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 , pattern formation  and active turbulence . However, how mechanical and chemical signaling are integrated at the cellular level to give rise to such collective behaviors remains unclear. We address this with a focus on the highly conserved phenomenon of spatiotemporal 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.