The Hill equation revisited: uses and misuses

The Hill coefficient is commonly used to estimate the number of ligand molecules that are required to bind to a receptor to produce a functional effect. However, for a receptor with more than one ligand binding site, the Hill equation does not reflect a physically possible reaction scheme; only under the very specific condition of marked positive cooperativity does the Hill coefficient accurately estimate the number of binding sites. The Hill coefficient is best thought of as an "interaction" coefficient, reflecting the extent of cooperativity among multiple ligand binding sites. Several relatively simple, physically plausible reaction schemes are shown here to produce a variety of ligand dose-response curve phenotypes more appropriately suited to modeling ligand-receptor interactions, especially if independent information about the stochiometry of the ligand-receptor interaction is available.