Stochastic Nonlinear Dynamics of Confined Cell Migration*

In many biological phenomena, cells migrate through confining environments. To study such confined migration, we place migrating cells in two-state micropatterns, in which the cells stochastically migrate back and forth between two square adhesion sites connected by a thin bridge. We adopt a data-driven approach where we learn an equation of motion directly from the experimentally determined short time-scale dynamics, decomposing the migration into deterministic and stochastic contributions. This equation captures the dynamics of the confined cell and accurately predicts the transition rates between the sites. We thereby derive the emergent non-linear dynamics that governs the migration directly from experimental data. In particular, we find that the deterministic dynamics is poised near a bifurcation between a limit cycle and bistable behaviour. As a result, we find that cells are deterministically driven into the thin constriction; a process that is sped up by noise. Our approach yields a conceptual framework that may be extended to describe cell migration in more complex confining environments.