Relaxation cross-correlation

The cross-correlation effects between the DD and CSA interactions also influence the transverse relaxation and lead to the phenomenon known as differential line broadening in a doublet [40], cf Figure Bl.13.8. There is a recent experiment, designed for protein studies, that I wish to mention at tire end of this section. It has been proposed by Pervushin etal [4T], is called TROSY (transverse relaxation optimized spectroscopy) and... 

Werbelow L G 1996 Relaxation processes cross correlation and interference terms Encyclopedia of Nuclear Magnetic Resonance ed D M Grant and R K Harris (Chichester Wiley) pp 4072-8... 

In the case where x and y are the same, C (r) is called an autocorrelation function, if they are different, it is called a cross-correlation function. For an autocorrelation function, the initial value at t = to is 1, and it approaches 0 as t oo. How fast it approaches 0 is measured by the relaxation time. The Fourier transforms of such correlation functions are often related to experimentally observed spectra, the far infrared spectrum of a solvent, for example, is the Foiuier transform of the dipole autocorrelation function. ... 

The relaxation data for the anomeric protons of the polysaccharides (see Table II) lack utility, inasmuch as the / ,(ns) values are identical within experimental error. Obviously, the distribution of correlation times associated with backbone and side-chain motions, complex patterns of intramolecular interaction, and significant cross-relaxation and cross-correlation effects dramatically lessen the diagnostic potential of these relaxation rates. 

Elucidation of the stereostructure - configuration and conformation - is the next step in structural analysis. Three main parameters are used to elucidate the stereochemistry. Scalar coupling constants (mainly vicinal couplings) provide informa-hon about dihedral bond angles within a structure. Another way to obtain this information is the use of cross-correlated relaxation (CCR), but this is rarely used for drug or drug-like molecules. 

Fig. 9.10 (A) Definition of the dihedral angle d between the spin-pairs ij and k,l. (B) Cross-correlated relaxation can be detected by differences in intensities of the multiplet components of double quantum coherences...

Reif, B., Steinhagen, H., Junker, B., Reggelin, M., Griesinger, C. Determination of the orientation of a distant bond vector in a molecular reference frame by cross-correlated relaxation of nuclear spins. 

Brutscher, B. Prindples and applications of cross-correlated relaxation in biomolecules. Concepts. Magn. Reson. 2000, 12, 207-229. 

W. Transferred cross-correlated relaxation complements transferred NOE structure of an IL-4R-derived peptide bound to STAT-6. J. Am. Chem. Soc. 1999, 121, 1949-1953. 

Carlomagno, T., Sanchez, V. M., Blommers, M. J. )., Griesinger, C. Derivation of dihedral angles from CH-CH dipolar-dipolar cross-correlated relaxation rates a C-C torsion involving a quaternary carbon atom in epothilone A bound to tubulin. Angew. Chem. Int. Ed. 2003, 42, 2515-2517. 

CROSS-RELAXATION (AND CROSS-CORRELATION) SOLOMON EQUATIONS... 

As seen from the above theoretical developments, accessing geometrical (and stereochemical) information implies at least an estimation of the dynamical part of the various relaxation parameters. The latter is represented by spectral densities which rest on the calculation of the Fourier transform of auto- or cross-correlation functions. These calculations require necessarily a model for describing molecular reorientation... 

To this end, Ilin et al. have developed the T-HMBC experiment,120 which is itself based on an experiment developed by Vincent and Zwahlen for measuring dipole-dipole cross-correlation in polysaccharides.121 These experiments allow determining the conformation around glycosidic bonds based on 3Jch couplings and C-H-dipolar cross-correlated relaxation. 

At this point, only one type of H% is considered. To account for possible interference effects or cross correlations among two different relaxation interactions X and V with ranks l and /, respectively, the above equation is modified to give39... 

When l l, the above gives the so-called cross-correlation functions and the associated cross-correlation rates (longitudinal and transverse). Crosscorrelation functions arise from the interference between two relaxation mechanisms (e.g., between the dipole-dipole and the chemical shielding anisotropy interactions, or between the anisotropies of chemical shieldings of two nuclei, etc.).40 When l = 1=2, one has the autocorrelation functions G2m(r) or simply... 

When r s, one has interconversion between operators Br and Bs, and Rrs is a cross-relaxation rate. Note that the cross-relaxation may or may not contain interference effects depending on the indices l and /, which keep track of interactions Cyj and C,. Cross-correlation rates and cross-relaxation rates have not been fully utilized in LC. However, there is a recent report41 on this subject using both the 13C chemical shielding anisotropy and C-H dipolar coupling relaxation mechanisms to study a nematic, and this may be a fruitful arena in gaining dynamic information for LC. We summarize below some well known (auto-)relaxation rates for various spin interactions commonly encountered in LC studies. 

A new NMR method for the determination of the anomeric configuration in mono- and disaccharides has been described.18 The protocol is based on the different cross-correlated relaxation between proton chemical shift anisotropy (CSA) and dipolar relaxation for the a and (3 anomers of sugars. Only the ot-anomers show the presence of CSA (HI or Hl )-proton dipole (H1-H2 or Hl -H2 ) in the longitudinal relaxation of the anomeric protons. The method is of special interest for cases in which vicinal coupling constants between HI and H2 in both anomers a and (3 are similar and small, such as D-mannose, and the non-ambiguous description of the anomeric configuration needs additional measurements. 

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