Single-substrate enzyme-catalyzed reactions

It is useful to have a high substrate (S) and a lower product (P) concentration (usually [P] = 0) before the start of the enzymic reaction since the presence of P affects the reaction negatively. The initial conversion speed (v ) can easily be specified at the beginning of the reaction (i) the concentration of all reactants are known at this point (ii) loss of enzymic activity has not yet occurred and, (iii) the backward reaction (inhibition by P) is negligible since the P concentration is very small (Michaelis and Menten, 1913). This rate is easier and more accurately determined by the appearance of P rather than by the disappearance of S which is very large at the beginning. 

An enzyme molecule is not working faster at higher [S]o, but a larger number of enzyme molecules will be involved reflecting a higher conversion rate Vq. At a certain limit (Fig.9.1) virtually no 

The equilibrium expression by Michaelis and Menten is, therefore, a special case of the more general steady-state assumption, namely 

In the cases where S is not in excess, the reverse direction of enzyme action (i.e., P - S) will decrease appreciably the net rate of P formation. It follows from eq. 3 that  

Many enzyme reactions have more than one intermediate for which King and Altman (1956) devised a method, based on matrix algebra, by establishing the rate equation of a given enzymic reaction simply by inspecting all complexes and the reactions between them. 

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There are many examples of first-order reactions dissociation from a complex, decompositions, isomerizations, etc. The decomposition of gaseous nitrogen pentoxide (2N2O5 4NO2 + O2) was determined to be first order ( d[N205]/dt = k[N205j) as is the release of product from an enzyme-product complex (EP E -t P). In a single-substrate, enzyme-catalyzed reaction in which the substrate concentration is much less than the Michaelis constant (i.e., [S] K ) the reaction is said to be first-order since the Michaelis-Menten equation reduces to... 

The derivation of the steady-state enzyme rate equation for the single substrate enzyme-catalyzed reaction is provided in the entry entitled Enzyme Rate Equations (L The Basics). 

The effect of an inhibitor I on the rate of a single-substrate enzyme-catalyzed reaction was investigated and gave the following results ... 

Yi Liang, Wang Cunxin, Wu Dingquan, and Qu Songsheng, Thermokinetic studies of the irreversible inhibition of single-substrate, enzyme-catalyzed reactions, Thermochim. Acta., 1995, vol. 268, pp. 17-25. 

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... 

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. 

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. 

Thus far, we have considered only the simple case of enzymes that act upon a single substrate, S. This situation is not common. Usually, enzymes catalyze reactions in which two (or even more) substrates take part. 

In contrast to laboratory reactions, enzyme-catalyzed reactions often give a single enantiomer of a chiral product, even when the substrate is achiral. One step in the citric acid cycle of food metabolism, for instance, is the aconitase-catalyzed addition of water to (Z)-aconitate (usually called ris-aconitate) to give isocitrate. 

The mode of action of enzymes can be found in detail in many biochemistry and enzymology textbooks31"33. The mechanisms of enzyme-catalyzed reactions are complex and all have several steps. The more generally written scheme involves a single substrate and a single intermediate ... 

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. 

Scheme 1 is a gross over-simplification for almost any enzyme-catalyzed reaction of a specific substrate, based as it is on a one-step reaction with a single, rate-determining transition state but it is appropriate for many, if not most reactions catalyzed by simple enzyme mimics. Most important for present purposes, it emphasises the most important properties of enzyme reactions which the design of mimics, or artificial enzymes, must address, namely ... 

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... 

A noncovalent complex between two molecules. Binary complex often refers to an enzyme-substrate complex, designated ES in single-substrate reactions or as EA or EB in certain multisubstrate enzyme-catalyzed reactions. See Michaelis Complex... 

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)... 

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... 

A single-substrate, two-product enzyme-catalyzed reaction scheme in which a substrate (A) binds to the free enzyme and is converted to two products (P and Q) which can be released in any order. Many enzymes described with this mechanism are actually random pseudo-Uni Bi schemes in which the second substrate is water. 

COMPOUNDING OF ERRORS. Data collected in an experiment seldom involves a single operation, a single adjustment, or a single experimental determination. For example, in studies of an enzyme-catalyzed reaction, one must separately prepare stock solutions of enzyme and substrate, one must then mix these and other components to arrive at desired assay concentrations, followed by spectrophotometric determinations of reaction rates. A Lowry determination of protein or enzyme concentration has its own error, as does the spectrophotometric determination of ATP that is based on a known molar absorptivity. All operations are subject to error, and the error for the entire set of operations performed in the course of an experiment is said to involve the compounding of errors. In some circumstances, the experimenter may want to conduct an error analysis to assess the contributions of statistical uncertainties arising in component operations to the error of the entire set of operations. Knowledge of standard deviations from component operations can also be utilized to estimate the overall experimental error. 

An enzyme-catalyzed reaction in which there are three substrates and a single product. See Multisubstrate... 

Reactions in which the velocity (v) of the process is independent of the reactant concentration, following the rate law v = k. Thus, the rate constant k has units of M sAn example of a zero-order reaction is a Michaelis-Menten enzyme-catalyzed reaction in which the substrate concentration is much larger than the Michaelis constant. Under these conditions, if the substrate concentration is raised even further, no change in the velocity will be observed (since v = Umax)- Thus, the reaction is zero-order with respect to the substrate. However, the reaction is still first-order with respect to total enzyme concentration. When the substrate concentration is not saturating then the reaction ceases to be zero order with respect to substrate. Reactions that are zero-order in each reactant are exceedingly rare. Thus, zero-order reactions address a fundamental difference between order and molecularity. Reaction order is an empirical relationship. Hence, the term pseudo-zero order is actually redundant. All zero-order reactions cease being so when no single reactant is in excess concentration with respect to other reactants in the system. 

In this chapter, step and intermediate refer to chemical species in the reaction pathway of a single enzyme-catalyzed reaction. In the context of metabolic pathways involving many enzymes (discussed in Part II), these terms are used somewhat differently. An entire enzymatic reaction is often referred to as a step in a pathway, and the product of one enzymatic reaction (which is the substrate for the next enzyme in the pathway) is referred to as an intermediate. ... 

A complete description of an enzyme-catalyzed reaction requires direct measurement of the rates of individual reaction steps—for example, measurement of the association of enzyme and substrate to form the ES complex. It is during the pre-steady state that the rates of many reaction steps can be measured independently. Experimenters adjust reaction conditions so that they can observe events during reaction of a single substrate molecule. Because the pre-steady state phase is gener-... 

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. 

Figure E5.7 displays the kinetic progress curve of a typical enzyme-catalyzed reaction and illustrates the advantage of a kinetic assay. The rate of product formation decreases with time. This may be due to any combination of factors such as decrease in substrate concentration, denaturation of the enzyme, and product inhibition of the reaction. The solid line in Figure E5.7 represents the continuously measured time course of a reaction (kinetic assay). The true rate of the reaction is determined from the slope of the dashed line drawn tangent to the experimental result. From the data given, the rate is 5 jumoles of product formed per minute. Data from a fixed-time assay are also shown on Figure E5.7. If it is assumed that no product is present at the start of the reaction, then only a single measurement after a fixed period is necessary. This is shown by a circle on the experimental rate curve. The measured rate is now 16 jumoles of product formed every 5 minutes or about 3 /rmoles/minute, considerably lower than the rate derived from the continuous, kinetic assay. Which rate measurement is correct Obviously, the kinetic assay gives the true rate because it corrects for the decline in rate with time. The fixed-time assay can be improved by changing the time of the measurement, in this example, to 2 minutes of reaction time, when the experimental rate is still linear. It is possible to obtain...

Structural studies of the oxy-Cope catalytic antibody system reinforce the idea that conformational dynamics of both protein and substrate are intimately intertwined with enzyme catalysis, and consideration of these dynamics is essential for complete understanding of biologically catalyzed reactions. Indeed, recent single molecule kinetic studies of enzyme-catalyzed reactions also suggest that different conformations of proteins are associated with different catalytic rates (Xie and Lu, 1999). In addition, a number of enzymes are known to undergo conformational changes on binding of substrate (Koshland, 1987) that lead to enhanced catalysis two examples are hexokinase (Anderson and Steitz, 1975 Dela-Fuente and Sols, 1970) and triosephosphate isomerase (Knowles, 1991). 

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