Dose–response relationship

Apr 20, 2026 - 16:49
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Dose–response relationship

Hill equation: add the reason for it following the Hill equation

← Previous revision Revision as of 11:18, 20 April 2026
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==== Hill equation ====
==== Hill equation ====
{{Main article|Hill equation (biochemistry)}}
{{Main article|Hill equation (biochemistry)}}
Logarithmic dose–response curves are generally [[Sigmoid function|sigmoidal-shape]] and monotonic and can be fit to a classical [[Hill equation (biochemistry)#Hill Equation - Measurement of Response|Hill equation]]. The Hill equation is a [[logistic function]] with respect to the logarithm of the dose and is similar to a [[logit model]]. A generalized model for multiphasic cases has also been suggested.{{cite journal |last1=Di Veroli |first1=Giovanni Y. |last2=Fornari |first2=Chiara |last3=Goldlust |first3=Ian |last4=Mills |first4=Graham |last5=Koh |first5=Siang Boon |last6=Bramhall |first6=Jo L. |last7=Richards |first7=Frances M. |last8=Jodrell |first8=Duncan I. |title=An automated fitting procedure and software for dose-response curves with multiphasic features |journal=Scientific Reports |date=1 October 2015 |volume=5 |issue=1 |article-number=14701 |doi=10.1038/srep14701 |pmid=26424192 |bibcode=2015NatSR...514701V |doi-access=free |pmc=4589737 }}
Due to [[cooperative binding]], logarithmic dose–response curves are generally [[Sigmoid function|sigmoidal-shape]] and monotonic and can be fit to a classical [[Hill equation (biochemistry)#Hill Equation - Measurement of Response|Hill equation]]. The Hill equation is a [[logistic function]] with respect to the logarithm of the dose and is similar to a [[logit model]]. A generalized model for multiphasic cases has also been suggested.{{cite journal |last1=Di Veroli |first1=Giovanni Y. |last2=Fornari |first2=Chiara |last3=Goldlust |first3=Ian |last4=Mills |first4=Graham |last5=Koh |first5=Siang Boon |last6=Bramhall |first6=Jo L. |last7=Richards |first7=Frances M. |last8=Jodrell |first8=Duncan I. |title=An automated fitting procedure and software for dose-response curves with multiphasic features |journal=Scientific Reports |date=1 October 2015 |volume=5 |issue=1 |article-number=14701 |doi=10.1038/srep14701 |pmid=26424192 |bibcode=2015NatSR...514701V |doi-access=free |pmc=4589737 }}


The [[Hill equation (biochemistry)|Hill equation]] is the following formula, where E is the magnitude of the response, [A] is the drug concentration (or equivalently, stimulus intensity) and [[EC50|\mathrm{EC}_{50}]] is the drug concentration that produces a 50% maximal response and n is the [[Hill coefficient]].
The [[Hill equation (biochemistry)|Hill equation]] is the following formula, where E is the magnitude of the response, [A] is the drug concentration (or equivalently, stimulus intensity) and [[EC50|\mathrm{EC}_{50}]] is the drug concentration that produces a 50% maximal response and n is the [[Hill coefficient]].
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