Probability distributions of thermodynamic affinities for heterogeneous receptor populations

A statistical approach to characterize the thermodynamic affinity distributions of heterogeneous receptor populations in terms of stoichiometric binding constants is presented. The use of stoichiometric density distributions provides a novel description of ligand binding systems. The distributions of stoichiometric constants, Ti(Ki)'s, are obtained assuming that the distribution of site constants N(k) is known. It is found that in the case of heterogeneous systems with multivalent receptors, N(k) is an average over all the Ti(Ki)'s even when there are positive or negative site-site interactions. It is seen that in the absence or in the presence of site-site interactions the mean and the variance of the Ki's can be derived from a Scatchard plot. Some of these results are particularly applicable to bivalent heterogeneous antibody populations and other results are applicable to bivalent heterogeneous systems with different binding sites.