A dynamic cell model for the formation of epithelial tissues

A dynamic model is proposed for monolayered epithelial tissue, in which the monolayer is assumed to consist of prismatic cells, so that the system is described as a two-dimensional polygonal pattern. Its dynamic behaviour is determined by equations of motion for vertices in the polygonal pattern and elementary change in the system (change in the connection of vertex pairs). The vertices are driven by the sum of interfacial tension on cell boundaries and the resistance force against the deformation of cells. It is shown by computer simulations that our model possesses the characteristics of epithelial tissue, that is it has a mechanism which makes the edge number and size of a cell uniform and the shape symmetric. This mechanism finally gives rise to a regular polygonal pattern similar to a honeycomb pattern, even though initial patterns have large variations. Local equilibrium dynamics under which the size of each cell is flexibly adapted to its local environment are compared with non-local equilibrium dynamics. The local equilibrium dynamics produce more natural cellular patterns.