Observed isotope effects

The calculated isotope effects for the solvolyses of t-butyl chloride-dg (previously estimated by Bartell, 1961a) and acetyl chloride-ds were much weaker than the experimentally observed ones. The authors conclude (Karabatsos et al., 1967) that in ordinary systems where hyperconjugation (from the j8-position) is possible, the effect of non-bonded interactions accounts for only a small part (less than 10%) of the observed isotope effect. 

Both sets of results may also be discussed in terms of inductive differences between hydrogen and deuterium (see Halevi, 1963). Brown et al. (1966) jDoint out that both the inductive and steric explanations qualitatively predict isotope effects in the same direction, but that an inductive effect would be expected to operate from the 3 and 4 positions nearly as effectively as from the 2 position . Furthermore, there is no observable isotope effect on the heat of reaction of 2,6-(dimethyl-de)-pyridine with the relatively small molecule diborane A AH = —20 18 cal mol ), but a significant effect is obtained with the larger molecule boron trifluoride AAH = 230 + 150 cal mol ). 

The lack of steric effects in oxidations of hydrocarbons by Cr(VI) renders D and E unacceptable. The activated complex of scheme C is non-linear and hence does not comply with the magnitude of the observed isotope effect. Two pieces of evidence are quoted which indicate A to be the more probable of the remaining two. Firstly, the p constant of —1.17 is more in agreement with that obtained for bromine atom abstraction from toluenes (—1.369 to —1.806) than those found for solvolyses involving electron-deficient carbon ( — 2.57 to —4.67) . Secondly, the correlation between the relative rates of oxidation of the series... 

Korzekwa KR, Trager WF, Gillette JR. Theory for the observed isotope effects from enzymatic systems that form multiple products via branched reaction pathways cytochrome P-450. Biochemistry 1989 28(23) 9012-9018. 

If we denote the rate constant for the light isotopomer as kL, that for the heavy one as kjr, and the rate constant for a mixture of isotopomers of mole fraction x of the heavier isotope as kx, then (kL/kH) is related to the observed isotope effect, (kx/kH), by ... 

Compare that figure with the result expected when enriched perdeuterated methane is mixed with unlabeled hydroxyl. The observed isotope effect corresponds to k(io.9)/k(io.i3) where ... 

The behavior described above has been verified by experiment and calculation on numerous substituted dienes and dienophiles. For example Fig. 10.13 shows results for 2°-D isotope effects on Diels-Alder reactions of 2-methyl-butadiene with cyano-ethylene and 1,1-dicyano-ethylene. The calculated and experimental isotope effects are in quantitative agreement with each other and with the results on (butadiene + ethylene). In each case the excellent agreement between calculated and observed isotope effects validates the concerted mechanism and establishes the structure of the transition state as that shown at the bottom center of Fig. 10.11 and the left side of Fig. 10.12a. 

Using the various simplifications above, we have arrived at a model for reaction 11.9 in which only one step, the chemical conversion occurring at the active site of the enzyme characterized by the rate constant k3, exhibits the kinetic isotope effect Hk3. From Equations 11.29 and 11.30, however, it is apparent that the observed isotope effects, HV and H(V/K), are not directly equal to this kinetic isotope effect, Hk3, which is called the intrinsic kinetic isotope effect. The complexity of the reaction may cause part or all of Hk3 to be masked by an amount depending on the ratios k3/ks and k3/k2. The first ratio, k3/k3, compares the intrinsic rate to the rate of product dissociation, and is called the ratio of catalysis, r(=k3/ks). The second, k3/k2, compares the intrinsic rate to the rate of the substrate dissociation and is called forward commitment to catalysis, Cf(=k3/k2), or in short, commitment. The term partitioning factor is sometimes used in the literature for this ratio of rate constants. 

If the overall reaction rate is controlled by step three (k3) (i.e. if that is the rate limiting step), then the observed isotope effect is close to the intrinsic value. On the other hand, if the rate of chemical conversion (step three) is about the same or faster than processes described by ks and k2, partitioning factors will be large, and the observed isotope effects will be smaller or much smaller than the intrinsic isotope effect. The usual goal of isotope studies on enzymatic reactions is to unravel the kinetic scheme and deduce the intrinsic kinetic isotope effect in order to elucidate the nature of the transition state corresponding to the chemical conversion at the active site of an enzyme. Methods of achieving this goal will be discussed later in this chapter. 

As a practical matter of cost, studies on solvent isotope effects are usually limited to D/H substituted solvents, although recently a few lsO solvent effects have been measured. Interpretation of enzymatic solvent isotope effects is even more complicated than it is when the isotopic probe is incorporated in the substrate(s). This is because enzyme proteins have many exchangeable protons and, also, this is frequently true for reactants (substrates). Thus the observed isotope effect is the collective result of many different isotopic substitutions, each of which may influence... 

For this reaction the transition state drawn in Equation 11.82 involving simultaneous proton and hydride transfers has been proposed to explain the observed isotope effects. 

From Chart 4, the observed isotope effect (H/D) for a multistep reaction with a single isotope-sensitive step will be given by ... 

Calculations based on this second model give the observed value for the entropy of activation. In addition, this model may be used to account for the observed isotope effect (Benson and Nangia, 1963). If the tetra-methylene biradical is involved then it is to be expected that appropriately substituted cyclobutanes might undergo cis-trans isomerization reactions. This will be referred to again later. One final point should be mentioned in connection with biradical intermediates in both cyclopropane and cyclobutane reactions. This concerns the absence of any effect of radical inhibitors on these systems, when it might be expected that they would interact with the biradicals. In fact calculations show that, under the conditions of formation, the biradicals have extremely short lifetimes sec) and hence, unless radical inhibitors are... 

As will be discussed presently, this suggestion receives some support from a consideration of the observed isotope effects. 

The value corresponding to the observed isotope effect, expressed as the ratio [(k/k ) - 1], as a consequence of other rate-contributing steps ... 

Observed Isotope Effects for Hydrolysis of Phenyl-4-0-(2-acetamido-2-deoxy-/S-D-glucopyranosyl)-/S-D-... 

INFLUENCE OF OTHER STEPS ON THE MAGNITUDE OF OBSERVED ISOTOPE EFFECTS. As noted earlier, nonenzymatic reaction mechanisms do not involve those complexities imposed by substrate binding order, rates of substrate binding/release, as well as conformational changes that attend enzyme catalysis. As a result, the opportunity for detecting isotope effects is... 

Dahlquist et al. also provided a useful appendix for converting radioactivity counting data into observed isotope effects. 

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