Enzyme kinetics competitive inhibitors

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. 

Reversible Inhibition One common type of reversible inhibition is called competitive (Fig. 6-15a). A competitive inhibitor competes with the substrate for the active site of an enzyme. While the inhibitor (I) occupies the active site it prevents binding of the substrate to the enzyme. Many competitive inhibitors are compounds that resemble the substrate and combine with the enzyme to form an El complex, but without leading to catalysis. Even fleeting combinations of this type will reduce the efficiency of the enzyme. By taking into account the molecular geometry of inhibitors that resemble the substrate, we can reach conclusions about which parts of the normal substrate bind to the enzyme. Competitive inhibition can be analyzed quantitatively by steady-state kinetics. In the presence of a competitive inhibitor, the Michaelis-Menten equation (Eqn 6-9) becomes... 

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. 

The inactivation is normally a first-order process, provided that the inhibitor is in large excess over the enzyme and is not depleted by spontaneous or enzyme-catalyzed side-reactions. The observed rate-constant for loss of activity in the presence of inhibitor at concentration [I] follows Michaelis-Menten kinetics and is given by kj(obs) = ki(max) [I]/(Ki + [1]), where Kj is the dissociation constant of an initially formed, non-covalent, enzyme-inhibitor complex which is converted into the covalent reaction product with the rate constant kj(max). For rapidly reacting inhibitors, it may not be possible to work at inhibitor concentrations near Kj. In this case, only the second-order rate-constant kj(max)/Kj can be obtained from the experiment. Evidence for a reaction of the inhibitor at the active site can be obtained from protection experiments with substrate [S] or a reversible, competitive inhibitor [I(rev)]. In the presence of these compounds, the inactivation rate Kj(obs) should be diminished by an increase of Kj by the factor (1 + [S]/K, ) or (1 + [I(rev)]/I (rev)). From the dependence of kj(obs) on the inhibitor concentration [I] in the presence of a protecting agent, it may sometimes be possible to determine Kj for inhibitors that react too rapidly in the accessible range of concentration. ... 

To refer to the kinetics of allosteric inhibition as competitive or noncompetitive with substrate carries misleading mechanistic implications. We refer instead to two classes of regulated enzymes K-series and V-se-ries enzymes. For K-series allosteric enzymes, the substrate saturation kinetics are competitive in the sense that is raised without an effect on V. For V-series allosteric enzymes, the allosteric inhibitor lowers... 

The kinetics of the lipoxygenase was studied in aqueous media [25]. The affinity of the enzyme for its substrate LA is very high. When LA is in excess in the medium it becomes the inhibitor of the reaction [Fig. 5(a)]. HP is also competitive inhibitor. The experimentally determined kinetic constants are ... 

An inhibitor that binds exclusively to the free enzyme (i.e., for which a = °°) is said to be competitive because the binding of the inhibitor and the substrate to the enzyme are mutually exclusive hence these inhibitors compete with the substrate for the pool of free enzyme molecules. Referring back to the relationships between the steady state kinetic constants and the steps in catalysis (Figure 2.8), one would expect inhibitors that conform to this mechanism to affect the apparent value of KM (which relates to formation of the enzyme-substrate complex) and VmJKM, but not the value of Vmax (which relates to the chemical steps subsequent to ES complex formation). The presence of a competitive inhibitor thus influences the steady state velocity equation as described by Equation (3.1) ... 

Diacylglycerol has long been known to be a weak competitive inhibitor of PLC/fc, whereas phosphorylcholine shows very little inhibition [40, 49, 116]. Recent kinetic assays of PLCB(. activity in the presence of DAG indicate that it is a competitive inhibitor with a Kl of the order of 10 mM, whereas phosphorylcholine was found to be an extremely weak (K = 30-50 mM), mixed inhibitor of PLC/J( [34]. Because diacylglycerol is a competitive inhibitor of the enzyme, the nature of the catalytic cycle dictates that it must be the last product to leave the enzyme active site. 

Aiming at a computer-based description of cellular metabolism, we briefly summarize some characteristic rate equations associated with competitive and allosteric regulation. Starting with irreversible Michaelis Menten kinetics, the most common types of feedback inhibition are depicted in Fig. 9. Allowing all possible associations between the enzyme and the inhibitor shown in Fig. 9, the total enzyme concentration Er can be expressed as... 

Another type of inhibitor combines with the enzyme at a site which is often different from the substrate-binding site and as a result will inhibit the formation of the product by the breakdown of the normal enzyme-substrate complex. Such non-competitive inhibition is not reversed by the addition of excess substrate and generally the inhibitor shows no structural similarity to the substrate. Kinetic studies reveal a reduced value for the maximum activity of the enzyme but an unaltered value for the Michaelis constant (Figure 8.7). There are many examples of non-competitive inhibitors, many of which are regarded as poisons because of the crucial role of the inhibited enzyme. Cyanide ions, for instance, inhibit any enzyme in which either an iron or copper ion is part of the active site or prosthetic group, e.g. cytochrome c oxidase (EC 1.9.3.1). 

Figure 8.7 The kinetic effects of a non-competitive inhibitor. The effect of a noncompetitive inhibitor is not reversed by high concentrations of substrate and the enzyme reaction shows a reduced value for the maximum velocity. The enzyme remaining is unaltered and gives the same value for the Michaelis constant as originally shown by the uninhibited enzyme.

Most enzyme inhibitors act reversibly—i. e., they do not cause any permanent changes in the enzyme. However, there are also irreversible inhibitors that permanently modify the target enzyme. The mechanism of action of an inhibitor—its inhibition type—can be determined by comparing the kinetics (see p.92) of the inhibited and uninhibited reactions (B). This makes it possible to distinguish competitive inhibitors (left) from noncompetitive inhibitors (right), for example. Allosteric inhibition is particularly important for metabolic regulation (see below). 

While requiring the availability of competitive inhibitors for each of the substrates, Fromm s use of competitive inhibitors to distinguish multisubstrate enzyme kinetic pathways represents the most powerful initial rate method. See Alternative Substrate Inhibition... 

Figure 1. Plot of v/V ax versus the millimolar concentration of total substrate for a model enzyme displaying Michaelis-Menten kinetics with respect to its substrate MA (i.e., metal ion M complexed to otherwise inactive ligand A). The concentrations of free A and MA were calculated assuming a stability constant of 10,000 M k The Michaelis constant for MA and the inhibition constant for free A acting as a competitive inhibitor were both assumed to be 0.5 mM. The ratio v/Vmax was calculated from the Michaelis-Menten equation, taking into account the action of a competitive inhibitor (when present). The upper curve represents the case where the substrate is both A and MA. The middle curve deals with the case where MA is the substrate and where A is not inhibitory. The bottom curve describes the case where MA is the substrate and where A is inhibitory. In this example, [Mfotai = [Afotai at each concentration of A plotted on the abscissa. Note that the bottom two curves are reminiscent of allosteric enzymes, but this false cooperativity arises from changes in the fraction of total "substrate A" that has metal ion bound. For a real example of how brain hexokinase cooperatively was debunked, consult D. L. Purich H. J. Fromm (1972) Biochem. J. 130, 63.

Enzyme kinetic studies of inhibitor are very important for considering as a therapeutic agent. It is interesting to note that isoprenoid-substituted flavonoids having non-steroidal structures are potent un-competitive inhibitors of 5a-reductase. So, it would be expected that the isoprenoid-substituted flavonoid derivative would be an interesting lead compounds for testosterone 5a-reductase 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. 

Impressed by the specificity of enzymatic action, biochemists early adopted a "lock-and-key" theory which stated that for a reaction to occur the substrate must fit into an active site precisely. Modem experiments have amply verified the idea. A vast amount of kinetic data on families of substrates and related competitive inhibitors support the idea and numerous X-ray structures of enzymes with bound inhibitors or with very slow substrates have given visual evidence of the reality of the lock-and-key concept. Directed mutation of genes of many enzymes of known three-dimensional structure has provided additional proof. 

A Lineweaver-Burk plot of enzyme kinetics in the presence and absence of a noncompetitive inhibitor is shown in Figure E5.5. Umax in the presence of a noncompetitive inhibitor is decreased, but KM is unaffected. The effect of a competitive inhibitor on the direct linear plot is shown in Figure E5.6. 

Inhibition kinetics are included in the second category of assay applications. An earlier discussion outlined the kinetic differentiation between competitive and noncompetitive inhibition. The same experimental conditions that pertain to evaluation of Ku and Vmax hold for A) estimation. A constant level of inhibitor is added to each assay, but the substrate concentration is varied as for Ku determination. In summary, a study of enzyme kinetics is approached by measuring initial reaction velocities under conditions where only one factor (substrate, enzyme, cofactor) is varied and all others are held constant. 

These were differently affected by different procedures. For example, when the enzyme was activated at 55°, the increment in ki was slight, but k2 increased 3.5-fold. Similarly, in the presence of EDTA, fc, and k2 values decreased independently, suggesting that the sites for both activities were different. Center and Behai (5) found that with the P. mirabilis enzyme, cyclic 2, 3 -UMP competitively inhibited the hydrolysis of bis(p-nitrophenyl) phosphate. The Ki was 40 pAf very close to the Km for the cyclic nucleotide (Km, 75 yM) which indicated that the two compounds could serve as alternate substrates being hydrolyzed at the same active site. In contrast, 3 -AMP was a mixed inhibitor of cyclic 2, 3 -UMP and bis(p-nitrophenyl) phosphate hydrolysis. Adenosine was a mixed inhibitor of bis(p-nitrophenyl) phosphate hydrolysis but a competitive inhibitor of 3 -AMP hydrolysis. From such kinetic studies Center and Behai (5) suggested that two separate and adjacent sites A and B are involved in the hydrolysis of the diester and phos-phomonoester substrates. Site A serves as a binding site for hydrolysis of ribonucleoside 2, 3 -cyclic phosphates and together with site B catalyzes the hydrolysis of the diester bond. During this reaction 3 -... 

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