Kinetic isotope effect tunneling

The only (to the best of our knowledge) theoretical treatment of hydrogen transfer by tunnelling to explicitly recognise the role of protein dynamics, and relate this in turn to the observed kinetic isotope effect, was described by Bruno and Bialek. This approach has been termed vibration-ally enhanced ground state tunnelling theory. A key feature of this theory... 

Based on C-H versus C-D zero point vibrational differences, the authors estimated maximum classical kinetic isotope effects of 17, 53, and 260 for h/ d at -30, -100, and -150°C, respectively. In contrast, ratios of 80,1400, and 13,000 were measured experimentally at those temperatures. Based on the temperature dependence of the atom transfers, the difference in activation energies for H- versus D-abstraction was found to be significantly greater than the theoretical difference of 1.3kcal/mol. These results clearly reflected the smaller tunneling probability of the heavier deuterium atom. 

More recent theoretical work has raised questions about these conclusions, how-ever. Particularly extensive calculational treatment of the rearrangement of 54 to vinyl chloride by several research groups failed to duplicate the predictions of an atypical kinetic isotope effect. These later studies indicate that tunneling effects should indeed be greater for H-shift than for the heavier D rearrangement. Consequently, the k /ko ratio should actually decrease at higher temperatures. The discrepancy in predicted results was eventually traced to an error in the earlier calculations. Nevertheless, it... 

Hydrogen motion, H+, H or H, is often involved in the rate-limiting step of many enzyme catalysed reactions. Here, QM tunnelling can be important and is reflected in the values of the measured kinetic isotope effects (KIEs) [75], Enzyme motion... 

The photolyses of diazirines 9a and 9b were similarly studied in Ar matrices at 10-34.5 K 59 Eq. 10. Benzylchlorocarbene (10a) and its ct,a-d2 analogue (10b) were observed by UV or IR (10b) spectroscopy, and their decay to styrenes 11 and 12 could be monitored. Tunneling in these 1,2-H(D) shifts was indicated by (a) much higher rates of carbene decay at 10 K than could be anticipated from extrapolation of the 298 K LFP kinetic data, (b) a kinetic isotope effect (KIE) for the 1,2-H(D) shifts estimated at 2000, and (c) little temperature dependence of the rate at low temperature.59 Accepting that QMT is important in the very low temperature H shifts of carbenes 10 and 18, the obvious question becomes is QMT important at higher or even ambient temperatures ... 

Kelley and co-workers [70, 71] measured the dynamics of the excited-state intramolecular proton transfer in 3-hydroxyflavone and a series of its derivatives as a function of solvent (Scheme 2.9). The energy changes associated with the processes examined are of the order of 3 kcal/mol or less. The model they employed in the analysis of the reaction dynamics was based upon a tunneling reaction path. Interestingly, they find little or no deuterium kinetic isotope effect, which would appear to be inconsistent with tunneling theories. For 3-hydroxy-flavone, they suggest the lack of an isotope effect is due to a very large... 

Kinetic Isotope Effects Continued Variational Transition State Theory and Tunneling... 

Abstract Some of the successes and several of the inadequacies of transition state theory (TST) as applied to kinetic isotope effects are briefly discussed. Corrections for quantum mechanical tunneling are introduced. The bulk of the chapter, however, deals with the more sophisticated approach known as variational transition state theory (VTST). 

Complications that arise with this simple reaction are twofold. First, because of the low mass of the hydrogen atom its movement frequently exhibits non-classical behavior, in particular quantum-mechanical tunneling, which contributes significantly to the observed kinetic isotope effect, and in fact dominates at low temperature (Section 6.3). Secondly, in reaction 10.2 protium rather than deuterium transfer may occur ... 

Not only primary but also secondary hydrogen isotope effects can be indicative of tunneling. The most frequently employed criteria of tunneling are the temperature dependence of kinetic isotope effects and the isotopic ratio of the pre-exponential factors in Arrhenius plots, but the pre-exponential criterion has been shown to be invalid for small secondary isotope effects. 

For heavy atom isotope effects tunneling is relatively unimportant and the TST model suffices. As an example the dehalogenation of 1,2-dichloroethane (DCE) to 2-chloroethanol catalyzed by haloalkane dehalogenase DhlA is discussed below. This example has been chosen because the chlorine kinetic isotope effect for this reaction has been computed using three different schemes, and this system is among the most thoroughly studied examples of heavy atom isotope effects in enzymatic reactions. 

Non-unit kinetic isotope effects such as the rate-constant ratio kn/k-Q also derive from isotopic zero-point energy differences in the reactant state and in the transition state. A second manifestation of the Uncertainty Principle may also contribute to kinetic isotope eff ects, namely isotopic differences in the probability of quantum tunneling through the energy barrier between the reactant state and the product state. 

Fig. 2 Schematic representation of the so-called semiclassical treatment of kinetic isotope effects for hydrogen transfer. All vibrational motions of the reactant state are quantized and all vibrational motions of the transition state except for the reaction coordinate are quantized the reaction coordinate is taken as classical. In the simplest version, only the zero-point levels are considered as occupied and the isotope effect and temperature dependence shown at the bottom are expected. Because the quantization of all stable degrees of freedom is taken into account (thus the zero-point energies and the isotope effects) but the reaction-coordinate degree of freedom for the transition state is considered as classical (thus omitting tunneling), the model is ealled semielassieal.

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... 

Karsten, W.E., Hwang, C.C. and Cook, P.F. (1999). Alpha-secondary tritium kinetic isotope effects indicate hydrogen tunneling and coupled motion occur in the oxidation of L-malate by NAD-malic enzyme. Biochemistry 38, 4398-4402... 

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