Suppressing exchange effects in diffusion-ordered NMR spectroscopy Journal of Magnetic Resonance

In diffusion-ordered spectroscopy (DOSY) the aim is to separate signals from different molecular species according to their different diffusion coefﬁcients. Each species has its individual diffusion coefﬁcient (that may accidentally coincide with that of another species, e.g. if they are of very similar size). In exchanging systems, however, there is a serious complication in that the apparent diffusion coefﬁcient of an exchanging signal will be a compromise that depends, among other factors, on the diffusion coefﬁcients of the exchange partners and the rate of exchange between them. The DOSY spectrum will be much harder to interpret and can often give the appearance of extra (spurious) components in the mixture. Here a new and surprisingly simple experiment is described that suppresses the effects of exchange on apparent diffusion coefﬁcients, restoring the simplicity of interpretation enjoyed by non-exchanging systems. (cid:2) 2013 The Authors. Published by Elsevier Inc.


Introduction
Diffusion-ordered spectroscopy (DOSY) is a family of NMR experiments used in mixture analysis to allow signals belonging to a given species to be correlated through their rate of diffusion. The technique is widely used [1][2][3][4][5][6][7][8][9][10] but is well-known to give misleading results when applied to systems undergoing chemical exchange [11]. While such effects can be put to good use [12,13], when using DOSY to identify mixture components they are a serious nuisance [14]. Thus, for example, where hydroxyl signals are seen in DOSY spectra they routinely appear at higher diffusion coefficients than non-exchanging signals from the same species, because of exchange with residual water [15] and other labile protons.
Almost all DOSY pulse sequences in common use, such as the Oneshot45 [16,17] sequence used to acquire the spectrum of Fig. 1a, use the stimulated echo (STE). The primary reason is to minimise J-modulation: the STE stores spatially-encoded magnetization along the z-axis for most of the diffusion time, minimising the time for which J acts. Any exchange of magnetization during this storage period, whether by chemical exchange [18][19][20] or nuclear Overhauser effect (NOE) [21], will affect the attenuation as a function of gradient pulse area for the signals involved. This changes the apparent diffusion coefficients and complicates analysis. The practical effect is that DOSY spectra show peaks with apparent diffusion coefficients intermediate between those of the exchanging sites, with the exact positions determined by the interplay between experimental parameters and the rate(s) of exchange, making it appear that more different species are present than is actually the case.
The effects of exchange are particularly frustrating in analysis problems such as mixtures of flavonoids [23], and in general in samples containing glycans [15]. Here OH signals can be much better resolved than CH [24], but exchange with residual water causes them to show increased apparent diffusion coefficients. It can be possible to suppress such exchange effects by addition of acid [24], but this is chemically invasive and risks sample degradation. Where magnetization exchange is mediated by the NOE, on the other hand, no general suppression method has been reported [21].
It is possible to suppress the effects of exchange (whether chemical or by cross-relaxation) on DOSY experiments in the special case where exchange with only a single species X (e.g. water) is concerned. If the initial excitation has a notch at the X frequency, then X magnetization is not encoded and therefore exchange with it does not lead to refocused signal at the end of a DOSY experiment. This approach has been used for determining protein NH exchange rates [25], but is not general. In the specific case that one of the exchanging spin pools is immobile, it is also possible to use a T 2 filter to suppress the effects of exchange [26].
In principle, a general solution to the problem of exchange is to use not the stimulated echo but the spin echo (SE). Here the magnetization remains transverse throughout the experiment. Because the phases of spins with different Larmor frequencies evolve at different rates, magnetization exchange (whether by chemical exchange or cross-relaxation) does not result in net magnetization transfer: exchange is incoherent, with spins exchanging at different times having different phases, and leads simply to signal loss. Thus a simple pulsed field gradient spin echo experiment would be expected to yield correct diffusion coefficients for species with different frequencies, even in the presence of exchange; the effects of the latter will only survive for chemical shift differences between exchange partners of the order of the inverse of the echo time or less. Unfortunately, for realistic diffusion times (of the order of tenths of a second), such experiments show severe J-modulation. Not only does this complicate the interpretation of spectra, it greatly increases signal overlap (because of the dispersion mode tails of signals) and thus degrades the accuracy of the diffusion data obtained [16].
The classic way to suppress J-modulation of spin echoes is to use the Carr-Purcell-Meiboom-Gill (CPMG) experiment [27][28][29][30], in which a train of spin echoes is performed, with a short echo time 2s of the order of the inverse of the chemical shift difference between the coupled spins. Unfortunately this requires a high radiofrequency pulse duty cycle, causing sample heating and risking convection (anathema to diffusion experiments), and in any case the rapid pulsing would restore the unwanted effects of chemical exchange and cross-relaxation (here the rotating frame Overhauser effect, ROE, as opposed to the NOE in STE experiments).
As has recently been pointed out [31], however, there is a simple and general way to suppress J modulation in a CPMG pulse sequence without resorting to rapid pulsing (i.e. to very short echo times 2s). The PROJECT (Periodic Refocusing Of J Evolution by Coherence Transfer) approach uses a CPMG sequence with quadrature 90°pulses inserted in the middle of each double spin echo, and is based on the so-called perfect echo [32,33]. The extra 90°p ulses refocus J-evolution, for arbitrary s in AX spin systems and for all spin systems if sJ ( 1. If diffusion weighting is added, for example by including field gradient pulses in each echo as in the PROJECTED (PROJECT Extended to DOSY) sequences of Fig. 2, then spin echo DOSY spectra may be obtained free of both exchange effects and J modulation if sk, sJ ( 1, where k is the exchange rate constant.

Results and discussion
The DOSY spectrum of Fig. 1a was acquired for a mixture of flavone and catechin. At first sight there appear to be two impurities  present. In fact these signals are simply the flavone hydroxyl resonances, but their diffusion coefficients are increased by exchange with the small amount of (protio-) water present in the sample. As noted above, such signals are typically better dispersed than backbone proton signals, but serve only to confuse in the spectrum of Fig. 1a. If exchange effects are suppressed using the PROJECTED sequence (Fig. 2, first and last gradient pulses omitted, no 45°p ulse), however, the assignment of the signals becomes obvious: hydroxyl and backbone signals alike align correctly in the diffusion domain, as shown in Fig. 1b. Of course the effect is not limited to exchanging OH signals (which can, if appropriate, be suppressed by addition of D 2 O), but is general (and extends to magnetization exchange through the Overhauser effect).
The use of PROJECT-based DOSY experiments is not limited to cases where exchange is a problem; if, as in small and mediumsized molecules, T 2 is not too short, they can be significantly more sensitive than their STE counterparts, because the SE retains the full signal while the STE discards half. However, as there is signal loss due to T 2 during the SE delay, for signals with a short T 2 a compromise between degree of diffusion weighting and signal-to-noise ratio may be required. Other important examples of applications for PROJECTED include T 2 -filtered DOSY and convection compensation. T 2 -filtration is commonly used where broad signals, for example from polymers or proteins, obscure signals of interest, and is typically implemented in STE-based DOSY pulse sequences by adding CPMG sequences either before [34], or after [35] the STE element. With PROJECTED, diffusion encoding and T 2 -filtering can be performed simultaneously, minimising signal losses, sample heating and J-modulation.
Convection compensation is a particularly attractive application. In STE-based DOSY experiments, convection compensation is normally achieved using a double stimulated echo (DSTE) [22], with a fourfold loss in signal compared to a SE experiment. In contrast, convection compensation can be implemented in a PRO-JECTED experiment without this sensitivity penalty, simply by dropping the field gradient pulses from the first and last echoes, as indicated by the outer square brackets in Fig. 2. To illustrate the potential, Fig. 3 compares Oneshot45 and convection-compensated double stimulated echo with PROJECTED DOSY spectra of the trisaccharide maltotriose in warm [D6]DMSO. In Fig. 3a convection causes all signals to show artificially high apparent diffusion coefficients. The conventional solution, the DSTE experiment (Fig. 3b), restores the CH signals to the correct positions in the diffusion domain, but leaves the exchanging signals with faster diffusion and shows poorer signal-to-noise ratio. The PROJECTED method (Fig. 3c) restores all signals to their correct positions, with good signal-to-noise ratio.

Conclusion
The PROJECTED experiment can simultaneously suppress the effects of chemical exchange, J-modulation and convection. It offers two to three times better sensitivity than the double stimulated echo pulse sequence (Supporting material, Fig. SI-1), and allows exchanging signals such as those of hydroxyl groups to be used in the identification of species in mixtures. The new method has the potential to find routine application in DOSY experiments on small molecules.

Experimental
A 1 mL sample of a mixture of catechin hydrate (53 mM) and flavone (47 mM) in [D6]DMSO was measured at 30°C on a 500 MHz Varian VNMRS spectrometer equipped with a 5 mm triple resonance probe with a z-gradient coil giving a maximum nominal gradient of 66 G cm À1 . DBPPSTE convection compensated and PROJECTED pulse sequences were used. In both cases 4 transients of 10739 complex points were averaged for each of 10 gradient increments ranging from 10.5 to 56.4 G cm À1 nominal amplitude. Equal increments in gradient squared were used, with rectangular gradient pulses of 1 ms duration, and the total experiment time was 4 min. A 0.7 mL sample of maltotriose (77 mM) in [D6]DMSO containing 10% H 2 O was measured at 27°C using the Oneshot45, BPPSTE and PROJECTED pulse sequences. 4 transients of 16 k complex points were averaged for each of 10 gradient increments, ranging from 10.4 to 56.4 G cm À1 nominal amplitude, in equal steps of gradient squared; 1.0 ms rectangular gradient pulses were used. For experiments using the PROJECTED sequence 15 cycles, n, were performed with cycle times, 4s, of 30 ms and 20 ms for the catechin-flavone and the maltotriose samples respectively. The gradient duty cycle was kept at 10% or below to minimise systematic errors in gradient pulse area due to amplifier or coil heating.