Transient NOEs

It has been repeatedly stressed in the preceding sections that the steady-state NOEs measured between two nuclei cannot readily be translated into internuclear separations because they result from a balance between the influences of all neighbouring spins. At best, they provide information on relative internuclear distances only. It has also been 

Although once popular, this experimental approach is rather less used nowadays and as such shall be considered no further. The more common approach to obtaining kinetic data is to instantaneously perturb a spin system not by saturation but by inverting the target resonance(s) (i.e. inverting the population differences across the corresponding transitions) and then allowing the NOE to develop in the absence of further external interference. The new populations are then sampled with a 90° pulse as usual (Fig. 8.20). In this case, the NOE is seen initially to build for some time but ultimately fades away as spin relaxation restores the equilibrium condition these enhancements are thus termed transient NOEs. 

The measurement of transient NOEs gained widespread popularity, initially in the biochemical community, in the form of the 2D NOESY experiment, which remains an extremely important structural tool in this area and increasingly in the analysis of smaller molecules. More recently, the ID transient 

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While the final magnitude of nOe depends, as indicated earlier, on the relaxation pathways Wi, W, and W), the initial rate of buildup of nOe (transient nOe) depends only on the rate of cross-relaxation between the nuclei, and this can provide valuable information about the distance between the nuclei (r). This rate of buildup can be proportional to r" , where r is the distance between the nuclei. Thus, if the proportionality constant is determined, we can calculate an approximate distance between the two nuclei. The best results are obtained in rigid molecules when the nuclei are less than 3 A apart. If only direct nOe s are involved in a two-spin... 

What is transient nOe, and why is it considered to provide a better estimate of the internuclear distance (r) than the normal nOe effect ... 

Transient nOe represents the rate of nOe buildup. The nOe effect (so-called equilibrium value) itself depends only on the competing balance between various complex relaxation pathways. But the initial rate at which the nOe grows (so-called transient nOe) depends only on the rate of cross-relaxation t, between the relevant dipolarly coupled nuclei, which in turn depends on their internuclear distance (r). 

The rate of growth of nOe (transient nOe) can be measured easily by the following pulse sequence ... 

The oldest and most widely used structural restraints in NMR spectroscopy are distance restraints derived from NOE experiments [1]. Transient NOE, 2D NOESY and ROESY spectra provide valuable information for interatomic distances up to 5 A that will be discussed in the following. 

Fig. 9.2 Schematic representation of the three basic experiments useful for the determination of (A) transient NOE experiment, (B) 2D NOESY and (C) 2D ROESY. The gray-filled half-circle represents a frequency-selective inversion pulse which inverts the spin to which the cross-relaxation...

There are two types of NOE experiments that can be performed. These are referred to as the steady-state NOE and the transient NOE. The steady-state NOE experiment is exemplified by the classic NOE difference experiment [15]. Steady-state NOE experiments allow one to quantitate relative atomic distances. However, there are many issues that can complicate their measurement, and a qualitative interpretation is more reliable [16]. Spectral artifacts can be observed from imperfect subtraction of spectra. In addition, this experiment is extremely susceptible to inhomogeneity issues and temperature fluctuations. 

ID-transient NOE experiments employing gradient selection are more robust and therefore are more reliable for measuring dipolar... 

TOPHAT-shaped 90° pulses are used in other cases as the best compromise with respect to the excitation profile, the phase homogeneity and length. Depending on the type of the detected spin-spin interaction - being either scalar or dipolar coupling - each selected spin is initially perturbed only once (ID TOCSY, ID INADEQUATE, ID C/H COSY, 2D TOCSY-COSY and 2D HMBC), or for several times (ID NOE). With each of the selected spins initially perturbed only once the inherently smaller transient NOEs would be detected in the latter case, whereas with the multiple excitation of a selected spin within the NOE build-up period the stronger steady-state NOEs are more or less approximated. 

In contrast to the 1D experiment, where steady-state NOEs may be obtained, only the less intense transient NOE.s are measured in the NOESY experiment. ROEs can only be obtained as transient effects in both the ID and the 2D experiment. Furthermore the intensities of the NOESY and ROESY cross peaks depend upon the molecular size as well as the length of the mixing period. In the case of large molecules, e.g. polypeptides, rather short mixing times are usually chosen to avoid spin diffusion. 

In the following sections we will go through the various classical experiments like steady state, truncated and transient NOE, as well as ROE. The presentation has the twofold purpose of sketching (or refreshing) the basic theory to... 

Note that the transient NOE effect is symmetrical, in the sense that by selective excitation of / or J the same variation in intensity of the other signal is observed, even in the case of different relaxation rates. 

In this type of experiment the NOE buildup tends to disappear with p/. In the steady state case, the saturation time is always long enough to allow spin / to cross-relax with other spins, even if pr is large. In transient experiments, the cross relaxation with spin / is by itself limited in time and, pj being the same, cross relaxation with other spins is drastically limited. In any case, spin diffusion is limited in that region of time in which NOE is growing (Fig. 7.6). Truncated and transient NOEs performed with short NOE buildup times are efficient in quenching spin diffusion. 

The ROE dependence on the spin lock time has the same profile as that of transient NOE, with the difference that the limiting values are 0.385 and 0.675 at the condition that o>itc < 1 (see Fig. 7.10). It appears that the ROE is less convenient than the transient and steady state NOEs in the sense that the expected effect is smaller when all other conditions are the same. Another disadvantage in paramagnetic molecules is that it is difficult to spin lock all the signals in a... 

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. 

As far as the transient NOE is concerned, the problem of the selective 180° pulse has already been addressed. The non-optimal selectivity leads to dramatic artifacts [42]. Therefore, transient NOE is not the technique of choice in paramagnetic systems [43]. 

The calculations are performed for a tr/(7> value of —1 s-1. Steady state NOE is always superior to transient NOE, except when T of the irradiated signal is more than twice the 7/ of the responding signal (upper right part of the table). 

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