Analytical expressions for the homotropic binding of ligand to protein dimers and trimers

Cooperative binding of a ligand to multiple subsites on a protein is a common theme among enzymes and receptors. The analysis of cooperative binding data (either positive or negative) often relies on the assumption that free ligand concentration, L, can be approximated by the total ligand concentration, L_T. When this approximation does not hold, such analyses result in inaccurate estimates of dissociation constants. Presented here are exact analytical expressions for equilibrium concentrations of all enzyme and ligand species (in terms of K_d values and total concentrations of protein and ligand) for homotropic dimeric and trimeric protein-ligand systems. These equations circumvent the need to approximate L and are provided in Excel worksheets suitable for simulation and least-squares fitting. The equations and worksheets are expanded to treat cases where binding signals vary with distinct site occupancy.