Modelling cell trapping phenomenon and sub-diffusive cell migration on slow relaxing substrates

Cell migration is an essential biological process that plays a key role in immune cell trafficking, embryogenesis, wound healing, and cancer metastasis. Biological tissues are compliant and exhibit viscoelasticity, showing stress relaxation in response to applied deformation. Substrate stress relaxation is emerging as a key mediator for diverse cellular processes such as cell proliferation, spreading, and stem cell differentiation. Cell migration on elastic substrates is frequently described as a purely diffusive, random walk. However, the impact of substrate stress relaxation on diffusive cell migration has not been studied. Here, by combining simulations and experiments, we systematically investigate the effect of substrate stress relaxation on cell migration phenotype. Using human HT1080 fibrosarcoma cells, our experiments found that faster substrate stress relaxation enhances the transition from sub-diffusive migration to super-diffusive migration. To understand the migration transition induced by stress relaxation, we have developed a cell migration model based on the motor clutch framework by introducing stochastic adhesion dynamics and membrane/cortex deformation. Our model shows, for the first time, that stochasticity (due to protein glassiness) in the binding dynamics of clutches causes cell trapping, leading to sub-diffusive migration on slow-relaxing substrates. Lastly, we have experimentally validated our model predictions by perturbating the system with different small molecule inhibitors (actin and myosin inhibitions) and analyzing their effects on migration phenotype. Thus, cell trapping and sub-diffusive migration governed by substrate stress relaxation facilitate new directions in cancer progression research.