Enzymatic kinetics

Michaelis and Menten assumed the formation of an enzyme-substrate complex ES complex is in rapid equilibrium with free enzyme and breakdown of ES to form products is assumed to be slower than 1) formation of ES and 2) breakdown of ES to re-form E and S. This assumption is equivalent to assumption of the quasi-equilibria for the first step. In fact in order to derive a kinetic expression for enzymatic kinetics this assumption is not needed. 

Since the reaction rate of product formation (sometimes defined as V (velocity)) is 

In fact this equation can be derived directly from the general equation for the two step sequence (4.93), which in instance of irreversible second step is 

Km is a constant derived from the rate constants and is the ratio of the rates of decomposition and formation. Therefore it differs from equilibrium constants in a pure chemical sense, which are defined as the ratio of formation constants to decomposition ones 

In the original derivation of Michaelis and Menten it was assumed that the first step is rapid and reversible, thus this step can be considered as a quasi-equilibrium with a constant Kcq. Note that it is defined as the ratio of constant in the reverse direction to the constant in the forward one (or the ratio of reactants to products) following a special bio logic. 

The reactant, A (called substrate in the bio field) and the enzyme, E, combine in a reversible way to form a complex A-E which decomposes into the product, P, thereby regenerating the enzyme  

Using mass action kinetics, the net rate of disappearance of A can be written  

There are two ways of arriving at rate equations for this process that do not contain the generally inaccessible concentration of the complex, C. e, any more. The first one considers the decomposition of A-E to be the rate determining step, the second applies the pseudo steady state approximation. 

If the decomposition of the complex A-E into the product P and the enzyme E is the rate determining step of the process, the first step, the formation of Ca-e, reaches equilibrium, so that 

This is the Michaelis-Menten equation for the rate of a simple enzymatic reaction and Km = K lk is known as the Michaelis-Menten constant. At high reactant concentration Ca much larger than iQ, the rate levels off and becomes zero order with respect to the reactant, =k Cl- At low Q (1.5.1-8) degenerates into a first order rate equation. This equation is entirely similar to the Hougen-Watson rate equations that will be derived in Chapter 2 for reactions catalyzed by solids. 

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On that basis, crystallization is often used in combination with other enantiose-lective techniques, such as enantioselective synthesis, enzymatic kinetic resolution or simulated moving bed (SMB) chromatography [10, 11]. In general, when referring to crystallization techniques, the aim is to obtain an enantiomeric enrichment in the crystallized solid. However, the possibility of producing an enrichment in the mother liquors [12, 13], even if this is not a general phenomenon [14], must be taken into account. 

Enantiomers, preferential crystallization of 59 Endo selectivity 798 Ene reactions 808, 809 Enones, synthesis of 732 Enthalpies of formation 102, 103 Enynes, synthesis of 956 Enzymatic kinetic resolution 829 Epimerization 399 Episulphides, oxidation of 237 Episulphones 650, 775 Episulphoxides, photolysis of 742 a,/J-Epoxysulphones reactions of 811, 812 rearrangement of 685 synthesis of 612 / ,y-Epoxysulphones 781 y,<5-Epoxysulphones 627, 628 Epoxysulphoxides reactions of 613 rearrangement of 744 synthesis of 327, 612 Erythronolides 831... 

Methyl-l,10-undecadiene, ADMET polymerization of, 442 Michaelis-Menten enzymatic kinetics, 84 Microbial hydrolysis, 43 Microcellular elastomers, 204-205 Microphase-separated block copolymers, 6-7... 

Table 4.20 Asymmetric Diels-Alder reactions via enzymatic kinetic resolution...

Despite its widespread application [31,32], the kinetic resolution has two major drawbacks (i) the maximum theoretical yield is 50% owing to the consumption of only one enantiomer, (ii) the separation of the product and the remaining starting material may be laborious. The separation is usually carried out by chromatography, which is inefficient on a large scale, and several alternative methods have been developed (Figure 6.2). For example, when a cyclic anhydride is the acyl donor in an esterification reaction, the water-soluble monoester monoacid is separable by extraction with an aqueous alkaline solution [33,34]. Also, fiuorous phase separation techniques have been combined with enzymatic kinetic resolutions [35]. To overcome the 50% yield limitation, one of the enantiomers may, in some cases, be racemized and resubmitted to the resolution procedure. 

Recently, an interesting example of the enzymatic kinetic resolution of a-acetoxyamide 8 was demonstrated using native wheat germ lipase and immobilized lipase PS (AMANO) (Scheme 5.6). 

Scheme 5.6 Influence of a cosolvent on enzymatic kinetic resolution.

For most chemical transformations, especially for industrial applications, the yield of 50% cannot be accepted. Since each enantiomer constitutes only 50% of the racemic mixture, the best way to increase the yield of the desired enantiomer is racemization of the unwanted one (Scheme 5.7). This reaction mustproceed simultaneously with the enzymatic kinetic resolution. In order to indicate the dynamic character of such processes, the term dynamic kinetic resolution has been introduced. 

Thus, racemic acid 12 (R = H) was obtained by [3+2] cycloaddition in 90-95% yield (Scheme 5.9) [28]. Its resolution into enantiomers could be achieved either by chiral preparative HPLC, or by fractional crystallization of its cinchonidine salts. Better results were obtained upon enzymatic kinetic resolution of its iso-butyl ester 12 (R = i-Bu) [29]. However, further work showed that racemic thiolester 13, which... 

Interestingly, for the transformation of both the racemic 1-hydroxyalkanephosphonates 41 and 2-hydroxyalkanephosphonates 43 into almost enantiopure acetyl derivatives 42 and 44, respectively, a dynamic kinetic resolution procedure was applied. Pamies and BackvalP used the enzymatic kinetic resolution in combination with a ruthenium-catalysed alcohol racemization and obtained the appropriate O-acetyl derivatives in high yields and with almost full stereoselectivity (Equation 25, Table 5). It should be mentioned that lowering... 

At equilibrium the net reaction velocity must be zero. In terms of the enzymatic kinetic constants, equation 7.3.40 then indicates that... 

A combination of an enzymatic kinetic resolution and an intramolecular Diels-Alder has recently been described by Kita and coworkers [23]. In the first step of this domino process, the racemic alcohols ( )-8-55 are esterified in the presence of a Candida antarctica lipase (CALB) by using the functionalized alkenyl ester 8-56 to give (R)-8-57, which in the subsequent Diels-Alder reaction led to 8-58 in high enantioselectivity of 95 and 91 % ee, respectively and 81 % yield (Scheme 8.15). In-... 

Additional studies featuring reactions of thiophene derivatives detail biohydrolysis of (S)-3-(thiophen-2-ylthio)butanenitrile <06TL8119>, lipase catalyzed resolution of thiotetronic acids <06TL7163>, enzymatic kinetic resolution of l,l-dioxo-2,3-dihydrothiophen-3-ol <06TL5273>, and efficient synthesis of 6-methyl-2,3-dihydrothieno[2,3-c]furan 55, a coffee... 

The evaluation of results of assay optimization experiments such as those described above (see Section 6.4.2.1) also provides valuable information about enzymatic kinetic behavior. For example, the results shown in Figures 6.45 and 6.46 already provide information on enzymatic activity at each time point. In general, when evaluating enzyme kinetics, assays are designed to yield a measured conversion close to initial velocity.32... 

Ketorolac 132, a nonstereoidal anti-inflammatory drug with cyclooxygenase (COX) inhibitory activity, was marketed as a racemic mixture. It is now well established that (V)-ketorolac is the active enantiomer <1999MI382>. Therefore, efforts were devoted to the selective synthesis of this active stereomer, either by enzymatic kinetic resolution <2001TA1865> or by enantioselective synthesis <2005AGE609>. 

Scheme 1.39 Enzymatic kinetic resolution approaches to abacavir...

Nechah, M., Azzi, N., Vanthuyne, N., Bertrand, M., Gastaldi, S. and Gil, G., Highly selective enzymatic kinetic resolution of primary amines at 80°C a comparative study of carboxylic acids and their ethyl esters as acyl donors. J. Org. Chem., 2007, 72, 6918-6923. 

Procedure 3 Enzymatic Kinetic Resolution of (/ ,S)-2-Ethoxyethyl Ibuprofen Ester with Immobilized Lipase... 

The procedure shows that it is feasible to combine racemization with the kinetic resolution process (hence the DKR) of R,S)- ethoxyethyl ibuprofen ester. The chemical synthesis of the ester can be applied to any esters, as it is a common procedure. The immobilized lipase preparation procedure can also be used with any enzymes or support of choice. However, the enzyme loading will need to be optimized first. The procedures for the enzymatic kinetic resolution and DKR will need to be adjusted accordingly with different esters. Through this method, the enantiopurity of (5)-ibuprofen was found to be 99.4 % and the conversion was 85 %. It was demonstrated through our work that the synthesis of (5)-ibuprofen via DKR is highly dependent on the suitability of the reaction medium between enzymatic kinetic resolution and the racemization process. This is because the compatibility between both processes is crucial for the success of the DKR. The choice of base catalyst will vary from one reaction to another, but the basic procedures used in this work can be applied. DKRs of other profens have been reported by Lin and Tsai and Chen et al. ... 

Rodriguez, C., de Gonzalo, G., Eraaije, M.W. and Gotor, V., Enzymatic kinetic resolution of racemic ketones catalyzed by Baeyer-Villiger monooxygenases. Tetrahedron Asymm., 2007, 18, 1338. 

In a succeeding publication, the same authors reported on an enantiose-lective approach to diquinane enones 6 and ent-6 by combining the above-described synthesis with an enzymatic kinetic resolution (Scheme 4) [12]. After lipase-catalyzed enantioselective transesterification of diol rac-12. 

An efficient method to prepare enantiomerically enriched hydroperoxides is the enzymatic kinetic resolution of racemic hydroperoxides using different kinds of enzymes (mainly lipases, chloroperoxidase, horseradish peroxidase). However, the scope of these reactions may be limit by the narrow substrate specificity of the enzyme. 

A variety of further methods for the enzymatic kinetic resolution of racemic hydroperoxides (equation 14) has been published. For comparison they are summarized in Table 5. 

This problem was solved by Adam and coworkers in 1994-1998. They presented a high-yielding and diastereoselective method for the preparation of epoxydiols starting from enantiomerically pure allyhc alcohols 39 (Scheme 69). Photooxygenation of the latter produces unsaturated a-hydroxyhydroperoxides 146 via Schenck ene reaction. In this reaction the (Z)-allylic alcohols afford the (5, 5 )-hydroperoxy alcohols 146 as the main diastereomer in a high threo selectivity (dr >92 8) as racemic mixmre. The ( )-allylic alcohols react totally unselectively threolerythro 1/1). Subsequent enzymatic kinetic resolution of rac-146 threolerythro mixture) with horseradish peroxidase (HRP) led to optically active hydroperoxy alcohols S,S) and (//,5 )-146 ee >99%) and the... 

Following route A (Fig. 1), Yan Xiao et al. reported the chemoenzymatic synthesis of poly(8-caprolactone) (PCL) and chiral poly(4-methyl-8-caprolactone) (PMCL) microparticles [5]. The telechelic polymer diol precursors were obtained by enzymatic polymerization of the corresponding monomers in the presence of hexanediol. Enzymatic kinetic resolution polymerization directly yielded the (R)-and (S )-enriched chiral polymers. After acrylation using acryloylchloride, the chiral and nonchiral particles were obtained by crosslinking in an oil-in-water emulsion photopolymerization. Preliminary degradation experiments showed that the stereoselectivity of CALB is retained in the degradation of the chiral microparticles (Fig. 2). 

In order to extend the comparison of enzymatic kinetic resolution and asymmetric catalysis of chapter 2 and identify the potential improvements of these processes, the derivation of the equations that determine the enantiomeric excess and yield are given in detail. 

Rakels, J.L.L., Paffen, H.T., Straathof, A.J.J. and Heijnen, J.J. (1994) Comparison of enzymatic kinetic resolution in a batch reactor and a CSTR. Enzyme Microbial Technology, 16,791-794. 

I.4.2. Enzymatic Kinetic Resolution of Alcohols and Carboxylic Acids... 

Alternative synthetic approaches include enantioselective addition of the organometallic reagent to quinoline in the first step of the synthesis [16], the resolution of the racemic amines resulting from simple protonation of anions 1 (Scheme 2.1.5.1, Method C) by diastereomeric salts formation [17] or by enzymatic kinetic resolution [18], and the iridium-catalyzed enantioselective hydrogenation of 2-substituted quinolines [19]. All these methodologies would avoid the need for diastereomer separation later on, and give direct access to enantio-enriched QUINAPHOS derivatives bearing achiral or tropoisomeric diols. Current work in our laboratories is directed to the evaluation of these methods. 

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