NOE intensities

Usually, simplified representations of the data are used to obtain preliminary structures. Thus, lower and upper bounds on the interproton distances are estimated from the NOE intensity [10], using appropriate reference distances for calibration. The bounds should include the estimates of the cumulative error due to all sources such as peak integration errors, spin diffusion, and internal dynamics. 

Depending on experimental parameters, NOE intensities will be affected by spin diffusion (Eig. 8). Magnetization can be transferred between two protons via third protons such that the NOE between the two protons is increased and may be observed even when the distance between the two protons is above the usual experimental limit. This is a consequence of the distance dependence of the NOE. Depending on the conformation, it can be more efficient to move magnetization over intennediate protons than directly. The treatment of spin diffusion during structure refinement is reviewed in more detail in Refs. 31, and 71-73. 

Another principal difficulty is that the precise effect of local dynamics on the NOE intensity cannot be determined from the data. The dynamic correction factor [85] describes the ratio of the effects of distance and angular fluctuations. Theoretical studies based on NOE intensities extracted from molecular dynamics trajectories [86,87] are helpful to understand the detailed relationship between NMR parameters and local dynamics and may lead to structure-dependent corrections. In an implicit way, an estimate of the dynamic correction factor has been used in an ensemble relaxation matrix refinement by including order parameters for proton-proton vectors derived from molecular dynamics calculations [72]. One remaining challenge is to incorporate data describing the local dynamics of the molecule directly into the refinement, in such a way that an order parameter calculated from the calculated ensemble is similar to the measured order parameter. 

A related experiment TOCSY (Total Correlation Spectroscopy) gives similar information and is relatively more sensitive than the REIAY. On the other hand, intensity of cross peak in a NOESY spectrum with a short mixing time is a measure of internuclear distance (less than 4A). It depends on the correlation time and varies as . It is positive for small molecules with short correlation time (o r <<1) and is negative for macromolecules with long correlation time (wr >>l) and goes through zero for molecules with 1 Relaxation effects should be taken into consideration for quantitative interpretation of NOE intensities, however. 

Intermolecular relaxation has little effect on intra-peptide exchange-transferred NOE intensities. J. Biomol. NMR 2002,... 

A combined approach is to use interproton distances determined by simulation and experimental NOE intensities to calculate the dynamic behavior of specific linkages in an oligosaccharide. The MM force field was employed for the computer simulation of calonyctin Ai (40) where interglycosidic NOEs served as experimental distance restraints for the molecular dynamics 104). 

Several peptides have been reported 108113114 that show distinct negative CD bands in the 215-220 nm region, pointing clearly to (3-hairpin formation. For the peptides exhibiting an identifiable (3-sheet feature, estimates of the (3-hairpin content have been made from CD and NMR that are in reasonable agreement. For example, the (3-hairpin 114 content of a model hexadecapeptide in water was found to be 55% by CD ([0]2i6), 41-47% by NOE intensities, and 47% by chemical shifts. In 20% MeOH, these percentages were 80, 70-78, and 66%, respectively. 

From comparison of Table 8.2 with Table 7.1 (or of Eq. (7.20) with Eq. (7.10)), i.e. of transient NOE or NOESY vs. steady state NOE intensities, it appears that the latter are superior under any circumstance. This superiority is striking if the intrinsic asymmetry of the steady state NOE with respect to the symmetry of transient NOE and NOESY experiments (Section 7.4) can be exploited, as in the case of irradiation of fast relaxing nuclei to detect NOE to slow relaxing nuclei. Of course, NOE experiments are advantageous over NOESY experiments if one is looking for dipolar connectivities from only a few specific signals. 

It is often necessary to obtain a profile of NOE intensities vs. the irradiation time, called NOE buildup. A series of truncated NOEs are thus needed (Section 7.3). The only caveat with respect to buildup experiments in a diamagnetic case is that there is a lower limit in the irradiation time because even a truncated NOE needs saturation of the irradiated signals. Since instantaneous saturations are... 

More quantitative information about host-guest proximity may be obtained by application of the nuclear overhauser effect (NOE). Very simply, the NOE involves the saturation of the spin of one nucleus by continuous irradiation, and monitoring the resulting intensity enhancements of the NMR resonances of adjacent atoms. The idea is that the irradiation of one nucleus causes it to become excited to a nonequilibrium distribution of spin states. Relaxation of this excited state situation occurs by dipole-dipole spin-lattice transfer of the excess energy, resulting in enhancement of the intensity of signals for nuclei physically close to the irradiated nucleus, irrespective of whether they are actually bonded. NOE intensity enhancements may be anywhere... 

The homonuclear NOE, almost always between two protons, is used to measure distances and determine stereochemical relationships. The NOE intensity (the percent increase or decrease of z magnetization observed at a nearby proton) is proportional to the inverse sixth power of distance between the two protons (1/r6), and is generally too weak to be observed for distances over 5 A. 

The second step in processing the 2D data is to perform a second Fourier transform on each of the columns of the matrix. Most of columns will represent noise, but when we reach a column which falls on an F2 peak, transformation of the t FID gives a spectrum in F, with a peak at the chemical shift of nucleus A (Fig. 9.15). The final 2D spectrum is a matrix of numerical values that has a pocket of intensity at the intersection of the horizontal line F = 2a and the vertical line F2 = 2b and has an overall intensity determined by the efficiency of transfer of magnetization from nucleus A to nucleus B. This efficiency tells us something about the relationship (/ value or NOE intensity) between the two nuclei... 

Because of all of the above pitfalls, NOE is probably the most misinterpreted experiment in organic chemistry. In my experience, /-coupling measurements, both homonuclear and heteronuclear, give far more reliable information than NOE measurements in the determination of small-molecule stereochemistry. To use NOE measurements for stereochemical determinations, it is always best to do the NOESY experiment on both isomers and compare the crosspeak intensities (relative to the diagonal peak intensities) and measure distances on both isomers using an energy-minimized computer model of the structures. If the differences in distance and NOE intensity are small between the two isomers, the experiment cannot be conclusive. 

The earliest attempts to account for the effect of spin diffusion relied on some iterative scheme wherein a full relaxation matrix analysis would be used to calculate distances from NOEs, and these distances could be used in a standard refinement procedure.59-64 Clearly a more elegant approach would be to base an energy term on the directly measured NOE intensity. 

This approach was first implemented by Yip and Case,65 who started with the well-known relationship between the NOE intensity matrix, A(rm), relaxation matrix, R, and NOESY mixing time, Tm ... 

Complete Relaxation Matrix Refinement of NMR Structures of Proteins Using Analytically Calculated Dihedral Angle Derivatives of NOE Intensities. 

Selected solution-state 1H- and 13C-NMR, and solid-state cp/mas 13C parameters have been listed in Table 9. It is seen that some of the aliphatic carbons (and some of the aromatic also, not listed) gave double signals in the cp/mas spectrum. H(31) was assigned as trans to H(41) (they are on opposite faces of the ring), and H(32) was assigned as trans to H(42) on the basis of the magnitudes of their respective 6.4 Hz 3/(31 11) and 8.6 Hz 3.7(32-42) values. In addition, a 6.9% NOE intensity... 

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