Quantitative 2D liquid-state NMR.

Feature article review Received: 27 January 2014

Revised: 7 March 2014

Accepted: 7 March 2014

Published online in Wiley Online Library

(wileyonlinelibrary.com) DOI 10.1002/mrc.4068

Quantitative 2D liquid-state NMR Patrick Giraudeau* Two-dimensional (2D) liquid-state NMR has a very high potential to simultaneously determine the absolute concentration of small molecules in complex mixtures, thanks to its capacity to separate overlapping resonances. However, it suffers from two main drawbacks that probably explain its relatively late development. First, the 2D NMR signal is strongly molecule-dependent and site-dependent; second, the long duration of 2D NMR experiments prevents its general use for high-throughput quantitative applications and affects its quantitative performance. Fortunately, the last 10 years has witnessed an increasing number of contributions where quantitative approaches based on 2D NMR were developed and applied to solve real analytical issues. This review aims at presenting these recent efforts to reach a high trueness and precision in quantitative measurements by 2D NMR. After highlighting the interest of 2D NMR for quantitative analysis, the different strategies to determine the absolute concentrations from 2D NMR spectra are described and illustrated by recent applications. The last part of the manuscript concerns the recent development of fast quantitative 2D NMR approaches, aiming at reducing the experiment duration while preserving – or even increasing – the analytical performance. We hope that this comprehensive review will help readers to apprehend the current landscape of quantitative 2D NMR, as well as the perspectives that may arise from it. Copyright © 2014 John Wiley & Sons, Ltd. Keywords: NMR; 1H; ultrafast 2D NMR

13

C; small molecules; 2D spectroscopy; quantitative analysis; concentration; calibration; standard additions;

Introduction Nuclear magnetic resonance (NMR) is one of the most versatile analytical techniques, as it offers a large range of experiments (liquid state and solid state, one and multidimensional spectroscopy, relaxometry, imaging, etc.) with applications in a large range of disciplines, from physics and chemistry to biology and medicine. It is widely used for its potential to provide structural information for the elucidation of complex molecular structures. While a great deal of attention has been paid to the capabilities of NMR for structural elucidation, its ability to determine the concentration of analytes in mixtures is generally less well known. However, NMR is a quantitative technique and has the recognized advantage of being both nondestructive and nonspecific (i.e. all molecular species can be detected simultaneously). Therefore, its potential for quantitative analysis is considerable. The quantitativity of NMR has been highlighted since its very early days, initially in the structural elucidation of organic compounds for the measurement of integrals.[1,2] In the field of analytical chemistry, the first quantitative analysis of a mixture by 1H NMR was reported in 1963 by Hollis.[3] Since then, 1H NMR has continuously been used for quantitative measurements in a wide range of domains, including but not limited to pharmaceutical analysis,[4] natural products,[5] in vivo spectroscopy[6] and metabolomics.[7] Actually, the ‘quantitative NMR’ terminology can be applied to a variety of situations where quantification is needed. It includes not only the measurement of absolute or relative concentrations but also the quantitative determination of other quantities such as isotopic ratios (at natural abundance or in enriched media), physical or chemical properties (diffusion coefficients, relaxation times, etc.). This manuscript is focused on the determination of concentrations, which forms the main application of quantitative NMR. The well-known drawback of quantitative 1H NMR is that precise and accurate quantification is often made difficult by

Magn. Reson. Chem. (2014)

the high degree of overlap characterizing 1H NMR spectra. In addition to the limited range of 1H chemical shifts, two main reasons can explain this overlap. First, samples often contain closely related compounds, for which the 1H NMR spectra are very similar. This example is illustrated in Fig. 1 (top) in the case of the 1H NMR spectrum of a mixture of tropine and nortropine, two similar tropane alkaloids with very close chemical shifts. The second reason explaining the complexity of 1H NMR spectra is the high number of compounds showing peaks in the same spectral region. This is particularly the case in biological samples such as mixtures of metabolites, as illustrated in Fig. 1 (bottom) in the case of a cancer cell metabolic extract. Several solutions have been considered to overcome this overlap problem. The first approach consists in determining – by deconvolution of the 1D NMR lineshapes – the individual 1D spectra of the different molecules present in the sample.[7,9,10] However, this processing strategy is appropriate only when the overlaps are relatively limited and when all the mixture components are known. A much more satisfying solution would be to separate the signals arising from the different compounds at the acquisition stage. This was first made possible by relying on other nuclei than 1H, which generally offers a much larger spectral width, thus leading to a much greater degree of discrimination. In particular, quantitative 13C NMR has been widely described[11–13] and applied in a variety of fields, from food science[14,15] or metabolic studies[16] to the isotopic analysis of natural or synthetic

* Correspondence to: Patrick Giraudeau, Chimie et Interdisciplinarité: Synthèse, Analyse, Modélisation (CEISAM), UMR 6230, Faculté des Sciences, BP 92208, 2 rue de la Houssinière, 44322 Nantes Cedex 03, France. E-mail: patrick. [email protected] EBSI Team, Chimie et Interdisciplinarité: Synthèse, Analyse, Modélisation (CEISAM), Université de Nantes, CNRS, UMR 6230, LUNAM Université, 2 rue de la Houssinière, B.P. 92208, 44322 Nantes Cedex 03, France

Copyright © 2014 John Wiley & Sons, Ltd.

P. Giraudeau

Figure 1. 1D proton NMR spectra recently acquired in our lab, showing the high degree of overlap between peaks that makes the accurate 1 quantification by 1D NMR difficult. (Top) H spectrum of a tropine (tro)– nortropine (nor) equimolar mixture, two tropane alkaloids with very 1 similar chemical shifts. The H shifts are numbered in decreasing chemical [8] shift, and the attributions refer to Giraudeau et al. (Bottom) 1D spectrum with water signal presaturation obtained from a breast cancer cell extract sample from the MCF-7 cell line.

molecules.[17–19] Quantitative studies relying on other nuclei have also been reported, such as 15N,[20] 31P[21] or 17O.[22] However, heteronuclei are generally characterized by a low NMR sensitivity because of their low natural abundance and/or of their small gyromagnetic ratio. As a consequence, relying on heteronuclei for quantitative measurements requires either highly concentrated samples or very long measurement times. Another appealing solution is to rely on multidimensional NMR, a technique proposed by Jeener in 1971 and applied for decades as a routine tool for the elucidation of small organic molecules or macromolecular structures.[23,24] From the quantitative point of view, 2D NMR has the high advantage of offering a

much better discrimination of resonances than 1D NMR, as the peaks are spread along an additional orthogonal dimension. Consequently, 2D NMR, which forms the subject of this review, offers a promising potential for the quantitative analysis of complex mixtures. However, the use of 2D NMR for quantitative analysis has been expanding only over the last decade.[8,25–33] There are two main reasons explaining this late development. The first one is that 2D NMR suffers from long acquisition times because of the need to repeat numerous 1D experiments with incremented delays in order to obtain a well-resolved 2D matrix. The second one is the complexity of the 2D NMR peak response that is highly site specific. After discussing the potentialities and limitations of 2D NMR for quantitative analysis of small molecule complex mixtures, this review presents the various recent acquisition and/or processing approaches that have been proposed by the NMR community to achieve absolute quantification in such samples. This presentation is illustrated by recent application in various fields of (bio)chemistry. In the last part, the different strategies to speed up the acquisition of quantitative 2D NMR data are also presented, highlighting the strong link between the experimental time and the analytical precision.

Potential and Drawbacks of 2D NMR for Quantification Figure 2 illustrates the capacity of two widely used 2D NMR experiments (COSY[34] and HSQC[35]) to separate the resonances arising from different molecules in a mixture. In addition to the higher signal separation brought by 2D spectroscopy, Fig. 2 also sheds light on one of the great advantages of 2D NMR: the variety of homonuclear and heteronuclear experiments that the experimentalist can rely on. Of course, none of them is better than the others for quantitative analysis, and the choice of the pulse sequence depends on the targeted analytical question. Each 2D experiment has its own advantages and drawbacks, as illustrated in Table 1. The acquisition of 2D NMR data requires the repetition of N 1D experiments with N = N1 · number of scans (NS), where NS is the number of transients and N1 the number of t1 increments, and two consecutive transients are spaced by a repetition time TR. The different pulse sequences presented in Table 1 are not

Figure 2. 2D spectra (500 MHz) of a 50-mM model mixture of metabolites (alanine, glutathione, myo-inositol, lactic acid, proline and taurine), illustrating the separation power of 2D NMR. On the left is homonuclear correlation (COSY-DQF) and on the right is heteronuclear correlation (HSQC). Reprinted with permission from P. Giraudeau, S. Akoka, Adv. Bot. Res. 2013, 67, 99–158. Copyright (2013) Elsevier.

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Quantitative 2D NMR Table 1. Parameters governing the choice of a 2D experiment for quantitative NMR of small molecules 1

1

Homonuclear H J-resolved

Relative sensitivity F1 parameter Experimental time* Separation power

++ JHH ++ --

13

1

15

Heteronuclear H– C or H– N 1

COSY, TOCSY, INADEQUATE- H

++ 1 δ H + +

X-detected

Proton-detected

2D INEPT

HSQC, HMQC, HMBC

1 δ H ++

+ δ

13

C ++

Relative sensitivity and parameters governing the F1 dimension, for different kinds of 2D NMR correlations with potential usefulness in quantitative studies. These parameters also impact the experimental time and the separation power of the experiment. * Based on the relative sensitivity and on the parameter governing the acquisition of the F1 dimension. ++ : Very favorable; + : Favorable; : Unfavorable; : Very unfavorable.

equivalent from this point of view. The NS per t1 increment is mainly governed by sensitivity considerations (and to a lesser extent by phase cycling, which can be advantageously replaced by coherence selection gradients in most cases[36]). Homonuclear 1 H experiments are more sensitive than heteronuclear ones, and among heteronuclear pulse sequences, those with inverse detection (such as HSQC) are more sensitive than those with direct detection (such as 2D INEPT). On the other hand, the indirect spectral dimension plays a key role in the experimental time. The total sampling time of the interferogram in the F1 dimension (AQ1) is proportional to the number of t1 increments (N1) and inversely proportional to the frequency range observed in the F1 dimension (SW1). Thus, larger ranges induce larger N1 for a given value of AQ1. If AQ1 is too low, this leads to truncation artifacts in the F1 dimension.[37] Therefore, the experiment time depends on the parameter that is sampled in F1. Homonuclear J-couplings require a smallest number of points than 1H chemical shifts, which in its turn is more favorable than 13C chemical shifts. As a consequence, J-resolved 1H spectroscopy can be shorter than COSY, and COSY requires a shorter experimental time than HSQC because of the larger frequency range of heteronuclei. It should be noticed that N1 can also be impacted by the choice of the frequency discrimination method in the indirect dimension. On the whole, the experiment time is governed by the sensitivity and by the parameter governing the acquisition of the indirect dimension. However, another major aspect to be taken into account is the capacity of the experiment to separate overlapping resonances. This feature improves when the spectral range increases, and as a consequence, it is inversely correlated with the experiment time aspects described previously. Given the multiparametric aspects of 2D NMR experiments, there is no universal recipe to choose a 2D pulse sequence for quantitative analysis. The ideal choice depends on the samples to be analyzed: While a fast 2D experiment (such as homonuclear J-resolved spectroscopy) will be sufficient to quantify mixtures with a limited number of compounds,[8] the analysis of very complex mixtures will require the use of more discriminating pulse sequences such as 1H–13C HSQC,[28] while having to pay a certain price in terms of sensitivity. Whatever the chosen pulse sequence, the first major drawback of multidimensional NMR is that peak volumes depend on a number of peak-dependent parameters: transverse and longitudinal relaxation times, homonuclear or heteronuclear coupling constants, pulse sequence delays, pulse angles, off-resonance effects, etc.[38] This is much more complex than in 1D quantitative


NMR where the NMR peak areas just depend on the number of equivalent spins and on the analyte concentration, provided that full relaxation is reached. Because of their multipulse character, 2D pulse sequences are generally recognized for their nonquantitative nature, and many NMR spectroscopists are convinced that they cannot be used to determine absolute concentrations. Fortunately, several NMR or analytical strategies have been proposed to successfully circumvent this drawback, as described in the next part of this review. The second well-known limitation of multidimensional quantitative NMR is the long experiment time because of the need to record a sufficient number of t1-incremented experiments to sample the indirect F1 dimension with a good resolution. This is further increased by the possible need to accumulate several transients for each t1 increment for sensitivity and/or coherence selection purposes. The impact of the incrementation procedure is particularly serious in the case of quantitative measurements, where the recovery delay generally has to be set to a long value (typically five times the highest longitudinal relaxation time T1) in order to allow for the full relaxation of all longitudinal magnetizations, except when working under partial saturation conditions. These long experimental durations have several consequences. The most evident one is the overload of spectrometer schedules, which translates into higher experimental costs. A more fundamental consequence is the impossibility to study samples in which the composition evolves within the timescale of the nD experiment because of kinetic or dynamic processes such as chemical or biochemical reactions. The last consequence of this long experimental time is less straightforward but has a high analytical impact. Actually, long experiments are more likely to be affected by spectrometer instabilities over time.[39,40] These include electronic variations (variations in pulse angle, phase, receiver gain, etc.), lock instabilities and magnetic field variations inside or outside the magnet. The impact of these instabilities is negligible along the direct F2 dimension, where all the points are acquired within a short period of time, but it is much higher in the indirect F1 dimension, where such instabilities generate additional noise in the indirect dimension because of the long time interval (TR) separating the physical acquisition of two successive FIDs. As a consequence of this ‘t1 noise’, the signal-to-noise ratio (SNR) is always lower in the indirect F1 dimension, leading to noise ridges parallel to the F1 axis. This t1 noise, which highly depends on the spectrometer and hardware configuration, can strongly affect the precision of quantitative 2D experiments[41,42] and can therefore decrease the limit of concentration that can be precisely



P. Giraudeau measured. The last part of this review will show how NMR spectroscopists are dealing with this time constraint to improve the speed and precision of quantitative 2D NMR experiments. The last 10 years have witnessed huge efforts to deal with the two limitations described previously; i.e. the experimental time and the fact that peak volumes do not directly reflect the concentration. Most of these developments are in fact applicable whatever the pulse sequence used; therefore, we chose to present them based on the analytical approach rather than on the pulse sequence.

Approaches to Determine Absolute Concentrations by 2D NMR As described previously, 2D peak volumes depend on a number of factors.[38] Some of them depend on the pulse sequence (pulse sequence delays and angles and off-resonance effects), and others depend on the molecular site, such as coupling constants and relaxation times. The latter even depend on external factors such as temperature, pH or magnetic field. Figure 3 presents the different generic approaches that have been described recently to reach absolute concentrations by 2D NMR. In the general case, we can consider that the 2D peak volume V is given by V ¼ k ðT 1 ; T 2 ; J CH ; J HH ; delays…Þ·p ·½c ·VS

developments have been mainly carried out for the 1H–13C HSQC pulse sequence, probably because it is the 2D NMR experiment with the highest resonance separation power. They were initiated by Heikkinen and coworkers, who first proposed a strategy to remove the effects of heteronuclear JCH couplings in the 1H–13C HSQC pulse sequence.[46] In the HSQC experiment, the 2D peak volumes are proportional to sin2(πΔ1JCH) where Δ is the duration of the INEPT polarization transfer delay.[38] In 2003, Heikkinen et al. proposed to average four HSQC spectra with different and suitably selected Δ values.[46] In the final spectrum, the 2D peak volumes are uniform over a ca 150 Hz range of JCH couplings. This strategy was applied to determine the relative amounts of different structural units in wood lignin, a complex polymer. The approach proposed by Heikkinen requires four times as many scans as the HSQC to achieve the same resolution in the indirect dimension. This drawback was circumvented in 2007 by Peterson and Loening, who proposed to acquire simultaneously from different slices of the sample the signals corresponding to different INEPT delays.[47] This approach, called quick, quantitative HSQC, is faster than the one described by Heikkinen for the same result. It was successfully applied to the elucidation of lignin structure by Sette et al.[48] However, the 2D peak volumes in the HSQC spectra are also influenced by homonuclear JHH couplings.[25] In theory, the cross-peak intensity can be attenuated by a factor: k

The factor p is the number of equivalent spins and is a priori known. VS is the sensitive coil volume, which is, in principle, the same for all samples analyzed with a given hardware configuration. [c] is the analyte concentration to be determined, and k is a proportionality constant that depends – in a complex manner – on J-couplings, relaxation times, pulse sequence delays, off-resonance effects, etc.† Because k is not known and is site specific, it is necessary to find a way to determine – or to get rid of – this constant for each peak to be used for quantification. Three families of approaches have been described to reach this goal. The first one consists in modifying the NMR experiment itself to remove the dependence of k on the different factors mentioned previously so that the peak volume is not site specific anymore.[25,43] A second strategy consists in determining, for each peak, the exact value of k, based on theoretical considerations.[44,45] A last family of approaches also determines the different k values but by relying on more classical analytical approaches such as calibration or standard additions.[28,31] These three strategies are described in the next paragraphs, based on the most recently published developments and applications. The last paragraph of this section is devoted to processing approaches, which are common to these three strategies and have a large impact on the precision and accuracy of quantification. Approaches relying on modified NMR acquisitions The first way to get rid of the k factor mentioned previously is to design NMR experiments where the peak volume is not further influenced by J-couplings or relaxation times. It requires modifying and/or combining several NMR experiments, and such

†

Note that the effect of longitudinal relaxation between two successive scans is similar to 1D NMR; therefore, it will not be described here. Such effect can be avoided by simply increasing the repetition time, like in 1D NMR.


∏

i¼1

2 1 ð1 þ cosð2πJ HHi ΔÞÞ 2

In 2005, Heikkinen et al. proposed to include Carr–Purcell– Meiboom–Gill (CPMG) pulse trains in the INEPT and retro-INEPT periods of the HSQC pulse sequence in order to remove this JHH dependence.[25] They also included composite CPMG pulse trains to reduce off-resonance effects on the edge of the 13C chemical shift range. More recently, they introduced adiabatic pulses in the evolution period of their pulse sequence to improve the quantitativity of the experiment.[49] The resulting pulse sequence, called quantitative, offset-compensated, CPMG-adjusted HSQC (Q-OCCAHSQC), including all these improvements is shown in Fig. 4. The authors evaluated the analytical performance of their methodology, and they reported errors of up to 17% on a strychnine sample, with a 7.3% standard deviation. The error increased even more when the 13C carrier was set off-resonance. A reason that could explain this relatively low performance is that peak volumes also depend on T2 transverse relaxation times, a dependence that is not taken into account in Heikkinen’s protocol. This means that the Q-OCCAHSQC protocol is better suited to quantify molecules with similar T2 values, as highlighted by Zhang and Gellerstedt who developed a protocol where cross peaks with the same T2 relaxation profiles were analyzed as individual groups.[33] More recently, a different strategy was proposed by Markley and his group to obtain k values that are independent of the site considered.[43] Their approach consists in calculating a time-zero HSQC spectrum (named HSQC0) where peak volumes are independent of the molecular site considered. This is carried out by recording several HSQC spectra with incremented repetitions of the HSQC pulse sequence. Assuming that the signal attenuation as a function of J-couplings, relaxation times and off-resonance effects is proportional to the number of repetitions i of the pulse sequence, the peak volume Vi,n for a given peak n follows the equation



Quantitative 2D NMR

Figure 3. Different strategies proposed to obtain absolute concentrations from 2D NMR spectra. The 2D peak volumes depend on a number of factors: relaxation times, coupling constants, pulse sequence delays, pulse angles, off-resonance effects, etc., and the factor k accounts for this dependence. p is the number of equivalent spins per site, [c] is the concentration to be determined, and VS is the sensitive detection volume. The first strategy (left arrows) tries to make k independent of the previously mentioned factors, via pulse sequence modifications. The second and third strategies rely on theoretical calculations (right arrows) or calibration approaches (center) to determine the value of k for each peak.

Figure 4. Q-OCCAHSQC experiment developed by Koskela and coworkers to remove the dependence of the HSQC pulse sequence on homonuclear and heteronuclear coupling constants. Narrow and wide filled rectangles represent the rectangular 90° and 180° pulses, respectively. The rounded open rectangles represent broadband inversion pulses, and the open rectangles with diagonal lines in the Section on Potential and Drawbacks of 2D NMR for Quantification represent broadband phase-modulated broadband excitation by optimized pulses.50 Pulse phases are along the x-axis if not stated otherwise. Phase cycles were ϕ1 = (x, x, x and x), ϕ2 = (x, x, x and x) and ϕR = (x, x, x and x). The pulsed field gradients are represented by half-ellipses. The constant-time CPMG-INEPT periods (Sections on Introduction and Approaches to Determine Absolute Concentrations by 2D NMR) consist of the XY-16 pulse trains with a total duration of Δmax. Each of the XY-16 pulse trains consists of 16 centered 180° pulses on both channels with phases (x, y, x, y, y, x, y, x, x, y, x, y, y, x, y and x) and 32 τ-delays. The delay τ in the CPMG-INEPT periods must be short enough to satisfy the condition τ < 1/(2 * Δνmax), where Δνmax is the maximum chemical shift difference (in Hz) of coupled protons. In order to give the uniform intensity 1 response over the wide range of JCH values, four acquisitions with different polarization transfer times (three of them being equal) for the constanttime CPMG-INEPT periods (Δmin, Δmin, Δmin and Δmax) were recorded for each increment (for both the echo and antiecho part). This was accomplished by setting the second XY-16 pulse train duration in the constant-time CPMG-INEPT period (Sections Introduction and Approaches to Determine Absolute Concentrations by 2D NMR) to Δmin and switching the carbon channel pulsing of the first XY-16 pulse train either on or off in the following order: off, off, off and on. Reprinted with permission from H. Koskela, O. Heikkilä, I. Kilpeläinen, S. Heikkinen, J. Magn. Reson. 2010, 202, 24–33. Copyright (2010) Elsevier.

ln V i;n ¼ ln V 0;n þ i· ln k A;n where kA,n is the amplitude attenuation factor specific for peak n. By plotting, for each peak, the logarithm of the peak volume ln(Vi,n) as a function of i, one can easily determine the ‘time-zero peak volume’ V0,n. It corresponds to the 2D peak volume that would have been obtained with a hypothetical HSQC pulse sequence where all evolution delays would have been set to zero. This virtual peak volume is therefore independent of peak-specific parameters such as T2, J-couplings or pulse sequence delays, thus giving access to absolute concentrations provided that a reference peak is used.


Even though the trueness of the method was not explicitly mentioned, the authors reported a good precision, with a standard deviation close to 7%. This approach was further improved in 2011 by incorporating suitably chosen coherence selection gradients yielding cleaner spectra.[51] It was successfully applied to quantify molecules in complex mixtures of natural products[52] and also in a targeted metabolomics context.[53] This method seems more complete than the one proposed by Heikkinen and coworkers, as it takes into account the effects of transverse relaxation. It assumes, however, that the NMR signal intensity is attenuated linearly as a function of the number of repetitions. Moreover, it was only developed for the HSQC pulse sequence, and further developments will



P. Giraudeau be necessary to apply this promising method to other NMR experiments. The combination of this approach with the pulse sequence developments proposed by Heikkinen et al. should also help in improving the performance of this methodology. The methods described in this paragraph are very promising from the quantitative point of view because they give access to 2D peak volumes directly reflecting the absolute concentration. However, they suffer from two drawbacks that limit their applications: First, they require specific acquisition and/or processing programs that are not commercially available, which may limit their general use. Second, they are, so far, limited to the HSQC experiment, which limits their application to relatively concentrated samples. Approaches relying on theoretical calculations A second, more recent, family of approaches aims at calculating the exact value of the proportionality coefficient k for each peak that needs to be used for quantification, which directly gives access to the absolute concentration of the corresponding metabolite. This procedure was first proposed by Rai et al. for the HSQC pulse sequence.[44] They split the proportionality coefficient as follows: k ¼ ηðT1 ; T2 ; d1 Þ·ζ ðJ CH Þ where d1 stands for the relaxation delay between two successive pulse sequences. The coefficient η is given by η¼

ð1 E 1 Þð1 E 2 cosφÞ ð1 E 1 Þð1 E 2 cosφÞ E 1 ðE 2 cosφÞE 2

where E1 = exp(d1/T1), E2 = exp(d1/T2), and φ is the receiver offset multiplied by d1. This coefficient takes into account the effects of relaxation between two successive scans but not those occurring during the pulse sequence. The coefficient ζ is given by 1 ζ ¼ sinðπJτ Þ sinðπJτ 1 Þ þ sinðπJτ 2 Þ cosn1 ðπJτ 1 Þ 2 where J stands for 1JCH and τ, τ1 and τ2 are the different delays involved in the HSQC pulse sequence. As can be seen from the equation previously mentioned, this coefficient totally neglects the effect of homonuclear 1H couplings. From these equations, the authors plotted the concentration determined by 2D HSQC versus the gravimetric concentration, for a model mixture of amino acids. The results obtained for 64 different signals are shown in Fig. 5. The dispersion of the values and the relatively low R2 highlight the low accuracy of the method: The concentration errors are between 10 and 20%. This is probably because of the numerous approximations described in the preceding texts. The authors applied their method to a series of urine samples, but they relied on spike-in experiments that actually correspond to the standard addition procedure described in the next paragraph. A more thorough theoretical approach was developed by Brüschweiler and his coworkers in the case of the constant-time TOCSY experiment applied to mixtures of 13C-labeled metabolites.[45] Based on the product operator formalism, they proposed several approaches simulating the homonuclear 13C TOCSY spectra, and the comparison of the experimental versus simulated 2D spectrum gave access to the metabolite concentrations. Their method was applied to a model metabolic mixture, but the errors were relatively high (up to 25% in some cases). Moreover, its


Figure 5. Regression curve obtained from 64 signals of different amino acids, showing the concentration determined by the quantitative 2D NMR approach of Rai et al. versus the gravimetric concentration. The method consists in calculating the exact value of the proportionality coefficient k for each peak, based on relaxation times and heteronuclear coupling constants. The poor quality of the linear regression is probably because of the numerous approximations of the methods (refer to details in the text). Reprinted with permission from R. K. Rai, P. Tripathi, N. Sinha, Anal. Chem. 2009, 81, 10232–10238. Copyright (2009) American Chemical Society.

extension to 1H–1H TOCSY is not straightforward, according to the authors themselves. The results obtained in these two recent papers demonstrate that there is still a long way to go before applying the methods based on theoretical calculations to the analysis of complex mixtures. The main limitation of these methods is that they require the accurate determination of coupling constants and relaxation times. As for coupling constants, this may be difficult in real samples, first, because of the spectral complexity and also because coupling constants (especially JHH) strongly depend on the molecular conformations, which can themselves depend on the molecular environment. Concerning relaxation times, they also depend on the concentration, temperature and pH, therefore taking them into account may be difficult. Finally, the methods relying on the theoretical determination of 2D peak volumes do not take off-resonance effects into account, which is particularly problematic for heteronuclear 2D experiments. Coupling them with the strategies described in the previous paragraph to compensate such effects could form an interesting perspective. Approaches based on analytical chemistry As shown in Fig. 3, the last family of approaches to reach absolute concentrations by 2D NMR is to rely on calibration curves. This methodology – which we described in a recent review[54] – is actually employed in many other analytical techniques such as spectrophotometry or chromatography. In this approach, calibration curves are first obtained by recording NMR spectra on a series of samples in different concentrations. For these calibration samples, the 2D NMR peak volume of the targeted compound is plotted versus its concentration determined by another method – generally by gravimetry. Then, a 2D spectrum is recorded on the sample containing the targeted analyte in an unknown concentration, and this concentration is determined through the



Quantitative 2D NMR equation of the regression curve. This approach – which was also successfully applied in 1D NMR[55,56] – offers an invaluable solution to the problem of accuracy in 2D NMR, provided that the 2D NMR response is linear versus concentrations, which was demonstrated in several recent studies.[8,29] Moreover, as the aim of quantitative 2D experiments is generally to quantify simultaneously a high number of analytes, a single calibration procedure is sufficient, if the calibration samples contain all the targeted molecules. This approach was successfully applied to quantify the most abundant metabolites in plant tissue extracts[28] or in biological fluids[57,58] by heteronuclear 1H–13C NMR. A similar strategy was used to quantify organic compounds in whole milk.[59] An accuracy of a few per cent was generally reported, as illustrated by Fig. 6 where this accuracy is illustrated for two 2D NMR experiments, 1H–1H TOCSY and 1H–13C HSQC, in the case of a model metabolic mixture. The calibration strategy described previously is well adapted to the simultaneous quantification of multiple compounds; however, it suffers from the differences that inevitably occur between the model samples used for calibration and the complex sample where the quantification is performed. This is particularly the case for biological samples characterized by a high diversity of metabolites. The external standards used for calibration cannot fully reproduce these conditions, even though they are trying to mimic them, e.g. by the use of buffers. As a consequence, the

NMR response of the external standards may differ from the one of the sample of interest. This limitation can be circumvented by relying on another wellknown analytical strategy: the standard addition procedure.[60,61] Here, known amounts of the target analyte (or mixture of analytes) are gradually spiked to the analyzed sample. For each analyte whose concentration needs to be determined, a standard addition curve is fitted by the linear regression equation: V = a · [c] + b, where V represents the 2D peak volume and [c] the concentration of the analyte in the sample. The initial concentration of the analyte in the sample is calculated by the b/a ratio, where a is the slope and b the y-intercept of the linear regression curve. Figure 7 shows the principle of this methodology, as well as its application to determine the concentration of major metabolites in breast cancer cell extracts[31] – relying on a fast 1H INADEQUATE experiment whose principle is described in the Section on Reducing the Experiment Time to Improve the Precision. An error as low as 1% was reported, making it possible to observe significant differences between breast cancer cell lines. This approach is probably the most accurate of the different approaches described in the preceding texts because the target analytes are acting as their own reference and because the whole procedure is carried out within the same NMR tube, thus avoiding the intersample variation drawback of the external calibration approach. However, this procedure is heavy and time

13

Figure 6. Concentration of 28 standard metabolites obtained by heteronuclear 2D NMR (top, with C-labeled mixtures) and homonuclear 2D NMR (bottom) combined with a calibration approach. The black bars represent the metabolite concentrations determined by 2D NMR, and the shaded bars represent the actual metabolite concentrations (determined by gravimetry). This figure illustrates the good accuracy and precision of the 2D NMR experiments associated with calibration. Reprinted with permission from G. A. N. Gowda, F. Tayyari, T. Ye, Y. Suryani, S. Wei, N. Shanaiah, D. Raftery, Anal. Chem. 2010, 82, 8983–8990 Copyright (2010) American Chemical Society.




P. Giraudeau

1

Figure 7. 2D NMR method to determine the concentration of major metabolites in breast cancer cell lines, by coupling the H INADEQUATE pulse sequence with a standard addition strategy. Breast cancer cell extracts are spiked with known amounts of a model solution containing all the 1 metabolites to quantify in known concentration. (Left) example of a standard addition curve obtained for the threonine signal from H INADEQUATE 2D spectra of a SKBR3 cell extract. The 2D peak volume is plotted as a function of the added concentration Ca, and Ci represents the initial metabolite concentration. (Right) metabolite concentrations of intracellular extracts obtained with such a protocol applied to three cell lines: SKBR3, MCF-7 and MDA-MB-468. Characteristic biomarkers of cell lines can be identified: histidine, threonine, valine, isoleucine, glutathione, proline, alanine and lactate. Standard deviations represent the biological variability (calculated on three growth times per cell line for each metabolite). Reprinted with permission from E. Martineau, I. Tea, S. Akoka, P. Giraudeau, NMR Biomed. 2012, 25, 985–992. Copyright (2012) Wiley.

consuming, as it requires taking the sample in and out of the spectrometer several times, spiking this sample and recording several NMR spectra. It is therefore ill suited for high-throughput studies involving a large number of samples. In this case, the external calibration approach should be preferred, even if there may be a price to pay in terms of precision. A common feature of the two strategies – external calibration and standard additions – described in this paragraph is that they rely on the assumption that the relaxation times do not vary significantly over the concentration range of the calibration curve. This hypothesis seems reasonable in a small molecule context,[29] and it actually makes it possible to shorten the experiment time by working under partial saturation conditions. On the whole, calibration and standard addition approaches lead to a higher trueness and precision than the two other families of approaches described in the preceding texts. This is probably because the calibration procedure accounts for almost all the effects that the other strategies are trying to compensate, i.e. the influence of coupling constants, pulse sequence delays, offsets, etc. The only condition to reach high accuracy on the determination of absolute concentrations is to reach a high repeatability and linearity on the 2D NMR experiments. This is ensured by the increasing quality of the NMR hardware and also by bringing special care to the problem of the experiment time, as described in the Section on Reducing the Experiment Time to Improve the Precision. Signal processing considerations Regardless of the NMR and analytical strategies described in the preceding texts, the processing and integration conditions play a major role in determining 2D peak volumes with a high degree of precision and accuracy. As we recently described it,[41] the optimum processing parameters depend on the pulse sequence and acquisition parameter, and it is impossible to give a unique set of processing conditions for quantitative 2D NMR. However, it is indispensable to keep in mind some general rules in order to minimize the impact of processing on the quality of quantitative results. The first one concerns the choice of the apodization functions: The preservation of the 2D peak volume, determined by the maximal amplitude of the FID, is indispensable.[62] The weighing function must therefore be optimized at the same time


as the number of increments in the F1 dimension by respecting two conditions: Its amplitude must decrease down to zero at the end of the sampling period, and its maximum has to coincide with the maximum of the NMR signal that is generally at the beginning of the FID. Measuring the peak volumes for quantitative analysis is also very sensitive to baseline distortions.[63] In 2D NMR, this effect is important because the baseline distortions occur in both dimensions. While the baseline correction can be made directly on the FID,[64] it is mostly applied in the frequency domain[64–66] using a modeling of the baseline by a polynomial or a spline function. The baseline correction itself can have a major influence on the precision of the measurements. Although this is not specific to multidimensional NMR, recent work showed that the correction is generally more efficient when (i) it is restricted to the spectral zone containing the peaks of interest and (ii) the polynomial degree of the baseline correction is lower than 3.[8,29] Indeed, when a polynomial of too high degree is used, the baseline correction function may consider certain peaks as being a part of the baseline, inducing a distortion of peaks detrimental to the quantitative analysis. A last precaution worth mentioning concerns the use of automated postprocessing procedures, such as symmetrization[67,68] (in the case of homonuclear spectra) or tilting (in the case of J-resolved spectra. Such procedures have been proposed in order to improve the quality of certain homonuclear correlation spectra, and they are generally efficient to suppress t1 noise. However, they could create artificial cross peaks and recovering small signals buried in noise may be difficult.[37] Furthermore, this operation leads to a modification of the peak volumes that can greatly affect the precision of the measurements.[41] Therefore, such procedures should be avoided for quantitative applications of 2D NMR. The methods employed to determine 2D peak volumes also play a vital role in implementing a reproducible quantitative strategy. Different methods of 2D peak integration have been proposed and are currently used. The simplest one is the direct summation of the spectral data points. It does not make any assumption on the peak shape, and integration tools are integrated in major commercial processing programs. However, this method is very sensitive to baseline distortions, t1 noise and tailing of adjacent peaks. It is particularly difficult to apply in cases



Quantitative 2D NMR of peak overlap, although Romano et al. proposed an approach to circumvent this problem.[69] A variant of the previous method is to make projections of the lines containing the targeted 2D peaks. The areas are then determined using the 1D integration tool on each of the projections, and their values are summed.[30] The most promising approaches to perform a reproducible analysis of 2D NMR spectra are to rely on a parametric model fitting approach to spectral deconvolution,[70,71] as it accounts for spectral overlaps and also makes an effective use of a priori information, e.g. the assumption of approximately uniform chemical shifts and line widths for corresponding signals within related spectra acquired on the same sample. Recent papers reported the use of such methods to determine peak volumes from 2D NMR spectra. In particular, the work of Chylla et al.[72] in a protein biomolecular context demonstrated the practicality of using hybrid time-domain, frequency-domain maximum likelihood fitting. Recently, the same team has developed an algorithm called fast maximum likelihood reconstruction (FMLR) that performs spectral deconvolution of 2D NMR spectra for the purpose of accurate signal quantification.[73] FMLR demonstrates greater accuracy (0.5– 5.0% error) than peak height analysis and peak integral analysis with greatly reduced operator intervention (Fig. 8). Therefore, such deconvolution approaches seem very promising; however, they are not currently implemented in commercial NMR software. Hopefully, this is just a question of time.

Reducing the Experiment Time to Improve the Precision In the previous section, we described the different strategies that were proposed to circumvent the first drawback of 2D NMR as regards quantification: the dependence of the 2D peak volumes

Figure 8. (Top) precision (% variance) and (bottom) accuracy (% deviation from a known concentration) of the fast maximum likelihood reconstruction method (light bars) compared with manual peak integration (dark bars), for the determination of absolute metabolite concentrations in a mixture. Reprinted with permission from R. A. Chylla, K. Hu, J. J. Ellinger, J. L. Markley, Anal. Chem. 2009, 83, 4871–4880. Copyright (2009) American Chemical Society.


on numerous site-specific parameters. The present section is devoted to the second drawback of 2D NMR mentioned at the beginning of this manuscript, i.e. the experiment time. Its impact on quantification is discussed, and the solutions that have been proposed to reduce the duration of quantitative 2D NMR experiments are described. From the strict point of view of quantitative analysis, the main drawback of the experiment duration is that long experiments are more likely to be affected by spectrometer instabilities over time.[39,40] Even if the resulting ‘t1 noise’ is not visible, the SNR is always lower in the indirect F1 dimension, which affects the precision and accuracy of quantitative 2D experiments. This drawback highlights the need for alternative and faster 2D acquisition strategies. Parameter optimization strategies The first approach to reduce the duration of quantitative 2D NMR experiments is to carefully optimize their acquisition parameters in order to reduce their duration while preserving – or even improving – their quantitative performance. Such an optimization may seem trivial, but the routine parameters generally associated with conventional 2D NMR pulse sequences are generally not optimized for quantitative applications. Depending on the 2D experiment considered (Table 1), the experiment time can be reduced by adjusting the number of t1 increments (N1) and/or the NS.[41] The reduction of N1 impacts the resolution in the indirect domain, but relatively low values of N1 can generally be reached while preserving a sufficient degree of separation between peaks. When sensitivity is not an issue, the number of transients – which is therefore determined by the basic phase cycling – can be reduced to a minimum value (generally 1 or 2). The phase cycling needs then to be replaced by gradient pulses to select the desired coherence pathways[74] and by composite[75] or adiabatic[76] pulses to compensate for RF pulse imperfections. In recent studies, we demonstrated that applying such an optimization strategy could greatly help in improving the precision of conventional 2D NMR experiments. For example, we showed that the precision of homonuclear J-resolved and DQF-COSY experiments was improved when the experimental time was reduced because of a higher immunity of these short experiments to spectrometer instabilities over time.[8] Short experiments are less affected by such instabilities and show a better repeatability, as long as the SNR and the resolution are sufficient to quantify relevant peaks with the target precision. In this study, J-resolved and DQF-COSY quantitative spectra were obtained on an equimolar mixture of tropine and nortropine in 2.7 and 12 min, respectively. We recently applied the same optimization approach to the 1H INADEQUATE pulse sequence.[29] This 2D experiment is generally used to establish 13C connectivities;[77] however, it also finds an interest in proton spectroscopy as it makes it possible to obtain a much cleaner diagonal than COSY or TOCSY.[78,79] This advantage makes it a useful tool to study compounds whose correlation peaks are close to the diagonal. Here, quantitative 1H INADEQUATE 2D spectra of metabolite mixtures were obtained in 7 min with repeatability better than 2% for metabolite concentrations as low as 100 μM and with an excellent linearity.[29] This fast protocol was then applied to determine and compare the metabolite content in three different breast cancer cell lines expressing different receptors[31] (Fig. 7). The optimization of acquisition parameters to shorten the experiment time was also applied in heteronuclear 2D NMR. In



P. Giraudeau particular, Lewis et al.[27] introduced a fast protocol for measuring metabolite concentrations in complex solutions using 2D 1H–13C HSQC NMR. This protocol, called fast metabolite quantification (FMQ), was validated for a model mixture of 26 metabolites, and a spectrum was obtained in 12 min. Calibration curves plotting absolute peak intensity against concentration were established for each metabolite. The average error on the calculated concentrations was 2.7% with a maximum of 10.3%, while equivalent values were 16.2 and 44.5%, respectively, for 1D 1H analysis. The FMQ protocol was then applied to biological extracts (Arabidopsis thaliana, Saccharomyces cerevasiae and Medicago sativa) to measure about 40 metabolite concentrations ranging from 40 μM to 230 mM. In conclusion, these parameter optimization approaches make it possible to reach a good degree of trueness and precision (generally below 10%) with a reasonable experiment time. So far, such approaches were systematically coupled with calibration or standard addition strategies (Section on Approaches to Determine Absolute Concentrations by 2D NMR). In this context, optimizing the experiment time has the additional advantage of shortening the overall analysis duration, which tends to be increased because of the need to record several points on the calibration curve. Still, some applications, such as the comparison of biological samples with very tiny differences, would benefit from a higher analytical performance. For this reason, the next paragraphs deal with recent alternatives to record 2D spectra relying on different data acquisition schemes and focusing on those whose interest for quantitative analysis was recently demonstrated. Alternative acquisition schemes In the last few decades, numerous strategies arose from the NMR community to reduce the duration of multidimensional NMR experiments. Describing the details of these methods is out of the scope of this review; consequently, their description is limited to basic principles, and the reader is referred to appropriate literature. The main idea here is to highlight those who have been recently applied in a quantitative context. A first family of approaches consists in the optimization of conventional pulse sequences in order to reduce the recovery delay separating two successive t1 increments.[80] The most famous example among these techniques is the band-selective optimized flip angle short transient heteronuclear multiple quantum coherence approach, developed by Schanda and Brutscher.[81] They carefully optimized the delays and pulse angles in the HMQC pulse sequence, leading to heteronuclear 2D spectra of proteins in a few seconds.[81] More recently, Vitorge et al. proposed a gradientbased coherence selection scheme allowing a dramatic reduction of the recovery delay in homonuclear 2D NMR experiments.[82] Another clever strategy is to rely on spectral aliasing, as described by Jeannerat.[83] Sampling a smaller spectral width in the indirect dimension makes it possible to record 2D spectra with a much smaller number of t1 increments and therefore in a reduced experimental time. Another possibility to reduce the experimental duration is to record a very limited number of t1 increments and to apply, after acquiring the data, a specific processing to reach the required resolution in the indirect dimension. This is the case of the well-known linear prediction (LP),[84,85] maximum entropy reconstruction[85,86] or covariance[87] approaches. While these strategies still rely on a conventional t1 incrementation procedure, a number of approaches departing from this


sampling scheme have also been proposed. An alternative consists in sparsely sampling the (t1, t2) space to reduce the number of increments. Several strategies have been proposed, including exponential,[88] radial,[89] or random sampling.[90] These nonlinear approaches need to be combined with nonconventional processing methods, such as covariance[91] or multidimensional decomposition.[92] Also noteworthy is the Hadamard 2D NMR spectroscopy, proposed by Kupče and Freeman, relying on an excitation in the frequency domain.[93] In spite of these numerous developments and applications that occurred in the last 10 years, few of them were evaluated or applied in a quantitative context. There are, however, noteworthy exceptions. The spectral aliasing approach[83] is fully compatible with quantitative analysis: It was successfully employed by Lewis et al. in their fast metabolite quantitation protocol.[28] More recently, we demonstrated that spectral aliasing did not affect the repeatability of 1H–13C quantitative experiments and that a repeatability of a few per milliliters could be reached with a 10-ppm HSQC experiment.[94] In the same study, we also showed that LP was a reliable tool to reduce the duration of quantitative 2D NMR experiments while preserving a very high precision. On the contrary, the use of nonuniform sampling was found detrimental to the precision of quantification, probably because of the nonlinearity of the associated data reconstruction method. Promising quantitative developments can also be expected in the field of covariance spectroscopy: Brüschweiler and coworkers developed a regularization procedure to improve the quantitative nature of this procedure.[95] This approach was successfully applied in a metabolomics context – even though not quantitative in the sense of determining absolute concentrations.[96] In the same field, a last study worth mentioning is the successful use of Hadamard spectroscopy in 2D metabolomics, by Günther and coworkers.[97] However, this approach requires an a priori knowledge of the resonances to be excited: Therefore, its application to complex mixtures is not straightforward. The studies mentioned in the preceding texts are very promising, but in most cases, their full quantitative performance remains to be evaluated. The next paragraph focuses on a different approach that departs from the previous ones: ultrafast (UF) 2D NMR. A specific paragraph is devoted to this technique that shows a particular interest in terms of precision for quantitative analysis. Ultrafast 2D NMR Ultrafast 2D NMR was proposed in 2002 by Frydman and coworkers.[98] This approach is inspired from imaging and consists in dividing the sample into N1 subensembles undergoing different evolution periods, all of them within a single scan. As a consequence, any kind of 2D NMR correlation map can be recorded in a fraction of a second provided that sensitivity is sufficient. The basic principles of UF 2D NMR have been widely described in recent literature[41,99–101] and will not be detailed here. At the heart of this methodology is a spatial-encoding period, made possible by a suitable combination of chirp pulses and magnetic field gradients, followed by a detection scheme inspired from echoplanar spectroscopic imaging.[102] The initial methodology suffered from a number of limitations that restrained its spectroscopic performance. Fortunately, numerous methodological developments have contributed to improve the sensitivity, resolution, spectral width and lineshape of UF 2D NMR.[103–115] The development of practical tools for the implementation and use of this methodology[99,116,117] enabled a



Quantitative 2D NMR number of research groups to apply it in various fields, including but not limited to the real-time study of chemical[118–121] or biological[122,123] dynamic processes, the coupling with hyphenated techniques[124–126] or the acquisition of 2D spectra in inhomogeneous fields.[127–129] However, UF 2D NMR was also shown to be a promising analytical tool[101] with a high potential for quantitative analysis. The first evaluation of UF 2D NMR for quantitative analysis was performed in 2009, on a series of model mixtures.[130] Two homonuclear UF techniques, J-resolved spectroscopy and TOCSY, were evaluated on model mixtures in terms of repeatability and linearity. Repeatability better than 1% for UF J-resolved spectra and better than 7% for TOCSY spectra was obtained. Moreover, both methods were characterized by an excellent linearity, thus opening promising perspectives for this new quantitative methodology called UF optimized quantitative NMR. However, the first studies also highlighted the sensitivity limitations of UF 2D NMR, mainly because of the fact that a single scan was recorded and also because of an increase of the

Figure 9. Coefficient of variation (CV) of the 2D peak volumes for the various metabolites of a 6-mM model mixture, for the hybrid M3S COSY approach relying on UF 2D NMR and for a conventional constant-time COSY experiment. Each CV was determined from three series of five spectra, acquired in 10 min per spectrum on a 500-MHz Avance III Bruker spectrometer with a cryoprobe. Adapted with permission from A. Le Guennec, I. Tea, I. Antheaume, E. Martineau, B. Charrier, M. Pathan, S. Akoka, P. Giraudeau, Anal. Chem. 2012, 84, 10831–10837. Copyright (2012) American Chemical Society.

noise level as a result of the wider filter bandwidth that needs to be applied during the acquisition.[131] It soon turned out that a pure single-scan approach would generally be impractical for the quantitative analysis of complex mixtures. This is especially true for metabolic mixtures, where metabolite concentrations are generally in the μM–mM range, whereas the limit of the detection of single-scan experiments – depending on the hardware – is rather in the mM–M range.[101] In this context, we developed a hybrid approach, termed multiscan single shot (M3S), which consists of a conventional accumulation of UF signals, by simply repeating several UF experiments separated by a classical recovery delay. We demonstrated that, while not purely single scan, this M3S approach was characterized by a better sensitivity per unit of time than its conventional counterpart – at least for homonuclear spectroscopy.[42] From the quantitative point of view, a major consequence is that for identical experiment durations, the M3S approach has a much higher analytical performance – in terms of repeatability and linearity – than the conventional one.[132] As shown in Fig. 9, the average repeatability of conventional COSY is around 10%, while it is close to 2% for the M3S COSY pulse sequence. The reason for this higher performance is that M3S experiments are much more immune to spectrometer instabilities over time, as the whole 2D FID is recorded within the same scan. This can be demonstrated based on SNR considerations: M3S spectra do not show any t1 noise, which is the main reason for the low repeatability of conventional 2D experiments.[42] Based on this higher performance, we recently applied the M3S COSY experiment to determine, with high precision, the absolute concentration of metabolites in breast cancer cell lines (Fig. 10).[116] High accuracy was ensured thanks to a standard addition approach. Other recent applications of the M3S approach include the quantitative determination of isotopic enrichments in metabolic mixtures[133] or the determination of residual dipolar couplings in oriented media.[134] These recent quantitative applications of the UF methodology open promising perspectives toward the fast, precise and accurate determination of concentrations in complex mixtures. Two main limitations, however, should be highlighted: The first one is that the M3S methodology was evaluated for homonuclear experiments only. In terms of quantitative analysis, the interest of heteronuclear UF experiments was not assessed so far. The

1

Figure 10. Data showing the potential of the hybrid M3S 2D NMR approach for quantitative analysis. (Left) 2D H ‘multiscan single shot’ COSY spectrum of a breast cancer cell line extract, obtained by CHCl3/MeOH/H2O extraction of breast cancer cells. The spectrum was acquired in 20 min (256 transients). (Right) metabolite concentrations of intracellular extracts obtained from three cell lines: SKBR3, MCF-7 and Cal 51 by a quantitative 2D ‘multiscan single shot’ COSY protocol associated with a standard addition procedure. The concentrations are normalized to a 100-mg mass of lyophilized cells. Reproduced with permission from A. Le Guennec, I. Tea, I. Antheaume, E. Martineau, B. Charrier, M. Pathan, S. Akoka, P. Giraudeau, Anal. Chem. 2012, 84, 10831–10837. Copyright (2012) American Chemical Society.




P. Giraudeau second limitation is that even though the M3S methodology is more repeatable than its conventional counterpart, it may fail to detect very low concentrated analytes: This would require hours of acquisition that are probably not recommended for the sake of the gradient hardware, and in some cases, conventional or other fast approaches may be preferred. More details on the analytical performance of UF NMR can be found in Giraudeau and Frydman101. In order to improve its performance, interesting perspectives will certainly arise from the combination of this exciting new methodology with the other time-reduction approaches, as suggested in recent papers.[135,136] The UF approach could also form an interesting basis to increase the dimensionality of NMR experiments while preserving a reasonable duration, as recently suggested by emerging fast hybrid 3D acquisition schemes.[137,138]

Conclusion As shown by this review, abundant literature has been devoted, in the last decade, to the development of 2D NMR approaches for the quantitative analysis of small molecule mixtures. The quantitative aspects have been considered through different angles. The first one is trying to make 2D NMR experiments intrinsically quantitative, based on pulse sequence modifications to improve the homogeneity of the 2D peak volume response. The other approaches rely on analytical chemistry approaches to circumvent the apparent nonquantitativeness of 2D experiments. They consist in determining and taking into account, for each signal, the proportionality factor between the peak volume and the concentration. This can be performed either by theoretical calculations or by calibration strategies. As highlighted in this manuscript, the different strategies are being developed and applied in parallel, and so far, none of them has taken the upper hand. This is probably because these different strategies have their own advantages and drawbacks, and future developments will certainly benefit from combining them to reach the highest analytical performance. With the current state-of-the-art, giving a universal quantitative 2D NMR recipe would be premature, and we hope that the arguments given in this review will help readers to choose the most appropriate approach to solve their own quantitative issue. The last part of this manuscript highlights how the duration of 2D NMR experiments can affect quantification, not only for spectrometer schedule reasons but also because the precision of quantitative 2D NMR experiments appears to be strongly impacted by the experiment time. Fortunately, the recent developments of alternative acquisition schemes will certainly help in solving this issue. Another major issue of quantitative NMR has been deliberately disregarded in this review: sensitivity. There are two main reasons for this choice: First of all, this problem is not specific to multidimensional experiments and is a well-known issue of NMR compared with other analytical techniques such as mass spectrometry. The other reason is that the limit of quantification (LOQ) of a method is highly hardware dependent, and all the methods described in the preceding texts were implemented on different spectrometers and probes. It would be nonsense to compare the LOQ of a method that was applied on a 400-MHz spectrometer with a room-temperature probe to the LOQ of another approach that was implemented on an 800 MHz with a cryoprobe. Of course, working at increasing field strengths with cryogenic probes will improve the performance of the experiments described in the


preceding texts, even though very high fields will certainly pose new challenges in terms of decoupling bandwidth that will probably impact the precision of quantitative measurements. In conclusion, the different strategies would certainly benefit from ring-test initiatives to compare the different existing methods in different laboratories equipped with various hardware configurations. Regarding the sensitivity issues of quantitative 2D NMR experiments, and of quantitative NMR in general, they will certainly benefit from recent advances in the domain of hyperpolarization. Dissolution dynamic nuclear polarization[139] and approaches based on parahydrogen[140] have shown high potentialities for solution-state NMR, and they have been successfully coupled to single-scan 2D NMR approaches.[124,126,141] However, this domain is still unexplored in terms of precise and accurate quantitative analysis, probably because the polarization techniques add a high degree of variability in the NMR signal. Obtaining quantitative results, for example, via calibration curves, would require that all these additional variability factors (sample preparation, polarization conditions and coupling conditions) are fully controlled so that the experiment is reproducible. Major NMR and analytical developments will be necessary before these techniques can be applied to quantitative issues. Acknowledgements The author is grateful to the members of the EBSI group and particularly to Prof. Serge Akoka for stimulating discussions over the last 10 years. Michel Giraudeau is also acknowledged for linguistic assistance. The author thanks the French National Research Agency (Agence Nationale de la Recherche grant 2010-JCJC-0804-01) and the Corsaire Metabolomics facility for funding.

References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23]

V. Rizzo, V. Pinciroli. J. Pharm. Biomed. Anal. 2005, 38, 851–857. J. L. Jungnickel, J. W. Forbes. Anal. Chem. 1963, 35, 938–942. D. P. Hollis. Anal. Chem. 1963, 35, 1682–1684. J. K. Kwakye. Talanta 1985, 32, 1069–1071. G. F. Pauli, B. U. Jaki, D. C. Lankin. J. Nat. Prod. 2005, 68, 133–149. F. Podo, O. Henriksen, W. M. M. J. Bovée, M. O. Leacj, D. Leibfritz, J. D. De Certaines. Magn. Reson. Imaging 1998, 16. D. S. Wishart. Trac Trend. Anal. Chem. 2008, 27, 228–237. P. Giraudeau, N. Guignard, H. Hillion, E. Baguet, S. Akoka. J. Pharm. Biomed. Anal. 2007, 43, 1243–1248. A. M. Weljie, J. Newton, P. Mercier, E. Carlson, C. M. Slupsky. Anal. Chem. 2006, 78, 4430–4442. G. Le Gall, I. J. Colquhoun, A. L. Davis, G. J. Collins, M. E. Verhoeyen. J. Agric. Food Chem. 2003, 51, 2447–2456. T. H. Mareci, K. N. Scott. Anal. Chem. 1977, 49, 2130–2136. J. N. Shoolery. Prog. Nucl. Magn. Reson. Spectrosc. 1977, 11, 79–93. D. J. Cookson, B. E. Smith. J. Magn. Reson. 1984, 57, 355–368. T. Mavromoustakos, M. Zervou, E. Theodoropoulou, D. Panagiotopoulos, G. Bonas, M. Day, A. Helmis. Magn. Reson. Chem. 1997, 35, S3–S7. G. Vlahov. Prog. NMR Spectrosc. 1999, 35, 341–357. M. Aursand, L. Jorgensen, H. Grasdalen. Comp. Biochem. Physiol. 1995, 112B, 315–321. E. Tenailleau, P. Lancelin, R. J. Robins, S. Akoka. J. Agric. Food Chem. 2004, 52, 7782–7787. E. Caytan, G. S. Remaud, E. Tenailleau, S. Akoka. Talanta 2007, 71, 1016–1021. U. Bussy, C. Thibaudeau, F. Thomas, J.-R. Desmurs, E. Jamin, G. Remaud, V. Silvestre, S. Akoka. Talanta 2011, 85, 1909–1914. G. C. Levy, T. Pehk, P. R. Srinivasan. Org. Magn. Reson. 1980, 14, 129–132. P. Dais, A. Spyros. Magn. Reson. Chem. 2007, 45, 367–377. D. G. Lonnon, J. M. Hook. Anal. Chem. 2003, 75, 4659–4666. J. Jeener, Lecture presented at Ampere International Summer School II, Basko Polje, Yugoslavia 1971.



Quantitative 2D NMR [24] W. P. Aue, E. Bartholdi, R. R. Ernst. J. Chem. Phys. 1976, 64, 2229–2246. [25] H. Koskela, I. Kilpeläinen, S. Heikkinen. J. Magn. Reson. 2005, 174, 237–244. [26] H. Koskela, T. Väänänen. Magn. Reson. Chem. 2002, 40, 705–715. [27] I. A. Lewis, R. H. Karsten, M. E. Norton, M. Tonelli, W. M. Westler, J. L. Markley. Anal. Chem. 2010, 82, 4558–4563. [28] I. A. Lewis, S. C. Schommer, B. Hodis, K. A. Robb, M. Tonelli, W. Westler, M. Sussman, J. L. Markley. Anal. Chem. 2007, 79, 9385–9390. [29] E. Martineau, P. Giraudeau, I. Tea, S. Akoka. J. Pharm. Biomed. Anal. 2011, 54, 252–257. [30] S. Massou, C. Nicolas, F. Letisse, J.-C. Portais. Phytochemistry 2007, 68, 2330–2340. [31] E. Martineau, I. Tea, S. Akoka, P. Giraudeau. NMR Biomed. 2012, 25, 985–992. [32] S. Massou, C. Nicolas, F. Letisse, J.-C. Portais. Metab. Eng. 2007, 9, 252–257. [33] L. Zhang, G. Gellerstedt. Magn. Reson. Chem. 2007, 45, 37–45. [34] A. Bax, R. Freeman. J. Magn. Reson. 1981, 44, 542–561. [35] G. Bodenhausen, D. J. Ruben. Chem. Phys. Lett. 1980, 69, 185–189. [36] P. Barker, R. Freeman. J. Magn. Reson. 1985, 64, 334–338. [37] R. R. Ernst, G. Bodenhausen, A. Wokaun, Principles of nuclear magnetic resonance in one and two dimensions, Oxford Science Publications ed, Oxford, 1987. [38] H. Koskela. Annu. Rep. NMR Spectrosc. 2009, 66, 1–31. [39] A. F. Mehlkopf, D. Korbee, T. A. Tiggelman, R. Freeman. J. Magn. Reson. 1984, 58, 315–323. [40] G. A. Morris. J. Magn. Reson. 1992, 100, 316–328. [41] P. Giraudeau, S. Akoka. Adv. Bot. Res. 2013, 67, 99–158. [42] M. Pathan, S. Akoka, I. Tea, B. Charrier, P. Giraudeau. Analyst 2011, 136, 3157–3163. [43] K. Hu, W. M. Westler, J. L. Markley. J. Am. Chem. Soc. 2011, 133, 1662–1665. [44] R. K. Rai, P. Tripathi, N. Sinha. Anal. Chem. 2009, 81, 10232–10238. [45] K. Bingol, F. Zhang, L. Brüschweiler-Li, R. Brüschweiler. Anal. Chem. 2013, 85, 6413–6420. [46] S. Heikkinen, M. M. Toikka, P. T. Karhunen, A. Kilpeläinen. J. Am. Chem. Soc. 2003, 125, 4362–4367. [47] D. J. Peterson, N. M. Loening. Magn. Reson. Chem. 2007, 45, 937–941. [48] M. Sette, R. Wechselberger, C. Crestini. Chem. Eur. J. 2011, 17, 9529–9535. [49] H. Koskela, O. Heikkilä, I. Kilpeläinen, S. Heikkinen. J. Magn. Reson. 2010, 202, 24–33. [50] T. E. Skinner, K. Kobzar, B. Luy, M. R. Bendall, W. Bermel, N. Khaneja, S. J. Glaser. J. Magn. Reson. 2006, 179, 241–249. [51] K. Hu, J. J. Ellinger, R. A. Chylla, J. L. Markley. Anal. Chem. 2011, 83, 9352–9360. [52] K. Hu, T. P. Wyche, T. S. Bugni, J. L. Markley. J. Nat. Prod. 2011, 74, 2295–2298. [53] S. Halouska, R. J. Fenton, D. K. Zinniel, D. D. Marshall, R. G. Barletta, R. Powers, J. Proteome Res. 2013, in press, doi:10.1021/pr4010579. [54] P. Giraudeau, I. Tea, G. S. Remaud, S. Akoka, J. Pharm. Biomed. Anal. 2014, in press, doi:10.1016/j.jpba.2013.07.020. [55] P. C. Castilho, S. C. Gouveia, A. I. Rodrigues. Phytochem. Anal. 2008, 19, 329–334. [56] J. A. Donarski, D. P. T. Roberts, A. J. Charlton. Anal. Meth. 2010, 2, 1479–1483. [57] G. A. N. Gowda, F. Tayyari, T. Ye, Y. Suryani, S. Wei, N. Shanaiah, D. Raftery. Anal. Chem. 2010, 82, 8983–8990. [58] W. Gronwald, M. S. Klein, H. Kaspar, S. R. Fagerer, N. Nurnberger, K. Dettmer, T. Bertsch, P. J. Oefner. Anal. Chem. 2008, 80, 9288–9297. [59] F. Hu, K. Furihata, Y. Kato, M. Tanokura. J. Agric. Food Chem. 2007, 55, 4307–4311. [60] T. Beyer, B. Diehl, U. Holzgrabe. Bioanal. Rev. 2010, 2, 1–22. [61] M. Rajabzadeh. J. Chem. Educ. 2012, 89, 1454–1457. [62] D. Canet, J.-C. Boubel, E. Canet Soulas, La RMN, Concepts, méthodes et applications, Dunod ed, Paris, 2002. [63] R. Freeman, A Handbook of Nuclear Magnetic Resonance, Longman ed, Harlow, 1998. [64] S. Braun, H.-O. Kalinowski, S. Berger, 150 and More Basic NMR Experiments: A Practical Course, Wiley-VCH ed, Weinheim, 1998. [65] J. C. Cobas, M. A. Bernstein, M. Martín-Pastor, P. G. Tahoces. J. Magn. Reson. 2006, 183, 145–151. [66] W. Dietrich, C. H. Rüdel, M. Neumann. J. Magn. Reson. 1991, 91, 1–11.


[67] R. Baumann, A. Kumar, R. R. Ernst, K. Wütrich. J. Magn. Reson. 1981, 44, 76–83. [68] R. Baumann, G. Wider, R. R. Ernst, K. Wütrich. J. Magn. Reson. 1981, 44, 402–406. [69] R. Romano, D. Paris, F. Acernese, F. Barone, A. Motta. J. Magn. Reson. 2008, 192, 294–301. [70] M. I. Miller, A. S. Greene. J. Magn. Reson. 1989, 83, 525–548. [71] R. A. de Graaf, G. M. I. Chowdhury, K. L. Behar. Anal. Chem. 2011, 83, 216–224. [72] R. A. Chylla, B. F. Volkman, J. L. Markley. J. Biomol. NMR 1998, 12, 277–297. [73] R. A. Chylla, K. Hu, J. J. Ellinger, J. L. Markley. Anal. Chem. 2011, 83, 4871–4880. [74] W. S. Price. Ann. Rep. NMR Spectrosc. 1996, 32. [75] R. Freeman, S. P. Kempsell, M. H. Levitt. J. Magn. Reson. 1980, 38, 453–479. [76] E. Kupce, R. Freeman. J. Magn. Reson. A 1995, 115. [77] A. Bax, R. Freeman, S. P. Kempsell. J. Am. Chem. Soc. 1980, 102, 4849–4851. [78] J. W. Lown, C. C. Hanstock. J. Biomol. Struct. Dyn. 1985, 2, 1097–1106. [79] F. Debart, B. Rayner, J. L. Imbach, D. K. Chang, J. W. Lown. J. Biomol. Struct. Dyn. 1986, 4, 343–363. [80] A. Ross, M. Salzmann, H. Senn. J. Biomol. NMR 1997, 10, 389–396. [81] P. Schanda, B. Brutscher. J. Am. Chem. Soc. 2005, 127, 8014–8015. [82] B. Vitorge, G. Bodenhausen, P. Pelupessy. J. Magn. Reson. 2010, 207, 149–152. [83] D. Jeannerat. Magn. Reson. Chem. 2003, 41, 3–17. [84] H. Barkhuijsen, R. De Beer, W. M. M. J. Bovée, D. Van Ormondt. J. Magn. Reson. 1985, 61, 465–481. [85] A. S. Stern, K.-B. Li, J. C. Hoch. J. Am. Chem. Soc. 2002, 124, 1982–1993. [86] J. C. Hoch. J. Magn. Reson. 1985, 64, 436–440. [87] R. Brüschweiler, F. Zhang. J. Chem. Phys. 2004, 120, 5253–5260. [88] J. C. J. Barna, E. D. Laue, M. R. Mayger, J. Skilling, S. J. P. Worrall. J. Magn. Reson. 1987, 73, 69–77. [89] E. Kupce, R. Freeman. J. Magn. Reson. 2005, 173, 317–321. [90] K. Kazimierczuk, A. Zawadzka, V. Kozminski, I. Zhukov. J. Magn. Reson. 2007, 188, 344–356. [91] O. Lafon, B. Hu, J.-P. Amoureux, P. Lesot. Chem. Eur. J. 2011, 17, 6716–6724. [92] V. Y. Orekhov, V. A. Jaravine. Prog. Nucl. Magn. Reson. Spectrosc. 2011, 59, 271–292. [93] E. Kupce, R. Freeman. J. Magn. Reson. 2003, 162, 300–310. [94] E. Martineau, S. Akoka, R. Boisseau, B. Delanoue, P. Giraudeau. Anal. Chem. 2013, 85, 4777–4783. [95] Y. Chen, F. Zhang, D. Snyder, Z. Gan, L. Brüschweiler-Li, R. Brüschweiler. J. Biomol. NMR 2007, 38, 73–77. [96] K. Bingol, R. Brüschweiler. Anal. Chem. 2014, 86, 47–57. [97] C. Ludwig, D. G. Ward, A. Martin, M. R. Viant, T. Ismail, P. J. Johnson, M. J. O. Wakelam, U. L. Günther. Magn. Reson. Chem. 2009, 47, S68– S73. [98] L. Frydman, T. Scherf, A. Lupulescu. Proc. Natl. Acad. Sci. U. S. A. 2002, 99, 15858–15862. [99] M. Gal, L. Frydman, in Encyclopedia of Magnetic Resonance (Eds.: G. A. Morris, J. W. Emsley), Wiley, Chichester, 2010, pp. 43–60. [100] A. Tal, L. Frydman. Prog. Nucl. Magn. Reson. Spectrosc. 2010, 57, 241–292. [101] P. Giraudeau, L. Frydman, Ann. Rev. Anal. Chem. 2014, 7, in press. [102] P. Mansfield. Magn. Reson. Med. 1984, 1, 370–386. [103] P. Giraudeau, S. Akoka. J. Magn. Reson. 2008, 190, 339–345. [104] P. Giraudeau, S. Akoka. J. Magn. Reson. 2008, 192, 151–158. [105] P. Giraudeau, S. Akoka. J. Magn. Reson. 2010, 205, 171–176. [106] P. Giraudeau, S. Akoka. Magn. Reson. Chem. 2011, 49, 307–313. [107] L. Rouger, B. Charrier, M. Pathan, S. Akoka, P. Giraudeau. J. Magn. Reson. 2014, 238, 87–93. [108] P. Pelupessy. J. Am. Chem. Soc. 2003, 125, 12345–50. [109] P. Pelupessy, L. Duma, G. Bodenhausen. J. Magn. Reson. 2008, 194, 169–174. [110] A. Tal, B. Shapira, L. Frydman. J. Magn. Reson. 2005, 176, 107–114. [111] B. Shapira, Y. Shrot, L. Frydman. J. Magn. Reson. 2006, 178, 33–41. [112] Y. Shrot, L. Frydman. J. Chem. Phys. 2008, 128, 052209. [113] Y. Shrot, L. Frydman. J. Chem. Phys. 2009, 131, 224516. [114] A. Tal, B. Shapira, L. Frydman. Angew. Chem. Int. Ed. 2009, 48, 2732–2736. [115] L. Rouger, D. Loquet, S. Massou, S. Akoka, P. Giraudeau. ChemPhysChem 2012, 13, 4124–4127.



P. Giraudeau [116] M. Pathan, B. Charrier, I. Tea, S. Akoka, P. Giraudeau. Magn. Reson. Chem. 2013, 51, 168–175. [117] L. H. K. Queiroz Junior, A. G. Ferreira, P. Giraudeau. Quim. Nova. 2013, 26, 577–581. [118] L. H. K. Queiroz Junior, P. Giraudeau, F. A. B. dos Santos, K. T. Oliveira, A. G. Ferreira. Magn. Reson. Chem. 2012, 50, 496–501. [119] A. Herrera, E. Fernandez-Valle, E. M. Gutiérrez, R. Martinez-Alvarez, D. Molero, Z. D. Pardo, E. Saez. Org. Lett. 2010, 12, 144–147. [120] A. Herrera, E. Fernández-Valle, R. Martínez-Álvarez, D. Molero, Z. D. Pardo, E. Sáez, M. Gal. Angew. Chem. Int. Ed. 2009, 48, 6274–6277. [121] Z. D. Pardo, G. L. Olsen, M. E. Fernández-Valle, L. Frydman, R. Martínez-Álvarez, A. Herrera. J. Am. Chem. Soc. 2012, 134, 2706–2715. [122] A. Corazza, E. Rennella, P. Schanda, M. C. Mimmi, T. Cutuil, S. Raimondi, S. Giorgetti, F. Fogolari, P. Viglino, L. Frydman, M. Gal, V. Bellotti, B. Brutscher, G. Esposito. J. Biol. Chem. 2010, 285, 5827–5835. [123] M.-K. Lee, M. Gal, L. Frydman, G. Varani. Proc. Natl. Acad. Sci. U. S. A. 2010, 107. [124] P. Giraudeau, Y. Shrot, L. Frydman. J. Am. Chem. Soc. 2009, 131, 13902–13903. [125] L. H. K. Queiroz Junior, D. P. K. Queiroz, L. Dhooghe, A. G. Ferreira, P. Giraudeau. Analyst 2012, 137, 2357–2361. [126] L. S. Lloyd, R. W. Adams, M. Bernstein, S. Coombes, S. B. Duckett, G. G. R. Green, R. J. Lewis, R. E. Mewis, C. J. Sleigh. J. Am. Chem. Soc. 2012, 134, 12904–12907. [127] P. Pelupessy, E. Renella, G. Bodenhausen. Science 2009, 324, 1693–1697. [128] Z. Wei, L. Lin, Y. Lin, S. Cai, Z. Chen. Chem. Phys. Lett. 2013, 581, 96–102.


[129] Z. Zhang, H. Chen, C. Wu, R. Wu, S. Cai, Z. Chen. J. Magn. Reson. 2013, 227, 39–45. [130] P. Giraudeau, G. S. Remaud, S. Akoka. Anal. Chem. 2009, 81, 479–484. [131] L. Frydman, A. Lupulescu, T. Scherf. J. Am. Chem. Soc. 2003, 125, 9204–9217. [132] A. Le Guennec, I. Tea, I. Antheaume, E. Martineau, B. Charrier, M. Pathan, S. Akoka, P. Giraudeau. Anal. Chem. 2012, 84, 10831–10837. [133] P. Giraudeau, S. Massou, Y. Robin, E. Cahoreau. Anal. Chem. 2011, 83, 3112–3119. [134] P. Giraudeau, T. Montag, B. Charrier, C. M. Thiele. Magn. Reson. Chem. 2012, 50, S53–S57. [135] M. Gal, P. Schanda, B. Brutscher, L. Frydman. J. Am. Chem. Soc. 2007, 129, 1372–1377. [136] A. Tal, B. Shapira, L. Frydman. Angew. Chem. Int. Ed. 2009, 48, 2732–2736. [137] P. Giraudeau, E. Cahoreau, S. Massou, M. Pathan, J.-C. Portais, S. Akoka. ChemPhysChem 2012, 13, 3098–3101. [138] R. Boisseau, B. Charrier, S. Massou, J.-C. Portais, S. Akoka, P. Giraudeau. Anal. Chem. 2013, 85, 9751–9757. [139] J. H. Ardenkjaer-Larsen, B. Fridlund, A. Gram, G. Hansson, L. Hansson, M. H. Lerche, R. Servin, M. Thaning, K. Golman. Proc. Natl. Acad. Sci. U. S. A. 2003, 100, 10158–10163. [140] T. C. Eisenschmid, R. U. Kirss, P. P. Deutsch, S. I. Hommeltoft, R. Eisenberg, J. Bargon, R. G. Lawler, A. L. Balch. J. Am. Chem. Soc. 2002, 109, 8089–8091. [141] L. Frydman, D. Blazina. Nat. Phys. 2007, 3, 415–419.



Evaluation of fast 2D NMR for metabolomics.

1H-NMR, 1H-NMR T2-edited, and 2D-NMR in bipolar disorder metabolic profiling.

Taxol: quantitative internuclear proton-proton distances in CDCl3 solution from nOe data: 2D nmr ROESY buildup rates at 500 MHz.

A single-scan method for NMR 2D J-resolved spectroscopy.

Ultrafast 2D NMR: an emerging tool in analytical spectroscopy.

Processing strategies to obtain clean interleaved ultrafast 2D NMR spectra.

2D Model-to-Image Registration for Quantitative Dietary Assessment.

Constant-time 2D and 3D through-bond correlation NMR spectroscopy of solids under 60 kHz MAS.

Dolphin: a tool for automatic targeted metabolite profiling using 1D and 2D (1)H-NMR data.

Liposcale: a novel advanced lipoprotein test based on 2D diffusion-ordered 1H NMR spectroscopy.

Criteria for sensitivity enhancement by compressed sensing: practical application to anisotropic NAD 2D-NMR spectroscopy.

Cannibalism Affects Core Metabolic Processes in Helicoverpa armigera Larvae-A 2D NMR Metabolomics Study.

Advanced solvent signal suppression for the acquisition of 1D and 2D NMR spectra of Scotch Whisky.

Application of 2D and 3D NMR experiments to the conformational study of a diantennary oligosaccharide.

Performance Assessment in Fingerprinting and Multi Component Quantitative NMR Analyses.

Universal quantitative NMR analysis of complex natural samples.

Earth's field NMR flow meter: preliminary quantitative measurements.

Quantitative NMR imaging of multiphase flow in porous media.

Expanding the analytical toolbox: pharmaceutical application of quantitative NMR.

Quantitative and dynamic analysis of PTEN phosphorylation by NMR.

Quantitative determination of cephalexin in cephradine by NMR spectroscopy.

Proton NMR characterization of intact primary and metastatic melanoma cells in 2D & 3D cultures.

2D NMR barcoding and differential analysis of complex mixtures for chemical identification: the Actaea triterpenes.

Differentiation of enantiomers by 2D NMR spectroscopy at 1 T using residual dipolar couplings.