Journal of Magnetic Resonance 238 (2014) 87–93

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Processing strategies to obtain clean interleaved ultrafast 2D NMR spectra Laetitia Rouger, Benoît Charrier, Meerakhan Pathan, Serge Akoka, Patrick Giraudeau ⇑ Université de Nantes, CNRS, Chimie et Interdisciplinarité: Synthèse, Analyse, Modélisation (CEISAM), UMR 6230, B.P. 92208, 2 rue de la Houssinière, F-44322 Nantes Cedex 03, France

a r t i c l e

i n f o

Article history: Received 11 September 2013 Revised 7 November 2013 Available online 22 November 2013 Keywords: Ultrafast 2D NMR Interleaved Artefact Pre-FT processing correction Post-FT processing correction Symmetrisation

a b s t r a c t Ultrafast (UF) 2D NMR enables the acquisition of 2D spectra in a single-scan. In spite of its promising potential, the accessible spectral width is highly limited by the maximum gradient amplitude, which limits the general applicability of the method. A number of solutions have been recently described to deal with this limitation, among which stands the possibility to record several interleaved scans. However, this alternative acquisition scheme leads to numerous ghost peaks characteristic of interleaved acquisitions. These artefacts highly affect the readability of 2D spectra for structural elucidation, as well as their quantitative performance. Here, we propose several pre-FT or post-FT processing corrections to clean artefacts from interleaved ultrafast NMR spectra. Their performances are compared, and their potentialities are illustrated in a small organic molecule context. Post-FT processing corrections such as ArSub (Artefact Subtraction) or symmetrisation appear to be the most efficient ones in terms of artefact removal. While not purely single-scan, these strategies open new perspectives towards the routine use of UF 2D NMR for structural or quantitative analysis. Ó 2013 Elsevier Inc. All rights reserved.

1. Introduction Nuclear Magnetic Resonance (NMR) represents an essential analytical tool in a wide range of situations, such as structural elucidation of organic or biological structures, quantitative analysis or in vivo spectroscopy. Most of these applications are made possible by multidimensional (nD) spectroscopy [1,2] which offers a high resolution enhancement and an incredible variety of experiments. However, this prominent analytical tool suffers from long acquisition durations inherent to the time incrementation procedure which forms the basis of nD NMR. Not only this long experiment time –from ten minutes to several hours – is often the source of overloaded spectrometer schedules, but it also makes nD NMR unsuitable for the study of short timescale phenomena such as chemical or biochemical dynamic processes. From the point of view of analytical chemistry, an additional drawback comes from the impact of hardware temporal instabilities [3] which strongly degrade the precision of nD quantitative experiments [4]. Many strategies have been developed to reduce the duration of nD NMR experiments. A first approach consists in optimizing pulse angles and interscan delays to reduce the recovery delay between successive scans, a strategy which is particularly efficient in ⇑ Corresponding author. Address: Chimie et Interdisciplinarité: Synthèse, Analyse, Modélisation (CEISAM), UMR 6230, Faculté des Sciences, BP 92208, 2 rue de la Houssinière, F-44322 Nantes Cedex 03, France. Fax: +33 (0)2 51 12 57 12. E-mail address: [email protected] (P. Giraudeau). 1090-7807/$ - see front matter Ó 2013 Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.jmr.2013.11.008

protein NMR [5,6]. Several other approaches have been proposed to reduce the number of t1 increments, thanks to processing methods that reconstruct the whole FID in the indirect dimension [7–9]. Other developments are based on alternatives to the Fourier Transform, such as the Filter Diagonalisation Method [10] or Hadamard spectroscopy [11–13]. Ten years ago, a new approach was designed by Frydman and co-workers [14,15], allowing the acquisition of 2D NMR spectra within a single scan. In the so-called ‘‘ultrafast’’ (UF) method, the usual t1 encoding is replaced by a spatial encoding thanks to frequency chirp pulses combined with magnetic field gradients. After a mixing period, the decoding is carried out by a detection block based on Echo Planar Spectroscopic Imaging (EPSI) [16,17]. This strategy has been widely described in recent papers and its principles will not be detailed here [18,19]. UF 2D NMR has opened promising perspectives in various areas of chemistry and biochemistry – from the real time monitoring of chemical and biochemical processes [20–22], to extensions in hyphenated techniques [23,24] and in quantitative applications [25]. In spite of its high potentialities, ultrafast 2D NMR still presents limitations in terms of sensitivity, resolution and spectral width [26,27]. A first trade-off concerns the sensitivity and the resolution in the spatially-encoded dimension – called ‘‘ultrafast’’ dimension in the rest of the manuscript. To improve the latter, the spatial encoding duration has to be increased, leading to significant sensitivity losses and line-shape distortions, mostly due to translational molecular diffusion [28,29]. We recently suggested several strategies to overcome this

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limitation, by the development of multi-echo spatial encoding [30] or by the physical reduction of molecular diffusion [31]. A second major limitation of UF experiments is the spectral width that can be accessed in a single-scan. For a given resolution DmUF in the spatially-encoded dimension, the maximum spectral widths that can be sampled in the two domains are limited by the maximum acquisition gradient amplitude Ga available [26]:

ca  Ga  L ¼ 2 

SW 1  SW 2 DmUF

where L represents the effective coil length and ca the gyromagnetic ratio of the detected nucleus. Moreover, increasing Ga also leads to sensitivity losses due to larger filter bandwidths [26]. Such limitations prevent the general application of UF NMR. They particularly limit the use of UF NMR by users such as organic chemists who often need to elucidate the structure of molecules with large chemical shift ranges. In order to increase the spectral range accessible by ultrafast NMR experiments without degrading SNR and resolution, several strategies have been proposed. A first possibility consists in classical peak aliasing along the FT EPSI dimension – called ‘‘conventional’’ dimension in the rest of the manuscript – an approach popularized by Jeannerat in conventional 2D NMR [32,33]. However, this strategy is not applicable in the spatially-encoded dimension where no Fourier Transform is applied. Several efficient methods were recently proposed to recover signals lying out of the observed range by playing with the peak positions in the k-space. Pelupessy et al. suggested to add a band-selective refocusing pulse flanked by a bipolar gradient pair before the mixing period [27]. We also proposed a gradient-controlled aliasing [34], which does not require any selective pulse. It is based on the use of suitably chosen gradients placed on each side of the mixing period. Finally, Shrot et al. described a very elegant spatial/spectral encoding approach [26] which was successfully applied in an organic chemistry context [20]. In the latter method, each peak undergoes a specific spectral encoding using selective pulses before the spatial encoding. All the previously described approaches share three limitations: (i) they require a priori knowledge of the spectral regions to be folded, (ii) the calibration of gradient and/ or pulse parameters is required and (iii) the folded peaks do not appear at their real chemical shifts. While NMR spectroscopists are used to deal with such aspects, the latter can form a limiting factor for the general use of UF NMR. Also worth mentioning is a processing alternative based on interlaced Fourier Transformation (FT), which doubles the effective spectral width in the FT dimension [35]. But if the experiment timescale allows acquiring a few scans, a much simpler – at least in principle – solution consists in interleaving several ultrafast acquisitions spanning different k-space trajectories in order to increase the accessible spectral widths and/or to ease the gradient demand. This solution was suggested in the very first papers on ultrafast 2D NMR [15], and it is directly inspired from interleaved EPSI [36,37]. While this approach seems relatively simple to implement in routine, its practical use was rarely described [38,39]. When attempting to implement this alternative acquisition scheme, we observed several artefacts reminding those frequently observed in interleaved EPSI [36,37]. These artefacts, which are the subject of this paper, will highly affect the readability of 2D spectra. Here, we propose several pre-FT or post-FT processing corrections to clean artefacts from interleaved ultrafast NMR spectra. Their potentialities are discussed and compared, and illustrated in a small organic molecule context.

2. Results and discussion 2.1. Principle of interleaved acquisitions The principle of interleaved ultrafast 2D NMR [15] is described in Fig. 1, in the case of UF COSY [40] with two interleaved scans. It consists in repeating the UF experiment while incrementing a prea acquisition delay by 2T , (where Ta is the acquisition gradient durani tion and ni the number of interleaved scans). The two acquired scans are then processed in an interleaved fashion, leading to a reduction of the effective dwell time by a factor ni and therefore inducing a spectral width extension by ni in the conventional dimension. The expression of the spectral width in the conventional dimension ni (SW1) becomes: SW 1 ¼ 2T . Interleaving also allows increasing the a spectral width in the ultrafast dimension (SW2) without reducing a T a L SW1. For example, as SW 2 ¼ cG2T , when Ta is doubled to increase e SW2, ni needs to be doubled too, in order to keep SW1 constant. Finally, interleaving can also be used to reduce the demand on the acquisition gradient amplitude Ga. Actually, reducing Ga constrains to increase Ta in order to keep SW2 constant. The impact of increasing Ta on SW1 is therefore compensated by means of interleaving. Fig. 1c shows a 2D spectrum recorded in such an interleaved fashion, compared to its regular (not interleaved) ultrafast counterpart, recorded with two scans to obtain comparable results (Fig. 1b). 1 Artefacts appear on the interleaved spectrum at a distance SW of ni each peak – i.e. with the periodicity of the interleaving process – reminding those observed in EPI [36,37]. These artefacts have a characteristic shape, different from that of the peaks of interest. As shown in Fig. 2, the artefacts are even enhanced when the interleaved scans are recorded under partial saturation conditions, i.e. with a short recovery delay. In this case, their shape is similar to the one of their corresponding main peak. 2.2. Origin of the artefacts and first attempts to remove them The superposition of these artefacts with peaks of interest is of course detrimental to the routine use of ultrafast spectroscopy, as it degrades the spectrum readability. It also potentially affects quantification, in the case where artefacts would overlap with peaks of interest. These artefacts can arise from multiple causes, and are in fact well known in the magnetic resonance imaging (MRI) community, where multi-shot interleaved Echo Planar Imaging (EPI) is a common procedure. In this case, these artefacts are observed in the form of ghost images with the periodicity of the interleaving process [36]. A very complete article by Reeder et al. describes the three main possible sources of such artefacts [37]: i. Amplitude discontinuities between successive scans create a modulation function of the signal, which depends on relaxation and repetition times. They are mainly due to partial saturation effects which occur when the repetition time is not long enough. As they depend on relaxation parameters, these amplitude effects are of course dependant on the chemical shifts. ii. Phase discontinuities introduce constant phase modulation effects in the conventional dimension. Phase shifts can result from field inhomogeneities, chemical shift, susceptibility, as well as from receiver-phase misregistrations. Phase errors in the transmitter can also cause constant-phase errors. iii. Time delays can create phase discontinuities in the ultrafast dimension. These can be due to time-lags in the filters or by eddy currents induced by gradient switching [36]. EPI specialists described different acquisition and processing strategies to decrease the intensity of these ghost images, in most

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(a) 1st scan π/2 H

π

Gz

+Ge

1

Ta

π/2

Te

π …

π/2

H

π

G2

-Ge

π/2

Te

2nd scan 1

G1

+Ga

-G a

+Ga

-G a

+Ga

-G a

Ta

π …

Gz

+Ge

G1 -Ge

+Ga

G2

(b)

-G a

+Ga

-G a

+Ga

(c)

Fig. 1. (a) Pulse sequence for the acquisition of interleaved ultrafast COSY spectra with two interleaved scans (ni = 2). Interleaving consists in repeating the UF experiment while incrementing a pre-acquisition delay by 2  Ta/ni, leading to a reduction of the effective dwell time by a factor ni. (b) Ultrafast COSY spectrum (2 scans, not interleaved) and (c) interleaved ultrafast COSY spectrum (ni = 2) of a 10% ethanol sample in D2O, recorded on a 500 MHz spectrometer with a cryoprobe. Acquisition and processing parameters are given in the experimental part.

cases by means of phase corrections [41,42]. While the sources of ghost peaks could be similar in EPI and in ultrafast spectroscopy, dealing with them is a relatively different problem, which is the purpose of the present article. We first made several attempts to eliminate artefacts such as those shown in Figs. 1 and 2, by reducing their possible sources in the acquisition process, thanks to a careful optimization of the NMR pulse sequences. Phase reset instructions were added at the beginning of each scan to ensure that artefacts did not arise from phase misregistrations between two successive scans. This did not affect the results. Dummy scans were inserted before the acquisition of real scans, however this procedure did not significantly reduce the intensity of the artefacts, except in the case of strong partial saturation conditions. Similarly, we added long gradient pulses before each interleaved scans, in order to remove the potential artefacts arising from interferences with residual signals from the previous scans – a strategy developed by Vitorge et al. in the SMART method [43]. Again, it did not significantly change the shape or intensity of the artefacts. These preliminary experiments showed that the artefacts arising from interleaved acquisitions could not be removed by these simple acquisition tricks. As a consequence, we decided to concentrate on processing procedures capable of removing them. We designed several pre-FT or post-FT processing corrections to obtain clean 2D spectra from interleaved data. Their principle and their performance are discussed in the next section. 2.3. Artefact corrections All the processing procedures are illustrated in Fig. 2 on the example of an interleaved ultrafast COSY (Correlated SpectroscopY) spectrum of a 10% ethanol sample in D2O, recorded with two interleaved scans (ni = 2). This spectrum was recorded with two different acquisition conditions: the first one (Fig. 2a) ensures

full longitudinal relaxation between the two scans (TR = 30 s, left column), while the second one (Fig. 2b) is recorded under partial saturation conditions (TR = 3 s, right column). As can be seen from the projections in the conventional (vertical) dimension, the amplitude of these artefacts is between 15% (full relaxation) and 45% (partial saturation) of the main peak amplitude. Two families of approaches can be considered to remove these artefacts. The first one consists in working on the potential sources of artefacts by pre-FT processing methods, while a second possibility is to remove them after processing the data. Regarding pre-FT processing approaches, two different corrections were developed, consisting in modifying the data recorded during the second scan. As described above, ghost peaks mainly arise from amplitude or phase discontinuities between the interleaved scans. Therefore, a solution consists in modifying the relative amplitude or phase of the interleaved scans in order to minimize ghosting artefacts. Fig. 2c and d presents the result of the amplitude correction on the data shown in Fig. 2a and b. Fig. 2d shows that, in the case of partial saturation conditions, the intensity of the ghost peaks is significantly reduced and reaches an amplitude similar to the one obtained in full relaxation conditions. It shows that amplitude differences between interleaved scans can be efficiently compensated. Of course, such a correction does not affect the data recorded in full relaxation conditions (Fig. 2c). While this correction makes it possible to obtain relatively clean spectra from interleaved data recorded in a fast fashion, it will certainly be limited in the case where sites with very different longitudinal relaxation times (T1) are considered. Moreover, when ni > 2, it will require optimizing simultaneously the amplitude of several FIDs. A second pre-FT processing correction consists in modifying the first order phase of the second dataset in the conventional dimension in order to minimize the ghost peaks resulting from potential phase differences between the two scans. As can be seen in Fig. 2e

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(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

(i)

(j)

Fig. 2. Interleaved ultrafast COSY spectra (ni = 2) of a 10% ethanol sample in D2O, recorded at 298 K on a 500 MHz Bruker Avance III spectrometer equipped with a cryoprobe. F2 is the ultrafast dimension and F1 is the conventional one. (a) Spectrum recorded under full relaxation conditions, with TR = 30 s. (b) Spectrum recorded under partial saturation conditions, with TR = 3 s. Several processing procedures were applied to spectrum a (left column) and b (right column). Pre-FT processing corrections were applied by modifiying the relative amplitude (c and d) and phase (e and f) of the two interleaved scans. Post-FT processing corrections were also applied by artefact subtraction (g and h) or symmetrisation (i and j). For each spectrum, a projection of the column at 3.6 ppm is shown. Details about acquisition parameters and processing procedures are given in the text.

and f, this correction – applied after the amplitude correction for the spectrum recorded under partial saturation – does not significantly reduce the intensity of the artefacts. Actually, a reduction of 2% of their relative intensity was observed, which is not visible on the projection. It means that first order phase discontinuities – which could potentially arise from pulse phase offsets and timing misregistrations – are not the main source of artefact in our case. Zero- and second-order phase corrections were also tested without success. In summary, the relative inefficiency of these pre-FT processing corrections demonstrates that the interleaving artefacts are probably not due to a well-identified cause such as a constant phase or amplitude distortion, but rather to a combination of numerous experimental non-idealities, which are certainly highly

hardware-dependant. Even in the ideal case where these non-idealities would be fully understood, taking them into account would require spectrometer-dependant optimization procedures that would certainly be incompatible with a routine use of ultrafast spectroscopy. Therefore, we chose to consider another family of approaches, which consists in removing the ghosting peaks by directly working on the processed data, without any consideration for their potential sources. The first one, called ‘‘ArSub’’ (for Artefact Subtraction) consists in applying the following procedure: a reference artefact is first selected by the user, and its intensity is measured in each point of a defined region. This intensity is called RAI (Reference Artefact Intensity). Peak-picking is then performed (manually or automatically) to define all the peaks of interest in the spectrum,

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then the RAI is subtracted from the spectrum – weighed by the relative intensity of the peak of interest giving rise to this artefact – at 1 a distance SW from each peak in the conventional dimension. This ni correction assumes that the peak intensity and shape is identical for all signals, relatively to their corresponding peak of interest. This is a reasonable assumption, as the factors that may affect the interleaved acquisitions (phase or delay errors) are potentially identical for all resonances. As can be seen in Fig. 2g, a perfectly clean 2D spectrum is obtained from the ArSub correction, showing the efficiency of this method. However, ArSub is less efficient when the data are recorded in partial saturation conditions (Fig. 2h, see the small residual ghost peaks), as in this case the relative amplitude of the artefacts is T1-weighed. Another drawback of this approach is that it is relatively heavy and requires user intervention. Attempts were made to automatize this procedure, by defining an ‘‘artefact threshold’’, under which all signals would be considered as artefacts, and above which all signals would be considered as peaks. However, this strategy works only if the highest artefact is smaller than the less intense peak of interest. This does not sound realistic for the analysis of complex mixtures, where peaks with very different intensities are generally observed. A last approach, which can only be applied to homonuclear spectra, consists in symmetrizing the spectrum relatively to the diagonal [44]. In a COSY or TOCSY experiment, peaks are in principle symmetric, which is not the case of interleaved artefacts. A simple symmetrisation operation should therefore remove them. This operation first consists in precisely defining the diagonal of the spectrum (UF spectra are not necessarily recorded with perfectly identical SWs in the two dimensions). In a second step, the resonance intensities in each pair of symmetry-related locations are compared and the smaller of the two values is inserted into both locations [44]. Choosing the lowest intensity is the method which is currently applied for the routine processing of conventional 2D spectra [44], and it is the only approach that totally removes the artefacts. Taking the average intensity, for instance, would only partially remove them. Fig. 2i and j demonstrates the efficiency of this correction in both acquisition conditions, as ghost peaks are totally removed. While some kind of wiggles parallel to the vertical axis appears on the projection, such effects were only observed for the very concentrated ethanol sample and not for real samples (see below). Therefore, no specific attempt was made to remove them. An additional benefit of this correction is that it

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leads to a resolution improvement in the ultrafast dimension, which is generally characterized by a lower resolution. Of course, this correction is not applicable in heteronuclear experiments, but it forms a great help towards the achievement of clean homonuclear spectra, even in the case of non-interleaved, single-scan experiments, where artefacts arising from imperfect spatial-encoding or gradient refocusing may appear. Finally, the results described above demonstrate that post-FT processing corrections appear more efficient in terms of artefact removal. They also present the advantage that they do not depend on the number of interleaved scans, whereas the complexity of the pre-FT processing corrections would certainly increase with ni. 2.4. Illustration on small molecule examples This section illustrates the potentialities of the corrections described above in two practical cases, in a small organic molecule context. Fig. 3 illustrates the potentialities of the symmetrisation method on the COSY spectrum of a cocoa butter lipid extract, formed of a mixture of triglycerides. Four interleaved scans were necessary to sample the 6 ppm spectral range in the two dimensions while keeping the gradient demand reasonable; this acquisition procedure generated significant ghosting artefacts (Fig. 3a). The symmetrisation totally removes them (Fig. 3b), moreover it improves the resolution in the ultrafast dimension. Fig. 4 demonstrates the interest of the ArSub method in an heteronuclear context: the HSQC spectrum of vanillin, recorded with four interleaved scans to sample the 4 ppm and 80 ppm spectral widths in 1H and 13C dimensions, respectively. Here again, the ghost peaks are totally removed by post-FT processing. The methods presented in this paper are also potentially interesting for quantitative applications. 2D NMR is increasingly used for the quantitative analysis of complex mixtures, thanks to its capacity to spread the resonance of the analytes over a second dimension [4]. In this context, we have recently demonstrated the interest of ultrafast 2D NMR to obtain an improved precision in a reduced time [25]. However, the quantitative application of 2D NMR is not straightforward, as 2D peak volumes depend on a number of factors (relaxation time, coupling constants and pulse sequence delays). This requires a precise calibration approach – relying on standard external samples or on standard additions – which can be used to determine the concentration of analytes in

Fig. 3. Ultrafast COSY spectrum of a cocoa butter lipidic extract in CDCl3, mainly formed of triglycerides, recorded in 20 s with four interleaved scans, before (a) and after (b) applying the symmetrisation post-FT processing correction. F2 is the ultrafast dimension and F1 is the conventional one. The processing procedure entirely removes the ghost peaks due to the interleaving procedure, as shown on the vertical projections below. The spectrum was recorded at 298 K on a 500 MHz Bruker Avance III spectrometer equipped with a cryoprobe.

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Fig. 4. Ultrafast HSQC spectrum of vanillin in aceton-d6, recorded in 20 s with four interleaved scans, before (a) and after (b) applying the ArSub post-FT processing correction. F2 is the ultrafast dimension (13C) and F1 is the conventional one (1H). The processing procedure entirely removes the ghost peaks due to the interleaving procedure, as shown on the vertical projections for each carbon. The spectrum was recorded at 298 K on a 500 MHz Bruker Avance III spectrometer equipped with a cryoprobe.

samples of unknown concentration. In this context, it can be expected that the interleaving artefacts will impact these calibration curves, in particular in the case where artefacts arising from strong peaks would overlap with small peaks of interest. The main predictable effect is the addition of a constant bias that would impact the y-intercept of the calibration curve, thus inducing a systematic error in the estimation of the concentration. Such effects, as well as the capacity of the processing procedures mentioned above to remove them, require a complete analytical study which will be the subject of future research. 3. Conclusion The results presented above highlight the potential of post-FT processing algorithms to obtain clean 2D spectra from interleaved ultrafast acquisitions. The symmetrisation method is probably the simplest and most efficient one, but is only applicable to homonuclear correlations. The ArSub approach is more general and is particularly useful in heteronuclear cases. These strategies open new perspectives towards the routine use of UF 2D NMR for structural or quantitative analysis. It would also be interesting to combine them with other processing strategies such as linear prediction [45] or covariance spectroscopy [46]. The acquisition of clean interleaved UF spectra will be particularly indispensable when working at high magnetic fields where the spectral width accessible in a single scan becomes really limited. It does not replace, however, the previously proposed strategies to fold peaks along the ultrafast dimension, as interleaved acquisitions are not compatible with pure single-scan acquisitions such as those required when UF is coupled to hyphenated techniques, or when very fast kinetic or dynamic processes are studied. 4. Experimental The ethanol sample was prepared by dissolving it in D2O (10% v/ v). The vanillin sample was prepared by weighing 300 mg of vanil-

lin and dissolving it in 600 lL of aceton-d6. The cocoa butter lipidic extract sample was obtained by dissolving 500 mg of such an extract (obtained from an ongoing study in our group, unpublished results) in 700 lL of CDCl3. It is mainly formed of triglycerides. All the NMR spectra were recorded at 298 K on a Bruker Avance III 500 spectrometer, at a frequency of 500.13 MHz with a cryogenically cooled probe including z-axis gradients and a p/2 pulse of duration (PW90) = 7.85 ls for 1H and 11.4 ls for 13C. The implementation of interleaved ultrafast pulse sequences is relatively straightforward from the usual single-scan ultrafast pulse sequences. A sample of pulse program code is given as Supplementary Information in the case of COSY (the principle is exactly the same for all pulse sequences). The main modification consists in the addition of a pre-acquisition delay between the mixing and acquisition periods. This delay is initially set to a value close to zero, then incremented between two successive scans by a value calculated automatically at the beginning of the pulse program. The increment is set to 2ðp15þd6Þ where p15 is the duration ni of one acquisition gradient, d6 is the gradient recovery delay (see below) and ni is the number of interleaved scans. For all experiments, the gradient recovery delay was set to 20 ls. This value is sufficient to ensure a total absence of artefacts in non-interleaved single-scan spectra. Other modifications consist in an additional phase reset instruction at the beginning of the pulse sequence, and in the addition of a long (10 ms) and intense (maximum strength available) gradient between each scan, in order to remove any residual transverse magnetization before starting a new scan. For all the ultrafast COSY experiments, the spatial encoding was performed using a constant–time spatial encoding scheme [47] (Fig. 1) with two successive 15 ms smoothed chirp pulses. The sweep range for the encoding pulses (60 kHz) was set to be significantly larger than the chemical shift range, and the amplitude of the encoding gradients was adapted to obtain a frequency dispersion equivalent to the frequency range of the pulses (Ge = 8.4 G/cm). The detection block for the non-interleaved COSY experiment (spectrum of Fig. 1c) was formed of 256 detection gradients of duration Ta = 256 ls and amplitude Ga = 92.7 G/cm. For

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interleaved COSY experiments with ni = 2 (Figs. 1d and 2), the detection block was formed of 128 detection gradients of duration Ta = 512 ls and amplitude Ga = 46.4 G/cm. For interleaved COSY with ni = 4 (Fig. 3), the detection block was formed of 64 detection gradients of duration Ta = 512 ls and amplitude Ga = 67.0 G/cm. The recovery delay was set either to 30 s or 3 s in the case of ethanol (corresponding to full relaxation or partial saturation, respectively), and to 5 s for the cocoa butter extract. The ultrafast HSQC experiment was performed using the pulse sequence described in Ref. [48], modified by inserting a multi-echo constant–time spatial encoding scheme [30] formed of four successive 7.5 ms smoothed chirp pulses. The sweep range was 57 kHz and the amplitude of the encoding gradients was Ge = 28.8 G/cm. The detection block was formed of 64 detection gradients of duration Ta = 1024 ls and amplitude Ga = 82.4 G/cm. The recovery delay was set to 5 s. The amplitude and duration of the pre-FT acquisition gradients were adapted to adjust the peak position in the ultrafast dimension. All the spectra were acquired using the Bruker program Topspin 2.1, and analyzed using the Bruker program Topspin 3.0. The specific processing for the ultrafast spectra (interleaved or not) and all the corrections were performed using home-written routines in Topspin using the Jython language (Jython is Python using Java classes). The processing included an optimized gaussian apodization in the ultrafast dimension to improve the line width and sensitivity, while a conventional processing (sinebell function and zero-filling) was performed in the conventional dimension. The processing also included an optional shearing transformation, which corrects the effects of a possible gradient amplifier offset during the acquisition gradient train. This correction, which was widely described in previous papers [14,15], is identical for all the interleaved scans of the experiments, as shearing effects appeared to be exactly the same for all of them. Actually, this result is not surprising as the gradient amplifier offset is generally constant from one experiment to another. Similarly, the data resulting from the different interleaved scans appeared to be perfectly aligned and did not require any other alignment apart from adjusting the k-domain offset between data arising from positive and negative gradients, a common procedure in ultrafast experiments. Acknowledgments We are grateful to Prof. Lucio Frydman and Dr. Tangi Roussel for stimulating discussions. We thank Didier Diomande, Dr. Illa Tea and Prof. Gérald Remaud for providing the cocoa butter sample, as well as Dr. Virginie Silvestre for discussions. We also acknowledge Michel Giraudeau for linguistic assistance. This research was supported by funding from the ‘‘Agence Nationale de la Recherche’’ for young researchers (ANR Grant 2010-JCJC-0804-01). Appendix A. Supplementary material Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.jmr.2013.11.008. References [1] W.P. Aue, E. Bartholdi, R.R. Ernst, J. Chem. Phys. 64 (1976) 2229–2246. [2] J. Jeener, Lecture Presented at Ampere International Summer School II, Basko Polje, Yugoslavia. [3] G.A. Morris, Systematic sources of signal irreproducibility and t1 noise in high field NMR spectrometers, J. Magn. Reson. 100 (1992) 316–328. [4] P. Giraudeau, S. Akoka, Fast and ultrafast quantitative 2D NMR: vital tools for efficient metabolomic approaches, Adv. Bot. Res. 67 (2013) 99–158. [5] A. Ross, M. Salzmann, H. Senn, J. Biomol. NMR 10 (1997) 389. [6] P. Schanda, B. Brutscher, J. Am. Chem. Soc. 127 (2005) 8014. [7] A.S. Stern, K.B. Li, J.C. Hoch, J. Am. Chem. Soc. 124 (2002) 1982.

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