Modeling the kinetics of cell membrane spreading on substrates with ligand density gradient

An analytical model is developed for the effect of surface gradient in ligand density on the adhesion kinetics of a curved elastic membrane with mobile receptors. The displacement and speed of spreading at the edge of adhesion zone as well as the density profile of receptors along the membrane are predicted as a function of time. According to results, in the diffusion-controlled regime, the front edge displacement of adhesion zone and the rate of membrane spreading decreased with increasing the ligand density in a certain direction. Furthermore, the displacement of the edge of the adhesion zone did not scale with the square root of time, as observed on substrates with uniform ligand density.