Concerted models, enzyme kinetics

The concerted model kinetic model Monod, Wyman and Changeux makes a number of assumptions. The enzyme can exist in 2 states Tense (T) and Relaxed (R), the first one T-state has low affinity for the reactant (KT large), while R-state has high affinity (Kr small). As mentioned above all the subunits of any one molecule are either in the T-state or the R-state. In the following treatment we will consider an enzyme with 4 subunits (Figure 6.27)... 

Goldbeter, A. 1976. Kinetic cooperativity in the concerted model for allosteric enzymes. Biophys. Chem. 4 159-69. 

Assuming that the enzymes Ei and E2 obey the concerted transition model, the kinetic equation for the transformed concentrations of S, Pi and P2 is ... 

The reactant A 3 is the ATP and enters the system at constant rate of Jrl at step (a). The, l2 is the ADP, which is the product of reaction and also the activator in step (d). The factor y (y> I) shows that the fixation of A 2 on the enzyme activates more than one reacting site because of the concerted conformational equilibrium. The kinetics of the model above is... 

Each of the two enzymes thus behaves as phosphofructokinase in the model considered for glycolytic oscillations (chapter 2). To limit the study to temporal organization phenomena, the system is considered here as spatially homogeneous, as in the case of experiments on glycolytic oscillations (Hess et ai, 1969). In the case where the kinetics of the two enzymes obeys the concerted allosteric model (Monod et al, 1965), the time evolution of the model is governed by the kinetic equations (4.1), which take the form of three nonlinear, ordinary differential equations ... 

Cooperative substrate binding results in sigmoidal v versus [S] curves (Fig. 8.1). The Michaelis-Menten model is therefore not appMcable to cooperative enzymes. Two major equihbrium models have evolved to describe the catalytic behavior of cooperative enzymes the sequential interaction and concerted transition models. The reader should be aware that other models have also been developed, such as equilibrium association-dissociation models, as well as several kinetic models. These are not discussed in this chapter. 

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