Simple Enzyme Reactions

In the following pages an account is given of some of the more simple reactions which enzymes catalyse. The reactions have been selected partly because they are of particular interest to the organic chemist, and partly because they are capable of simple and ready demonstration in the laboratory. 

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. 

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 substrate concentration when the half maximal rate, (Vmax/2), is achieved is called the Km. For many simple reactions it can easily be shown that the Km is equal to the dissociation constant, Kd, of the ES complex. The Km, therefore, describes the affinity of the enzyme for the substrate. For more complex reactions, Km may be regarded as the overall dissociation constant of all enzyme-bound species. 

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. 

The term kcJKm is also the second-order rate constant for the reaction of the free enzyme (E) with the substrate (S) to give product. The kc.JKm is a collection of rate constants, even for the simple reaction mechanism shown earlier. Formally, kcJKm is given by the pile of rate constants kik3/(k2 + k3). If k3 > k2, this reduces to ku the rate of encounter between E and S. Otherwise, kcJKm is a complex collection of rate constants, but it is still the second-order rate constant that is observed for the reaction at low substrate concentration. 

What about reactions of the type A + B — C This is a second-order reaction, and the second-order rate constant has units of M min-1. The enzyme-catalyzed reaction is even more complicated than the very simple one shown earlier. We obviously want to use a second-order rate constant for the comparison, but which one There are several options, and all types of comparisons are often made (or avoided). For enzyme-catalyzed reactions with two substrates, there are two Km values, one for each substrate. That means that there are two kcJKm values, one for each substrate. The kcJKA5 in this case describes the second-order rate constant for the reaction of substrate A with whatever form of the enzyme exists at a saturating level B. Cryptic enough The form of the enzyme that is present at a saturating level of B depends on whether or not B can bind to the enzyme in the absence of A.6 If B can bind to E in the absence of A, then kcJKA will describe the second-order reaction of A with the EB complex. This would be a reasonably valid comparison to show the effect of the enzyme on the reaction. But if B can t bind to the enzyme in the absence of A, kcat/KA will describe the second-order reaction of A with the enzyme (not the EB complex). This might not be quite so good a comparison. 

Suppose that the reaction between A and B to give the intermediate is very fast and very favorable. If we have more B than A to start with, all the A is converted instantly into the intermediate. If we re following P, what we observe is the formation of P from the intermediate with the rate constant k2. If we increase the amount of B, the rate of P formation won t increase as long as there is enough B around to rapidly convert all the A to the intermediate. In this situation, the velocity of P formation is independent of how much B is present. The reaction is zero-order with respect to the concentration of B. This is a special case. Not all reactions that go by this simple mechanism are zero-order in B. It depends on the relative magnitudes of the individual rate constants. At a saturating concentration of substrate, many enzyme-catalyzed reactions are zero-order in substrate concentration however, they are still first-order in enzyme concentration (see Chap. 8). 

Acid and base catalysis of a chemical reaction involves the assistance by acid or base of a particular proton-transfer step in the reaction. Many enzyme catalysed reactions involve proton transfer from an oxygen or nitrogen centre at some stage in the mechanism, and often the role of the enzyme is to facilitate a proton transfer by acid or base catalysis. Proton transfer at one site in the substrate assists formation and/or rupture of chemical bonds at another site in the substrate. To understand these complex processes, it is necessary to understand the individual proton-transfer steps. The fundamental theory of simple proton transfers between oxygen and nitrogen acids and... 

The kinetics of the general enzyme-catalyzed reaction (equation 10.1-1) may be simple or complex, depending upon the enzyme and substrate concentrations, the presence/absence of inhibitors and/or cofactors, and upon temperature, shear, ionic strength, and pH. The simplest form of the rate law for enzyme reactions was proposed by Henri (1902), and a mechanism was proposed by Michaelis and Menten (1913), which was later extended by Briggs and Haldane (1925). The mechanism is usually referred to as the Michaelis-Menten mechanism or model. It is a two-step mechanism, the first step being a rapid, reversible formation of an enzyme-substrate complex, ES, followed by a slow, rate-determining decomposition step to form the product and reproduce the enzyme ... 

The simple Michaelis-Menten model does not deal with all aspects of enzyme-catalyzed reactions. The model must be modified to treat the phenomena of inhibition and... 

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 ... 

The Kemp elimination is of special interest because it is known to be extraordinarily sensitive to the medium, and particularly well suited as a test reaction for potential enzyme mimics because it is a simple, one-step process. The joint conclusions from this work were that catalysis involves a combination of a number of different factors, even for this simple reaction by these simple catalysts. 

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). 

As far as the use of ferrocene molecules as amperometric sensors is concerned, they have found wide use as redox mediators in the so-called enzymatic electrodes, or biosensors. These are systems able to determine, in a simple and rapid way, the concentration of substances of clinical and physiological interest. The methodology exploits the fact that, in the presence of enzyme-catalysed reactions, the electrode currents are considerably amplified.61 Essentially it is an application of the mechanism of catalytic regeneration of the reagent following a reversible charge transfer , examined in detail in Chapter 2, Section 1.4.2.5 ... 

The observation of hidden reactions during solvolysis, through the use of chiral or isotopically labeled substrates has created considerable excitement in communities interested in the mechanisms of nonenzymatic and enzyme catalyzed reactions. These hidden reactions reveal something interesting about reaction mechanisms. However, chemists and biochemists are still working on the problem of extracting simple and definitive conclusions from analysis of data for these isomerization reactions. 

The components listed in Table 20-1 are typical for PCR. As can be seen, it is a fairly simple reaction to set up. The template and primer concentrations must be determined beforehand the buffer, enzyme, and deoxynucleotide triphosphate (dNTP) mixture are commercially available. 

As the above discussion indicates, assigning mechanisms to simple anation reactions of transition metal complexes is not simple. The situation becomes even more difficult for a complex enzyme system containing a metal cofactor at an active site. Methods developed to study the kinetics of enzymatic reactions according to the Michaelis-Menten model will be discussed in Section 2.2.4. Since enzyme-catalyzed reactions are usually very fast, experimentahsts have developed rapid kinetic techniques to study them. Techniques used by bioinorganic chemists to study reaction rates will be further detailed in Section 3.7.2.1 and 3.72.2. 

If a detailed theoretical knowledge of the system is either not available or is too complex to be useful, it is often possible to construct an empirical model which will approximately describe the behavior of the system over some limited set of factor levels. In the enzyme system example, at relatively low levels of substrate concentration, the rate of the enzyme catalyzed reaction is found to be described rather well by the simple expression... 

Information is currently available which allows more definite conclusions than have previously been possible. Rate enhancements have been obtained in several simple chemical reactions that are of similar magnitude to those observed in analogous enzyme-catalysed reactions, and the goal of analysing the individual factors that can give such large rate accelerations is now perhaps within reach. The recent work will be stressed in this review. 

The kinetics of enzyme-catalyzed reactions (i. e the dependence of the reaction rate on the reaction conditions) is mainly determined by the properties of the catalyst, it is therefore more complex than the kinetics of an uncatalyzed reaction (see p.22). Here we discuss these issues using the example of a simple first-order reaction (see p.22)... 

Carrier-mediated passage of a molecular entity across a membrane (or other barrier). Facilitated transport follows saturation kinetics ie, the rate of transport at elevated concentrations of the transportable substrate reaches a maximum that reflects the concentration of carriers/transporters. In this respect, the kinetics resemble the Michaelis-Menten behavior of enzyme-catalyzed reactions. Facilitated diffusion systems are often stereo-specific, and they are subject to competitive inhibition. Facilitated transport systems are also distinguished from active transport systems which work against a concentration barrier and require a source of free energy. Simple diffusion often occurs in parallel to facilitated diffusion, and one must correct facilitated transport for the basal rate. This is usually evident when a plot of transport rate versus substrate concentration reaches a limiting nonzero rate at saturating substrate While the term passive transport has been used synonymously with facilitated transport, others have suggested that this term may be confused with or mistaken for simple diffusion. See Membrane Transport Kinetics... 

Except for very simple systems, initial rate experiments of enzyme-catalyzed reactions are typically run in which the initial velocity is measured at a number of substrate concentrations while keeping all of the other components of the reaction mixture constant. The set of experiments is run again a number of times (typically, at least five) in which the concentration of one of those other components of the reaction mixture has been changed. When the initial rate data is plotted in a linear format (for example, in a double-reciprocal plot, 1/v vx. 1/[S]), a series of lines are obtained, each associated with a different concentration of the other component (for example, another substrate in a multisubstrate reaction, one of the products, an inhibitor or other effector, etc.). The slopes of each of these lines are replotted as a function of the concentration of the other component (e.g., slope vx. [other substrate] in a multisubstrate reaction slope vx. 1/[inhibitor] in an inhibition study etc.). Similar replots may be made with the vertical intercepts of the primary plots. The new slopes, vertical intercepts, and horizontal intercepts of these replots can provide estimates of the kinetic parameters for the system under study. In addition, linearity (or lack of) is a good check on whether the experimental protocols have valid steady-state conditions. Nonlinearity in replot data can often indicate cooperative events, slow binding steps, multiple binding, etc. 

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