Figure 10.14

(Chapter 8) uses the transient NOE, in which a selective 180° pulse is applied to one nucleus and then the enhancement of z magnetization on a nearby nucleus is measured after a mixing delay (Fig. 10.14: the DPFGSE—90° sequence is replaced by a single selective 180° pulse for simplicity). For two nuclei Ha and Hb that are nearby in space, interaction of their magnetic dipoles leads to the phenomenon of cross-relaxation. This means that any sudden perturbation of the Ha populations away from the Boltzmann distribution will lead to a relaxation process that perturbs the Hb populations away from the Boltzmann distribution temporarily. The effect will build up during the relaxation process, but eventually a Boltzmann distribution for both nuclei is reestablished and the effect on Hb goes away. For "small" molecules, this effect enhances the z magnetization of Hb up to a few percent above Mo at the optimum mixing time.

In product operator terms, we can say that the inverted z magnetization on Ha leads to the generation of additional z magnetization on Hb:

Consider now the common "front end" of the homonuclear 2D experiments: 90°—11—90°. If we put it in place of the selective 180° pulse of the transient NOE experiment (Fig. 10.14), it will give us the following terms:

—I^cos(^at1) + l£sin(^at1) (if Ha and Hb are not J coupled)

The first term, which is not observable in the COSY experiment, is now exactly what we need for a transient NOE experiment. We have "inverted" the Ha magnetization in a way that carries the information of its chemical shift encoded in the cos(^a 11) term. Depending on the value of 11, sometimes Ha will be completely inverted (cosine = 1), leading to a maximum NOE transfer to Hb, and sometimes it will not be inverted at all (cosine = —1), leading to no NOE transfer to Hb. Thus, the transferred magnetization will also carry the chemical shift information of Ha:

The final "read" pulse rotates the Hb z magnetization into the x'-y' plane and the FID is recorded with the frequency Qb. Fourier transformation of the FIDs gives in each one a peak at F2 = Qb whose amplitude is oscillating as a function of 11 at the frequency Qa. Fourier transformation of the 11 FID gives a crosspeak at F2 = Qb, F1 = Qa. Because for small molecules, the transferred z magnetization is opposite in sign from the original

Figure 10.15

perturbation of Ha (—^ Ib), the crosspeaks will be of negative intensity if we phase the diagonal peaks (coming from untransferred —IZ) to positive intensity.

10.3.2 The NOESY Pulse Sequence

The NOESY is a simple extension of the COSY pulse sequence, with one additional delay and one additional 90° pulse added (Fig. 10.15). The mixing part of the 2D pulse sequence now consists of two 90° pulses separated by a delay. The first 90° pulse converts magnetization in the x'-y' plane into z magnetization (population difference). To the extent that this z magnetization differs from Mo, it will undergo cross relaxation during the mixing delay tm, altering the population difference and thus the z magnetization of nearby nuclei. The final pulse converts the transferred z magnetization into observable x'-y' magnetization on the nearby nuclei, which precesses during 12 and induces the FID signal in the probe coil. As with all 2D experiments, magnetization transfer is the basis for the appearance of crosspeaks in the spectrum (cf. Chapter 9, efficiency of transfer Gab), but in this case it is z magnetization that is transferred and the intensity of crosspeaks will depend on the cross-relaxation rate for that pair of nuclei. As in the transient NOE experiment, the intensity of the crosspeak will increase with increasing mixing time tm, but will eventually reach a maximum and then drop off to zero.

A simple way to gradient enhance the NOESY experiment is to add a single gradient during the mixing delay (Fig. 10.16). This will destroy any SQC present during the mixing time (p = 1) as well as any DQC (p = 2), as there is no other gradient to "untwist" the coherence. z magnetization and ZQC (p = 0) are not affected. Phase cycling is also used to remove artifacts. Because we are only interested in z magnetization during the mixing delay, we can use any phase we want for the final pulse as long as the receiver phase is the same as the pulse phase. So usually this final pulse is cycled as x, y, —x, —y with the receiver making the same cycle: x, y, —x, —y. We can also phase cycle the second 90° pulse (x, —x), which will reverse the perturbation of z magnetization at the start of the mixing delay: —I^cos(^at1) for an xf pulse and +I^cos(^at1) for a — xf pulse. This reverses the sign of the final detected Hb magnetization:

1 NOE Tb

— Ia[—cos(^at1)] ^ Ib[—cos(^at1)] ^ — Ib[—cos(^t1)]

If we then reverse the phase of the receiver we will get addition of the desired Hb magnetization with each scan and cancellation of any magnetization that was not affected by that pulse.

Gradient-enhanced NOESY

Gradient-enhanced NOESY

Figure 10.16

10.3.3 The 2D NOESY Spectrum

The NOESY spectrum (Fig. 10.17) looks very much like the COSY spectrum, except that we will see additional crosspeaks that are not present in the COSY or TOCSY spectra. These are the interesting ones—pairs of protons that are close in space but not close enough in the bonding network to be J coupled. Classic examples of this are 1,3-diaxial relationships in rigid cylcohexane chairs, 1,3-diaxial relationships between a proton and a methyl group (e.g., H4ax and H19 in cholesterol: Chapter 8, Fig. 8.35), CH-O-CH across a glycosidic linkage, CHa-CO-NH (observed in p sheets and p turns), and NH-Ca-CO-NH (observed in an a-helix) across a peptide bond. When there is a large J coupling between two protons, we can see zero-quantum artifacts, just as we noticed in the selective 1D NOE experiment. These result from ZQC that is produced by the "front end" sequence 90°x-t 1-902:

Crosspeak ZQ artifact Diagonal Not observed where c, s, c' and s' are as defined in Chapter 9. The second term is a mixture of ZQC and DQC. The DQC part can be removed by phase cycling or by gradients, but there is no simple way to remove ZQC because it has coherence order zero, just like z magnetization. During the mixing delay tm, it undergoes chemical-shift evolution at a rate determined by the chemical-shift difference Qa — Qb, and the third 90o pulse completes the coherence

transfer from Ha to Hb:

where c'' is cos((^a - ^b) Tm). So this is a COSY-like antiphase crosspeak resulting from antiphase-to-antiphase INEPT coherence transfer with an intermediate ZQC state. The mixing time tm can be randomly varied to try to average the artifacts to zero, taking advantage of the cosine dependence on Tm, but this will also introduce t\ noise. The artifacts are easily recognized in the 2D spectrum because they have equal amounts of positive and negative intensities, usually in a star-like pattern (Hb-Hc, Fig. 10.17). Sometimes you will see NOE crosspeaks that are distorted in shape because the in-phase negative intensity of the NOE crosspeak is added to the twisted antiphase shape of the ZQ artifact at the same position (Hd-He, Fig. 10.17).

Pure NOE crosspeaks in a NOESY spectrum are in-phase (normal multiplets) where there is J coupling. The transferred magnetization is on the z axis, and the "read" (third) 90° pulse produces in-phase magnetization in the x'-y' plane at the start of the acquisition period. The lack of a sin(nJti) term in the observed crosspeak magnetization means that peaks will also be in-phase in the F1 dimension. Integration of NOESY crosspeaks will give nonzero peak areas (actually volumes, as we are dealing with 2D crosspeaks) that are representative of the intensity of the NOE interaction. The crosspeaks in a phase-sensitive COSY experiment are antiphase and have a zero net volume because equal areas are found in the positive and negative components. Thus, the NOESY and TOCSY experiments lead to net transfer of magnetization and the COSY experiment does not.

The sign of NOESY crosspeaks relative to the diagonal depends on the sign of the NOE interaction. Magnetization that does not transfer during the mixing period (Tm) will have opposite sign to transferred magnetization as long as the cross-relaxation rate Rab is a positive number:

-IZ cos(^a t1) — -I£cos(na t1) + RabTm I>s(^a h)

Diagonal peak Crosspeak where Rab is the cross-relaxation rate and we are looking at short mixing times where the NOE buildup is still linear as a function of mixing time. This is true for small organic molecules (molecular weight less than about 2000 Da) in nonviscous solvents for which anc ^ 1, where a is the Larmor frequency in the laboratory frame (e.g., 2n x 600 MHz) and tc is the correlation time for tumbling of the molecule. The double-quantum relaxation pathway dominates and we see an increase in z magnetization on nearby spins. If the diagonal peaks are phased to be positive absorptive peaks, the crosspeaks will be negative (upside down) absorptive peaks. This is called a "negative NOE" because the cause (perturbation of Ha's z magnetization by reducing it) is opposite in sign to the effect (enhancement of Hb's z magnetization). For large molecules, such as proteins, the tumbling rate is much slower (i.e., tc is long) and aTc > 1. In this case, the zero-quantum relaxation pathway dominates over the double-quantum pathway, so Rab (W2-Wo) becomes negative. The crosspeaks will then be the same sign as the diagonal peaks. As the initial perturbation on Ha (reducing its z magnetization) results in the same type of perturbation on Hb during the mixing period (reduction of z magnetization), we call this a "positive NOE."

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