Mechanics and remodelling of cell packings in epithelia

Epithelia are sheets of cells that are dynamically remodelled by cell division and cell death during development. Here we describe the cell shapes and packings as networks of polygons: stable and stationary network configurations obey force balance and are represented as local minima of a potential function. We characterize the physical properties of this vertex model, including the set of ground states, and the energetics of topological rearrangements. We furthermore discuss a quasistatic description of cell division that allows us to study the mechanics and dynamics of tissue remodelling during growth. The biophysics of cells and their rearrangements can account for the morphology of cell packings observed in experiments.