Binding of Multivalent Ligands to Cells: E ects of Cell and Receptor Density Condensed title: Binding of Multivalent Ligands (Keywords: Multivalent Ligands, Crosslinking

We study the equilibrium binding properties of multivalent ligands and mixtures of ligands of diierent valence to cell surface receptors. We examine the eeects of changing cell density or number of receptors per cell, i.e., receptor concentration, over a wide but physiologically relevant range. Qualitatively diierent behaviour arises in the excess receptor regime, where the volume concentration of receptors is much greater than the ligand concentration, and the excess ligand regime, where the ligand concentration is much greater than the receptor concentration. In the excess receptor regime a ligand binds at as many sites as possible as determined by the crosslinking aanity constant and the valence of the ligand. Thus ligands tend to be bound at many sites. In the excess ligand regime, ligands compete for receptor binding and hence tend to bind at a low number of sites per molecule. However, the total number of ligands bound per cell is higher in the excess ligand regime than at the same total ligand concentration in the excess receptor regime. When cells are exposed to an ensemble of ligand of diierent valence there is a preference for binding of larger valence ligands both in the excess receptor regime and in the transition range from the excess receptor to the excess ligand regime. Increasing the volume concentration of receptors, say by increasing the cell density, reduces this preference. We apply our theory to the binding of chemically crosslinked oligomers of immunoglobulin to Fc receptors on various cell types. We also examine the binding of haptenated polymers to B cells and reinterpret experiments related to the immunon theory of B cell activation.