A thermodynamic model of binding of flexible bivalent haptens to antibody

Studies by Wilderet al. (1975b) of the binding of Fab' fragments to small haptens have shown that the cross-linking constant (the equilibrium constant for binding an additional Fab' fragment to a hapten-Fab' complex) is strongly dependent on the length of the hapten. We present a simple model for predicting the relationship between the intermolecular cross-linking constant and the monovalent hapten-antibody binding constant. In particular we use the model to obtain the dependence of the cross-linking constant on the length of the hapten, the depth to which the hapten fills the Fab' binding site, and the size of the Fab' fragment.

To make contact with experiment, we devise expressions which allow us to analyze the data of Wilderet al. (1975b). From their data we determine the values of two parameters which we take to be unknown in the theory, the size of the Fab' fragment and the depth to which the hapten fills the Fab' binding site. The values arrived at in this way agree well with published measurements of these parameters.