Enzyme kinetics single-substrate inhibition

In the presence of sucrose alone as the single substrate, initial reaction rates follow Michaelis-Menten kinetics up to 200 mM sucrose concentration, but the enzyme is inhibited by higher concentrations of substrate.30 The inhibitor constant for sucrose is 730 mM. This inhibition can be overcome by the addition of acceptors.31,32 The enzyme activity is significantly enhanced, and stabilized, by the presence of dextran, and by calcium ions. 

Substrates may affect enzyme kinetics either by activation or by inhibition. Substrate activation may be observed if the enzyme has two (or more) binding sites, and substrate binding at one site enhances the alfinity of the substrate for the other site(s). The result is a highly active ternary complex, consisting of the enzyme and two substrate molecules, which subsequently dissociates to generate the product. Substrate inhibition may occur in a similar way, except that the ternary complex is nonreactive. We consider first, by means of an example, inhibition by a single substrate, and second, inhibition by multiple substrates. 

Reversible inhibition occurs rapidly in a system which is near its equilibrium point and its extent is dependent on the concentration of enzyme, inhibitor and substrate. It remains constant over the period when the initial reaction velocity studies are performed. In contrast, irreversible inhibition may increase with time. In simple single-substrate enzyme-catalysed reactions there are three main types of inhibition patterns involving reactions following the Michaelis-Menten equation competitive, uncompetitive and non-competitive inhibition. Competitive inhibition occurs when the inhibitor directly competes with the substrate in forming the enzyme complex. Uncompetitive inhibition involves the interaction of the inhibitor with only the enzyme-substrate complex, while non-competitive inhibition occurs when the inhibitor binds to either the enzyme or the enzyme-substrate complex without affecting the binding of the substrate. The kinetic modifications of the Michaelis-Menten equation associated with the various types of inhibition are shown below. The derivation of these equations is shown in Appendix S.S. 

For a detailed review of simple to complex enzyme kinetics, a book by Segel (21) is recommended. Most P450 oxidations show hyperbolic saturation kinetics and competitive inhibition between substrates. Therefore, both Km values and drug interactions can be predicted from inhibition studies. Competitive inhibition suggests that the enzymes have a single binding site and only one substrate can bind at any one time. For the inhibition of substrate A by substrate B to be competitive, the following must be observed ... 

Previous sections of this chapter have focused on developing general principles for enzyme-catalyzed reactions based on analysis of single-substrate enzyme systems. Yet the majority of biochemical reactions involve multiple substrates and products. With multiple binding steps, competitive and uncompetitive binding interactions, and allosteric and covalent activations and inhibitions possible, the complete set of possible kinetic mechanisms is vast. For extensive treatments on a great number of mechanisms, we point readers to Segel s book [183], Here we review a handful of two-substrate reaction mechanisms, with detailed analysis of the compulsory-order ternary mechanism and a cursory overview of several other mechanisms. 

The various kinds of reversible inhibition that have been identified all depend on non-covalent binding, but inhibitors differ in how they act, with consequent differences in their kinetic effects. Figure 8-6 depicts a general scheme for enzyme inhibition of a simple single substrate-single product reaction. 

A frequent case in enzyme kinetics is the ability of enzymes to form numerous non-productive complexes with substrates, that do not break down (Fersht, 1999). If an enzyme molecule binds a single substrate molecule in a productive complex EA, but also another substrate molecule in a non-productive complex AE, we are referring to non-productive binding of this substrate. Akinetic model is analogous to that for a linear competitive inhibition (Section 5.2). 

The Michaelis-Menten kinetic scheme, which involves a single substrate and a single product, is obviously the simplest type of enzyme catalysis. Equation (1.7) may hold for many mechanisms, but the mechanisms can be different from each other and the expression of kinetic parameters may also differ. When there is a substrate inhibition or activation due to the binding of a second substrate molecule, the Michaelis-Menten equation does not hold. 

Figure E5.7 displays the kinetic progress curve of a typical enzyme-catalyzed reaction and illustrates the advantage of a kinetic assay. The rate of product formation decreases with time. This may be due to any combination of factors such as decrease in substrate concentration, denaturation of the enzyme, and product inhibition of the reaction. The solid line in Figure E5.7 represents the continuously measured time course of a reaction (kinetic assay). The true rate of the reaction is determined from the slope of the dashed line drawn tangent to the experimental result. From the data given, the rate is 5 jumoles of product formed per minute. Data from a fixed-time assay are also shown on Figure E5.7. If it is assumed that no product is present at the start of the reaction, then only a single measurement after a fixed period is necessary. This is shown by a circle on the experimental rate curve. The measured rate is now 16 jumoles of product formed every 5 minutes or about 3 /rmoles/minute, considerably lower than the rate derived from the continuous, kinetic assay. Which rate measurement is correct Obviously, the kinetic assay gives the true rate because it corrects for the decline in rate with time. The fixed-time assay can be improved by changing the time of the measurement, in this example, to 2 minutes of reaction time, when the experimental rate is still linear. It is possible to obtain...

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