  The response of cell populations to external stimuli plays a central role in
biological phenomena such as epithelial wound healing and developmental
morphogenesis. Wave propagation of a protein signal has been shown to direct
collective migration in one direction, but this mechanism based on active
matter under a traveling wave is not fully understood. To elucidate how the
traveling wave of the protein signal directs collective migration, we study the
mechanics of the epithelial cell monolayer, taking into account the
signal-dependent coordination of contractile stress and cellular orientation.
By constructing an optogenetically controlled experimental cell model, we found
that local signal activation induces changes in cell density and orientation
with the direction of propagation, increasing the net motion relative to the
wave. In addition, the migration exhibits an optimal speed with the propagation
speed of the signal. This occurs because the mechanical deformation is not
fully relaxed for rapid signal activation, resulting in an optimal signal
propagation speed. The presented mechanical model can also be extended to wound
healing, providing a versatile model for understanding the interplay between
mechanics and signaling in active matter.
