The influence of polyvalency on the binding properties of antibodies.

Abstract We present a general formalism for predicting the relationship between the binding affinities in several kinds of antigen-antibody interactions. The reference binding constant is that of monovalent antibody for monovalent antigen. The equations then allow one to predict the ratio of this constant to that for attaching divalent antibody to divalent antigen. We further develop the theory to consider the binding of multivalent antibodies to a multideterminant antigen particle, in the restricted case of small fractional occupancy of the determinant sites by antibodies. There is good agreement between the calculated results and certain data from the literature. In situations where multisite adherence to a single particle and cross-linking of discrete particles are both possible, the former is predicted to predominate strongly. That the opposite appears sometimes to be experimentally the case means that special features favoring agglutination reactions must be present in these instances. Finally, those factors that potentially make polyvalent γM antibodies more effective agglutinators than bivalent γG antibodies are delineated briefly.