Ligand binding reaction diffusion processes

At this stage we may briefly re-examine the conditions for a diffusion controlled process. (For a more detailed discussion cf.86 ). Any reaction between two separate particles M and L is preceded by an encounter, in which the partners owing to their diffusional motion meet within a critical distance Rml before they undergo reaction, e.g. the substitution of solvent molecules by binding groups of the ligand L. 

We will begin by looking at the binding of ligand to receptor when both are free in solution (Fig. 9a) and will follow the approach by Shoup and Szabo (1982). Our aim is to obtain expressions for the overall forward and reverse rate constants, k and kr, as they depend on diffusion coefficients and free receptor number. In order to accomplish this, we will calculate the rate at which a ligand molecule would be expected to bind to a receptor molecule by the two-step diffusion and intrinsic reaction process. 

---