Exact analysis of ligand-induced dimerization of monomeric receptors

This paper analyzes the equilibria involved in the dimerization of monomeric receptors with homo-bifunctional ligands. We provide analytical expressions that can be used to estimate the concentration of each species present in a mixture of homo-bifunctional ligand and monomeric proteins, given initial conditions defining the total concentration of bivalent ligand [L-2](0), the total concentration of protein [P](0), one dissociation constant K-d, and a parameter to account for cooperativity alpha. We demonstrate that the fraction of protein present in a complex of two proteins and one bivalent ligand (P center dot L-2 center dot P) is maximized at [L-2](0) = K-d/2 + [P](0)/2.