Stability of asymmetric cell division under confinement: A deformable cell model of cytokinesis applied to C. elegans development

Abstract

Cell division during early embryogenesis has been linked to key morphogenic events such as embryo symmetry breaking and tissue patterning. It is thought that boundary conditions together with cell intrinsic cues act as a mechanical “mold”, guiding cell division to ensure these events are more robust. We present a novel computational mechanical model of cytokinesis, the final phase of cell division, to investigate how cell division is affected by mechanical and geometrical boundary conditions. The model reproduces experimentally observed furrow dynamics and predicts the volume ratio of daughter cells in asymmetric cell divisions based on the position and orientation of the mitotic spindle. We show that the orientation of confinement relative to the division axis modulates the volume ratio in asymmetric cell division and quantified the mechanical contribution of cortex mechanics, relative to the mechanical properties of the furrow ring. We apply this model to early C. elegans development, which proceeds within the confines of an eggshell, and simulate the formation of the three body axes via sequential (a)symmetric divisions up until the six cell stage. We demonstrate that spindle position and orientation alone can be used to predict the volume ratio of daughter cells during the cleavage phase of development. However, for compression perturbed egg geometries, the model predicts that the change in confinement alone is insufficient to explain experimentally observed differences in cell volume, inferring an unmodeled underlying spindle positioning mechanism. Finally, the model predicts that confinement stabilizes asymmetric cell divisions against bubble-instabilities, which can arise due to elevated mitotic cortical tension.

Single and two‐cells shape analysis from energy functionals for three‐dimensional vertex models

“…Here, no restrictions on the geometry are imposed, other than the size of the discretisation, which is regulated by the density of the nodal cloud. Models with finer density can be found for instance in, 13,29 which may be considered as an extension of the coarser vertex models.…”

“…Two-dimensional vertex models have been widely exploited to describe fluidity of tissues, 17 topological transitions [18][19][20][21] or jamming. 22 Three-dimensional extensions have been developed for epithelial rheology, 23,24 folding, 25 blastocytes analysis, 26 wound healing, 27 cyst formation, 28 or cell division, 29 to cite a few.…”

Interacting active surfaces: A model for three-dimensional cell aggregates

“…From a computational perspective, there has been a growing attention to the simulation of the dynamics of fluid interfaces both with prescribed [43][44][45][46] and with time-evolving shape [41,42,[47][48][49][50][51][52][53]. In addition, recent discrete deformable cell models have described cellular aggregates by representing cells by triangular meshes with viscoelastic edges [54][55][56][57].…”