Cross-correlated Relaxation Experiments

3 Cross-Correlated Relaxation Experiments. - dipole-dipole (DD) 

The CSA/DD cross-correlated relaxation leads to the differential attenuation of the doublet components of HN groups, thus allowing the evaluation 

The distortions in the measured cross-correlated relaxation rates due to violations of secular approximation and differential effects of the non-symmetri-cal coherence transfer periods flanking the relaxation measurement delay can be minimised with the symmetrical reconversion approach introduced in the previous review period. In this approach four experiments are recorded with all combinations of the coherence transfer periods, producing automatic correction of the measured relaxation rate. The method was applied to the measurement of cross-correlated relaxation between CO CSA and long-range CO-HA DD interactions that depends on the backbone angle ip. The cross-correlated rate is evaluated from the relaxation of 2C yNz and 4H zC yNz coherences, recorded separately. The sequence is based on HNCO and HN(CO)CA experiments. The rates measured for ubiquitin show good correlation with the theoretical values. 

The CH-CH DD/DD cross-correlated relaxation in protein side-chains can be easily measured in HCCH experiment. For larger proteins the resolution of the experiment may not be sufficient to extract the relaxation parameters. Car-lomagno et al proposed a modification of HBHA(CBCACO)NH sequence for the measurement of C H-C H DD/DD cross-correlated relaxation in the spectra 

Motions slower than the overall rotational correlation time, including conformational exchange on the ps-ms time scale, can lead to effects similar to cross-correlated relaxation in multiple-quantum coherences. These slow motions can only modulate isotropic spin interactions, such as J-couplings and isotropic chemical shifts, as the anisotropic interactions are already averaged out by the fast dynamics. The cross-correlated modulation of the isotropic chemical shifts (CSM) of two nuclei has the same effect as their CSA/CSA cross-correlation and can be measured from the difference in relaxation rates of ZQ and DQ coherences of the two nuclei. Two publications presented different schemes for the measurement of the CSM/CSM cross-correlated relaxation. Majumdar and Ghose proposed to evaluate the cross-relaxation rates from the conversion 

The usefulness of cross-correlated relaxation measurements for deriving structural information was described previously in several publications. More examples of that appeared in the reviewed year. Kloiber and Konrat presented a method for measurement of (DD) / (CSA) cross- 

Riek demonstrated the correlation between hydrogen bond length in Watson-Crick base pairs with (CSA)/ N--- H (DD with proton acceptor) cross-correlated relaxation rates. The measurements are performed with modified 2D N- H-ZQ TROSY experiment. The cross-correlated relaxation rates are evaluated from the cross-peaks ratio in the spectra where the relaxation is either active or deactivated with a selective pulse. The hydrogen bond length is estimated from the ratio of cross-correlated relaxation rate involving DD interaction with the acceptor to the rate of the relaxation in the reference experiment involving DD interaction with the donor. 

Backbone torsion angles a and in oligonucleotides can be estimated from the DD/ CSA cross-correlated relaxation. A modified /-resolved 

2D CT T-DQ/ZQ-HCP experiment was proposed by Richter et al. for the relaxation rate measurement. The rate is evaluated from the intensities of the multiplet component of DQC and ZQC cross-peaks observed in a single spectrum. The cross-correlated relaxation has a complex dependence on several torsion angles some of which can be determined from the values of V(H,P) and V(C,P). 

In addition to structural information cross-correlated relaxation is used to monitor local dynamics on different time-scales. Combinations of cross-correlated relaxation rates involving backbone atoms can be used to analyse fast backbone motions. The authors suggested an experiment based on the HNCO sequence that allows one to measure T (C C ,NH ) + (C H, NC ), r (N,NC ) + and T (C, NH ) + 

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Cross-Correlated Relaxation Experiments. - Cross-correlated relaxation is usually evaluated from the comparison between a spectrum collected when the cross-correlated relaxation is active, and the reference spectrum with the suppressed cross-correlated relaxation. This approach relies heavily on the effective suppression of the cross-correlated relaxation, which is often difficult to assess. Two independent publications " suggested to use spin-state selection to monitor the relaxation of the individual doublet components and to derive the cross-correlated relaxation contribution from their difference. In such scheme artefacts from the incomplete suppression of one of the components appear in the separate spectrum region and do not interfere with the result. In addition, the number of the cross-peaks remains the same as in the corresponding HSQC spectrum, not creating additional overlap. Vasos et alP used S E element prior the transverse relaxation measurement period, while Bouguet-Bonnet et al opted for the S ED sequence. In addition, the later publication presents a version of the experiment that allows to measure both transverse and longitudinal relaxation rates. 

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. 

The DD-CSA cross-correlated relaxation, namely that between 13C-1H dipole and 31P-CSA, can also be used to determine backbone a and C angles in RNA [65]. The experiment requires oligonucleotides that are 13C-labeled in the sugar moiety. First, 1H-coupled, / - DQ//Q-II CP spectra are measured. DQ and ZQ spectra are obtained by linear combinations of four subspectra recorded for each q-increment. Then, the cross-relaxation rates are calculated from the peak intensity ratios of the doublets in the DQ and ZQ spectra. The observed cross-correlation rates depend on the relative orientations of CH dipoles with respect to the components of the 31P chemical shift tensor. As the components of the 31P chemical shift tensor in RNA are not known, the barium salt of diethyl phosphate was used as a model compound with the principal components values of -76 ppm, -16 ppm and 103 ppm, respectively [106]. Since the measured cross-correlation rates are a function of the angles / and e as well, these angles need to be determined independently using 3/(H, P) and 3/(C, P) coupling constants. 

For the measurement of cross-correlated relaxation rates, there are mainly three methods that have been used in practice. In the /-resolved constant time experiment, the multiplet Hnes exhibiting differential relaxation are resolved by the f couplings, and the line width is translated into intensity in a constant time experiment (Fig. 7.19a,d). In the J-resolved real time experiment the line width of each multiplet line is measured instead (Fig. 7.19b, d). This experiment has been applied so far only for the measurement of... 

The method relies on the measurement of cross-correlated relaxation rates in a constant time period such that the cross-correlated relaxation rate evolves during a fixed time r. In order to resolve the cross-correlated relaxation rate, however, the couplings need to evolve during an evolution time, e.g. tt. The first pulse sequence published for the measurement of the cross-correlated relaxation rate between the HNn and the Ca j,Ha i vector relied on an HN(CO)CA experiment, in which the Ca chemical shift evolution period was replaced by evolution of 15N,13C double and zero quantum coherences (Fig. 7.20). 

Fig. 7.20 J-resolved constant r HN (CO)CA experiment for the measurement of cross-correlated relaxation rates, especially rcNH The experiment has two 90° (15N) pulses (shaded part) simulta-...

Fig. 7.23 shows the quantitative r sequence that measures the same rcNH CH cross-correlated relaxation rate as the sequence of Fig. 7.20. Again N-C DQ/ZQ coherence is excited using an HN(CO)CA experiment. Because of cross-correlated relaxation, N-C DQ/ ZQ coherence evolves as described in Eq. (7) ...

Therein, cross-correlated relaxation T qHj c h °f the double and zero quantum coherence (DQ/ZQ) 4HizCixCjj generated at time point a creates the DQ/ZQ operator 4HjzCjJCiy. In the second part of the experiment, the operator 4HJZCjxQy is transferred via a 90° y-pulse applied to 13C nuclei to give rise to a cross peak at an(i... 

By combining the quantitative approach [23] to extract cross-correlated relaxation with resolution enhancement methods using restricted coherence transfer in a so-called forward directed TOCSY [27], Richter et al. could determine the ribose sugar conformation for all but two residues in a uniformly 13C,15N labeled 25mer RNA [28] and compare them to 3J(H, H) values determined using a forward-directed HCC-TOCSY-CCH-E.COSY experiment [29]. 

As an example of the measurement of cross-correlated relaxation between CSA and dipolar couplings, we choose the J-resolved constant time experiment [30] (Fig. 7.26 a) that measures the cross-correlated relaxation of 1H,13C-dipolar coupling and 31P-chemical shift anisotropy to determine the phosphodiester backbone angles a and in RNA. Since 31P is not bound to NMR-active nuclei, NOE information for the backbone of RNA is sparse, and vicinal scalar coupling constants cannot be exploited. The cross-correlated relaxation rates can be obtained from the relative scaling (shown schematically in Fig. 7.19d) of the two submultiplet intensities derived from an H-coupled constant time spectrum of 13C,31P double- and zero-quantum coherence [DQC (double-quantum coherence) and ZQC (zero-quantum coherence), respectively]. These traces are shown in Fig. 7.26c. The desired cross-correlated relaxation rate can be extracted from the intensities of the cross peaks according to ... 

Fig. 7.26 J-resolved constant r C,H-HSQC experiment (a) to measure the cross-correlated relaxation rates in RNA with a geometry given in b.

Due to the fact that cross-correlated relaxation depends linearly on the correlation time, it can be used to determine the conformation of ligands when bound to target molecules, provided that the off rate is fast enough to enable detection of the cross-correlated relaxation rate via the free ligand [33, 34]. The conditions under which such an experiment can be performed are similar to those found for transferred NOEs [35], and, for Kd values... 

Fig. 7.27 a Transferred NOESY, b cross and c reference traces from the transferred rcCH CH-HCCH experiment that display the dependence of the rate of the transferred cross-correlated relaxation... 

Yang, D. W., Konrat, R., and Kay, L. E. (1997). A multidimensional NMR experiment for measurement of the protein dihedral angle psi based on cross-correlated relaxation between (H alpha-13C alpha) XH dipolar and 13C (carbonyl) chemical shift anisotropy mechanisms. J. Am. Chem. Soc. 119,11938-11940. 

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). 

In liquid-state NMR, spin relaxation due to cross-correlation of two anisotropic spin interactions can provide useful information about molecular structure and dynamics. These effects are manifest as differential line widths or line intensities in the NMR spectra. Recently, new experiments were developed for the accurate measurement of numerous cross-correlated relaxation rates in scalar coupled multi-spin systems. The recently introduced concept of transverse relaxation optimized spectroscopy (TROSY) is also based on cross-correlated relaxation. Brutscher outlined the basic concepts and experimental techniques necessary for understanding and exploiting cross-correlated relaxation effects in macromolecules. In addition, he presented some examples showing the potential of cross-correlated relaxation for high-resolution NMR studies of proteins and nucleic acids. 

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