Elastic interactions in confinement direct cell motility

Animal cells adhered to elastic substrates crawl and sense stiffness by exerting mechanical forces and actively deforming the underlying substrate. Many such cells exhibit durotaxis or preferential migration towards stiffer regions in the substrate. We present a physical model of durotaxis where cells are described as motile agents that exert contractile, traction forces on the underlying substrate. We combine agent-based Brownian dynamics simulations with linear elastic cell-substrate interactions to show how cell dynamics is influenced by mechanical interactions with clamped and free boundaries that represent interfaces with stiffer and softer regions, respectively. This is therefore a realization of elastic interaction-driven active matter in complex media. The speed of the motile cell determines the probability of it reaching the interface, which is either enhanced or reduced by the elastic forces and torques generated at the interface which in turn depend on the elastic boundary condition and stiffness gradient. We then analyze the density and orientation profiles of the model cells close to the interface to quantitatively predict the extent of durotaxis and its dependence on cell motility and traction forces.