The Monod-Wyman-Changeaux Model

Each subunit exists in a conformational state that has either a low affinity (T state) or a high affinity (R state) for substrate. 

In any one enzyme molecule, all the subunits are in the same conformational state. 

In the absence of substrate, the T state is favored. In the presence of substrate, the R state is favored. 

The model most often invoked to rationalize cooperative behavior is the MWC (Monod-Wyman-Changeaux), or concerted, model. This model is 1.5 times more complicated than the Michaelis-Menten model and took three people to develop instead of two. Most texts describe it in detail. In the absence of substrate, the enzyme has a low affinity for substrate. The MWC folks say that the enzyme is in a T (for tense or taut) state in the absence of substrate. Coexisting with this low-affinity T state is another conformation of the enzyme, the R (for relaxed) state, that has a higher affinity for substrate. The T and R states coexist in the absence of substrate, but there s much more of the T state than the R. This has always seemed backward, since one would expect the enzyme to be more tense in the presence of substrates when some work is actually required. In keeping with the tradition of biochemistry, the MWC folks obviously wanted this to be backward too (Fig. 8-8). 

The MWC model says that in the R state, all the active sites are the same and all have higher substrate affinity than in the T state. If one site is in the R state, all are. In any one protein molecule at any one time, all subunits are supposed to have identical affinities for substrate. Because the transition between the R and the T states happens at the same time to all subunits, the MWC model has been called e concerted model for allosterism and cooperativity. The MWC model invokes this symmetry principle because the modelers saw no compelling reason to think that one of the chemically identical subunits of a protein would have a conformation that was different from the others. Alternative models exist that suggest that each subunit can have a different conformation and different affinities for substrate. Experimentally, examples are known that follow each model. 

---

With the mathematical evaluation of cooperativity based on the Hill and Adair equations, the question remains. How does the enzyme convey ligand binding between sites Historically, the mechanisms by which proteins convey cooperativity in ligand binding have been described by two models Monod-Wyman-Changeaux (6) (MWC) and Koshland-Nem-ethy-Filmer (7)/Dalziel-Engel (8) (KNF/DE). These two models serve as starting points to... 

Figure 10.15 Quantitative description of the MWC model. In this description of the MWC Monod, Wyman, and Changeaux) model, fractional activity, K is the fraction of active sites bound to substrate and is directly proportional to reaction velocity a is the ratio of [S] to the dissociation constant of 5 with the enzyme in the R state and L Is the ratio of the concentration of enzyme in the T state to that in the R state, The binding of the regulators ATP and CTP to ATCase changes the value of L and thus the response to substrate concentration. To construct these curves, the formula on page 200 was used, with c = 0.1 and n — 6.

---