On Hill coefficients and subunit interaction energies

The study of cooperative ligand binding to multimeric proteins aims to explain complex cooperative binding phenomena using concepts derived from ideal binding isotherms. The purpose of such efforts is the dissection of the cooperative binding isotherm into its interacting components, a result with a clear mechanistic value. Historically, cooperative binding is usually quantified using the Hill coefficient, n _H, defined as the slope of the Hill plot at 50 % saturation. It was previously shown that the slope of the Hill plot throughout the titration is equal to the ratio of the binding variance in the system under study, to the binding variance of a reference non-interacting system. In the present contribution, this leads to a broader approach towards quantifying cooperativity, which empirically links cooperativity to the ensemble average of the subunit interaction energy. The resulting equations can be used to derive average differential subunit interaction energies directly from experimental binding isotherms. Combined with recent experimental advances in assessing binding distributions in multimeric proteins, these equations can also be used to calculate individual subunit interaction energies for specific n-ligated protein species.