Molecular binding is an interaction between molecules that results in a stable physical association between those molecules. Cooperative binding occurs in binding systems containing more than one type, or species, of molecule and in which one of the partners is not mono-valent and can bind more than one molecule of the other species.
For example, consider a system where one molecule of species A can bind to molecules of species B. Species A is called the receptor and species B is called the ligand. Binding can be considered "cooperative" if the binding of the first molecule of B to A changes the binding affinity of the second B molecule, making it more or less likely to bind. In other words, the binding of B molecules to the different sites on A do not constitute mutually independent events.
Cooperativity can be positive or negative. Cooperative binding is observed in many biopolymers, including
proteins and
nucleic acids. Cooperative binding has been shown to be the mechanism underlying a large range of biochemical and physiological processes.
History and mathematical formalisms
Christian Bohr and the concept of cooperative binding
In 1904,
Christian Bohr
Christian Harald Lauritz Peter Emil Bohr (1855–1911) was a Danish physician, father of the physicist and Nobel laureate Niels Bohr, as well as the mathematician and football player Harald Bohr and grandfather of another physicist and Nobel lau ...
studied
hemoglobin binding to
oxygen under different conditions.
When plotting hemoglobin saturation with oxygen as a function of the
partial pressure of oxygen, he obtained a sigmoidal (or "S-shaped") curve. This indicates that the more oxygen is bound to hemoglobin, the easier it is for more oxygen to bind - until all binding sites are saturated. In addition, Bohr noticed that increasing
CO2 pressure shifted this curve to the right - i.e. higher concentrations of CO
2 make it more difficult for hemoglobin to bind oxygen.
[ This latter phenomenon, together with the observation that hemoglobin's affinity for oxygen increases with increasing pH, is known as the ]Bohr effect
The Bohr effect is a phenomenon first described in 1904 by the Danish physiologist Christian Bohr. Hemoglobin's oxygen binding affinity (see oxygen–haemoglobin dissociation curve) is inversely related both to acidity and to the concentration o ...
.
A receptor molecule is said to exhibit cooperative binding if its binding to ligand scales non-linearly with ligand concentration. Cooperativity can be positive (if binding of a ligand molecule increases the receptor's apparent affinity, and hence increases the chance of another ligand molecule binding) or negative (if binding of a ligand molecule decreases affinity and hence makes binding of other ligand molecules less likely). The "fractional occupancy" of a receptor with a given ligand is defined as the quantity of ligand-bound binding sites divided by the total quantity of ligand binding sites:
:
If , then the protein is completely unbound, and if , it is completely saturated. If the plot of at equilibrium as a function of ligand concentration is sigmoidal in shape, as observed by Bohr for hemoglobin, this indicates positive cooperativity. If it is not, no statement can be made about cooperativity from looking at this plot alone.
The concept of cooperative binding only applies to molecules or complexes with more than one ligand binding sites. If several ligand binding sites exist, but ligand binding to any one site does not affect the others, the receptor is said to be non-cooperative. Cooperativity can be homotropic, if a ligand influences the binding of ligands of the same kind, or heterotropic, if it influences binding of other kinds of ligands. In the case of hemoglobin, Bohr observed homotropic positive cooperativity (binding of oxygen facilitates binding of more oxygen) and heterotropic negative cooperativity (binding of CO2 reduces hemoglobin's facility to bind oxygen.)
Throughout the 20th century, various frameworks have been developed to describe the binding of a ligand to a protein with more than one binding site and the cooperative effects observed in this context.
The Hill equation
The first description of cooperative binding to a multi-site protein was developed by A.V. Hill. 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:
:
where is the "Hill coefficient",