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The Hill coefficient, or , may describe cooperativity (or possibly other biochemical properties, depending on the context in which the Hill equation is being used). When appropriate, [clarification needed] the value of the Hill coefficient describes the cooperativity of ligand binding in the following way:
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:
Deoxy-hemoglobin has a relatively low affinity for oxygen, ... The Hill coefficient is a measure of ultrasensitivity (i.e. how steep is the response curve).
) that states a Hill coefficient 1.6-1.7 for the Hemocyanin from Tachypleus gigas. This is the highest I can find amoung articles of hemocyanin with stated Hill coefficients, many of which state coefficients of 1 or less. Hemoglobin has a coefficient of 2.8. Hemocyanin from Tachypleus gigas.
Hill coefficients vary depending on species and laboratory measurement settings. Hemoglobin, for comparison, has a Hill coefficient of usually 2.8–3.0. In these cases of cooperative binding hemocyanin was arranged in protein sub-complexes of 6 subunits (hexamer) each with one oxygen binding site; binding of oxygen on one unit in the complex ...
In other words, a very small change in stimulus causes a very large change in response, producing a sigmoidal dose-response curve. An ultrasensitive response is described by the general equation V = S n /(S n + K m), known as the Hill equation, when n, the Hill coefficient, is more than 1. The steepness of the sigmoidal curve depends on the ...
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. A Hill coefficient greater than one is indicative of positive cooperativity and thus, the system exhibits ultrasensitivity. [34]
The Hill equation [40] is often used to describe the degree of cooperativity quantitatively in non-Michaelis–Menten kinetics. The derived Hill coefficient n measures how much the binding of substrate to one active site affects the binding of substrate to the other active sites.