Cross peak volume

The quantification of an NOE amounts to determining the volume of the corresponding cross peak in the NOESY spectrum. Since the linewidths can vary appreciably for different resonances, cross-peak volumes should in principle be determined by integration over the peak area rather than by measuring peak heights. However, one should also keep in mind that, according to Eq. (1), the relative error of the distance estimate is only one sixth of the relative error of the volume determination. Furthermore, Eq. (1) involves factors that have their origin in the complex internal dynamics of the macromolecule and are beyond practical reach such that even a very accurate measurement of peak volumes will not yield equally accurate conformational constraints. 

Upper bounds b on the distance between two hydrogen atoms are derived from the corresponding NOESY cross peak volumes V according to calibration curves , V=f(b). Assuming a rigid molecule, the calibration curve is... 

Cross peak volumes were converted to distance constraints via the use of an expression of the form ... 

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.

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... 

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). 

As can be seen, the density function is the same for all CH groups. The cross peak volume is naturally dependent on proton number in the CH group, i.e. the CH3 cross peak is generally three times more intense than CH group. The CH2 cross peak intensity follows also the number of protons present, so if the protons are equivalent, the cross peak intensity is twice the intensity of the CH cross peak. The magnetization intensity is maximum whenever A equals 1 /(n I /1), where n is a positive even integer. From the point of relaxation, the first solution, A = 1 /(21 /1), is the most practical one. The effect of INEPT optimization can be more easily followed if the polarization transfer delay A is defined as 1/ (2/opt)... 

The other common inverse-detection method, heteronuclear multiple quan-turn coherence (HMQC) relies on multiple-quantum coherence transitions during the pulse sequence. Due to the multiple-quantum coherence transitions it is more laborious to theoretically follow the course of magnetization, and the cross peak will be broader in the Fi dimension due to the /hh evolution. Unlike HSQC, HMQC can also be optimized for Jch couplings. This heteronuclear multiple bond correlation experiment, or HMBC, ° ° has lower sensitivity than HMQC/HSQC experiments, and the Jch correlations can appear as artefacts in the spectrum. However, the cross peak volume should follow the concentration of analyte, so with proper method validation HMQC and HMBC should also be applicable for quantification. 

It is now possible to follow what is the polarization transfer efficiency from proton to carbon for each CH group, and also how the mismatch between true Jch and the /opt used for polarization transfer delay calculation affects the signal intensity (Figure 8). When the /chS of the sample are known, suitable coefficients can be formulated to correct the cross peak volumes. 

The nOe data may be obtained by either one- or two-dimensional methods. These through-space effects may be used to estimate intemuclear distances. However, nOe cross-peak volumes are inversely proportional to the sixth power of the distance between the correlated protons only in the case of rigid spherical molecules whose tumbling is isotropic. The simplest method that has been proposed for the interpretation of nOe-derived distance data is the isolated spin pair approximation. The matrix treatment is more rigorous, although rel5dng also on several approximations. A set of equations describing the cross-relaxation pathways of all the protons in the molecule is cast into a matrix form and solved. 

Figure 2.14 Expansion of the phase nsitive proton NOESY spectrum at 500 MHx and 80 °C, showing only the methylene region [62]. Geminal interactions are indicated by crosshatched cross peaks, and intermethylene interactions by stippled cross peaks. The designations S, M, and W refer to the strengths (cross peak volumes) of the intermethylene proton interactions...

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