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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 dissociation rate in chemistry, biochemistry, and pharmacology is the rate or speed at which a ligand dissociates from a protein, for instance, a receptor. [1] It is an important factor in the binding affinity and intrinsic activity (efficacy) of a ligand at a receptor. [1]
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.
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.
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]
Hill equation may refer to Hill equation (biochemistry) Hill differential equation This page was last edited on 28 ...
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: