Kinetics, enzyme catalyzed

Enzyme kinetics is studied for two reasons (1) it is a practical concern to determine the activity of the enzyme under different conditions (2) frequently the analysis of enzyme kinetics gives information about the mechanism of enzyme action. Chapter 7, Enzyme Kinetics, begins with an introductory section on the discovery of enzymes, basic enzyme terminology and a description of the six main classes of enzymes and the reactions they catalyze. The remainder of the chapter deals with basic aspects of chemical kinetics, enzyme-catalyzed reactions and various factors that affect the kinetics. 

The effect of temperature satisfies the Arrhenius relationship where the applicable range is relatively small because of low and high temperature effects. The effect of extreme pH values is related to the nature of enzymatic proteins as polyvalent acids and bases, with acid and basic groups (hydrophilic) concentrated on the outside of the protein. Finally, mechanical forces such as surface tension and shear can affect enzyme activity by disturbing the shape of the enzyme molecules. Since the shape of the active site of the enzyme is constructed to correspond to the shape of the substrate, small alteration in the structure can severely affect enzyme activity. Reactor s stirrer speed, flowrate, and foaming must be controlled to maintain the productivity of the enzyme. Consequently, during experimental investigations of the kinetics enzyme catalyzed reactions, temperature, shear, and pH are carefully controlled the last by use of buffered solutions. 

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. 

Enzyme-Catalyzed Asymmetric Synthesis. The extent of kinetic resolution of racemates is determined by differences in the reaction rates for the two enantiomers. At the end of the reaction the faster reacting enantiomer is transformed, leaving the slower reacting enantiomer unchanged. It is apparent that the maximum product yield of any kinetic resolution caimot exceed 50%. 

The variety of enzyme-catalyzed kinetic resolutions of enantiomers reported ia recent years is enormous. Similar to asymmetric synthesis, enantioselective resolutions are carried out ia either hydrolytic or esterification—transesterification modes. Both modes have advantages and disadvantages. Hydrolytic resolutions that are carried out ia a predominantiy aqueous medium are usually faster and, as a consequence, require smaller quantities of enzymes. On the other hand, esterifications ia organic solvents are experimentally simpler procedures, aHowiag easy product isolation and reuse of the enzyme without immobilization. 

Various racemic secondary alcohols with different substituents, eg, a-hydroxyester (60), are resolved by PFL neatly quantitatively (75). The effect of adjacent unsatuiation on enzyme-catalyzed kinetic resolutions was thoroughly studied for a series of aHyUc (61), propargyUc (62), and phenyl-substituted 2-aIkanols (76,77). Excellent selectivity was observed for (E)-aHyhc alcohols whereas (Z)-isomers showed poor selectivity (76). 

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. 

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. 

The simplest kinetic scheme that can account for enzyme-catalyzed reactions is Scheme XX, where E represents the enzyme, S is the substrate, P is a product, and ES is an enzyme-substrate complex. 

Kinetics of Enzyme-Catalyzed Reactions Involving Two or More Substrates... 

Thus far, we have considered enzyme-catalyzed reactions involving one or two substrates. How are the kinetics described in those cases in which more than two substrates participate in the reaction An example might be the glycolytic enzyme glyceraldehyde-3-phosphate dehydrogenase (Chapter 19) ... 

Gray, C. J., 1971. Enzyme-Catalyzed Reactions. New York Van Nostrand Reinhold. A monograph on qnantitative aspects of enzyme kinetics. 

If the enzyme-catalyzed reaction is to be faster than the uncatalyzed case, the acceptor group on the enzyme must be a better attacking group than Y and a better leaving group than X. Note that most enzymes that carry out covalent catalysis have ping-pong kinetic mechanisms. 

Because this enzyme catalyzes the committed step in fatty acid biosynthesis, it is carefully regulated. Palmitoyl-CoA, the final product of fatty acid biosynthesis, shifts the equilibrium toward the inactive protomers, whereas citrate, an important allosteric activator of this enzyme, shifts the equilibrium toward the active polymeric form of the enzyme. Acetyl-CoA carboxylase shows the kinetic behavior of a Monod-Wyman-Changeux V-system allosteric enzyme (Chapter 15). 

Runge-Kutta. Consider the disappearance of substrate in an enzyme-catalyzed reaction that follows Michaelis-Menten kinetics ... 

The kinetics of enzyme reactions were first studied by the German chemists Leonor Michaelis and Maud Menten in the early part of the twentieth century. They found that, when the concentration of substrate is low, the rate of an enzyme-catalyzed reaction increases with the concentration of the substrate, as shown in the plot in Fig. 13.41. However, when the concentration of substrate is high, the reaction rate depends only on the concentration of the enzyme. In the Michaelis-Menten mechanism of enzyme reaction, the enzyme, E, and substrate, S, reach a rapid preequilibrium with the bound enzyme-substrate complex, ES ... 

Application of an aldolase to the synthesis of the tricyclic microbial elicitor (-)-syringolide (Figure 10.34) is another excellent example that enzyme-catalyzed aldolizations can be used to generate sufficient quantities of enantiopure material in multistep syntheses of complex natural and unnatural products [159]. Remarkably, the aldolase reaction established absolute and relative configuration of the only chiral centers that needed to be externally induced in the adduct (95) from achiral precursor (94) during the subsequent cyclization events, all others seemed to follow by kinetic preference. 

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. ... 

Complex inactivation kinetics caused by enzyme-catalyzed decomposition of epoxide kinetic constants calculated from initial rates of inactivation. Approximate value calculated from half-life in the presence of 50 mAf inhibitor. 

The study of enzyme kinetics—the factors that affect the rates of enzyme-catalyzed reactions—reveals the individual steps by which enzymes transform substrates into products. 

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