Effect of substrate viscosity on stick-slip dynamics of migrating cells

Migration is central to many cellular processes such as wound healing, morphogenesis, embryonic development, tissue regeneration to name a few. 'Stick-slip' motion, observed during cell crawling, has been found to be strongly sensitive to the substrate stiffness. The stick-slip behaviour has been investigated before typically using purely elastic substrates. For a more realistic understanding of this phenomenon, we propose a theoretical model to study the dynamics on a viscoelastic substrate. Our model based on a reaction-diffusion framework, incorporates known important interactions such as retrograde flow of actin, myosin contractility, force dependent assembly and disassembly of focal adhesions coupled with cell-substrate interaction. We show that consideration of a viscoelastic substrate not only captures the usually observed stick-slip patterns, but also predicts the existence of an optimal substrate viscosity corresponding to a maximum traction force and minimum retrograde flow which was hitherto unexplored. Moreover, our theory predicts the evolution of individual bond force which provides insights into the stick-slip jumps on soft versus stiff substrates. Our analysis also elucidates the dependence of the duration of stick-slip cycles on various system parameters.