The Hill equation and the origin of quantitative pharmacology

This review addresses the 100-year-old Hill equation (published in January 22, 1910), the first formula relating the result of a reversible association (e.g., concentration of a complex, magnitude of an effect) to the variable concentration of one of the associating substances (the other being present in a constant and relatively low concentration). In addition, the Hill equation was the first (and is the simplest) quantitative receptor model in pharmacology. Although the Hill equation is an empirical receptor model (its parameters have only physico-chemical meaning for a simple ligand binding reaction), it requires only minor a priori knowledge about the mechanism of action for the investigated agonist to reliably fit concentration-response curve data and to yield useful results (in contrast to most of the advanced receptor models). Thus, the Hill equation has remained an important tool for physiological and pharmacological investigations including drug discovery, moreover it serves as a theoretical basis for the development of new pharmacological models.