Modeling Cell Motility Dependence on Substrate Adhesion Using the Phase-field Method

Migration of eukaryotic cell plays an important role in many biological processes including development, chemotaxis, and cancer metastasis. Despite significant experimental and theoretical efforts, the role of cell-substrate adhesions in migration is still unclear. Here, we use the phase-field approach to model adhesive interactions between cell and substrate and determine the relationship between adhesion and cell velocity. For this, we model a 2D cross-sectional slice with conserved area and with active stresses confined near the substrate. We find that as the adhesion strength increases, the cell spreads more, becomes thinner, and, surprisingly, moves faster. To further understand this, we study an analytical model for cell motility and find its results to be consistent with our simulations: cells with conserved volume experience a stronger adhesion and therefore spread more, reduce their height, and increase their speed. Furthermore, we extend the model by introducing an adhesion-dependent friction force and find that the velocity-adhesion curve is bell-shaped with a clear maximum. Our model provides an explanation for the experimentally observed biphasic dependence of cell motility on adhesion.