Orientation constraints in diffusion-limited macromolecular association. The role of surface diffusion as a rate-enhancing mechanism.

Ligand association to a reactive site on a macromolecular surface could be very slow if the site is small. The effective capture radius of the reactive site can be significantly increased if the ligand can bind weakly to the nonspecific surface around the site and then slide in a two-dimensional diffusion along the surface. In this model, the diffusion along the surface has to be properly coupled with the free diffusion in solution and the effective bimolecular association rate constant to the reactive site can be calculated as a function of the nonspecific affinity. This is carried out both for a plane and spherical surface, modeling the association to a membrane receptor or to the catalytic site on an enzyme. The result of these calculations can be used to assign reasonable values to the parameters in the quasichemical approximation of K. Solc and W. H. Stockmayer (1973, Int. J. Chem. Kinet., 5:733-752). In this way a simple analytical expression can be derived for the diffusion-limited association rate constant of two asymmetrically reactive molecules, with or without surface diffusion contributing.