L Rouger

B Gouilleux

M Pourchet-Gellez

J.-N Dumez

P Giraudeau
email: patrick.giraudeau@univ-nantes.fr

Ultrafast double-quantum NMR spectroscopy with optimized sensitivity for the analysis of mixtures

Introduction

NMR spectroscopy is an essential analytical tool in a wide array of applications such as structure elucidation of organic or biological analytes, quantitative analysis or in vivo spectroscopy. Two-dimensional experiments [START_REF] Jeener | Lecture presented at Ampere International Summer School II[END_REF][START_REF] Aue | [END_REF] are particularly informative, and when associated with analytical procedures such as calibration or standard addition they become an efficient tool for the quantitative analysis of complex mixtures of small molecules. [3][4][5][6][7] The classic acquisition strategy of 2D NMR spectra, however, does suffer from long experiment durations. This is due to the requirement to repeat the same sub-experiment multiple times, with an incremented delay, to sample the indirect time dimension (t1). This long experiment duration -from ten minutes to several hours-is not compatible with high-throughput analysis, the study of unstable samples or the coupling with on-flow techniques. Moreover, it makes conventional 2D NMR spectroscopy sensitive to hardware instabilities in the course of the experiment. 8 Such instabilities may lead to significant additional noise-like features, the so-called "t1 noise", which affects the precision of quantitative analysis. This is particularly critical when the samples contain analytes whose concentrations are spread over a large range of values, as the signals of low-concentrated analytes can be hidden in the noise ridges generated by the high-concentrated ones. Several strategies have been developed to overcome this major time limitation. [START_REF] Rouger | Encyclopedia of Spectroscopy and Spectrometry[END_REF] For example, the inter-scan delay can be optimized together with the radio-frequency (RF) pulse angles. [START_REF] Schanda | [END_REF] Several "non-uniform sampling" (NUS) strategies have also been proposed, which consists of collecting only a randomly selected subset of t1 increments and use non-Fourier signal processing methods. [11][12][13] Other developments are based on alternatives to time encoding, such as Hadamard spectroscopy. 14,15 A decade ago, a generic multidimensional approach was designed by Frydman and co-workers, which makes it possible to acquire 2D NMR spectra within a single scan. 16,17 In this socalled "ultrafast" (UF) method, the incremented evolution period (t1) is replaced by a spatial encoding scheme, based on a combination of bipolar gradients and linearly frequencyswept pulses, 18 and the acquisition is carried out with an MRIinspired strategy. 19,20 The sensitivity and resolution of UF NMR have been significantly improved during the last decade thanks to several methodological developments, and UF NMR spectroscopy is nowadays applied in a variety of fields such as real-time monitoring, metabolomics, or coupled techniques like chromatography or dissolution dynamic nuclear This journal is © The Royal Society of Chemistry 20xx

Please do not adjust margins Please do not adjust margins polarization (DNP). 21 UF NMR has been applied recently to the quantitative analysis of complex mixtures, showing a precision and an accuracy of a few percent. 22 In spite of its high potential, ultrafast 2D NMR still suffers from the need to compromise between sensitivity, spectral widths and resolution. 23,24 However, when the targeted applications are compatible with experiment durations of a few seconds to a few minutes, spatial-encoding-based techniques still form a valuable alternative to conventional 2D NMR. Such "hybrid" approaches remain faster than conventional experiments and address the main limitations of the UF approach. For example, the sensitivity limit of UF experiments can be pushed forward by the use of signal averaging. For a similar experiment duration, this approach is more repeatable than conventional 2D NMR. 22 In a complementary approach, the spectral widths -for a given resolution-can be increased by the use of "interleaving". 17,25 The question of resolution is particularly acute in UF-COSYone of the most widely used UF experiments. Indeed, the presence of intense auto-correlation ("diagonal") peaks can impede the analysis of such spectra, particularly when signals of interest are close to the diagonal, or for samples with large dynamic ranges. This limitation affects the trueness and precision of quantitative analysis, as recently highlighted in the case of plant extracts where signals from sugars are heavily overlapped. 26 The recently introduced UF-DISSECT pulse sequence leads to the acquisition of a homonuclear correlation 2D spectra, with diagonal peak suppression. 27 Multiplequantum spectroscopy [28][29][30][31][32] is another valuable method to circumvent this overlap issue, as the lower density of peaks in multiple-quantum spectra leads to a better peak separation and removes the strong diagonal peaks, thus lowering the dynamic range. 33,34 Double-quantum spectroscopy (DQS) is particularly interesting for the quantitative analysis of complex mixtures, since it provides the same information as COSY while considerably reducing peak overlap. 35 Recently, the possibility to record double-quantum NMR spectra in an ultrafast fashion has been demonstrated. 36 An added benefit of UF multiplequantum experiments is that the artifacts arising from the interleaving procedure, which can affect the quantification in cases where they overlap the peaks of interest, are fewer and weaker, with no need for specific post-processing. 25 In order to turn this UF-DQS experiment into an analytical tool, an indepth understanding of the experiment is essential to maximize the resulting sensitivity. In this paper, we show how the recent concept of UF-DQS can be turned into an accurate analytical approach for the quantitative analysis of mixtures. First, we exploit a combined experiment, theory and simulation approach 37 to provide a full mechanistic description of the UF-DQS pulse sequence and assess the parameters that govern its sensitivity. We then compare experimentally the sensitivity of UF-DQS to that of conventional and ultrafast methods that are currently used for quantitative 2D NMR. Finally, we assess its quantitative performance, with the quantification of taurine in a homemade and a commercial energy drink. The UF-DQS experiment emerges as a promising analytical tool for the quantitative analysis of complex mixtures.

Methods

Numerical simulations

In all simulations, a B0 field of 9.40 T•m -1 was considered and ideal pulses were assumed. Spatial encoding was performed by using a CT spatial encoding scheme, that is, double spin echo with smoothed chirp encoding pulses. Those pulses were defined with 1000 points, with a WURST envelope, sweeping a bandwidth of 11 kHz in 15 ms. Excitation gradients of 0.013 T•m -1 and 0.016 T•m -1 were applied for the alanine sample and the AMX spin system respectively. The CTP was completed as shown in Figure 1. Acquisition gradients were fixed at 0.654 T•m -1 for the alanine sample and 0.484 T•m -1 for the AMX spin system. 512 points separated by a dwell time of 0.55 µs were used to compute the indirect dimension, whereas the direct one was obtained with 128 loops in the detection block. The sample length was fixed at 1.6 cm and the simulation was performed with 500 grid points in the z direction. The simulated 2D FID was processed in the same way as the experimental data: a sinusoidal apodization was applied in the direct dimension and a spatial Gaussian apodization was applied in the indirect dimension. 38 Zero filling was applied in both dimensions.

Sample preparation

The experimental UF-DQS spectra of alanine (Ala, Figure 3) were recorded on a 100 mmol•L -1 alanine sample in D2O. The metabolite mixture related to Figure 1 was prepared with five metabolites: Ala, threonine (Thr), lactate (Lac), histidine (His) and choline (Cho), dissolved in a mixture of phosphate buffer (pH 7) and D2O (2.4 mL; 37.5/62.5 v/v) leading to a concentration of 50 mmol•L -1 for each metabolite. A stock solution of homemade energy drink (spectra shown in Figure 4) was prepared, consisting of 41.63 mg of taurine (Tau), 434.04 mg of glucose and 644.2 mg of sucrose dissolved in 10 mL of water. Each sample used in the standard addition procedure contains 650 µL of this stock solution, 150 µL of D2O and graded amounts of Tau (0 mg, 3.03 mg, 6.20 mg, 9.82 mg and 12.15 mg). For the standard addition procedure performed on commercial energy drink, each sample contained 650 µL of this drink, 150 µL of D2O and graded amounts of Tau (0 mg, 3.31 mg, 6.31 mg, 9.49 mg and 12.05 mg).

NMR spectrometry

Experimental NMR spectra of the alanine sample, of the homemade and of the commercial energy drinks were recorded at 298 K on a Bruker 400 Avance I spectrometer, at a frequency of 400.13 MHz with a 5 mm dual+ 1 H/ 13 C probe equipped with z-axis gradients. NMR spectra recorded on the metabolite mixture were performed at 298 K on a Bruker Avance III spectrometer equipped with a cryogenic probe 1 H/ 13 C and z-axis gradients, at a frequency of 700.28 MHz.

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UF experiments

For all UF experiments, spatial encoding was performed by using a CT spatial encoding scheme, that is, double spin echo with 15 ms smoothed chirp encoding pulses. The sweep range for the encoding pulses was set to 10 kHz for the Ala sample, 7 kHz for the homemade and commercial energy drinks, and 20 kHz for the metabolic mixture. The amplitude of the encoding gradients was adapted to obtain a frequency dispersion equivalent to the frequency range of the pulses: Ge = 0.012 T•m -1 ; 0.009 T•m -1 ; 0.022 T•m -1 respectively. Coherence-selection gradients were added, flanking the reading pulse (amplitude ratios: -1:2 for UF-DQS and -1:1 for UF-COSY). The acquisition gradient parameters were set as follows: 0.646 T•m -1 for the sample of Ala, 0.404 T•m -1 for the homemade and commercial energy drinks and 0.325 T•m -1 for the metabolite mixture. For all the experiments, the detecting block used 128 detection gradient pairs. The duration of acquisition gradients was Ta = 274.4 µs for the Ala sample as for homemade and commercial energy drinks, and Ta = 266.6 µs for the metabolite mixture. For UF-DQS experiments, the double-quantum buildup delay was set to Δ = 1 4 ⁄ • 𝐽 𝐻-𝐻 (34.5 ms for Ala and an average value of 35.7 ms for the metabolite mixture and both homemade and commercial energy drinks). UF-DQS spectra of Ala were recorded in 1 minute with 16 scans. Both UF-COSY and UF-DQS spectra of energy drinks were recorded in 4 minutes with 45 scans. All spectra of the metabolite mixture were recorded in four interleaved scans to increase the observable spectral width, with 28 and 46 scans for UF-COSY and UF-DQS respectively, resulting in acquisition times of 10 and 16 minutes equivalent to those of conventional 2D experiments (see below). The specific processing of the UF spectra was performed with Matlab by using the same method as the one described for the simulated spectra.

Conventional experiments

Conventional experiments performed on the metabolite mixture used a CT scheme, the time spent in the transverse plane being set to 34.8 ms as for UF experiments. In order to reach the desired spectral widths, COSY spectra were acquired with 93 t1 increments, and DQS spectra with 150 t1 increments. Other experimental parameters (CTP, spectral widths) are similar to those used in ultrafast experiments. A sinusoidal apodization was performed in both dimensions on COSY spectra, whereas a Gaussian apodization was used in both dimensions for DQS spectra.

Results and discussion

The UF-DQS pulse sequence

The pulse sequence for ultrafast double-quantum NMR is shown in Fig. 1. During the preparation period, multiple quantum coherences are generated thanks to a spin-echo block flanked by 90° pulses. The evolution consists of a "constant-time" (CT) phase-modulated spatial encoding, implemented with a pair of 180° chirp pulses applied during alternating gradients. The CT nature of this scheme is due to the identical time spent in the DQ state by all spins regardless of their position along the z-axis. The final "mixing" pulse converts the multiple-quantum coherence back into observable magnetization, prior to acquisition with an Echo Planar Spectroscopic Imaging (EPSI) scheme. Double-quantum 2D spectra display pairs of correlation peaks for J-coupled spins. Figure 1 (b andc) shows examples of UF-COSY and UF-DQS spectra recorded on a model metabolite mixture. The direct dimension is displayed vertically, and the indirect one is horizontal. In the UF-COSY spectrum, singlequantum frequency offsets are measured in each dimension. In contrast, in the UD-DQS spectrum, single-quantum frequency offsets are measured in the direct dimension only, and in the indirect dimension double-quantum frequency offsets are measured, i.e. the sum of two offsets.

Analysis and optimization

The UF-DQS pulse sequence involves several parameters that have a subtle effect on the resulting spectra and govern in part its analytical potential. In particular, because of the "constanttime" nature of the spatial encoding block, the duration of the evolution period, T has a strong impact on peak amplitudes and in turn sensitivity, as commonly found in UF NMR. 37,39 Here we, extend the framework developed for UF-COSY to assess this influence using theory and simulation. The case of an AMX system (i.e., a system of 3 weakly coupled spins I = ½), where X coupled to spins A and M, is of particular interest, as it is the minimal set of spins that displays a modulation of correlation-peak intensities by the J coupling interaction during the encoding period. Analytical expressions can be obtained, using a product-operator calculation, for the intensity of the correlation peaks in the double-quantum spectrum of such AMX system (details of the calculation are available in Supplementary Information). For the peak located at [Ω 𝐴 ; Ω 𝐴 + Ω 𝑋 ], the peak intensity can be written: 𝑆 𝐴;𝐴𝑋 ∝ cos(𝛽 2 ⁄ ) 2 sin 𝛽 cos(𝜋𝐽 𝑀𝑋 𝑇) (1) Where 𝐽 𝑀𝑋 is the coupling constant between spins M and X. The J-dependence of DQS peaks is illustrated in Fig. 2. Using this knowledge, the duration of the evolution period, 𝑇, can be adjusted by the addition of a delay, 𝑡 𝑚𝑖𝑥 , prior to the spatial encoding scheme, in order to maximize the intensity of the correlation peaks, as demonstrated in the case of UF-COSY. 37 In addition to J-modulation, Eq. 1 shows the usual dependence of DQS peaks with respect to the flip angle of the final mixing pulse, β, resulting in optimal sensitivity with a 60° (resp. 120°) angle for the anti-echo (resp. echo) coherence transfer pathway. This dependence is reproduced in numerical simulations, as shown in Fig. S1. Analytical product-operator calculations become cumbersome when dealing with larger spin systems, and inadequate in the case of strong coupling. Numerical simulations are then an efficient approach to J-modulation. The Spinach simulation package 40 has been adapted to include the simulation of spatial encoding schemes. 37 This framework can first be assessed by comparing simulated results to analytical calculations for the AMX spin system. Figure 2 shows an example of simulated DQS spectrum; J-modulation can be obtained by integration of the peak volumes in simulated spectra obtained for a series of values of 𝑡 𝑚𝑖𝑥 . As illustrated in figure 2, the effect of J-modulation matches very well with the analytical expressions obtained from theoretical calculationssimulations of beta-modulation are shown in Fig. S1. The results from simulations can be further validated by comparison to experimental data for a larger spin system. The example of alanine was selected here as it provides an A3X spin system commonly encountered in small molecules. The Jmodulations of the A3X spin system from alanine (Figures 3a and3b) show a good match between experimental and simulated curves. These results demonstrate that the numerical simulations performed with the Spinach package can be used to optimize the sensitivity of UF-DQS spectra of small molecules. As recently shown in the case of UF-COSY, predicting the effects of J-modulation can indeed prevent unnecessary sensitivity losses. 37 Here, from the simulated and experimental Jmodulation curves of the A3X spin system from alanine, an optimum 𝑡 𝑚𝑖𝑥 of 100 ms can be chosen as the best compromise between the J-modulations of the two peaks, leading to a sensitivity enhancement of about 50 % for the peak located at [Ω 𝐴 ; Ω 𝐴 + Ω 𝑋 ] and 20 % for the one at [Ω 𝑋 ; Ω 𝐴 + Ω 𝑋 ] (Figure 3c and3d). This significant sensitivity enhancement for both peaks allows a reduction of the limit of c,d) show a significant increase in sensitivity when 𝑡 𝑚𝑖𝑥 is set to the optimal value determined thanks to these J-modulation curves, i.e.100 ms (d), compared to 𝑡 𝑚𝑖𝑥 = 0 ms (c). All the spectra are recorded on a 400 MHz spectrometer equipped with a 5 mm dual+ 1 H/ 13 C probe; within 16 scans, resulting in an acquisition time of 1 min. Please do not adjust margins Please do not adjust margins detection, non-negligible in the case of UF experiments for which sensitivity remains one of the major limitations. The optimization of sensitivity for complex samples containing different spin systems will obviously require compromising between different coupling constants. An appropriate approach consists in avoiding situations in which some peaks are missing, whereas others have a maximum intensity under the influence of J-modulation effects. This strategy was recently described for UF-COSY, 37 as well as a multi-scan approach which consists in adding several spectra recorded with different tmix values. These methods should be easily transposed to the case of UF-DQS.

Sensitivity considerations

The sensitivity of the UF-DQS approach should be compared to the one of related methods for quantitative 2D NMR, i.e. conventional DQS on the one hand, and UF-COSY on the other hand. In order to perform such comparison, UF-COSY and UF-DQS experiments and their conventional counterparts are performed on a metabolite mixture. Both UF and conventional experiments use a CT scheme. The time spent in the transverse plane is the same for all experiments, making the impact of Jmodulation comparable in conventional and UF spectra. The spectral widths are identical between conventional and UF-COSY, as between conventional and UF-DQS. As the indirect spectral width is larger for DQS vs COSY experiments, the two conventional approaches are compared with identical numbers of points per Hertz in the indirect dimension. For conventional experiments, it results in a longer experiment time for DQS vs COSY (16 min vs 10 min). UF spectra are recorded with a number of scans yielding the same overall duration as their conventional equivalent. Apodization functions are optimized to yield the best compromise between signal-to-noise ratio (SNR) and resolution, as previously described. 41 SNR measurements are performed in both direct and indirect dimensions and normalized by the root mean square of the experiment duration. The peaks considered for each metabolite in the UF spectra are indicated on figures 1c and 1d. The corresponding peaks are used in the conventional spectra (shown in supplementary figure S1). The DQS/COSY and UF/conventional relative sensitivity is calculated from the ratios of their respective SNR values, i.e. SNR DQS /SNR COSY and SNR UF /SNR Conv (Tables 1 and2

respectively).

Considering SNR DQS /SNR COSY ratios, the nature of the more sensitive experiment between DQS and COSY appears to be peak dependent, both in conventional and in ultrafast experiments. This is explained in part by the different Jmodulation effects in the two experiments, which were not optimized for a specific case. Still, on average no significant losses are observed using DQS, both in the conventional or UF cases. Regarding the SNR UF /SNR Conv ratios, the sensitivity effects are dimension-dependent. In the indirect dimension which is the limiting dimension in terms of sensitivity, SNR UF /SNR Conv ratios for COSY experiments show that the nature of the more sensitive experiment is peak-dependent. This is coherent with previous observations. 42 On the contrary, for all metabolites, UF-DQS experiments appear to be more sensitive than their conventional counterparts in the indirect dimension. This feature may be explained by the large t1-noise ridges observed on the conventional DQS spectra. In the direct dimension, conventional experiments are more sensitive, which is a wellknown characteristic of UF 2D NMR. 21 Nevertheless, the sensitivity issues are mainly governed by the indirect dimension, as described recently. 42 Overall, Tables 1 and2 show that the sensitivity is similar for UF-COSY and UF-DQS, but that the sensitivity of UF-DQS experiments is noticeably higher than its conventional counterpart in the limiting dimension. UF-DQS appears as a powerful alternative to existing methods for the analysis of complex mixtures, especially when peak overlaps in COSY spectra prevent the accurate quantification of some analytes.

Evaluation of the quantitative performance

In order to assess the quantitative performance of the UF-DQS approach, we consider here the quantification of taurine, a small-molecule analyte, in an energy drink. We consider both a homemade and a commercial sample; the homemade sample of known true concentration (29.56 mM) is needed to evaluate the trueness of the quantitative method. Energy drinks usually contain highly concentrated sugars, which result in strong overlap and a high dynamic range in COSY spectra. This is illustrated in Fig. 4b for the homemade sample. The DQS approach is expected to overcome these two limitations. The UF-DQS spectrum of the homemade sample drink, shown in Fig. 4c, indeed has a lower density of peaks than the COSY This journal is © The Royal Society of Chemistry 20xx

Please do not adjust margins Please do not adjust margins spectrum and thus less overlap. In addition, the absence of auto-correlation peaks leads to a significant reduction of the dynamic range. An additional benefit is the absence, in these interleaved experiments, of artefactual "ghost" peaks. 36 Quantification is performed here with a standard addition procedure, an approach commonly used to obtain accurate quantitative results from 2D NMR spectra. 22,35,43 The standard addition approach ensures that the trueness of the result does not depend on peak-specific parameters such as J-modulation.

Here, to ensure accurate results, all spectra are recorded in 4 minutes using 45 scans. Such signal averaging yields sufficient SNR even for the sample containing the lowest amount of taurine. The resulting standard addition curves are shown in figures 4c and 4d.

The analytical properties -linearity, precision and trueness-of the UF-DQS pulse sequence are compared to those obtained from UF-COSY in table 3.

Even though a good linearity and precision are obtained for both sequences, the trueness of the method is far better using the UF-DQS pulse sequence than UF-COSY. The high error on the determination of concentration in UF-COSY is a clear sign of bias, which is most likely explained by the strong overlap between the signals of interest and the neighbouring peaks from glucose (Fig. 4 b). On the contrary, these peaks do not overlap with the taurine signals on the UF-DQS spectrum (Fig. 4 d) thanks to the spectral simplification obtained through

Conclusions

The detailed characterization of the recently introduced UF-DQS NMR methods provides an in-depth understanding of its properties and a clear illustration of its analytical potential. Theory and simulation studies make it possible to fine-tune experimental parameters: 𝑡 𝑚𝑖𝑥 , the delay placed prior to the spatial encoding step, and β, the angle achieved by the mixing pulse. As we demonstrate in the case of an example smallmolecule, these optimizations can lead to a significant enhancement of the sensitivity of UF-DQS experiments, thus lowering the limit of detection. Sensitivity considerations and evaluation of the analytical performance show comparable results between UF-COSY and UF-DQS, however the latter appear to be far more sensitive than its conventional counterpart in the indirect dimension which governs the sensitivity limitations.

As illustrated by the quantification of taurine in energy drinks by a standard addition procedure, the UF-DQS experiment yields more accurate results than UF-COSY (one of the most widely used ultrafast pulse sequences) in cases of high dynamic ranges and overlaps in the UF-COSY spectrum, thanks to the absence of auto-correlation peaks and lower density of peaks in this type of spectra. UF-DQS is thus expected to become a useful component of the NMR toolbox for the analysis of complex mixtures.

Figure 1 .

 1 Figure 1. (a) UF-DQS pulse sequence, (Δ = 1 4 ⁄ • 𝐽 𝐻-𝐻 ). (b) UF-COSY and (c) UF-DQS spectra of a metabolite mixture recorded on a 700 MHz spectrometer equipped with a cryoprobe. The two spectra were recorded in four interleaved scans to increase the observable spectral width, 28 and 46 scans for UF-COSY and UF-DQS respectively, resulting in acquisition times of 10 min and 16 min, using a double-quantum buildup delay Δ = 35.7 ms.

cho

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Figure 2 .

 2 Figure 2. Theoretical (solid line) and simulated (circles) J-modulation for an AMX spin system where spin M is coupled to spins A and X. J-modulation is studied for the peak located at [Ω 𝐴 ; Ω 𝐴 + Ω 𝑋 ]. The curves are normalized to their maximum.

Figure 3 .

 3 Figure 3. Integrals of the simulated versus experimental signals as a function of 𝑡 𝑚𝑖𝑥 for both peaks on the UF-DQS spectrum of alanine (a and b). 2D spectra and relative projections (c, d) show a significant increase in sensitivity when 𝑡 𝑚𝑖𝑥 is set to the optimal value determined thanks to these J-modulation curves, i.e.100 ms (d), compared to 𝑡 𝑚𝑖𝑥 = 0 ms (c). All the spectra are recorded on a 400 MHz spectrometer equipped with a 5 mm dual+ 1 H/13 C probe; within 16 scans, resulting in an acquisition time of 1 min.

[

  Ω 𝐴 ; Ω 𝐴 +Ω 𝑋 ] [Ω 𝑋 ; Ω 𝐴 +Ω 𝑋 ]

Figure 4 .

 4 Figure 4. Quantification of taurine (a) in a homemade energy drink by a standard addition procedure. The latter is performed using both UF-COSY -spectrum shown in (b) and corresponding standard curve in (c) -and UF-DQS experiments -spectrum shown in (d) and corresponding standard curve in (e). The 2D peak volume is plotted as a function of the added concentration Ca. Ci represents the initial taurine concentration. The signals arising from taurine are indicated in both spectra (red square). All the spectra are recorded on a 400 MHz spectrometer equipped with a 5 mm dual+ 1H/13C probe; within 45 scans, resulting in an acquisition time of 4 min, thus allowing a sufficient SNR for quantification even for the sample containing the lowest amount of taurine.

  double-quantum spectroscopy, leading to a strong reduction of the error on concentration (1.4 %). The same procedure is performed on the commercial energy drink RedBull. The indicative value of concentration in taurine given by the supplier is 32.2 mM. By the use of UF-DQS, the calculated concentration (27.88 mM) is close to this indicative value, whereas by the use of UF-COSY the calculated concentration reaches 52.17 mM. These results are in agreement with the discrepancies in terms of trueness between UF-COSY and UF-DQS determined by the study of our homemade energy drink. These results highlight the usefulness of the UF-DQS pulse sequence for cases where UF-COSY spectra are characterized by high dynamic ranges and strong overlaps.

Table 1 .

 1 SNR DQS /SNR COSY along the two dimensions of conventional (Conv.) and UF experiments, for the different metabolites observed in the spectra shown in Fig.1

		Direct dimension	Indirect dimension
		Conv.	UF	Conv.	UF
	Thr	1.25 ± 0.13 1.05 ± 0.26	1.38 ± 0.54 2.58 ± 0.27
	Lac	0.38 ± 0.09 1.67 ± 0.25	1.67 ± 0.41 3.28 ± 0.28
	Ala	1.88 ± 0.11 1.06 ± 0.34	1.97 ± 0.41 2.36 ± 0.27
	His	1.01 ± 0.16 0.79 ± 0.14	0.65 ± 0.22 1.08 ± 0.38
	Cho	1.17 ± 0.13 0.53 ± 0.35	0.80 ± 0.22 0.78 ± 0.44

Table 2 .

 2 SNR UF /SNR conv along the two dimensions of COSY and DQS experiments, for the different metabolites observed in the spectra shown in Fig.1

		Direct dimension	Indirect dimension
		COSY	DQS	COSY	DQS
	Thr	0.18 ± 0.24	0.15 ± 0.16	0,78 ± 0.58	1,45 ± 0.17
	Lac	0.15 ± 0.24	0.66 ± 0.13	1,38 ± 0.45	2,71 ± 0.21
	Ala	0.27 ± 0.33	0.15 ± 0.13	1,72 ± 0.46	2,07 ± 0.18
	His	0.25 ± 0.14	0.19 ± 0.16	0,63 ± 0.35	1,05 ± 0.27
	Cho	0.62 ± 0.15	0.28 ± 0.35	5,36 ± 0.39	5,24 ± 0.30

Table 3 .

 3 Analytical properties of UF-COSY and UF-DQS pulse sequences in the quantification of taurine in a homemade energy drink by a standard addition procedure. True concentration in taurine: 29.56 mM.

		UF-COSY	UF-DQS
	Linearity (R²)	0.9991	0.9998
	Precision (RSD)	0.82 %	2.09 %
	Trueness ([tau]calc)	47.52 mM	29.96 mM
	Error	60.8 %	1.4 %

This journal is © The Royal Society of Chemistry 20xx J. Name., 2013, 00, 1-3 | 5

Acknowledgements

We warmly thank Prof. Malcolm H. Levitt and Dr. Ilya Kuprov (University of Southampton) for fruitful discussions. We also acknowledge Michel Giraudeau for linguistic assistance.


Laetitia Rouger

Maxime Yon

Vincent Sarou-Kanian

Franck Fayon

Jean ̵ Nicolas Dumez
email: jeannicolas.dumez@cnrs.fr

Patrick Giraudeau
email: patrick.giraudeau@univ-nantes.fr

Ultrafast acquisition of 1 H-1 H dipolar correlation experiments in spinning elastomers

Keywords: ultrafast NMR, solid-state NMR, double quantum, spin diffusion

We show that two widely used 2D solid-state NMR (ssNMR) pulse sequences can be implemented in an ultrafast (UF) manner, and yield 2D spectra of elastomers in a single scan, under magic-angle spinning. UF 2D ssNMR provides an acceleration of one to several orders of magnitude for classic experiments.

Introduction

Multidimensional nuclear magnetic resonance spectroscopy (NMR) [START_REF] Jeener | Lecture Presented at Ampere International Summer School II[END_REF][START_REF] Aue | Two-dimensional spectroscopy. Application to nuclear magnetic resonance[END_REF] is a major tool for elucidating the structure of solid samples in chemical, materials and biological sciences. [START_REF] Baccile | Structural Characterization of Hydrothermal Carbon Spheres by Advanced Solid-State MAS 13C NMR Investigations[END_REF][START_REF] Brown | Advanced Solid-State NMR Methods for the Elucidation of Structure and Dynamics of Molecular, Macromolecular, and Supramolecular Systems[END_REF][START_REF] Li | Structure Elucidation of Three Triterpenoid Saponins from Alphitonia zizyphoides Using 2D NMR Techniques[END_REF][START_REF] Topcu | Structure elucidation of organic compounds from natural sources using 1D and 2D NMR techniques[END_REF] Classic 2D NMR spectroscopy, however, relies on a scheme that is intrinsically timeconsuming, even when ample sensitivity is available. This is due to the need to repeat multiple 1D sub-experiments to sample incrementally the additional time dimension. This long experiment duration is a major obstacle to the analysis of samples with very long longitudinal relaxation times, which include a variety of organic and inorganic materials. It also prevents the acquisition of detailed structural information, which is usually obtained in the form of series of 2D experiments. [START_REF] Bennett | Quantitative conformational measurements in solid state NMR by constant-time homonuclear dipolar recoupling[END_REF][START_REF] Ramamoorthy | 2D 1H/1H RFDR and NOESY NMR Experiments on a Membrane-Bound Antimicrobial Peptide Under Magic Angle Spinning[END_REF] Several strategies have been developed to overcome the speed limitations of multidimensional (ND) solid-state NMR (ssNMR). Paramagnetic doping is a convenient method to shorten relaxation delays, with the caveat of possibly inducing unwanted structural changes. [START_REF] Ganapathy | Paramagnetic doping as an aid in obtaining high-resolution carbon-13 NMR spectra of biomolecules in the solid state[END_REF] More recently, "non-uniform sampling" (NUS) schemes have been implemented, which consist of collecting only a randomly selected subset of increments, and using non-Fourier processing methods. [START_REF] Hoch | Maximum entropy reconstruction of complex (phase-sensitive) spectra[END_REF][START_REF] Stern | Modern spectrum analysis in multidimensional NMR spectroscopy: comparison of linear-prediction extrapolation and maximum-entropy reconstruction[END_REF] In solution-state NMR, the most dramatic acceleration of ND acquisitions is obtained with the so-called "ultrafast (UF) NMR" approach, which makes it possible to acquire 2D NMR spectra within a single scan. [START_REF] Frydman | The acquisition of multidimensional NMR spectra within a single scan[END_REF] UF NMR relies on a spatial rather than temporal encoding of the NMR interactions. Resonances are encoded with a combination of bipolar gradients and linearly frequency-swept pulses, and decoded during acquisition with an echo-planar spectroscopic imaging (EPSI) scheme. Applications of liquid-state UF NMR have been reported in a variety of fields such as metabolomics, real-time reaction monitoring, or hyphenated techniques such as chromatography or dissolution dynamic nuclear polarization (DNP). [START_REF] Giraudeau | Ultrafast 2D NMR: An Emerging Tool in Analytical Spectroscopy[END_REF] The possibility to accelerate ND ssNMR experiments with spatial encoding, however, remains largely unexplored.

Magic-angle spinning (MAS) probes are rarely equipped with a magnetic field gradient.

While "high-resolution MAS" (HR-MAS) probes more commonly have gradients, and may be used for UF 2D NMR, [START_REF] Andre | Ultrafast high-resolution magic-anglespinning NMR spectroscopy[END_REF] they do not deliver the radio-frequency (RF) power needed for most ssNMR experiments. Gradient-enhanced experiments may still be a carried out, using a standard ssNMR probe together with external microimaging gradients. [START_REF] Maas | Magnetic Field Gradients in Solid State Magic Angle Spinning NMR[END_REF][START_REF] Fischbach | PFG-assisted selection and suppression of 1H NMR signals in the solid state under fast MAS[END_REF] In a pioneering study, Frydman and co-workers used such a setup to acquire UF NOESY spectra of rubber samples. They also characterised the detrimental effects of misalignments of the rotor spinning axis and the magnetic field gradient. [START_REF] Gal | Solid-state single-scan 2D NMR under magic-angle-spinning[END_REF] An alternative was also proposed, based on orientational encoding. [START_REF] Bhattacharyya | Ultrafast Solid-State 2D NMR Experiments via Orientational Encoding[END_REF] Nonetheless, to the best of our knowledge, no UF implementation of an ssNMR pulse sequence has been reported.

In this communication, we show that two of the most widely used 2D ssNMR experiments, double-quantum correlation (DQ) [START_REF] Sommer | Dipolar Heteronuclear Multiple-Quantum NMR Spectroscopy in Rotating Solids[END_REF][START_REF] Schnell | High-Resolution 1H NMR Spectroscopy in the Solid State: Very Fast Sample Rotation and Multiple-Quantum Coherences[END_REF] and RF-driven proton spin diffusion (PSD) [START_REF] Bennett | Chemical shift correlation spectroscopy in rotating solids: Radio frequency-driven dipolar recoupling and longitudinal exchange[END_REF][START_REF] Bennett | Homonuclear radio frequency-driven recoupling in rotating solids[END_REF] can be recorded in a single scan, using spatial encoding. We chose to investigate 1 H correlation experiments since they offer optimum sensitivity and spectral width conditions for UF experiments. These experiments are performed at very high field (17.6 T), using a double resonance MAS probe together with microimaging gradients, on a natural rubber sample. Such ultrafast 2D experiments make it possible to expedite the acquisition of spin-diffusion build-up curves, which are a central tool for structural studies in disordered solids.

Results and discussion

The pulse sequences for ultrafast double-quantum correlation experiments (UF-DQ) and proton spin diffusion (UF-PSD) are shown in Fig. 1. Their main features compared to their conventional counterpart are i) the replacement of the conventional t1 incremented evolution by a spatial encoding block consisting of a pair of 180° chirp pulses applied during alternating gradients; ii) the replacement of the conventional detection by an EPSI scheme. Pulsed field gradients are used also for coherence selection, a feature that is rarely used in solid-state NMR and that is found to work appropriately here. The other pulse sequence elements are similar to those of conventional pulse sequences. In the UF-DQ experiment, rotor-synchronized back-toback (BABA) 90° radiofrequency pulse cycles [START_REF] Saalwächter | BaBa-xy16: Robust and broadband homonuclear DQ recoupling for applications in rigid and soft solids up to the highest MAS frequencies[END_REF] are applied during 3.28 ms (64 rotor periods) to generate double quantum coherences between dipolar-coupled spins. During the reconversion period, BABA cycles are used again to reconvert double quantum coherences back to longitudinal magnetisation. In the UF-PSD experiment, radio frequency-driven recoupling (RFDR) 180° radiofrequency pulse cycles with xy-8 phase alternation are used to reintroduce dipole-dipole couplings during the mixing period and induce a transfer of longitudinal magnetisation. [START_REF] Bennett | Chemical shift correlation spectroscopy in rotating solids: Radio frequency-driven dipolar recoupling and longitudinal exchange[END_REF] Two complementary measures were taken to avoid interferences between sample rotation and the periodic acquisition gradient train. [START_REF] Andre | Ultrafast high-resolution magic-anglespinning NMR spectroscopy[END_REF] First, a composition of the gradients along the three physical axes was used to yield a spatial encoding gradient sufficiently aligned with the MAS axis. This alignment is obtained by careful calibration on a silicone sample (see SI). Second, the duration of a readout gradient (Ta) is chosen to be an even multiple of the rotor period. With these precautions, echo trains of 131 ms were recorded without significant signal losses due to interferences, and no spinning sidebands were observed.

The UF-DQ and UF-PSD spectra of a sample of natural rubber are shown in Fig. 2, together with their conventional counterparts. The UF-PSD spectrum was recorded in a single scan of 275 ms, which is over 500 times faster than the conventional spectrum. For the UF-DQ spectrum, 8 scans were accumulated, in order to observe the least intense cross peak. While not single-scan, the UF experiment remains much shorter than the conventional one.

A comparison between UF and conventional spectra reveals that the UF implementation yields the same information, in a much shorter time. Note that the conventional spectra were also acquired using pulsed-field gradients for coherence selection and no phase cycling. The UF spectra were recorded with folding in the direct dimension to optimize the compromise between spectral widths, resolution and gradient amplitudes -a well-known feature of UF experiments. [START_REF] Giraudeau | Ultrafast 2D NMR: An Emerging Tool in Analytical Spectroscopy[END_REF] The appropriate spectral width to avoid overlap can be determined from the 1D spectrum. If needed, a larger spectral width could be recovered by means of interleaving, albeit at the cost of an extended experiment time. [START_REF] Frydman | Principles and features of single-scan twodimensional NMR spectroscopy[END_REF][START_REF] Rouger | Processing strategies to obtain clean interleaved ultrafast 2D NMR spectra[END_REF] One should also note that the resolution of UF spectra is governed by intrinsic characteristics of UF pulse sequences, as already described for liquids. [START_REF] Giraudeau | Resolution and sensitivity aspects of ultrafast J-resolved 2D NMR spectra[END_REF][START_REF] Giraudeau | Sources of sensitivity losses in ultrafast 2D NMR[END_REF][START_REF] Shrot | The effects of molecular diffusion in ultrafast 2D NMR[END_REF][START_REF] Giraudeau | Sensitivity losses and line shape modifications due to molecular diffusion in continuous encoding ultrafast 2D NMR experiments[END_REF] In particular, a compromise has to be set along the indirect dimension between resolution, spectral width and sensitivity. The UF spectra also display a peak splitting at 2.98 ppm in the conventional dimension, along with an important sensitivity loss, which is not observed in the conventional ones. The sensitivity loss is due to a short-T2 component, as illustrated in Fig. 2. The supplementary modulation observed, leading to the splitting of the peak, has not been analyzed in detail, but it illustrates the limitation of the method for samples with short T2 values. It should also be noted that, in the conventional DQ experiment, the cross-correlation peaks show elongated lineshapes (along the DQ diagonal with a slope of 2) characteristic of correlated disorder. [START_REF] Sakellariou | High-Resolution NMR Correlation Spectra of Disordered Solids[END_REF] These features are however masked in the UF-DQ spectra due to apodization in the ultrafast dimension.

Accelerated acquisitions are particularly promising for arrayed 2D experiments, e.g., for the acquisition of DQ or PSD build-up curves. Such data plays a central role in the structural characterization of solids by NMR, but the corresponding experiments are time-consuming due to the need to acquire multiple 2D spectra. Figure 3 shows experimental spin diffusion buildup curves, obtained on a natural rubber sample with a series of UF experiments compared to conventional experiments. The UF implementation is considerably faster than the conventional one, since only 5 min are necessary to record the UF spin-diffusion curves, versus 57 min with the conventional pulse sequence. A qualitative agreement is observed between UF and conventional curves. Several key features, such as the initial delay of some build-up curves (e.g., CH → CH3) or the bell shape of the CH2 → CH curves, are well captured by the UF implementation. The offset observed in some cases between UF and conventional build-up curves, as well as the non-zero initial values for some cross-peaks, are due to peak overlap and residual artefacts (see the caption of figure 3). Future developments will consider improving the spectral resolution of UF spectra through alternative spatial encoding schemes. Such offsets could also be accounted for at a modeling stage. The quantitative description of spin diffusion in such complex sample, however, is beyond the scope of this communication.

This type of curves can provide relevant qualitative information about complex samples.

By offering the possibility to acquire the entire data set more than 10 times faster than it conventional counterpart, the UF-PSD MAS pulse sequence appears as a promising tool to perform a quick and advanced screening of real systems of industrial interest such as complex polymers.

While it may provide a dramatic acceleration for a variety of samples and experiments, UF MAS NMR will be of limited use when dealing with short transverse relaxation times, since the spatial encoding duration cannot be reduced significantly without resolution losses. [START_REF] Giraudeau | Resolution and sensitivity aspects of ultrafast J-resolved 2D NMR spectra[END_REF] Thus, the ultrafast method will prove to be particularly useful in the case of soft, compared to hard solids characterised by short transverse relaxation times. Nevertheless, the study of a broad variety of materials could benefit from the acceleration offered by this technique. In addition, UF 2D NMR suffers from well-characterised sensitivity losses due the single-scan nature of the experiment, or to the large frequency dispersion induced by the gradients during acquisition, as well as from artefacts arising in MAS-UF NMR potentially masking the low intensity cross peaks. [START_REF] Andre | Ultrafast high-resolution magic-anglespinning NMR spectroscopy[END_REF] These specific features of UF experiments have been widely characterized in previous studies, whose conclusions also apply to the present methods. [START_REF] Giraudeau | Ultrafast 2D NMR: An Emerging Tool in Analytical Spectroscopy[END_REF] Improvements may be obtained, at a reasonable time cost, with the use of "hybrid" multi-scan methods. [START_REF] Akoka | Fast hybrid multi-dimensional NMR methods based on ultrafast 2D NMR[END_REF]

Conclusion

We have shown that two of the most widely used solid-state NMR experiments can be recorded in a single scan, using spatial encoding. Such ultrafast experiments are particularly promising for structural studies by solid-state NMR, which require arrays of 2D spectra. UF 2D ssNMR experiments will also prove useful for applications to samples with long longitudinal relaxation times. The sensitivity requirements of UF 2D NMR can be commonly met for nuclear such as 1 H or 31 P and may be extended to other nuclei with dynamic nuclear polarisation. The ultrafast method could also be used to speed up higher dimensional solid-state experiments in a pure ultrafast fashion [START_REF] Shrot | Single-scan NMR spectroscopy at arbitrary dimensions[END_REF] or in an hybrid fashion [START_REF] Giraudeau | UFJCOSY: a Fast 3D NMR Method for Measuring Isotopic Enrichments in Complex Samples[END_REF], leading to an acquisition time for a 3D experiment equivalent to a conventional 2D experiment.

Experimental

All the measurements were carried out on a Bruker AVANCE III spectrometer operating at a magnetic field of 17.6 T (corresponding to 1 H Larmor frequency of 750.13 MHz), equipped with a Bruker 3.2 double resonance MAS probe and a Bruker Micro 2.5 gradient system (triple axis, 2.5 G/cm/A, 40 A/axis).

To apply a gradient exactly along the MAS axis, the three laboratory-frame gradient coils have to deliver the same gradient strengths. The currents applied to the three coils were thus carefully adjusted by maximizing the center band intensity in a 1D profile of a rotating cylindrical silicone sample when applying combinations of two (of the three) laboratory-frame gradients. The intensity maximum is obtained when the resulting gradient is perpendicular to the MAS axis (corresponding to equivalent intensities of the two applied gradients). The spinning frequency was set to 19532 Hz, such that the duration of an acquisition gradient (1024 µs) was an even multiple of the rotor period (51.2 µs).

For all the ultrafast (UF) experiments, spatial encoding was performed by using a constant-time scheme, consisting of a double spin echo with 8 ms smoothed chirp encoding pulses. The sweep range of the encoding pulses was set to 20 kHz. The amplitude of the encoding gradients was adapted to obtain a frequency dispersion equivalent to the frequency range of the pulses: 0.052 T/m. The acquisition block used 64 detection gradient pairs. The duration of each acquisition gradient was 1024 µs with an amplitude of 0.433 T/m. A single scan was recorded for the UF-PSD spectrum; 8 scans were recorded for the UF-DQ spectrum, with a recovery delay of 3 s. Coherence selection was performed by 1024 µs gradients as indicated in Figure 1a with 0.727 T/m and 0.346 T/m gradient amplitudes for the UF-DQ experiment, and as indicated Figure 1b with 1.039 T/m and 1.143 T/m gradient amplitudes for the UF-PSD experiment. The specific processing of the UF spectra was performed with a homewritten Matlab routine. A sinusoidal apodization was applied in the direct dimension and a spatial Gaussian apodization was applied in the indirect dimension. [START_REF] Giraudeau | Sensitivity and lineshape improvement in ultrafast 2D NMR by optimized apodization in the spatially encoded dimension[END_REF] Zero-filling was applied in both dimensions as described in reference 29 for the indirect dimension.

The conventional DQ spectrum (Fig. 2a) was acquired with 16 dummy scans, 256 t1 increments and 4 scans with a recovery delay of 0.25 s, resulting in an acquisition time of approximatively 5 min. The conventional PSD spectrum (Fig. 2c) was acquired with 8 dummy scans, 256 t1 increments and 8 scans with a recovery delay of 0.25 s, resulting in an acquisition time of approximatively 9 min. Phase cycling was performed in 8 steps for the DQ experiment, and 4 steps for the PSD experiment. For these two spectra, an exponential apodization was performed in both dimensions, and zero-filling was only used in the direct dimension.

For PSD build-up curves (Fig. 3), 26 conventional PSD and UF-PSD spectra were acquired. The conventional ones were acquired with 8 dummy scans, 128 t1 increments and 4 scans with a recovery delay of 0.25 s, resulting in an acquisition time of 130 s. Phase cycling was performed in 4 steps. A sinusoidal apodization and zero filling were applied in both dimensions. UF-PSD spectra were acquired and processed with the same conditions as those described for figure 2d. Peak volumes were determined with Topspin 3.2, and the whole datasets were normalized with Matlab in order to minimize the global intensity differences between UF and conventional curves.

In the UF-DQ experiment, rotor-synchronized back-to-back (BABA) 90° radiofrequency pulse cycles [START_REF] Saalwächter | BaBa-xy16: Robust and broadband homonuclear DQ recoupling for applications in rigid and soft solids up to the highest MAS frequencies[END_REF] were applied during 3.28 ms (64 rotor periods) with a radio frequency field of 80 kHz to generate double quantum coherences between dipolar-coupled spins. The same number of BABA cycles was used to reconvert double quantum coherences back to longitudinal magnetisation. In the UF-PSD experiment, radio frequency-driven recoupling (RFDR) cycles with xy-8 phase alternation were employed to promote longitudinal magnetisation transfer during the mixing period. [START_REF] Bennett | Chemical shift correlation spectroscopy in rotating solids: Radio frequency-driven dipolar recoupling and longitudinal exchange[END_REF] Figures

Fig. 2

 2 Fig.2Conventional (a) and ultrafast (b) DQ spectra spectra of a natural rubber sample recorded in 5 min and 36 s, respectively. Conventional (c) and ultrafast (d) PSD spectra of the same sample, recorded in 9 min and less than 1 s, respectively. The spectral regions displayed in the ultrafast spectra are highlighted by a red square in the corresponding conventional spectrum, while the folded region appears in purple. 1D spectra of this sample, with a non-delayed (e) and a delayed (f) acquisition, show the peak shape deformation of the peak at 2.08 ppm.

Fig. 1 Fig. 3

 13 Fig.2Conventional (a) and ultrafast (b) DQ spectra spectra of a natural rubber sample recorded in 5 min and 36 s, respectively. Conventional (c) and ultrafast (d) PSD spectra of the same sample, recorded in 9 min and less than 1 s, respectively. The spectral regions displayed in the ultrafast spectra are highlighted by a red square in the corresponding conventional spectrum, while the folded region appears in purple. 1D spectra of this sample, with a non-delayed (e) and a delayed (f) acquisition, show the peak shape deformation of the peak at 2.08 ppm.

Acknowledgements

Financial support from the TGIR-RMN-THC Fr3050 CNRS for conducting the research is gratefully acknowledged.