MWC model

FIGURE 15.9 Monod-Wyman-Changeux (MWC) model for allosteric transitions. Consider a dimeric protein that can exist in either of two conformational states, R or T. Each subunit in the dimer has a binding site for substrate S and an allosteric effector site, F. The promoters are symmetrically related to one another in the protein, and symmetry is conserved regardless of the conformational state of the protein. The different states of the protein, with or without bound ligand, are linked to one another through the various equilibria. Thus, the relative population of protein molecules in the R or T state is a function of these equilibria and the concentration of the various ligands, substrate (S), and effectors (which bind at f- or Fj ). As [S] is increased, the T/R equilibrium shifts in favor of an increased proportion of R-conformers in the total population (that is, more protein molecules in the R conformational state). 

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 file 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. 

The arithmetic of the MWC model is not worth going into, but the sigmoidal behavior arises from the fact that the enzyme is capable of interacting with multiple ligands with reactions of the type (E + 4S ES4). 

A substrate or effector that binds preferentially to the R state increases the concentration of the R state at equilibrium. This can only happen if, in the absence of substrate or effector, the enzyme is predominantly in the T state. If the enzyme were predominantly in the R state to begin with, it would already have increased affinity for the substrate and there would be no allosteric or cooperative effects. Consequently, the MWC model cannot account for negative cooperativity (but this is rare anyway). 

This is essentially the same PF as that of the model treated in Section 4.5 with the replacement of everywhere by <2 aa- essence, the MWC model is equivalent... 

The MWC model is presently known as the concerted model, since the entire protein changes its conformation concertedly. The induced-fit model was later developed by Koshland, Nemethy, and Filmer (KNF) and is presently known as the... 

The chief limitation of this plotting method is that, unlike the Adair Equation, the plot requires that the system obey all of the conditions required by the MWC model. This assumption will often prove to be incorrect ... 

Figure 2. Top Effect of the magnitude of the allosteric constant on ligand saturation behavior of a dimer obeying the MWC model. Bottom Fraction of total dimeric protein present in various T- and R-species.

Figure 5. Free energy diagrams showing the salient differences between the Monod and Koshland models. The MWC model is a two-state model with equivalent ligand binding interactions (indicated here by the equal spacing between Rq and Rb states and between RLi and RL2 states). In the KNF model, the amount of energy released determines whether binding will be independent or show negative or positive cooperativity.

A quite different mechanism for altering subunit interactions is through polymerization-depolymerization of subunits.54,55 If different polymeric states of the enzyme have different turnover numbers and/or different affinities for substrates and effectors, a model can be generated that is similar to the MWC model except that the cooperativity is also dependent on the enzyme concentration. Both K and V systems are possible with all the models. 

Fig. 6. A general allosteric model for the binding of substrate S to a four-subunit enzyme. The squares and circles represent different conformations of the subunits. The MWC model is shown by dashed lines and the AKNF model by dotted lines. The free substrate and arrows connecting the states are omitted for the sake of clarity.

The first model was proposed by Jacques Monod, Jeffries Wyman, and Jean-Pierre Changeux in 1965, and is called the MWC model or the concerted model... 

If both Kaa and XBB are large enough, there will be no dissociation into monomers. The transition between conformation A and conformation B can occur cooperatively within the dimer or higher oligomer, and the mathematical relationships shown in Fig. 7-21 are still appropriate. One further restriction is needed to describe the MWC model. Only symmetric dimers are allowed. That is, Kaa and KBB KAB (see Eq. 7-31), and only those equilibria indicated with green arrows in Fig. 7-21 need be considered.30 In the absence of ligand X, the ratio [B2] / [A2] is a constant, 1 / L in the MWC terminology (Eq. 7-36 see also Eq. 7-31). 

However, we must ask what uncertainties are present in the data used to obtain these constants. To extract four successive binding constants from a curve like that in Fig. 7-24A is extremely difficult.129 130 This fact has encouraged the widespread use of the simpler MWC model 30a 127a When the same data were treated by Imai131 using the MWC model it was found that L = 2.8 x 106 and c = K( (T) / Kf (R) = 0.0038. Changes in... 

Figure 9-13 (A) An enzyme with binding sites for allosteric inhibitor I and activator J. Conformer A binds inhibitor I strongly but has little affinity for activator J or for substrate S. Conformer B binds S and catalyzes its reaction. It also binds activator J whose presence tends to lock the enzyme in the "on" conformation B. Conformers A and B are designated T and R in the MWC model of Monod, Wyman, and Changeux.80 (B) Inhibited and activated dimeric enzymes.

According to the MWC model, in the presence of inhibitor and activator at normalized concentrations P and y an enzyme will still follow Eq. 9-65, but the allosteric constant L will be replaced by an apparent allosteric constant L (Eq. 9-70).86 Figure 9-14 shows plots of Y vs. log a for two different values of L for a tetramer with a specific value assumed for c. In both... 

For many enzymes the MWC model is unrealistically simple. The more general treatment of binding equilibria given in Chapter 7 may be applicable. However, in addition to K systems there are V systems in which a conformational change alters the maximum velocity (see Eq. 9-62)87 and sometimes both substrate... 

Figure 9-14 Fractional saturation Y and "function of state" R for hypothetical tetrameric enzymes following the MWC model. Curves are calculated for two different values of the apparent allosteric constant L (Eq. 9-70) and for c = 0.1 (Eq. 9-66). After Rubin and Changeux.86...

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