Collective Motion of Epithelial Cells in Tissues and the Active Vertex Model

Epithelial tissues consist of cells attached to each other by junctions that may move collectively. We review results obtained by numerical simulations of vertex models in which cells are polygons that tile a region of the plane. In particular, we present results for wound healing assays, in which cells migrate to an empty space, and for antagonistic migration assays, in which cells from one tissue invade an adjacent tissue comprising cells of different type. We discuss coarse-graining the active vertex model to obtain continuum equations at macroscopic scales and review a selection of results on the anisotropy transition of homogeneous phases, their stability and the effects of shear.