The Effects of Isotopes

Each lipid class in a cellular lipidome comprises a variety of lipid species that contain an identical head group but various fatty acyl chains containing a differential number of carbon atoms and differential degrees of unsaturation. Therefore, if an equal molar mixture of lipid species of a class is analyzed by MS, the monoisotopie peak intensities of these species displayed in the mass spectrum decrease as the number of carbon atoms in the species increases. This is due to the differential distribution of isotopologues in those species. 

In general, the isotopologue distribution of each species of a class mainly depends on the number of total carbon atoms in the species. This is due to the following facts. First, all the species of a class of interest should contain identical numbers of O, N, P, or other atoms if the lipid species of interest is not a modified one. This means that these atoms equally contribute their isotopologues to all the species of the class. Therefore, their contribution to the ion intensities does not cause any difference for relative comparison to the selected internal standard(s). Second, the natural 

Quantification by ratiometric comparison with an internal standard is based on the ratio of the sum of the isotopologue intensities of a species to that of the internal standard. The fact is that the monoisotopic peak is the most intense peak in the isotopologue cluster of a lipid species for almost all lipids, and its intensity can therefore be determined more accurately compared to the intensities of other isotopic peaks of the species. Therefore, correcting for differential isotopologue distribution is based on the deduction of the intensity of each isotopologue of a species from the determined monoisotopic peak intensity. 

Taken together, the total ion intensity /totaiW of isotopologue cluster of a lipid species is 

Zj has previously been called the type I isotope correction factor [22] n and s are the numbers of total carbon atoms in the species of interest and the selected internal standard, respectively / and are the monoisotopic peak intensities of the species and the internal standard, respectively c and are the concentration of the species of interest and the internal standard, respectively. The dots represent the contribution of other isotopologues which contain more than two atoms. These terms can be ignored in most cases without affecting the accuracy of quantification. 

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The physical and thermodynamic properties of elemental hydrogen and deuterium and of their respective oxides illustrate the effect of isotopic mass differences. 

The measurement of both 14C and 12C is necessary to estimate the radiocarbon age on the basis of the isotopic ratio 14R measuring 13C allows us to evaluate the effects of isotopic fractionation, according to which the measured radiocarbon concentration can be corrected. For details, see Aitken.1... 

The effect of isotopic or chemical substitutions on the vibrational frequency leads to the identification of the species that comprise a defect complex. For example, the large frequency shift that results upon the substitution of D for H leads to an unambiguous identification of the H motions. For a series of chemically similar complexes, such as the acceptor-H complexes, the frequency shifts that occur for group III substitutions show that the acceptor is indeed involved in the complex. 

The effect of isotopic substitution on the position of a peak can also be estimated using this relationship. 

The concept of the atom as the smallest particle of matter (from the Greek word for indivisible) was promulgated by John Dalton about 1803. Within about a century and a quarter of scientific investigation which will be briefly described in this chapter, this concept yielded the idea of the periodic table and the understanding of the periodic table including the nuclear atom, the concept of isotopes, and the discovery of the majority of the isotopes which are used in the studies of the isotope effects. It is appropriate to point out that this book deals with the study of the effect of isotopic substitution on the physical and chemical properties of molecular (or atomic) systems. The book does not deal with the use of isotopes as tracers, a use which usually depends on the assumption that isotope effects are small and can be ignored in tracer studies. 

Figure 1. Translation, rotation, and vibration of a diatomic molecule. Every molecule has three translational degrees of freedom corresponding to motion of the center of mass of the molecule in the three Cartesian directions (left side). Diatomic and linear molecules also have two rotational degrees of freedom, about rotational axes perpendicular to the bond (center). Non-linear molecules have three rotational degrees of freedom. Vibrations involve no net momentum or angular momentum, instead corresponding to distortions of the internal structure of the molecule (right side). Diatomic molecules have one vibration, polyatomic linear molecules have 3V-5 vibrations, and nonlinear molecules have 3V-6 vibrations. Equilibrium stable isotope fractionations are driven mainly by the effects of isotopic substitution on vibrational frequencies.

Obviously, mass spectrometry is ideally suited for distinguishing between isotopic species, and isotopic labeling is used for mechanistic as well as analytical applications (Chap. 3.2.9). However, the effect of isotopic substitution is not only an effect on ionic mass, but isotopic substitution can have several simultaneous effects, and this complication sometimes produces results which are at first sight curious. [65]... 

This situation applies with weak hydrogen bonds at one extreme and very strong hydrogen bonds at the other with H and D confined to the same potential well. However, when the potential energy barrier has fallen sufficiently to allow the proton to escape the confines of its parent well, but leaves the deuteron trapped, then different values of the isotopic ratio can be observed (Fig. 7). The effect of isotopic exchange is now much more than merely one of doubling the reduced mass of the vibrating bond. When the proton is above the barrier, the force constant of the A—H bond, k A.—H),... 

Since potential energy surfaces of isotopic molecules are nearly identical, equilibrium isotope effects can only arise from the effect of isotopic mass on the nuclear motions of the reactants and products. Thus the ratio can be expressed in terms of partition functions for nuclear... 

Any observable effect of isotopic substitution on the rate or extent of a chemical/physical process. Equilibrium isotopic perturbation measurements can provide valuable information about kinetic isotope effects on enzymic catalysis. NMR shift difference measurements are also useful in detecting the effects of isotopic substitution on a fast (degenerate) equilibrium between two species differing only in their specific isotopic substitution . 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 ... 

Static dielectric measurements [8] show that all crystals in the family exhibit a very large quantum effect of isotope replacement H D on the critical temperature. This effect can be exemphfied by the fact that Tc = 122 K in KDP and Tc = 229 K in KD2PO4 or DKDP. KDP exhibits a weak first-order phase transition, whereas the first-order character of phase transition in DKDP is more pronounced. The effect of isotope replacement is also observed for the saturated (near T = 0 K) spontaneous polarization, Pg, which has the value Ps = 5.0 xC cm in KDP and Ps = 6.2 xC cm in DKDP. As can be expected for a ferroelectric phase transition, a decrease in the temperature toward Tc in the PE phase causes a critical increase in longitudinal dielectric constant (along the c-axis) in KDP and DKDP. This increase follows the Curie-Weiss law. Sc = C/(T - Ti), and an isotope effect is observed not only for the Curie-Weiss temperature, Ti Tc, but also for the Curie constant C (C = 3000 K in KDP and C = 4000 K in DKDP). Isotope effects on the quantities Tc, P, and C were successfully explained within the proton-tunneling model as a consequence of different tunneling frequencies of H and D atoms. However, this model can hardly reproduce the Curie-Weiss law for Sc-... 

The ability to compute the free energy difference between two minima on a PES allows the effect of isotopic substitution on the equilibrium constant between them to be calculated. Similarly, a kinetic isotope effect (KIE) can be predicted from the effect of isotopic substitution on the free energy difference between a minimum and a TS (i.e., a free energy of activation). 

Information about the extent and nature of the bond making and breaking steps in the transition state may sometimes be obtained by studying the effects of isotopic substitution on the reaction rates. The effects may be divided into two classes, depending on the position of the substitution. 

Most papers dealing with the spectrum of the carbonate ion CO7 neglect to mention the important paper by Decius, Malan and Thompson 42> on the effect of intermolecular forces on molecules in the crystalline state which refer specifically to the out-of-plane bending mode of CO In this paper they derive the dependence of this mode upon the 12C-13C isotopic ratio. Sterzel and Chlorinski 43) also discuss the effect of isotopes upon the CO2" vibrations these two papers should be consulted when assigning C03 -spectra because the modes depend very much upon the t2C-13C ratio. Orville-Thomas 20> has discussed the dependence of the C03 force constants upon the C-O distance, and shows that this leads to a bond intermediate between a single and a double bond. 

Spectra of the CH3CHOH radical have been obtained from the radiolysis of pure and aqueous ethanol77. These are shown in Fig. 11. The assignment is based on a combination of esr studies in the solid state, the effects of isotopic substitution, and product analysis. In aqueous solution the radical arises via the reactions... 

For isotopes other than those of hydrogen, equilibrium isotope effects are usually small (ca. <3%), and such isotopes are more often used in labelling studies with their concentrations at a particular position reflecting the probability of a mechanistic pathway, without consideration of the effects of isotopic substitution upon stability of isotopomers. Positional exchange in recovered reactants, for example, provides supporting evidence of intermediates and their nature, and Scheme 9.15 illustrates one dissociative process and one associative process. 

Plasma MS is usually based on quadrupole mass analysers. The atmospheric ICP, optimised for ion formation, is placed on its side facing a sample cone (Fig. 4.3). The mass spectrometer operates at reduced pressure and therefore a two- or three-stage differentially pumped interface is needed to transfer the ions from the plasma to the mass analyser. The interface for GC-ICP-MS is generally the same as for ICP emission systems. In one of the earliest GC-MS speciation studies (Chong and Houk, 1987) a packed GC column was used to obtain mass spectra of organic compounds with detection limits in the range 0.001-500 ngs The effects of isotopic fractionation by natural physico-chemical processes were also studied. 

Furthermore, the generality of the effect of isotopic enantiomers in chiral initiation was exemplified using chiral tolyl methanol-a-d, 2,2-naphthyl... 

The ratio of a sample is measured in relation to a standard to improve the accuracy and precision of accelerator mass spectrometry measurements (Elmore and Phillips, 1987). Multiplying the ratio by 1000 results in the delta (del) values having units of parts per thousand, also know as per mil (%o). For standards, it is necessary to use wood from trees harvested before about 1850 pre-industrial, to avoid the Suess effects. The standard value for pre-industrialized atmospheric CO2 is 13.56 dpm g-1 or 14C/C equals 1.176 x 10-12 (Broecker and Peng, 1982). A correction term involving the effects of isotopic fractionation (IF) are also subtracted out of this equation. Isotopes are fractionated due to physical and chemical reactions (more details in the following section), thereby making the abundance of carbon isotopes (12C, 13C, and 14C) different in plants (Faure, 1986). The National Bureau of Standards currently provides an oxalic acid 14C standard that is used for this correction however, there have been many problems associated with development of this standard (Craig, 1954, 1961 Stuiver and Polach, 1977). 

The effect of isotopes substitution on fast nuclear vibrations and, therefore, nuclear tunneling and KIE can be derived from Marcus-Jortner Eq. 2.17. As seen from Eq. 2.17, both energy activation and preexponential factors are dependent on the vibration frequency. 

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