A hybrid model framework for studying mechanics of epithelial morphogenesis*

Embryonic morphogenesis requires many stages of complex bending, twisting, and positioning of tissues as the organism develops. These coordinated movements often require complex coordination and regulation of biomechanical forces, the nature of which is often not well understood. Here we present a simulation framework for modeling morphogenetic events in early embryogenesis from a mechanics perspective. To accomplish this, we have implemented a hybrid model, which takes advantage of the benefits of vertex models and particle models while avoiding their respective drawbacks. We represent each cell membrane as a polygon consisting of a given number of nodes with elastic springs forming the polygon’s edges. Cells can then be assigned additional force components which act on the cell’s nodes such as forces originating from apical constriction. Additionally, we use a simple collision method implementing a ray casting algorithm to handle cell-cell collisions. The model has been used to successfully model the folding of mesoderm epithelium during Drosophila gastrulation and has illustrated how changing mechanical properties of cells can lead to “mutant” varieties. We further anticipate that the simplicity in development of new physics components and models using this framework will lead to its application to model several different morphogenetic events as well as allowing for identification of the regulatory role of mechanical forces in development.