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 nH 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.