Steady-state NOE measuring

The previous section considered the NOE for the hypothetical case of a two-spin system in which the spins relax exclusively via mutual dipole-dipole relaxation. In progressing to consider more realistic multispin systems two key issues will be addressed how the presence of other spins affects the magnitudes of steady-state NOEs and how these reintroduce distance dependence to the NOE. These considerations lead to the conclusion that steady-state NOE measurements must be used in a comparative way to provide structural data, and that they do not generally provide estimates of intemuclear distances per se. 

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... 

Besides measuring and T2 for nuclei such as C or N, relaxation studies for these nuclei also include measurements of the NOE factor, cf equation B 1.13.6. Knowing the (pj) and the steady-state NOE... 

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. 

The measured spin relaxation parameters (longitudinal and transverse relaxation rates, Ri and P2> and heteronuclear steady-state NOE) are directly related to power spectral densities (SD). These spectral densities, J(w), are related via Fourier transformation with the corresponding correlation functions of reorientional motion. In the case of the backbone amide 15N nucleus, where the major sources of relaxation are dipolar interaction with directly bonded H and 15N CSA, the standard equations read [21] ... 

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. 

When measuring steady state NOE, the effect measured on saturating / or on saturating J may be different because p and pj are in general different. We say that steady state NOE is not symmetric. It follows that larger NOEs, and then more favorable cases, occur when the signal with larger p is saturated. 

Up to now steady state NOEs have been considered, i.e. when one signal is saturated for a long time with respect to T of the nucleus on which NOE is going to be measured. Let s consider here what happens when the saturation time is short and variable. The resulting NOE is called truncated NOE [17] because not enough time is left for full polarization transfer. These experiments are of fundamental importance for the measurement of pi, for evaluating cross relaxation, and to avoid or to measure spin diffusion. 

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/. 

The magnitude of the NOE is proportional to the inverse sixth power of the distance between two nuclei only for very short times between the perturbation and the measurement of the effect on other nuclei. The magnitude of the steady-state NOE is dependent on many other competing relaxation processes, so it cannot be used as an accurate measure of distance. To accurately measure distances, you need to measure the transient NOE with a number of different times between perturbation and measurement ( mixing times ) and measure the initial slope of the curve as the effect increases with time. 

In Chapter 5 we observed NOE interactions by ID NOE difference, measuring the steady-state NOE resulting from a long (several seconds), low-power continuous-wave irradiation of one nucleus. The modern selective (DPFGSE) ID NOE experiment... 

Steady-state NOEs are those measured after a period of continuous S-spin saturation during which a new steady-state equilibrium condition has developed for the I-spin populations. The NOE enhancement is usually denoted t]i S and quoted as a percentage. 

Steady-state NOEs can provide information on relative intemuclear distances only, not on absolute measurements of intemuclear separation. 

This also means that steady-state NOEs are rarely symmetrical. That is, the NOE observed at spin A on saturating spin B, t1a B, is unlikely to equal the reverse measurement from saturating A and observing B, tib A. This is a consequence of the fact that the neighbours surrounding A are unlikely to match those surrounding B in number and in distance. 

The clear advantages of the gradient-selected NOE experiment over the conventional steady-state NOE difference means this is becoming a popular tool in small molecule structural studies. However, there are fundamental differences between the data presented by the two experimental protocols, with steady-state experiments observing equilibrium NOEs and transient experiments observing kinetic NOEs. As a consequence, ID NOESY experiments demand a somewhat different approach to data interpretation over that currently adopted for steady-state NOE difference measurements, some of the key considerations include ... 

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