The contact formation between cell membrane and a bio-adhesive substrate is driven by binding between transmembrane mobile receptors (e.g., integrin) and complementary ligand molecules on the substrate (fibronectin, collagen, etc.) This short range specific adhesion is alleviated by a phalanx of interfacial non-specific forces. In addition to cell-substrate interfacial interactions, cell adhesion can be mediated by a wide range of substrate physiochemical properties. In particular, mechanical stiffness of the substrate has been recognized as one of the major regulators for bio-adhesion. Cells in general, exhibit an apparent adhesion preference for stiffer substrates and switch from a round to spread morphology as the substrate stiffness increases. Understanding the mechano-chemical pathways mediating the interplay between the substrate properties and cell behavior could be critical for effective performance of synthetic biomaterials in tissue engineering applications. In this study, we consider the effect of substrate elasticity on the dynamics of membrane spreading and growth of focal adhesion zone. The formation and growth of the focal adhesion points during the early stage of adhesion process is a result of spontaneous spreading of membrane on the substrate. This can be considered as a non-equilibrium kinetic process which is controlled by the diffusibility of receptor molecules. In order to study the effect of substrate elasticity on the kinetics of membrane-substrate association, receptors are assumed as ideal solute particles laterally diffusing within the plane of the membrane until they are stabilized through association with their complementary ligands which are immobilized on the surface of a compliant substrate. Considering different mechanical stiffness for the substrates, the displacement and speed of spreading at the edge of adhesion zone are predicted as a function of time. Results show that decreasing the stiffness of bio-adhesive substrates reduces the rate of membrane spreading, due to a weaker thermodynamic force which drives the membrane-substrate association. This mechanism restrains the growth of focal adhesion zones on compliant substrates and can be considered as a reason for smaller spread area of the cells after stabilization of adhesion.
