ESPCI web site
Instabilities and geometry of growing tissues
The vertex model is a discrete often used to described cellular media, where elastic energy depends on the difference of cells’ actual area and perimeter from a reference values. Cells are allowed to change neighbors via different topological transition - including division, apoptosis and so - called T1 transitions. We derive a complete, coarse grained, continuum model of the 2D vertex model, applicable for different underlying geometries, and allows for analytical analysis. Using a geometric approach and out-of-equilibrium statistical mechanics, we calculate both mechanical and dynamical instabilities within a tissue, and their dependence on different variables, including activity, and disorder. Most notably, the tissue’s response depends on the existence of mechanical residual stresses on a cellular level. Thus, even freely growing tissues may exhibit a growth instability depending on food consumption. Using this geometric model we can readily distinct between elasticity and plasticity in a growing, flowing, tissue.