The Hill equation and the origin of quantitative pharmacology
- 1.8k Downloads
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.
KeywordsHill Equation Receptor Model Richards Equation Hill Model Nonparametric Function
Unable to display preview. Download preview PDF.
- Clark A.J. (1926) The antagonism of acetylcholine by atropine. Journal of Physiology (London) 61: 547–556Google Scholar
- Hill A.V. (1909) The mode of action of nicotine and curari, determined by the form of the contraction curve and the method of temperature coefficients. Journal of Physiology (London) 39: 361–373Google Scholar
- A. V. Hill. 1910. The possible effects of the aggregation of the molecules of haemoglobin on its dissociation curves. Journal of Physiology (London) 40: Proceedings iv–vii.Google Scholar
- Keller F., Giehl M., Czock D., Zellner D. (2002) PK-PD curve-fitting problems with the Hill equation? Try one of the 1-exp functions derived from Hodgkin, Douglas or Gompertz. International Journal of Clinical Pharmacology and Therapeutics 40: 23–29Google Scholar
- Michaelis L., Menten M.L. (1913) Die Kinetik der Intertinwerkung. Biochemische Zeitschrift 49: 333–369Google Scholar
- Motulsky, H.J., and A. Christopoulos. 2003. Fitting models to biological data using linear and nonlinear regression. A practical guide to curve fitting. Oxford: Oxford Press (Corrected online version: http://www.graphpad.com/manuals/Prism4/RegressionBook.pdf).
- Neubig R.R., Spedding M., Kenakin T., Christopoulos A. (2003) International union of pharmacology committee on receptor nomenclature and drug classification. XXXVIII. update on terms and symbols in quantitative pharmacology. Pharmacological Reviews 55: 597–606Google Scholar
- Pelner L. (1972) Corpora non agunt nisi fixata. Maxim behind all of Ehrlich’s great discoveries. New York State Journal of Medicine 72: 620–624Google Scholar
- Rang, H.P. 2006. The receptor concept: Pharmacology’s big idea. British Journal of Pharmacology 147: S9–16.Google Scholar
- Scheindlin S. (2001) A brief history of pharmacology. Modern Drug Discovery 4: 87–88Google Scholar
- Stephenson R.P. (1956) A modification of receptor theory. British Journal of Pharmacology 11: 379–393Google Scholar
- Van der Graaf P.H., Danhof M. (1997) Analysis of drug-receptor interactions in vivo: A new approach in pharmacokinetic-pharmacodynamic modelling. International Journal of Clinical Pharmacology and Therapeutics 35: 442–446Google Scholar
- Weiss J.N. (1997) The Hill equation revisited: Uses and misuses. FASEB Journal 11: 835–841Google Scholar
- Zimmer, H.G. (1996) Carl Ludwig: the man, his time, his influence. Pflugers Archiv 432: R9–22.Google Scholar