Reactions enzyme-catalyzed

Enzyme-catalyzed reactions cycles, transients, and non-equilibrium steady states 

There is almost no biochemical reaction in a cell that is not catalyzed by an enzyme. (An enzyme is a specialized protein that increases the flux of a biochemical reaction by facilitating a mechanism [or mechanisms] for the reaction to proceed more rapidly than it would without the enzyme.) While the concept of an enzyme-mediated kinetic mechanism for a biochemical reaction was introduced in the previous chapter, this chapter explores the action of enzymes in greater detail than we have seen so far. Specifically, catalytic cycles associated with enzyme mechanisms are examined non-equilibrium steady state and transient kinetics of enzyme-mediated reactions are studied an asymptotic analysis of the fast and slow timescales of the Michaelis-Menten mechanism is presented and the concepts of cooperativity and hysteresis in enzyme kinetics are introduced. 

While the majority of these concepts are introduced and illustrated based on single-substrate single-product Michaelis-Menten-like reaction mechanisms, the final section details examples of mechanisms for multi-substrate multi-product reactions. Such mechanisms are the backbone for the simulation and analysis of biochemical systems, from small-scale systems of Chapter 5 to the large-scale simulations considered in Chapter 6. Hence we are about to embark on an entire chapter devoted to the theory of enzyme kinetics. Yet before delving into the subject, it is worthwhile to point out that the entire theory of enzymes is based on the simplification that proteins acting as enzymes may be effectively represented as existing in a finite number of discrete states (substrate-bound states and/or distinct conformational states). These states are assumed to inter-convert based on the law of mass action. The set of states for an enzyme and associated biochemical reaction is known as an enzyme mechanism. In this chapter we will explore how the kinetics of a given enzyme mechanism depend on the concentrations of reactants and enzyme states and the values of the mass action rate constants associated with the mechanism. 

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. 

In reversible inhibition, the inhibitor may bind or associate to enzyme or enzyme-substrate complex. Depending on the binding/combination inhibitor, the reversible inhibition may be of three types. 

When the inhibitor and substrate are structurally similar, the inhibitor forms a complex or associate with enzyme and decrease the rate of enzyme catalyzed reaction by reducing the proportion of enzyme-substrate complex as follows  

Equation (2) in form of Lineweaver-Burk plot can be written as 

In uncompetitive inhibition, the inhibitor combines with enzyme-substrate complex to form an uncreative complex (InES) as follows  

A typical enzyme kinetic scheme resembles that of the catalyzed reaction described above, with the symbols modified. The enzyme forms a complex with the substrate as in step i. above, which then decomposes into the products as in step ii. 

The simplified version of this rate, v = P[E]j[S]j, can be seen to serve for either enzyme or substrate concentration determinations. If the enzyme substrate complex formation rate is not rapid, as often occurs, the rate expression that applies is somewhat more complicated and is known as the Michaelis - Menten equation 

This is the maximum value of D, and leads to the value of %K exchanged as 

Obviously, the assumption of total exchange is a poor one.The exact formula for D is 

This formidable equation yields readily to the method of successive approximations (See Chapter 1), as seen from the following spreadsheet table. 

In conventional synthetic transformations, enzymes are normally used in aqueous or organic solvent at moderate temperatures to preserve the activity of enzymes. Consequently, some of these reactions require longer reaction times. In view of the newer developments wherein enzymes can be immobilized on solid supports [183], they are amenable to relatively higher temperature reaction with adequate pH control. The application of MW irradiation has been explored with two enzyme systems namely Pseudomonas lipase dispersed in Hyflo Super Cell and commercially available SP 435 Novozym (Candida antarctica lipase grafted on an acrylic resin). 

Anastas, J. C. Warner, Green Chemistry Theory and Practice, Oxford University Press, New York, 1998. 

Advances in Green Chemistry Chemical Synthesis Using Microwave Irradiation, AstraZeneca Research Foundation India, Bangalore, India, (free copy available from azrefi astrazeneca.com) 2002. 

4 (a) P. Wasserscheid, T. Welton (Eds.), Ionic Liquid in Synthesis, Wiley-VCH Verlag, Weinheim, 2003 (b) J. D. Holbrey, 

Turner, R. D. Rogers, Ionic Liquids as Green Solvents, ACS Symposium Series 856, American Chemical Society, Washington, DC, 2003, pp. 2-12 

Nature has always been a source of inspiration for scientists. While most of research developments are centered on simulating nature, it would be worthwhile to challenge nature s ingenuity to mimic the synthetic reactions. To this end, catalytic C—H bond amination is an excellent platform for the development of a non-natural enzymatic reaction. Whereas enzymes are capable of inserting oxygen atoms into even inactivated C—H bonds, the sites into 

In 2013, Arnold and co-workers revisited the possibility of engineering an enzyme eatalyst for this useful transformation. Combining ortho-substituted benzenesulfonyl azides 142 with engineered P450 enzymes which include a reduced Fe center resulted in an efficient intramolecular benzylic C—H bond amination reaction. The desired aminated products 143 were produced in 73% ee with a total turnover number (TTN) of 383. In addition, expression of the eatalyst in E. coli makes the reaction proceed smoothly on a 50 mg scale with high ee value (Seheme 1.54). 

Biological processes at the level of the single cell or at the level of the more complex, multicellular forms of life constitute some of the most intricate and challenging problems of chemistry and chemical kinetics. From the enormous amount of work that has been done on elucidating the elementary kinetic pathways in biological processes, some few generalizations can be made. One of these is that most discrete structural steps in biochemical processes are catalyzed by large molecules called enzymes. 

000 to 80,000, they may be lower or very much higher. The specificity of enzymes is usually indicated by the very particular reaction they catalyze. Thus the isolatable material fumarase catalyzes the eciuilibrium between malic and fumaric acid  

Urease catalyzes the hydrolysis of urea to ammonia, while catalase is capable of rapidly decomposing II2O2 to H2O + 02. In a number of cases, enzyme catalysis requires the participation of a smaller molecule usually referred to as a coenzyme. Many of the vitamins and simple nucleotides such as adenosine triphosphate (ATP) have been shown to act as coenzymes. 

The kinetic role of enzymes was first given a general formulation by Michaelis and Menten/ They proposed that the molecule undergoing reaction (substrate S) is adsorbed reversibly on a specific site E of the enzyme to form a stable enzyme-substrate S E complex whose subsequent decomposition into products is rate-controlling. This scheme, which resembles that suggested by Langmuir for surface catalysis, can be represented by 

If the total initial concentration of enzyme is (Eo) = (E) + (S E) and we assume that (S-E) reaches a stationary state, the latter is given by 

The secondary subsystem might be treated differently from the primary one both in terms of the potential energy surface and the dynamics. For example, with regard to the former aspect, the primary subsystem might be treated by a quantum mechanical electronic structure calculation, and the secondary subsystem might be treated by molecular mechanics [68] or even approximated by an electrostatic field or a continuum model, as in implicit solvation modeling [69]. The par- 

We will distinguish six levels of theory for treating environmental aspects of condensed-phase reactions. These levels may be arranged as follows in a hierarchy of increasingly more complete coupling of primary and secondary subsystems  

In practical terms, though, it is easier to consider these methods in terms of two parallel hierarchies. The first contains SES, ESP, and NES the second contains PMF-VTST, EA-VTST-SSZ, and EA-VTST-ESZ. There is, however, a complication. While the first five rungs on the ladder correspond to successively more complete theories, the final rung (ESZ) may be considered an alternative to the fifth rung (SSZ), which may be better or may be worse, depending on the physical nature of the dynamics. 

In the rest of this section we briefly review the six rungs of the condensed-phase VTST ladder. In Section 27.6 we provide two examples that illustrate the application of the general theory. 

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The biological dehydrogenation of succinic acid described in Section 5 8 is 100% stereoselective Only fumaric acid which has a trans double bond is formed High levels of stereoselectivity are characteristic of enzyme catalyzed reactions... 

Optically inactive starting materials can give optically active products only if they are treated with an optically active reagent or if the reaction is catalyzed by an optically active substance The best examples are found m biochemical processes Most bio chemical reactions are catalyzed by enzymes Enzymes are chiral and enantiomerically homogeneous they provide an asymmetric environment m which chemical reaction can take place Ordinarily enzyme catalyzed reactions occur with such a high level of stereo selectivity that one enantiomer of a substance is formed exclusively even when the sub strate is achiral The enzyme fumarase for example catalyzes hydration of the double bond of fumaric acid to malic acid m apples and other fruits Only the S enantiomer of malic acid is formed m this reaction... 

Phenolic compounds are commonplace natural products Figure 24 2 presents a sampling of some naturally occurring phenols Phenolic natural products can arise by a number of different biosynthetic pathways In animals aromatic rings are hydroxylated by way of arene oxide intermediates formed by the enzyme catalyzed reaction between an aromatic ring and molecular oxygen... 

We 11 see numerous examples of both reaction types m the following sections Keep m mind that m vivo reactions (reactions m living systems) are enzyme catalyzed and occur at far greater rates than those for the same transformations carried out m vitro ( m glass ) m the absence of enzymes In spite of the rapidity with which enzyme catalyzed reactions take place the nature of these transformations is essentially the same as the fundamental processes of organic chemistry described throughout this text... 

Before leaving this biosynthetic scheme notice that PGE2 has four chirality cen ters Even though arachidomc acid is achiral only the stereoisomer shown m the equa tion IS formed Moreover it is formed as a single enantiomer The stereochemistry is controlled by the interaction of the substrate with the enzymes that act on it Enzymes offer a chiral environment m which biochemical transformations occur and enzyme catalyzed reactions almost always lead to a single stereoisomer Many more examples will be seen m this chapter... 

Isopentenyl pyrophosphate undergoes an enzyme catalyzed reaction that converts It m an equilibrium process to 3 methyl 2 butenyl pyrophosphate (dimethylallyl pyrophosphate)... 

The enzyme catalyzed reactions that lead to geraniol and farnesol (as their pyrophosphate esters) are mechanistically related to the acid catalyzed dimerization of alkenes discussed m Section 6 21 The reaction of an allylic pyrophosphate or a carbo cation with a source of rr electrons is a recurring theme m terpene biosynthesis and is invoked to explain the origin of more complicated structural types Consider for exam pie the formation of cyclic monoterpenes Neryl pyrophosphate formed by an enzyme catalyzed isomerization of the E double bond m geranyl pyrophosphate has the proper geometry to form a six membered ring via intramolecular attack of the double bond on the allylic pyrophosphate unit... 

The imidazole nng of the histidine side chain acts as a proton acceptor in certain enzyme catalyzed reactions Which is the more stable protonated form of the histidine residue A or Why" ... 

Enzyme-Catalyzed Reactions Enzymes are highly specific catalysts for biochemical reactions, with each enzyme showing a selectivity for a single reactant, or substrate. For example, acetylcholinesterase is an enzyme that catalyzes the decomposition of the neurotransmitter acetylcholine to choline and acetic acid. Many enzyme-substrate reactions follow a simple mechanism consisting of the initial formation of an enzyme-substrate complex, ES, which subsequently decomposes to form product, releasing the enzyme to react again. 

Determining and for Enzyme-Catalyzed Reactions The value of Vmax and... 

Perez-Bendito, D. Silva, M. Kinetic Methods in Analytical Chemistry. Ellis Horwood Chichester, England, 1988. Additional information on the kinetics of enzyme catalyzed reactions maybe found in the following texts. 

Pisakiewicz, D. Kinetics of Chemical and Enzyme-Catalyzed Reactions. Oxford University Press New York, 1977. 

Immobilization. The fixing property of PEIs has previously been discussed. Another appHcation of this property is enzyme immobilization (419). Enzymes can be bound by reactive compounds, eg, isothiocyanate (420) to the PEI skeleton, or immobilized on soHd supports, eg, cotton by adhesion with the aid of PEIs. In every case, fixing considerably simplifies the performance of enzyme-catalyzed reactions, thus faciHtating preparative work. This technique has been appHed to glutaraldehyde-sensitive enzymes (421), a-glucose transferase (422), and pectin lyase, pectin esterase, and endopolygalacturonase (423). 

Measurement Considerations A prototype enzyme-catalyzed reaction where one substrate (S) produces only one product (P) may be described by... 

Assays using equiUbrium (end point) methods are easy to do but the time requited to reach the end point must be considered. Substrate(s) to be measured reacts with co-enzyme or co-reactant (C) to produce products (P and Q) in an enzyme-catalyzed reaction. The greater the consumption of S, the more accurate the results. The consumption of S depends on the initial concentration of C relative to S and the equiUbrium constant of the reaction. A change in absorbance is usually monitored. Changes in pH and temperature may alter the equiUbrium constant but no serious errors are introduced unless the equihbrium constant is small. In order to complete an assay in a reasonable time, for example several minutes, the amount and therefore the cost of the enzyme and co-factor maybe relatively high. Sophisticated equipment is not requited, however. 

Enzymes are basically specialty proteins (qv) and consist of amino acids, the exact sequence of which determines the enzyme stmcture and function. Although enzyme molecules are typically very large, most of the chemistry involving the enzyme takes place in a relatively small region known as the active site. In an enzyme-catalyzed reaction, binding occurs at the active site to one of the molecules involved. This molecule is called the substrate. Enzymes are... 

The pH dependency of enzyme-catalyzed reactions also exhibits an optimum. The pH optima for enzyme-catalyzed reactions cover a wide range of pH values. Eor instance, the subtihsins have a broad pH optima in the alkaline range. Other enzymes have a narrow pH optimum. The nature of the pH profile often gives clues to the elucidation of the reaction mechanism of the enzyme-catalyzed reaction. The temperature at which an experiment is performed may affect the pH profile and vice versa. 

This chapter presents the implementaiton and applicable of a QM-MM method for studying enzyme-catalyzed reactions. The application of QM-MM methods to study solution-phase reactions has been reviewed elsewhere [44]. Similiarly, empirical valence bond methods, which have been successfully applied to studying enzymatic reactions by Warshel and coworkers [19,45], are not covered in this chapter. 

Figure 11.1 A plot of the reaction rate as a function of the substrate concentration for an enzyme catalyzed reaction. Vmax is the maximal velocity. The Michaelis constant. Km, is the substrate concentration at half Vmax- The rate v is related to the substrate concentration, [S], by the Michaelis-Menten equation ...

Scheme 2.11. Enantioselective lyansfomiatlons Based on Enzyme-Catalyzed Reactions Which Differentiate Enantiotopic Substituents...

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. 

Inhibition The decrease of the rate of an enzyme-catalyzed reaction by a chemical compound including substrate analogues. Such inhibition may be competitive with the substrate (binding at die active site of die enzyme) or non-competitive (binding at an allosteric site). 

Lineweaver-Burk plot Method of analyzing kinetic data (growth rates of enzyme catalyzed reactions) in linear form using a double reciprocal plot of rate versus substrate concentration. 

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