Kinetics of ligand binding to a cluster of membrane-associated receptors

The process of ligand binding to a cluster of membrane-associated receptors is examined theoretically. The theoretical model proposed involves the diffusion of ligands from the solution to the disc-like cluster of receptors on the surface of the spherical cell. When the ligand hits the internal part of the disc-like cluster, it begins to move laterally until it leaves the disc through its outer surface or is bound by one of the receptors inside the disc. If the ligand leaves the cluster, it returns to the solution and hits the disc again after a certain period, etc. According to our model the transition from a diffusion-limited to a reaction-limited process of binding is determined by the dimensionless parameter λ ≡Dt_c/a², where D is the lateral diffusion coefficient, t_c is the characteristic time of reaction, and a is the radius of the disc-like cluster. The forward rate constant k_f turns out to be a function of λ. Comparing the results of our calculations of k_f with some experimental data we found that agreement is achieved at high γ, i.e. the process of ligand binding by clustered receptors is predominantly reaction-limited.