# Hill equation

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## Hill e·qua·tion

(hil),
the equation y(1 - y) = [S]n/Kd, where y is the fractional degree of saturation, [S] is the binding ligand concentration, n is the Hill coefficient, and Kd is the dissociation constant for the ligand. The Hill coefficient is a measure of the cooperativity of the protein: the larger the value, the higher the degree of cooperativity. This coefficient cannot be higher than the number of binding sites. For the oxygen binding curve of hemoglobin, an association constant, Ka, is used and the equation becomes y/(1 - y) = Ka[S]n. For human hemoglobin A, n = 2.5. Compare: Hill plot.
[Archibald V. Hill]

## Hill e·qua·tion

(hil ĕ-kwā'zhŭn)
The equation y(1 - y) = [S]n/Kd, where y is the fractional degree of saturation, [S] is the binding ligand concentration, n is the Hill coefficient, and Kd is the dissociation constant for the ligand. The Hill coefficient is a measure of the cooperativity of the protein; the larger the value, the higher the cooperativity. This coefficient cannot be higher than the number of binding sites. For the oxygen binding curve of hemoglobin, an association constant, Ka, is used and the equation becomes y/(1 - y) = Ka[S]n. For human hemoglobin, n = 2.5.
[Archibald V. Hill]

## Hill,

Archibald V., English biophysicist and Nobel laureate, 1886-1977.
Hill equation - used to express the fractional saturation of a molecule with a ligand as a function of ligand concentration.
Hill plot - a graphical representation of enzyme kinetic data or of binding phenomena to assess the degree of cooperativity of a system.
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References in periodicals archive ?
Most applications of the Hill equation, in any form, have focused on deterministic problems.
Because of the advantages of the reversible Hill equation and its applicability to different intracellular reaction networks [8,10-12], the present work has studied the performance of this equation under the impact of intra-cellular noise.
The basic Hill equation [1] provides a method to express the rate of formation of a product, P, from a substrate, S, through catalysis by an allosteric enzyme, E.
A major attraction of the Hill equation is its ability to describe quantitatively the behavior of reactions with complex mechanisms that are not known accurately.
The absence of a mechanistic foundation also limits the applicability of the irreversible Hill equation.
reversible Hill equation is the limiting form of Eq.
For the reversible Hill equation, these are the (dimensionless) concentrations of the substrate ([sigma]) , the product ([pi]) and the moderator ([zeta]).
The reversible Hill equation is widely used to model the kinetics of biochemical reaction networks with allosteric inhibitors and/or activators.
In general, the response coefficients were relatively larger at low concentrations, suggesting that the inapplicability of the deterministic reversible Hill equation under extreme conditions becomes stronger in the presence of noise.
Ironically, however, these difficulties do not seriously undermine the usefulness of the reversible Hill equation, possibly because of its weak reliance on mechanistic information.

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