Theory of mechanochemical patterning and optimal migration in cell monolayers

Collective cell migration offers a rich field of study for non-equilibrium physics and cellular biology, revealing phenomena such as glassy dynamics, pattern formation and active turbulence. However, how mechanical and chemical signalling are integrated at the cellular level to give rise to such collective behaviours remains unclear. We address this by focusing on the highly conserved phenomenon of spatiotemporal waves of density and extracellular signal-regulated kinase (ERK) activation, which appear both in vitro and in vivo during collective cell migration and wound healing. First, we propose a biophysical theory, backed by mechanical and optogenetic perturbation experiments, showing that patterns can be quantitatively explained by a mechanochemical coupling between active cellular tensions and the mechanosensitive ERK pathway. Next, we demonstrate how this biophysical mechanism can robustly induce long-ranged order and migration in a desired orientation, and we determine the theoretically optimal wavelength and period for inducing maximal migration towards free edges, which fits well with experimentally observed dynamics. We thereby provide a bridge between the biophysical origin of spatiotemporal instabilities and the design principles of robust and efficient long-ranged migration.