NOESY cross-relaxation rate

Fig. 6. Basic scheme of the NOESY sequence which provides essentially homo-nuclear cross-relaxation rates from a double Fourier transform of the signal S( 2)-...

To get better insight into the importance of temperature selection, we have recorded a series of NOESY spectra of cyclo(Pro-Gly) at different temperatures. The dashed lines in fig. 6 show theoretical dependence of the laboratory frame cross-relaxation rate on the correlation time (according to... 

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. 

Cross-relaxation rates and interproton distances in cyclo(Pro-Gly) from the full matrix analysis of NOESY spectrum recorded at Tm = 80 ms and T = 233 K. Cross-relaxation rates are obtained from the volumes shown in table 2 according to eq. (11) by Matlab (Mathworks Inc). Error limits were obtained from eq. (27) with Aa = 0.015 (table 2). 

Feenstra KA, Peter C, Scheek RM, et al. A comparison of methods for calculating NMR cross-relaxation rates (NOESY and ROESY intensities) in small peptides. J Biomol NMR 2002 23 181-194. 

Recently NOESY MAS was used to study molecular motions in technically relevant materials such as rubbers [46, 47]. For the evaluation of these parameters, it is necessary to understand the cross-relaxation process in the presence of anisotropic motions and under sample spinning. Such a treatment is provided in [47] and the cross-relaxation rates were found to weakly depend on fast motions in the Larmor-frequency range and strongly on slow motions of the order of the spinning frequency vR. Explicit expressions for the vR dependent cross-relaxation rates were derived for different motional models. Examples explicitly discussed were based on a heterogeneous distribution of correlation times [1,8,48] or on a multi-step process in the most simple case assuming a bimodal distribution of correlation times [49-51]. 

Fig. 18. The pulse sequence used for the two-dimensional NOESY experiment for measuring H- H cross-relaxation rates in soft polymers. The entire experiment is conducted under magic-angle spinning. Gradient pulses are used to remove unwanted coherences, as this allows for much faster experiments than phase cycling.

Most of protein structural information from NMR is obtained in the form of nuclear Overhauser effects or NOEs between pairs of protons that are less than 6 A apart through space. An NOE between a spin pair carries distance information, but only short distances are observed because NOEs have an inverse sixth power dependence on distance. However, the distance cannot be uniquely determined given a measured NOE intensity without making some assumption about the environment of the spin pair and the motion of the vector between them. The simplest model for obtaining a distance from cross peak intensities in a nuclear Overhauser effect spectrum (NOESY) is the isolated ri d spin pair (RRNN - rigid rotor nearest neither) approximation (Jardetzky and Roberts, 1981). In this approximation the observed cross peak intensity, which is proportional to the cross relaxation rate, is related to a sini e intemudear distance, r. 

If we have tiie relaxation matrix and an approximate structure, we can back calculate the NOESY spectra. The problem with the relaxation matrix method is that some of the cross relaxation rates are not observed due to spectral overlap, dynamic averaging and exchange. Boelens et al. (1988 1989) attempted to solve the problem by supplementing the imobserved NOEs with those calculated from a model structure. From a starting structure, the authors use NOE build-ups, stereospedfic assignments and model-calculated order parameters to construct the relaxation matrix. An NOE matrix is then calculated. This NOE matrix is used to calculate the relaxation matrix and it is in turn used to calculate the new distances. The new distances are then used to calculate a new model structure. The new structure can be used again to construct a new NOE matrix and the process can be iterated to improve the structures. The procedure is called IRMA or iterated relaxation matrix analysis. 

It is possible to derive the absolute value of the cross relaxation rate from NOESY spectra provided one diagonal peak is resolved. Most of the time, this is not the case or not done for the following reason when one intemu-clear distance is known in a molecule, e.g., between two geminal protons or two vicinal protons on an aromatic ring, the cross-relaxation rates of all proton proton pairs in this molecule can be calibrated with this distance and thus be translated directly into the intemuclear distance. 

Transfer NOE measures the NOESY of a drug in the presence and absence of the target molecule. The cross-relaxation rates are averages due to the conformation of the free and the bound form. Comparison of the NOEs... 

Cross-relaxation rates and the ensuing interproton distances are determined by Eq.[2], which requires full relaxation. However, with Eq. [4] it is possible to extrapolate from partially relaxed NOE intensities to the fully relaxed quantities (32, 34). This approach, however, requires that accurate Ti values are available for individual protons, which might be an obstacle in the case of macromolecules. Another possibility to correct for partial relaxation effects utilizes the ratio between above- and below-diagonal crosspeak intensities which in the case of a partially relaxed NOESY spectrum deviate significantly from 1. The details of this approach are beyond the scope of this chapter and have been described elsewhere (35). Both correction procedures have been implemented in our program SYMM (35), which we have used for the correction of the SRP 28mer NOESY data, which had been acquired with a typical, short repetition delay of 2.5 sec. 

Dipolar cross-relaxation rates, and thus distances, can be determined through NOESY or ROESY experiments using various approaches. The measurement of build-up rates involves the recording of several NOESY spectra with different mixing times. To ensure equal conditions, the measurements should be made in succession. The integrals of cross peaks are determined, and the volumes are plotted as a function of mixing time ... 

In this context, it is also worth noting that alternative methods exist for quantitative comparisons to NOESY intensities, based mainly on iterative refinements of the rate matrix itself. These models provide a translation from observed intensities to cross-relaxation rates, providing a useful intermediate step in the generation of structural and dynamic models that fit observed data. Much work remains to be done to determine the best approach to refinement and the benefits of going beyond the more common conventional level of structure determinations that uses distance bounds derived by empirical calibration from short-mixing time experiments. 

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