Kinetic isotope effects approach

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... 

Today a good understanding of transition state structure can be obtained through a combination of experimental measurements of kinetic isotope effects (KIE) and computational chemistry methods (Schramm, 1998). The basis for the KIE approach is that incorporation of a heavy isotope, at a specific atom in a substrate molecule, will affect the enzymatic reaction rate to an extent that is correlated with the change in bond vibrational environment for that atom, in going from the ground state to the... 

The physical organic chemistry of very high-spin polyradicals, 40, 153 Thermodynamic stabilities of carbocations, 37, 57 Topochemical phenomena in solid-slate chemistry, 15, 63 Transition state analysis using multiple kinetic isotope effects, 37, 239 Transition state structure, crystallographic approaches to, 29, 87 Transition state structure, in solution, effective charge and 27, 1... 

The use of reduced isotopic partition function ratios to study kinetic isotope effects was first undertaken by Bigeleisen this work was corrected and elaborated by Bigeleisen and Wolfsberg. References are cited at the end of this chapter. Application of the equations developed above to specific chemical reactions will be found in Chapter 10, where other theoretical approaches will also be presented. 

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). 

To begin we are reminded that the basic theory of kinetic isotope effects (see Chapter 4) is based on the transition state model of reaction kinetics developed in the 1930s by Polanyi, Eyring and others. In spite of its many successes, however, modern theoretical approaches have shown that simple TST is inadequate for the proper description of reaction kinetics and KIE s. In this chapter we describe a more sophisticated approach known as variational transition state theory (VTST). Before continuing it should be pointed out that it is customary in publications in this area to use an assortment of alphabetical symbols (e.g. TST and VTST) as a short hand tool of notation for various theoretical methodologies. 

The third equation in Equation 11.47 represents a kinetic isotope effect of the first isotopomer pair measured in the presence of the second (which IE has perturbed the commitment). In order to make the changes in apparent commitment (cf/H2k3) sufficiently pronounced, deuterium is usually selected as the second isotope (H2). The first, (HI), on the other hand, is usually a heavy-atom (e.g. 13C, lsO, etc.). Most frequently this approach has been used for carbon kinetic isotope effects in which case Equation 11.47 becomes ... 

Another approach to modeling the chlorine kinetic isotope effect of this reaction has been carried out using a true QM/MM scheme. 

Startup effects. Startup effects must also be considered in the interpretation of laboratory experiments. For example, during sulfate reduction, the first small amormt of sulfur to pass through the chain of reaction steps would be subject to the kinetic isotope effects of all of the reaction steps. This is because it takes some time for the isotopic compositions of the pools of intermediates to become enriched in heavier isotopes as described above for the steady-state case. Accordingly, the first HjS produced would be more strongly enriched in the lighter isotopes than that produced after a steady state has been approached. This principle was modeled by Rashid and Krouse (1985) to interpret kinetic isotope effects occurring during abiotic reduction of Se(IV) to Se(0) (see below). Startup effects may be particularly relevant in laboratory experiments where Se or Cr concentrations are very small, as is the case in some of the studies reviewed 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,... 

Kinetic Approaches to Identieication oe Ion-Radical Reactions 4.3.4.1 Kinetic Isotope Effect... 

Such considerations raise the concept of the intrinsic kinetic isotope effect—the effect of isotopic substitution on a specific step in an enzyme-catalyzed reaction. The magnitude of an intrinsic isotope effect may not equal the magnitude of an isotope effect on collective rate parameters such as Vmax or Emax/ m, unless the isotopi-cally sensitive step is the rate-limiting or rate-contributing step. To tackle this problem, Northrop extended the kinetic theory for primary isotope effects in enzyme-catalyzed reactions. His approach can be illustrated with the following example of a one-substrate/two-intermedi-ate enzyme-catalyzed reaction ... 

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