Initiation of motility on a compliant substrate

The conditions under which biological cells switch from a static to a motile state are fundamental to the understanding of many healthy and pathological processes. In this paper, we show that even in the presence of a fully symmetric protrusive activity at the cell edges, such a spontaneous transition can result solely from the mechanical interaction of the cell traction forces with an elastic substrate. The loss of symmetry of the traction forces leading to the cell propulsion is rooted in the fact that the surface loading follows the substrate deformation. The bifurcation between the static and motile states is characterized analytically and, considering the measurements performed on two cell types, we show that such an instability can realistically occur on soft in vivo substrates.