Theory of mechano-chemical 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 [1], pattern formation [2] and active turbulence [3]. However, how mechanical and chemical signaling are integrated at the cellular level to give rise to such collective behaviors remains unclear. We address this by focusing on the highly conserved phenomenon of spatio-temporal waves of density [2, 4–8] and ERK/MAPK activation [9–11], 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 mechano-chemical coupling between three-dimensional active cellular tensions and the mechano-sensitive ERK/MAPK pathway. Next, we demonstrate how this biophysical mechanism can robustly induce migration in a desired orientation, and we determine a theoretically optimal pattern for inducing efficient collective migration fitting well with experimentally observed dynamics. We thereby provide a bridge between the biophysical origin of spatio-temporal instabilities and the design principles of robust and efficient long-ranged migration.