Finite element-based computer simulation of motility, sorting, and deformation in biological cells

Abstract

Computer simulations are an efficient and powerful tool fer investigating the complex processes involved in embryo morphogenesis. A survey of the literature shows that computer simulation have been applied at both the tissue level and the cell level. Here, a novel cell element is derived to model individual epithelial cells. Apical microfilament bundles, microtubules, intermediate filaments, adhesion and other cytoskeletal components are included in the model. The cell cytoplasm is assumed to be viscous. Each cell is allowed to undergo large deformations, but its area is kept constant using a Lagrange multiplier. Cells can rearrange and thus change the topology within the aggregate. This cell element is then used to model the behaviour of both homotypic and heterotypic cell aggregates.

In one set of simulations, a sheet of homotypic cells is subjected to large strains. Reaction forces on the edge of the sheet are calculated, and not compared with analytical results. Significant shape changes and cell rearrangements are observed. The simulations show how bulk mechanical properties arise from sub-cellular structure, and provide a basis for sophisticated simulation models of an entire embryo.

In addition, heterotypic cell aggregates consisting of two kinds of cells are investigated. Important cell phenomena, including cell sorting, tissue spreading and checker-board formation, are simulated. Some hypotheses about the mechanisms of cell sorting and motility are tested. The simulation results agree with fundamental aspects of real cell behaviour. They also provide useful insights into the behaviour of embryonic cells during morphogenetic processes, and can serve as a guide to future experiments.