The extra-embryonic space and the local contour are crucial geometric constraints regulating cell arrangement

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

Cell division during early embryogenesis is linked to key morphogenic events such as embryo symmetry breaking and tissue patterning. It is thought that the physical surrounding of cells together with cell intrinsic cues act as a mechanical "mold," guiding cell division to ensure these events are robust. To quantify how cell division is affected by the mechanical and geometrical environment, we present a novel computational mechanical model of cytokinesis, the final phase of cell division. Simulations with the model reproduced experimentally observed furrow dynamics and describe the volume ratio of daughter cells in asymmetric cell divisions, based on the position and orientation of the mitotic spindle. For dividing cells in geometrically confined environments, we show how the orientation of confinement relative to the division axis modulates the volume ratio in asymmetric cell division. Further, we quantified how cortex viscosity and surface tension determine the shape of a dividing cell and govern bubble-instabilities in asymmetric cell division. Finally, we simulated the formation of the three body axes via sequential (a)symmetric divisions up until the six-cell stage of early C. elegans development, which proceeds within the confines of an eggshell. We demonstrate how model input parameters spindle position and orientation provide sufficient information to reliably predict the volume ratio of daughter cells during the cleavage phase of development. However, for egg geometries perturbed by compression, the model predicts that a change in confinement alone is insufficient to explain experimentally observed differences in cell volume. This points to an effect of the compression on the spindle positioning mechanism. Additionally, the model predicts that confinement stabilizes asymmetric cell divisions against bubble-instabilities.

MorphoSim: an efficient and scalable phase-field framework for accurately simulating multicellular morphologies

The phase field model can accurately simulate the evolution of microstructures with complex morphologies, and it has been widely used for cell modeling in the last two decades. However, compared to other cellular models such as the coarse-grained model and the vertex model, its high computational cost caused by three-dimensional spatial discretization hampered its application and scalability, especially for multicellular organisms. Recently, we built a phase field model coupled with in vivo imaging data to accurately reconstruct the embryonic morphogenesis of Caenorhabditis elegans from 1- to 8-cell stages. In this work, we propose an improved phase field model by using the stabilized numerical scheme and modified volume constriction. Then we present a scalable phase-field framework, MorphoSim, which is 100 times more efficient than the previous one and can simulate over 100 mechanically interacting cells. Finally, we demonstrate how MorphoSim can be successfully applied to reproduce the assembly, self-repairing, and dissociation of a synthetic artificial multicellular system - the synNotch system.

Delineating mechanisms and design principles of Caenorhabditis elegans embryogenesis using in toto high-resolution imaging data and computational modeling

The nematode (roundworm) Caenorhabditis elegans is one of the most popular animal models for the study of developmental biology, as its invariant development and transparent body enable in toto cellular-resolution fluorescence microscopy imaging of developmental processes at 1-min intervals. This has led to the development of various computational tools for the systematic and automated analysis of imaging data to delineate the molecular and cellular processes throughout the embryogenesis of C. elegans, such as those associated with cell lineage, cell migration, cell morphology, and gene activity. In this review, we first introduce C. elegans embryogenesis and the development of techniques for tracking cell lineage and reconstructing cell morphology during this process. We then contrast the developmental modes of C. elegans and the customized technologies used for studying them with the ones of other animal models, highlighting its advantage for studying embryogenesis with exceptional spatial and temporal resolution. This is followed by an examination of the physical models that have been devised—based on accurate determinations of developmental processes afforded by analyses of imaging data—to interpret the early embryonic development of C. elegans from subcellular to intercellular levels of multiple cells, which focus on two key processes: cell polarization and morphogenesis. We subsequently discuss how quantitative data-based theoretical modeling has improved our understanding of the mechanisms of C. elegans embryogenesis. We conclude by summarizing the challenges associated with the acquisition of C. elegans embryogenesis data, the construction of algorithms to analyze them, and the theoretical interpretation.