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The Hill equation is useful for determining the degree of cooperativity of the ligand(s) binding to the enzyme or receptor. The Hill coefficient provides a way to quantify the degree of interaction between ligand binding sites. [5] The Hill equation (for response) is important in the construction of dose-response curves.
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:
One manifestation of this is enzymes or receptors that have multiple binding sites where the affinity of the binding sites for a ligand is apparently increased, positive cooperativity, or decreased, negative cooperativity, upon the binding of a ligand to a binding site. For example, when an oxygen atom binds to one of hemoglobin's four binding ...
This model explains sigmoidal binding properties (i.e. positive cooperativity) as change in concentration of ligand over a small range will lead to a large increase in the proportion of molecules in the R state, and thus will lead to a high association of the ligand to the protein. It cannot explain negative cooperativity.
A multimeric protein's affinity for a ligand changes upon binding to a ligand, a process known as cooperativity. This phenomenon was first discovered by Christian Bohr's analysis of hemoglobin, whose binding affinity for molecular oxygen increases as oxygen binds its subunits. [1]
Hofmeyr and Cornish-Bowden first published the reversible form of the Hill equation. [1] The equation has since been discussed elsewhere [ 3 ] [ 4 ] and the model has also been used in a number of kinetic models such as a model of Phosphofructokinase and Glycolytic Oscillations in the Pancreatic β-cells [ 5 ] or a model of a glucose-xylose co ...
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 would increase the affinity of the neighboring units. Each hexamer complex was ...
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]