Equilibrium theory for the clustering of bivalent cell surface receptors by trivalent ligands. Application to histamine release from basophils

For certain cell types, the cross-linking of bivalent cell surface receptors by multivalent ligands is an important biochemical step in the transmission of information across the cell's membrane to its interior. The formation of cell surface receptor-ligand aggregates has been shown to "turn on" and "turn off" particular cell responses. It has been hypothesized that very large aggregates generate signals that small aggregates cannot. This hypothesis has not been rigorously tested as yet, in part because of a lack of quantitative information about aggregate sizes. Here we develop a general equilibrium theory for the clustering of bivalent receptors by trivalent ligands. In addition to predicting the concentrations of receptor-ligand aggregates of all possible sizes, we show that a range of ligand concentrations exists at which extremely large aggregates, i.e., superaggregates, form on the cell surface. The formation of a superaggregate corresponds to a sol-gel phase transition, and we study this transition in some detail. For the biologically interesting case of histamine release by basophils, we show, using realistic parameter values, that such transitions should occur when the cells are from highly allergic individuals. We prescribe in detail experimental conditions under which such transitions should occur. These conditions can be used as a guide to test whether or not large aggregates provide signals to cells that small aggregates do not