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. In contrast to most of the previous studies, which assumed the ligand concentration to be much larger than the receptor concentration, we examine the influence on the binding properties of cell density and number of receptors per cell, i.e., receptor concentration, over a wide but physiologically relevant range. In the “excess receptor regime,” where the volume of concentration of receptors is much greater than the ligand concentration, a ligand binds at as many sites as possible as determined by the crosslinking affinity constant and the valence of the ligand. Thus ligands tend to be bound at many sites. In the “excess ligand regime,” where the ligand concentration is much greater than the receptor concentration, ligands compete for receptor binding and hence tend to bind at a low number of sites per molecule. We show that ligand-induced cell proliferation may be self-limited at fixed ligand concentration, since ligand depletion reduces the signal received by individual cells once the cell population has grown into the excess receptor regime. 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.