Receptor clustering on a cell surface. III. theory of receptor cross-linking by multivalent ligands: description by ligand states

Abstract The interaction of multivalent ligand with cell surface receptors is the first step in triggering a number of biological responses. Here I present and analyze a mathematical model for the binding of a multivalent ligand, containing v identical reactive sites, to monovalent or multivalent cell surface receptors. The initial binding of such ligands to a cell is followed by further reactions on the surface which cross-link receptors and lead to the formation of ligand-receptor clusters. In the presence of monovalent haptens, I consider the possibility that clustering can be competitively inhibited. By introducing the concept of an effective valence for the ligand, which is the number of reactive groups that can simultaneously bind to surface receptors, one can take into account steric hindrance and the inability of some ligand determinants to participate in cross-linking reactions because they are oriented incorrectly. When the ligand's effective valence is greater than two, a number of different criteria can be used to measure receptor clustering: (1) the fraction of receptor sites occupied by multiply bound ligand, (2) the concentration of cross-links holding distinct receptors together, and (3) the concentration of cell surface aggregates. The dependence of these three aggregation measures on ligand and monovalent hapten concentration is studied. A number of theorems are proven about the general shape and characteristics of cross-linking curves. For ligands which can simultaneously bind more than two cell surface receptors the cross-linking curve is not symmetric, although as in the case of bivalent ligands, the curve generated using criteria (1) or (2) has a single maximum. Throughout the analysis intramolecular reactions and ring formation are ignored. A criterion is developed which indicates that the theory can break down at high degrees of cross-linking for receptors which have two or more combining sites. In such cases intramolecular reactions need to be considered. As an application, the theory is used to interpret previously published experiments on the release of histamine by basophils.