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.
References in periodicals archive ?
KEY WORDS: activity calls, concentration-response, Hill equation, quantitative high throughput screening, Tox21.
For instance, a maximal response at the lowest tested concentration will not be adequately explained by fitting the conventional Hill equation (Hill 1910).
The following form of the Hill equation model is used here:
Although proposed almost a century ago, the Hill equation [1] continues to be popular and useful in describing complex biochemical and metabolic reactions.
On the other hand, the Hill equation requires just one parameter (the Hill coefficient) in addition to those required by the corresponding non-cooperative equation.
In such situations the Hill equation is useful since it can capture the dynamic behavior accurately [4] and only a small number of parameters have to be fitted to the data.
The reversible Hill equation was generalized further by Westermark et al.
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.