Hydrodynamic Stability and Pattern Formation in Hexatic Epithelial Layers

Abstract

We investigate the hydrodynamic stability and the formation of patterns in a continuum model of epithelial layers, able to account for the interplay between mechanical activity, lateral adhesion, and the sixfold orientational order originating from the hexagonal morphology of the cells. Unlike in other models of active liquid crystals, the balance between energy injection and dissipation can here involve multiple length scales, resulting in a large spectrum of dynamical behaviors. When kinetic energy is dissipated by the cells' adhesive interactions at a rate higher than at which is injected by active stresses, the quiescent state of the cellular layer is generically stable: i.e., hydrodynamically stable regardless of its size. However, as the cellular layer becomes progressively more active, this homeostatic condition is altered by a hierarchy of pattern-forming instabilities, where the system organizes in an increasingly large number of counterflowing lanes of fixed width. In two-dimensional periodic domains, the latter organization is itself unstable to the proliferation of vortices and the dynamics of the cellular layer becomes eventually chaotic and yet different from the more common active turbulence.