NOESY interproton distances

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. 

Fig. 6. Normalized cross-peak volumes of five representative spin pairs from NOESY spectra of cyclo(Pro-Gly) at different temperatures, recorded with Tm = 300 ms. Circles, crossrelaxation rates calculated from eq. (27a) using only the linear term. Dashed lines were drawn according to eqs (la) and (2a) using uiol2n = 500 MHz (actual resonance frequency) and interproton distances, r, from the model (table 1). Solid lines connect the points of one spin pair at different temperatures. Experimental temperatures indicated at the top are superimposed on the correlation time axis according to eq. (5) logTc 1/T. Reciprocal temperature axis is scaled and shifted to produce the best visual overlap of the theoretical curves and experimental data points. Inset represents the indicated region around the crossrelaxation rate maximum in the extreme-narrowing regime, magnified 14 times.

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). 

In a typical free NOESY experiment of a molecule in the absence of any interacting protein, cross-peak volumes are interpreted in terms of a set of interproton distances r that can be used as distance restraints in structure determination procedures, like restrained simulated annealing protocols [44], In a tr-NOESY, i.e. a NOESY measured under exchange-transferred conditions in the presence of a protein - i.e., an excess of soluble ligand is in fast exchange equilibrium with a smaller amount of protein-bound ligand -, these r reflect the interproton distances of the ligand in the bound... 

We have seen that NOESY provides information on internuclear (principally interproton) distances. For many organic molecules (as distinguished from macromolecules such as proteins and nucleic acids) structure elucidation often involves only the establishment of the structural formula and bonding scheme. However, where ambiguities in configuration or preferred conformation remain to be settled, NOESY is often crucial for establishing stereochemistry. 

At least three factors complicate the analysis of NOESY spectra. First, COSY signals may be present from scalar couplings and may interfere with interpretations intended to be based entirely on interproton distances. (Vicinal couplings, for example, are largest when the coupled nuclei are farthest apart, a condition that obtains in the antiperiplanar geometry.) Such unwanted spectral features are called artifacts. COSY signals may be reduced through... 

In addition to the arbitrary model, distance calculations with MARDIGRAS require isotropic rotational correlation time rc as input parameter. Effective rotational correlation time can be estimated by a number of experimental approaches.1 6 An approach that usually produces self-consistent results is to estimate rc based on the same NOESY data that are used for distance calculations. MARDIGRAS can be run at a series of correlation times, and a rc range can be selected that reproduces best fixed interproton distances and distances with limited variation, see, for example, Ulyanov et al 20 For that purpose, the experimental NOE intensities (which are integrated in arbitrary units) must be normalized based on the total sum of all observed intensities if possible, intensities of diagonal peaks must also be integrated and included to make the dependence of calculated distances on rc more apparent, see a discussion in Tonelli.176 Fixed interproton distances and distances with limited variation in nucleic acids are listed in Table 2. 

If quantitative information on interproton distance is required, then it is necessary to plot the NOESY off-diagonal peak intensity against the mixing time after which mutual proton spin flips are monitored. The slope of this plot, (T, is given by [39]... 

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. 

Several methods have been described for using 3D NOESY-NOESY cross-peak intensities for structural refinement such as the two-spin approximation (4,5), Taylor series expansion of the NOE-rate equation (6), and direct gradient refinement method (7). The two-spin approximation requires that the NOESY derived distances be obtained from vanishingly short experimental mixing times where the build-up of NOE intensity is linear with respect to interproton distance and the effect of spin diffusion (NOE intensity mediated by multiple relaxation pathways) are minimal. 

Where Aij (x , x ,2) is the 3D NOESY-NOESY volume and r, is the interproton distance between spins a and b. This model provides a simple description of the 3D NOESY-NOESY interaction, however it does not include the effects of spin diffusion (multiple relaxation pathways). This oversimplification leads to dramatic systematic errors in the form of overestimation of all distances. 

NMR structures of d(CGCGAATTCGCG) have been reported by Nerdal et al. (39) and Lane et al. (40) based on 2D-NOESY data. Nerdal et al, proposed a highly underwound structure with kinks at the primary and secondary roll points and at the ApT step. Lane et al. propose an NMR structure much closer to that of conventional B DNA. The limit of the nuclear Overhauser effect to interproton distances -4.5 A makes unequivocal determination of the helix parameters in an... 

For molecules with a regular secondary structure, like RNA duplexes, there are numerous characteristic interproton distances below 5 A between adjacent nucleotides [41, 42] which give rise to typical cross peak patterns in the NOESY spectra. For a regular A-RNA, the distance between the aromatic proton (C6H or C8H) of a given nucleotide and the 2 -ri-bose proton of the 3 -neighboured nucleotide, as well as the one between the aromatic proton and the 3 -ribose proton of the same residue is particularly small (ca. 2.0-2.5 A). The cross peaks in the NOESY spectrum caused by the interaction between the corresponding protons are therefore especially strong. 

Greater accuracy can be achieved by methods that involve calculation of a full relaxation matrix from the NOESY data to generate interproton distances. A model protein structure can then be iteratively refined by back calculation until differences in the empirical and calculated data are minimized. The resulting distances can be used as restraints for further refining the protein structure by distance geometry or molecular dynamics methods. 

The nuclear Overhauser effect (NOE) is another important NMR parameter used in conformational analysis because the magnitude of the NOE is inversely proportional to the sixth power of the interproton distance in space (/noe° NOE spectroscopy (NOESY) is two-dimensional experiment that may be run routinely in which the NOE is manifested as a crosspeak between two resonances indicating that the two protons are near in space. 

There are several potentially serious problems involved in the interpretation of NMR data in terms of distance constraints. First, a phenomenon called spin diffusion may result in spurious NOESY cross-peaks between protons that share a common neighboring proton, but which themselves are greater than 5 A apart. Second, biological macromolecules are always flexible to at least some degree, and NOESY cross-peak intensities are expected to reflect the inverse average sixth root of the interproton distances. As a result, it is entirely possible for a proton to appear to be adjacent to two other protons simultaneously, when the other two protons are nevertheless always greater than 10 A apart. Finally, NOESY cross-peak intensities are affected by numerous spectral artefacts and well as by other sources of relaxation, which may cause many cross-peaks to be missing. 

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