Reversibility, enzyme-catalyzed reactions

Since the reaction has been reviewed recently (12) only a few additional facts will be mentioned. Many optically active cyanohydrins can be prepared (33) with e.e. s of 84 to 100% by the use of the flavopnotein D-oxynitrilase adsorbed on special (34) cellulose ion-exchange resins. Although the enzyme is stable, permitting the use of a continuously operating column, naturally only one enantiomer, usually the R isomer, is produced in excess. This (reversible) enzyme-catalyzed reaction is very rapid (34). Nonenzymic catalysts, such as the cinchona alkaloids, permit either enantiomer to be prepared in excess. 

The protocol described in Section 7.1.2 involves isotopic competition, but with the different isotopomers held in separate containers. Equations 7.10 to 7.13 apply equally well to a type of competition experiment known in biochemistry as the perturbation method for determining KIE s of reversible enzyme catalyzed reactions. The perturbation method differs from simultaneous non-competitive measurements in several important ways. One begins by mixing equilibrium concentrations of substrate and product but with one component (substrate or product) at a different isotopic composition than the other. Thus, the mixture is in chemical, but not isotopic equilibrium. At this stage no enzyme is present and the interconversion is... 

As in any other chemical reaction, there is a relationship between the rate constants for forward and reverse enzyme-catalyzed reactions and the equilibrium constant. This relationship, first derived by the British kineticist J. B. S. Haldane and proposed in his book Enzymes41 in 1930, is known as the Haldane relationship. It is obtained by setting v( = vr for the condition that product and substrate concentrations are those at equilibrium. For a single substrate-single product system it is given by Eq. 9-42. 

Duggleby, R. G. (1994). Product inhibition of reversible enzyme-catalyzed reactions. Bio-chim. Biophys. Acta. 1209,238-240. 

Szedlacsek, S. E., Ostafe, V., Duggleby, R. G., Serban, M., Vlad, M. O. (1990). Rrogress-Curve Equations for Reversible Enzyme-Catalyzed Reactions Inhibited by Tight-Binding Inhibitors. Biochem. J. 265,647-653. 

Equation 11-15 is known as the Michaelis-Menten equation. It represents the kinetics of many simple enzyme-catalyzed reactions, which involve a single substrate. The interpretation of as an equilibrium constant is not universally valid, since the assumption that the reversible reaction as a fast equilibrium process often does not apply. 

The interest and success of the enzyme-catalyzed reactions in this kind of media is due to several advantages such as (i) solubilization of hydrophobic substrates (ii) ease of recovery of some products (iii) catalysis of reactions that are unfavorable in water (e.g. reversal of hydrolysis reactions in favor of synthesis) (iv) ease of recovery of insoluble biocatalysts (v) increased biocatalyst thermostability (vi) suppression of water-induced side reactions. Furthermore, as already said, enzyme selectivity can be markedly influenced, and even reversed, by the solvent. 

Unidirectional arrows are also used to describe reactions in living cells where the products of reaction (2) are immediately consumed by a subsequent enzyme-catalyzed reaction. The rapid removal of product P or Q therefore precludes occurrence of the reverse reaction, rendering equation (2) functionally irreversible under physiologic conditions. 

Most measurements of the rates of enzyme-catalyzed reactions employ relatively short time periods, conditions that approximate initial rate conditions. Under these conditions, only traces of product accumulate, hence the rate of the reverse reaction is negligible. The initial velocity (vj) of the reaction thus is essentially that of... 

A measurement of the rate of an enzyme-catalyzed reaction generally employs initial rate conditions, for which the essential absence of product precludes the reverse reaction. 

In this chapter we have seen that enzymatic catalysis is initiated by the reversible interactions of a substrate molecule with the active site of the enzyme to form a non-covalent binary complex. The chemical transformation of the substrate to the product molecule occurs within the context of the enzyme active site subsequent to initial complex formation. We saw that the enormous rate enhancements for enzyme-catalyzed reactions are the result of specific mechanisms that enzymes use to achieve large reductions in the energy of activation associated with attainment of the reaction transition state structure. Stabilization of the reaction transition state in the context of the enzymatic reaction is the key contributor to both enzymatic rate enhancement and substrate specificity. We described several chemical strategies by which enzymes achieve this transition state stabilization. We also saw in this chapter that enzyme reactions are most commonly studied by following the kinetics of these reactions under steady state conditions. We defined three kinetic constants—kai KM, and kcJKM—that can be used to define the efficiency of enzymatic catalysis, and each reports on different portions of the enzymatic reaction pathway. Perturbations... 

Although the Michaelis-Menten equation is applicable to a wide variety of enzyme catalyzed reactions, it is not appropriate for reversible reactions and multiple-substrate reactions. However, the generalized steady-state analysis remains applicable. Consider the case of reversible decomposition of the enzyme-substrate complex into a product molecule and enzyme with mechanistic equations. 

The kinetic data below were reported for an enzyme catalyzed reaction of the type E + S ES E + P. Since the data pertain to initial reaction rates, the reverse reaction may be neglected. Use a graphical method to determine the Michaelis constant and Fmax for this system at the enzyme concentration employed. 

Assuming that the reactions are reversible and that a one-substrate enzyme-catalyzed reaction is being studied, one can derive the Michaelis-Menten rate ... 

The kinetics of the general enzyme-catalyzed reaction (equation 10.1-1) may be simple or complex, depending upon the enzyme and substrate concentrations, the presence/absence of inhibitors and/or cofactors, and upon temperature, shear, ionic strength, and pH. The simplest form of the rate law for enzyme reactions was proposed by Henri (1902), and a mechanism was proposed by Michaelis and Menten (1913), which was later extended by Briggs and Haldane (1925). The mechanism is usually referred to as the Michaelis-Menten mechanism or model. It is a two-step mechanism, the first step being a rapid, reversible formation of an enzyme-substrate complex, ES, followed by a slow, rate-determining decomposition step to form the product and reproduce the enzyme ... 

In enzyme catalyzed reactions the inhibitor may interact in various ways either reversibly or irreversibly. In irreversible inhibition, the inhibitor associates with enzyme and block the active site of the enzyme or form a unstable complex with enzyme and thus retards the rate of reaction. 

A kinetic description of large reaction networks entirely in terms of elementary reactionsteps is often not suitable in practice. Rather, enzyme-catalyzed reactions are described by simplified overall reactions, invoking several reasonable approximations. Consider an enzyme-catalyzed reaction with a single substrate The substrate S binds reversibly to the enzyme E, thereby forming an enzyme substrate complex [/iS ]. Subsequently, the product P is irreversibly dissociated from the enzyme. The resulting scheme, named after L. Michaelis and M. L. Menten [152], can be depicted as... 

It appears from a survey of the literature that the essential properties of micelles in nonpolar solvents are understood, namely their stability and variations of size, the dissociation behavior, and their solubilizing capacities. Reverse micelles can dissolve relatively large amounts of water (1-10% w/v depending on emulsion formula) as well as polar solutes and, of course, water-soluble compounds. Consequently, they can be used as media for a number of reactions, including enzyme-catalyzed reactions. Very few attempts to investigate such reverse micelles at subzero temperatures are known, in spite of the fact that hydrocarbon solutions present very low freezing points. 

This term usually applies to reversible inhibition of an enzyme-catalyzed reaction in which nonlinearity is detected (a) in a double-reciprocal plot (i.e., 1/v versus 1/ [S]) in the presence of different, constant concentrations of inhibitor or (b) in replots of slope or intercept values obtained from primary plots of 1/v versus 1/[S]). Nonline-... 

A sequential enzyme-catalyzed reaction scheme in which two substrates (A and B) react and form a single product and in which the substrates bind to the enzyme in a distinct order (i.e., only A and the product P can bind to the free enzyme). The reverse scheme of this mechanism is the ordered Uni Bi system. (See also Ordered Uni Bi Mechanism)... 

By using NMR in the presence of the enzyme, an investigator can identify bridged-to-nonbridge (and the reverse) isotope exchanges and thereby identify probable intermediates on the reaction pathway. The procedure is useful for any enzyme-catalyzed reaction in which the individual atoms of a functional group within a substrate, intermediate, or product become torsionally equivalent during the course of a reaction. 

An enzyme-catalyzed reaction scheme in which the two substrates (A and B) can bind in any order, resulting in the formation of a single product of the enzyme-catalyzed reaction (hence, this reaction is the reverse of the random Uni Bi mechanism). Usually the mechanism is distinguished as to being rapid equilibrium (/.c., the ratedetermining step is the central complex interconversion, EAB EP) or steady-state (in which the substrate addition and/or product release steps are rate-contributing). See Multisubstrate Mechanisms... 

The number of reactants partaking in an enzyme-catalyzed reaction. Because most enzyme reactions have an unequal number of substrates and products, one must specify the reactancy for a specified direction of the reaction. As an example, a multisubstrate reaction having two substrates and three products has a reactancy of two in the forward direction and three in the reverse direction. Cleland introduced the prefixes Uni , Bi , Ter , and Quad to indicate reactancies of one, two, three, and four, respectively. Thus, the example given above can be called a Bi Ter reaction. Water molecules and protons are not usually considered when specifying reactancy. 

From bisubstrate, kinetic analysis with a transferase from hen oviduct that, under the conditions of the assay, formed only GlcNAc-PP-Dol, it followed that both dolichol phosphate and UDP-GlcNAe have to he bound to the enzyme before release of the product occurs.52 However, the fact that only partially purified preparations have thus far been obtained (the preparations may also still be contaminated with substrates and product), together with experimental difficulties in handling both the substrate dolichol phosphate (which, furthermore, is not one compound, see the earlier discussion) and the unstable enzyme (enveloped in micelles of detergent), make difficult a sensible interpretation and comparison of the kinetic parameters detenuined for the different enzvme-preparations. The solubilized enzymes catalyzing reactions 1,2, and 3 have in common their alkaline pH optima and dependence on Mg2+ or Mn2+ ions. The latter fact makes (ethylenedinitrilo)tetraacetic acid (EDTA) a reversible inhibitor of enzyme activity and an important experimental tool. 

Proteins and enzymes have been successfully entrapped in surfactant-solubilized water pools in organic solvents [268-278]. Furthermore, many reversed-micelle-entrapped enzymes retained their activity and could be used for peptide synthesis [273,274]. That the water pools corresponding to very small w-values exhibited freezing points Mow — 50°C enabled both the enzyme structures and the rates of enzyme-catalyzed reactions to be investigated at low temperatures. These studies much aided the development of cryoenzymology [279, 180],... 

Michaelis and Menten proposed a simple model that accounts for most of the features of enzyme-catalyzed reactions. In this model, the enzyme reversibly combines with its substrate to form an ES complex that subsequently breaks down to product, regenerating the free enzyme. The model, involving one substrate molecule, is represented below ... 

Any substance that can diminish the velocity of an enzyme-catalyzed reaction is called an inhibitor. Reversible inhibitors bind to enzymes through noncovalent bonds. Dilution of the enzyme-inhibitor complex results in dissociation of the reversibly bound inhibitor, and recovery of enzyme activity. Irreversible inhibition occurs when an inhibited enzyme does not regain activity on dilution of the enzyme-inhibitor complex. The two most commonly encountered types of inhibition are competitive and noncompetitive. 

For some enzyme-catalyzed reactions the equilibrium lies far to one side. However, many other reactions are freely reversible. Since a catalyst promotes reactions in both directions, we must consider the action of an enzyme on the reverse reaction. Let us designate the maximum velocity in the forward direction as Vf and that in the reverse direction as Vr There will be a Michaelis constant for reaction of enzyme with product Kmp, while Kms will refer to the reaction with substrate. 

Figure Cl. 1.2 shows a typical time course resulting from a continuous assay of product formation in an enzyme-catalyzed reaction. The hyperbolic nature of the curve illustrates that the reaction rate decreases as the reaction nears completion. The reaction rate, at any given time, is the slope of the line tangent to the curve at the point corresponding to the time of interest. Reaction rates decrease as reactions progress for several reasons, including substrate depletion, reactant concentrations approaching equilibrium values (i.e., the reverse reaction becomes relevant), product inhibition, enzyme inactivation, and/or a change in reaction conditions (e.g., pH as the reaction proceeds). With respect to each of these reasons, their effects will be at a minimum in the initial phase of the reaction—i.e., under conditions corresponding to initial velocity measurements. Hence, the interpretation of initial velocity data is relatively simple and thus widely used in enzyme-related assays.

Zha, D., Wilensek, S., Hermes, M. Jaeger, K. E. Reetz, M. T. Complete reversal of enantioselectivity of an enzyme-catalyzed reaction by directed evolution. Chem. Commun. 2001,2664-2665. 

Enzyme-catalyzed reactions, which are characteristically reversible under physiologic conditions, are ideally suited to the generation of dynamic combinatorial libraries. Many enzymes with broad specificity (required for library diversity) are already commercially available, and the application of modem techniques in directed evolution may be expected to increase their number. 

Lipases are a special class of esterases that also catalyze the hydrolytic cleavage of ester bonds, but differ in their substrate spectrum. Lipases have the special capability to catalyze the hydrolysis of water-insoluble substrates such as fats and lipids. Like many other enzyme-catalyzed reactions, the ester hydrolysis is a reversible process, which allows using lipases and other esterases for the synthesis of esters. The use of lipases as catalysts in synthetic chemistry is described elsewhere in this chapter. 

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