Isotopic labeling coupled systems

One of the possibilities is to study experimentally the coupled system as a whole, at a time when all the reactions concerned are taking place. On the basis of the data obtained it is possible to solve the system of differential equations (1) simultaneously and to determine numerical values of all the parameters unknown (constants). This approach can be refined in that the equations for the stoichiometrically simple reactions can be specified in view of the presumed mechanism and the elementary steps so that one obtains a very complex set of different reaction paths with many unidentifiable intermediates. A number of procedures have been suggested to solve such complicated systems. Some of them start from the assumption of steady-state rates of the individual steps and they were worked out also for stoichiometrically not simple reactions [see, e.g. (8, 9, 5a)]. A concise treatment of the properties of the systems of consecutive processes has been written by Noyes (10). The simplification of the treatment of some complex systems can be achieved by using isotopically labeled compounds (8, 11, 12, 12a, 12b). Even very complicated systems which involve non-... 

Hammaker et al (34) deduced approximate expressions for the frequencies of the two infrared active modes of the system composed of a central adsorbed molecule of one isotopic species coupled to an environment of the other species. In one mode the labelled molecule vibrates in phase with its neighbours giving a frequency tojj higher than the frequency of the other mode where the motion is 180° out of phase. The two frequencies are related to wJ (the frequency of the 2-D lattice in the absence of the labelled molecule) and u>2 (the frequency of the labelled molecule in the absence of surrounding molecules, i.e. a labelled single-ton) by... 

Let us consider the photolysis of DBK on NaX as a standard system (Table 3). Under a vacuum or in an argon atmosphere, the major product is 1,2-diphenyl ethane (DPE) which results from diffusional separation of the primary radical pair, followed by decarbonylation and random coupling of the benzyl radicals produced in the secondary radical pair. These results, along with isotopic labelling experiments, show that diffusional motion of primary and secondary radical pairs is fast compared to coupling or decarbonylation reactions of the primary or the secondary radical pairs. The results for... 

Paramagnetic species with g-factor and hyperfine coupling anisotropy were analysed by simulations at an early stage in frozen solutions of, for instance, copper enzymes [25]. In this section the powder spectra of two well-known species, the NO2 molecule and the isotope labelled COj anion radical are used to illustrate visual and simulation procedures for the analysis. The reader is referred to the classical textbook by Carrington and McLachlan [1] for an account of the electronic structures of these isoelectronic molecules (23 electron system) based on ESR data. 

Although the idea of dynamically similar but thermodynamically different polymers seems at first to be a rather contrived and artifical model, there is one class of systems that are actually quite close realisations of it. These are pairs of isotopically substituted polymers of high relative molecular mass, approaching those relative molecular masses for which phase separation would take place. The composition dependence of the mutual diffusion coefficient for such diffusion couples has been measured directly for interfaces between polystyrene and deuterated polystyrene (Green and Doyle 1987) and the results are in excellent agreement with theory (figure 4.21). This also means that we can use equation (4.4.7) to check whether isotopic labelling is likely to perturb an attempted self-diffusion measurement. 

The use of infrared to probe the details of interactions (especially in hydrogen-bonded systems) was demonstrated nicely by Keiderling s group [108]. Coupling the use of specific isotopic labeling with the aid of ab initio calculations for the analysis, they were able to establish the pattern of cross-strand coupling in a (3-hairpin peptide. 

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