An empirical extremum principle for the Hill coefficient in ligand-protein interactions showing negative cooperativity

The Hill coefficient (n(H)) is a central parameter in the study of ligand-protein interactions, which measures the degree of cooperativity between subunits that bind the ligand in multisubunit proteins. The most common usage of n(H) is as an estimate of the minimal number of interacting binding sites in positively cooperating systems. In the present study, a statistical interpretation of n(H) for a generalized system of multiple identical binding sites is developed. This interpretation is then applied to the derivation of an empirical extremum principle for n(H) in negatively cooperating systems of identical binding sites, which can be used for the estimation of the minimal number of interacting sites in such systems.