Experimental Determination of Kinetic Isotope Effects

Choosing a method to determine isotope effects on rate constants, and selecting a particular set of techniques and instrumentation, will very much depend on the rate and kind of reaction to be studied, (i.e. does the reaction occur in the gas, liquid, or solid phase , is it 1st or 2nd order , fast or slow , very fast or very slow , etc.), as well as on the kind and position of the isotopic label, the level of enrichment (which may vary from trace amounts, through natural abundance, to full isotopic substitution). Also, does the isotopic substitution employ stable isotopes or radioactive ones, etc. With such a variety of possibilities it is useless to attempt to generate methods that apply to all reactions. Instead we will resort to discussing a few examples of commonly encountered strategies used to study kinetic isotope effects. 

The illustrations used in this chapter usually employ first order reactions and unit stoichiometry. Generalization to more complicated cases is straightforward but sometimes tedious. 

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The simplest method of the experimental determination of kinetic isotope effects is to compare the reaction rates of the pure isotopic variants under the same experimental conditions. This technique is simple and does not require the isotope analysis of the reactants and products however, it requires pure isotopic compounds. In addition to that, the reaction rate should be measured with an accuracy that is at least one order of magnitude higher than the difference between the reaction rates of the isotopic variants. 

The haloalkane dehalogenase DhlA mechanism takes place in two consecutive Sn2 steps. In the first, the carboxylate moiety of the aspartate Aspl24, acting as a nucleophile on the carbon atom of DCE, displaces chloride anion which leads to formation of the enzyme-substrate intermediate (Equation 11.86). That intermediate is hydrolyzed by water in the subsequent step. The experimentally determined chlorine kinetic isotope effect for 1-chlorobutane, the slow substrate, is k(35Cl)/k(37Cl) = 1.0066 0.0004 and should correspond to the intrinsic isotope effect for the dehalogenation step. While the reported experimental value for DCE hydrolysis is smaller, it becomes practically the same when corrected for the intramolecular chlorine kinetic isotope effect (a consequence of the two identical chlorine labels in DCE). 

Just as in the preceding examples, early indications of tunneling in enzyme-catalyzed reactions depended on the failure of experiments to conform to the traditional expectations for kinetic isotope effects (Chart 3). Table 1 describes experimental determinations of -secondary isotope effects for redox reactions of the cofactors NADH and NAD. The two hydrogenic positions at C4 of NADH are stereochemically distinct and can be labeled individually by synthetic use of enzyme-catalyzed reactions. In reactions where the deuterium label is not transferred (see below), an... 

Computational QM/MM studies presented thus far provide better understanding of enzymatic catalysis and description of interactions within the active sites. Comparison of experimentally determined isotope effects with corresponding values predicted theoretically serves to indicate that theoretical methods yield meaningful results. In the remaining part of this contribution we will show how information about properties of the transitions state gathered collectively from molecular modeling and measurements of kinetic isotope effects can be effectively used in devising new compounds with therapeutic applications. 

The experimental determination, theory, and application of kinetic isotope effects are treated in a number of excellent monographs and book chapters (Bigeleisen and Wolfsberg 1958 Melander 1960 Van Hook 1971 Wolfsberg 1972 Shiner 1975 Buddenbaum and Shiner 1977 Cleland et al. 1977 Melander and Saunders 1980 Willi 1983 Sims and Lewis 1984 Vertes and Kiss 1987). 

The density functional theory calculations of primary 14C KIE and secondary deuterium kinetic isotope effects (SKIE)220 did not reproduce satisfactorily all the experimentally determined 14C KIE and deuterium (4,4-2H2)- and 6,6-2H2-SKIE, though the non-local DFT methods provide transition state energies on a par with correlated molecular orbital theory221. 

It can be concluded that the [3+2] pathway seems to be the only feasible reaction pathway for the dihydroxylation by permanganate. The study on the free activation energies for the oxidation of a. P unsaturated carboxylic acids by permanganate shows that the [3+2] mechanism is in better agreement with experimental data than the [2+2] pathway. Experimentally determined kinetic isotope effects for cinnamic acid are in good agreement with calculated isotope effects for the [3+2] pathway, therefore it can be concluded that a pathway via an oxetane intermediate is not feasible. 

Abstract In this chapter we discuss practical techniques and instrumentation used in experimental measurements of kinetic and equilibrium isotope effects. After describing methods to determine IE s on rate constants, brief treatments of mass spectrometry and isotope ratio mass spectrometry, NMR measurements of isotope effects, the use of radio-isotopes, techniques to determine vapor pressure and other equilibrium IE s, and IE s in small angle neutron scattering are presented. 

As a first example we discuss a mechanism in which the formation of the enzyme-intermediate complex, El, is sensitive to hydrogen isotopic substitution, while the next step characterized by rate constants ks and k6 exhibits a carbon kinetic isotope effect. Expressions for the three kinetic isotope effects that can be determined experimentally are ... 

Equation 11.57 signifies that when the competitive method is used (i.e., both iso-topomers are present simultaneously in the reaction mixture) the experimentally determined kinetic isotope effect corresponds to the isotope effect on V/K regardless of the actual concentration of the substrate. In other words, one cannot measure the isotope effect on Vmax using this method even when concentration is much larger than the Michaelis constant Km-... 

The practical usefulness of Equations 11.46 through 11.53 has been demonstrated for the malic enzyme catalyzed conversion of L-malate to pyruvate (Equation 11.72). Table 11.1 lists experimentally determined isotope effects for this reaction. Comparison of carbon kinetic isotope effects for protio and deutero-malate substituted at position 2 (the carbon that undergoes sp3 to sp2 transition) rules out the possibility that the hydride transfer and the decarboxylation events are concerted. This conclusion follows from Equation 11.48 which, for a concerted reaction, predicts that 13(V/K) should be smaller than 13(V/K)D, which is opposite to the order observed experimentally. 

The reactions of A-phenyl a-r-butyl nitrone (PEN) with maleimides, maleic anhydride, and diethyl maleate have been studied by EPR and two types of spin adduct detected. They arise from the reductive addition of PEN to the alkenes and the degradation product of DEN (2-methyl-2-nitropropane). The deuterium and muonium kinetic isotope effects for the addition of the hydrogen atom to a variety of alkenes have been determined experimentally and theoretically. ... 

Methane is slightly soluble in HF-SbF5 even at atmospheric pressure (0.005 M), which facilitates direct kinetic studies by NMR. Thus the transition states for methane activation in this medium have been studied experimentally by Ahlberg et al.49 The first-order rate constants [Eqs. (5.9) and (5.10)], determined experimentally on the basis of2H -decoupled 600-MHz 1H NMR time-dependent spectra (Figure 5.2), are on the order of 3.2 x 10 1 s 1 at —20°C and show a secondary kinetic isotope effect (SKIE) of 1 0 02. 

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