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The Hill equation reflects the occupancy of macromolecules: the fraction that is saturated or bound by the ligand. [1] [2] [nb 1] This equation is formally equivalent to the Langmuir isotherm. [3] Conversely, the Hill equation proper reflects the cellular or tissue response to the ligand: the physiological output of the system, such as muscle ...
Although Hill's equation looks very much like the van der Waals equation, the former has units of energy dissipation, while the latter has units of energy. Hill's equation demonstrates that the relationship between F and v is hyperbolic. Therefore, the higher the load applied to the muscle, the lower the contraction velocity.
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 ...
In biochemistry and pharmacology, the Hill and Hill–Langmuir equations are sigmoid functions. In computer graphics and real-time rendering, some of the sigmoid functions are used to blend colors or geometry between two values, smoothly and without visible seams or discontinuities.
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]
Hill's equation is an important example in the understanding of periodic differential equations. Depending on the exact shape of (), solutions may stay bounded for all time, or the amplitude of the oscillations in solutions may grow exponentially. [3] The precise form of the solutions to Hill's equation is described by Floquet theory. Solutions ...
Studies of light intensities revealed that the effect was largely on the light-independent steps of the Hill reaction. These observations are explained in terms of a proposed method in which phosphate esterifies during electron transport reactions, reducing ferricyanide, while the rate of electron transport is limited by the rate of ...
Hill equation may refer to Hill equation (biochemistry) Hill differential equation This page was last edited on 28 December 2019, at 18:37 (UTC). Text is available ...