Kinetics random bisubstrate reactions

The general rule for writing the rate equation according to the quasi-equilibrium treatment of enzyme kinetics can be exemplified for the random bisubstrate reaction with substrates A and B forming products P and Q (Figure 7.1), where KaKab = KbKba and KpKpq = KqKqp. 

In practice, uncompetitive and mixed inhibition are observed only for enzymes with two or more substrates—say, Sj and S2—and are very important in the experimental analysis of such enzymes. If an inhibitor binds to the site normally occupied by it may act as a competitive inhibitor in experiments in which [SJ is varied. If an inhibitor binds to the site normally occupied by S2, it may act as a mixed or uncompetitive inhibitor of Si. The actual inhibition patterns observed depend on whether the and S2-binding events are ordered or random, and thus the order in which substrates bind and products leave the active site can be determined. Use of one of the reaction products as an inhibitor is often particularly informative. If only one of two reaction products is present, no reverse reaction can take place. However, a product generally binds to some part of the active site, thus serving as an inhibitor. Enzymologists can use elaborate kinetic studies involving different combinations and amounts of products and inhibitors to develop a detailed picture of the mechanism of a bisubstrate reaction. 

TABLE 11.5 Cleland nomenclature for bisubstrate reactions exemplified. Three common kinetic mechanisms for bisubstrate enzymatic reactions are exemplified. The forward rate equations for the order bi bi and ping pong bi hi are derived according to the steady-state assumption, whereas that of the random bi bi is based on the quasi-equilibrium assumption. These rate equations are first order in both A and B, and their double reciprocal plots (1A versus 1/A or 1/B) are linear. They are convergent for the order bi bi and random bi bi but parallel for the ping pong bi bi due to the absence of the constant term (KiaKb) in the denominator. These three kinetic mechanisms can be further differentiated by their product inhibition patterns (Cleland, 1963b)... 

Why product inhibition occurs. The products of reaction are formed at the active site of enzyme and are the substrates for the reverse reaction. Consequently, a product may act as an inhibitor by occupying the same site as the substrate from which it is derived. In the Rapid Equilibrium Random bisubstrate mechanism, most ligand dissociations are very rapid compared to the interconversion of EAB and EPQ. Thus, the levels of EP and EQ are essmtiaUy zero in the absence of added P and Q. In the presence of only one of the products, the reverse reaction can be neglected, as the concentration of the other product is essentially zero during the early part of the reaction. Nevertheless, the forward reaction will be inhibited because finite P (or Q) ties up some of the enzyme. The type of this product inhibition depends on the number and type of enzyme-product complexes that can form. Consequently, product inhibition studies can be very valuable in the diagnostics of kinetic mechanisms (Rudolph, 1979). 

The order of addition of substrates in the Bi Bi mechanisms, with a central ternary complex, can be strictly ordered, completely random or partially random. We can employ reaction (10.7) in order to analyze most kinetic mechanisms that occur in bisubstrate systems ... 

The first synthetic bisubstrate analog inhibitor 18 was successfully designed for al,2-FucT II by Palcic et al., based on the proposed ion-pair mechanism shown in Scheme 8 [22]. Analog 18, where the Gal unit is attached to the terminal phosfor of GDP through a flexible ethylene linkage, was found to be a competitive inhibitor with respect to both donor and acceptor substrates with K values of 16 and 2.3 pM, respectively. Inhibition studies with the bisubstrate analog also helped establish the kinetic mechanism of the enzyme reaction. These dual competitive inhibition patterns are only consistent with a random kinetic mechanism where either substrate can bind to free enzyme. 

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