Information from relaxation data

The above describes the fundamental processes that determine the relaxation behavior of spins due to dipolar interactions. Thus, magnitudes of the relaxation parameters Tj, Tj and the NOE for a spin under consideration are determined by the number, strength and distance of neighboring dipoles, and the abundance of motions of these dipoles near the Larmor frequency of the nucleus. Quantitative determination of the contribution of molecular motions to the relaxation parameters of spins in macToraolecules is fraught with complications, which we describe here in brief (see Ref. 61 for a more complete discussion). 

There is less of a problem in relaxation, at least for C-H bonds, because the geometry is fixed (bond length, wl.l A) and the directly bonded protons will be the only ones sufficiently close to cause substantial relaxation. In this case, relaxation data can be analysed without knowing precise geometries. It is in principle possible to 

1 Slichter, C.P. (1978) Principles of Magnetic Resonance, 2nd Edn., Springer, New York. 

2 Farrar, T.C. and Becker, E.D. (1971) Pulse and Fourier Transform NMR Introduction to Theory and Methods, Academic Press, New York. 

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Quadrupolar Interactions. - Quadrupolar coupling constants are sensitive probes of hydrogen bonding. Their accurate knowledge is a major prerequisite when trying to extract dynamical information from relaxation data of quadrupo-... 

NMR provides one of the most powerful techniques for identification of unknown compounds based on high-resolution proton spectra (chemical shift type integration relative numbers) or 13C information (number of nonequivalent carbon atoms types of carbon number of protons at each C atom). Structural information may be obtained in subsequent steps from chemical shifts in single-pulse NMR experiments, homo- and heteronuclear spin-spin connectivities and corresponding coupling constants, from relaxation data such as NOEs, 7) s 7is, or from even more sophisticated 2D techniques. In most cases the presence of a NOE enhancement is all that is required to establish the stereochemistry at a particular centre [167]. For a proper description of the microstructure of a macromolecule NMR spectroscopy has now overtaken IR spectroscopy as the analytical tool in general use. 

Significantly reduced rates for proton-deuterium exchange prove that the corresponding amide proton is either involved in stable hydrogen bonds, shielded from solvent access or both. Because of the ambiguity in interpretation, additional information about the persistence of hydrogen bonds stemming from structure calculations or from relaxation data should be available. 

This approach yields spectral densities. Although it does not require assumptions about the correlation function and therefore is not subjected to the limitations intrinsic to the model-free approach, obtaining information about protein dynamics by this method is no more straightforward, because it involves a similar problem of the physical (protein-relevant) interpretation of the information encoded in the form of SD, and is complicated by the lack of separation of overall and local motions. To characterize protein dynamics in terms of more palpable parameters, the spectral densities will then have to be analyzed in terms of model-free parameters or specific motional models derived e.g. from molecular dynamics simulations. The SD method can be extremely helpful in situations when no assumption about correlation function of the overall motion can be made (e.g. protein interaction and association, anisotropic overall motion, etc. see e.g. Ref. [39] or, for the determination of the 15N CSA tensor from relaxation data, Ref. [27]). 

Despite the limitations discussed in earlier Subsections, relaxation time data are useful for characterizing porous media. For instance, NMR well logging experiments provide valuable information that may be critical in determining whether a particular borehole will be profitable. As well as pore size information, other parameters characterizing the pore space have also been obtained from relaxation data. 

To extract information about xj from NMR data, the transverse relaxation time Tj may be used as well as the longitudinal time T. For gaseous nitrogen it was done first with Ti in [81] and confirmed later [82] when T was measured and used for the same goal. The NMR linewidth of 15N2 is the inverse of T2, and the theory, relating to Ti to x.1, is well known [39, 83]. For the case of diatomic and linear molecules the formula is... 

The electron spin resonance (ESR) technique has been extensively used to study paramagnetic species that exist on various solid surfaces. These species may be supported metal ions, surface defects, or adsorbed molecules, ions, etc. Of course, each surface entity must have one or more unpaired electrons. In addition, other factors such as spin-spin interactions, the crystal field interaction, and the relaxation time will have a significant effect upon the spectrum. The extent of information obtainable from ESR data varies from a simple confirmation that an unknown paramagnetic species is present to a detailed description of the bonding and orientation of the surface complex. Of particular importance to the catalytic chemist... 

As another example, the three-dimensional structure of Cytochrome c has been determined on the basis of structural information from pseudocontact paramagnetic chemical shifts, Curie-Dipolar cross-correlation, secondary structure constraints, dipolar couplings and 15N relaxation data [103]. This protein has a paramagnetic center, and therefore the above-mentioned conformational restraints can be derived from this feature. Dipolar couplings do not average to zero because of the susceptibility tensor anisotropy of the protein. The structure determination of this protein without NOE data gives an RMSD (root... 

Several spectroscopic techniques, namely, Ultraviolet-Visible Spectroscopy (UV-Vis), Infrared (IR), Nuclear Magnetic Resonance (NMR), etc., have been used for understanding the mechanism of solvent-extraction processes and identification of extracted species. Berthon et al. reviewed the use of NMR techniques in solvent-extraction studies for monoamides, malonamides, picolinamides, and TBP (116, 117). NMR spectroscopy was used as a tool to identify the structural parameters that control selectivity and efficiency of extraction of metal ions. 13C NMR relaxation-time data were used to determine the distances between the carbon atoms of the monoamide ligands and the actinides centers. The II, 2H, and 13C NMR spectra analysis of the solvent organic phases indicated malonamide dimer formation at low concentrations. However, at higher ligand concentrations, micelle formation was observed. NMR studies were also used to understand nitric acid extraction mechanisms. Before obtaining conformational information from 13C relaxation times, the stoichiometries of the... 

The applications of 13C nuclear relaxation in the peptide field have been reviewed very recently (Deslauriers and Smith, 1976). We can therefore restrict the discussion here to a few comments. It was pointed out that the general assumption that relaxation of all carbon atoms of a peptide are dipolar is not necessarily true (Cutnell et al., 1975). It is emphasized that NOE measurements should be obligatory before motional assumptions are made from 7j data. The kind of information one obtains from relaxation work for small peptides of perhaps up to 10 amino-acid residues may be seen from the... 

It is usually the case that there is a considerable contact shift on the resonances of nuclei of atoms in the first coordination sphere of Ln(III) ions. The contact shifts can be separated from the dipolar shifts by quite simple procedures15,16) involving the study of complexes of the ligand with different Ln(III) assuming that the dipole shifts have axial symmetry, Fig. 2. The deduced contact shifts are quite useful in that they show which atoms are directly bound to Ln(III) in the complexes. We shall not concern ourselves further with contact terms in this article as no detailed structural information is available from them. The coordination sphere is usually generated by the searches using only dipolar shift and relaxation data. 

Fortunately in a number of cases there is experimental information on these points from broad band pump/probe experiments when the anharmonicity A is larger than the linewidth but much smaller than the bandwidth 8(o of the laser. Then the 0-1 transition is seen as a bleaching signal and the 1-2 (66,67,71) as well as the 2-3 and often higher quantum number transitions (68,95) appear as new absorptions to an extent that depends on the pump intensity. A direct comparison of the total linewidths (1/T2) of these transitions, and the population relaxation times for the v = 1, v = 2 and perhaps higher levels can be obtained from such data. For N3 we found that ratio of the state to state relaxation from v = 2 to v = 1 was 1.8 times that for v = 1 to v = 0, not far from the harmonic value of 2 (50,95). However, the bandwidth of both transitions was roughly the same. 

One of the most widely used tools to assess protein dynamics are different heteronuclear relaxation parameters. These are in intimate connection with internal dynamics on time scales ranging from picoseconds to milliseconds and there are many approaches to extract dynamical information from a wide range of relaxation data (for a thorough review see Ref. 1). Most commonly 15N relaxation is studied, but 13C and 2H relaxation are the prominent tools to characterize side-chain dynamics.70 Earliest applications utilized 15N Ti, T2 relaxation as well as heteronuclear H- N) NOE experiments to characterize N-H bond motions in the protein backbone.71 The vast majority of studies applied the so-called model-free approach to translate relaxation parameters into overall and internal mobility. Its name contrasts earlier methods where explicit motional models of the N-H vector were used, for example diffusion-in-a-cone or two- or three-site jump, etc. Unfortunately, we cannot obtain information about the actual type of motion of the bond. As reconciliation, the model-free approach yields motional parameters that can be interpreted in each of these motional models. There is a well-established protocol to determine the exact combination of parameters to invoke for each bond, starting from the simplest set to the most complex one until the one yielding satisfactory description is reached. The scheme, a manifestation of the principle of Occam s razor is shown in Table l.72... 

We find LSV to be the kinetic method which gives the most detailed information related to the mechanism of the reaction of the intermediate. As will be discussed in some detail later, the reaction orders in all species appearing in the rate law can be derived from the LSV response (Parker, 1981f). The reaction orders in substrate and primary intermediate are not directly separable using the data from the other techniques. Because of the possibility of obtaining homogeneous relaxation data in addition to the direct response, spectroelectrochemistry can offer more kinetic detail than the other direct techniques. 

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