Multiple solvent signal presaturation in 13C NMR

. The analysis by proton-decoupled carbon-13 nuclear magnetic resonance spectroscopy of samples dissolved in solvents presenting strong multiple resonances can be facilitated by the suppression of these resonances by multi–site presaturation. The advantage drawn from this operation is the elimination of the possible artifacts that arise from the solvent signals in non–optimized decoupling conditions. Solvent presaturation was implemented on glycerol, 1,2–propanediol, 1,3–propanediol, 1,2–butanediol, 1,3–butanediol with at least 94 % on–resonance efﬁciency and a bandwidth of less than 50 Hz measured at 5 50 % signal intensity decrease. The experimental measurement of the signal suppression bandwidth leads to unexpected selectivity proﬁles for frequency close resonances. Computer resolution of the Bloch equations during multi–site presaturation provide an insight into the origin of the observed proﬁle perturbations.

1 Introduction 10 Nuclear magnetic resonance (NMR) is the only spectroscopic method used for the structural elucidation of organic molecules that produces information at the atomic level. Liquid state NMR of proteins strongly relies on the observation of the amide NH proton resonances and is therefore carried out in a solvent mainly composed of light water. The concentration of hydrogen in protein NMR samples (close to 100 mol L −1 ) compared to the one of the protein itself (1 mmol L −1 or less, (Zheng and Price, 2010)) forced NMR spectroscopists to create efficient water signal suppression techniques (Lee et al., 2017;Chen et al., 2017; 15 Duarte et al., 2013;Gouilleux et al., 2017). Without them, the water signal would cover a wide band of signals of high structural importance and would also hamper the accurate operation of analog to digital signal conversion devices (Mo and Raftery, 2008) resulting in detection sensitivity reduction. Small molecule NMR also benefits from solvent signal suppression techniques when hyphenated to liquid chromatography in the study of fluids of biological (plasma, urine, ...) or food (fruit juices, alcoholic beverages, ...) interest (Friedbolin, 2011;Kew et al., 2017). 20 A high signal rejection ratio, a low pertubation of the baseline, and a narrow signal attenuation frequency window define a high quality of a solvent signal suppression technique (Zheng and Price, 2010). A narrow suppression window ensures that the 1 intensities of resonances close to the one of the solvent will be preserved at best. Solvent resonance presaturation is the oldest of these techniques and consists in the application during the relaxation delay of a low power radiofrequency (RF) field on resonance with the solvent signal (Hoult, 1976) (Ross et al., 2007). 25 Multiple solvent signal suppression is a necessity in LC-NMR (Parella et al., 1998) and was involved in the study of the interactions of organic solvents with biomolecules (Dalvit, 1998). The suppression methods derived in these two cases from the original excitation sculpting pulse sequence (Hwang and Shaka, 1995) The eight signals produced by water and ethanol can be efficiently attenuated by presaturation for the study of alcoholic beverages by 1 H NMR (Monakhova et al., 2011). However, the presence of solvents is not a problem in 13 C NMR spectroscopy since their resonance lines are very sharp, relatively to the 30 width of the observation frequency window, and are not likely to overlap those of interest. The context of the present study is the characterization by 13 C NMR of compounds within natural extracts (Hubert et al., 2014) (Tsujimoto et al., 2018 (Bakiri et al., 2017). Plant extracts may be conditioned as dry products or as solutions in diverse solvents, possibly prepared from renewable resources and for which evaporation to dryness may be not feasible or not compatible with the chemical integrity of the solutes.
Alcohols like glycerol, propanediols, butanediols and pentanediols are employed for such applications (Chemat et al., 2019) 35 (Shehata et al., 2015). Their boiling points range from 188 • C to 290 • C under atmospheric pressure. The characterization of the solutes by 13 C NMR spectroscopy can be carried out on extracts or on fractions obtained by chromatographic methods.
The fractions of interest may also contain an important amount of these high boiling point solvents.
NMR data acquisition of series of samples is often carried out in automation mode with standard acquisition parameters. An accurate calibration of pulses on the 1 H RF channel is necessary to record 13 C{ 1 H} spectra in proper decoupling conditions.

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The optimal power of the decoupling pulses depend on probe tuning quality and on the nature the analytes. Decoupler power miscalibration may cause decoupling artifacts around the intense solvent signals, at a point their intensity is comparable to the one of the signals of interest (Blechta and Schraml, 2015).
Analytically misleading decoupling artifacts were observed during the analysis by 13 C NMR of chromatographic fractions containing glycerol, even though the probe was automatically tuned before each spectrum recording. The elimination of decou-45 pling artifacts through the reduction of their parent glycerol signals was achieved by multi-site presaturation, using multiple modulation of the RF field (Patt, 1992). The advantage drawn from this operation is not only the intensity reduction of the solvent signals but also the elimination of the possible artifacts that arise from the solvent signals in non-optimized decoupling conditions. To the best of our knowledge, solvent signal elimination has not been reported in the context of 13 C NMR spectroscopy.

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The assessment of the method included the determination of the frequency profile of signal attenuation around the presaturation frequencies. Samples that contain 1,2-propanediol show 13 C NMR spectra with two close resonance lines, a few Hz apart from each other, depending on concentration. The corresponding saturation profile showed unexpected features that incited us to investigate in detail the underlying spin dynamics by numerical simulation. The apparent interference effect between saturation pulses recalled the one observed for two closely frequency-shifted BURP pulses, as reported in the article entitled 55 "Close encounters between soft pulses" (Kupce and Freeman, 1995). In this article,Ē. Kupce and R. Freeman demonstrated that when the difference between the two frequency shifts has the same order of magnitude as the selective pulse operation bandwidth, then the resulting operation frequency profile presents a cahotic aspect.
The first part of the following section deals with simple theoretical aspects of presaturation. Experimental results include the study of a sucrose sample diluted in glycerol and show that presaturation is effective for decoupling artefact removal and 60 the handling of other solvents that present up to four resonances such as 1,2-propanediol, 1,3-propanediol, 1,2-butanediol and 1,3-butanediol.

Theory
Resonance saturation in NMR occurs when an RF field is continuously applied at a frequency equal to the resonance frequency of a nucleus. The magnetization dynamics of a collection of many identical isolated spins that constitutes a macroscopic sample 65 is governed by the Bloch equations (Bloch, 1946). The components M x , M y , and M z of the macroscopic magnetization M , when observed in the rotating frame of reference, evolve as follows, in which Ω 0 is the precession angular frequency of the nuclei, Ω 1 is the norm of the nutation vector expressed as an angular frequency, and (Ω 1x , Ω 1y ), the components of the latter on the X and Y axis of the rotating frame. Nuclear spin relaxation is phenomenologically described by the two rate constants R 1 and R 2 defined as the reciprocals of the longitudinal and transverse relaxation times T 1 and T 2 , respectively. M eq z denotes the value of the sample equilibrium nuclear magnetization and intervenes in the description of the longitudinal relaxation. In the case Ω 0 = 0 of an on-resonance constant intensity applied RF field, the 75 components of the magnetization vector tend toward a stationary limit for which If Ω 2 1 T 1 T 2 ≫ 1, then the stationary magnetization is much lower than the one of equilibrium, corresponding to an equalization of spin state populations induced by the RF field, as expected from saturation. Solvent signal suppression in NMR spectroscopy can be obtained by selective saturation of one or more solvent signals 80 during the relaxation delay. This technique is named presaturation because it precedes the non-selective excitation of the sample resonances. Presaturation at a single site is easily achieved by continuous wave RF irradiation. Multi-site presaturation relies on multiple-frequency-shifted laminar pulses, a particular species of shaped pulse (Patt, 1992). Such a shaped pulse serves as presaturation module of duration T and is applied repetitively to the sample so that the overall RF irradiation time is equal to the desired relaxation delay. A presaturation module is constituted by N elementary pulses, named slices hereafter, of and of the list of the frequency offsets Ω sat k associated to each site. The values of Ω 1x and Ω 1y are obtained from which states that RF field intensities are equally distributed among the n sites and phases arbitrarily are set to zero at t = 0.
The Ω sat k values are calculated relatively to an auxiliary carrier frequency determined as the average of the highest and the 90 lowest offsets of the signals to presaturate. The emission of the presaturation pulse has to take into account the difference between the auxiliary frequency and the actual transmitter frequency, the so-called shaped pulse offset, as described in Fig. 1. The value of δt is chosen so that the highest precession angle |Ω sat k |δt for the highest |Ω sat k | during that time must be kept below a small threshold value in the order of π/15. The value of N should be as high as possible and depends on the memory size available for shaped pulses in the pulse program sequencer. N = 50,000 was used throughout the present study. The N δt constituting slices. The action of each shaped pulse slice should be calculated by resolution of the Bloch equation system (Eqn. 1) over duration δt, even though a different method was followed, as explained hereafter.

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Exact solutions of the Bloch equations have been reported but bear some degree of complexity (Canet et al., 1994;Madhu and Kumar, 1995). They take account of magnetization precession, nutation and relaxation processes simultaneously. The approach followed here makes use of an easy to implement approximate solution. It relies on the observation that magnetization evolution induced by relaxation alone is slow compared to the one induced by simultaneous precession and nutation. The evolution of M solely under precession and nutation resumes to a rotation at angular frequency Ω eff , the norm of vector Ω eff (Ω 1x , Ω 1y , Ω 0 ) 110 when reported in the rotating frame of reference. The rotation axis is defined by the unitary vector u = Ω eff /Ω eff . For practical calculations, one needs to express the elements of the rotation matrix R u,θ in which θ = Ω eff δt and u(u x , u y , u z ).
Relaxation alone is taken into account by the following transformation of M .

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The evolution of M during a time slice of duration δt is simply calculated by the successive application of rotation and relaxation transformations. The approximation that consists in alternating rotation and relaxation instead of considering them simultaneously improves when δt tends to zero. A given δt time interval can be divided in two (or more) parts and the replace-ment of rotation(δt)-relaxation(δt) by two consecutive rotation(δt/2)-relaxation(δt/2) calculations provides a way to evaluate the error induced by the proposed calculation method.

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An identical approach to Bloch equations resolution was used for the optimization of band-selective uniform response pulses (BURP) in the presence of relaxation, leading to the design of pulses with silhouette largely unaffected by relaxation processes (SLURP), for which the underlying calculation details were not reported (Nuzillard and Freeman, 1994). The action of relaxation on frequency-domain profiles of BURP pulses were recalculated using exact solutions of the Bloch equations and the results were visually identical to those derived from the approximate treatment (Canet et al., 1994).

Results
The unwanted effect on 13 C NMR spectra of the presence of glycerol in high concentration was reproduced by the analysis of a solution of sucrose (29 mM) in DMSO-d 6 to which glycerol (3.62 M) was added. This sample constitutes a good approximation of a real case, as industrially prepared plant extracts are often delivered as solutions in high boiling point solvents like glycerol, at metabolite concentrations close to or lower than that of sucrose in our model preparation.
130 Fig. 3a presents the 13 C NMR spectrum of sample sucrose in glycerol and its comparison with the 13 C NMR spectrum of sucrose alone in DMSO-d 6 . The spectrum in Fig. 3c shows the residual signal of DMSO-d 6 and the twelve peaks from sucrose, two of them at δ 73.13 and δ 73.15 being not well resolved. The 13 C NMR spectrum of sucrose in glycerol contains supplementary peaks, the two intense ones of glycerol apart. Glycerol clearly introduced unexpected signals in the spectra, some with abnormal phases, but others that may be considered genuine, thus creating confusion in the analysis of unknown samples.

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Glycerol also introduces peaks that arise from production side-products present at very low but detectable concentrations. A possible origin of the artifact signals was first searched in a possible saturation of the spectrometer receiver or an intermodulation related problem; changing the receiver gain did not influence their position and phase, so that this hypothesis was not further considered (Marshall and Verdun, 1990). Receiver gain was set to its maximum value in all following experiments.
Broadband heteronuclear decoupling constitutes another source of artifacts in 13 C{ 1 H} NMR spectra. A proper adjustment 140 of power in the 1 H channel is required for the recording of an optimal, artifact-free 13 C spectrum with WALTZ-16 composite pulse decoupling (Shaka et al., 1983). Slight changes in decoupling RF power resulted in changes of position and phase of artifacts. The strongest signals being by far those of glycerol, their intensity reduction brought the decoupling artifact intensity below the noise level as shown by Fig. 3b. Obviously, a better calibration of the RF pulses in the decoupler channel would also reduce, if not eliminate, the decoupling artifacts. No attempt was undertaken to investigate other decoupling schemes. The 145 recording of series of samples in automation mode with a sample changer does not favor the calibration of decoupler RF pulse on a sample-to-sample basis, so that the study of strong signal reduction was undertaken.
Glycerol signal reduction in 13 C NMR was achieved by presaturation. As observed in Fig. 3b, reducing the intensity of solvent signals by double presaturation removed decoupling artifacts and the observed signals only arose from the compounds present in the sample. This procedure was carried out on more than 30 samples of natural extracts diluted in glycerol. The "#" sign indicates a signal from a minor compound contained in bio-sourced glycerol; b) Analysis of the same sample as in a) but with multiple presaturation of glycerol signals. The framed inserts show spectra overviews drawn at full vertical scale. In spectrum a) the resonance peaks of DMSO-d6 (the rightmost ones) are much smaller than those of glycerol while in b) the latter are hardly visible, thus demonstrating the efficiency of the glycerol resonance peak elimination. c) 13 C NMR spectrum of D(+)-sucrose (24 mM) in DMSO-d6. All acquisitions required the recording of 128 scans preceded by 8 dummy scans.
The characterization of glycerol signal presaturation was further undertaken by means of a sample made only of glycerol in DMSO-d 6 . The study relied on the pulse sequence in Fig. 4, which is a straighforward adaptation of zgpg from the TopSpin library, in which presaturation is implemented as the repeated emission of an RF shaped pulse. The minimal two-step phase program ensures that peaks are all identically phased and that their height is proportional to the amount of longitudinal magnetization present at the end of the presaturation period. Glycerol, C 3 H 8 O 3 , produces only two 13 C NMR signals by symmetry,  intensity reduction while simultaneous presaturation at sites A and B caused an attenuation better than than 97 %, as shown in Experimental saturation profiles were measured in order to evaluate the width of the frequency band concerned by signal attenuation. For this purpose, the frequency offset of the presaturation pulse was varied in 1 Hz steps around the value that 160 corresponds to the on-resonance RF field application. The presaturation bandwidth is defined by the interval of frequency offsets in which signal intensity is reduced at least by 50 %. The profile of the signal from position A in glycerol presented a bell shape whose full width at half height was 15 Hz for Ω 1 /2π = 11.7 Hz, that represents a bandwidth of 0.1 ppm at 151 MHz The power of presaturation RF pulses influences the on-resonance residual longitudinal magnetization and therefore the intensity of the residual signal. This power must be low enough to keep the presaturation band sufficiently narrow and high enough to achieve a useful signal suppression. Five experiments (not shown) were carried out by reducing the power of RF 170 pulse intensity from 58.7 Hz to 5.9 Hz. The intensity of the two residual signals were similar: signal attenuation was always at least 95 %. Based on this result, an intensity of 11.7 Hz was retained for presaturation pulses in all subsequent spectra recordings.
Multiple site presaturation was extended to other heavy solvents used as natural product extractants: 1,2-propanediol, 1,3propanediol, 1,2-butanediol and 1,3-butanediol. For all but 1,2-propanediol, presaturation reduced solvent signal intensity 175 by at least 94 %. Presaturation was also carried out on samples containing sucrose and each of the heavy solvents mentioned here above. The spectra recorded with and without presaturation as well as the corresponding raw NMR data are available for download. As expected, presaturation has resulted in a strong decrease of targeted signals and the removal of decoupling artifacts. Table 1 summarizes the results obtained for each heavy solvent, concerning signal attenuation and signal attenuation bandwidth.

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The elimination of the 13 C resonances of 1,2-propanediol led to an unexpected presaturation profile in the region of two oxygen-bearing carbons, due to their very close chemical shift values, 67.8 ppm and 67.9 ppm, as shown in Fig. 7. The profile showed puzzling irregular features that motivated the undertaking of a numerical simulation work. In this case δΩ sat /2π = 10 Hz. The simulated profile in Fig. 2f , corresponding to a 10 Hz offset, has similarities with the experimental one as shown in the Fig. 7 zoom frame. Indeed, a wavy effect is also observed at ± 20 Hz offset around the resonance. This phenomenon 185 generates a bandwidth for the two close signals of 1,2-propanediol (δ 63.8) higher than the one for the isolated signal (δ 20.4), respectively 46 Hz and 20 Hz. However, since 46 Hz corresponds to 0.3 ppm on our spectrometer, this result is still acceptable. Solvent signal suppression was automated for the five studied solvents by means of computer scripts written in C language.
The creation of the shaped pulse of the presaturation module was carried out by recording first a 13 C-{ 1 H} spectrum with the zgpg pulse sequence, noting the solvent resonance frequencies by spectrum peak picking, calculating the Ω sat k /2π frequencies sucrose were purchased from VWR. 1,3-propanediol and 1,3-butanediol were purchased from Alfa Aesar. 1,2-butanediol, was purchased from Sigma Aldrich. The sample containing D(+)-sucrose (29 mM) and glycerol in 0.6 mL of DMSO-d 6 was left overnight at room temperature to obtain a homogeneous solution.
All experiments were performed at 298 K on a Bruker Avance AVIII-600 spectrometer (Karlsruhe, Germany) equipped with a cryoprobe optimized for 1 H detection and with cooled 1 H, 13 C, and 2 H coils and preamplifiers. 13 C NMR spectra acquisition time. The pulse length for excitation was 13.7 µs and the relaxation delay was 3 s. Spectra were referenced for a central signal of DMSO-d 6 at δ 39.52.
The computer source code used in the present study was written in C language; it relied on the libxml2 library for the reading of the input data file (this may be an overkill for such a task, admittedly) and on the libsimu1 library for the calculation 205 of rotation matrices by means of Eqn. (4), as programmed for the design of SLURP pulses. The libsimu1 archive file also contains a proof of Eqn. (4). The computer code for saturation simulations is available from GitHub; its installation was tested with Cygwin in Windows 10 but should be easily carried out on any other platform that provides a C language compiler and UNIX-like tools.

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The present work provides a method for the saturation of intense solvent resonances in 13 C NMR spectroscopy, as those occurring during the analysis of complex plant extracts prepared in high boiling point solvents. The signal reduction of these solvents was successfully achieved using the multi-site presaturation technique.
Numerical simulation therefore helped us to understand the origin of unexpected presaturation profile related to the saturation of frequency close resonances, even though it neither takes into account instrumental shortcomings such as B 0 and B 1 215 field inhomogeneities nor incomplete relaxation between transient signal recordings. The evolution of the sample magnetization was determined through the use of a simple approximation for the resolution of the Bloch equations that might find applications in other contexts. This approach offers perspectives in signal suppression from other natural sample matrices and in the quantitative 13 C NMR analysis of extracts diluted in high boiling point solvents.
Code and data availability. The PresatSimul source code is available from https://github.com/nuzillard/PresatSimul. The libsimu1 source 220 code is available from https://github.com/nuzillard/Libsimu1. The data files, pulse sequence and script from which Figs Competing interests. The authors declare that they have no conflict of interest.