Lateral Diffusion from Ligand Dissociation and Rebinding at Surfaces^†

The lateral diffusion coefficient of a ligand which repeatedly dissociates and rebinds to sites on a planar surface is described. An analytical expression showing the manner in which the diffusion coefficient depends on the propensity for rebinding after dissociation, as the molecule moves through the solution and across the surface, is derived. The diffusion coefficient is time dependent and ranges from the surface diffusion coefficient (at time zero when a tagged molecule is placed on the surface) to the solution diffusion coefficient (at time infinity). The time-dependent diffusion coefficient depends only on the intrinsic dissociation rate and a "rebinding parameter", which in turn depends on a group of constants including the intrinsic association and dissociation rates, the density of unoccupied surface binding sites, and the diffusion coefficient in solution.