title: Theory of hapten binding to IgM: the question of repulsive interactions between binding sites.
abstract: Various workers in their studies of the binding of haptens to IgM have observed that at low hapten concentration IgM has an apparent valence of five or near five, while at high hapten concentration IgM has a valence of ten. A possible explanation for this is that there is an interaction between binding sites on the same F(ab')2 region of the IgM molecule. In this paper the theory for such an interaction is presented and an expression for the apparent valence is derived. It is shown that the apparent valence depends on both the interaction between binding sites on the IgM molecule and on the width of the affinity distribution which characterizes the antiserum. A broad affinity distribution can give an apparent valence of five even when there is no interaction between sites, i.e., even when the ten binding sites on the IgM molecule are identical and independent. The general properties of a Scatchard plot are also discussed. When there is no interaction between sites it is shown that the average affinity and the variance of the affinity distribution can be obtained from a Scatchard plot. To illustrate the theory, an antiserum with affinities characterized by a normal distribution is considered and a simple method is presented for determining alpha, the parameter which measures the width of the normal distribution.
mesh_terms: D000818:Animals; D001666:Binding Sites, Antibody; D006241:Haptens; D007140:Immunoglobulin Fab Fragments; D007074:Immunoglobulin G; D007075:Immunoglobulin M; D007700:Kinetics; D008433:Mathematics; D011485:Protein Binding; D011817:Rabbits / Q000276:immunology
chemical_list: D006241:Haptens; D007140:Immunoglobulin Fab Fragments; D007074:Immunoglobulin G; D007075:Immunoglobulin M