Dans les tissus, les cellules génèrent et sont soumises en permanence à des forces mécaniques. Les perturbations biochimiques à l'intérieur des cellules, ainsi que les altérations de leur environnement mécanique peuvent modifier l'équilibre physiologique et mener à des pathologies, comme le cancer. Bien que les propriétés mécaniques puissent être modifiées à l'échelle du tissus, la compréhension de la mécanique au niveau de la cellule unique demeure importante. En particulier, la différenciation, la migration des cellules immunitaires et le caractère invasif d'un cancer dépendent fortement des propriétés mécaniques des cellules uniques. Les déformations mécaniques peuvent induire un changement de la surface et du volume cellulaires. Nous nous intéressons particulièrement à la régulation du volume cellulaire chez les cellules mammifères dans le contexte de déformations à différentes échelles de temps. Jusqu'à présent, la régulation du volume dans ce contexte n'a été que très peu étudiée, en raison de la difficulté d'obtention de mesures précises, et du fait que le volume de la cellule est généralement considéré comme constant. Nous avons développé une méthode de mesure du volume cellulaire reposant sur l'exclusion de fluorescence, qui nous permet d'effectuer des mesures de volume précise au niveau de la cellule unique. Dans cette étude, nous nous sommes concentrés sur la régulation du volume cellulaire au cours de l'étalement dynamique sur un substrat (échelle de temps : minutes). Nous avons démontré qu'il existe différents régimes de régulation du volume lors de l'étalement : les cellules réduisent, augmentent ou ne modifient pas leur volume, en fonction de l'état du cortex d'actomyosine et de la vitesse d'étalement. Nous avons constaté que les cellules s'étalant plus vite ont tendance à perdre davantage de volume. Notre hypothèse est que lors d'une extension rapide de lamellipode dépendante d'Arp2/3, l'actine tire sur la membrane et génère une tension et l'activation de transport ionique, s'accompagnant d'une perte de volume compensatoire. L'inhibition de la polymérisation de l'actine ou de sa ramification dépendante d'Arp2/3 réduit la vitesse d'étalement et ainsi la perte de volume. Nous avons ensuite montré que l'inhibition de la contractilité augmente la vitesse d'étalement et la perte de volume. Cependant, l'inhibition d'Arp2/3 dans des cellules à faible contractilité conduit à un étalement rapide sans perte de volume. En effet, l'inhibition d'Arp2/3 induit des bulles de membranes, une déformation rapide n'induirait donc pas de perte de volume car la cellule peut relâcher la tension en dépliant la membrane. Nous avons également montré que la régulation du volume en réponse à une compression mécanique rapide (échelle de temps : millisecondes) indépendante de l'adhérence dépend également de l'état du cortex d'actomyosine. Les cellules perdent jusqu'à 30% de leur volume lorsqu'elles sont confinées, car la membrane plasmique est attachée au cortex et ne peux pas être dépliée en réponse à l'augmentation de la tension. La perturbation du cortex d'actine induit le détachement de la membrane et limite la perte de volume. Enfin, nous avons montré que la réponse du volume à un choc osmotique (échelle de temps : secondes) est plus que complexe que décrite dans la littérature. Nos données indiquent qu'au niveau de la cellule unique, la réponse initiale du volume au changement de l'osmolarité extérieure n'est pas un processus passif uniforme. En utilisant la technique du choc osmotique, nous avons également confirmé que les cellules ont un large excès de membrane repliée dans des réservoirs. Nos résultats montrent que le volume et l'aire cellulaires sont couplés par l'homéostasie de la tension de surface, et, étant donné que les déformations induisent une augmentation de la tension de surface, elles conduisent à des modifications du volume et de l'aire de la cellule. / The field of biomechanics significantly progressed in the last two decades. The importance of the feedback between biochemical signaling and physical properties was revealed in many studies. Cells within tissues constantly generate and experience mechanical forces. Biochemical perturbations inside the cells as well as alterations in the mechanical environment can shift the tiny balance of normal physiological state and lead to pathologies, e.g. cancer. Although the mechanical properties of individual cells can alter when they are within the tissues, the understanding of single cell mechanics is still important. Differentiation, immune cell migration, and cancer invasion strongly depend on the mechanical properties of individual cells. Mechanical deformations can lead to a change in cell surface area and volume. We are particularly interested in single mammalian cell volume regulation in the context of deformations of different timescales. For the moment, volume regulation in this context was out from the research interest, probably due to the difficulties of accurate measurements, and cell volume often considered as a constant parameter. We developed a method for cell volume measurements based on a fluorescent exclusion that allowed us to perform precise volume measurements of individual live cells. In the present study, we mainly focused on cell volume regulation while dynamic spreading on a substrate (timescale – minutes). We demonstrated that there are different regimes for volume regulation while spreading: cells decrease, increase or do not change volume, and a type of the regime depends on the state of the actomyosin cortex and spreading speed. We obtained that faster-spreading cells tend to lose more volume. Our hypothesis is that during fast Arp2/3-driven lamellipodia extension actin pull on the membrane that generates tension and activation of ion transport and regulatory volume loss. Inhibition of actin polymerization or Arp2/3-dependent actin branching decreases spreading speed and volume loss. Next, we showed that inhibition of contractility increases spreading speed and volume loss. However, inhibition of Arp2/3 complex in cells with low contractility leads to fast spreading without volume loss. Our explanation is that inhibition of Arp2/3 induces cell blebbing and even fast deformation does not lead to volume loss as a cell can relax tension by membrane unfolding. We also showed that volume regulation in response to fast mechanical compression (timescale – milliseconds) independent of adhesion also depends on the actomyosin cortex state. Control cells lose up to 30% of volume under confinement, as the cell membrane is attached to the cortex and cannot be unfolded in response to the tension increase. Disruption of actin cortex leads to membrane detachment and prevents volume loss under confinement. Additionally, we showed that cell volume response to the osmotic shock (timescale – seconds) is more complex than it used to be known in the literature. For instance, our data indicate that at the level of individual cells initial volume response to the change of external osmolarity is not a uniform passive process. Using osmotic shock technique, we also confirmed that cells have a large excess of membrane folded in reservoirs. Taken together, our data show that cell volume and surface area are coupled through surface tension homeostasis and as deformations induce surface tension increase, they lead to change volume and surface area.

Development of a single-cell embryo into an adult multi-cellular organism features the establishment of upto three anatomical body axes - anteroposterior, dorsoventral and left-right. It has been observed in many organisms that these body axes can consistently orient relative with respect to the geometric features of the embryo in many organisms. One such example is observed in the model organism Caenorhabditis elegans (C. elegans), where the Anteroposterior (AP) axis coincides with the geometric long axis of the ellipsoidal embryo -- the shape being imposed by the surrounding eggshell. In C. elegans, the Anteroposterior axis is established at the one-cell stage via its polarization by PAR polarity proteins. This cell polarization proceeds via a self-organized mechanochemical feedback between the PAR proteins and mechanical flows in the actomyosin cortex, resulting in the formation of two mutually exclusive domains of Anterior PAR and Posterior PAR proteins on the cortex denoting the future anterior and posterior end of the embryo -- and thus establishing the Anteroposterior axis. The initial orientation of the Anteroposterior axis is determined by the site of sperm entry at fertilization. However, the nascent Anteroposterior axis that forms after fertilization is observed to actively re-orient -- indicated by the movement of the PAR domains and concurrent migration (here termed posteriorisation) of the sperm-donated male pronucleus -- such that it aligns with the long axis of the ellipsoidal embryo, if it is not already aligned. In effect, the site of sperm entry only determines which half of the embryo becomes the posterior half of the embryo. This phenomenon of active re-orientation of the Anteroposterior axis, that ensures that the Anteroposterior axis aligns with the long axis of the embryo, is termed Anteroposterior axis alignment. The work described in this thesis investigates the mechanism of this Anteroposterior axis alignment in the C. elegans embryo. Anterior-directed flows in the actomyosin cortex observed during Anteroposterior axis establishment have also been found to be essential for Anteroposterior axis alignment. In this thesis, two possible mechanisms of Anteroposterior axis alignment are considered, both of which are consequences of these cortical flows. Cortical flows at the embryo surface can drive flows in the bulk cytoplasm in the embryo, generating cytoplasmic flows which point towards the sperm-donated male pronucleus as it posteriorises. Previous studies have proposed that these cytoplasmic flows could push onto the male pronucleus, and due to the ellipsoidal geometry of the embryo, drive it towards the closest tip of the embryo. This proposed mechanism is referred to as the cytoplasmic flow-dependent mechanism in this thesis. Another mechanism proposed in this thesis postulates that the reorientation of the Anteroposterior axis occurs via the repositioning of the pseudocleavage furrow. The pseudocleavage furrow is a contractile ring-like structure that forms at the boundary of the two PAR domains during Anteroposterior axis establishment. The pseudocleavage furrow forms as a result of compressive alignment of actin filaments in the actomyosin cortex due to cortical flows. In cases where the Anteroposterior axis is not aligned with the long axis of the embryo, the pseudocleavage furrow is not perpendicular to the long axis of the embryo. In such cases, active anisotropic stresses generated in the actomyosin cortex could force the rotation of the pseudocleavage furrow akin to an elastic rubber-band on an ellipsoid, and cause the Anteroposterior axis to re-orient towards the long axis of the embryo. This proposed mechanism is referred to as the pseudocleavage furrow-dependent mechanism in this thesis. This thesis investigates the role played by the two mechanisms in Anteroposterior axis alignment. This is accomplished in the following way: a theoretical model of the Anteroposterior axis alignment is introduced, consisting of a description of the actomyosin cortex as an active nematic fluid present on the 2D surface of a fixed ellipsoid representing the embryo. This description of the cortex incorporates both the cytoplasmic flow-dependent mechanism and the pseudocleavage furrow-dependent mechanism. RNAi experiments in the C. elegans embryo that remove the pseudocleavage furrow, in conjuction with numerical simulations using the theoretical model, show that the pseudocleavage furrow-dependent mechanism is the predominant mechanism that drives Anteroposterior axis alignment, while cytoplasmic flow-dependent mechanism plays only a minor role. RNAi experiments that modify the geometry of the C. elegans embryo -- specifically, generate rounder embyros -- show that embryo geometry can influence the rate of re-orientation of the Anteroposterior axis during Anteroposterior axis alignment -- with slower Anteroposterior axis alignment in rounder embryos. Such an relation between embryo geometry and Anteroposterior axis alignment is found to be consistent with pseudocleavage furrow-dependent mechanism, both via predictions made using the theoretical model and using a simplified effective model of a contractile ring (or elastic rubber-band) on a fixed ellipsoid. Altogether, the work presented in this thesis shows Anteroposterior axis alignment observed in the C. elegans embryo is driven primarily by the anisotropic stresses in the actomyosin cortex that generate the pseudocleavage furrow. The work here also shows that the Anteroposterior axis alignment process is sensitive to the geometry of the embryo. In effect, active mechanical flows in the actomyosin cortex translate the ellipsoidal geometry of the embryo into a robust orientation of the Anteroposterior axis of the C. elegans embryo. Mechanical flows such as these are not exclusive to C. elegans, nor are specific orientations of the body axes with respect to the embryo geometry. The results in this thesis thus point towards a possibly general role of the interactions between mechanical flows and embryo geometry to properly orient the body axes of the developing embryos of many multi-cellular organisms.:Contents Abbreviations iii Abstract iv 1 Introduction 1 1.1 Cytoskeleton 3 1.1.1 Main constituents of the cytoskeleton 3 1.1.2 Actomyosin cortex 7 1.2 Hydrodynamic theory of active fluids 8 1.2.1 Conservation Laws 9 1.2.2 Continuously broken symmetries 11 1.2.3 Irreversible thermodynamics of active fluids 13 1.2.4 Constitutive equations of active nematic fluids 19 1.3 C. elegans as a model organism 21 1.3.1 Early embryogenesis in C. elegans 22 1.4 AP axis establishment in C. elegans 24 1.4.1 PAR polarity system . 24 1.4.2 Mechanism of AP axis establishment 26 1.4.3 AP axis alignment 27 1.5 Overview 29 2 A theoretical model for AP axis alignment 30 2.1 A model of AP axis establishment in C. elegans 30 2.1.1 Turing-like system for PAR polarity system 31 2.1.2 Active isotropic description of actomyosin cortex 33 2.1.3 Guiding cues for AP axis establishment 34 2.1.4 Full model of AP axis establishment in [1] 35 2.2 A model of pseudocleavage furrow formation in C. elegans 36 2.2.1 Dynamics of Actin alignment 37 2.2.2 Active stress generated by alignment of actin filaments 38 2.3 A model of AP axis alignment in C. elegans 39 2.3.1 A thin film active nematic description of the cortex 40 2.3.2 Description of the Cytoplasm and Male pronucleus 46 2.3.3 Numerical simulations of the theoretical model 48 3 Materials and Methods 52 3.1 Culture conditions, strains and worm handling 52 3.2 Genetic perturbations by RNAi 53 3.3 Time-lapse microscopy 53 3.4 Image analysis 54 3.4.1 Pre-processing 54 3.4.2 Tracking posteriorisation of the male pronucleus 56 3.4.3 Measuring cortical flows 66 3.4.4 Measuring cytoplasmic flows 67 3.5 Data analysis 67 4 Experimental investigation of AP axis alignment 71 4.1 Characterising AP axis alignment in unperturbed embryos 71 4.2 Cortical flows are required for AP axis alignment 76 4.3 Role of Pseudocleavage furrow in AP axis alignment 83 4.3.1 Removing Pseudocleavage furrow via RNAi 83 4.3.2 Comparing numerical simulations to experimental results 88 4.4 Role of embryo geometry in AP axis alignment 99 4.4.1 Rounder embryos show slower AP axis alignment 99 4.4.2 Relation between embryo geometry and AP axis alignment 108 4.5 Additional experiments 118 4.5.1 Exploring relation between embryo geometry and AP axis alignment in ima-3 RNAi embryos 118 4.5.2 Are pseudocleavage furrow-dependent and cytoplasmic flow-dependent mechanisms sufficient to explain AP axis alignment? 121 4.5.3 Role of microtubules in AP axis alignment 127 5 Conclusions and Outlook 134 Appendix 139 Bibliography 142 List of publications 156 Acknowledgements 157