Thiels, W. | bioRxiv Science

bioRxiv2022

Cell shape characterization, alignment and comparison using FlowShape

MotivationThe shape of a cell reflects, among other things, actomyosin activity and adhesion properties. Cell shape is further tightly linked to cell differentiation and can reveal important cellular behaviors such as polarization. Hence, it is useful and informative to link cell shape to genetic and other perturbations. However, most currently used cell shape descriptors capture only simple geometric features such as volume and sphericity. We propose FlowShape, a new framework to study cell shapes in a complete and generic way. ResultsIn our framework a cell shape is first represented as a single function on a sphere. The curvature of the shape is measured and next mapped onto a sphere in a conformal manner. This special curvature map is then approximated by a series expansion: the spherical harmonics decomposition. This decomposition facilitates a wide range of shape analyses, including shape alignment, statistical cell shape comparison and inference of cell shape deformations over time. From this representation, we can reconstruct the cell shape using the Dirac equation. The new tool is applied to perform a complete, generic analysis of cell shapes, using the early Caenorhabditis elegans embryo as a model case. We distinguish and characterize the cells at the seven-cell stage. Next, a filter is designed to identify protrusions on the cell shape to highlight lamellipodia in cells. Furthermore, we use our framework to identify any shape changes following a gene knockdown of the Wnt pathway. Cells are first optimally aligned using the fast Fourier transform, followed by calculating an average shape. Shape differences between conditions are next quantified and compared to an empirical distribution. Finally, we put forward a highly performant implementation of the core algorithm, as well as routines to characterize, align and compare cell shapes, through the open-source software package FlowShape. AvailabilityThe data and code needed to recreate the results are freely available at https://doi.org/10.5281/zenodo.7391185. The most recent version of the software is maintained at https://bitbucket.org/pgmsembryogenesis/flowshape/. Author summaryWe present FlowShape, a framework for cell shape analysis, based on the concept of spherical harmonics decomposition. This decomposition allows for any function defined on a sphere to be rewritten as a weighted sum of basis functions. Contrary to previous work, we use a single function to describe a shape, the mean curvature, which implies that the decomposition weights can be used as a complete shape description. The expression of a shape in this manner allows for very efficient calculations, as we illustrate with the C. elegans embryo as a model. The decomposition permits efficient comparison and alignment of shapes. We demonstrate this by clustering the cells in the early embryo and illustrating the different shapes by cluster. The decomposition further facilitates averaging of shapes and searching for particular features on the shape by defining filters that can then be efficiently applied. Finally, we illustrate how the framework can facilitate statistical comparisons between shapes.

bioinformatics↗

bioRxiv2022

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

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. Author summaryA crucial morphogenic step during early embryonic development is symmetry breaking in the embryo. For C. elegans the formation of the three body axes can be traced back to the six cell stage, where tissue-topology is the result of symmetric and asymmetric divisions. How cell mechanical boundary conditions and cell intrinsic cues influence this process of symmetry breaking is still an open question, as currently, a quantitative mechanical description of cytokinesis in complex architectures is lacking. We developed a simple mechanical model of cell division, incorporated in an existing mechanical cortex model, to simulate cytokinesis in geometrically confined environments. Our approach was able to both capture furrow ring dynamics and predict the volume ratio of daughter cells accurately. By simulating early C. elegans development with different geometrical boundary conditions, we were able to trace back the origin of volume discrepancies between the experimental setups to a quantifiable shift in spindle positioning during cytokinesis. Finally, we showed how embryo confinement partially stabilizes bubble-instabilities that arise during asymmetric cell division during the early cleavage phase.

biophysics↗