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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 ...
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 ...
If the enzyme is irreversible the equation turns into the simple Michaelis-Menten equation that is irreversible. When setting the equilibrium constant to infinity, the equation can be seen to revert to the simpler case where the product inhibits the reverse step. A comparison has been made between the MWC and reversible Hill equation. [9]
Download as PDF; Printable version; ... move to sidebar hide. Hill equation may refer to Hill equation (biochemistry) Hill differential equation ; This page was last ...
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 ...
The first description of cooperative binding to a multi-site protein was developed by A.V. Hill. [4] Drawing on observations of oxygen binding to hemoglobin and the idea that cooperativity arose from the aggregation of hemoglobin molecules, each one binding one oxygen molecule, Hill suggested a phenomenological equation that has since been named after him:
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.
One such relation is the Hill equation: = [] + [] = [] + [], where is the Hill coefficient which quantifies the steepness of the sigmoidal stimulus-response curve and it is therefore a sensitivity parameter. It is often used to assess the cooperativity of a system.