Transition states reactions. KIEs

Finally, yet another issue enters into the interpretation of nonlinear Arrhenius plots of enzyme-catalyzed reactions. As is seen in the examples above, one typically plots In y ax (or. In kcat) versus the reciprocal absolute temperature. This protocol is certainly valid for rapid equilibrium enzymes whose rate-determining step does not change throughout the temperature range studied (and, in addition, remains rapid equilibrium throughout this range). However, for steady-state enzymes, other factors can influence the interpretation of the nonlinear data. For example, for an ordered two-substrate, two-product reaction, kcat is equal to kskjl ks + k ) in which ks and k are the off-rate constants for the two products. If these two rate constants have a different temperature dependency (e.g., ks > ky at one temperature but not at another temperature), then a nonlinear Arrhenius plot may result. See Arrhenius Equation Owl Transition-State Theory van t Hoff Relationship... 

Rate constants kY (M 1 s 1) and ksoiv (s 1) for the reversible addition of methanethiol to 48 and the overall reaction equilibrium constant (Scheme 51) have been reported.83 It was shown that the transition state for addition of RSH... 

The combination of Eqs. (150) and (151) provides a rate expression for the dehydrogenation/hydrogenation reactions that is dependent on the values of k, and Kx (as well as the overall equilibrium constant, Kcq). Estimates of these kinetic parameters can be made in terms of physically meaningful quantities such as entropies and enthalpy changes. Transition state theory gives the following expression for ky. 

Like all reactions, pericyclic reactions are reversible in principle (even though they may be irreversible in practice). The forward and reverse reactions always go through the same transition state. As an analogy, if you wanted to travel from Lexington, Ky., to Richmond, Va., you would choose the path that went through the lowest gap in the Appalachian mountains. If you wanted to go from Richmond back to Lexington, you would choose the same route, only in reverse. The path you chose would not depend on which direction you were traveling. Reactions obey the same principle. 

In a study of the cathodic reduction of cyclo-octatetraene in DMF and DMSO, Allendoerfer and Rieger used cyclic voltammetry and a.c. polarography to show that the reduction to the radical anion is quasi-reversible with a rate constant, ky, equal to 8.5 x 10" cm s at 25°C. The heat of activation was found to be 7.7 kcal mol" and the small values of a which were observed were interpreted in terms of the transition state at the equilibrium potential resembling the product radical anion more closely than it resembles the reactant molecule. The transition state is therefore presumably planar, as is the radical anion. This conclusion is supported by the similarity of the experimental value for the free energy of activation to the literature derived values for the free energy of activation in the bond isomerisation reaction of cyclo-octatetraene. 

It is easy to show that the primary kinetic isotope effect, ky lk ), for breakage of C-H and C-D bonds, amounts to = 7 (if in the reaction transition state, the proton or deuteron are half transferred to the base, causing a maximum energy change on the other hand, if the proton or deuteron are more or less than half transferred to the base, the energy change is smaller than its maximum change, so k lk < 7 is to be expected). 

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