Uncompetitive inhibitor, enzyme kinetics

In this chapter we described the thermodynamics of enzyme-inhibitor interactions and defined three potential modes of reversible binding of inhibitors to enzyme molecules. Competitive inhibitors bind to the free enzyme form in direct competition with substrate molecules. Noncompetitive inhibitors bind to both the free enzyme and to the ES complex or subsequent enzyme forms that are populated during catalysis. Uncompetitive inhibitors bind exclusively to the ES complex or to subsequent enzyme forms. We saw that one can distinguish among these inhibition modes by their effects on the apparent values of the steady state kinetic parameters Umax, Km, and VmdX/KM. We further saw that for bisubstrate reactions, the inhibition modality depends on the reaction mechanism used by the enzyme. Finally, we described how one may use the dissociation constant for inhibition (Kh o.K or both) to best evaluate the relative affinity of different inhibitors for ones target enzyme, and thus drive compound optimization through medicinal chemistry efforts. 

Figure 8.4 The Lineweaver-Burk plot (A) and the Hanes plot (B) of typical enzyme kinetics in presence of a competitve (a) noncompetive (b), mixed type (c) and uncompetitive (d) inhibitor.

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. 

FIGURE 4.17 Effect of an uncompetitive, reversible inhibitor on enzyme kinetics... 

Substances that cause enzyme-catalyzed reactions to proceed more slowly are termed inhibitors, and the phenomenon is termed inhibition. When an enzyme is subject to inhibition, the reaction still may obey Michaelis-Menten kinetics but with apparent Km and Vmax values that vary with the inhibitor concentration. If the inhibitor acts only on the apparent Km, it is a competitive inhibitor if it affects only the apparent Vmax, it is a noncompetitive inhibitor and if it affects both constants, it is an uncompetitive inhibitor. 

The non-competitive and uncompetitive modes of inhibition described above are special cases that in practice arise very rarely in these simple forms. In reality, the situation is usually more complex in that inhibitors bind with differing affinities to the free and substrate-bound forms of the enzyme, and also the ternary EIS complex may be able to undergo catalysis, albeit at a lower rate. These circumstances define what is called mixed inhibition, which is less easy to characterise since the kinetic behaviour and equations are much more complex. The reader is referred to Cor-nish-Bowden (1995) for a comprehensive and authoritative account of this and other aspects of enzyme kinetics. 

Figure 8.18 Kinetics of an uncompetitive inhibitor. The reaction pathway shows that the inhibitor binds only to the enzyme-substrate complex. Consequently, cannot be attained, even at high substrate concentrations. The apparent value for Km is lowered, becoming smaller as more inhibitor is added.

In textbooks dealing with enzyme kinetics, it is customary to distinguish four types of reversible inhibitions (i) competitive (ii) noncompetitive (iii) uncompetitive and, (iv) mixed inhibition. Competitive inhibition, e.g., given by the product which retains an affinity for the active site, is very common. Non-competitive inhibition, however, is very rarely encountered, if at all. Uncompetitive inhibition, i.e. where the inhibitor binds to the enzyme-substrate complex but not to the free enzyme, occurs also quite often, as does the mixed inhibition, which is a combination of competitive and uncompetitive inhibitions. The simple Michaelis-Menten equation can still be used, but with a modified Ema, or i.e. ... 

There is some confusion in the literature about the use of the term "allosteric" for an enzyme. Many authors restrict this term to multi-subunit enzymes that show substrate cooperativity and sigmoidal kinetics. Other authors, however, are less specific and their definitions include enzymes that follow Michaelis- Menten kinetics and have non- or uncompetitive inhibitors. Fortunately, in metabolism, regulated enzymes are generally multi-subunit, cooperative, enzymes and fall into the more specific use of the term. 

Fig. 5.14 Scheme of the kinetics of reaction S Pj + P2 (Pi competitive inhibitor P2 noncompetitive inhibitor S substrate, uncompetitive inhibitor), and enzyme inactivation according to a two-stage series mechanism... 

In the simplest monosubstrate case, an uncompetitive inhibitor would bind reversibly to the enzyme-substrate complex yielding an inactive EAI complex the inhibitor does not bind to the free enzyme. The kinetic model for this type of inhibition would be... 

Figure 5.10. Demonstration of the four basic types of inhibitions of enzyme kinetics in Lineweaver-Burk plots (see Fig. 4.24c) (a) competitive, (b) noncompetitive, (c) uncompetitive, and (d) substrate inhibition. The parameters and can be estimated from the intercepts and slope of the line with p — 0, where p = inhibitor concentration.

Interaction matrix this matrix is suggested to identify the different interactions that can exist between compounds and enzymes in the process. In this case, the reaction structure defined in the previous step is useful to visuahze and classify those relationships that can happen with a higher degree of probabihty. Similar ideas about the interaction between compounds can be found in the scientific literature or from experimental experience in the laboratory. In order to build the matrix, the compounds involved in the process (i.e., substrates, intermediates, by-products, products, etc.) are arranged in rows (i.e.. A, B, C,...), and the enzymes E ) are arranged in columns (for i = 1, 2, 3,...). In this way, the matrix is filled defining the relationship between each compound and enzyme in turn, that is, (S) for substrate, (P) for product, (I) for inhibitor, or (X) when there is no interaction between one compound and one enzyme. This compiled information is extremely useful to make decisions about the relevant terms or kinetic parameters that must be added or removed from the reaction rate expressions and process model. The position of the new term/parameter in the final expression is defined by the enzyme kinetic mechanism which shows how the compound inhibits the enzyme, for example, competitive, uncompetitive, noncompetitive, or mixed inhibition. 

Inhibitors structurally related to the substrate may be bound to the enzyme active center and compete with the substrate (competitive inhibition). If the inhibitor is not only bound to the enzyme but also to the enzyme-substrate complex, the active center is usually deformed and its function is thus impaired. In this case the substrate and the inhibitor do not compete with each other (noncompetitive inhibition). Competitive and noncompetitive inhibitions affect the enzyme kinetics differently. A competitive inhibitor does not change but increases the on the contrary, a noncompetitive inhibition results in an unchanged and in a decrease in In the case of mixed inhibition, the inhibitor binds the enzyme and the enzyme-substrate complex with a different affinity. For uncompetitive inhibition, the inhibitor binds only when the enzyme-substrate complex is formed [21]. 

The equilibrium constant or dissociation constant of the enzyme-inhibitor complex, Ki, also known as the inhibitor constant, is a measure of the extent of inhibition. The lower the value of Ki, the higher the affinity of the inhibitor for the enzyme. Kinetically, three kinds of reversible inhibition can be distinguished competitive, non-competitive and uncompetitive inhibition (examples in Table 2.10). Other possible cases, such as allosteric inhibition and partial competitive or partial non-competitive inhibition, are omitted in this treatise. 

Substrate and product inhibitions analyses involved considerations of competitive, uncompetitive, non-competitive and mixed inhibition models. The kinetic studies of the enantiomeric hydrolysis reaction in the membrane reactor included inhibition effects by substrate (ibuprofen ester) and product (2-ethoxyethanol) while varying substrate concentration (5-50 mmol-I ). The initial reaction rate obtained from experimental data was used in the primary (Hanes-Woolf plot) and secondary plots (1/Vmax versus inhibitor concentration), which gave estimates of substrate inhibition (K[s) and product inhibition constants (A jp). The inhibitor constant (K[s or K[v) is a measure of enzyme-inhibitor affinity. It is the dissociation constant of the enzyme-inhibitor complex. 

Enzyme reaction kinetics were modelled on the basis of rapid equilibrium assumption. Rapid equilibrium condition (also known as quasi-equilibrium) assumes that only the early components of the reaction are at equilibrium.8-10 In rapid equilibrium conditions, the enzyme (E), substrate (S) and enzyme-substrate (ES), the central complex equilibrate rapidly compared with the dissociation rate of ES into E and product (P ). The combined inhibition effects by 2-ethoxyethanol as a non-competitive inhibitor and (S)-ibuprofen ester as an uncompetitive inhibition resulted in an overall mechanism, shown in Figure 5.20. 

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. 

Competitive inhibition occurs, when substrate and inhibitor compete for binding at the same active site at the enzyme. Based on the Michaelis-Menten kinetics, Vmax is unchanged whereas Km increases. In case of noncompetive inhibition, the inhibitor and the substrate bind to different sites at the enzyme. Vmax decrease whereas the Km value is unaffected. Binding of the inhibitor only to the enzyme-substrate complex is described as uncompetitive inhibition. Both, Vmax and Km decrease. Finally, mixed (competitive-noncompetitive) inhibition occurs, either the inhibitor binds to the active or to another site on the enzyme, or the inhibitor binds to the active site but does not block the binding of the substrate. 

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