title: 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.
mesh_terms: D000818:Animals; D000906:Antibodies / Q000502:physiology*; D001491:Basophils / Q000276:immunology / Q000378:metabolism*; D006636:Histamine Release; D006801:Humans; D007073:Immunoglobulin E / Q000378:metabolism; D008024:Ligands; D008956:Models, Chemical; D051381:Rats
chemical_list: D000906:Antibodies; D008024:Ligands; D007073:Immunoglobulin E