Reaction rate, enzyme-catalyzed

Table 16-7 The surface or enzyme-catalyzed reaction rate constant, Mn/ for oxidation of Mn normalized for oxygen concentration [O2], pH and particulate concentration [X]. d[Mn ]/dt = Mn [Mn][02][0H] [X]...

Quantitative measurements of simple and enzyme-catalyzed reaction rates were under way by the 1850s. In that year Wilhelmy derived first order equations for acid-catalyzed hydrolysis of sucrose which he could follow by the inversion of rotation of plane polarized light. Berthellot (1862) derived second-order equations for the rates of ester formation and, shortly after, Harcourt observed that rates of reaction doubled for each 10 °C rise in temperature. Guldberg and Waage (1864-67) demonstrated that the equilibrium of the reaction was affected by the concentration ) of the reacting substance(s). By 1877 Arrhenius had derived the definition of the equilbrium constant for a reaction from the rate constants of the forward and backward reactions. Ostwald in 1884 showed that sucrose and ester hydrolyses were affected by H+ concentration (pH). 

A quantitative measure of an enzyme s ability to lower the activation barrier for the reaction of a substrate in solution. Catalytic proficiency (a unitless parameter) equals the enzyme-catalyzed reaction rate constant (expressed as Acat/Xm) divided by the rate constant (Anon) for the noncatalyzed reference reaction. 

Enzyme-based processes for the resolution of chiral amines have been widely reported [2, 3] and are used in the manufacture of pharmaceuticals, for example, BASF s process for chiral benzylic amine intermediates. Scheme 13.1 [4]. The methods used are enantioselective hydrolysis of an amide and enantioselective synthesis of an amide, both of which are kinetic resolutions. For high optical purity products the processes depend upon a large difference in the catalyzed reaction rates of each enantiomer. 

At any given instant in an enzyme-catalyzed reaction, the enzyme exists in two forms, the free or uncombined form E and the combined form ES. At low [S], most of the enzyme is in the uncombined form E. Here, the rate is proportional to [S] because the equilibrium of Equation 6-7 is pushed toward formation of more ES as [S] increases. The maximum initial rate of the catalyzed reaction (Prnax) is observed when virtually all the enzyme is present as the ES complex and [E] is vanishingly small. Under these conditions, the enzyme is saturated with its substrate, so that further increases in [S] have no effect on rate. This condition exists when [S] is sufficiently high that essentially all the free enzyme has been converted to the ES form. After the ES complex breaks down to yield the product P, the enzyme is free to catalyze reaction of another molecule of substrate. The saturation effect is a distinguishing characteristic of enzymatic catalysts and is responsible for the plateau observed in Figure 6-11. The pattern seen in Figure 6-11 is sometimes referred to as saturation kinetics. 

Acid-Catalyzed Reaction. A number of enzyme-catalyzed reactions, including the sucrose inversion to be studied in this experiment, can also be carried out under non-physiological conditions by using H ions as a less efficient catalyst. In the present case, the acid-catalyzed reaction rate has the form... 

Factors that affect the rate of enzyme-catalyzed reactions include enzyme and substrate concentration, pH, temperature, and the presence of inhibitors, activators, co-enzymes, and prosthetic groups. 

The first applications of enzymes in bioanalytical chemistry can be dated back to the middle of nineteenth century, and they were also used for design of first biosensors. These enzymes, which have proved particularly useful in development of biosensors, are able to stabilize the transition state between substrate and its products at the active sites. Enzymes are classified regarding their functions, and the classes of enzymes are relevant to different types of biosensors. The increase in reaction rate that occurs in enzyme-catalyzed reactions may range from several up to e.g. 13 orders of magnitude observed for hydrolysis of urea in the presence of urease. Kinetic properties of enzymes are most commonly expressed by Michaelis constant Ku that corresponds to concentration of substrate required to achieve half of the maximum rate of enzyme-catalyzed reaction. When enzyme is saturated, the reaction rate depends only on the turnover number, i.e., number of substrate molecules reacting per second. 

Typical antibody-catalyzed reaction rates are several hundredfold to 100,000-fold faster than the uncatalyzed reaction of the substrate. Several fundamental postulates have been proposed to explain the rate enhancements that nevertheless fall short of the enormous rate accelerations of enzymes. Is activity truly due solely to transition state stabilization by antibody-binding interactions Can additional binding interactions be built into the combining site or into the substrate molecule itself to increase the overall rate of the reaction Can new screening methods and immunological methods be developed to uncover novel catalysts with diverse activities Most important, can novel esterolytic catalysts be developed based on currently available catalytic antibody technology to efficiently hydrolyze and detoxicate cocaine ... 

Effect of pH on the rate of an enzyme-catalyzed reaction. The enzyme functions most efficiently at pH 7. The rate of the reaction falls rapidly as the solution is made either more acidic or more basic. 

Fii. ee.e. Dependence of enzyme-catalyzed reaction rate on substrate concentration. At high concentrations, the enzyme becomes saturated with substrate and the reaction rate becomes maximum and constant since [ES] becomes constant (Equation 22.13). 

The dependence of an enzyme-catalyzed reaction rate on substrate concentration is illustrated in Figure 22.2. An enzyme is characterized by the number of molecules of substrate it can complex per unit time and convert to product, that is, the turnover number. As long as the substrate concentration is small enough with respect to the enzyme concentration that the turnover number is not exceeded, the reaction rate is directly proportional to substrate concentration, that is, it is first order with respect to substrate (Equation 22.13). If the enzyme concentration is held constant, then the overall reaction is first order and directly proportional to substrate concentration (k[E] = constant in Equation 22.13). This serves as the basis for substrate determination. However, if the amount of substrate exceeds the turnover number for the amount of enzyme present, the enzyme becomes saturated with respect to the number of molecules it can complex (saturated with respect to substrate), and the reaction rate reaches a maximum value. At this point, the reaction becomes independent of further substrate concentration increases, that is, becomes pseudp zeroj5r if the enzyme concentration is constant (Figure 22.2) in Equation 22.13, [ES] becomes constant and R = constant. 

This derivation is commonly used to describe the kinetics of product formation in enzyme-catalyzed reactions (substitute enzyme for carrier protein and product formation for the conformational change of the carrier protein). Under the assumptions of this simple model, carrier conformational change is the rate-limiting step, so it is reasonable to assume further that k2 is much less than k. n this case, the constant is approximately equal X.o Ki=k i/kx, the dissociation constant for the binding of solute to carrier. For this reason, it is common to refer to as the affinity of the solute for the carrier (note the analogy to Equation 3-53). F ax is the maximum flux due to this carrier-mediated transport, which occurs when all of the carrier-binding sites are occupied (Figure 5.11). 

Such an enzyme under normal steady-state conditions tends to have the concentrations of its substrates and products at or near to their equilibrium values. Any enzyme enhances equally both the forward and the reverse rates of its catalyzed reaction. Those enzymes that catalyze seemingly irreversible reactions usually involve hydrolysis and since the water concentration in cells and tissues is thousands of times greater than metabolites, the equilibrium position of these reactions is poised in favor of the forward or hydrolytic process. In reactions not involving water, the net direction of the reactions depends on the relative concentration of the substrates and products. If the activity of the enzyme is sufficiently high, relative to others in a metabolic pathway, altering the activity of the enzyme simply makes both the forward and reverse reactions go faster, thus maintaining a pseudo-equilibrium. 

The use of enzymes to lyse cells, hydrolyze fat emulsions, solubilize proteinaceous colloids, liquify or saccharify starch gels and granules, and degrade various components of celluloslc substrates indicates that many substrates are present in a particulate form. Kinetic forms for such enzyme catalyzed reaction rates are here noted, and will be revisited in the subsequent discussion of immobilized enzyme kinetics. 

The first assumption is arguable as in fact more than three ionic species can exist in the active center (Dixon and Webb 1979) however, for simplicity, only three are considered which is not far from reality (the active center is usually conformed by a very low number of amino acid residues) and allows a simpler analysis of the phenomenon. The second assumption, as seen below, is supported by experimental evidence since it is consistent with the shape of the pH profiles of enzyme-catalyzed reaction rates. The following scheme represents that hypothesis ... 

Figure 10.7 The effect of temperature on enzyme-catalyzed reaction rates.

Figure 1 illustrates the dependence of an enzyme-catalyzed reaction rate on the substrate concentration. An enzyme is characterized by the number of molecules of substrate that it can convert to the product that is, turnover number. As long as the substrate concentration is small enough with respect to the enzyme concentration that the turnover number is not exceeded, the reaction rate is directly proportional to the substrate concentration that is, it is first order with respect to substrate. If the enzyme concentration is held constant, then the overall... 

Figure 1 Dependence of enzyme-catalyzed reaction rate on substrate concentration.

Presents the development of rate eqrrations for solid catalyzed reactions and enzyme catalyzed biochemical reactions... 

FIGURE 16.2 Michaelis-Menten kinetics of an enzyme-catalyzed reaction rate dependence on substrate concentration. The example is plot for Vniax=4 mol 1 s and K = 1 mol 1 . ... 

Craig D B, Arriaga E A, Wong J C Y, Lu H and Dovichi N J 1996 Studies on single alkaline phosphatase molecules reaction rate and activation energy of a reaction catalyzed by a single molecule and the effect of thermal denaturation—the death of an enzyme J. Am. Chem. See. 118 5245-53... 

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... 

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