Plasticity in vertex model of epithelial tissues

In order to properly develop living organisms are required to change and maintain shape. These properties exists in a class of materials called amorphous solids such as colloidal gels, emulsions and foams: they respond elastically when exposed to low external stress but at a critical value of stress they yield and permanently change shape, allowing them to retain the memory of past stresses. Could such plasticity play a role during biological morphogenesis? Motivated by this question in this work we study plastic properties of vertex model of epithelial tissues, in which mechanical properties of cells are prescribed and emerging tissue mechanics is obtained from their collective behaviour. We investigate mechanical properties of elementary plastic event, a so called T1 transition in which two pairs of cells exchange neighborship. We demonstrate that they are analogous to plastic events in amorphous solids and find that elastic interactions among T1 transitions lead to non-linear steady state rheology and mechanical stability in the vertex model that are the same as found in mesoscopic models of amorphous solids. Finally, we devise observables quantifying a ’distance’ to the critical stress in flowing vertex model and epithelial tissues.