Role of diffusion in ligand binding to macromolecules and cell-bound receptors

The association and dissociation rates of partially diffusion-controlled bimolecular reactions are considered. A simple expression for the equilibrium constant is derived using classical statistical mechanics. The relationship is established between the Collins-Kimball treatment, which is based on the "radiation" boundary condition involving an intrinsic rate constant k, and the kinetic scheme A + B in equilibrium A . . . B in equilibrium AB where A . . . B is an encounter complex. It is shown that with the appropriate choice of the interaction potential, Debye's expression for the association rate constant becomes identical to that obtained using the radiation boundary condition if k is evaluated using Kramers' theory of diffusive barrier crossing. Finally, the competitive binding of ligand to a spherical cell, whose surface is partially covered by multiple reactive sites, is studied by treating the cell as a partially reacting sphere.