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

@article{Goutelle2008TheHE,
  title={The Hill equation: a review of its capabilities in pharmacological modelling},
  author={Sylvain Goutelle and Michel Maurin and Florent Rougier and Xavier Barbaut and Laurent Bourguignon and Michel Ducher and Pascal Maire},
  journal={Fundamental \& Clinical Pharmacology},
  year={2008},
  volume={22}
}
The Hill equation was first introduced by A.V. Hill to describe the equilibrium relationship between oxygen tension and the saturation of haemoglobin. [] Key Result 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.
The Hill equation and the origin of quantitative pharmacology
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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.
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This paper presents several equivalent versions of the Hill model, and shows that they are equivalent in terms of yielding the same prediction for a given dose, and are equivalent to the four-parameter logistic model in this same sense; and deduces which parameterization is optimal in the sense of having the least statistical curvature and preferable multicollinearity.
Analysing force–pCa curves
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The Hill coefficient was found to be sufficiently log-normally distributed that log-transformed values should be used to test for statistically significant differences, and either EC50 or pCa50 may be used for significant differences.
Kinetic model selection and the Hill model in geochemistry
This study introduces the Hill model for modelling sorption kinetics and illustrates its efficacy using formal model selection procedures. Although the coefficient of determination (R2) value can be
Kinetic interpretation of log-logistic dose-time response curves
TLDR
Positive results suggest that the proposed dose-response relationship for the toxicity of agents to organisms can be extended to inanimate systems especially in cases where accurate mechanistic models are lacking.
An overview of pharmacodynamic modelling, ligand-binding approach and its application in clinical practice
  • M. Salahudeen, P. Nishtala
  • Biology
    Saudi pharmaceutical journal : SPJ : the official publication of the Saudi Pharmaceutical Society
  • 2017
Bohr equation and the lost allosteric Bohr effects in symmetry
  • L. Lee
  • Biology
    Biophysics and physicobiology
  • 2019
TLDR
The logistic-derived Bohr equation and its half-saturated P50 equation successfully used the embedded P50 values in the 1904 sigmoidal curves to quantify their hyperbolic conformational shifts and Hill coefficients (n) pending for a century.
A danger of low copy numbers for inferring incorrect cooperativity degree
  • Z. Konkoli
  • Physics
    Theoretical Biology and Medical Modelling
  • 2010
TLDR
The validity of the Hill function has been studied from an entirely different point of view in the limit of low copy numbers, to see in what ways the effects of the fluctuations change the form of the dose-response curves.
Safe uses of Hill's model: an exact comparison with the Adair-Klotz model
  • Z. Konkoli
  • Physics
    Theoretical Biology and Medical Modelling
  • 2011
TLDR
A strongly cooperative Adair-Klotz model can be replaced by a suitable Hill model in such a way that any property computed from the two models, even the one describing stochastic features, is approximately the same.
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