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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 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:
This equation illustrates the idea that elasticities need not be constants (as with mass-action laws) but can be a function of the reactant concentration. In this case, the elasticity approaches unity at low reactant concentration (s) and zero at high reactant concentration. A.
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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 ...
The EC 50 represents the point of inflection of the Hill equation, beyond which increases of [A] have less impact on E. In dose response curves, the logarithm of [A] is often taken, turning the Hill equation into a sigmoidal logistic function. In this case, the EC 50 represents the rising section of the sigmoid curve.
Dick Van Dyke still makes time for leg day. The actor celebrated his 99th birthday on Dec. 13, then appears to have hit the gym a few days later, according to a video shared on his Instagram page ...
However, a series of publications by Popova and Sel'kov [2] derived the MWC rate equation for the reversible, multi-substrate, multi-product reaction. The same problem applies to the classic Hill equation which is almost always shown in an irreversible form. Hofmeyr and Cornish-Bowden first published the reversible form of the Hill equation. [1]