cautious, the inducible system with the active form and the dead version of the phosphatase should be cloned again with a promoter homogeneously active in the SAM. However, because PI(4,5)P2 accumulates in boundary regions, as well as the dOCRL phosphatase, the iDePP system could remain pertinent to perturb the PI(4,5)P2 pattern at the boundary in the short term and to study the related effects.

Other functions could be explored, notably relating to organ growth. I obtained some preliminary results that are summarized here. Dissected floral meristems expressing the iDePP tool with the active dOCRL form were transferred in ACM medium supplemented with 10µM of DEX, and imaged under a confocal microscope during several days. Organ growth were first monitored by measuring the size to each organ every 24h. Preliminary results suggest that organ growth could be slightly reduced in meristems with lower PI(4,5)P2 levels (Figure 27B). However, these results should be considered with a lot of caution since no statistical tests have been performed due to the few numbers of replicates. Moreover, several controls are required to further confirm or not this trend (e.g., quantification on meristems expressing the dead version, DEX effects on growth?).

Last, PI (4,5)P2 can also serve as precursor of secondary messengers. Indeed, hydrolysis of PI (4,5)P2 by phospholipases generates two metabolites: diacylglycerol (DAG) and inositol 1,4,5-trisphosphate (IP3), that have been reported to be involved in signaling pathways [START_REF] Di Paolo | Phosphoinositides in cell regulation and membrane dynamics[END_REF]. While it is known that the DAG is rapidly phosphorylated in PA to have a number of regulatory effects [START_REF] Yao | Phosphatidic acid plays key roles regulating plant development and stress responses: PA in regulating plant signaling and development[END_REF], the IP3-related pathways in plants remains almost completely unknown, and this tool may be used to investigate that question too in the future.

In plants, apart from the studies highlighting a role of the PI(4,5)P2 in the regulation of clathrinmediated endocytosis, evidence supporting signaling roles for this phosphoinositide remains limited. Here, using the iDePP tool, we not only confirmed that PI(4,5)P2 regulates clathrinmediated endocytosis process, but we also revealed that PI(4,5)P2 homeostasis affects plant cytoskeleton organization. Indeed, after DEX induction, actin dynamics as well as microtubule anisotropy were affected in the root elongation zone. However, how PI(4,5)P2 might regulate plant cytoskeleton dynamics remains largely unknown. Although, no direct evidence of a regulation of the actin cytoskeleton by the PI(4,5)P2 has been provided so far, in vitro experiments have indicated that the PI(4,5)P2 could promote actin polymerization by inhibiting actin-depolymerization enzymes [START_REF] Gungabissoon | Interaction of maize actin-depolymerising factor with actin and phosphoinositides and its inhibition of plant phospholipase C.: Maize ADF: interaction with actin and lipids[END_REF]. In contrast to plants, PI(4,5)P2related signaling pathways have been extensively studied in animal cells, and this phosphoinositide has been involved in a myriad of cell events (e.,g., trafficking, cell adhesion, cell migration, cytoskeleton assembly) [START_REF] Sun | Phosphatidylinositol 4,5bisphosphate: Targeted production and signaling: Prospects & Overviews[END_REF]. PI(4,5)P2 interact with the actin cytoskeleton, and many cytoskeleton-binding proteins [START_REF] Yin | Phosphoinositide Regulation of the Actin Cytoskeleton[END_REF] . For instance, PI(4,5)P2 can promote actin polymerization through its interaction with actin binding proteins [START_REF] Yamamoto | Phosphatidylinositol 4,5-Bisphosphate Induces Actin Stress-Fiber Formation and Inhibits Membrane Ruffling in Cv1 Cells[END_REF][START_REF] Yin | Phosphoinositide Regulation of the Actin Cytoskeleton[END_REF].These interactions between the plasma membrane and the cytoskeleton are crucial for many cellular processes, such as cell adhesion and cell migration, and also play a key role in mechano-transduction.

In animal cells, focal adhesions are large macromolecular assemblies, through which external mechanical signals are perceived and converted into biochemical signaling events [START_REF] Jansen | Mechanotransduction at the cell-matrix interface[END_REF]. Several studies have suggested a key role of PI (4,5)P2 in the regulation of focal adhesions formation and activity, notably through its interaction with several focal adhesion proteins (e.g., talin, vinculin). For instance, PI(4,5)P2 is critical for the anchorage of focal adhesion kinases, which are involved in diverse functions during embryonic development [START_REF] Zhou | Mechanism of Focal Adhesion Kinase Mechanosensing[END_REF]. In addition, PI(4,5)P2 enrichment increases talin-1 affinity for ß3-integrin, which allows integrin activation [START_REF] Moore | Affinity of talin-1 for the 3-integrin cytosolic domain is modulated by its phospholipid bilayer environment[END_REF]. Integrins are key proteins of focal adhesions, linking the extra cellular matrix to the actin cytoskeleton through its interaction with different cytoskeletal binding proteins (e.g., vinculin, talin). Therefore, by affecting integrin interaction with the other component of focal adhesions, PI(4,5)P2 directly modulate the actin cytoskeleton dynamics in response to mechanical stress.

Overall, these data strongly suggest that PI(4,5)P2 content indirectly control mechanotransduction signaling pathways by affecting either the localization or the activity of focal adhesion proteins. Although no focal adhesion analogs have been yet identified in plants (except for Hechtian strands, arguably), these data could highlight a scenario in which, PI (4,5)P2 could contribute to mechano-transduction pathways in plants. Interestingly, PI (4,5)P2 pattern observed at the SAM correlates with the predicted mechanical stress pattern, with an accumulation of PI(4,5)P2 biosensors where mechanical stress is of high magnitude and highly anisotropic. In addition, microtubules are also highly organized in these regions. The iDePP tool offers an avenue to investigate the contribution of PI(4,5)P2 in microtubule dynamics, and to move beyond a mechanics-PI(4,5)P2-microtubule correlation.

2-Cortical tension overrides geometrical cues to orient microtubules in confined protoplasts

2-1 Summary

In plants, microtubules largely determine the direction of cell expansion, through the guidance of cellulose microfibrils deposition, and the orientation of cell division planes. However, what processes orient the microtubules has remained debated. Indeed, several in silico and in vitro studies have highlighted a longitudinal CMT orientation, i.e., following the cell long axis [START_REF] Dixit | Encounters between Dynamic Cortical Microtubules Promote Ordering of the Cortical Array through Angle-Dependent Modifications of Microtubule Behavior[W][END_REF][START_REF] Lagomarsino | Microtubule Organization in Three-Dimensional Confined Geometries: Evaluating the Role of Elasticity Through a Combined In Vitro and Modeling Approach[END_REF][START_REF] Mirabet | The self-organization of plant microtubules inside the cell volume yields their cortical localization, stable alignment, and sensitivity to external cues[END_REF], suggesting a role of geometrical cues in CMT orientation. Interestingly, analysis of CMT orientation in planta has rather revealed a transverse orientation of CMTs (Hamant et al., 2008;[START_REF] Kutschera | The epidermal-growth-control theory of stem elongation: An old and a new perspective[END_REF][START_REF] Sampathkumar | Subcellular and supracellular mechanical stress prescribes cytoskeleton behavior in Arabidopsis cotyledon pavement cells[END_REF], which correlates with the predicted maximal tension direction in cylindrical pressurized vessels. In this study, we took advantage of single-cell systems to analyze the response of microtubules to cell geometry and cortical tension. The set-up was initially tested at the MechanoBiology Institute in Singapore (by Antoine Chevallier (M2 student) and Olivier Hamant (on sabbatical with Tim Saunders and Virigile Viasnoff), and was then imported in the team in Lyon. This is when I took over to perform all the experiments listed below.

By using an adapted version of a microwell set-up, we confined protoplasts in different size and shaped-microwells to impose a curvature ratio, and we modulated the cortical tension through the addition of either hypotonic (i.e., increased surface tension) or hypertonic (i.e., decreased surface tension) solutions. The analysis of the distribution of CMT orientation in two different rectangular shaped-microwells (15x20µm and 12x40µm) revealed a transverse CMT orientation in pressurized cells, suggesting that CMT align with the predicted maximal tension direction in these protoplasts. Consistently, protoplasts confined in a square-shaped microwells, i.e. where tension is isotropic, did not display this transverse orientation bias, and CMT orientation appeared isotropic. Based on the Laplace-Young law, the maximal tensile stress is predicted to be transverse in such pressurized shapes. The tension pattern in pressurized protoplasts confined in rectangular shapes was also confirmed using FEM simulations for a confined ellipsoid with an aspect ratio (length/width) of 1.15, which is similar with what we measured in confined cells (1.13-1.17). The simulations were performed by Florian Gacon, in Christophe Godin's team. Altogether, these results suggest that mechanical cues can affect CMT orientation, independently of cell geometry.

To really assess the contribution of the surface tension in CMT orientation, we then confined cells in same rectangular microwells but protoplasts were exposed to a hypertonic solution (800mOsmol/L mannitol instead of 280mOsmol/L mannitol) to reduce the surface tension. We hypothesized that if CMTs align with the tension pattern, the transverse bias should be less pronounced when the cortex tension is decreased. Depressurization allowed highly deformed protoplast geometry, with the protoplast edge following the microwell geometry, consistent with reduced tension. As predicted, the CMT transverse bias was lost in these cells, and a global longitudinal bias was observed, i.e., CMT aligned with the cell long axis. Overall, these experiments highlighted that in absence (or reduced) of surface tension CMTs align according to cell geometry (long axis), and that pressurization is required for CMT transverse orientation, suggesting that mechanical cues could overcome geometrical information.

Because CMTs are dynamic structure, time-lapse experiments were then conducted in order to catch CMT reorientation process. Protoplasts were confined for 2h in 12x40µm rectangular microwells in a hypertonic solution (600mOsmol/L of mannitol) and a first image was taken. Then, the hypertonic solution was replaced by a hypotonic solution (280mOsmol/L of mannitol) to increase the tension surface, and cells were images each 20min during 1hour. New transverse CMT progressively appeared upon pressurization, suggesting that pressurization could drive CMT orientation. To test whether CMT maintain their transverse orientation along the time without any osmolarity changes, we performed long-term kinetics, and we imaged pressurized cells confined in 12x40µm 16h hours after their introduction in microwells. While the same population of cells displayed a transverse orientation bias after 2h in microwells, this transverse bias shift to a longitudinal orientation bias after 16h in microwells, indicating that CMT transverse orientation is not stable during time. These results are consistent with a scenario in which CMTs align with changes in maximal tension, and return to their geometry-derived orientation in absence of tension changes.

2-2 PUBLICATION 2

Cortical tension overrides geometrical cues to orient microtubules in confined protoplasts In plant cells, cortical microtubules (CMTs) generally control morphogenesis by guiding cellulose synthesis. CMT alignment has been proposed to depend on geometrical cues, with microtubules aligning with the cell long axis in silico and in vitro. Yet, CMTs are usually transverse in vivo, i.e., along predicted maximal tension, which is transverse for cylindrical pressurized vessels. Here, we adapted a microwell setup to test these predictions in a single-cell system. We confined protoplasts laterally to impose a curvature ratio and modulated pressurization through osmotic changes. We find that CMTs can be longitudinal or transverse in wallless protoplasts and that the switch in CMT orientation depends on pressurization. In particular, longitudinal CMTs become transverse when cortical tension increases. This explains the dual behavior of CMTs in planta: CMTs become longitudinal when stress levels become low, while stable transverse CMT alignments in tissues result from their autonomous response to tensile stress fluctuations.

microtubule | cell geometry | cortical tension | protoplast | Arabidopsis
T he relative contribution of cell geometry and forces in cyto- skeleton organization has been a long-lasting debate in cell and developmental biology, particularly given the implications for cell division plane determination (1)(2)(3)(4). In plants, the organization of the cytoskeleton has a direct impact on cell expansion and morphogenesis (5). Contrary to animal cells, which are often soft and contractile, plant cells are stiff and pressurized. Their mechanics rely on two parameters: turgor pressure (of osmotic origin) and a stiff cell wall which physically constrains the cell (6). Cellulose microfibrils are the main load-bearing components of the wall. Their deposition occurs at the plasma membrane through the activity of cellulose synthases. While the trajectory of cellulose synthase can be biased by preexisting cellulose microfibrils (7), the deposition of new cellulose microfibrils is usually guided by cortical microtubules (CMTs) (8) In silico simulations of microtubule self-organization suggest that, because of their high persistence length, microtubules should align along the cell long axis (9). Consistently, microtubules growing in confined environments in vitro (microwells) tend to align with the longitudinal axis of the well (10). More recently, wallless plant cells, also called protoplasts, have been confined in agar microwells and hyperosmotic conditions, and CMTs were found to align with the long axis of the protoplast (11). Although such alignments can be observed in nongrowing plant cells in vivo, CMTs are usually transverse in growing cells in vivo (5). To explain this discrepancy, additional factors thus need to be considered.

First, molecular factors at cell edges, like CLASP proteins, could allow CMTs to bend as they grow and, thus, bias the final orientation of the CMT arrays (12). However, microtubules can have transverse and longitudinal orientations in adjacent cells at the shoot apical meristem [START_REF] Burian | A correlative microscopy approach relates microtubule behaviour, local organ geometry, and cell growth at the Arabidopsis shoot apical meristem[END_REF]. Furthermore, microtubules can rapidly shift from transverse to longitudinal orientation upon light-induced growth arrest without any change in cell geometry [START_REF] Lindeboom | A mechanism for reorientation of cortical microtubule arrays driven by microtubule severing[END_REF]. Last, local ablations can induce reorientations of CMTs, without major change in cell geometry (15). Therefore, additional factors must be involved, e.g., to modulate CLASP localization or CMT dynamics. A three-dimensional (3D) computational model managed to recapitulate CMT behavior in the first stages of Arabidopsis embryo development by including CLASP-dependent microtubule stability at cell edges and auxin regulation of microtubule dynamics (16).

Although molecular regulators at cell edges are likely to play a key role in CMT orientation, the transverse orientation of CMTs could also be explained without a contribution of cell edges. Indeed, CMTs may indirectly align with maximal tensile stress direction in the cell wall, i.e., the transverse direction for a pressurized elongated cylinder (17,15). This stress-based scenario is supported by the frequent correlation between predicted tensile stress direction and CMT orientation in several tissues, with or without mechanical perturbations (18). It also provides a mechanism for plant cells to resist tensile stress, as in Wolff's law where bones remodel themselves to resist the load. However, the exact pattern of stress remains debatable, because of the additional complexity brought about by the tissue context. Furthermore, how the CMTs sense the tensile status of the cell wall remains an open problem. In a recent perspective, we proposed that microtubules may be able to autonomously align with changes

Significance

In plants, microtubules largely determine the direction of cell expansion and the orientation of cell division planes. However, what processes orient the microtubules has remained debated. Here, we used microfabricated wells to confine and deform wallless plant cells in a controlled way to analyze the response of microtubules to cell geometry and surface tension. We demonstrate that microtubules align with cell geometry by default, whereas when surface tension increases (e.g. when turgor pressure increases), they align with the direction of maximal tension. Not only does this explain many observations in plant tissues, but it also provides a simple mechanism at the core of plant morphogenesis, in which microtubules can spontaneously align with tension, in a typical self-organized system.

in maximal tension (18). Here, we adapted a single-cell microwellbased method on wallless Arabidopsis protoplast to test this prediction.

Here, we find that CMT orientation depends on curvature anisotropy. CMTs shift their orientation from curvature-derived steric constraints to curvature-derived maximal tension depending on pressurization. Because this behavior does not rely on the presence of a cell wall, this also provides further support for an autonomous microtubule mechanosensing mechanism.

Results

Cortical Microtubules Primarily Align in the Transverse Direction in Confined and Pressurized Protoplasts. CMTs are sensitive to curvature-derived steric constraints due to their high bending stiffness. In elongated cells, they are expected to align longitudinally, i.e., along the direction of lower curvature (or the flattest direction) (Fig. 1A). For a pressure vessel, tension and curvature are related by Laplace-Young law, ΔP = 2γ/R, with P for pressure, γ for surface tension, and R for radius of the vessel. In short, at equilibrium, maximal tension is in the direction of minimal radius or maximal curvature (SI Appendix, Text and Fig. S1). In an elongated pressure vessel like a plant cell, maximal tension is transverse to the long axis (Fig. 1A). If CMTs are sensitive to curvature-derived tension, they are predicted to align transversely. To test the relative contribution of these opposing curvature-derived cues, we took inspiration from a method initially developed to mimic the cellular microenvironment for animal cells (19). To be able to rapidly deform the cell cortex and obtain simple global geometries, we used wallless plant cells (spherical protoplasts) and confined them in rectangular wells. We then modified their pressurization using solutions of different osmolarity (Fig. 1B;s e eMaterials and Methods; SI Appendix,F i g . S2A). Note that there was no detectable wall synthesis within the timeframe of the experiment (SI Appendix,F i g .S 3 ).

To confirm the shape and pressurized status of protoplasts, we monitored protoplast deformation, using the pUbQ10::LTI6b-TdTomato membrane marker reporter line (Fig. 1 C-F). When viewed from the bottom, confined protoplasts appeared elongated in rectangular wells. Orthogonal sections and 3D reconstruction confirmed their pressurized status, with hemispherical top and bottom membranes (Fig. 1 C-F and Movies S1 and S2). The protoplasts only appeared to be geometrically deformed laterally, as if they were confined between two plates. Importantly, such confinement did not induce sharp edges, as the protoplast contour remained almost tangential to the microwell walls (Fig. 1 C-F and SI Appendix,F i g .S 2 B). Thus, the cell-edge contribution to CMT behavior is not explicitly studied in this work. Using the measured aspect-ratio (length/width between 1.13 and 1.17), we confirmed that predicted maximal tensile stress is transverse in confined protoplasts (Fig. 1G and SI Appendix, Text).

To follow microtubule dynamics, we used the microtubule reporter line p35S::GFP-MBD (Fig. 1H) (Microtubule Binding Domain of rat MAP4; ref. 15). Note that protoplasts were still alive after 17 h in the wells, confirming that this environment is not toxic for the protoplast, as already shown for animal cells (Fig. 1I). To test whether CMTs exhibit a bias in their orientation in these conditions, we used 15 × 20 μm microwells, and we observed the GFP-MBD signal 2 h after transfer from 600 mOsmol/ L to 280 mOsmol/L mannitol. Qualitatively, we observed a wide diversity of CMT behaviors in confined and pressurized protoplasts (Fig. 1J). To quantify this pattern, we measured the orientation of microtubules on small regions of interest (ROIs), thus providing a local quantification of each microtubule segment, using the subcellular fibrillar tool (SFT hereafter,Fig. 1K;ref. 20). Typically, we obtained a distribution of orientations per protoplast. This method revealed that CMTs in confined and pressurized protoplasts indeed exhibit a bias in the transverse orientation (n = 126 protoplasts, P < 10 -3 [Rayleigh's test for uniformity], Fig. 1L). This conclusion was independent on the analysis method, as a similar trend was obtained using the ImageJ plugin Ori-entationJ (SI Appendix,F i g .S 4 ).

We also checked whether local curvature could affect the CMT orientation globally. To do so, we analyzed a subset of confined protoplasts that were large enough to touch four walls of the wells, instead of just two, when confined (SI Appendix, Fig. S2C). Our analysis revealed the same transverse bias in CMT orientation in this population of protoplasts, consistent with a response of CMTs to global curvature anisotropy in our setup (SI Appendix, Fig. S2D). Altogether, this suggests that CMTs can align with maximal tension. This also suggests that such alignment does not depend on the cell wall.

Challenging the Transverse Orientation of CMTs in Confined and

Pressurized Protoplasts. To challenge our finding, we performed three additional tests. First, in principle, the transverse bias could be caused by the adhesion of the protoplast to the well edges. Yet, the tangential curvature suggests very weak adhesion to the well sides (Fig. 1D and SI Appendix,F ig .S2 B). To check this formally, we pretreated the microwells with pluronic acid, which is classically used in cell cultures to inhibit surface-tissue adhesion (21). In these conditions, we still observed a transverse bias in CMT orientation (n = 29 protoplasts, P < 10 -3 [Rayleigh's test for uniformity], Fig. 2 A andB).

Second, if the bias in orientation truly depends on curvature anisotropy, it should be lost in square-shaped wells. To test this, we used 14 × 14 μm microwells. In these wells, as expected, we did not observe any significant bias in CMT orientation (n = 74 protoplasts, P = 0.11 [Rayleigh's test for uniformity], Fig. 2 C and D).

Last, if CMTs align with the direction of maximal tension at the protoplast cortex, they should do so for any rectangular geometry, with the bias increasing when curvature anisotropy increases, in accordance with the Laplace-Young law. To test that prediction, we used 12 × 40 μm microwells. As expected, we found a significant bias of CMT orientation in the transverse direction (n = 99 protoplasts, P < 10 -3 [Rayleigh's test for uniformity], Fig. 2 E andF). Interestingly, the bias in the transverse direction was indeed stronger in the 12 × 40 μm microwells than in the 15 × 20 μmmicrowells(P < 10 -3 , null hypothesis: mean angle of 12 × 40 > mean angle of 15 × 20) permutation test). Altogether, this supports a scenario in which CMTs orient with predicted maximal tension in confined and pressurized protoplasts.

Pressurization Determines CMT Orientation in Confined Microwells. If CMTs align with the pattern of tension for a given geometry, this alignment should become less pronounced when tension decreases. Recently, the analysis of protoplasts confined in agar wells in hyperosmotic conditions has shown that CMTs align with the long axis of the protoplast, consistent with this prediction (11). To test this in our setup, protoplasts were introduced in 12 × 40 μm microwells in a hypertonic solution (600 mOsmol/L mannitol) as previously, and then the protoplasts were exposed to an even more hypertonic solution (800 mOsmol/L mannitol, compared with 280 mOsmol/L mannitol). As expected, because of reduced pressurization, protoplasts were more deformable (Fig. 3A and SI Appendix,F i g .S 4 ). In these conditions, the transverse CMT bias was lost in all replicates 2 h after the addition of the hypertonic solution. Instead, a global bias in the longitudinal distribution was observed (n = 97 protoplasts, P < 10 -3 [Rayleigh's test for uniformity], Fig. 3 B andC).

Consistent with their reduced pressure-dependent stiffness and increased deformability, several protoplasts exhibited a very elongated shape (Fig. 3B). This increased range of shapes allowed us to check the correlation between protoplast aspect-ratio and CMT orientation. We first calculated a mean CMT orientation per protoplast, with the OrientationJ, Dominant Direction plugin, and second, we calculated a deformation ratio (Materials and Methods). We found that average CMT orientation is longitudinal for the most elongated protoplasts (Fig. 3 D andF). Yet, such a bias was significantly reduced in protoplasts with an aspect-ratio below 2.5; in such protoplasts, CMT orientation was more isotropic (p <2.5 = 0.052 vs. p >2.5 = 0.020 [Rayleigh's test for uniformity], Fig. 3 D andE). Altogether, this confirms that the transverse orientation of CMTs depends on the degree of protoplast pressurization. Our results also suggest that CMTs align with geometry when surface tension is low, i.e., the long axis of the protoplasts.

Microtubule Orientation Respond to Deviations in Cortical Tension.

So far, our results are consistent with CMTs aligning with predicted maximal tension at the protoplast cortex. Results obtained in vitro suggest that the microtubule response to tension is transient (22). Taking advantage of time-lapse imaging within our setup, we next investigated the transient nature of the microtubule response in vivo.

When observing a confined protoplast over a long time, changes in CMT orientations could be detected, further confirming that the protoplast is alive. Note that CMT reorientations appeared slow when compared to in vivo data. In the example shown in SI Appendix,Fig. S5A andB, subtle changes were observed (see also Movie S3): Upon transfer from 800 mOsomol/L to 400 mOsmol/ L, the initial bias in the longitudinal orientation was progressively lost in favor of a more uniform, and even transverse, orientation and then back to longitudinal. As shown in SI Appendix, Fig. S5 C-E, CMTs could completely change their orientations while being confined over long time periods. Within the same geometry, protoplasts can thus acquire new CMT orientation depending on pressure.

The use of 800 mOsm/L mannitol conditions can generate highly deformed protoplasts and is perfectly adapted to show the contribution of cell geometry, as an aspect-ratio superior to 2.5 was required to induce a significant bias in CMT orientation along the long axis of the protoplast (SI Appendix,F i g .3D and E,a n d ref . 11). However, such high osmolarity may also induce artifacts, or even trigger slowed life mechanisms, as in dormant seeds for instance (23). In fact, high osmolarity has been proposed to slow microtubule dynamics in yeast because of cytoplasmic crowding [START_REF] Molines | Physical properties of the cytoplasm modulate the rates of microtubule growth and shrinkage[END_REF]. We thus focused on the comparison between 600 and 280 mOsm/L mannitol, even if, in these conditions, we could not induce such high aspect-ratios. Long-term kinetics showed changes in CMT orientation during the switch from hyperosmotic to hypoosmotic conditions and vice versa (SI Appendix, Figs. S6-S8 and Movies S4-S6). CMT arrays appear to retain their ability to modify orientation when osmotic conditions fluctuate. Strikingly, as we followed CMT behavior in protoplasts being transferred from 600 to 280 mOsmol/L mannitol, we observed new microtubules appearing in the transverse orientation (Fig. 4A, arrows; SI Appendix,F i g s .S 6a n dS 8 ,a rrows). This is consistent with a scenario in which transverse tension promotes the polymerization of microtubules in that direction.

To test whether CMTs are able to maintain their stress-derived transverse orientation in the long term, without any imposed change in osmolarity, we examined CMT orientations in protoplasts 16 h after the transfer from 600 to 280 mOsmol/L mannitol (Fig. 4B). In such conditions, protoplast shape appeared stable. It is possible that many aspects of the protoplast change in this timeframe (e.g., plasma membrane composition, metabolism), yet transverse curvature remains higher than longitudinal curvature. After 16 h, the transverse CMT bias was lost in 12 × 40 μm microwells (n = 69 protoplasts, P <10 -3 (null hypothesis: mean angle in 12 × 40 μmm i c r o w e l l sa t1 6h< mean angle in 12 × 40 μm microwells at 2 h), Fig. 4 C andD). This is consistent with a scenario in which CMTs align with changes in maximal tension and usually return to their geometry-derived orientation if no more changes in tension direction occur.

Discussion

We have demonstrated that CMTs can change their orientation in confined protoplasts without cell walls or sharp edges. This provides a hierarchical scenario: 1) CMTs align with the long axis of the cell by default, because of their high flexural rigidity (also consistent with refs. 9 and 11); 2) tension promotes alignment of CMTs with maximal tension, which is transverse for an elongated cell; and 3) although cell edges are dispensable for CMT self-organization and reorientation, the associated molecular regulators can modulate the final CMT orientation in vivo.

The microtubule response to mechanical stress is supported by many studies from different groups, on different plant parts, and in response to different mechanical perturbations (17,[START_REF] Hejnowicz | Tensile tissue stress affects the orientation of cortical microtubules in the epidermis of sunflower hypocotyl[END_REF]15,[START_REF] Robinson | Global compression reorients cortical microtubules in Arabidopsis hypocotyl epidermis and promotes growth[END_REF]. Yet, most of the obtained results so far relate to CMT behavior in tissues, in which the exact stress pattern can be difficult to predict. Here, using a confined protoplast protocol, we not only demonstrate that a full cell wall is not required for the microtubule response to stress, but we also show that microtubules are able to perceive both cell geometry and cortical tension, depending on a threshold in cortical tension. These results are consistent with the proposal that microtubules may spontaneously orient with maximal tension (18), building on in vitro data on stretched microtubules [START_REF] Franck | Tension applied through the Dam1 complex promotes microtubule elongation providing a direct mechanism for length control in mitosis[END_REF] and on the predicted weakness of the geometrical cue for CMT self-organization (9).

Here, we have focused on the role of cell geometry and cortical tension in determining CMT behavior. Yet, cell edges are also important players to explain CMT orientations in vivo (12,16). Interestingly, the three contributions-cell geometry, cortical tension, cell edges-are highly interconnected. In particular, curvature depends on cell geometry, prescribes tension stress pattern, and can locally become an obstacle for CMTs at cell edges. One avenue for future studies will be to check whether cell edge components are sensitive to shape or tension and, in turn, whether changes in tension can modify global shape and cell edge geometry. At this stage, we also cannot completely exclude the possibility that specific regulators may be recruited at cell edges, independent from cell geometry and tension.

The MBD construct induces known artifacts, such as extra microtubule bundling and twisted organs [START_REF] Celler | Microtubules in plant cells: Strategies and methods for immunofluorescence, transmission electron microscopy, and live cell imaging[END_REF]. One cause of our observed transverse CMT bias in pressurized protoplasts may be the MBD domain. However, longitudinal CMTs were observed in protoplasts confined in agar wells using the same GFP-MBD line [START_REF] Durand-Smet | Cytoskeletal organization in isolated plant cells under geometry control[END_REF]. Furthermore, as protoplast curvature and aspect-ratio do not change over 16 h, and CMT orientation can change, the MBD domain does not prevent CMT reorientation, independent of curvature or protoplast geometry.

More interestingly, our results support a scenario in which CMTs respond to changes in tension, rather than the pattern of tension at steady state. This observation is consistent with in vitro data on transiently stretched microtubule networks (22). This allows us to revisit the role of cell geometry in defining microtubule orientation. As our system imposes a stable geometry, it allows us to reveal that the microtubule response to stress requires fluctuations in shape and stress pattern (cycles of pressurization and depressurization in our experiments). Fluctuations are often viewed as extra noise on top of an average situation. Here, we provide clear evidence that, instead, fluctuations allow cells to perceive stress, to which they respond. In other words, the average orientation of microtubules in cells seem to be the result of stress fluctuation rather than a product of cell geometry alone.

Is there evidence of such stress fluctuations in planta? Low frequency fluctuations could easily be explained by circadian turgor rhythms. Nastic movement of leaves and stems further suggest that variations in the mechanical status of the plant are subcircadian [START_REF] Derr | Fluttering of growing leaves as a way to reach flatness: Experimental evidence on Persea americana[END_REF]. The analysis of hypocotyl growth also suggests that shorter period fluctuations exist in Arabidopsis seedlings, from which our protoplasts were extracted [START_REF] Takatani | Microtubule response to tensile stress is curbed by NEK6 to buffer growth variation in the Arabidopsis hypocotyl[END_REF]. Last, the calcium waves at the shoot apical meristem, every 10-30 min, may indicate that mechanical fluctuations in plant tissues are underestimated [START_REF] Li | Calcium signals are necessary to establish auxin transporter polarity in a plant stem cell niche[END_REF]. These different systems suggest that such fluctuations may be the norm, rather than the exception.

Our setup opens avenues for other future research questions. In particular, such a single cell system offers the opportunity to revisit the molecular factors involved in the microtubule-cell wall continuum, which remains largely ill-described. This may also prove useful for the analysis of other cortical factors like auxin transporters. Our protocol may fill a missing link in the study of plant mechanotransduction, playing a similar role as in vitro studies of fibroblasts in animal mechanotransduction studies, i.e., to provide a context in which mechanical parameters are better controlled and in which conclusions can then be tested in a multicellular context.

Materials and Methods

Experiments were conducted in two laboratories (Mechanobiology Institute [MBI] in Singapore and Laboratoire de Reproduction et Développement des Plantes [RDP] in Lyon, France).

Plant Growth Conditions (MBI and RDP). At MBI, Arabidopsis thaliana plants were grown at room temperature in long-day conditions (16 h/8 h light/dark cycle), on medium containing 11.94 g/L of Arabidopsis medium (Duchefa) supplemented with 2 mM Ca(NO 3 ) 2 , pH 5.8 for 7-15 d. At RDP, A. thaliana seeds were sown on MS (Murashige and Skoog) medium and grown in vitro in long-day conditions (16 h/8 h light/dark period) for 7-15 d. The microtubule reporter line (p35S::GFP-MBD) and the plasma membrane reporter line (pUbq10::LTI6b-TdTomato) were previously described (15).

Protoplast Generation (MBI and RDP). Protoplasts were obtained from 7-to 15-d-old seedlings. Cell wall was digested through seedling immersion in 1.1 mL of solution A (D-Mannitol [600 mOsmol/L], CaCl 2 [2 mM], MgCl 2 [2 mM], L-ascorbic acid [1 mM], BSA [3.5 mg/mL], MES [10 mM at pH 5.5]) supplemented with wall digesting enzymes (Cellulysine [Calbiochem] [17 mg/mL], Cellulase RS [17 mg/mL], Pectolyase Y23 [0.4 mg/mL]). Ca. 10 seedlings were incubated in the enzymatic solution. At RDP, the incubation lasted for 2 h under slow agitation on a rotating wheel (12 rpm) at room temperature (i.e., ca. 21-25 °C). At MBI, the incubation lasted overnight under agitation (40 rpm) at room temperature (i.e., ca. 20 °C). After incubation, the seedling suspension was aspired up and down five or six times using a 1-mL pipette to break the tissue and free the protoplasts. Samples were centrifuged at 1,000 rpm for 4 min, the supernatant was discarded and protoplasts were washed for 1 min with 1 mL of solution A. A second centrifugation (1,000 rpm, 4 min) was performed, and most of the supernatant was discarded, keeping ca. 200 μL of a suspension of protoplasts in solution A. Protoplasts were then placed at 4 °C for 30 min. We did not select for a specific type of protoplasts (e.g., with different size or different number of chloroplasts, SI Appendix,Fig. S2A) to ensure that our observations were robust with respect to the diversity of protoplasts. The digestion of the cell wall was confirmed by the absence of calcofluor (cellulose dye) and propidium iodide (pectin dye) staining (SI Appendix,F i g .S 3 ).

Microwell Fabrication (MBI).

A PDMS (90% silicone elastomer base, Sylgard + 10% silicone elastomer curing agent, Sylgard) stamp was first fabricated using lithography (SU8 method) and silanized (Trichloro(1H,1H,2H,2H-perfluorooctyl)-silane, Aldrich) for 2 h under vacuum. PDMS was then poured on the mold and degassed 15 min at 10 mBar before curing 2 h at 80 °C. After removing, the stamp was cut into pieces of about 1 cm × 0.5 cm and silanized 2 h under vacuum. Microwells were obtained by pressing PDMS molds into a drop of ultraviolet (UV) curable monomers of Norland Optical Adhesive 73 (NOA73), beforehand deposited in ibidi dish (ibidi glass bottom dish 35 mm). At MBI, UV curing was performed with UV-KUB 9 (Kloé SA, 200 mW/cm 2 ) for 30 s. At RDP, UV curing was performed with UV-KUB 2 (Kloé SA, 40 mW/cm 2 ) for 3 min. Ibidi dish were filled with 3 mL of water, and the PDMS mold was carefully removed with tweezers to avoid formation of air bubbles in the microwells. For a more detailed protocol, see ref. 19.

Surface Passivation with Pluronic Acid. To test the contribution of protoplast adhesion to CMT behavior, microwells were treated for 30 min at 37 °C with 2% (vol/vol) pluronic acid (a nonionic surfactant). The negative impact of pluronic acid on protoplast adhesion was confirmed with the following control experiment: We added 300 μL from the same protoplast's suspension on Ibidi dish either pretreated for 30 min at 37 °C with 2% (vol/vol) pluronic acid or incubated with water in the same conditions. Protoplasts were let to sediment for 2 h. Then, the Ibidis were tilted in a similar way (being attached to the same support) to let the protoplast suspension flow down and the number of remaining protoplasts (i.e., still attached to the Ibid's coverslip) was counted. Many protoplasts were still attached in the control (water) Ibidi (n = 6,216 protoplasts), whereas, in the pluronic-treated Ibidi, fewer protoplasts were present (n = 2,003 protoplasts) and most of them were located at the coverslip-plastic edge of the Ibidi. This confirms that the pluronic acid surfactant hinders adhesion of Arabidopsis protoplasts.

Protoplast Confinement (MBI and RDP). Microwells in Ibidi dishes were washed with solution A before protoplast confinement. After removing solution A from the Ibidi dish, 50 μL of protoplast solution was deposited on microwells and let to sediment at room temperature for 5 min. The Ibidi dish was then centrifuged at 300 × g for 3 min (using a plate holder). The step of sedimentation increases the number of confined protoplasts into the microwells. After centrifugation, 3 mL of solution B (identical to solution A except for D-Mannitol [280 m to 800 mOsmol/L]) were added to induce hypoosmotic (D-Mannitol 280 mOsmol/L), mild hypoosmotic (D-Mannitol 400 mOsmol/L) or hyperosmotic (D-Mannitol 800 mOsmol/L) shock.

Microscopy and Imaging (MBI and RDP).

For the experiments reported in Figs. 123, live imaging started 2 h after the addition of the hypotonic or hypertonic solution and stopped ∼2 h later. For the experiments reported in Fig. 4, kinetics was performed immediately after the addition of solution B, and late time points (t = 16 h) were also considered.

At MBI, images were acquired on a spinning-disk confocal microscope (Yokogawa W1 on Nikon T1E) and an inverted confocal LSM710 microscope (Zeiss) using 100× lens (oil immersion, N.A.= 1.45 [Nikon] and 1.46 [Zeiss]). At RDP, images were acquired on LSM800 inverted confocal microscope (Zeiss) using 63x lens (oil immersion, N.A. = 1.4).

Time-lapse experiments: Protoplasts were prepared as described above and were confined in 12 × 40μm microwells in hypertonic solution (Movie S1: 800 mOsmol/L mannitol, and Movies S2-S4: 600 mOsmol/L mannitol). The Ibidi dishes were installed under the microscope, and specific microwell positions on plate were recorded. Movie S3 was performed on widefield inverted microscope (Zeiss) using 63× lens (oil immersion, N.A. = 1.4) and Movies S1, S2, and S4-S6 were performed on LSM800 inverted confocal (Zeiss), using 63× lens (oil immersion, N.A. = 1.4). For Movie S3,th e80 0mO sm ol/Lma nn itolsolution was replaced by a 400 mOsmol/L mannitol solution, and imaging started immediately after the addition of the 400 mOsmol/L mannitol solution. Images were taken every 30 min for 8 h. For Movies S4-S6, imaging started in 600 mOsmol mannitol solution, and at t = 0, the 600 mOsm/L mannitol solution was replaced by the 280 mOsm/L mannitol solution. Further changes in solutions were performed every 2 h, as shown in the figures. Images were taken every 20 min until protoplast'sd e a t h .

Cell wall staining: p35S::GFP-MBD seedlings (positive control for the dyes) and p35S::GFP-MBD protoplasts (obtained after 2 h of enzymatic digestion at RDP) were immersed in solution A containing either 0.3 mg/mL of propidium iodide, which stains demethyl-esterified pectins (33), for 10 min or 0.01% of calcofluor, which stains cellulose microfibrils (34), for 15 min. Seedlings and protoplasts were then imaged on LSM800 inverted confocal microscope as described above. The absence of cell wall was tested immediately after digestion and 22 h after digestion.

Image Processing. The first five slices of the confocal stack were used to make a maximal projection. This removed most of the cytoplasmic signal in the images, including cytoplasmic microtubules. Then, all projections corresponding to one technical replicate were assembled as a stack, projections were aligned with the ImageJ plugin AlignSlice, and all images were cropped to keep the central part of the protoplast (to avoid artifacts on the sides of the cells due to the projection). Finally, a Gaussian blur (radius: 2.00 pixels) was performed on the images. Then, microtubule orientation analysis was performed using SFT (20). This method is based on nematic tensors and provide orientation and anisotropy of the microtubule arrays. Each protoplast is divided in ROIs, and the orientation of each ROI is then analyzed. On average, this represented 394 ROIs (i.e., CMT fragment angles) per protoplast. The orientation is measured from an imaginary horizontal line, and the angle between this line and the ROIs is calculated. A polar histogram was constructed, displaying the global probability for each orientation to belong to a class of angle, ranging from 0°to 90°. Thus, 10 classes of angles of 9°w ere formed, from 0°-9°to 81°-90°. We used the probability density function where (probability) = sum of (probability density function) × (bin width) over bins. When 10 classes of angles (0-90°) are defined, bin width is (π/2)/10 ∼ 0.157. In the figures, we plotted the probability in each bin, which is (probability density function) × (bin width). The probability in each bin is about 0.1, and the sum of all histogram area is 1 with 10 bins.

To confirm the results obtained with SFT, the plugin OrientationJ, Distribution in the ImageJ software was used (35) on the images previously assembled (with the same crop and Gaussian blur). As in SFT, protoplasts were divided in several ROIs (one ROI = 8 pixels). The orientation of CMTs in each ROI was measured. For each technical replicate, all of the orientations were then distributed into six classes of angles, ranging from 0°to 90°, each class measuring 15°. Data were normalized and histograms were constructed, displaying the proportion of ROIs in each class of angles. Both of these methods (i.e., SFT and OrientationJ plugin) allow a very local analysis of each microtubule orientation.

Correlation between protoplast deformation and CMT orientation was obtained with the OrientationJ, Dominant direction plugin. This plugin measures the mean orientation of microtubule in each cell. The cell deformation was estimated by drawing an ellipse around each protoplast with the ImageJ software and calculating a ratio between the major and the minor axis of that ellipse. The scatterplot represents the average orientation of the microtubule for each protoplast according to their aspect-ratio after confinement.

Statistical Analysis. Statistical tests were conducted with R software. Statistical analysis of the results (sample size [n], P value, type of test) is presented in Results.

Data Availability. All study data are included in the article and supporting information.

Determination of T L

Consider a cut of the ellipsoid by a plane passing through the equator circle. This divides the ellipsoid in upper and lower identical halves. The internal pressure creates a vertical force F acting on the upper half, outwards:

𝐹 = 𝑃. 𝜋𝑎
This force is exactly balanced when the pressure vessel is at equilibrium by a density of forces T L in the shell structure acting through the shell perimeter, of thickness e, leading to a force:

𝐹 = 2𝜋𝑎 𝑒 𝑇 Since F = F', we get: 𝑇 = 𝑃𝑎/2𝑒
Determination of T T Locally, at any point Q on the shell structure, the stresses follow the generalized Laplace's law:

𝑇 𝑅 + 𝑇 𝑅 = 𝑃 𝑒
where R L and R T are respectively the longitudinal and transversal radii of curvature at point Q. In an ellipsoid of revolution at a point Q located at the equator, we have R L = b 2 /a and R T = a. Then Laplace's equation becomes:

𝑎𝑇 𝑏 + 𝑇 𝑎 = 𝑃 𝑒
Replacing the value of T L found above leads to:

𝑇 = 𝑃𝑎 2𝑒 (2 - 𝑎 𝑏 ) or 𝑇 = 𝑇 (2 - 𝑎 𝑏 )
This formula shows that, as expected on a point of the equator, T T = T L if b = a (case of a sphere). For elongated ellipsoid of revolution (b>a) reminiscent of a cylinder, we consistently get T T > T L . However, in our confined protoplasts, b<a, leading to T T < T L .

In our experiments, we measured a/b = 17/15 = 1.133 for 15 µm x 20 µm microwells, and a/b = 14/12 = 1.166 for 12 µm x 40 µm microwells, leading to ratios, T T / T L = 0.866 and T T / T L = 0.834 respectively.

2-3 Discussion

By controlling both cell geometry and surface tension, we have demonstrated that CMTs can change their orientation in wall-less confined cells, and that this orientation shift is triggered by pressurization of the protoplast. These results are consistent with a scenario, in which CMT align with the cell geometry (i.e., the cell long axis) by "default". This geometry-derived orientation can be overridden when the cortical tension is increased. However, long-term kinetics experiments highlighted that CMT alignment with the maximal tension direction is not stable in time, suggesting that CMTs align with changes in maximal tension, and return to their geometry-derived orientation in absence of tension changes.

Many different groups have investigated the microtubule response to mechanical perturbations, focusing on different parts of the plant, and testing different types of mechanical perturbations (Hamant et al., 2008;[START_REF] Hush | Interphase microtubule re-orientation predicts a new cell polarity in wounded pea roots[END_REF][START_REF] Robinson | Global Compression Reorients Cortical Microtubules in Arabidopsis Hypocotyl Epidermis and Promotes Growth[END_REF][START_REF] Sampathkumar | Subcellular and supracellular mechanical stress prescribes cytoskeleton behavior in Arabidopsis cotyledon pavement cells[END_REF]. However, most of these works have been done in plant tissues, where mechanical stress pattern is difficult to predict, notably because in addition to their own intrinsic mechanical stress (i.e. the turgor pressure), cells undergo mechanical forces provided by their neighboring cells.

Here, using a single-cell system, we have shown that CMT can respond to both cell geometry and cortical tension, depending on a threshold in cortical tension, indicating that CMT response does not depend on an intact cell wall, or hormone gradient. These results are consistent with the proposal that microtubules may spontaneously align with the maximal tension, suggesting that microtubule could act as mechanosensors [START_REF] Hamant | Are microtubules tension sensors?[END_REF]. This proposal is based on previous in vitro data showing that tension can directly promote microtubule polymerization [START_REF] Franck | Tension applied through the Dam1 complex promotes microtubule elongation providing a direct mechanism for length control in mitosis[END_REF], and in silico experiments, which have highlighted that a very low circumferential bias in an ellipsoid cell is sufficient to disrupt the geometry-derived orientation of the microtubule network [START_REF] Mirabet | The self-organization of plant microtubules inside the cell volume yields their cortical localization, stable alignment, and sensitivity to external cues[END_REF].

Here, single-cell approaches enable to tackle precisely the contribution of cell geometry and cortical tension on CMT behavior. Yet, other players have to be considered to explain CMT orientation in vivo. For instance, several studies have demonstrated that cell edges are important player contributing to CMT behavior (Ambrose et al., 2011a;[START_REF] Chakrabortty | A Plausible Microtubule-Based Mechanism for Cell Division Orientation in Plant Embryogenesis[END_REF]. Indeed, it has been shown that microtubules depolymerize when encountering sharp cell edges headon. However, this behavior can be overcome by CLASP proteins, which specifically accumulate in cell edges, and which works as a 'tuneable' microtubule organizer, allowing microtubule growth around sharp edges (Ambrose et al., 2011a). Because cell geometry, cortical tension and cell edges are intimately correlated through cell curvature, which depends on cell shape, and which prescribes mechanical stress pattern, further work should determine whether cell edges components are affected by tension and geometry.

The microtubule response to mechanical stress also depends on the dynamic behavior of CMTs, in other words of the polymerization and depolymerization rates of CMTs. Microtubule markers, and notably the MBD construct has been reported to affect CMT dynamics, promoting CMT stabilization [START_REF] Celler | Microtubules in Plant Cells: Strategies and Methods for Immunofluorescence, Transmission Electron Microscopy, and Live Cell Imaging[END_REF].

Considering this artefact, one cause of the observed transverse bias in confined and pressurized cells could be related to the presence of the MBD domain. However, the observation of shift in CMT orientation in long-term kinetics indicates that the MBD domain does not prevent CMT reorientation. In addition, longitudinal orientation of CMT has been observed in protoplasts confined in agar microwells and expressing the same GFP-MBD marker [START_REF] Durand-Smet | Cytoskeletal organization in isolated plant cells under geometry control[END_REF].

A recent study has shown that the physical properties of the cytoplasm (cytoplasmic crowding) also affect microtubule dynamics in yeast [START_REF] Molines | Physical properties of the cytoplasm modulate the rates of microtubule polymerization and depolymerization[END_REF]. In this article, the authors have modified cytoplasm density through osmotic treatments, and they have reported that hypoosmotic shifts, (i.e., decrease cytoplasmic concentration), induce an increase of microtubule polymerization and depolymerization rates, while hyperosmotic shifts (i.e., increase of cytoplasmic concentration), decrease microtubule dynamics [START_REF] Molines | Physical properties of the cytoplasm modulate the rates of microtubule polymerization and depolymerization[END_REF]. These results are consistent with what we observed in the time-lapse experiments, in which newly synthetized CMTs appear in the transverse orientation after the addition of the hypoosmotic solution.

Altogether, these observations might highlight a scenario, in which cortical tension may prescribe the orientation of microtubules, while, the cytoplasm density could promote CMT dynamics. To further investigate the dynamic behavior of CMTs, the use of drugs, such oryzalin and taxol, which depolymerize and stabilize CMT network respectively, should be considerate to assess whether CMTs are only newly synthesized or also reoriented upon changes of mechanical tension.

While the question of 'what' drives CMT orientation in plant cells has often opposed the mechanical stress pattern versus the cell geometry, our observations suggest a more complex CMT behavior, and support a scenario in which CMTs rather respond to changes in tension. Indeed, we observed that CMT alignment with cortical tension is not stable in time, and seems to depend on fluctuations in shape and stress pattern through cycles of pressurization and depressurization (i.e., triggered by the addition of osmotic solutions) in our experiments. Interestingly, in a recent review, Moulia and colleagues, have discussed the role of such mechanical fluctuations during plant development, highlighting that developing plants undergo mechanical fluctuations from the intracellular level to the whole organism scale [START_REF] Moulia | Fluctuations shape plants through proprioception[END_REF]. At the whole plant scale, mechanical variations can be provided by the environment, such as strong wind, which could induce possible resonance in stems for instance. At the cellular level, these fluctuations would be mainly derived from cell growth conflicts (e.g., differential growth rates between cells) [START_REF] Moulia | Fluctuations shape plants through proprioception[END_REF]. This last point is consistent with hypocotyl growth analysis, which have suggested that mechanical stress fluctuates [START_REF] Takatani | Microtubule response to tensile stress is curbed by NEK6 to buffer growth variation in the Arabidopsis hypocotyl[END_REF]. These variations in mechanical stress status could be explained by the circadian turgor rhythms, thus the mechanical stress status would be constantly revised or updated, triggering the CMT response. This hypothesis could be consistent with what it is observed in tissues, where CMT often align with the mechanical stress pattern. Finally, at the intracellular levels, the dynamic behavior of the cytoskeleton (microtubules and actin filaments) also provide instabilities through its constant assembly-disassembly [START_REF] Moulia | Fluctuations shape plants through proprioception[END_REF].

Therefore, instead of providing additional background noise, it has been suggested that mechanical fluctuations, deriving from different growth events, may contribute to modulate plant development, serving as instructive cues form stem straightness, leave flatness, tissues folding or growth heterogeneity for instance [START_REF] Moulia | Fluctuations shape plants through proprioception[END_REF].

3-Contribution of plasma membrane composition during cell wall synthesis

3-1 Preliminary results

Plant cells are surrounded by a stiff cell wall, which connects neighboring cells together, preventing cell migration and cell reorganization. Cell walls are dynamics structures, mainly composed of polysaccharidic components embedded in a hydrated matrix. Among these components, cellulose microfibrils, which consist of chains of ß-1,4-linked glucose units, have been identified as the main load-bearing component of cell walls, playing a key role in cell morphogenesis (Baskin, 2005). Cellulose microfibrils are synthesized at the plasma membrane (PM) by large, motile trans-membrane cellulose synthase (CESA) complexes (CSCs) [START_REF] Mutwil | Cellulose synthesis: a complex complex[END_REF][START_REF] Somerville | Cellulose Synthesis in Higher Plants[END_REF]. CSCs are assembled in the Golgi apparatus before being transported to the cell cortex where they are inserted into the PM [START_REF] Crowell | Regulated trafficking of cellulose synthases[END_REF][START_REF] Gutierrez | Arabidopsis cortical microtubules position cellulose synthase delivery to the plasma membrane and interact with cellulose synthase trafficking compartments[END_REF]. It has been established that CSCs are guided through the PM by cortical microtubules (CMTs) [START_REF] Paredez | Visualization of Cellulose Synthase Demonstrates Functional Association with Microtubules[END_REF], and that this CMT-based guiding mechanism is mediated by CELLULOSE SYNTHASE INTERACTIVE1 (CSI1) protein, which connect CMT array with CSCs at the PM (Bringmann et al., 2012b;[START_REF] Li | Cellulose synthase interactive protein 1 (CSI1) links microtubules and cellulose synthase complexes[END_REF]. During this process, nascent cellulose microfibrils are extruded from the CSCs into the apoplast, and incorporated in the existing cell wall [START_REF] Somerville | Cellulose Synthesis in Higher Plants[END_REF].

PM lipid composition depends, in part, on the activity of phospholipases. A previous study have shown that the overexpression of phospholipase PLAIIIß (p35S::PLAIIIß) induces a decrease in the PM content of most PM phospholipids [START_REF] Li | Patatin-Related Phospholipase pPLAIII -Induced Changes in Lipid Metabolism Alter Cellulose Content and Cell Elongation in Arabidopsis[END_REF]. Additionally, plants overexpressing this phospholipase exhibit severe developmental defects (i.e. reduced size, morphology defects) and decreased plant mechanical strength, which has been related with a reduced cellulose content in their walls [START_REF] Li | Patatin-Related Phospholipase pPLAIII -Induced Changes in Lipid Metabolism Alter Cellulose Content and Cell Elongation in Arabidopsis[END_REF]. Altogether, these data might suggest an effect of PM composition of cellulose biosynthesis mechanism. However, whether the lipid environment of CSCs could modulate their activities remain an open question. To address this question, we investigated the cellulose synthesis mechanism in PLAIIIß OE plants.

Plants overexpressing the phospholipase PLAIIIß can be easily identified as early as at their seedling stage: they exhibit curvy cotyledons and shorter hypocotyls (N=137 hypocotyls) compared to WT seedlings (N= 96 hypocotyls) (Figure 28A and B). At the cellular level, PLAIIIß OE plants exhibit roundish (i.e., less lobed) pavement cells instead of the typical puzzle shape of these cells (Figure 28C). Interestingly, PLAIIIß OE plants display reduced mechanical strength (as shown with more brittle stems and petioles), a feature also observed in the katanin mutant [START_REF] Bichet | BOTERO1 is required for normal orientation of cortical microtubules and anisotropic cell expansion in Arabidopsis[END_REF].

As mentioned before, CMTs provide a scaffold responsible for CSC trajectories in the PM. This process involves CSI1 proteins, which connect the CMT array to the PM. Thus, we hypothesized that the CMT-CSI1-based guiding mechanism could be affected in PLAIIIß OE plants. To investigate this guiding mechanism in PLAIIIß OE plants, I used the pCSI1::CSI1-YFP marker line to visualize CSI1 trajectories in cells surrounding an ablation in hypocotyls. Since CSI1 proteins connect CMTs to CSCs, we hypothesized that CSI1 proteins should be repositioned along reoriented CMTs in cells surrounding ablations in the WT, but not in the PLAIIIß OE line. To visualize CSI1 trajectory orientation, I used the Fibritool plugin [START_REF] Boudaoud | FibrilTool, an ImageJ plug-in to quantify fibrillar structures in raw microscopy images[END_REF](see material and methods part). I observed that in both Col-0 (N=7 hypotoctyls) and PLAIIIß OE (N= 12 hypocotyls), CSI1 proteins reoriented around the ablation, suggesting that CSI1 proteins are well connected to CMTs in PLAIIIß OE (Figure 29A). These results must be confirmed, with a quantification of the orientations of CSI1 protein trajectories.

Additional experiments using the PLAIIIß OE line expressing both the CMT marker and the CSI1 marker (when it will be available) could also be used to further confirm these results.

Altogether, these results suggest that the PLAIIIß OE phenotype and reduced cellulose content in PLAIIIß OE plants is not directly related to CMT defects. In parallel, I also performed cellulose microfibrils staining using Calcofluor and Direct Red dye, to assess cellulose microfibril orientation in cell walls. I observed a few numbers of stained pavement cells in both Col-0 and PLAIIIß OE cotyledons, in which I could detect cellulose microfibril orientation (Figure 29B). To increase the dye penetration efficiency, I then performed staining in fixed samples. With this approach, I improved cellulose microfibrils staining in WT samples (Figure 29C), however, I did not manage to obtain similar images with PLAIIIß OE cotyledons (Figure 29D). Although these observations did not allow a comparative analysis of cellulose microfibrils in Col-0 and PLAIIIß OE, these results are consistent with the reduced cellulose content previously reported in PLAIIIß OE.

To further investigate CSI1 behavior in PLAIIIß OE plants, I also analyzed CSI1 velocity in pavement cells. To do so, I performed timelapse experiments (every 2s for 5min) using TIRF microscopy to focus on the cell cortex while having high spatio-temporal resolution (Figure 30A). CSI1 trajectories were analyzed with the Imaris software (see material and methods). Similar velocities were measured in both Col-0 (N=202 particles) and PLAIIIß OE (N=1011 particles) plants (around 2400nm/min) (Figure 30B). Note however, that these values are different from what is published in the literature on hypocotyls (around 416 nm/min [START_REF] Gu | Identification of a cellulose synthase-associated protein required for cellulose biosynthesis[END_REF].

Several studies have estimated the average lifetime of CSI1 at the PM to be between10 min to 20 min [START_REF] Gu | Identification of a cellulose synthase-associated protein required for cellulose biosynthesis[END_REF][START_REF] Paredez | Visualization of Cellulose Synthase Demonstrates Functional Association with Microtubules[END_REF]. After this time, CSCs are removed from the PM via endocytosis. Studies have also reported that PM lipid composition is a key regulator of cellular trafficking events (Noack and Jaillais, 2017). Therefore, we decided to test whether cellulose defects observed in PLAIIIß OE plants could be caused by alteration of endocytosis process in these plants. To explore this hypothesis, I used FM4-64 dye as a tool to label endocytic pathways in root cells. FM4-64 first labels the PM, before being integrated through the cells via the endosomes, ultimately staining the full vesicular network from the PM to the tonoplast [START_REF] Rigal | Live Cell Imaging of FM4-64, a Tool for Tracing the Endocytic Pathways in Arabidopsis Root Cells[END_REF]. Accordingly, endocytosis alterations can be highlighted by monitoring the time required for vacuole staining. I treated both Col-0 and PLAIIIß OE seedlings with FM4-64 (1µM) during 1hour, and then, I imaged the root elongation zone in both genotypes. Both Col-0 and PLAIIIß OE displayed many cells (Col-0: N= 94cells/130 total number of cells and

PLAIIIß OE: N=211cells/237 total number of cells) with stained tonoplasts after 1h of FM4-64 treatment (Figure 30C). These preliminary results do not allow us to conclude about a hypothetic altered endocytic process in PLAIIIß OE, and further experiments (e.g., accurate kinetics of FM4-64 internalization with several intermediate timepoints, or by using endocytic markers, such as clathrin markers) are required to conclude about the dynamics of endocytosis in these overexpressor.

3-2 Discussion and perspectives

This project aimed to explore the potential contribution of PM lipid composition for the CMT response to stress and for cellulose synthesis. To address this question, I used the PLAIIIß OE line, previously described in [START_REF] Li | Patatin-Related Phospholipase pPLAIII -Induced Changes in Lipid Metabolism Alter Cellulose Content and Cell Elongation in Arabidopsis[END_REF], and majorly affected in its global lipid content in their PM. I found that a major alteration of the PM in this line does not have a strong impact on the CMT response to mechanical perturbations (ablations). Interestingly, these plants are also characterized by a reduced cellulose content. Despite my efforts, I could not identify the cause of this defect, when monitoring CSC behavior and vesicle trafficking.

Most of the presented results are preliminary. This study will require further quantifications and/or complementary experiments to build robust conclusions. So far, we have determined that CMT dynamics seems to be not majorly affected in PLAIIIß OE plants, and our current data suggest that the CMT-CSI1-based guiding mechanism is not drastically altered in these plants. Although CSI1 velocity results must be taken with a lot of caution, our data did not highlight a different trend between PLAIIIß OE and WT. Similarly, experimental data obtained with FM4-64 staining in root cells, did not allow us to conclude about major alterations of the endocytic pathway in the over-expressor. Overall, these results do not allow us to conclude on the impact of PM lipid composition on cellulose synthesis process. This opens the discussion to many other hypotheses.

First, CESA behavior may be different from that of CSI1. One could investigate CESA behavior in PLAIIIß OE by performing similar experiments as on CSI1 proteins for instance (e.g., CESA reorientation after ablation, CESA dynamics at the PM using FRAP experiments for instance).

CESAs are major components of CSCs, organized in rosette in the PM. By using electron microscopy and/or biochemical approaches, we could also assess whether the formation of CSC rosette is altered in PLAIIIß OE (e.g. altered number of of CESA per rosette). In the case where CSCs are correctly assembled and addressed to the PM, it would be interesting to monitor CSC activity too (cellulose synthesis rate). In conclusion, how PM composition could affect cell wall organization and regulation (i.e., synthesis, remodeling, stability) remained to be defined so far. Last, other CSC members could be more dependent on lipid composition than others, and should be the primary targets for further studies.

In this project, we were specifically interested in the role of the PM composition in the cellulose synthesis process. Although few data are available on this topic, a previous study has reported a potential role of sterols during cellulose synthesis process, and perturbation of sterol biosynthesis lead to reduced cellulose content [START_REF] Schrick | A link between sterol biosynthesis, the cell wall, and cellulose in Arabidopsis[END_REF]. However, whether sterols are directly involved in cellulose synthesis process remains to be defined, since sterols are involved in many different pathways, including in biosynthesis on sitosterol-ß-glucoside and the brassinosteroid phytohormone, which have been both involved in cellulose biosynthesis [START_REF] Peng | Sitosterol-beta -glucoside as Primer for Cellulose Synthesis in Plants[END_REF][START_REF] Xie | Brassinosteroids can regulate cellulose biosynthesis by controlling the expression of CESA genes in Arabidopsis[END_REF].

Cellulose microfibrils are synthesized by CSCs, which are directly embedded in the PM. The lipid composition of the PM largely contributes to define both biochemical and biophysical properties of the PM. Interestingly, in their study, Diotallevi and Mulder, proposed a biophysical model for the propulsion of CSCs, in which they have shown that membrane elasticity impact CSC movements [START_REF] Diotallevi | The Cellulose Synthase Complex: A Polymerization Driven Supramolecular Motor[END_REF]. Reciprocally, considering the size of CSCs (estimated around 40-50nm in diameter and 30-35nm tall [START_REF] Bowling | The cytoplasmic domain of the cellulose-synthesizing complex in vascular plants[END_REF]), it would be also interesting to considerate the impact of CSC movements on the PM composition.

CSC activity has also been correlated with the activity of KORRIGAN1 (KOR1) protein, a membrane-bound 1,4-ß-D glucanase, which physically interact with several CESAs, including CESA3 and CESA6, involved in the primary cell wall synthesis [START_REF] Vain | The Cellulase KORRIGAN Is Part of the Cellulose Synthase Complex[END_REF]. Interestingly, mutation of KOR1 has been associated with a reduced cellulose content in primary cell wall, and alteration in cell wall architecture [START_REF] Nicol | A plasma membrane-bound putative endo-1,4-beta -D-glucanase is required for normal wall assembly and cell elongation in Arabidopsis[END_REF]. It might be interesting to explore whether KOR localization and/or activity is altered in PLAIIIß OE, which could impact cellulose synthesis process in these plants. Although the exact role of KOR in the cellulose biosynthesis process is still not well understood, it has been proposed that KOR might be involved in the correct deposition of the cellulose and hemicellulose network in expanding cell wall [START_REF] Nicol | A plasma membrane-bound putative endo-1,4-beta -D-glucanase is required for normal wall assembly and cell elongation in Arabidopsis[END_REF]. Microscopical techniques associated with various probes have revealed that the pectin network is also altered in kor (His and Driouich). How KOR might affect pectins is still an opened question, but it highlights that cellulose/hemicellulose organization in the cell wall might impact the global composition of the cell wall, e.g. through compensation mechanisms. This hypothesis is supported by the dramatic disorganization of the innermost layer of the wall in kor compared to the WT during pectin extraction with hot water (His and Driouich), suggesting a profound alteration of pectin cross-linking within the wall in kor (His and Driouich).

More generally, most of the cell wall components transit through the PM before being inserted into the cell wall. Therefore, the global organization of the cell wall could be affected in PLAIIIß

OE. An ongoing collaboration with Gregory Mouille's lab will provide more information about cell wall composition in PLAIIIß OE plants, including data on pectins. PLAIIIß OE display altered pavement cell shape, suggesting defects during pavement cell morphogenesis process. Interestingly, several recent studies have highlighted that accumulation of dimethylesterified pectin could regulate lobe formation, and thus contribute to pavement cell shape establishment [START_REF] Altartouri | Pectin Chemistry and Cellulose Crystallinity Govern Pavement Cell Morphogenesis in a Multi-Step Mechanism[END_REF][START_REF] Haas | Pectin homogalacturonan nanofilament expansion drives morphogenesis in plant epidermal cells[END_REF]. Conclusions by Altartouri et al., are more nuanced, since the authors have highlighted the role dimethyl-esterification of pectins in lobes formation under reduced cellulose crystallinity conditions [START_REF] Altartouri | Pectin Chemistry and Cellulose Crystallinity Govern Pavement Cell Morphogenesis in a Multi-Step Mechanism[END_REF].

Overall, these data support a scenario, in which cell wall mechanical properties are not only regulated by the cell wall composition, but also depends of cell wall component interactions (e.g., between pectins and cellulose), and might highlight a different mechanical behavior of each component, relating to their local environment (e.g., percentage of crystallin cellulose or dimethyl-esterifed pectins).

3-3 Material and Methods

Plant material and growth conditions:

We used the following lines: Columbia 0 (Col-0), pPDF1::MBD-mCherry (microtubule marker), pCSI1::CSI1-YFP kindly donated by Arun Sampathkumar's lab, and p35S::PLAIIIß was previously generated and described in [START_REF] Li | Patatin-Related Phospholipase pPLAIII -Induced Changes in Lipid Metabolism Alter Cellulose Content and Cell Elongation in Arabidopsis[END_REF]. pPDF1::MBD-2xmCherry was generated by LR triple reaction (LR clonasII+) between pDonor P4-P1r (PDF1 promoter), pDonor221 (2xmCherry) and pDonor P2r-P3 (MBD) in the pDestination pK7m34GW (Kanamycin resistant). The construct was transformed in Agrobacterium tumefaciens C58pMP90 strain and selected on YEB media (5g/L beef extract; 1g/L yeast extract; 5g/L peptone; 5g/L sucrose; 15g/L bactoagar; pH 7.2) supplemented with antibiotics (Spectinomycin, Gentamycin, Rifampicin). After two days of growth at 28°C, bacteria were scooped and re-suspended in roughly 200mL of transformation buffer (10mM MgCl2; 5% sucrose; 0.25% silwet) and Col0 were transformed by the dipping flowers as described in [START_REF] Clough | Floral dip: a simplified method forAgrobacteriummediated transformation ofArabidopsis thaliana: Floral dip transformation of Arabidopsis[END_REF]. Primary transformant T1 were selected in vitro on MS medium (0.8% of agar, pH 5.7) supplemented with kanamycin.

p35S::PLAIIIß pCSI1::CSI1-YFP and p35S::PLAIIIß pPDF1::MBD-mCherry were obtained by crossing the respective markers with the p35S::PLAIIIß line.

Seeds were surface sterilized, and sown on MS medium (0.8% of agar, pH 5.7) in long-day conditions (Light 16h/dark 8h, 20°C) for 7days.

Staining:

Cellulose staining:

In vivo staining:

Samples were immerged in a solution containing cell wall digesting enzymes (Final solution: 250mL of enzymatic solution (125mg of pectolyase-Y23 (Duchefa) and 375mg of pectinase from Aspergillus niger (SERVA) diluted into 50mL H2O) in 1mL of PBS (10X)) for 20min for Col0 seedling and 10min for p35S::PLAIIIß under a slow agitation at room temperature for 1h-1h30. Samples were then transferred in solution of containing 0.1% Calcofluor (Fluorescent Brightener 28 Sigma) + Silwet (Ci: 3µL of Silwett diluted into 997µL of water, 50µL of the Ci were then diluted into 2mL of Calcofluor solution). Samples were let overnight at 4°C in the dark before imaging.

Fixed samples:

7-day-old seedling of Col-0 and p35S::PLAIIIß were fixed in a solution containing 50% ethanol and 10% acetic acid (Vf :50mL: 25ml of absolute ethanol, 5mL of acetic acid and 20mL of H2O) for 2 hours. Seedlings were immerged in 3mL of the solution of fixation, and placed under the vacuum. After 30min, the vacuum was broken. This operation was repeated 3times. The fixing solution was removed and the samples were washed with 70% ethanol for 30min, and then with a solution of absolute ethanol for 30min. Absolute ethanol solution was removed and replaced by 3mL of methanol. Samples were conserved in the freezer (for at minima 1night).

Before the staining:

The methanol solution was discarded and samples were successively washed (for 30min each time) with solution containing decreasing concentration of ethanol (70% ethanol, 50% of ethanol, 30% of ethanol, water). Samples were then immerged in a solution containing cell wall digesting enzymes (Final solution: 250mL of enzymatic solution (125mg of pectolyase and 375mg of pectinase diluted into 50mL H2O) in 1mL of PBS (10X)) for 30min for Col0 samples and 20min for p35S::PLAIIIß samples, under a slow agitation at room temperature. This step is crucial for the dye penetration.

Staining: Samples were then transferred in solution of containing 0.1% Calcofluor (Fluorescent Brightener 28 Sigma) + Silwet (Ci: 3µL of Silwett diluted into 997µL of water, 50µL of the Ci were then diluted into 2mL of Calcofluor solution). Samples were let overnight at 4°C in the dark before imaging. Similar protocol for staining with Direct Red 23 (0.1%), (Aldrich).

FM4-64 staining:

Col0 and p35S::PLAIIIß 7days-old seedlings were immerged in a FM4-64 solution (MS ½ medium supplemented with FM4-64 dye, final concentration 1µM) for 1hour.

After 1hour, seedlings were removed from the solution and immediately transferred between slide and cover-slip, where root cells in the elongation zone were imaged.

Mounting of seedlings for microscopy experiments

Microtubule response to ablation in cotyledons

Col-0 and p35S::PLAIIIß 7days-old seedlings expressing the microtubule marker pPDF1::MBD-mCherry were placed into petri dishes containing MS medium (0.8% of agar).

Cotyledons were positioned at the surface of the MS medium as flat as possible, and cell ablations were performed with a needle. Samples were then covered by water and positioned under the confocal microscope. The first image was taken directly after the ablation (=t0h), and the second image was taken 7hours (=t7h) after the ablation.

CSI1 protein response to ablation

Seedling of Col-0 and PLAIIIß OE expressing the pCSI1::CSI1-YFP marker were grown for 7days on MS medium (0.8% of agar) in long-day conditions. The day before the imaging: Seedlings were placed on MS medium (0.8% of agar) in petri dished and ablations were performed approximately in the middle of hypocotyls by using a needle (Minutien pin, 0.15 mm rod diameter, 0.02 mm tip width, RS-6083-15, Roboz Surgical Instrument Co.). Seedling were then let overnight in the SANYO in long day conditions.

The day of imaging: Seedling were imaged around 18hours after the ablation. For technical reasons, cotyledons were removed by using tweezers, and hypocotyls were mounted between slide and cover slip, and then position under a spinning disk microscope.

Microscopy

Microtubule response to ablation in cotyledons

Microtubule imaging was performed on a Leica SP8 upright scanning confocal microscope equipped with a water immersion objective (HCX IRAPO L 25x/0.95 W). mCherry fluorophore was excited using led laser emitting at wavelength of 552 nm, and signal was collected between 521nm to 560nm. The following scanning settings were used: pinhole size 1AE, 1.61 zoom, resonant scanner (scanning speed of 8000Hz), frame averaging 6, Z intervals 0.5µm.

Cellulose staining

Cellulose microfibrils stained in vivo with 0.1% of calcofluor were imaged on a Leica SP8 upright scanning confocal microscope equipped with a water immersion objective (HCX IRAPO L 25x/0.95 W). Calcofluor was excited using led laser emitting at wavelength of 405nm, and signal was collected between 410nm to 500nm. The following scanning settings were used: pinhole size 1AE, 1.61 zoom, non-resonant scanner, frame averaging 4.

Cellulose microfibrils stained in fixed samples with 1% of Direct Red were imaged with the same confocal microscope using an oil immersion objective (40x), non-resonant scanner, frame averaging 4. Direct red was excited using led laser emitting at wavelength of 552nm, and signal was collected between 600nm to 650nm. Samples were mounted between glass and coverslip with Citifluor (AF87-10).

CSI1 response to ablation

CSI1 proteins imaging was performed on a spinning disk confocal microscope; using the following set-up: inverted Zeiss microscope (AxioObserver Z1, Car Zeiss Group) equipped with a spinning disk module (CSU-W1-T3, Yokogawa) and a ProEM+ 1024B camera, using a x63 Plan-Apochromat objective (numerical aperture 1.4, oil immersion). YFP fluorophore was excited with the 488nm laser. Z intervals 0.5µm.

FM4-64 staining:

Similar set-up as described for CSI1 response to ablation were applied, except that FM4-64 was observed using the 561nm laser. Imaging was performed on the root elongation zone.

Timelapse experiments

CSI1 proteins time-lapse were performed using the TIRF mode to restrict the illumination in the cortex region. Total Internal Reflection Fluorescence (TIRF) Microscopy was done using the inverted Zeiss microscope previously described (AxioObserver Z1) equipped with azimuthal TIRF iLas2 system (Roper Scientific) and a 100x Plan-Apochromat objective (numerical aperture 1.46, oil immersion). The azimuth calibration was performed using the manufacturer recommendation and the iLas2 module in Metamorph software. The optimum critical angle was determined as giving the best signal to noise ratio. Images were acquired each 2s during 5min with 600ms exposure time.

Image analysis

Hypocotyl length measurements

Col-0 and p35S::PLAIIIß seeds were sown on plates containing MS medium (0.8% agar pH 5.7) and store at 4°C for 24h. After 24h, plates were transferred in long days conditions for 6days. Hypocotyl length was measured using ImageJ software (straight line tool) and length were plotted in Excel.

Microtubule response to ablation in cotyledons

Microtubule organization was quantified with Fibritool plugin [START_REF] Boudaoud | FibrilTool, an ImageJ plug-in to quantify fibrillar structures in raw microscopy images[END_REF] after flattening the images with the SurfCut macro (https://github.com/sverger/SurfCut) in the ImageJ software.

Microtubule reorientation was quantified using the Angle2Ablation_ Workflow (https://github.com/VergerLab/MT_Angle2Ablation_Workflow) developed by Stéphane Verger (unpublished data).

CSI1 protein response to ablation

CSI1 organization after cell ablations in hypocotyls was qualitatively analyzed with Fibriltool plugin. We took advantage of red bars generated by Fibritool to qualitatively estimate the orientation of CSI1 trajectories.

CSI1 velocity analysis

Short time-lapses (1 image every 2sec during 5min) of pCSI1::CSI1-YFP marker in both Col-0 and p35S::PLAIIIß were analyzed to estimate CSI1 velocity. Registration of stacks was performed in ImageJ software, using the StackReg plugin. The contrast was enhanced and normalized for each slice of the stack using ImageJ. Due to the large size of pavement cells, a small region of each cells has been cropped for the analysis. These crops were then exported in the IMARIS software for CSI1 trajectory analysis. In IMARIS software, an automated particle detection was performed, and tracks were generated over the lifetime of the particle. Only particles detected for 14s were analyzed as previously published in [START_REF] Gu | Identification of a cellulose synthase-associated protein required for cellulose biosynthesis[END_REF]. A manual cleaning of tracks was then performed to remove aberrant trajectories (e.g., trajectories detected on crop borders, or tracks detected between too clos particles). Data corresponding to the Track Speed Mean of each crop were exported in excel for analysis. These data recapitulate the mean speed of each particles (µm/s). The mean velocity of CSI1 proteins was estimated by calculated the global mean recapitulating all particle velocity mean was calculated and then plotted.

DISCUSSION

During my PhD, I have conducted several projects all centered around one main question: how mechanical signals at the cell cortex contribute to plant development? More specifically, I have investigated the impact of mechanical stress on plasma membrane composition, on cytoskeleton behavior and on cell wall synthesis.

More than a century ago, D'Arcy [START_REF] Thompson | On Growth and Form[END_REF] suggested that each shape, from individual cell to full organisms can be explained as the results of the action of physical forces (On growth and Forms, D'Arcy [START_REF] Thompson | On Growth and Form[END_REF]. Since, the improvement of live-imaging methods, genome editing technics, single cell omics, but also mathematical modelling have reinforced the idea that mechanical forces acts in concert with biochemistry and at multiscale to shape an organism. This has led to the emergence of a new field called "developmental mechanobiology", in which, many opened questions remain to be explored, such as how mechanical forces are transduced across scales? How are they sense and converted into informative signals? How are mechanical forces coordinated to shape an organ? However, addressing these questions requires to determine the pattern of mechanical forces, which are by definition, invisible. To increase again the level of complexity, many of these studied structures are multicellular structures (i.e., tissue and organ), undergoing growth and shape changes, which means that the mechanical stress pattern is dynamic, and concomitantly modified with shape changes.

To approximate the mechanical stress pattern in plant tissues (i.e., the direction and the intensity of the principal stresses in a structure), many studies have used continuum mechanical models. These models assume that the studied structure is always at the mechanical equilibrium, in other words, that all forces applying to the structure are compensated. In the case of a growing structure, this means that growth is described as a quasi-static developmental process in these models. This hypothesis is widely accepted, since the growth is a continuous process, in which the mechanical equilibrium is almost instantaneously reached. By contrast, the timeframe required for the organ formation for instance, is significantly higher compared to the time required to achieve this mechanical equilibrium. The combination of such modelling approaches and live-imaging technics have highlighted that cortical microtubules align with the maximal tensile stress direction in different structures an organs such as in the SAM or in pavement cells (Hamant et al., 2008;[START_REF] Sampathkumar | Subcellular and supracellular mechanical stress prescribes cytoskeleton behavior in Arabidopsis cotyledon pavement cells[END_REF].

Since, many studies have confirmed the alignment of cortical microtubules with the maximal tensile stress direction in other contexts, cortical microtubules have frequently been used as a proxy for the mechanical stress pattern [START_REF] Heisler | Alignment between PIN1 Polarity and Microtubule Orientation in the Shoot Apical Meristem Reveals a Tight Coupling between Morphogenesis and Auxin Transport[END_REF][START_REF] Sampathkumar | Primary wall cellulose synthase regulates shoot apical meristem mechanics and growth[END_REF]. However, microtubule orientation also largely depends on other biological process, and can be affected by other molecular components (e.g., hormones) [START_REF] Bouquin | The Arabidopsis lue1 mutant defines a katanin p60 ortholog involved in hormonal control of microtubule orientation during cell growth[END_REF][START_REF] Fischer | Interaction of auxin, light, and mechanical stress in orienting microtubules in relation to tropic curvature in the epidermis of maize coleoptiles[END_REF], as well as external cues (e.g., blue light), which might not correlate with the stress pattern. Therefore, cortical microtubule orientation can only be used in specific context, where mechanical stress has been already determined.

Mechanical stress patterns have also been investigated through different experimental approaches, as already mentioned in this manuscript, such as AFM which allow the estimation of cell wall mechanical properties (see box1). Old extensometers have also been recently revisited. In particular, a new automated confocal micro-extensometer (ACME) device has been developed to address cell wall mechanics in plant hypocotyls [START_REF] Robinson | An Automated Confocal Micro-Extensometer Enables in Vivo Quantification of Mechanical Properties with Cellular Resolution[END_REF]. Contrary to classical indentation methods, ACME device measures mechanical properties in the plane of growth, and thus provide different type of information than AFM. This system also allows the application of quantifiable stress within the physiological range contrary to many other mechanical tests, such as tissue ablation, drug treatments or osmotic shock for instance. Last, the use of mutants with mechanical integrity defects can also provide information on the mechanical stress pattern in the tissue. For instance, stems cracks observed in the clavata3de-etiolated3 (clv3det3) mutant has been linked with differential growth between the inner tissues (growing faster) and the epidermis, in which the growth is slowed down, leading to crack in the stem and revealing that the epidermis is under tension [START_REF] Asaoka | Stem integrity in Arabidopsis thaliana requires a loadbearing epidermis[END_REF]. Similarly, the quasimodo1 (qua1) mutant, defective in cell adhesion, displays a clear cell-detachment phenotype (Bouton et al., 2002b). The analysis of the orientation of cracks provide indications of the underlying mechanical stress patterns. By combining all these approaches, it is now possible to estimate the global mechanical stress pattern of a tissue, and to investigate its contribution during developmental processes, and to explore how it feeds back on biological processes.

At a lower scale, membrane tension is a major contributor of many cellular processes, including endocytosis and cell division. The recent emergence of mechanosensitive probes enables to investigate how membrane tension affects biological process in vivo, and to reveal micromechanical stress patterns at the membrane levels. The development of such probes often relies on fluorescence lifetime imaging microscopy (FLIM) techniques, which measure the time a fluorophore remains in an excited state before emitting a photon. This lifetime directly depends on the microenvironment of the fluorochrome and thus, can provide crucial information on the molecular environment of the probe. In biological membranes, this fluorescent lifetime depends linearly on membrane tension within the cells, and thus, has been used to quantify mechanical stress in membranes.

Recently, Michels and colleagues, have designed four microviscosity probes, which function as molecular rotors, each one targeting a specific compartment of the cell (i.e., cell wall, plasma membrane, cytoplasm and vacuole) [START_REF] Michels | Complete microviscosity maps of living plant cells and tissues with a toolbox of targeting mechanoprobes[END_REF]. Molecular rotors are fluorescent probes, characterized by a fluorescent lifetime and intensity, and which, upon photoexcitation, induce an internal rotation. The rotation rate can be estimated through the fluorescent lifetime and directly depend on the environment of the probe, thus providing information about the viscosity and the solvent polarity for instance. Using these probes, the authors managed to observe changes in cell wall flexibility during root hair formation. They were also able to establish time-dependent micro-viscosity maps of multicellular tissues with a subcellular resolution, providing a new tool to address the role of mechanics in the regulation of biological events [START_REF] Michels | Complete microviscosity maps of living plant cells and tissues with a toolbox of targeting mechanoprobes[END_REF].

Similarly, the recent development of the Fluorescent Lipid Tension Reporter (FliptR), also based on lifetime measurements, have also demonstrated its efficiency to measure membrane tension in cells, and to detect tension changes after osmotic treatment [START_REF] Colom | A fluorescent membrane tension probe[END_REF].

Globally, the use of mechanosensitive probes can reveal, in a non-invasive method, how plasma membrane and cell wall mechanical behavior is adaptively modified during dynamics events, such as cell growth process. In addition, these probes can be used in combining approaches, with markers highlighting of plasma membrane microdomains (that remain to be developed) for example, to provide critical information about the impact of membrane composition and/or ordering on plasma membrane mechanical behavior. The combination of all these approaches can provide good estimates of the mechanical stress pattern, at several scales, making the invisible visible.

Introduction

Phospholipids, also referred to as glycerophospholipids, are a class of lipids whose structure is based on a glycerol backbone that connects a hydrophobic tail -consisting of two long-chain fatty acids linked at the sn-1 and sn-2 position (diacylglycerol) -and a hydrophilic head group (Figure 1a). Because of their amphiphilic nature, phospholipids are key structural components of membrane bilayers, with the fatty acid chains aggregating together in the core of the bilayer and the hydrophilic heads on both sides. The simplest phospholipid class, with only a phosphate group at position sn-3, is phosphatidic acid (PA). The phosphate head group can be further modified to form the different classes of phospholipids, by addition of a choline, serine, ethanolamine, inositol or glycerol molecule, forming phosphatidylcholine (PC), phosphatidylserine (PS), phosphatidylethanolamine (PE), phosphatidylinositol (PI) or phosphatidylglycerol (PG), respectively (Figure 1a). PG main functions are in plastids and mitochondria and will not be discussed hereafter [1]. Phosphatidylinositol can be further phosphorylated on the 3rd, 4th and/or 5th position of the inositol head group to form phosphoinositides (PIPs, also referred to as polyphosphoinositides) such as phosphatidylinositol-4-phosphate (PI4P) and phosphatidylinositol-4,5-bisphosphate (PI(4,5)P2) (Figure 1a) [2].

There are different ways to classify phospholipids based on for example: i) their relative abundance (abundant vs minor lipids, i.e. less than 5% of total phospholipids), ii) their net charges (neutral vs anionic), iii) their metabolic fluxes (relatively stable concentration vs acute production/interconversion and fast turn-over), iv) their site of production (produced at the site of action or exported), v) their shape (conical, straight or inverted conical) or vi) their fatty acid chains (number of carbons:number of unsaturation) (Figure 1a andb). Overall, abundant phospholipids (e.g. PC, PE) are often considered as "structural" lipids in the sense that they are essential to establish a hydrophobic barrier. These phospholipids are produced by biosynthetic enzymes mainly in the endoplasmic reticulum (Figure 1b andc). Low abundant lipids (e.g. PA and PIPs) are labelled as "signaling" lipids in the sense that they mostly have regulatory effects on membrane functions. These signaling lipids are negatively charged, which enable specific interactions with proteins. In addition, they have fast turn-over and can be produced in an acute manner by lipid kinases, phosphatases or phospholipases at their site of action outside of the endoplasmic reticulum (Figure 1b andc) [2].

However, the frontiers between the "structural" and "signaling" lipids are not always clear-cut.

Indeed, these categories mostly arise from considerations at the cellular scale, initially drawn from studies using single cell systems such as yeast or in vitro cell culture. As such, phospholipid biosynthesis and localization are often depicted in a single cell. However, recent evidence suggests that specific pattern of phospholipid accumulation arise at the tissue or organ level in plants, particularly for classical "signaling" lipids but also for "structural" lipids. These

Phosphatidylinositol-4,5-bisphosphate patterns and their roles in tissue differentiation

Phosphoinositides are minor phospholipids, making less than 1% of total phospholipids (Figure 1a). They have specific accumulation patterns in the different compartments of the cell and as such they determine organelle identity [2,3]. Furthermore, because of their respective charges and shape, they are key determinants of membrane physicochemical parameters (Figure 1b) [2]. Some of these parameters appears to be invariant between different tissues. For example, in all cell types analyzed so far, the plasma membrane is the most electronegative compartment, a feature that specifies its identity [4]. The strong electrostatic field of the plasma membrane is powered by the accumulation of PI4P in this membrane, the most abundant phosphoinositide species in plants (Figure 1a) [4]. PI4P accumulation at the plasma membrane appears to be invariant when analyzing different tissue and organ [4]. However, during cell division, PI4P strongly accumulates at the cell plate, which is therefore highly electrostatics [4][5]. The accumulation of PI4P at the cell plate correlates with the localization of PI4K in this organelle and the double mutant pi4k12 is defective in cytokinesis and phragmoplast establishment [6,7]. By contrast, PI(4,5)P2 is not only patterned at the level of the cell but also at the tissue/organ scales.

Evidence for PI (4,5)P2 patterning at the tissue scale comes from quantitative imaging studies of PI(4,5)P2 sensors lines [8]. These transgenic lines stably express PI(4,5)P2 binding domains fused to a fluorescent protein as an indirect way to localize this phospholipid [9][10][11][12]. Indeed, such fusion proteins are recruited to membranes that accumulate this lipid [12]. By contrast, in the absence of its target lipid, the sensor accumulates in the cytoplasm as a default localization [12]. In some cases, the chronic absence of the biosensor cognate lipid induces its subsequent destabilization and degradation. For example, the C2 domain of the bovine Lacthaderin protein (C2Lact), a PS-binding domain, is unstable and degraded when expressed in a mutant background that lacks PS biosynthesis [START_REF] Burian | A correlative microscopy approach relates microtubule behaviour, local organ geometry, and cell growth at the Arabidopsis shoot apical meristem[END_REF]. Quantitative 3-D imaging revealed that the PI(4,5)P2-binding Plekstrin Homology (PH) domain of Phospholipase C (PHPLC) accumulates to a low extent at the center of the shoot apical meristem in Arabidopsis, while it is stabilized in the boundary region (Figure 2a) [8]. By analogy to the C2Lact sensor, one may speculate that destabilization of PHPLC occurs when PI(4,5)P2 levels are low. This hypothesis was recently substantiated in cotyledons, as PHPLC accumulates about four fold when seedling are treated with a high concentration of NaCl (a condition known to induce PI(4,5)P2 synthesis [10]) or U-73122 (which inhibits PI(4,5)P2 hydrolysis by phosphoinositide-specific-PLC (PI-PLC) and thereby promotes its accumulation) [START_REF] Lindeboom | A mechanism for reorientation of cortical microtubule arrays driven by microtubule severing[END_REF]. Although the exact role of the PI(4,5)P2 pattern in the shoot apical meristem needs to be defined, it could be involved in the two main functions of the meristem: stem cell maintenance and organogenesis. For instance, in the clv3-17 mutant, which displays a larger central zone with more stem cells, the PI(4,5)P2 pattern tends to disappear, suggesting that destabilization of the PHPLC sensor correlates with stem cell maintenance [8].

The shoot apical meristem is also characterized by a typical mechanical stress pattern, with strong and highly anisotropic tensions in boundaries compared to the central zone (Figure 2a) [15]. A positive correlation between the accumulation of PI(4,5)P2 sensors and mechanical stresses in the boundary zones suggests that the PI(4,5)P2 pattern could be linked with tissue mechanics and mechanical signal transduction [8]. Future work will reveal how this PI(4,5)P2

pattern is established and what its function is in shoot meristem biology.

Lipid sensors are not the only clues pointing at the importance of specific PI (4,5)P2 patterns at the tissue level. Indeed, PI4P 5-kinases (PIP5K), PI(4,5)P2 5-phosphatases and PI-PLCs have tissue specific expression patterns [16][17][18][19][20][21]. For example, PIP5K1, PIP5K2, PLC3 and PLC5

are expressed in the root meristem and in vascular tissues and PIP5K2 expression is regulated by the phytohormone auxin [16-18][19,20]. Furthermore, the plasma membrane-localized 5phosphatase COTYLEDON VASCULAR PATTERN2 (CVP2) is expressed in developing vascular cells in various organs and displays exquisite expression specificity for the protophloem in the root [22][23][START_REF] Molines | Physical properties of the cytoplasm modulate the rates of microtubule growth and shrinkage[END_REF][START_REF] Hejnowicz | Tensile tissue stress affects the orientation of cortical microtubules in the epidermis of sunflower hypocotyl[END_REF]. CVP2 and its homolog CVP2-LIKE1 (CVL1), as well as PIP5K1 and PIP5K2 are involved in venation pattern establishment in cotyledons, while plc2, plc3 and plc5 mutants have root architecture phenotypes [17,19,20,22]. The cvp2 cvl1 double mutant root protophloem fails to fully differentiate, as revealed by the presence of undifferentiated "gap" cells within protophloem strands (Figure 2b) [START_REF] Hejnowicz | Tensile tissue stress affects the orientation of cortical microtubules in the epidermis of sunflower hypocotyl[END_REF]. Surprisingly, CVP2 overexpression, which promotes PI(4,5)P2 processing into PI4P, also induces protophloem gap cells and phenocopies the cvp2 cvl1 double mutant, which accumulates PI(4,5)P2 (Figure 2b) [START_REF] Hejnowicz | Tensile tissue stress affects the orientation of cortical microtubules in the epidermis of sunflower hypocotyl[END_REF]. Furthermore, inducible overexpression at the plasma membrane of a highly processive PIP5K, which boosts PI(4,5)P2 production at the expense of the PI4P pool, also induces gap cells in developing protophloem (Figure 2b) [START_REF] Molines | Physical properties of the cytoplasm modulate the rates of microtubule growth and shrinkage[END_REF]. Therefore, it appears that the PI(4,5)P2/PI4P balance, specifically in protophloem cells, rather than the absolute amount of PI (4,5)P2 is critical for the correct differentiation of this tissue (Figure 2b).

Cellular analyses revealed a correlation between increased vacuolar trafficking upon the alteration of the PI(4,5)P2/PI4P ratio and protophloem differentiation, suggesting that vacuole biogenesis and/or related endocytic trafficking regulated by these phosphoinositides could be linked with phloem development [START_REF] Molines | Physical properties of the cytoplasm modulate the rates of microtubule growth and shrinkage[END_REF]. Furthermore, PIP5K1 and PIP5K2 are not only localized at the plasma membrane but also in the nucleus [17,18]. Nuclear targeting is actively regulated, at least in the case of PIP5K2 [START_REF] Robinson | Global compression reorients cortical microtubules in Arabidopsis hypocotyl epidermis and promotes growth[END_REF]. These localizations suggest that PI (4,5)P2 could also have a direct role in gene expression regulation, which has been reported in animal systems [START_REF] Franck | Tension applied through the Dam1 complex promotes microtubule elongation providing a direct mechanism for length control in mitosis[END_REF][START_REF] Celler | Microtubules in plant cells: Strategies and methods for immunofluorescence, transmission electron microscopy, and live cell imaging[END_REF].

Overall, these data indicate that the establishment of specific PI (4,5)P2 accumulation pattern at the tissue level are hallmarks of tissue differentiation, at least in some cases. Some of the future challenges will be to sort which of the pleiotropic functions of this signaling lipids could be instrumental to regulate tissue differentiation.

Phosphatidylserine variations at the tissue level regulate plasma membrane organization at the nanoscale PS shares characteristics with both above-mentioned phospholipid categories. Similar to "structural" phospholipids, it is synthesized in the endoplasmic reticulum by a single enzyme called PHOSPHATIDYLSERINE SYNTHASE 1 (PSS1) in Arabidopsis and PS is not acutely produced in compartments outside of the endoplasmic reticulum (Figure 1b andc) [START_REF] Durand-Smet | Cytoskeletal organization in isolated plant cells under geometry control[END_REF].

However, it is acidic, interacts with specific proteins and is present at low levels (i.e. from 1 to 5% of total phospholipids depending on the tissue [START_REF] Durand-Smet | Cytoskeletal organization in isolated plant cells under geometry control[END_REF]), which is a hallmark of "signaling" lipids (Figure 1a andb) [2]. PS in produced in the luminal leaflet of the endoplasmic reticulum and is then actively orientated by flippases in the cytoplasmic membrane leaflet [START_REF] Derr | Fluttering of growing leaves as a way to reach flatness: Experimental evidence on Persea americana[END_REF]. This regulation is organelle specific, which allows the accumulation of PS in the cytoplasmic leaflet of post-Golgi compartments [START_REF] Derr | Fluttering of growing leaves as a way to reach flatness: Experimental evidence on Persea americana[END_REF]. Localization studies using PS specific biosensors revealed that it accumulates at the plasma membrane and all along the endocytic pathway in Arabidopsis [4,[START_REF] Burian | A correlative microscopy approach relates microtubule behaviour, local organ geometry, and cell growth at the Arabidopsis shoot apical meristem[END_REF]. This accumulation gradient is critical to define an "electrostatic" membrane territory within the cell, which specifies the identity of plasma membrane-derived organelles [START_REF] Burian | A correlative microscopy approach relates microtubule behaviour, local organ geometry, and cell growth at the Arabidopsis shoot apical meristem[END_REF].

Interestingly, the relative accumulation of PS biosensors at the plasma membrane or endosomes varies during root epidermis differentiation (Figure 3a) [START_REF] Takatani | Microtubule response to tensile stress is curbed by NEK6 to buffer growth variation in the Arabidopsis hypocotyl[END_REF]. Indeed, PS biosensors mostly accumulate at the plasma membrane in meristematic cells, while they partition more evenly between the cell surface and endosomes in differentiating epidermal cells (Figure 3a).

Experimental manipulation of the PS content by knock-out, knock-down or overexpression of the Arabidopsis PSS1 gene leads to the graded activation of plasma membrane auxin signaling pathway, which is regulated by the small GTPase RHO-OF-PLANTS6 (ROP6) [START_REF] Takatani | Microtubule response to tensile stress is curbed by NEK6 to buffer growth variation in the Arabidopsis hypocotyl[END_REF][START_REF] Li | Calcium signals are necessary to establish auxin transporter polarity in a plant stem cell niche[END_REF].

Interestingly, PS is dispensable for the proper targeting of ROP6 to the plasma membrane [START_REF] Takatani | Microtubule response to tensile stress is curbed by NEK6 to buffer growth variation in the Arabidopsis hypocotyl[END_REF].

However, super resolution microscopy and single molecule imaging revealed that PS is required for the auxin-induced clustering and stabilization of ROP6 in plasma membrane nanodomains (Figure 3b andc). ROP6 stabilization in nanoclusters is required for downstream auxin signaling. This effect is dose-dependent, with no stabilization of ROP6 in nanodomains in the absence of PS and therefore no downstream signaling, even when ROP6 is constitutively active (Figure 3c). By contrast, ROP6 is hyper stabilized in nanodomains in response to auxin in PSS1 overexpressing plants (Figure 3c). Accordingly, these plants have the same phenotypes as plants expressing a constitutive active version of ROP6, including the chronic inhibition of endocytosis and a hypergravitropic root response [START_REF] Takatani | Microtubule response to tensile stress is curbed by NEK6 to buffer growth variation in the Arabidopsis hypocotyl[END_REF].

One of the future challenges will be to decipher how is the PS pattern developmentallycontrolled during cell differentiation, a process which could involve lipid flippases or regulation of PS transfer at membrane contact sites, which are close (below 30nm) and stable apposition of two membranes involves, among other functions, in lipid exchanges [START_REF] Derr | Fluttering of growing leaves as a way to reach flatness: Experimental evidence on Persea americana[END_REF][33][34][35][START_REF] Wang | An equal opportunity collaboration between lipid metabolism and proteins in the control of membrane trafficking in the trans-Golgi and endosomal systems[END_REF].

Furthermore, PS itself is present in plasma membrane nanodomains, and single molecule tracking experiments revealed that these PS molecules are slow moving within the plane of the plasma membrane [START_REF] Takatani | Microtubule response to tensile stress is curbed by NEK6 to buffer growth variation in the Arabidopsis hypocotyl[END_REF]. This raises the question of how a phospholipid may be immobilized within a membrane and whether this process could also be regulated at the tissue scale.

Temporal phospholipid patterns

The last example is perhaps the least expected as it entails PC, an archetype "structural" lipid.

Indeed, transgenic lines with imbalanced PE/PC ratio, obtained by inducible knock-down or overexpression of CTP:PHOSPHORYLETHANOLAMINE CYTIDYLYLTRANSFERASE1 (PECT1, a rate limiting enzyme in PE biosynthesis), revealed that PC levels at the shoot apex correlate with flowering time: lines with heightened PC content flower early, while plants with reduced PC levels are late flowering (Figure 4a) [START_REF] Nakamura | Arabidopsis florigen FT binds to diurnally oscillating phospholipids that accelerate flowering[END_REF][START_REF] Nakamura | Membrane Lipid Oscillation: An Emerging System of Molecular Dynamics in the Plant Membrane[END_REF]. The early flowering time phenotype observed in plants with heightened PC content is dependent upon expression of FLOWERING LOCUS T (FT), a master regulator of flowering time [START_REF] Matsoukas | Florigens and antiflorigens: a molecular genetic understanding[END_REF]. Interestingly, FT directly binds to PC but not PE in vitro [START_REF] Nakamura | Arabidopsis florigen FT binds to diurnally oscillating phospholipids that accelerate flowering[END_REF]. Furthermore, PC but not PE oscillate depending of the time of day, with specific molecular species of PC showing various temporal pattern of accumulation (Figure 4b). For example, PC species containing less unsaturated fatty acids are predominant during the day, while PC species with linolenic acid (18:3) increase during the night (Figure 4b). In vitro, PC species with linolenic acid bind poorly to FT by contrast to less unsaturated PC species [START_REF] Nakamura | Arabidopsis florigen FT binds to diurnally oscillating phospholipids that accelerate flowering[END_REF]. Transgenic plants that overexpress FATTY ACID DESATURASE3 (FAD3)

show high content in PC species with 18:3 fatty acids and are late flowering (Figure 4b) [START_REF] Nakamura | Arabidopsis florigen FT binds to diurnally oscillating phospholipids that accelerate flowering[END_REF][START_REF] Arondel | Map-based cloning of a gene controlling omega-3 fatty acid desaturation in Arabidopsis[END_REF].

Together these data suggest that FT preferentially interacts with the PC species that accumulate during the day to promote flowering (Figure 4b) [START_REF] Nakamura | Arabidopsis florigen FT binds to diurnally oscillating phospholipids that accelerate flowering[END_REF]. However, it remains unclear how PC contributes to FT activity at the molecular level and how FT discriminates the different PC species based on their degree of unsaturation.

Of note, PC is not the only phospholipid showing temporal pattern of accumulation; and some molecular species of PA or PS also cycle diurnally [START_REF] Maatta | Levels of Arabidopsis thaliana Leaf Phosphatidic Acids, Phosphatidylserines, and Most Trienoate-Containing Polar Lipid Molecular Species Increase during the Dark Period of the Diurnal Cycle[END_REF]. These cycling are not just regulated by the light/dark cycle but they are under direct circadian regulation and are abolished in clock mutants [START_REF] Kim | Interaction and Regulation Between Lipid Mediator Phosphatidic Acid and Circadian Clock Regulators[END_REF]. Interestingly, PA itself regulates the core clock components LONG ELONGATED HYPOCOTYL (LHY) and CIRCADIAN CLOCK ASSOCIATED1 (CCA1).

PA directly binds to both LHY and CCA1, which inhibits their DNA binding capacity [START_REF] Kim | Interaction and Regulation Between Lipid Mediator Phosphatidic Acid and Circadian Clock Regulators[END_REF].

Together these results suggest that the interaction of PA with LHY/CCA1 may function in a negative feedback loop to integrate the circadian clock with lipid metabolism (Figure 4c).

Concluding remarks and future perspectives

The examples highlighted in this review show that phospholipid patterns are multiscales, from membrane nanodomains up to the organismal scale, with specific phospholipid patterns arising according to the cell type, the tissue differentiation status or the time of day. Tissue-specific control of lipid patterns is an emerging concept, but its exploration is somewhat limited by our ability to monitor their dynamics and crosstalks. By design, genetically encoded phospholipid biosensors reveal lipid subcellular localization, but not their respective accumulation [12]. As such, these biosensors are suited to detect changes in phospholipid localization, as exemplified for PS [START_REF] Takatani | Microtubule response to tensile stress is curbed by NEK6 to buffer growth variation in the Arabidopsis hypocotyl[END_REF]. However, if the levels of phospholipids vary but not their subcellular localization, the current tools are not quantitative enough to measure these variations with spatial resolution.

In some cases, the stability of the lipid sensor is dependent on the quantity of this lipid within the cell. However, we do not understand the mechanistic bases for such lipid-induced stabilization/destabilization. We therefore urgently need new methods to image and quantify phospholipid accumulation and turnover with tissue and cellular resolution. Such methods could include for example the design of new quantitative lipid sensors, the use of lipid immunolocalization or mass spectrometry imaging of lipid species. The latter is particularly promising since it can not only discriminate different phospholipids but also their various unsaturation degree [START_REF] Woodfield | Spatial and Temporal Mapping of Key Lipid Species in Brassica napus Seeds[END_REF][START_REF] Lu | Spatial analysis of lipid metabolites and expressed genes reveals tissue-specific heterogeneity of lipid metabolism in high-and low-oil Brassica napus L. seeds[END_REF][START_REF] Sturtevant | Three-dimensional visualization of membrane phospholipid distributions in Arabidopsis thaliana seeds: A spatial perspective of molecular heterogeneity[END_REF][START_REF] Sturtevant | Matrix assisted laser desorption/ionization-mass spectrometry imaging (MALDI-MSI) for direct visualization of plant metabolites in situ[END_REF]. However, this technique is still limited to very abundant phospholipids, such as PC. In addition, the best resolution reported in plant samples to date is ~10 µm, which is sufficient for analyses at the organ/tissue scales but not cellular/subcellular levels [START_REF] Woodfield | Spatial and Temporal Mapping of Key Lipid Species in Brassica napus Seeds[END_REF][START_REF] Lu | Spatial analysis of lipid metabolites and expressed genes reveals tissue-specific heterogeneity of lipid metabolism in high-and low-oil Brassica napus L. seeds[END_REF][START_REF] Sturtevant | Three-dimensional visualization of membrane phospholipid distributions in Arabidopsis thaliana seeds: A spatial perspective of molecular heterogeneity[END_REF][START_REF] Sturtevant | Matrix assisted laser desorption/ionization-mass spectrometry imaging (MALDI-MSI) for direct visualization of plant metabolites in situ[END_REF].

While we begin to uncover some of the enzymes involved in lipid patterning at the tissue scale, the next challenge will be to decipher what are the downstream targets that respond to these patterns, and what are the developmental consequences. This is a particularly daunting task since phospholipids have pleiotropic targets and are therefore expected to affect the localization or activity of many effector proteins. Pinpointing relevant interactions will therefore require in depth biochemical knowledge of the protein/lipid binding interfaces in order to modulate these interactions both from the lipid but also protein sides. At the same time, such efforts will require integrative biology approaches to blend deep biochemical knowledge into their cellular and developmental contexts. Using a collection of phospholipid sensors and membrane surface charge probes, this study shows that there is an electrostatic gradient along the plant endocytic pathway that is set up by specific combinations of the anionic lipids PI4P, PA and PS.

• 14. Lee E, Vanneste S, Perez-Sancho J, Benitez-Fuente F, Strelau M, Macho AP, Botella MA, Friml J, Rosado A: Ionic stress enhances ER-PM connectivity via phosphoinositide-associated SYT1 contact site expansion in Arabidopsis. Proc Natl Acad Sci U S A 2019. Using PI (4,5)P2 biosensors, this study shows that PI (4,5)P2 content increases upon ionic stress, which in turn recruits synaptotagmins (SYTs) and remodels endoplasmic reticulum/plasma membrane contact sites.

•• 24. Gujas B, Cruz TMD, Kastanaki E, Vermeer JEM, Munnik T, Rodriguez-Villalon A:

Perturbing phosphoinositide homeostasis oppositely affects vascular differentiation in Arabidopsis thaliana roots. Development 2017, 144:3578-3589. This work, together with Ref 25, shows that the PI(4,5)P2/PI4P balance, as regulated by plasma membrane localized phosphatases and kinases, is critical for the differentiation of the root protophloem. Using various genetic background with impaired PI(4,5)P2/PI4P balance, this study establishes that both an increase or a decrease of the PI (4,5)P2 content in protophloem induce the production of undiferentiated gap cells in protophloem tracks. Furthemore, it shows that a skewed PI(4,5)P2/PI4P ratio impact vacuolar trafficking, which could in turn impact phloem diffrentiation. This work shows that PIP5K2 is not only localized at the plasma membrane but also in the nucleus. PIP5K2 is actively addressed to the nucleus by a functional nuclear localization signal, and interacts with alpha-importin. Furthermore, using immunolocalization, this study shows that both PI4P and PI(4,5)P2, which are the substrate and product of PIP5K2, respectively, are presents in the nucleus, more specicaly the nucleoplasm. Together, this work open the possibility that some of the phenotypes attributed to PI (4,5)P2 may be due to gene expression regulation rather than membrane-related events. Résumé de la thèse Au-delà de leur nature biochimique, les organismes vivants sont aussi des objets physiques, subissant des contraintes mécaniques. Les plantes subissent des stress mécaniques internes, résultant du conflit entre leur pression de turgescence interne élevée (pouvant atteindre 1 MPa) et leur paroi cellulaire rigide capable d'y résister. Pendant ma thèse, je me suis intéressée aux rôles de ces signaux mécaniques internes lors du développement des plantes. A travers différents projets, j'ai étudié la contribution du cortex cellulaire dans la mécano-transduction. Avec mes collaborateurs, j'ai adapté une approche cellule unique pour étudier la contribution relative de la géométrie cellulaire et de la tension corticale sur le comportement des microtubules corticaux (CMT). Nous avons observé que les CMTs s'alignent sur l'axe long de la cellule lorsque les protoplastes sont confinés mais non pressurisés et avec la direction de tension maximale prédite (axe transversal) lorsque les protoplastes sont confinés et pressurisés. Cela suggère que les signaux mécaniques peuvent contrebalancer les contraintes géométriques. Cette réponse semble dynamique puisqu'en l'absence de nouvelle stimulation mécanique, les CMTs s'alignent sur l'axe long de la cellule : les CMTs répondent aux changements de tension plutôt qu'à la pressurisation uniquement. En parallèle, j'ai également contribué au développement d'un nouvel outil génétique éliminant spécifiquement le phosphoinositide PI(4,5)P2 de la membrane plasmique, et révélant ainsi un rôle potentiel du PI(4,5)P2 lors de l'organogénèse dans le méristème apical. Par ailleurs, les CMTs sont également impliqués dans le processus de synthèse de la cellulose, un composant majeur des parois cellulaires. Les plantes sur-exprimant la phospholipase PLAIIIß présentent une teneur en cellulose diminuée et une résistance mécanique réduite des tissus aériens. J'ai étudié comment l'altération de la composition de la membrane plasmique pouvait affecter la machinerie de synthèse de la cellulose, ouvrant la voie à l'analyse du rôle de la composition de la membrane plasmique dans la réponse des CMTs aux contraintes mécaniques, à la synthèse de la cellulose et au développement.

Rodriguez-Villalon

Beyond their biochemical nature, living organisms can also be considered as physical objects, experiencing mechanical constraints. Plants experience growth-derived stress, resulting from the conflict between their high internal turgor pressure (which can reach 1MPa) and the stiff cell wall surrounded plant cells. In my PhD, I focused on the role of these internal mechanical signals during plant development. More specifically, I investigated the contribution of the cell cortex in mechano-transduction. Together with my collaborators, I adapted a single cell approach to investigate the relative contribution of cell geometry and cortical tension on cortical microtubule (CMT) behavior. We found that CMTs align with the cell long axis when protoplasts are confined but not pressurized and with predicted maximal tension direction (transverse axis) when they are confined and pressurized. This suggests that mechanical signals can override geometrical cues. I also found that this response is dynamic: in absence of new mechanical stimulation, MTs align with the cell long axis, indicating that CMTs respond to tension changes rather than pressurization only. In parallel, I also contributed to the development of new genetic tool specifically removing PI (4,5)P2 from the plasma membrane. This highlighted a potential role of PI (4,5)P2 during organ initiation at the shoot apical meristem. Whether PI (4,5)P2 also affects the MT response to stress remains to be explored. CMTs are involved in cellulose synthesis through the guidance of cellulose synthase complexes at the plasma membrane, and thus ensuring anisotropic cell growth. Interestingly, plant overexpressing the phospholipase PLAIIIß display reduced cellulose content and reduced mechanical strength of aerial tissues. I investigated how plasma membrane composition could affect the cellulose synthesis machinery, opening the path to the analysis of the role of plasma membrane composition in CMT response to stress, cellulose synthesis, and development.

  : shape and growth, a question of geometry Defining shape

Fig. 1 .

 1 Fig. 1. Cortical microtubule response to protoplast confinement. (A) Main hypothesis: In a confined protoplast, transverse curvature is higher than longitudinal curvature, resulting in a competition between steric and mechanical cues; lower curvature would accommodate microtubule high bending stiffness, while high curvature would prescribe high tension to which microtubules may align with. (B) Schematic summary of the protocol used to confine and image protoplasts in microwells. (C) pUbQ1O::LTI6b-TdTomato (membrane marker) protoplast. Transmitted light channel (Left) and TdTomato fluorescence channel (Right). (D) pUBQ10::LTI6b-tdTomato images of a deformed and turgid (280 mOsmol/L mannitol) protoplast. Transmitted light channel (Left) and fluorescence of TdTomato channel (Right). Orthogonal views are presented at Right.( E) FEM representation of an unconfined protoplast (sphere, Upper) and confined protoplast (Lower). (F) Three-dimensional reconstruction from confocal stacks for an unconfined (Upper) and confined (Lower) protoplast expressing pUBQ10::LTI6b-tdTomato (280 mOsmol/L mannitol). (G) FEM simulation for a confined ellipsoid with an aspect-ratio (length/width) of 1.15, as measured in our experiments (1.13-1.17). Maximal tensile stress is predicted to be transverse, following Laplace-Young law. (H) p35S::GFP-MBD protoplast. (Left) Transmitted light channel. (Right) GFP fluorescence channel. Red, autofluorescence of chloroplasts; green, microtubule signal. (I, Left) Transmitted light channel and GFP fluorescence channel, 2 h after protoplast's insertion in the microwell. (I, Right) Transmitted light channel and GFP fluorescence channel, 16 h after protoplast's insertion in the microwell. Two different protoplasts are shown. (J) Examples of p35S::GFP-MBD protoplast images, illustrating the diversity of microtubule orientations in 15 × 20 μm microwells in pressurized (280 mOsmol/L mannitol) and confined protoplasts. Protoplasts were imaged 2 h after their transfer into hypotonic solution. (K) Analysis of CMT orientation with SFT. The cropped zone is delineated with the dotted red lines. The orientation of CMTs in each ROI is color coded. Polar histograms represent the CMT angle distribution for the protoplast. Each bar corresponds to an angle range of 9°. (L) Polar histograms of the probability of CMT orientations (classes of 9°angles) in all protoplasts, confined in 15 × 20 μm microwells, imaged 2 h after their transfer in 280 mOsmol/L mannitol (n = 126 protoplasts, three independent replicates). (Scale bars, 5 μm.)

Fig. 2 .

 2 Fig. 2. Challenging the transverse orientation of CMTs in confined and pressurized protoplasts. (A) Schematic representation of the stress pattern in 15 × 20 μm microwell. p35S::GFP-MBD pressurized protoplast, confined in 15 × 20 μm microwell, was pretreated with pluronic acid to reduce protoplasts adhesion to the well sides, and in 280 mOsmol/L mannitol. (Lower Left)Transmitted light channel. (Lower Right) GFP fluorescence channel. (B) Polar histograms representing the probability of CMT orientations (classes of 9°angles) in protoplasts confined in 15 × 20 μm passivated microwells and imaged 2 h after their transfer to 280 mOsmol/L mannitol (n = 29 protoplasts). (C) Schematic representation of protoplast curvature in 14 × 14 μm square-shaped wells. p35S::GFP-MBD protoplast was confined in 14 × 14 μm microwell in 280 mOsmol/L mannitol. (Lower Left)Transmitted light channel. (Lower Right) GFP fluorescence channel. (D) Polar histograms representing the probability of CMT orientations (classes of 9°angles) in protoplasts confined in 14 × 14 μm microwells and imaged 2 h after their transfer to 280 mOsmol/L mannitol (n = 74 protoplasts, three independent replicates). (E) Schematic representation of protoplast curvature in 12 × 40 μm wells. p35S::GFP-MBD protoplast was confined in 12 × 40 μm microwell in 280 mOsmol/L mannitol. (Lower Left) Transmitted light channel. (Lower Right) GFP fluorescence channel. (F) Polar histograms representing the probability of CMT orientations (classes of 9°angles) in protoplasts confined in 12 × 40 μm microwells, imaged 2 h after their transfer to 280 mOsmol/L mannitol (n = 99 protoplasts, four independent replicates). (Scale bars, 5 μm.)

Fig. 3 .

 3 Fig. 3. Pressurization determines CMT orientation in confined microwells. (A) p35S::GFP-MBD-confined protoplast in 12 × 40 μm microwell in hypertonic solution (800 mOsmol/L mannitol). (Left) Schematic representation. (Center) Transmitted light channel. (Right) GFP fluorescence channel. (B) Examples of highly deformed p35S::GFP-MBD protoplasts in 800 mOsmol/L mannitol. (C ) Polar histograms representing the probability of CMT orientations (classes of 9°angles) in protoplasts in hypertonic solution and imaged 2 h after their transfer to 800 mOsmol/L mannitol (n = 102 protoplasts, six independent replicates). (D) Scatterplot representing the dominant orientation of CMTs in each protoplast (OrientationJ, Dominant direction plugin analysis) according to the protoplast aspect-ratio after confinement (each dot represents a protoplast, n = 97 protoplasts, six independent replicates). (E and F ) CMT orientations (classes of 15°angles) for protoplasts with an aspect ratio inferior to 2.5 (n = 90 protoplasts) (E ) and superior to 2.5 (n = 12 protoplasts) (F ). (Scale bars, 5 μm.)

Fig. 4 .

 4 Fig. 4. Pressurization determines CMT orientation in confined microwells. (A) Time-lapse imaging of a p35S::GFP-MBD-confined protoplast in a1 2× 40 μm microwell as it is transferred from 600 to 280 mOsmol/L mannitol (at t = 0 min). New transverse CMTs progressively appear upon pressurization (red arrows). (B) Schematic representation of the experiment: Protoplasts were isolated in 600 mOsmol/L mannitol and then confined 12 × 40 μm microwells in the presence of 280 mOsmol/L mannitol for 16 h. (C ) p35S::GFP-MBD-confined protoplast in a 12 × 40 μmm i c r owell, imaged 16 h after transfer to 280 mOsmol/L mannitol. (Left)T r a n smitted light channel. (Right) GFP fluorescence channel. (D) Polar histograms representing the probability of CMT orientations (classes of 9°angles) in protoplasts in 12 × 40 μm microwells and imaged 16 h after transfer to 280 mOsmol/L mannitol (n = 72 protoplasts, three independent replicates). (Scale bars, 5 μm.)

Fig. S1 .

 S1 Fig. S1. Tensile stress pattern and curvature anisotropy Pattern of tensile stress is simulated following the protocol described in supplementary text. (a) Laplace-Young law predicts that curvature anisotropy also prescribes tensile stress anisotropy. (b) Simulation in sphere, ellipsoid and cylindrical shapes representing Cauchy stress (orientation and anisotropy). (c) Close-ups from (b)

Fig. S3 .

 S3 Fig. S3. Cell wall staining in seedling and protoplasts (a) Propidium iodide staining. p35S::GFP-MBD pavement cell from 7-day old seedling (top and middle) and p35S::GFP-MBD protoplast (bottom). Red: propidium iodide staining, green: GFP signal. (b) Calcofluor staining. p35S::GFP-MBD root cell from 7day old seedlings (top) and p35S::GFP-MBD protoplast (bottom). Red: chlorophyll autofluorescence, green: GFP signal and calcofluor staining. Scale bars: 5 µm

Fig

  Fig. S6. CMT dynamics in confined microwells (600 to 280 mOsmol/L mannitol), example 1 (a,b) p35S ::GFP-MBD Protoplasts were confined in 12x40µm microwell in 600 mOsmol/L mannitol and pressurized by decreasing the osmolarity of the medium (280 mOsmol/L mannitol) at t=0h. Further changes in osmolarity are indicated. Images are projections of timepoints from Movie S2. The osmolarity of the solution is indicated with a color code (green: 600 mOsm/L mannitol, red: 280 mOsm/L mannitol). (a) Protoplast deformation following changes in osmolarity is highlighted by the blue dotted line marking the contour of the protoplast. Grayscale signal was inverted in ImageJ. (b) p35S::GFP-MBD signal imaged every 20min for 240min in protoplast confined in 12x40µm microwell. Red arrows at t=20min and t=40min indicate new transverse microtubules.

Fig

  Fig. S7. CMT dynamics in confined microwells (600 to 280 mOsmol/L mannitol), example 2 (a,b) p35S ::GFP-MBD Protoplasts were confined in 12x40µm microwell in 600 mOsmol/L mannitol and pressurized by decreasing the osmolarity of the medium (280 mOsmol/L mannitol) at t=0h. Further changes in osmolarity are indicated. Images are projections of timepoints from Movie S3. The osmolarity of the solution is indicated with a color code (green: 600 mOsm/L mannitol, red: 280 mOsm/L mannitol). (a) Protoplast deformation following changes in osmolarity is highlighted by the blue dotted line marking the contour of the protoplast. Grayscale signal was inverted in ImageJ. (b) p35S::GFP-MBD signal imaged every 20min for 240min in protoplast confined in 12x40µm microwell.

Fig

  Fig. S8. CMT dynamics in confined microwells (600 to 280 mOsmol/L mannitol), example 3 (a,b) p35S ::GFP-MBD Protoplasts were confined in 12x40µm microwell in 600 mOsmol/L mannitol and pressurized by decreasing the osmolarity of the medium (280 mOsmol/L mannitol) at t=0h. Further changes in osmolarity are indicated. Images are projections of timepoints from Movie S4. The osmolarity of the solution is indicated with a color code (green: 600 mOsm/L mannitol, red: 280 mOsm/L mannitol). (a) Protoplast deformation following changes in osmolarity is highlighted by the blue dotted line marking the contour of the protoplast. Grayscale signal was inverted in ImageJ. (b) p35S::GFP-MBD signal imaged every 20min for 240min in protoplast confined in 12x40µm microwell. Red arrows at t= -10 min and t= 100 min indicate new transverse microtubules.

  patterns have downstream consequences on cell behaviors ultimately impacting plant development. Here, we review three examples in which spatiotemporal phospholipid pattern impacts plant development in different ways, highlighting the importance of integrative approaches to study phospholipid biology.

• 13 .

 13 Platre MP, Noack LC, Doumane M, Bayle V, Simon MLA, Maneta-Peyret L, Fouillen L, Stanislas T, Armengot L, Pejchar P, et al.: A Combinatorial Lipid Code Shapes the Electrostatic Landscape of Plant Endomembranes. Dev Cell 2018, 45:465-480 e411.

  A, Gujas B, van Wijk R, Munnik T, Hardtke CS: Primary root protophloem differentiation requires balanced phosphatidylinositol-4,5biphosphate levels and systemically affects root branching. Development 2015, 142:1437-1446. • 26. Gerth K, Lin F, Daamen F, Menzel W, Heinrich F, Heilmann M: Arabidopsis phosphatidylinositol 4-phosphate 5-kinase 2 contains a functional nuclear localization sequence and interacts with alpha-importins. Plant J 2017, 92:862-878.

27 .FiguresFigure 1 :

 271 Figures

Figure 2 :

 2 Figure 2: PI(4,5)P2 patterning in meristematic tissues and impact of imbalanced PI(4,5)P2/PI4P ratio on protophloem differentiation. (a) Schematic representation of the shoot apical meristem organization (top) and PI(4,5)P2 accumulation pattern together with the predicted tensile stress pattern (bottom). (b) Schematic representation of protophloem differentiation in Arabidopsis root meristem and phenotype associated with experimental variations in the PI(4,5)P2/PI4P balance. Root schematic was modified from B. Peret: https://figshare.com/articles/Primary_and_lateral_root_ai/5143987

Figure 3 :Figure 4 :

 34 Figure 3: Impact of PS variations on ROP6-mediated auxin signaling. (a) Variation of PS content at the plasma membrane during root differentiation. (b) Stabilization of ROP6 into PScontaining nanodomains upon auxin treatment and (c) impact of experimental variations of total PS content on ROP6 nanoclustering and downstream auxin signaling. Root schematic was modified from B. Peret: https://figshare.com/articles/Primary_and_lateral_root_ai/5143987

  P2 phosphoinositide is stereotypically distributed in the SAM, accumulating in boundary zones and being less present in the central zone. However, how PI(4,5)P2 pattern is established and how this lipid could contribute to SAM activities remained unexplored. A new genetically and inducible encoded system, called iDePP, encoding a phosphatase converting the PI(4,5)P2 located at the plasma membrane into PI4P, enables to address the role(s) of the PI(4,5)P2 during plant development. My first goal was to investigate the efficiency of this inducible tools in several aerial part of the plant, including in the SAM, and to deduce the role(s) of PI(4,5)P2 in SAM activities.

  Leia Colin a,1 , Antoine Chevallier a,b,1 , Satoru Tsugawa c , Florian Gacon a , Christophe Godin a , Virgile Viasnoff b,d,e , Timothy E. Saunders b,d , and Olivier Hamant a,2  Laboratoire de Reproduction et Développement des Plantes, Université de Lyon, ENS de Lyon, UCBL, INRAE, CNRS, 69364 Lyon Cedex 07, France; National University of Singapore, 117411 Singapore, Singapore; c Division of Biological Science, Graduate School of Science and Technology, Nara Institute of Science and Technology, Nara 630-0192, Japan; d Department of Biological Sciences, National University of Singapore, 117558 Singapore, Singapore; and e Centre National pour la Recherche Scientifique, UMI 3639, 117411 Singapore, Singapore Edited by Dominique C. Bergmann, Stanford University, Stanford, CA, and approved November 6, 2020 (received for reviewMay 5, 2020)

a b Mechanobiology Institute,

  The main rate-limiting enzymes involved in phospholipid interconversion are indicated (enzymes in red are discussed in this review). Abbreviations: DAG, diacylglycerol; PA, phosphatidic acid; PC, phosphatidylcholine; PE, phosphatidylethanolamine; PG, phosphatidylglycerol; PS, phosphatidylserine; PI, phosphatidylinositol; PI3P, phosphatidylinositol-3-phosphate; PI4P, phosphatidylinositol-4-phosphate; PI5P, phosphatidylinositol-5-phosphate; PI(3,5)P2,

	phosphatidylinositol-(3,5)-bisphosphate; PI(4,5)P2, phosphatidylinositol-(4,5)-bisphosphate;
	LPAAT, LYSOPHOSPHATIDIC ACID ACYLTRANSFERASE; PAP, PA PHOSPHATASE;
	AAPT, AMINOALCOHOL AMINOPHOSPHOTRANSFERASE; DGK, DAG KINASE;
	PECT,	CYTIDINE	TRIPHOSPHATE:PHOSPHORYLETHANOLAMINE
	CYTIDYLYLTRANSFERASE; PSS, PS SYNTHASE; CDS, CYTIDINE DIPHOSPHATE-
	DAG SYNTHASE; CMP-PA, CYTIDINE MONOPHOSPHATE PA; PIS, PI SYNTHASE;
	PI4K, PI4-KINASE; PIP5K, PI4P 5-KINASE; PLC, PHOSPHOLIPASE C; PLD,
	PHOSPHOLIPASE D.

1-2 PUBLICATION 1

| www.pnas.org/cgi/doi/10.1073/pnas.2008895117 Colin et al.

| www.pnas.org/cgi/doi/10.1073/pnas.2008895117 Colin et al.

| www.pnas.org/cgi/doi/10.1073/pnas.2008895117 Colin et al.

Remerciements

ACKNOWLEDGMENTS. We thank the MBI, Singapore, for hosting A.C. and O.H. for 6 months, where the original experiments were performed. We also thank our colleagues for constructive discussions about this project and for critical reading of the manuscript. We thank Platim for help with imaging and Gianluca Grenci for the design of the microwell casts at MBI. This work was supported by European Research Council Grant 615739 "MechanoDevo" (to O.H.), Ministry of Education, Culture, Sports, Science and Technology KAKENHI Grant-in-Aid for Scientific Research on Innovative Areas "Plant-Structure Optimization Strategy" GrantJP18H05484) (to S.T.) and MBI seed grant support (to V.V. and T.E.S.).

Acknowledgements.

We thank the L. Armengot, P. Moreau, O. Hamant, M. Platre and T. Stanislas for comments on the manuscript, Y.J. is funded by the French National Research Agency ANR caLIPSO (ANR-18-CE13-0025-02) and ANR STAYING-TIGHT (ANR-18-CE13-0016-02), L.C. is funded by a PhD fellowships from the French Ministry of Higher Education.

Author contributions: C.G., V.V., T.E.S., and O.H. designed research; L.C., A.C., F.G., and O.H. performed research; L.C., A.C., S.T., F.G., and O.H. analyzed data; and O.H. wrote the paper with assistance from T.E.S.. The authors declare no competing interest. This article is a PNAS Direct Submission.

Supplementary Information for

Cortical tension overrides geometrical cues to orient microtubules in confined protoplasts

Leia Colin 1 *, Antoine Chevallier 1,2 *, Satoru Tsugawa 3 , Florian Gacon 1 , Christophe Godin 1 , Virgile Viasnoff 2,4,5 , Timothy E. Saunders 2,4 , Olivier Hamant 1 Correspondence: Olivier.hamant@ens-lyon.fr

This PDF file includes:

Supplementary text Figures S1 to S8

Abbreviations:

PI4P, phosphatidylinositol-4-phosphate; PI(4,5)P2, phosphatidylinositol-