The Hill equation: a review of its capabilities in pharmacological modelling

The Hill equation was first introduced by A.V. Hill to describe the equilibrium relationship between oxygen tension and the saturation of haemoglobin. In pharmacology, the Hill equation has been extensively used to analyse quantitative drug–receptor relationships. Many pharmacokinetic–pharmacodynami...

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Bibliographic Details
Published in:Fundamental & clinical pharmacology 2008-12, Vol.22 (6), p.633-648
Main Authors: Goutelle, Sylvain, Maurin, Michel, Rougier, Florent, Barbaut, Xavier, Bourguignon, Laurent, Ducher, Michel, Maire, Pascal
Format: Article
Language:English
Subjects:
Animals
Binding Sites
Biological and medical sciences
curve-fitting
Drug Dosage Calculations
Drug Interactions
equation
Humans
law of mass action
Life Sciences
Logistic Models
Medical sciences
Models, Biological
Models, Statistical
Multivariate Analysis
Nonlinear Dynamics
nonlinear modelling
Other
Oxygen - blood
Oxyhemoglobins - metabolism
Pharmacokinetics
Pharmacology - methods
Pharmacology. Drug treatments
Probability
probability distribution
Receptors, Cell Surface - metabolism
Receptors, Cytoplasmic and Nuclear - metabolism
Risk Assessment
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Summary:The Hill equation was first introduced by A.V. Hill to describe the equilibrium relationship between oxygen tension and the saturation of haemoglobin. In pharmacology, the Hill equation has been extensively used to analyse quantitative drug–receptor relationships. Many pharmacokinetic–pharmacodynamic models have used the Hill equation to describe nonlinear drug dose–response relationships. Although the Hill equation is widely used, its many properties are not all well known. This article aims at reviewing the various properties of the Hill equation. The descriptive aspects of the Hill equation, in particular mathematical and graphical properties, are examined, and related to Hill’s original work. The mechanistic aspect of the Hill equation, involving a strong connection with the Guldberg and Waage law of mass action, is also described. Finally, a probabilistic view of the Hill equation is examined. Here, we provide some new calculation results, such as Fisher information and Shannon entropy, and we introduce multivariate probabilistic Hill equations. The main features and potential applications of this probabilistic approach are also discussed. Thus, within the same formalism, the Hill equation has many different properties which can be of great interest for those interested in mathematical modelling in pharmacology and biosciences.
ISSN:0767-3981
1472-8206
DOI:10.1111/j.1472-8206.2008.00633.x