The properties of immune complex-forming systems. A new theoretical approach

A new mathematical model for antigen-antibody interactions has been developed. The new model is based on the assumption that the formation of complexes between a bivalent antibody and a multivalent antigen is determined thermodynamically by the concentrations and valences of antigen as well as antibody, together with one association constant which is common to all mutual interactions. Formulae have been derived for calculation of the distributions of compositionally different antigen-antibody complexes either from knowledge of equilibrium concentrations of free antigen and antibody, or from knowledge of total amounts of antigen and antibody in the system. A computer program for these calculation is described. The model is found to yield precise predictions of the formation of soluble immune complexes, as studied by zonal centrifugation. It is found through use of the model that 'complex formation' as such differs in binding characteristics from adsorption, especially for high concentrations of antigens and antibodies. 'Complex formation' implies that association constants estimated through a Sips plot method will vary with antibody concentration, and that certain curvatures of the lines in a Sips plot reflect inherent properties of complex-forming systems.