Substrate properties and actin polymerization speed dictate universal modes of cell migration: gripping, slipping, and stick-slip

Understanding how cells sense mechanical cues and regulate migration is crucial in the development, fibrosis, and oncogenesis processes. However, a comprehensive physical picture of cell migration remains lacking, given the diverse environmental properties and cell physiologies. Here, we generalize the motor-clutch model to the whole-cell level and systematically investigate the effects of substrate stiffness, friction, and actin polymerization speed on cell migration. We unveil three distinct migration modes: gripping, slipping, and stick-slip. Notably, stiffness sensing occurs exclusively in the stick-slip mode, which requires a low substrate stiffness and a minimum actin polymerization speed as necessary conditions. Intriguingly, the optimal substrate stiffness that maximizes the migration speed is inversely proportional to the actin polymerization speed. Moreover, the maximal speed only depends on the nature of the clutch molecules, independent of substrate properties. We reveal the boundary criteria between the three migration modes and demonstrate that fast- and slow-migrating cells can coexist in an isogenic cell population without the need for biochemical feedback loops.