Biphasic curvature-dependence of cell migration inside microcylinders: persistent randomness versus directionality

Cell-scale curvature plays important roles in controlling cell and tissue behaviors. However, these roles have not been well quantified, and the underlying mechanisms remain elusive. We combine experiments with theory to study systematically the curvature-dependence of cell migration inside PDMS microcylinders. We find that persistence is positively correlated with speed, following the universal speed-persistence coupling relation, i.e., faster cells turn less. Cell migration inside microcylinders is anisotropic and depends on curvature in a biphasic manner. At small curvatures, as curvature increases, the average speed and anisotropy both increase, but surprisingly, the average persistence decreases. Whereas as the curvature increases over some threshold, cells detach from the surface, the average speed and anisotropy both decrease sharply but the average persistence increases. Moreover, interestingly, cells are found to leave paxillins along their trajectories (on curved but not planar surfaces), facilitating the assembly of focal adhesions of following cells. We propose a minimal model for the biphasic curvotaxis based on three mechanisms: the persistent random "noise", the bending penalty of stress fibers, and the cell-surface adhesion. The findings provide a novel and general perspective on directed cell migration in the widely existing curved microenvironment of cells in vivo.