Equilibrium binding of multivalent ligands to cells: effects of cell and receptor density

We study the equilibrium binding properties of multivalent ligands to cell surface receptors. We examine the effects of cell density and number of receptors per cell, that is, receptor concentration, on ligand binding. These parameters can significantly affect the formation of receptor aggregates and cross-links. We then use our general results to show that ligand-induced cell proliferation may be self-limiting, since ligand depletion reduces the signal received by individual cells once the cell population has expanded. We discuss the concept of avidity and show its limitations. As a specific example, we examine the binding of haptenated polymers to B cells and reinterpret experiments related to the immunon theory of B-cell activation.