Stick-slip dynamics of crawling cells: nonlinear response of actin retrograde flow with varying substrate rigidity

Stick-slip motion, a common phenomenon observed during the crawling of cells, is found to be strongly sensitive to substrate stiffness. Here, we present a theoretical model for the stick-slip dynamics at the cell leading edge to investigate the nonlinear response of biphasic vs monotonic behaviour of the actin retrograde flow and cell traction force with substrate rigidity. Our model, based on a reaction-diffusion framework, incorporates known important interactions such as retrograde actin flow, myosin contractility, force-dependent assembly, and disassembly of focal adhesions integrated with the viscoelasticity of the cell-matrix system. Our study shows that the difference in cellular behaviours could arise due to the cell’s ability to sense and adapt to fast-varying forces. Our theory further elucidates how the substrate viscoelasticity alters these nonlinear cellular responses. Besides, it also predicts the loss of cell sensitivity to differentiate between soft and stiff substrates when the substrate viscosity is high and vice versa.