Compliance of bio-adhesive substrates controls the kinetics of membrane-substrate association

Mechanical stiffness of bio-adhesive substrates is one of the major regulators of the cell adhesion and migration. In this study, we propose a theoretical model for the spontaneous growth of focal adhesion (FA) sites, on compliant elastic substrates, at the early stages of cellular adhesion. Using a purely thermodynamic approach, we demonstrate that the rate of membrane-substrate association decreases with increasing the compliance of the substrate. This can be considered as a reason for smaller spread area of the FA points after the stabilization of adhesion on compliant substrates, as reported by experiments. We also show that the extent to which the compliance of the substrate modulates the growth rate of adhesion site depends on the areal density of cell-adhesive ligands on the substrate.