Geometry of T1 transitions in epithelia

Abstract: The flows of tissues of epithelial cells often involve T1 transitions. These neighbour exchanges are irreversible rearrangements crossing an energy barrier. Here, by an exact geometric construction, I determine this energy barrier for general, isolated T1 transitions dominated by line tensions. I show how deviations from regular cell packing reduce this energy barrier, but find that line tension fluctuations increase it on average. By another exact construction, I show how nonlinear tensions in vertex models of epithelial tissues also resist T1 transitions. My results thus form the basis for coarse-grained descriptions of cell neighbour exchanges in continuum models of epithelia.