Kinetics uncompetitive inhibition

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. 

These equilibrium-binding relationships give rise to four different kinetic responses competitive inhibition, uncompetitive inhibition, non-competitive inhibition, mixed inhibition. Details of the kinetics of these types of inhibition and how dissociation constants for the reactions can be measured are provided in Appendix 3.6. 

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. 

The kinetic rate law for a substrate-inhibited enzyme is given by Eq. (5.18), which reveals that substrate inhibition is a special case of uncompetitive inhibition (Scheme 5.1). 

The primary considerations in studies of inhibition mechanisms are reversibility and selectivity. The inhibition kinetics of reversible inhibition give considerable insight into the reaction mechanisms of enzymes and, for that reason, have been well studied. In general, reversible inhibition involves no covalent binding, occurs rapidly, and can be reversed by dialysis or, more rapidly, by dilution. Reversible inhibition is usually divided into competitive inhibition, uncompetitive inhibition, and noncompetitive inhibition. Because these types are not rigidly separated, many intermediate classes have been described. 

Recognize competitive, noncompetitive, and uncompetitive inhibitions by their kinetic effects. 

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. 

MichaeUs-Menten kinetics predict that as the concentration of the substrate increases, the rate increases hyperbolically. However, some enzymes exist in which a maximum velocity is obtained at low substrate concentration, but further increases in the substrate concentration lead to a decrease in velocity. This effect is known as substrate inhibition and can eventually lead to complete enzyme inhibition or partial enzyme inhibition. It is thought that substrate inhibition occurs if two substrate molecules bind to the enzyme simultaneously in an incorrect orientation and produce an inactive E S S complex, analogous to that discussed for uncompetitive inhibition. The rate of the enzyme reaction that undergoes substrate inhibition is given by Equation 17, where K represents the... 

CYP2D6 biosensor for antidepressants (sertraline and fluxetine). Previous studies on PANI- and polythiophene-based CYP-biosensors for fluoxetine showed that the uncompetitive inhibition kinetics between the CYP enzyme and fluoxetine is based on the mono-oxygenation reaction of the enzyme [13], The response of the Au PANSA/CYP2D6... 

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. ... 

One special form of uncompetitive inhibition is substrate inhibition. Here a second substrate molecule binds at the ES complex resulting in an inactive ESS complex. This form of inhibition is often found and will be discussed below (see acylase kinetics, Fig. 7-20 A). 

As with competitive inhibition, two additional reaction steps are addr the Michaelis-Menten kinetics for uncompetitive inhibition as shown in i tion Steps 4 and 5. 

Equation 6-30 serves as a general expression for the effects of reversible inhibitors, simplifying to the expressions for competitive and uncompetitive inhibition when a = 1.0 or a = 1.0, respectively. From this expression we can summarize the effects of inhibitors on individual kinetic parameters. For all reversible inhibitors, apparent Vmzx =, because the right side of Equation 6-30... 

D23.4 Refer to eqns 23.26 and 23.27, which are the analogues of the Michaelis-Menten and Lineweaver-Burk equations (23.21 and 23,22), as well as to Figure 23.13, There are three major modes of inhibition that give rise to distinctly different kinetic behavior (Figure 23.13), In competitive inhibition the inhibitor binds only to the active site of the enzyme and thereby inhibits the attachment of the substrate. This condition corresponds to a > 1 and a = 1 (because ESI does not form). The slope of the Lineweaver-Burk plot increases by a factor of a relative to the slope for data on the uninhibited enzyme (a = a = I), The y-intercept does not change as a result of competitive inhibition, In uncompetitive inhibition, the inhibitor binds to a site of the enzyme that is removed from the active site, but only if the substrate is already present. The inhibition occurs because ESI reduces the concentration of ES, the active type of the complex, In this case a = 1 (because El does not form) and or > 1. The y-intercepl of the Lineweaver-Burk plot increases by a factor of a relative to they-intercept for data on the uninhibited enzyme, but the slope does not change. In non-competitive inhibition, the inhibitor binds to a site other than the active site, and its presence reduces the ability of the substrate to bind to the active site. Inhibition occurs at both the E and ES sites. This condition corresponds to a > I and a > I. Both the slope and y-intercept... 

Biocatalyst inhibitors I are substrate-like molecules that interact with a given biocatalyst and interfere with the progress of biocatalysis. Inhibitors usually act in one of three ways, either by competitive inhibition, non-competitive inhibition or uncompetitive inhibition. The mode of inhibition is different in each case and as a result a different steady state kinetic scheme is required to account for each mode of inhibition. Consequently, each mode of inhibition is characterised by a different steady state kinetic equation that gives rise to a different graphical output of V versus [S] data, as we will show below. These substantial differences in graphical output can be used to diagnose the type of inhibition if unknown. 

FIGURE 4.10 Diagnostic plots to determine the type of inhibition occurring in a kinetic reaction. Left side, panels (a), (b), and (c) are Dixon plots representative of competitive, mixed, and uncompetitive inhibition, respectively. Right side, panels (d), (e), and (f) are Cornish-Bowden plots representative of competitive, mixed, and uncompetitive inhibition, respectively. 

Except for the case of uncompetitive inhibition by high substrate concentration (see Eq. 3.44), all mechanisms of inhibition can be represented by Eq. 3.45 (see, for instance, Eqs. 3.42 and 3.43) which is a very convenient expression for determining the kinetic parameters of the corresponding rate equations. 

Fig. 3.6 Secondary plots for the determination of kinetic parameters. Cl competitive inhibition NCI non-competitive inhibition UCl uncompetitive inhibition MTl mixed-type inhibition...

A similar analysis can be made for any other type of inhibition. An interesting situation occurs in the case of uncompetitive inhibition by high substrate concentration. In this case, a steady-state analysis renders a third-order equation in ps that for certain values of the kinetic and diffusion parameters may give three positive values of Ps for one value of Po and a stability analysis should be made to assess the right value. The intermediate value is always unstable but the upper or lower... 

This kinetic model is the usual description of an uncompetitive inhibition in biochemical textbooks, again usually without specifying that it is a rare case. 

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