Effect of boundary elastic interactions on motile cells

Elastic substrate-adhered cells actively deform and exert mechanical forces on the underlying substrate to sense their environment and crawl. Cells have been observed to perform durotaxis or preferential migration towards a stiffer substrate region. We explain this with a physical model where cells are described as motile agents that exert contractile, traction forces on the underlying substrate, which lead to elastic forces and torques on the cells at boundaries. Specifically, we model a sharp stiffness gradient as a clamped or free boundary, which corresponds to an interface with a stiffer or softer medium. The persistent motion of the particle and the elastic interactions with the boundary determine its probability of localization at or away from the boundary, a measure of its ability to cross the substrate interface. We characterize the dependence of the mean escape time from the attractive clamped boundary on elastic interactions and motility. Varying reorientation time yields qualitatively different escape behavior, whereas higher motility does not ensure lower escape time.