# MWC model

An allosteric transition of a protein between R and T states, stabilised by an Agonist, and Inhibitor and a Substrate.

In biochemistry, the MWC model (Monod-Wyman-Changeux model, also known as the concerted model or symmetry model) describes allosteric transitions of proteins made up of identical subunits. It was proposed by Jean-Pierre Changeux based on his PhD experiments, and described by Jacques Monod, Jeffries Wyman, and Jean-Pierre Changeux. It stands in opposition to the sequential model.

The concept of two distinct symmetric states is the central postulate of the MWC model.The main idea of the model 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, alternatively termed the MWC model, is defined by the following rules: 1. An allosteric protein is an oligomer of protomers that are symmetrically related (for hemoglobin, we shall assume, for the sake of algebraic simplicity, that all four subunits are functionally identical). 2. Each protomer can exist in (at least) two conformational states, designated T and R; these states are in equilibrium whether or not ligand is bound to the oligomer. 3. The ligand can bind to a protomer in either conformation. Only the conformational change alters the affinity of a protomer for the ligand. The regulators merely shift the equilibrium toward one state or another. For instance, an agonist will stabilize the active form of a pharmacological receptor. Phenomenologically, it looks as if the agonist provokes the conformational transition. One crucial feature of the model is the dissociation between the binding function (the fraction of protein bound to the regulator), and the state function (the fraction of protein under the activated state), cf below. In the models said of "induced-fit", those functions are identical.

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):

Where ${\displaystyle L=[T]_{0}/[R]_{0}}$ is the allosteric constant, that is the ratio of proteins in the T and R states in the absence of ligand, ${\displaystyle c=K_{R}/K_{T}}$ is the ratio of the affinities of R and T states for the ligand, and ${\displaystyle \alpha =[X]/K_{R}}$, the normalised concentration of ligand.

This model explains sigmoidal binding properties as change in concentration of ligand over a small range will lead to a vast increase in the proportion of molecules in the R state, and thus will lead to a high association of the ligand to the protein.

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. Extension of the model have been proposed for lattices of proteins, for instance by Changeux, Thiery, Tung and Kittel, by Wyman or by Duke, Le Novere and Bray.

## References

• Changeux J.-P. (1964). Allosteric interactions interpreted in terms of quaternary structure. Brookhaven Symposia in Biology, 17: 232-249.
• Monod J., Wyman J., and Changeux J.-P. (1965). On the nature of allosteric transitions: a plausible model. J. Mol. Biol. 12: 88-118.
• Changeux J.-P., Thiery J., Tung Y., Kittel C. (1967). On the cooperativity of biological membranes. PNAS 57: 335-341
• Wyman J (1969). Possible allosteric effects in extended biological systems. J. Mol Biol. 14:523-538.
• Edelstein SJ (1971). Extensions of the allosteric model for haemoglobin. Nature. 230:224-227.
• Changeux JP, Edelstein SJ (1998). Allosteric receptors after 30 years. Neuron 21: 959-980.
• Duke TA, Le Novere N, Bray D (2001). Conformational spread in a ring of proteins: a stochastic approach to allostery. J. Mol Biol. 308:541-553.
• Changeux JP, Edelstein SJ. (2005) Allosteric mechanisms of signal transduction. Science, 2005 Jun 3;308(5727):1424-8.