Temporal dependence of ligand dissociation and rebinding at planar surfaces

In a previous work, conditions for which a ligand reversibly bound to a pla nar surface dissociates and then rebinds to the surface were theoretically examined (Lagerholm, B. C.; Thompson, N. L. Biophys. J. 1998, 74, 1215). Th e coupled differential equations that describe the reversible interaction o f ligands in three-dimensional solution with sites on a planar surface were solved to find analytical solutions for the probabilities of finding a lig and on the surface or in solution, given initial placement on the surface. An expression was also found for the probability that a ligand rebinds to t he surface at a given position and time after its release. In this work, th e formalism is extended to calculate analytical, closed form expressions fo r the average number and rate of rebinding events that have occurred, on th e average, at a given lime after placing a ligand on the surface. These fun ctions depend only on the intrinsic dissociation rate and a "rebinding para meter," which depends on a group of constants including the intrinsic assoc iation and dissociation rates, the density of surface binding sites, and th e diffusion coefficient in solution. The results are interpreted in terms o f typical conditions for biologically relevant ligands and their receptors.