Editing Stimulus–response model (section)

=== Hill equation ===

In [[biochemistry]] and [[pharmacology]], the [[Hill equation (biochemistry)|Hill equation]] refers to two closely related equations, one of which describes the response (the physiological output of the system, such as muscle contraction) to [[Drug]] or [[Toxin]], as a function of the drug's [[concentration]].<ref name = Terms>{{cite journal |title=International Union of Pharmacology Committee on Receptor Nomenclature and Drug Classification. XXXVIII. Update on Terms and Symbols in Quantitative Pharmacology|url=https://www.guidetopharmacology.org/pdfs/termsAndSymbols.pdf|last1=Neubig|first1=Richard R.|journal=Pharmacological Reviews|year=2003|volume=55|issue=4|pages=597–606|doi=10.1124/pr.55.4.4|pmid=14657418|s2cid=1729572}}</ref> The Hill equation is important in the construction of [[dose-response curves]]. The Hill equation is the following formula, where <math>E</math> is the magnitude of the response, <chem>[A]</chem> is the drug concentration (or equivalently, stimulus intensity), [[EC50|<math>\mathrm{EC}_{50}</math>]] is the drug concentration that produces a half-maximal response and <math>n</math> is the [[Hill coefficient]].

:[[File:Ivan Pavlov nobel.jpg|thumb|Ivan Pavlov]]<math>\frac{E}{E_{\mathrm{max}}}=\frac{1}{1+\left(\frac{\mathrm{EC}_{50}}{[A]}\right)^{n}}</math><ref name = Terms/>

The Hill equation rearranges to a logistic function with respect to the logarithm of the dose (similar to a logit model).