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 prese...

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Bibliographic Details
Published inArchive for history of exact sciences Vol. 66; no. 4; pp. 427 - 438
Main Authors Gesztelyi, Rudolf, Zsuga, Judit, Kemeny-Beke, Adam, Varga, Balazs, Juhasz, Bela, Tosaki, Arpad
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer 01.07.2012
Springer-Verlag
Subjects
Agonists
Astronomy
Binding sites
Biology
Coefficients
Drug design
Hills equation
History and Philosophical Foundations of Physics
History of Mathematical Sciences
History of Science
History of science and technology
Life sciences
Ligands
Mathematical constants
Mathematics
Mathematics and Statistics
Medicine; surgery; pharmacy
Observations and Techniques
Pharmacology
Philosophy of Science
Physiology
Receptors
Therapeutics
Richards Equation
Nonparametric Function
Hill Equation
Receptor Model
Hill Model
Hill equation
Pharmacology
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Summary: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.
ISSN:0003-9519
1432-0657
DOI:10.1007/s00407-012-0098-5