This thesis presents an in-depth investigation into the dynamics of the actin cortex and the mechanisms underlying cytoplasmic flow during anaphase in zebrafish embryogenesis. These two themes, connected through the theoretical tools and numerical simulations, are approached in two distinct chapters.
Chapter 1: Polymerizing active gel with mixed polar and nematic order In the first chapter, we developed an active gel theory combining both polar and nematic order.
In the first chapter, we developed an active gel theory combining both polar and nematic order. This framework enabled us to systematically investigate active gel theory, considering configurations without orientation or with polar, nematic or both orders. We discovered a novel mechanism for stabilizing topological defects. This mechanism is governed by density turnover and reinforced by active isotropic contractile stress. The findings revealed that topological defects can self-organize into square or hexagonal lattices. We observed that the stabilization of defect pairs by turnover does not depend on orientational order. We saw that polar order results in integer topological defects, while nematic order leads to half-integer defects.
This exploration was extended to consider the effects of the membrane, and we incorporated polymerization forces at the membrane through boundary conditions. With this setup we observed two phenomena: first a change in the orientation of the polar and nematic field through the density step-profile formed above the membrane, and second, formation of figer-like structures of density. These results allowed us to propose explanations for the observed changes in actin filament orientation within the lamellipodium of zebrafish keratocytes, and for the formation of actin protrusions. These explanations rely solely on the mechanical properties of the active gel.
Chapter 2: Physical investigation of cytoplasmic-flow scaling during anaphase in zebrafish early embryogenesis.
The second chapter focuses on elucidating the scaling of cytoplasmic flow during anaphase in zebrafish early embryogenesis, integrating biological observations with theoretical descriptions and numerical methods. After rigorously exploring various hypotheses to explain the mechanism generating the cytoplasmic flow, we concluded that the only plausible explanation is that flow is generated by dynein motors pulling mitochondria and other cargo toward the center of the aster and reciprocally pulling the aster in a direction depending on the aster asymmetry. Asters are initially asymmetric, and due to their growth while being pulled apart, this asymmetry is conserved throughout anaphase. The presence of friction between the cytosol and the microtubule aster ensures that the velocity of asters remains independent of their size. Analytical predictions support this mechanism as the only stable solution that adequately explains chromosome separation with constant aster growth and separation. Furthermore, through numerical simulations, we demonstrated that the scaling observed in nuclear envelope reformation can be attributed to confinement effects arising from the no-slip boundary condition at the membrane. Our study represents a significant advancement in our understanding of anaphase in zebrafish embryogenesis, shedding light on the intricate processes underlying cell division and development.
