Spin diffusion effect

For irradiation times of J short with respect to the relaxation time of / the NOE extent is independent of the relaxation time of the nucleus and provides a direct measurement of time required to saturate signal J is not negligible compared with t, the response of the system is not linear [18]. The truncated NOE is independent of paramagnetism as it does not depend on p/, which contains the electron spin vector S in the R[m term, and only depends on gkj), which does not contain S. If then the steady state NOE is reached, the value of p/ can also be obtained. This is the correct way to measure p/ of a nucleus, provided saturation of J can be considered instantaneous. In general, measurements at short t values minimize spin diffusion effects. In fact, in the presence of short saturation times, the transfer of saturation affects mainly the nuclei directly coupled to the one whose signal is saturated. Secondary NOEs have no time to build substantially. As already said, this is more true in paramagnetic systems, the larger the R[m contribution to p/. 

For an evaluation of these methods, it is important to analyze the effects of the delays on cross-relaxation and on the efficiency of Hartmann-Hahn transfer. In order to avoid spin diffusion effects, the effective crossrelaxation rate should be averaged to zero on a time scale that is short compared to the inverse cross-relaxation rates. In practice, this implies that the delays must be separated by less than about 10 ms (Bearden et al., 1988). This condition is excellently fulfilled by Methods C and D, and can also be fulfilled by Method B if the delays are introduced after only a few repetitions of the basis sequence. However, in most cases spin diffusion effects cannot be suppressed using Method A. 

The relationship between NMR chemical shifts and the secondary structure of a protein has been well established (19,20,21). The C and carbonyl carbons experience an upfield shift in extended structures, such as a P-strand, and a downfield shift in helical structures. Both the Cp and the Ha proton chemical shifts exhibit the opposite correlation. These shifts have proven to be sufficiently consistent to permit the prediction of secondary structural elements for a number of proteins (1,19,20). Knowledge of the secondary structure of a protein can be useful in identifying spin-diffusion effects during the analysis of 4D N/ N-separated NOES Y data collected with long mixing times as described below. The secondary structure can also be used as a constraint in the calculation of protein global folds. 

A much more general consideration is the question of whether there are any processes other than spin diffusion that can affect the detected signal. An almost universal problem in this regard is Tj relaxation during the evolution period, which can change not only the total amount of magnetisation detected, but also the relative populations of the regions in a manner similar to spin diffusion effects. 

Only one T2 was observed at low temperatures but two were found for the 50/50 mixtures above 25The interpretation of multiple T2 is not completely unambiguous but it is known that T2 measurements is more sensitive for the detection of multicomponent systems than because it is free of spin-diffusion effects. Taken at face value, the T2 results suggest that heterogeneity may exist but on a scale small compared to the distance of effective spin diffusion. But an improvement in interpretation is clearly desirable. 

As mentioned above, the cross peak intensities from NOESY spectra taken at long mixing times caimot be related in a simple and direct way to distances between two protons due to spin diffusion effects that mask the actual proton distances. A possibiUty to extract such information is provided by relaxation matrix analysis that accounts for all dipolar interactions of a given proton and hence takes spin diffusion effects explicitly into consideration. Several computational procedures have been developed which iteratively back-calculate an experimental NOESY spectrum, starting from a certain molecular model that is altered in many cycles of the iteration process to fit best the experimental NOESY data. In each cycle, the calculated structures are refined by restrained molecular dynamics and free energy minimization [42,43]. 

Figure 5. Schematic representation of three spins, A, B, and C interaeting via direct dipolar contacts (black arrows) and/or spin diffusion (dashed arrows), a) Trace of a 2D NOESY spectrum (right) and a corresponding trace from a 2D ROESY spectrum (left). Spins A and B are close in space, and spin diffusion mediates magnetization transfer between protons A and C, that are not close in space. The 2D ROESY experiment allows unambiguous discrimination between direct and spin diffusion effects, b) Protons A and C are close in space, and in addition magnetization is transferred between the two protons via spin diffusion. The effect is a cancellation of the 2D ROESY signal. A cancellation can also occur if indirect magnetization transfer involves more than one relay proton (proton B in this case). Therefore, a discrimination between spin diffusion and direct dipolar interaction is not possible in this case.

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