DIFFUSION-CONTROLLED REACTIONS AMONG LIGANDS AND RECEPTOR CLUSTERS - EFFECTS OF COMPETITION FOR LIGANDS

A general model has been developed to investigate the steady-state kinetics for a ligand-receptor system. The receptors are simulated by a fixed array of chemically active sites distributed over a planar surface (the cell membrane). The ligands are described as diffusing bodies floating over the receptor-containing plane. The chemical transformation of the ligands takes place only at the receptor sites and for proper relative orientations, otherwise they are reflected. The resulting roto-translational diffusion equation (RTDE) has been solved with simultaneous boundary conditions both on the function and its derivative in the different domains of the membrane. The RTDE with the above mixed boundary conditions has been solved in the framework of the constant-radiation condition without any further approximation. The kinetic constant (i.e., the total ligand flux crossing the receptor surface) has been calculated and expressed as a function of physical parameters such as the rotational and translational diffusion coefficients of the ligands, the number and relative distance of the receptors, and the width of the reactive orientations. Some useful limiting formulas have been obtained for very large clusters of randomly distributed receptors, and they agree with the results obtained by previous models.