Steric effects in antibody reactions with polyvalent antigen

Antigen valency has been defined (Singer, 1965) as the maximum number of epitopes per antigen which can be simultaneously occupied by antibody. If the epitopes are closely spaced, steric hindrance prevents the simultaneous occupancy of all epitopes. Current methods of estimating both the antigen valency and the association constant (Ka) from equilibrium binding data do not allow for the effects of steric hindrance. We have developed a theory which accounts rigorously for steric hindrance when monovalent ligands of quite general shape (antibodies) react reversibly with multivalent acceptor molecules (antigens). The surfaces of the acceptors are modelled by completely general two-dimensional lattices. Using this theory we demonstrate that curvature of Scatchard plots can arise from steric effects alone in the absence of other known causes such as cross-linking, cooperativity and heterogeneous epitope affinities. Our results generalize the conclusions of McGhee & von Hippel (1974) who dealt with one-dimension acceptor molecules such as DNA. We discuss inaccuracies in the estimation of both Ka and antigen valency using the traditional approach of fitting straight lines to Scatchard plots.