Quantitative explanation for increased affinity shown by mixtures of monoclonal antibodies: importance of a circular complex

Abstract

Mixtures of some but not all monoclonal antibodies which bind to separate epitopes on human chorionic gonadotropin (hCG) show an increased affinity for the hormone. To find an explanation for the increase in affinity, we developed a mathematical model which predicts the quantities of intermediates formed when pairs of IgG1 mouse monoclonal antibodies having affinities of approximately 10(8) M-1 for hCG are mixed with the hormone. At low antibody concentrations (i.e. less than 1 nM or 0.15 micrograms/ml) analysis of possible antibody-hormone combinations, including linear and circular chains composed of less than 12 molecules of antibody and 12 molecules of hCG, suggests the increase in affinity is due to formation of a circular complex containing two molecules of antibody and two of hCG. Further, the model predicts that the circular complex will be the major species formed at antibody-antigen equivalence. This prediction is supported by experimental observations on the molecular weight of a new complex formed in the presence of hCG and the mixture of the monoclonal antibodies. In addition, based on experimental values of binding constants for individual antibodies to hCG, the model correctly quantifies the loss in complex observed in the presence of excess hCG antigen. At high antibody concentrations (i.e. greater than 10 nM or 1.5 micrograms/ml) the formation of linear chains of antibody hCG pairs becomes appreciable and contributes to the increase in apparent affinity of the mixture for hCG. These results suggest that the observed affinity of complex mixtures of antibody for antigens containing multiple epitopes calculated from Scatchard plots may not be related to the affinity or avidity of any of the antibody species for a given epitope.