Why epithelial cells collectively move against a traveling signal wave

The response of cell populations to external stimuli plays a central role in biological mechanical processes such as epithelial wound healing and developmental morphogenesis. Wave-like propagation of a signal of ERK MAP kinase has been shown to direct collective migration in one direction; however, the mechanism based on continuum mechanics under a traveling wave is not fully understood. To elucidate how the traveling wave of the ERK kinase signal directs collective migration, we constructed the mechanical model of the epithelial cell monolayer by considering the signal-dependent coordination of contractile stress and cellular orientation. The proposed model was studied by using an optogenetically controlled cell system where we found that local signal activation induces changes in cell density and orientation with the direction of propagation. The net motion of the cell population occurred relative to the wave, and the migration velocity showed a maximum in resonance with the velocity of the ERK signal wave. The presented mechanical model was further validated in an <i>in vitro</i> wound healing process.