Active escape of motile cells from elastic interfaces predicts durotactic probability

Many cells crawling on extracellular substrates exhibit durotaxis, i.e., directed migration toward stiffer substrate regions. Here, we aim to describe the statistical properties of single cell durotaxis through long-range sensing of a distant stiffness interface using a phenomenological model that incorporates both elastic deformation-mediated cell-substrate interactions and the stochasticity of cell migration. We model migrating cells as self-propelling, persistently motile agents that exert contractile traction forces on their elastic substrate. The resulting substrate deformations induce elastic interactions with mechanical boundaries, captured by an elastic potential. We relate the durotactic index to an escape time from this attractive potential, which we calculate from agent-based simulation and compare with a modified Kramer’s theory for active particles in a long-range potential. We define metrics quantifying boundary accumulation and durotaxis, and present a phase diagram that identifies three possible regimes: durotaxis, and adurotaxis with and without motility-induced boundary accumulation. Next, we extend our elastic dipole interaction model to describe anti-durotaxis, i.e., cells moving to softer regions. Overall, our model predicts how durotaxis depends on cell contractility and motility, successfully explains some previous observations, and provides testable predictions to guide future experiments.