Collective cell migration induced by the interplay of contractile force and adhesion with delay under ERK signal propagation.

Collective migration is ubiquitously observed in epithelial cell sheets during wound healing and morphogenesis. For epithelial MDCK cells, ERK MAP kinase forms solitary wave and propagate across migrating cells. Cells orient their directions of migration oppose to the ERK wave, however, their guidance is distinct from tactic behavior. To understand the underlying mechanism of ERK directed collective migration, we propose simple theoretical model where interplay of focal adhesion and contractile force is regulated by ERK signal. Given that ERK signal locally increases both contractile force and focal adhesion onto substrate, we construct the equation of force-balance between viscous cellular fluid and dissipative friction. When ERK signal moves in two-dimensional space, local gradients of enhanced contractile force and reduced friction make viscous cell body easily streamed. Then, the net motion of fluids occurs and its velocity is given by an analytical solution. We test theoretical result by using optogenetic control of cell migration and find that cells are steered opposite to synthetic ERK signal. Our finding, including optimal velocity of cell migration against ERK wave, suggests the guidance of collective migration is driven by dissipative mechanics of cells.