Binding of multivalent ligands to mobile receptors in membranes

We present a model to describe the equilibrium binding properties for the attachment of multivalent ligands to mobile receptors in membranes. The interaction is assumed to be governed by two inherently different association constants. The first of these controls the initial attachment of a ligand to its first receptor, by adsorption from bulk solution, while the second governs subsequent receptor attachments to this initially bound ligand by rearrangement of membrane-bound species. Simple statistical mechanical expressions are used to estimate contributions to these association constants that are attributable to losses of translational and rotational degrees of freedom occurring upon binding. Suitable combinatorial expressions are combined with these association constants to derive the concentrations of bound species and the binding isotherms. Examination of these expressions leads to the conclusion that once initially bound, most multivalent ligands will be completely saturated by receptors and that partially bound species will be essentially nonexistent. This behavior is attributable to the generally high overall affinities of these ligands and to the mobility of the membrane-bound species. Some specific comments are made, in light of this theory, about the binding of cholera toxin to its membrane receptor, the ganglioside G_M1.