Isotopic Competitive Methods

Chemical vs. Isotopic Competitive Methods Two types of competitive methods can and have been used. They are the chemical competitive and the isotopic fractionation techniques. In the chemical competitive method, the isotopic compounds A or A compete with a chemically different species, B, for reaction with C. The method is, therefore, not applicable to unimolecolar reactions and requires samples of A and A of appreciable isotopic enrichment. Furthermore, the species B must react with C at a rate of similar order of magnitude s A or A do. Consider for simplicity reactions first order in each of the reactants 

Inasmuch as the fractional amounts of conversion can be determined with an accuracy of better than a half per cent only in a limited number of favorable cases, and because of the requirement of samples of high isotopic enrichment, the chemical competitive method is essentially limited to studies of the isotopes of hydrogen. 

The isotopic competitive method is one of wide versatility and simplicity, especially when the isotopic pair have an abundance ratio of the order of 10 or less. For many of the stable isotopes e.g. C13, N15, O18, such studies have been carried out with material of natural abundance and many difficult synthetic problems are eliminated. However, in the use of this method, care must be exercised to eliminate effects due to isotopic exchange between reactants, intermediates, and products. In a number of cases the problem of isotopic homogeneity arises. We shall discuss the latter in connection with the problem of intramolecular isotope effects. 

---

Application of the Isotopic Competitive Method to Systems at the Tracer Concentration Level... 

Intramolecular Isotope Effects — A Special Case of the Isotopic Competitive Method... 

The isotopic competitive method, whether the analyses are made mass spectrometrically or by radioactivity measurements, is very sensitive to impurities. In the use of radioactive isotopes, the sample to be counted must be decontaminated of other chemical species containing the same radioactive nuclide and it must be chemically pure to avoid dilution. Both of these effects must be reduced to the order of 0.1 per cent, which is a very exacting restriction. In the mass spectrometric method one must avoid impurities which give ion peaks (mjq), either from the parent or from a fragment, at the same mfe as the product analyzed. A scan of the mass spectrum usually enables one to detect such impurities and provides the basis for further purification processes. The latter must all be isotopically nonfractionating. 

In either the radioactive or the mass spectrometric determination only the relative isotope ratios need be determined for the isotopic competitive method, except for the correction factors of the form (l + Ra0)/(l + Rxf). 

It is often more advantageous to use comparative methods, that is, to work with the mixture of the two compounds in the experiments, which ensures identical experimental conditions for the parallel reactions. The isotope competition method does not require pure isotopic compounds, it can be used even with compounds of natural isotopic composition, and thus it can be applied to the determination of C, N, and 0 isotope effects. However, the isotopic composition must be measured with high accuracy, in the case of stable isotopes usually by mass spectrometry, in the case of radioisotopes by measuring the change in the specific activity. In order to obtain the kinetic isotope effect, one needs to determine the isotopic composition of the test compound, first at the start of the reaction then again after the reaction has taken place to a known extent. The isotope effect can also be obtained from the isotopic analysis of the reaction products. In the latter case, the method of the evaluation of k /k from the experimental data can be found, for example, in the book of Vertes and Kiss (1987). 

Since the bond to the isotopic atom is not formed or broken in the transition state of the rate-determining step of the reaction, the difference between the rate constant for the reaction of the undeuterated and deuterated substrates is usually small. As a result, secondary deuterium KIEs are usually close to unity, i.e. the maximum secondary deuterium KIE is 1.25 per deuterium (Shiner, 1970a) and most of these KIEs are less than 1.10 (Westaway, 1987a). Therefore, careful kinetic measurements with an error of approximately 1 % in each rate constant or specially designed competitive methods are required to determine them with an acceptable degree of accuracy. 

Secondary isotope effects are small. In fact, most of the secondary deuterium KIEs that have been reported are less than 20% and many of them are only a few per cent. In spite of the small size, the same techniques that are used for other kinetic measurements are usually satisfactory for measuring these KIEs. Both competitive methods where both isotopic compounds are present in the same reaction mixture (Westaway and Ali, 1979) and absolute rate measurements, i.e. the separate determination of the rate constant for the single isotopic species (Fang and Westaway, 1991), are employed (Parkin, 1991). Most competitive methods (Melander and Saunders, 1980e) utilize isotope ratio measurements based on mass spectrometry (Shine et al., 1984) or radioactivity measurements by liquid scintillation (Ando et al., 1984 Axelsson et al., 1991). However, some special methods, which are particularly useful for the accurate determination of secondary KIEs, have been developed. These newer methods, which are based on polarimetry, nmr spectroscopy, chromatographic isotopic separation and liquid scintillation, respectively, are described in this section. The accurate measurement of small heavy-atom KIEs is discussed in a recent review by Paneth (1992). 

Conceptually, the simplest way to measure a kinetic isotope effect (KIE) is to use a non-competitive method, in which two separate kinetic runs are carried out, each starting with a different isotopomer of the reactant. The rate constants for both species are determined and the kinetic isotope effect (KIE) is the ratio of the two rate constants. This procedure is frequently referred to as the direct method . 

This non-competitive method has several practical limitations. Since the ordinary precision of determination of rate constants, (8kL/kL) or (Ske/kn), is on the order of a few percent, the method is limited as a practical matter to large, primary kinetic isotope effects, generally of hydrogen. This, because deuterium, the common heavy isotopomer for hydrogen, is available at 100% abundance at reasonable cost, and for hydrogen KIE s are usually large enough to constrain the relative error, 8(kL/kH)/(kL/kH), to acceptable values. 

One disadvantage of the non-competitive method is the necessity to synthesize samples of isotopically pure (or at least highly enriched) reactants, and this can be tedious and expensive. Since light and heavy isotopomers are very often obtained using different synthetic pathways (in order to optimize isotopic yield), they may carry different impurities or different concentrations of the same impurity. Therefore it is necessary to meticulously purify both samples before running experiments. In this... 

The protocol described in Section 7.1.2 involves isotopic competition, but with the different isotopomers held in separate containers. Equations 7.10 to 7.13 apply equally well to a type of competition experiment known in biochemistry as the perturbation method for determining KIE s of reversible enzyme catalyzed reactions. The perturbation method differs from simultaneous non-competitive measurements in several important ways. One begins by mixing equilibrium concentrations of substrate and product but with one component (substrate or product) at a different isotopic composition than the other. Thus, the mixture is in chemical, but not isotopic equilibrium. At this stage no enzyme is present and the interconversion is... 

While competitive methods to determine KIE s are free from errors due to differences in reaction conditions (impurities, temperature, pH, etc.) they do require access to equipment that allows high precision measurements of isotope ratios. The selection of an appropriate analytical technique depends on the type of the isotope and its location in the molecule. For studies with stable isotopes the most commonly used technique (and usually the most appropriate) is isotope ratio mass spectrometry (IRMS). 

Equation 11.57 signifies that when the competitive method is used (i.e., both iso-topomers are present simultaneously in the reaction mixture) the experimentally determined kinetic isotope effect corresponds to the isotope effect on V/K regardless of the actual concentration of the substrate. In other words, one cannot measure the isotope effect on Vmax using this method even when concentration is much larger than the Michaelis constant Km-... 

KINETIC ISOTOPE EEEECT REACTION COORDINATE DIAGRAM Triose-phosphate isomerase energetics, REACTION COORDINATE DIAGRAM TRIPLE-COMPETITIVE METHOD TRIPLET STATE FLUORESCENCE TRIPLET-TRIPLET ANNIHILATION ANNIHILATION... 

This chapter mainly focuses on the reactivity of 02 and its partially reduced forms. Over the past 5 years, oxygen isotope fractionation has been applied to a number of mechanistic problems. The experimental and computational methods developed to examine the relevant oxidation/reduction reactions are initially discussed. The use of oxygen equilibrium isotope effects as structural probes of transition metal 02 adducts will then be presented followed by a discussion of density function theory (DFT) calculations, which have been vital to their interpretation. Following this, studies of kinetic isotope effects upon defined outer-sphere and inner-sphere reactions will be described in the context of an electron transfer theory framework. The final sections will concentrate on implications for the reaction mechanisms of metalloenzymes that react with 02, 02 -, and H202 in order to illustrate the generality of the competitive isotope fractionation method. 

Isotopes of chemical elements represent a tool which can do certain jobs more easily, quickly, simply, and cheaply than competitive methods. Some measurements could not be done at all without the use of isotopes as there are no alternative methods available. 

Polymeric membranes for separation of hydrogen and oxygen isotopes were studied at INCT, Warsaw [92-95,140-141]. Both hydrophUic barriers, such as regenerated cellulose and hydrophobic PTFE membranes, were tested. The regenerated cellulose appeared to be a very good system to get high separation factors and to consider membrane permeation as possible and competitive method for enrichment deuterium and 0 in natural water. 

Whereas alteration of enzyme or substrate structure causes large perturbations to the potential energy functions describing enzyme-substrate interactions, a consequence of the Born-Oppenheimer approximation is that isotopic substitution causes no perturbation of potential energy functions at all. Isotope effects are therefore amongst the most powerful methods of determining enzyme mechanism. If they are measured by any sort of competition method (for example, isotope enrichment in the unreacted starting material or product) then, because one isotopomer acts as a competitive inhibitor of the... 

---