Relaxation measurement, interproton distances

This simple theoryis based on the expectation that, to a reasonable degree of approximation, proton-proton, dipolar contributions to the measured spin-lattice relaxation-rate are pairwise additive and decrease as a simple sixth power of the interproton distance. The simplified version of the dipole-dipole mechanism is summarized in the following two equations for spin i coupled intramolecularly with a group of spins j... 

Thus, identification of all pairwise, interproton relaxation-contribution terms, py (in s ), for a molecule by factorization from the experimentally measured / , values can provide a unique method for calculating interproton distances, which are readily related to molecular structure and conformation. When the concept of pairwise additivity of the relaxation contributions seems to break down, as with a complex molecule having many interconnecting, relaxation pathways, there are reliable separation techniques, such as deuterium substitution in key positions, and a combination of nonselective and selective relaxation-rates, that may be used to distinguish between pairwise, dipolar interactions. Moreover, with the development of the Fourier-transform technique, and the availability of highly sophisticated, n.m.r. spectrometers, it has become possible to measure, routinely, nonselective and selective relaxation-rates of any resonance that can be clearly resolved in a n.m.r. spectrum. 

This simple relaxation theory becomes invalid, however, if motional anisotropy, or internal motions, or both, are involved. Then, the rotational correlation-time in Eq. 30 is an effective correlation-time, containing contributions from reorientation about the principal axes of the rotational-diffusion tensor. In order to separate these contributions, a physical model to describe the manner by which a molecule tumbles is required. Complete expressions for intramolecular, dipolar relaxation-rates for the three classes of spherical, axially symmetric, and asymmetric top molecules have been evaluated by Werbelow and Grant, in order to incorporate into the relaxation theory the appropriate rotational-diffusion model developed by Woess-ner. Methyl internal motion has been treated in a few instances, by using the equations of Woessner and coworkers to describe internal rotation superimposed on the overall, molecular tumbling. Nevertheless, if motional anisotropy is present, it is wiser not to attempt a quantitative determination of interproton distances from measured, proton relaxation-rates, although semiquantitative conclusions are probably justified by neglecting motional anisotropy, as will be seen in the following Section. 

Interproton distances of 0-ceIIobiose (see Ref. 49) error 0.01 A. Interproton distances of 1,6-anhydro- -D-glucopyranose (see Ref. 49) error 0.01 A. Interproton distances of -cellobiose octaacetate (see Ref. 49) error 0.05 A. Interproton distances of 2,3,4-tri-0-acetyl-l,6-anhydro- -D-glucopyranose (see Ref. 49) error 0.05 A. Error calculations based on the errors of the measured quantities in Eqs. 18 and 21. Interproton distances calculated from the relaxation parameters of the methylene protons. 

The second separation method involves n.O.e. experiments in combination with non-selective relaxation-rate measurements. One example concerns the orientation of the anomeric hydroxyl group of molecule 2 in Me2SO solution. By measuring nonselective spin-lattice relaxation-rat s and n.0.e. values for OH-1, H-1, H-2, H-3, and H-4, and solving the system of Eq. 13, the various py values were calculated. Using these and the correlation time, t, obtained by C relaxation measurements, the various interproton distances were calculated. The distances between the ring protons of 2, as well as the computer-simulated values for the H-l,OH and H-2,OH distances was commensurate with a dihedral angle of 60 30° for the H-l-C-l-OH array, as had also been deduced by the deuterium-substitution method mentioned earlier. 

R,1S isomer. However, this proposal is tentative, because X-ray diffraction has shown that another specimen of asperlin, possessing a different crystalline form, has structure 49b. It should be noted that 1 tumbles somewhat anisotropically, with D /D = 1.3, as deduced from C relaxation measurements. If, however, the anisotropic motion of 1 were not properly corrected for, the largest error in the measurement of its interproton distances would not exceed 4%. 

The significance of n.m.r. spectroscopy for structural elucidation of carbohydrates can scarcely be underestimated, and the field has become vast with ramifications of specialized techniques. Although chemical shifts and spin couplings of individual nuclei constitute the primary data for most n.m.r.-spectral analyses, other n.m.r. parameters may provide important additional data. P. Dais and A. S. Perlin (Montreal) here discuss the measurement of proton spin-lattice relaxation rates. The authors present the basic theory concerning spin-lattice relaxation, explain how reliable data may be determined, and demonstrate how these rates can be correlated with stereospecific dependencies, especially regarding the estimation of interproton distances and the implications of these values in the interpretation of sugar conformations. 

Besides the advantage of the high-temperature measurements for quantitative interpretation of NOESY spectra, fig. 6 also indicates a special role of the high temperature maximum (note that positive cross-relaxation rates increase downward) of u". If the NOESY spectrum can be recorded at several temperatures around the cr" maximum, than calculated cross-relaxation rates can be used to obtain simultaneously the correlation time and the interproton distances without the necessity of any other knowledge. A typical problem in the cross-relaxation experiments is that cross-relaxation rate depends on two parameters, Tc and r (eq. (la)), and to calculate one of them the other must be independently known. However, the position of the maximum uniquely determines correlation time, and its height uniquely determines interproton distances. 

In going from the cross-relaxation rates to the interproton distances the relative error reduces and is six times smaller because of the sixth-power dependence. Error limits for the distances shorter then 3 A are meaningful but for the larger distances are unacceptably high. The large error limits indicate the obvious fact that distances cannot be measured for those spin pairs for which cross-peaks of appreciable volume are not detected. 

Two conformations of EpoA in complex with tubulin have been proposed on the basis of EC [26] and NMR [76, 96] data, respectively (Fig. 11). The tubulin-bound conformation of EpoA was determined by solution NMR spectroscopy [96] before the EC structure of EpoA bound to tubulin was available. The observation that, in a 100 1 mixture with tubulin, NOE cross-peaks of EpoA have negative sign, indicated that there is a fast exchange equilibrium in solution. This offered the opportunity to measure transferred NMR experiments, that report on the bound conformation of the ligand. A total of 46 interproton distances were derived from cross-peak volumes in tr-NOE spectra. However, these distance restraints did not suffice to define a unique conformation, as several distinct structures were consistent with them. Transferred cross-correlated relaxation (Sect. 2.2.1.3) provided the additional dihedral restraints that were crucial to define the bound conformation [96, 97], One requirement to measure CH-CH dipolar and CH-CO dipolar-CSA CCR rates is that the carbon atoms involved in the interaction are labeled with 13C. The availability of a 13C-labeled sample of EpoA offered the opportunity to derive seven of these dihedral angle restraints from tr-CCR measurements (Fig. 12). 

Clearly though, even a purely qualitative evaluation of the geometric influences of the anomeric and exo-anomeric effects based on a new independent measurement tool, has some considerable relevance and further studies on this topic are being actively pursued at this time. And to leave the more sceptical readers of this article with some positive food-for-thought, we summarise below in Table V the interproton distances, determined (22.) by proton relaxation measurement, for an organic molecule, the bicycloheptene portion of XII which is, according to all presently available criteria, tumbling isotropically. 

In general, care must be taken to recognize both intra- and intermolecular contributions to relaxation however, intermole-cular relaxation is often neglected in discussions of liquids at surfaces. With this assumption there is direct access to characterization of liquid dynamics at a surface (, 3,4). A study of the relaxation rate at different temperatures or frequencies provides a measure of the correlation time for water at the surface of a protein if the interproton distance, r, in the water molecule is known. The temperature dependence for longitudinal and transverse relaxation times predicted by equations 3 and 4 is shown schematically as the solid lines in Figure 1. At the position of the minimum in the longitudinal relaxation time, wTp is about 0.616 and Ti/To is about 1.6. 

NOE, a relaxation mechanism based upon magnetic dipole-dipole interactions of the nuclei, allows measurement of interproton distances with the basic r distance proportionality. This provides major distance restraints for strucmral calculations. Supplemented with additional data, such as original dihedral angle restraints obtained from J-coupUngs or more recent information about the orientation of the bond vectors connecting magnetically active nuclei with respect to the external magnetic field, this approach has been the foundation for NMR-based protein structure determination since its dawn in 1984 [11]. 

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