Kinetically perfect enzymes

Another way of evaluating enzymatic activity is by comparing k2 values. This first-order rate constant reflects the capacity of the enzyme-substrate complex ES to form the product P. Confusingly, k2 is also known as the catalytic constant and is sometimes written as kcal. It is in fact the equivalent of the enzyme s TOF, since it defines the number of catalytic cycles the enzyme can undergo in one time unit. The k2 (or kcat) value is obtained from the initial reaction rate, and thus pertains to the rate at high substrate concentrations. Some enzymes are so fast and so selective that their k2/Km ratio approaches molecular diffusion rates (108—109 m s-1). This means that every substrate/enzyme collision is fruitful, and the reaction rate is limited only by how fast the substrate molecules diffuse to the enzyme. Such enzymes are called kinetically perfect enzymes [26],... 

But k must always be greater than or equal to k h / (A i + kf). That is, the reaction can go no faster than the rate at which E and S come together. Thus, k sets the upper limit for A ,. In other words, the catalytic effieiency of an enzyme cannot exceed the diffusion-eontroUed rate of combination of E and S to form ES. In HgO, the rate constant for such diffusion is approximately (P/M - sec. Those enzymes that are most efficient in their catalysis have A , ratios approaching this value. Their catalytic velocity is limited only by the rate at which they encounter S enzymes this efficient have achieved so-called catalytic perfection. All E and S encounters lead to reaction because such catalytically perfect enzymes can channel S to the active site, regardless of where S hits E. Table 14.5 lists the kinetic parameters of several enzymes in this category. Note that and A , both show a substantial range of variation in this table, even though their ratio falls around 10 /M sec. 

Some enzymes are so fast and so selective that their k2/Km ratio approaches the molecular diffusion rates (108-109m s-1). Such enzymes are called kinetically perfect [21]. With these enzymes, the reaction rate is diffusion controlled, and every collision is an effective one. However, since the active site is very small compared to the entire enzyme, there must be some extra forces which draw the substrate to the active sites (otherwise, there would be many fruitless collisions). The work of these forces was dubbed by William Jencks in 1975 as the Circe effect [22], after the mythological sorceress of the island of Aeaea, who lured Odysseus men to a feast and then turned them into pigs [23,24]. 

During the evolution of a natural enzyme, selection is not solely dependent on rate improvement. Therefore, there is no requirement for enzymes to be kinetically perfect, and it should be possible to develop catalytic antibodies that are faster than their natural counterparts. The designed substrate 52 has a rate of 1.4 s-1 with 84G3-catalyzed retro-aldol reaction (Zhong et al., 1999). Its kinetic parameters hold the current world record for antibody catalysis (KM = 4.2 /ulM, = 2 X... 

In the liquid phase diffusion to the catalyst may become the limiting step. Diffusion limitations provides an upper bound to the observed reaction rate (see Chapter 8). It appears that some enzyme catalytic reactions are so fast, e.g. carbonic anhydrase or acetyl cholesterase, that they exhibit this phenomenon. Catalysis under such condition is called "kinetic perfection". 

The fecat/J M ratios of the enzymes superoxide dismutase, acetylcholinesterase, and triosephosphate isomerase are between 10 and lO" s Enzymes such as these that have fecat/ M ratios at the upper limits have attained kinetic perfection. Their catalytic velocity is restricted only by the rate at which they encounter substrate in the solution (Table 8.8). Any further gain in catalytic rate can come only by decreasing the time for diffusion. Remember that the active site is only a small part of the total enzyme structure. Yet, for catalytically perfect enzymes, every encounter between enzyme and substrate is productive. In these cases, there may be attractive electrostatic forces on the enzyme that entice the substrate to the active site. These forces are sometimes referred to poetically as Circe effects. 

Explain the significance of K, k2, fecat> and bca/l M- C>efine kinetic perfection as it pertains to enzyme catalysis. 

In the above situation, a perfect enzyme should function by organizing all kinetically important species, including the substrate and the possible intermediates, in a stereoelectronically favorable conformation. This scenario would require a conformationally flexible enzyme active site with the multiplicity of conformational states, each suited for a different intermediate/tiansition state combination. 

Finally, it is useful to note that the catalytic efficiency reaches a maximum when the formation of the enzyme-substrate complex ES is rate-determining. This corresponds to the situation where k2> > k i, so that every ES which is formed is converted to product, none re-dissociates to E + S. However, the rate cannot exceed the rate of the collisions of E and S, and this upper limit is determined by the rate of diffusion in the solution. Experiments on the kinetics of enzyme-catalysed reactions demonstrate that a number of them achieve this state of catalytic perfection [2, p. 372],... 

In an ideal kinetic resolution (common in enzyme-catalyzed processes), one enantiomer of a racemic substrate is converted tvhile the other is unreactive [70]. In such a kinetic resolution of 5-methyl-2-cyclohexenone, even with 1 equivalent of Me2Zn, the reaction should virtually stop after 50% conversion. This near perfect situation is found with ligand 18 (Fig. 7.10) [71]. Kinetic resolutions of 4-methyl-2-cyclohexenone proceed less selectively (s = 10-27), as might be expected from the lower trans selectivity in 1,4-additions to 4-substituted 2-cyclohexenones [69]. 

The quasi-steady approximation, which was introduced in Section 3.1.3.2 and justified on the basis of rapid cycle kinetics in Section 4.1.1, forms the basis of the study of enzyme mechanisms, a field with deep historical roots in the subject of biochemistry. In later chapters of this book, our studies make use of this approximation in building models of biochemical systems. Yet there remains something unsatisfying about the approximation. We have seen in Section 3.1.3.2 that the approximation is not perfect. Particularly during short-time transients, the quasisteady approximation deviates significantly from the full kinetics of the Michaelis-Menten system described by Equations (3.25)-(3.27). Here we mathematically analyze the short timescale kinetics of the Michaelis-Menten system and reveal that a different quasi-steady approximation can be used to simplify the short-time kinetics. 

The kinetic approach can be more efficiently manipulated than the thermodynamic approach, but serine and cysteine proteases are not perfect acyl transferases. Undesired reactions may take place parallel to acyl transfer, for instance hydrolysis of the acyl-enzyme, secondary hydrolysis of the formed peptide bond, and other undesired proteolytic cleavages of possible protease-labile bonds in reactants and product. The elimination or minimization of these disadvantages can be performed by various manipulations on the level of the reaction medium, the enzyme, and the substrate, as well as on mechanistic features of the process. 

EIA often makes use of solid phases. The relative merits and disadvantages of such techniques, as well as ways to optimize them will be discussed. An important aspect, which has not yet been investigated in detail for EIA, is the influence immobilization of enzymes has on enzyme kinetics. The solid-phase may cause strong local differences in the microenvironment of the enzyme, the implications of which can only be inferred from studies on immobilized enzymes in solid-phase biochemistry (Chapter 9). Major or minor flaws in EIA design, which may discredit an otherwise perfectly valid EIA, will be discussed. 

MichaeUs-Menten (MM) kinetics, although not perfect and in many cases inadequate for a number of reasons, have been used widely to describe the dynamics of catalysis of most enzymes. Databases such as BRENDA [5], containing sets of MM kinetic constants for most enzymes in a wide array of organisms, are widely available. The basic MM equation (Fig. 7-2) is derived for a simple system as shown ... 

A synthesis of lamivudine in optically pure form requires the use of a-acetoxysulfide (R) -40.25 This can be produced in optically pure form by a kinetic resolution using the lipase from Pseudomonas fluorescens. This enzyme hydrolyses the enantiomer that we do not want and leaves behind the one that we do. The authors investigated a range of sulfide side chains and the acetal 40 that is used in the synthesis of lamivudine worked perfectly.26 The solvent is important. The use of chloroform instead of f-BuOMe gives low ees in the opposite sense. 

These substances metabolized within the CNS illustrate well one of the difficulties that may be encountered with prodrug kinetics. The prodrug may follow an ADME pattern perfectly well described by its systemic availability, volume of distribution, and both hepatic and renal clearances, but still have a pharmacological effect whose dependency on blood kinetics is only indirect. This is particularly true if the drug must diffuse through the blood-brain barrier, and is then metabolized by enzyme systems different from those found in the liver. 

Novel kinetic formulations. The description given above of the calculation of measures of enzyme catalytic power relies initially on empirically determined rate constants for enzymic and non-enzymic reactions. The numerical results at the initial stage are therefore theory-free and may be used for many purposes with perfect confidence. 

In addition, reviews dealing with aspects of enzyme-catalyzed dynamic resolution and related processes such as stereoinversion and deracemisation have also been published[4 71. Details of the kinetic principles of dynamic kinetic resolution reactions have also been reported,7 9). Interestingly, a dynamic kinetic resolution reaction can provide a product with higher enantiomeric excess than the corresponding kinetic resolution. In a conventional kinetic resolution, the enantiomeric excess of the product often decreases as a function of conversion. This happens because as the reaction proceeds, the proportion of the preferred enantiomer of substrate decreases. Unless the enzyme is able to discriminate perfectly between the substrate enantiomers, it will catalyze the reaction of the less preferred enantiomer of substrate (the proportion of which grows as the reaction proceeds). However, in a dynamic kinetic resolution where the substrate enantiomers are interconverting rapidly, the ratio of substrate enantiomers will be constant at 1 1. Consequently, the enantiomeric excess of the product will not decrease as the reaction proceeds. 

The related dynamic resolutions of the furanone and pyrrolinone substrates were achieved with higher selectivities (Fig. 9-7) U). Again, these substrates underwent spontaneous racemization under the reaction conditions. Appropriate choice of enzyme afforded a good example of an essentially perfect dynamic kinetic resolution process in the case of the esterification of the hydroxypyrrolinone substrate. 

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