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The Hill equation was originally formulated by Archibald Hill in 1910 to describe the sigmoidal O 2 binding curve of hemoglobin. [ 4 ] The binding of a ligand to a macromolecule is often enhanced if there are already other ligands present on the same macromolecule (this is known as cooperative binding ).
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.
The Lineweaver–Burk plot or double reciprocal plot is a common way of illustrating kinetic data. This is produced by taking the reciprocal of both sides of the Michaelis–Menten equation. As shown on the right, this is a linear form of the Michaelis–Menten equation and produces a straight line with the equation y = m x + c with a y ...
The sequential model (also known as the KNF model) is a theory that describes cooperativity of protein subunits. [1] It postulates that a protein's conformation changes with each binding of a ligand, thus sequentially changing its affinity for the ligand at neighboring binding sites.
The description of a protein three dimensional structure as a network of hydrogen bonding interactions (HB plot) [12] was introduced as a tool for exploring protein structure and function. By analyzing the network of tertiary interactions, the possible spread of information within a protein can be investigated.
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]