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 ?
Additionally, the Hill equation was applied to describe the imbibition process.
The parameters of the Hill equation are within the defined ranges.
Nevertheless, in cases of the second phase and the entire process (gelatin concentration of 0.05% and 0.1%, the dispersed phase concentration of 20%) the determined coefficients of the Hill equation are distinguished and do not follow defined tendency (see Table 4).
By plotting moxifloxacin concentration (100 mmol/L) on the x-axis and tail current inhibition (%) on the y-axis, a dose-response curve was generated and the data were fitted to a Hill equation, y = [([A.sub.1] - [A.sub.2])/(1 + (x/C)[n.sub.H])] + [A.sub.2].
Data are fitted with the Hill equation: Percent increase = maximum increase/(1 + [EC.sub.50]/[BPA]), where maximum increase = 37%, and [EC.sub.50] = 0.15 nM.
Data are fitted with the Hill equation: Percent inhibition = maximum inhibition/(1 + [IC.sub.50]/[BPA]), where maximum inhibition = 43%, and [IC.sub.50] = 27.4 nM.
The design of formation-flying order using Hill equation can appear as a biggish excursion under [J.sub.2] absorb impetus.
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.
Given age-independent fecundity, the Hill equation can be expressed in terms of seasonal parameters plus the mean generation time T [T = ([T.sub.m] + [T.sub.f])/2, where [T.sub.f] and [T.sub.m] are the generation times of females and males respectively], and the average adult life span as A [A = ([A.sub.m] + [A.sub.f])/2, where the [A.sub.i] are the average life span of the two sexes].
For instance, a maximal response at the lowest tested concentration will not be adequately explained by fitting the conventional Hill equation (Hill 1910).
(g.) RMAX, maximal activity from the Hill Equation. (h) R0, baseline activity from the Hill Equation.