Tunnel and coupled motions

For further important work on this and related concepts, see Rucker, J. and Kliman, J.P. (1999). Computational study of tunneling and coupled motion in alcohol dehydrogenase-catalyzed reactions Implication for measured hydrogen and carbon isotope effects. J. Am. Chem. Soc. 121, 1997 -2006, and Kohen, A. and Jensen, J.H. (2002). Boundary conditions for the Swain-Schaad relationship as a criterion for hydrogen tunneling. J. Am. Chem. Soc. April 17, 124(15), 3858-3864. 

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... 

Klinman, J.P. (1991). Hydrogen tunneling and coupled motion in enzyme reactions. In Enzyme Mechanism from Isotope Effects, Cook, P.F. (ed.), pp. 127-148. CRC Press, Boca Raton... 

Kohen, A. (2005). Probes for hydrogen tunneling and coupled motion in enzymatic systems. In Schowen, R., Klinman, J. and Hynes, J. (eds), Handbook of Hydrogen, Vol. 2 Biological Aspects of Hydrogen Transfer. Wiley, Weinheim... 

It is the combined effect of coupled motion and turmeling that leads to the largest anomalies [25, 52]. In addition to the classical effects of coupled motion, tunneling further increases the a-secondary KIE while significantly increasing the primary KIE. In ADH, as well as several other enzymatic and chemical examples, both tunneling and coupled motion have been invoked to reproduce the experimentally observed primary and a-secondary KIEs [6, 10, 25, 26, 49, 53-55]. 

Current Issues in Enzymatic Hydrogen Transfer from Carbon Tunneling and Coupled Motion from Kinetic Isotope Effect Studies... 

To date, the only experimental examples where a 2° Swain-Schaad relationship resulted in a breakdown of semidassical models and implicated tunneling and coupled motion were from studies of alcohol dehydrogenases (ADH). Furthermore, all these studies were conducted on the oxidation of the alternative substrate benzyl alcohol to aldehyde. The only attempt so far to conduct similar measurements used a very different system (DHFR). These experiments revealed no deviation from the semidassical EXP [45]. Until such experiments are extended to other systems or at least extended to the reduction of aldehyde to alcohol for the same system, the generalization of their interpretation should be taken with some discretion. These examples are discussed in great detail in Chapter 10, Section 10.5.1.1, and only a concise summary of two seminal examples is presented below. 

Kinetic complexity definition, 43 Klinman s approach, 46 Kinetic isotope effects, 28 for 2,4,6-collidine, 31 a-secondary, 35 and coupled motion, 35, 40 in enzyme-catalyzed reactions, 35 as indicators of quantum tunneling, 70 in multistep enzymatic reactions, 44-45 normal temperature dependence, 37 Northrop notation, 45 Northrop s method of calculation, 55 rule of geometric mean, 36 secondary effects and transition state, 37 semiclassical treatment for hydrogen transfer,... 

Table 1 Experimental studies that led to the coupled motion and tunneling model... 

In 1983, Huskey and Schowen tested the coupled-motion hypothesis and showed it to be inadequate in its purest form to account for the results. If, however, tunneling along the reaction coordinate were included along with coupled motion, then not only was the exaltation of the secondary isotope effects explained but also several other unusual feamres of the data as well. Fig. 4 shows the model used and the results. The calculated equilibrium isotope effect for the NCMH model (the models employed are defined in Fig. 4) was 1.069 (this value fails to agree with the measured value of 1.13 because of the general simplicity of the model and particularly defects in the force field). If the coupled-motion hypothesis were correct, then sufficient coupling, as measured by the secondary/primary reaction-coordinate amplimde ratio should generate secondary isotope effects that... 

The overall conclusion drawn by Huskey and Schowen was that a combination of coupled motion and tunneling through a relatively sharp barrier was required to explain the exaltation of secondary isotope effects. They also noted that this combination predicts that a reduction of exaltation in the secondary effect will occur if the transferring hydrogen is changed from protium to deuterium for point A in Fig. 4, the secondary effect is reduced by a factor of 1.09. Experimentally, reduction factors of 1.03 to 1.14 had been reported. For points B, C, and D on the diagram, all of which lack a combination of coupled motion and tunneling, no such reductions in the secondary isotope effect were calculated. 

These studies had therefore found the tunneling phenomenon, with coupled motion, as the explanation for failures of these systems to conform to the expectations that the kinetic secondary isotope effects would be bounded by unity and the equilibrium effect and that the primary and secondary effects would obey the Rule of the Geometric Mean (Chart 3), as well as being consistent with the unusual temperature dependences for isotope effects that were predicted by Bell for cases involving tunneling. 

Cheng MC, Marsh ENG. Evidence for coupled motion and hydrogen tunneling of the reaction catalyzed by glutamate mutase. Biochemistry 2007 46 883-889. 

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