The Hill equation and the origin of quantitative pharmacology

@article{Gesztelyi2012TheHE,
  title={The Hill equation and the origin of quantitative pharmacology},
  author={Rudolf Gesztelyi and Judit Zsuga and Adam Kemeny-Beke and B{\'a}lazs Andr{\'a}s Varga and B{\'e}la Juh{\'a}sz and {\'A}rp{\'a}d T{\'o}saki},
  journal={Archive for History of Exact Sciences},
  year={2012},
  volume={66},
  pages={427-438}
}
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… 
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References

SHOWING 1-10 OF 33 REFERENCES
The Hill equation: a review of its capabilities in pharmacological modelling
TLDR
The Hill equation has many different properties which can be of great interest for those interested in mathematical modelling in pharmacology and biosciences, and is introduced as a probabilistic view of the Hill equation.
Analysis of drug-receptor interactions in vivo: a new approach in pharmacokinetic-pharmacodynamic modelling.
TLDR
The operational model of agonism can provide meaningful measures of agonist affinity and efficacy in vivo and may serve as a practical guide for future development of partial adenosine A1 receptor agonists and help to elucidate the mechanisms underlying adenosines A1 receptors-mediated responses in vivo.
Assessing the (a)symmetry of concentration-effect curves: empirical versus mechanistic models.
Operational models of pharmacological agonism
  • J. Black, P. Leff
  • Biology
    Proceedings of the Royal Society of London. Series B. Biological Sciences
  • 1983
TLDR
An alternative model is proposed, representing the cognitive and transducer functions of a receptor, that describes agonist action with one fewer parameter than the traditional model, and provides a chemical definition of intrinsic efficacy making this parameter experimentally accessible in principle.
A modification of receptor theory.
TLDR
An attempt has been made to determine the relation between log concentration and effect for acetylcholine and the frog rectus abdominis after blocking the cholinesterase activity of isolated rabbit auricles.
Analysis of asymmetry of agonist concentration-effect curves.
The receptor concept: pharmacology's big idea
  • H. Rang
  • Biology
    British journal of pharmacology
  • 2006
TLDR
The way in which the receptor concept originated early in the 20th century, and evolved through a highly innovative stage of quantitative theory based on chemical kinetics, to the point where receptors were first isolated and later cloned, is described, until the authors now have a virtually complete catalogue of all the receptors present in the genome.
The Hill equation revisited: uses and misuses
  • James N. Weiss
  • Biology
    FASEB journal : official publication of the Federation of American Societies for Experimental Biology
  • 1997
TLDR
Several relatively simple, physically plausible reaction schemes are shown here to produce a variety of ligand dose‐response curve phenotypes more appropriately suited to modeling ligand–receptor interactions, especially if independent information about the stochiometry of the ligand-receptor interaction is available.
PK-PD curve-fitting problems with the Hill equation? Try one of the 1-exp functions derived from Hodgkin, Douglas or Gompertz.
TLDR
The sigmoid functions investigated have differing characteristics and can be used interchangeably for solving specific problems in non-linear modeling.
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