Initial rate equations three-substrate reactions

An enzyme reaction scheme in which there are two substrates (A and B) and three products (P, Q, and R) and in which the substrates bind and the products are released in an ordered fashion. This reaction scheme is exemphfied by the malic enzyme The initial rate expression, in the absence of abortive complexes and products, is identical to the corresponding equation for the ordered Bi Bi mechanism. See Multisubstrate Mechanisms Ordered Bi Bi Mechanism... 

Trisubstrate reactions (Chapter 72). In trisubstrate reactions, initially, one is trying to detect the absence of particular term(s) from the general rate equation for trisubstrate mechanisms by graphical methods, simply by trying the proper combinations of aU three substrates in double reciprocd plots (Section 12.1). When the kinetic mechanism is established in this way, the rate data are fitted to an appropriate rate equation by computer. 

Experiments are designed in a matrix where initial reaction rates are collected at different substrate and inhibitor concentrations. Linearization of the initial rate is given in Equation 4.39, and Table 4.1 represents the apparent constants for each of the three inhibition mechanisms. A graphic representation is shown in Figure 4.3. Once the mechanism has been identified the parameters can be identified. 

However, the further increases in the substrate concentration to 15mM decreased the initial reaction rate. This behavior may be due to substrate or product inhibition. Since the Michaelis-Menten equation does not incorporate the inhibition effects, we can drop the last two data points and limit the model developed for the low substrate concentration range only (Cs < lOmM). Figure 2.8 shows the three plots prepared from the given data. The two data points which were not included for the linear regression were noted as closed circles. 

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