Elucidating the mechanism of AP axis alignment in the C. elegans embryo

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 15