Interaction of focal adhesions mediated by the substrate elasticity

Abstract

Cell spreading and migration result from the formation of extensive adhesive contacts between the cell and the extracellular matrix involving interaction and cooperation between the adhesive system, the actin cytoskeleton, and the extracellular matrix. We develop here a visco-elastic model of the interaction between the adhesive contacts mediated by the finite rigidity of the substrate. No prior study focuses on this type of interaction. The model takes into account the interference between the long range elastic stress fields created by the adhesive contacts on the substrate. We show that even in the absence of a velocity gradient, a stress gradient appears in the direction of motion and that the stress is maximal at the edges of the cell in accordance with the experimental observations. Moreover, the model gives the position dependent friction coefficient between the adhesive contacts of the cell and the substrate. Finally, we calculate the velocity distribution of the active actin–myosin gel as a function of the relative gel–substrate rigidity.