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The Gaddum equation is a further generalisation of the Hill-equation, incorporating the presence of a reversible competitive antagonist. [1] The Gaddum equation is derived similarly to the Hill-equation but with 2 equilibria: both the ligand with the receptor and the antagonist with the receptor.
He showed that for many drugs, the relationship between drug concentration and biological effect corresponded to a hyperbolic curve, similar to that representing the adsorption of a gas onto a metal surface [11] and fitted the Hill–Langmuir equation. [3] Clark, together with Gaddum, was the first to introduce the log concentration–effect ...
An equation derived from the Gaddum equation can be used to relate r to [], as follows: = + [] where r is the dose ratio ... This is the Hill-Langmuir equation, ...
Hofmeyr and Cornish-Bowden first published the reversible form of the Hill equation. [1] The equation has since been discussed elsewhere [ 3 ] [ 4 ] and the model has also been used in a number of kinetic models such as a model of Phosphofructokinase and Glycolytic Oscillations in the Pancreatic β-cells [ 5 ] or a model of a glucose-xylose co ...
The Hill equation can be used to describe dose–response relationships, for example ion channel-open-probability vs. ligand concentration. [9] Dose is usually in milligrams, micrograms, or grams per kilogram of body-weight for oral exposures or milligrams per cubic meter of ambient air for inhalation exposures. Other dose units include moles ...
The EC 50 represents the point of inflection of the Hill equation, beyond which increases of [A] have less impact on E. In dose response curves, the logarithm of [A] is often taken, turning the Hill equation into a sigmoidal logistic function. In this case, the EC 50 represents the rising section of the sigmoid curve.
The IC 50 value is converted to an absolute inhibition constant K i using the Cheng-Prusoff equation formulated by Yung-Chi Cheng and William Prusoff (see K i). [4] [5]
Like Gaddum and Clark, he used quantitative approaches whenever possible. His name is immortalised by the Schild equation. [3] He built on the work of Clark and Gaddum on competitive antagonism, by realising that the null method was key to extraction of physical equilibrium constants from simple functional experiments.