The effect of co-operativity on the equilibrium binding of symmetric bivalent ligands to antibodies: Theoretical results with application to histamine release from basophils

Abstract

A theory for the co-operative binding of bivalent ligands to cell surface or solution antibody is presented. The theory treats both negative co-operativity, where the binding of a ligand to one site on an antibody makes it more difficult to bind to the second site, and positive co-operativity, where the binding of a ligand to one site on an antibody makes it easier to bind to the second site. Candidates for bivalent ligands exhibiting negative co-operativity (caused probably by steric hindrance) are certain anti-immunoglobulin antibodies. We show how to calculate the amount of ligand bound, the fraction of antibody in cross-links (i.e. in ligand—antibody aggregates) and the fraction of antibody in any size ligand-antibody aggregate. With sample calculations it is demonstrated that there can be major differences in the binding and cross-linking properties of co-operative and non-co-operative bivalent ligands. We discuss how the theory can be used to analyze experiments where human basophils or rat basophilic leukemia cells are exposed to bivalent ligands that bind co-operatively to immunoglobulin E.