Intrinsic isotope effect

The intrinsic isotope effects on CS are caused by a change in the zero-point energy. 

This change leads in the asymmetric potential to a change in the average bond 

The deuterium isotope effect observed at the neighboring atom C can be approximated by 

A very useful finding for further discussion is the fact that a few Schiff bases have been found to exist entirely on the NH form [25, 26]. This helps in the analysis of tautomeric Schiff bases. 

2 Intrinsic Deuterium Isotope Effects on Chemical Shifts 

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The deuterium isotope effects on chemical shift consists of intrinsic isotope effect (direct perturbation of the shielding of X atom) and equilibrium isotope effect (perturbation of the equilibrium caused by the isotopic substitution). The values of deuterium isotope effects are to some extent independent of chemical shifts and allow determination of the mole fraction of the forms in equilibrium. 

A primary isotope effect results when the breaking of a carbon-hydrogen versus a carbon-deuterium bond is the rate-limiting step in the reaction. It is expressed simply as the ratio of rate constants, i wlky,. The full expression of k /kn measures the intrinsic primary deuterium isotope for the reaction under consideration, and its magnitude is a measure of the symmetry of the transition state, e.g., -C- H- 0-Fe+3 the more symmetrical the transition state, the larger the primary isotope effect. The theoretical maximum for a primary deuterium isotope effect at 37°C is 9. The less symmetrical the transition state, the more product-like or the more substrate-like the smaller the intrinsic isotope effect will be. 

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. 

If the isotope sensitive step is reversible the equations get more complicated and cannot be solved explicitly for the intrinsic isotope effects (unless Cf = 0, or the equilibrium isotope effect is unity). The last two equations in Equation 11.48 demonstrate that a normal deuterium kinetic isotope effect diminishes the apparent commitment if both isotopes are present. Thus 13(V/K) is smaller than 13(V/K)d when both isotope effects are related to the same step. 

It is not always possible to determine intrinsic isotope effects. However, other useful information about the reaction can still be obtained. Above we assumed a single rate determining step sensitive to each isotope substitution. More frequently, however, the isotope sensitivity is found in different steps. Studies with multiple isotope effects can be used to determine the sequence of steps. To illustrate, a more complicated reaction scheme is needed ... 

As mentioned in Section 11.3.5 for the case where the rate determining step is sensitive to both isotopic species, elucidation of the intrinsic isotope effects is not possible using the equations given thus far (if neither the reverse nor the forward commitment is zero). Even then, however, it is possible to solve for the intrinsic iso-... 

Isotope effects on both the carbon and hydrogen of the breaking C-H bond have been measured. However, for this reaction both forward and reverse commitments are sizable so the three equations corresponding to Equation 11.48 have four unknowns the forward and reverse commitments and two intrinsic isotope effects. Measurements of the secondary deuterium kinetic isotope effect (at position 4 of nicotinamide ring of NADP+) and the carbon kinetic isotope effect with the secondary position deuterated introduce two additional equations, but only one more unknown ... 

Table 11.2 Observed and intrinsic isotope effects on the glucose-6-phosphate dehydrogenase reaction (Hermes, J. D. and Cleland, W. W. J. Am. Chem. Soc. 106, 7263 (1984)) ... 

The haloalkane dehalogenase DhlA mechanism takes place in two consecutive Sn2 steps. In the first, the carboxylate moiety of the aspartate Aspl24, acting as a nucleophile on the carbon atom of DCE, displaces chloride anion which leads to formation of the enzyme-substrate intermediate (Equation 11.86). That intermediate is hydrolyzed by water in the subsequent step. The experimentally determined chlorine kinetic isotope effect for 1-chlorobutane, the slow substrate, is k(35Cl)/k(37Cl) = 1.0066 0.0004 and should correspond to the intrinsic isotope effect for the dehalogenation step. While the reported experimental value for DCE hydrolysis is smaller, it becomes practically the same when corrected for the intramolecular chlorine kinetic isotope effect (a consequence of the two identical chlorine labels in DCE). 

The three protocols discussed in this section show that QM/MM techniques available presently are capable of reproducing, and thus hopefully predicting, intrinsic isotope effects, provided that a sufficient part of the enzyme is included... 

Chart 4. The expression of intrinsic isotope effects in multistep reactions... 

Chart 6. Northrop s method for intrinsic isotope effects... 

After an exceedingly cautious extraction had been made of the intrinsic isotope effects from the data, the wild-type enzyme (c, 155 kDa) gave an A-ratio (D/T) of 0.98, essentially consistent with a semiclassical mechanism, and the deglycosylated enzyme (a, 136 kDa) 0.81, a borderline indication of tunneling, while the fully glycosylated enzyme (e, 320 kDa) and the two PEG-derivatives... 

Kinetic complexity can produce apparently temperature-independent isotope effects. For example, a rise in temperature produces a smaller intrinsic isotope effect, in agreement with the conventional expectations of Chart 3, for an isotope-sensitive step that is partially rate limiting. If at the same time the rise in temperature makes other steps relatively more rapid so that the isotope-sensitive step then becomes more nearly rate-limiting, then the intrinsic isotope effect will be more fully expressed (Chart 4). If these effects roughly balance, then the isotope effect may appear to be independent of temperature while in fact fully in accord with semiclassical expectations. Seymour and Klinman have discussed in detail the problem of kinetic complexity in isotope-effect temperature dependences. 

Karsten, W.E., Gavva, S.R., Park, S.H. and Cook, P.E. (1995). Metal ion activator effects on intrinsic isotope effects for hydride transfer from decarboxylation in the reaction catalyzed by the NAD-malic enzyme from Ascaris suum. Biochemistry 34, 3253-3260... 

Figure 5A shows experimentally derived profiles of pH vs rate for reactions in H2O and D2O [30, 50, 71]. The magnitude of the apparent isotope effect (ratio of rate constants in H2O and D2O) is 4.4 and the profiles appear to support the possibility that a proton is transferred from (Mg -bound) water molecules. However, careful analysis led us to conclude that a metal ion binds directly to the 5 -oxygen. Since the concentration of the deproto-nated 2 -oxygen in H2O should be higher than that in D2O at a fixed pH, we must take into account this difference in pKa, namely ApKa (=pKa °-pKa ), when we analyze the solvent isotope effect of D2O [30, 50, 68, 71]. We can estimate the pKa in D2O from the pKa in H2O using the linear relationship shown in Fig. 5B [30, 68, 73-75]. If the pKa for a Mg -bound water molecule in H2O is 11.4, the ApKa is calculated to be 0.65 (solid line in Fig. 5B). Then, the pKa in D2O should be 12.0. Demonstrating the absence of an intrinsic isotope effect (kH2o/kD20=l)> the resultant theoretical curves closely fit the experimental data, with an approximate 4-fold difference in...

Fig. 5A The dependence on pH of the deuterium isotope effect in the hammerhead ri-bozyme-catalyzed reaction. Black circles show rate constants in H2O gray circles show rate constants in D2O. Solid curves are experimentally determined curves. The apparent plateau of cleavage rates above pH 8 is due to disruptive effects on the deprotonation of uridine and guanosine residues. Dotted lines are theoretical lines calculated from pKa values of hydrated Mg ions of 11.4 in H2O and 12.0 in D2O and on the assmnption that there is no intrinsic isotope effect (a=kH2o/kD2o=l is the coefficient of the intrinsic isotope effect). The following equation was used to plot the graph of pL vs log(rate) log kobs=log(kmax)-log(l+10

Selected entries from Methods in Enzymology [vol, page(s)] Add-base catalysis [with site-directed mutants, 249, 110-118 altered pH dependencies, 249, 110] commitment to [in determination of intrinsic isotope effects, 249, 343, 347-349 in interfacial catalysis, 249, 598-599 equilibrium isotope exchange in, 249, 443-479 hydrogen tunneling in, 249, 373-397] interfacial [competitive inhibitors, kinetic characterization, 249, 604-605 equilibrium parameters, 249, 587-594 forward commitment to, 249, 598-599 interpretation, 249, 578-586 (constraining variables for high processivity, 249, 582-586 kinetic variables at interface,... 

An effect of isotopic substitution within a reactant or substrate 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 F ax or unless the... 

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 ... 

With this background, let us examine how Northrop was able to develop a way to extract the true (or as we more commonly say, intrinsic) isotope effect. Recognizing that an underdetermined system can often be solved if an additional quantitative relation is considered, Northrop proposed to measure two isotope effects, namely VIK)nl VIK)j and (V K) l V K)t and to take advantage of the following relationship ... 

Isotope effects have also been applied extensively to studies of NAD+/NADP+-linked dehydrogenases. We typically treat these enzymes as systems whose catalytic rates are limited by product release. Nonetheless, Palm clearly demonstrated a primary tritium kinetic isotope effect on lactate dehydrogenase catalysis, a finding that indicated that the hydride transfer step is rate-contributing. Plapp s laboratory later demonstrated that liver alcohol dehydrogenase has an intrinsic /ch//cd isotope effect of 5.2 with ethanol and an intrinsic /ch//cd isotope effect of 3-6-4.3 with benzyl alcohol. Moreover, Klin-man reported the following intrinsic isotope effects in the reduction of p-substituted benzaldehydes by yeast alcohol dehydrogenase kn/ko for p-Br-benzaldehyde = 3.5 kulki) for p-Cl-benzaldehyde = 3.3 kulk for p-H-benzaldehyde = 3.0 kulk for p-CHs-benzaldehyde = 5.4 and kn/ko for p-CHsO-benzaldehyde = 3.4. 

A procedure using both deuterium and tritium isotope effects on to obtain intrinsic isotope effects for... 

A method used to determine primary intrinsic isotope effects. In this procedure, three differently labeled substrates are used to react with a labeled cosubstrate and the distribution of the labels in the products is measured. 

Intrinsic isotope effects on enzyme-catalyzed reactions,... 

Similar isotope effects for human isoenzyme I (157c) on kc t and Km for C02 hydration are 1.7. Silverman and Tu (161) report an isotope effect of 2.5 for H2180 release and suggest that the intrinsic isotope effect of intramolecular H+ transfer might be significantly smaller in isoenzyme I than in isoenzyme II. Hence, the H20-splitting step might also limit the rate of C02 hydration in isoenzyme I. Human isoenzyme I has three titratable active-site histidines with pKa values... 

In order to determine intrinsic isotope effects of benzylic hydroxylations, the metabolism of different deuterated toluenes was investigated in detail with rat liver microsomes and compared with the chemical radical chlorination of... 

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