Monod-Wyman-Changeux model

In biochemistry, the Monod-Wyman-Changeux model (MWC model, also known as the symmetry model) describes allosteric transitions of proteins made up of identical subunits. It was proposed by Jean-Pierre Changeux in his PhD thesis, and described by Jacques Monod, Jeffries Wyman, and Jean-Pierre Changeux. It contrasts with the sequential model.
The concept of two distinct symmetric states is the central postulate of the MWC model. The main idea is that regulated proteins, such as many enzymes and receptors, exist in different interconvertible states "in the absence of any regulator". The ratio of the different conformational states is determined by thermal equilibrium. This
model is defined by
the following rules:
In the historical model, each allosteric unit, called a protomer (generally assumed to be a subunit), can exist in two different conformational states - designated 'R' (for relaxed) or 'T' (for tense) states. In any one molecule, all protomers must be in the same state. That is to say, all subunits must be in either the R or the T state. Proteins with subunits in different states are not allowed by this model. The R state has a higher affinity for the ligand than the T state. Because of that, although the ligand may bind to the subunit when it is in either state, the binding of a ligand will increase the equilibrium in favor of the R state. 
Two equations can be derived, that express the fractional occupancy of the ligand binding site (Y) and the fraction of the proteins in the R state (R):
formula_1
formula_2
Where formula_3 is the allosteric constant, that is the ratio of proteins in the T and R states in the absence of ligand, formula_4 is the ratio of the affinities of R and T states for the ligand, and formula_5, the normalized concentration of ligand. It is not immediately obvious that the expression for formula_6 is a form of the Adair equation, but in fact it is, as one can see by multiplying out the expressions in parentheses and comparing the coefficients of powers of formula_7 with corresponding formula_8 coefficients in the Adair equation.
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 MWC model proved very popular in enzymology, and pharmacology, although it has been shown inappropriate in a certain number of cases. The best example of a successful application of the model is the regulation of hemoglobin function. Extensions of the model have been proposed for lattices of proteins by various authors. Edelstein argued that the MWC model gave a better account of the data for hemoglobin than the sequential model could do. He and Changeux applied the model to signal transduction. Changeux has discussed the status of the model after 50 years.