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The Hill coefficient, or , may describe cooperativity (or possibly other biochemical properties, depending on the context in which the Hill equation is being used). When appropriate, [clarification needed] the value of the Hill coefficient describes the cooperativity of ligand binding in the following way:
where is the "Hill coefficient", [] denotes ligand concentration, denotes an apparent association constant (used in the original form of the equation), is an empirical dissociation constant, and a microscopic dissociation constant (used in modern forms of the equation, and equivalent to an ).
The Hill coefficient is a measure of ultrasensitivity (i.e. how steep is the response curve).
The Hill equation is the following formula, where is the magnitude of the response, [] is the drug concentration (or equivalently, stimulus intensity) and is the drug concentration that produces a 50% maximal response and is the Hill coefficient.
The EC 50 relates to the Hill equation, which is a function of the agonist concentration, [A]: = [] [] + [3] where E is the observed response or effect above baseline, and n, the Hill coefficient reflects the slope of the curve. [7]
In other words, a very small change in stimulus causes a very large change in response, producing a sigmoidal dose-response curve. An ultrasensitive response is described by the general equation V = S n /(S n + K m), known as the Hill equation, when n, the Hill coefficient, is more than 1. The steepness of the sigmoidal curve depends on the ...
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 ...
Hill's equation is an important example in the understanding of periodic differential equations. Depending on the exact shape of f ( t ) {\displaystyle f(t)} , solutions may stay bounded for all time, or the amplitude of the oscillations in solutions may grow exponentially. [ 3 ]