Turnover number enzyme reactions

Table 4.10 Maximum turnover numbers, and reaction time for enzymes...

Km for an enzymatic reaction are of significant interest in the study of cellular chemistry. From equation 13.19 we see that Vmax provides a means for determining the rate constant 2- For enzymes that follow the mechanism shown in reaction 13.15, 2 is equivalent to the enzyme s turnover number, kcat- The turnover number is the maximum number of substrate molecules converted to product by a single active site on the enzyme, per unit time. Thus, the turnover number provides a direct indication of the catalytic efficiency of an enzyme s active site. The Michaelis constant, Km, is significant because it provides an estimate of the substrate s intracellular concentration. 

Enzyme and substrate first reversibly combine to give an enzyme-substrate (ES) complex. Chemical processes then occur in a second step with a rate constant called kcat, or the turnover number, which is the maximum number of substrate molecules converted to product per active site of the enzyme per unit time. The kcat is, therefore, a rate constant that refers to the properties and reactions of the ES complex. For simple reactions kcat is the rate constant for the chemical conversion of the ES complex to free enzyme and products. 

The turnover number of an enzyme, is a measure of its maximal catalytic activity, is defined as the number of substrate molecules converted into product per enzyme molecule per unit time when the enzyme is saturated with substrate. The turnover number is also referred to as the molecular activity of the enzyme. For the simple Michaelis-Menten reaction (14.9) under conditions of initial velocity measurements, Provided the concentration of... 

The turnover number of methylmalonyl-CoA epimerase is 100 sec and thus the enzyme enhances the reaction rate by a factor of 10. ... 

They have an exceedingly high specific activity per active site the turnover number y is as high as 10 to 10 s in certain enzyme reactions, while at ordinary electrocatalysts having a number of reaction sites on the order of 10 cm , yhas a value of about 1 s at a current density of lOmA/cm. Thus, the specific catalytic activity of tfie active sites of enzymes is many orders of magnitude fiigher tfian tfiat of all other known catalysts for electrochemical (and also chemical) processes. 

Different enzymes exhibit different specific activities and turnover numbers. The specific activity is a measure of enzyme purity and is defined as the number of enzyme units per milligram of protein. During the purification of an enzyme, the specific activity increases, and it reaches its maximum when the enzyme is in the pure state. The turnover number of an enzyme is the maximal number of moles of substrate hydrolyzed per mole of enzyme per unit time [63], For example, carbonic anhydrase, found in red blood cells, is a very active enzyme with a turnover number of 36 X 106/min per enzyme molecule. It catalyzes a very important reaction of reversible hydration of dissolved carbon dioxide in blood to form carbonic acid [57, p. 220],... 

The turnover number of an enzyme is defined as the maximum number of moles of substrate reacted per mole of enzyme (or molecules per molecule) per minute under optimum conditions (i.e., saturating substrate concentration, optimum pH, etc). If 2 mg/cm3 of a pure enzyme (50,000 molecular weight, Michaelis constant Km = 0.03 mole/m3) catalyzes a reaction at a rate of 2.5 jumoles/nUksec when the substrate concentration is 5 x 10 3 moles/m3, determine the turnover number corresponding to this definition and the actual number of moles of substrate reacting per minute per mole of enzyme. 

The question arises as to whether comparisons with protein enzymes are justified. In other words, what can ribozymes really do An important parameter for measuring the efficiency of enzymes is the value of kc-JK. This quotient is derived from the values of two important kinetic parameters kc-Al is a rate constant, also called turnover number, and measures the number of substrate molecules which are converted by one enzyme molecule per unit time (at substrate saturation of the enzyme). Km is the Michaelis-Menten constant it corresponds to the substrate concentration at which the rate of reaction is half its maximum. 

Rhin(bpy)3]3+ and its derivatives are able to reduce selectively NAD+ to 1,4-NADH in aqueous buffer.48-50 It is likely that a rhodium-hydride intermediate, e.g., [Rhni(bpy)2(H20)(H)]2+, acts as a hydride transfer agent in this catalytic process. This system has been coupled internally to the enzymatic reduction of carbonyl compounds using an alcohol dehydrogenase (HLADH) as an NADH-dependent enzyme (Scheme 4). The [Rhin(bpy)3]3+ derivative containing 2,2 -bipyridine-5-sulfonic acid as ligand gave the best results in terms of turnover number (46 turnovers for the metal catalyst, 101 for the cofactor), but was handicapped by slow reaction kinetics, with a maximum of five turnovers per day.50... 

In addition to KM and vmax, the turnover number (molar activity) and the specific activity are two important parameters in enzyme catalyzed reactions. The turnover number indicates the number of substrate molecules converted per unit time by a single enzyme molecule. The specific activity is given in units and one international unit (i.u.) is the amount of enzyme that consumes or forms 1 pmol of substrate or 1 pmol of product per minute under standard conditions. 

Several approaches have been undertaken to construct redox active polymermodified electrodes containing such rhodium complexes as mediators. Beley [70] and Cosnier [71] used the electropolymerization of pyrrole-linked rhodium complexes for their fixation at the electrode surface. An effective system for the formation of 1,4-NADH from NAD+ applied a poly-Rh(terpy-py)2 + (terpy = terpyridine py = pyrrole) modified reticulated vitreous carbon electrode [70]. In the presence of liver alcohol dehydrogenase as production enzyme, cyclohexanone was transformed to cyclohexanol with a turnover number of 113 in 31 h. However, the current efficiency was rather small. The films which are obtained by electropolymerization of the pyrrole-linked rhodium complexes do not swell. Therefore, the reaction between the substrate, for example NAD+, and the reduced redox catalyst mostly takes place at the film/solution interface. To obtain a water-swellable film, which allows the easy penetration of the substrate into the film and thus renders the reaction layer larger, we used a different approach. Water-soluble copolymers of substituted vinylbipyridine rhodium complexes with N-vinylpyrrolidone, like 11 and 12, were synthesized chemically and then fixed to the surface of a graphite electrode by /-irradiation. The polymer films obtained swell very well in aqueous... 

Different from conventional chemical kinetics, the rates in biochemical reactions networks are usually saturable hyperbolic functions. For an increasing substrate concentration, the rate increases only up to a maximal rate Vm, determined by the turnover number fccat = k2 and the total amount of enzyme Ej. The turnover number ca( measures the number of catalytic events per seconds per enzyme, which can be more than 1000 substrate molecules per second for a large number of enzymes. The constant Km is a measure of the affinity of the enzyme for the substrate, and corresponds to the concentration of S at which the reaction rate equals half the maximal rate. For S most active sites are not occupied. For S >> Km, there is an excess of substrate, that is, the active sites of the enzymes are saturated with substrate. The ratio kc.AJ Km is a measure for the efficiency of an enzyme. In the extreme case, almost every collision between substrate and enzyme leads to product formation (low Km, high fccat). In this case the enzyme is limited by diffusion only, with an upper limit of cat /Km 108 — 109M. v 1. The ratio kc.MJKm can be used to test the rapid... 

There is huge potential in the combination of biocatalysis and electrochemistry through reaction engineering as the linker. An example is a continuous electrochemical enzyme membrane reactor that showed a total turnover number of 260 000 for the enantioselective peroxidase catalyzed oxidation of a thioether into its sulfone by in situ cathodic generated hydrogen peroxide - much higher than achieved by conventional methods [52],... 

Perhaps the only distinct advantage of enzymic catalysts is their (occasionally) very high turnover rate in situ. Thus, the molar activity (formerly called the turnover number) of some enzymes approaches 36,000,000/min/molecule (7). This latter number pertains to carbonic anhydrase C, the enzyme that converts C02 to HC03 . However, chemists do not need enzymes to convert COz to HCO3-, as long as we are not considering in vivo reactions. Since many enzymes have molar activities as low as 1150/min/molecule, we need not consider molar activities of 100 to 500 (for nonenzymic catalysts) as a severe handicap. It is evident that enzymes and nonenzymic chiral catalysts, rather than being competitors, complement one another. 

Carbonic anhydrase is a metalloprotein with a co-ordinate bonded zinc atom immobilized at three histidine residues (His 94, His 96 and Hisl 19) close to the active site of the enzyme. The catalytic activity of the different isoenzymes varies but cytosolic CA II is notable for its very high turnover number (Kcat) of approximately 1.5 million reactions per second. 

In the equations describing enzyme kinetics in this chapter, the notation varies a bit from other chapters. Thus v is accepted in the biochemical literature as the symbol for reaction rate while Vmax is used for the maximum rate. Furthermore, for simplification frequently Vmax is truncated to V in complex formulas (see Equations 11.28 and 11.29). Although at first glance inconsistent, these symbols are familiar to students of biochemistry and related areas. The square brackets indicate concentrations. Vmax expresses the upper limit of the rate of the enzyme reaction. It is the product of the rate constant k3, also called the turnover number, and the total enzyme concentration, [E]o. The case u, = Vmax corresponds to complete saturation of all active sites. The other kinetic limit, = (Vmax/KM)[S], corresponds to Km >> [S], in other words Vmax/KM is the first order rate constant found when the substrate concentration approaches zero ... 

In the absence of an enzyme, the reaction rate v is proportional to the concentration of substance A (top). The constant k is the rate constant of the uncatalyzed reaction. Like all catalysts, the enzyme E (total concentration [E]t) creates a new reaction pathway, initially, A is bound to E (partial reaction 1, left), if this reaction is in chemical equilibrium, then with the help of the law of mass action—and taking into account the fact that [E]t = [E] + [EA]—one can express the concentration [EA] of the enzyme-substrate complex as a function of [A] (left). The Michaelis constant lknow that kcat > k—in other words, enzyme-bound substrate reacts to B much faster than A alone (partial reaction 2, right), kcat. the enzyme s turnover number, corresponds to the number of substrate molecules converted by one enzyme molecule per second. Like the conversion A B, the formation of B from EA is a first-order reaction—i. e., V = k [EA] applies. When this equation is combined with the expression already derived for EA, the result is the Michaelis-Menten equation. 

The ratio of the rate of an enzyme- (or ribozyme-) catalyzed reaction to the rate of the reaction in the absence of catalysis. This ratio equals kcJknon, where Acat is the turnover number and Anon is the noncatalyzed rate constant. See Catalytic Proficiency... 

The ratio of the turnover number (i.e., Emax/[Etotai]) to the Xn, value of a substrate in a particular enzyme-catalyzed reaction. When kcat and are the true steady-state parameters, this ratio (or the ratio Emax/T m) is an excellent gauge of the specificity of the enzyme for that substrate. The larger the ratio, the more effective that substrate is used by the enzyme under study. In addition, the effects of a number of mechanistic probes of enzyme action on this ratio (for example, pH effects, isotope effects, temperature effects, the influence of various modifiers, etc.) can provide much information on the catalytic and binding mechanism. See... 

Thymidylate synthase also catalyzes an exchange of tritium of [5- H]dUMP for water protons in the absence of CH2H4folate. The turnover number for this exchange reaction is about 1/45,000 that of dTMP formation, and the Kjn is 1.2 X 10 M, about the same as the of the enzyme-dUMP complex estimated by equilibrium dialysis. The exchange reaction provided compelling evidence that the enzymic reaction involves attack of an enzyme nucleophile on the 6 position of dUMP to pro-... 

At one extreme diffusivity may be so low that chemical reaction takes place only at suface active sites. In that case p is equal to the fraction of active sites on the surface of the catalyst. Such a polymer-supported phase transfer catalyst would have extremely low activity. At the other extreme when diffusion is much faster than chemical reaction p = 1. In that case the observed reaction rate equals the intrinsic reaction rate. Between the extremes a combination of intraparticle diffusion rates and intrinsic rates controls the observed reaction rates as shown in Fig. 2, which profiles the reactant concentration as a function of distance from the center of a spherical catalyst particle located at the right axis, When both diffusion and intrinsic reactivity control overall reaction rates, there is a gradient of reactant concentration from CAS at the surface, to a lower concentration at the center of the particle. The reactant is consumed as it diffuses into the particle. With diffusional limitations the active sites nearest the surface have the highest turnover numbers. The overall process of simultaneous diffusion and chemical reaction in a spherical particle has been described mathematically for the cases of ion exchange catalysis,63 65) and catalysis by enzymes immobilized in gels 66-67). Many experimental parameters influence the balance between intraparticle diffusional and intrinsic reactivity control of reaction rates with polymer-supported phase transfer catalysts, as shown in Fig. 1. 

Regulation of enzymic activity occurs via two modes (cf. Ref. 50) alteration of the substrate binding process and/or alteration of the catalytic efficiency (turnover number) of the enzyme. The initial rate of a simple enzymatic reaction v is governed by the Michaelis-Menten equation... 

Supramolecular systems can be considered as new tools of modern physical organic chemistry. The study of catalytic processes using supramolecular model systems aims to explain the observed rate enhancement in terms of structure and mechanism. In some cases, the model systems may even provide a simplified simulation of the action of an enzyme and lead to further understanding of the different mechanism by which enzymes are able to achieve impressive reaction rate accelerations and turnover numbers. 

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