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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:
Negatively cooperative binding: Once one ligand molecule is bound to the enzyme, its affinity for other ligand molecules decreases. n = 1 {\displaystyle n=1} . Noncooperative (completely independent) binding : The affinity of the enzyme for a ligand molecule is not dependent on whether or not other ligand molecules are already bound.
The sigmoidal shape of hemoglobin's oxygen-dissociation curve results from cooperative binding of oxygen to hemoglobin. An example of positive cooperativity is the binding of oxygen to hemoglobin. One oxygen molecule can bind to the ferrous iron of a heme molecule in each of the four chains of a hemoglobin molecule.
In the tetrameric form of normal adult hemoglobin, the binding of oxygen is, thus, a cooperative process. The binding affinity of hemoglobin for oxygen is increased by the oxygen saturation of the molecule, with the first molecules of oxygen bound influencing the shape of the binding sites for the next ones, in a way favorable for binding.
A slight change in the conformation of an enzyme improves its binding affinity to the transition state of the ligand, thus catalyzing a reaction. This follows the KNF model, which models cooperativity as the changing conformation of the ligand binding site upon ligand binding to another subunit. Two essential assumptions guide the KNF model: [6]
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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 ...