Enzyme-inhibitor complex, kinetics

The often fast binding step of the inhibitor I to the enzyme E, forming the enzyme inhibitor complex E-I, is followed by a rate-determining inactivation step to form a covalent bond. The evaluation of affinity labels is based on the fulfillment of the following criteria (/) irreversible, active site-directed inactivation of the enzyme upon the formation of a stable covalent linkage with the activated form of the inhibitor, (2) time- and concentration-dependent inactivation showing saturation kinetics, and (3) a binding stoichiometry of 1 1 of inhibitor to the enzyme s active site (34). 

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. 

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. ... 

As an illustration of first-order kinetics, let us consider the simple dissociation of a binary enzyme-inhibitor complex ( 7) to the free enzyme (E) and the free inhibitor (/),... 

Inhibition Effects in Enzyme Catalyzed Reactions. Enzyme catalyzed reactions are often retarded or inhibited by the presence of species that do not participate in the reaction in question as well as by the products of the reaction. In some cases the reactants themselves can act as inhibitors. Inhibition usually results from the formation of various enzyme-inhibitor complexes, a situation that decreases the amount of enzyme available for the normal reaction sequence. The study of inhibition is important in the investigation of enzyme action. By determining what compounds behave as inhibitors and what type of kinetic patterns are followed, it may be possible to draw important conclusions about the mechanism of an enzyme s action or the nature of its active site. 

In practice, great care must be taken that the reaction is followed for at least 10 half-lives of the exponential phase to ensure that the steady state rate is reached. During that time, the substrate should not be so depleted that the rate falls off as a consequence or there is onset of product inhibition. Even so, it may still be difficult to distinguish between the kinetics of mechanism A and variants of mechanism B if the free enzyme and the two forms of enzyme inhibitor complex are in not in steady state equilibrium.28... 

Scheme 1 is the simplest one that is consistent with the inactivation of an enzyme while a drug is metabolized (25). As with conventional enzyme kinetics, there is an initial, reversible step that combines the inhibitor and free enzyme to form an enzyme-inhibitor complex. 

It should be noted that the mechanism depicted in Scheme 1 is the simplest that is consistent with mechanism-based inhibition. The mechanism for a given inhibitor and enzyme may be considerably more complex due to (a) multiple intermediates [e.g., MIC formation often involves four or more intermediates (29)], (b) detectable metabolite that may be produced from more than one intermediate, and (c) the fact that enzyme-inhibitor complex may produce a metabolite that is mechanistically unrelated to the inactivation pathway. Events such as these will necessitate alternate definitions for Z inact, Kh and r in terms of the microrate constants of the appropriate model. The hyperbolic relationship between rate of inactivation and inhibitor concentration will, however, remain, unless nonhyperbolic kinetics characterize this interaction. Silverman discussed this possibility from the perspective of an allosteric interaction between inhibitor and enzyme (5). Nonhyperbolic kinetics has been observed for the interaction of several drugs with members of the CYPs (30). 

Crystallographic studies of native cysteine proteinases and enzyme-inhibitor complexes have been used to interpret much or the kinetic data for cysteine protemsse-caUlyzed hydrolysis of amide bonds. Analysis of the crystal structures of papain [16]. caricain [38], actinidain [56], etc. shows that these structures are closely related. The active site of all these cysteine proteinases contains the Cys-25 sulfhydryl group in close proximity to the His-159 imidazole ring nitrogens, where the latter can abstract the sulfhydryl proton to facilitate attack on the substrate amide carbonyl group [17]. 

Competitive inhibitors do not change the value of Vmax> which is reached when sufficiently high concentrations of the substrate are present so as to completely displace the inhibitor. However, the affinity of the substrate for the enzyme appears to be decreased in the presence of a competitive inhibitor. This happens because the free enzyme E is not only in equilibrium with the enzyme-substrate complex E. S, but also with the enzyme-inhibitor complex E. L Competitive inhibitors increase the apparent of the substrate by a factor of (1 + The evaluation of the kinetics is again greatly facilitated by the conversion of Equation 17.15 into a linear form using Line-weaver-Burk, Eadie-Hofstee, or Hanes-Woolf plots, as shown in Fig. 17.7. 

Hydrolysis of phosphate esters is one of the fundamental biochemical reactions and a vast amount of research has been devoted to the study of phosphoryl transfer reactions [57-60], both in solution and in enzymes. Despite these efforts there are still ambiguities regarding the interpretation of experimental data (e.g., linear free energy relationships, kinetic isotope effects, crystal structures of enzyme-inhibitor complexes etc.) in terms of detailed reaction mechanisms [21,25,59,60]. Of particular interest has been to determine... 

Kinetic studies of reversible inhibition by substrate analogs give evidence of the mode of action of the inhibitor and the types of enzyme-inhibitor complex formed, and estimates of their dissociation constants. The complexes may be isolated and sometimes crystallized. Studies of the stabilities, optical properties, and structures of ternary complexes of enzymes, coenzymes, and substrate analog in particular, as stable models of the catalytically active ternary complexes or of the transition state for hydride transfer (61,79,109,115-117), can only be touched upon here there is direct evidence with several enzymes that the binding of coenzymes is firmer in such complexes than in their binary complexes (85,93,118), which supports the indirect, kinetic evidence already mentioned for a similar stabilization in active ternary complexes. 

Finasteride was subsequentiy shown to be a slow-onset inhibitor of type 1 5AR by researchers at Glaxo Research Institute. Attempts to dialyze and remove the inhibitor from a saturated enzyme—inhibitor complex again failed to display any reactivation of the enzyme even after 3 days. This led to the conclusion that the complex is either irreversible or has a half-life of greater than 10 days. The authors of the second study also demonstrated that the presence of a double bond in ring A of 5AR inhibitors is responsible for the appearance of the slow-onset kinetics. This, combined with the inability to demonstrate reversibility, was cited as further evidence for a covalent modification of the enzyme active site. 

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