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The rate of binding a fairly large ligand molecule to a protein is reduced below the usual diffusion-controlled rate by the requirement of a certain rotational orientation. A simple, approximate treatment of this effect is given for special cases of spherical and ellipsoidal ligands. As the center of an ellipsoidal ligand approaches a protein surface, there is an effective repulsive potential between ligand and surface owning to restricted rotation of the ligand. The frequency factor kT/h of the Eyring rate theory is replaced in these reactions involving diffusion in solution by D/Rlambda, where D = diffusion coefficient of ligand, lambda = thermal deBroglie wavelength of ligand, and R = "capture" distance around the binding site on the protein.

Effect of rotation on the diffusion-controlled rate of ligand-protein association.