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Dissect and Divide: Putting NMR spectra of mixtures under the knife Guilherme Dal Poggetto, Laura Castañar, Ralph W. Adams, Gareth A. Morris, and Mathias Nilsson J. Am. Chem. Soc., Just Accepted Manuscript • Publication Date (Web): 19 Mar 2019 Downloaded from http://pubs.acs.org on March 19, 2019

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Journal of the American Chemical Society

Dissect and Divide: Putting NMR spectra of mixtures under the knife Guilherme Dal Poggetto, Laura Castañar, Ralph W. Adams, Gareth A. Morris and Mathias Nilsson* School of Chemistry, University of Manchester, Oxford Road, Manchester M13 9PL, United Kingdom

Supporting Information Placeholder ABSTRACT: Efficient, practical and non-destructive analysis of complex mixtures is vital in many branches of chemistry. Here

we present a new type of NMR experiment that allows the study of very challenging intact mixtures, in which subspectra of individual components can be extracted when other NMR means fail, for the case of a single, intact, static (constant composition) sample. We demonstrate the new approach, SCALPEL (Spectral Component Acquisition by Localized PARAFAC Extraction of Linear components), on a natural fermented beverage, beer, and other carbohydrate mixtures, obtaining individual carbohydrate component subspectra. This new class of NMR experiment is based on dissecting the spectrum rather than the sample, using pulse sequences tailored to generate data suitable for powerful tensor decomposition methods to allow highly complex spectra to be analyzed stepwise, one small section at a time. It has the clear potential to attack problems beyond the reach of current methods.

INTRODUCTION Chemists frequently encounter mixtures that are too complex to analyse intact. They are then driven – reluctantly – to the use of tedious and costly separation and purification methods, such as chromatography. These can sometimes destroy the very system under study: the chemistry of an intact living cell is poorly represented by the result of lysing it and analysing the resultant solution. What are desperately needed in such cases are powerful methods that allow studies of the native state. In principle Nuclear Magnetic Resonance (NMR) spectroscopy ought to be able to meet this need, but current methods generally struggle to separate the spectral contributions from different species. A wide variety of multidimensional methods are available, for example combining TOCSY methods with automated analysis,1-2 but these are all limited to a greater or lesser extent by the problem of spectral overlap. At present the most powerful NMR methods for disentangling overlapping component spectra require either a single sample with time-varying composition 3-4 or a large number of samples (e.g. STOCSY5). Here we describe a new approach, SCALPEL (Spectral Component Acquisition by Localized PARAFAC Extraction of Linear components), that can be applicable to a single, unchanging sample of even the most complex mixtures. It allows complex spectra to be dissected piecemeal, by focusing on individual small spectral regions and using multivariate analysis to extract the spectra of those coupled spin systems that have a resonance within that region, even when their spectra are severely overlapped, as shown in figure 1 where we extract very clean spectra of different individual glucose spin systems from the highly complex 1H NMR spectrum of stout beer, without the need for any physical separation. When NMR signals are well resolved it is relatively easy to distinguish different components by differences in their

diffusion behaviour, using Diffusion-Ordered SpectroscopY (DOSY) experiments.6-9 Even in systems with moderate spectral overlap, a skilled spectroscopist can often interpret DOSY spectra.10-11 For spectra that are highly overlapped but have few components, there are efficient multivariate data analysis methods that exploit the fact that all signals of a given species show the same diffusional behaviour.12-17 Component spectra can be extracted using such methods, but

Figure 1. SCALPEL results (1 h 49 min) for a sample of stout (Mackeson), with 20% added D2O. (a) 1H NMR spectrum, and (b-d) PARAFAC spectral modes for the terminal β-glucose components of maltose/maltotriose, lactose, and free glucose, respectively. Grey text indicates spin systems not selected in the spectra, and black text the spin systems that are selected. Data were acquired using the sequence of Figure 2, with

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diffusion and TOCSY-t1 evolution encoding; full experimental details are given in the ESI.

Figure 2. A prototypical pulse sequence for SCALPEL experiments using TOCSY-t1 evolution encoding (outlined in green) and either diffusion (outlined in red) or T2 relaxation (outlined in blue) encoding. Black and white rectangles represent 90◦ and 180◦ hard pulses, respectively. White trapezoids with arrows represent chirp pulses used to suppress the effects of zero-quantum coherences,18 and DIPSI-219 is used for isotropic mixing. The unbounded grey shapes represent 180◦ selective refocusing pulses (Reburp or RSnob), and can usefully be frequency modulated to also refocus the reference signal, TSP-d4, in order to allow reference deconvolution to be used.20 Light grey trapezoids and half-sine shapes represent correspondingly shaped field gradient pulses. Only a small number of values is used for the evolution time t1, chosen for efficient sampling of differences in signal evolution, rather than the large number of equal increments that would be used in a 2D experiment. For diffusion encoding, the delays τ are kept constant and gradients strengths G4 are incremented, while for relaxation encoding gradient strengths G4 are kept constant and delays τ are incremented. Further information is given in the ESI. only if the number of individual components is small, they are not of very different concentration, and they have wellseparated diffusion coefficients. Unfortunately, many of the most interesting mixtures have both severe signal overlap, and large numbers of components with different concentrations. For such systems, current NMR methods can at best deliver only limited information – and only when the species of interest diffuse at different rates.21-23 Two potential ways forward, used in combination here, are to exploit more types of behaviour to discriminate between species, and to reduce the number of signals excited in a given acquisition in order to reduce the number of different species involved. Relaxation is an alternative source of discrimination between species to diffusion, provided that all the spins in a spin system of a given species can be given the same relaxation weighting. Recently, we proposed the REST (Relaxation-Encoded Selective TOCSY)24 family of experiments, in which a combination of selective excitation25-26 and isotropic mixing2730 is used to label each spin in a given system with the same relaxation weighting, so that the experimental data obtained can be subjected to univariate analysis as Relaxation-Ordered Spectroscopy (ROSY)31 data. This means that every signal in a given spin system behaves (i.e. decays) in the same way as the spin selected. As with DOSY, univariate analysis only works for species with well-separated relaxation times. The inclusion of a selective TOCSY step to restrict the number of different species observed at a time can also be used reduce overlap problems in DOSY experiments, giving the DESTO (DiffusionEncoded Selective TOCSY) experiment (see Figure ESI5). A third, and hitherto unexploited, way to achieve speciesspecific NMR labelling of signals is again to label a single spin and share its coherence with the rest of its spin system, but this time to label using the evolution and mixing period of a conventional 2D experiment (e.g. COSY, NOESY or TOCSY)

before the selective TOCSY step, not as a prelude to 2D Fourier transformation but to give each spin system a characteristic (and complicated) t1 dependence (see Figure ESI2). TOCSY-t1 encoding in this way is particularly powerful because the signal amplitude dependence on t1 is a sensitive function of the coupling constants in the spin system. With both relaxation and TOCSY-t1 encoding, one constraint is that the initial labelling should involve only one spin per spin system, but with a narrow bandwidth excitation pulse this is not normally a problem. Combining two or more of these species-specific labelling methods, as demonstrated here for the first time, brings a crucial advantage: it enables the use of multiway (or tensor) decomposition, which exploits the multilinearity of the measured experimental data. While bilinear analysis yields only linear combinations of the true component spectra (the problem of “rotational ambiguity” or “rotational freedom”),32 multilinear analysis resolves this ambiguity and decomposes the experimental data into physically meaningful components, in this case NMR spectra of single species. Three-way methods such as parallel factor analysis,33 PARAFAC, have been shown to be very powerful for analysing spectral data that change with time (e.g. as a result of chemical reaction)3-4 and one other species-specific parameter.34-36 However, the vast majority of samples of interest are static, with concentrations that do not change on the timescale of analysis, so in order to obtain a multivariate advantage for such samples we need, as here, to encode further NMR parameters into the spectral data. To summarise, rather than physically separating the sample into more manageable fractions (and running the risk of fatally perturbing the system), we focus on one small part of the spectrum of the intact sample at a time, encode two or more characteristic properties (e.g. diffusion coefficient, T1 or T2) into the signal amplitudes, and then propagate those


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Journal of the American Chemical Society amplitudes to the rest of the coupled spin systems by selective TOCSY. This approach unlocks multivariate analysis of the full spectrum, allowing the subspectra of spin systems of selected individual mixture components to be extracted, even where univariate analysis methods such as DOSY and REST are completely defeated by signal overlap.29-30

RESEULTS & DISCUSSION The SCALPEL method thus consists in acquiring experimental data using a narrow bandwidth selective TOCSY pulse sequence in which signals are encoded with two or more types (e.g. diffusion, T1 or T2 relaxation, TOCSY-t1) of speciesselective labelling, and then using a multivariate analysis method such as PARAFAC to extract the contributions from each of the different species present. The PARAFAC model for a trilinear data can be written as the decomposition of the data set, M, into its N components:

(∑ 𝑵

𝐌=

𝒊=𝟏

)

𝒂𝒊 ⨂ 𝒃𝒊 ⨂ 𝒔𝒊 + 𝐄𝐫𝐫𝐨𝐫

(1)

where in our case si is the spectrum of component i as a function of frequency while ai and bi are the additional dimensions (e.g. relaxation and diffusion) and ⨂ denotes the Kronecker product. Because each experiment focuses on a narrow spectral window, the number of species involved in any given experiment is far fewer than the total number of mixture components present. Repeating the process for a series of different selected spectral regions allows the spectrum of a complex mixture to be dissected, in a manner analogous to that of an anatomist, faced with the complexity of a whole organism, focusses on each limb and organ in turn. The SCALPEL method is illustrated here using TOCSY-t1 labelling in combination with either diffusion or relaxation weighting. Using two different labelling modalities in the same experiment changes the structure of the data obtained

from bilinear, as in DOSY or REST, (spectra as a function of frequency are measured as a function of some second parameter, e.g. gradient strength) to trilinear (spectra as a function of two independent parameters, e.g. gradient strength and evolution time). The prototype pulse sequence of Figure 2 allows for encoding dependence on TOCSY-t1 (time) evolution and one of two different possible second dimensions. Here these are diffusion and T2 relaxation, but a range of other NMR parameters could also be exploited. In principle all three types of encoding in Figure 2 could be used at once, but in the examples presented here two were sufficient (diffusion and TOCSY-t1 evolution in the case of Figure 1). The conventional 1H spectrum of a sample of a British stout (Figure 1a) shows a highly overlapped region, with signals mainly from carbohydrates and ethanol. Using SCALPEL, selecting just the anomeric signals around 4.65 ppm and using diffusion and TOCSY-t1 evolution weighting, it is possible to extract the three component subspectra shown in Figure 1b-d. Because diffusion is one of the dimensions used here, it is also possible to classify the components by size from large (Figure 1b) to small (Figure 1d) (see Figure ESI3a). Maltose and maltotriose (Figure 1b) are returned as a single component because the spectra of their terminal β-glucose moieties are essentially degenerate. Other NMR methods such as selective TOCSY (see Figure ESI3), and even HSQC-TOCSY (see Figure ESI4), are unable to provide clean component spectra here, because the number of components present and degree of overlap are too great for any bilinear multivariate processing to succeed. Figure 1 shows just a small fraction of the chemical space spanned by beer; applying SCALPEL to further spectral regions in turn would allow more of the spectrum to be dissected. Multilinear decomposition of SCALPEL data yields not only the NMR subspectra (as a chemical shift selective filter(CSSF,37)-TOCSY method could where chemical shifts are fully resolved), but also the forms (or ‘modes’) of the signal

Figure 3. SCALPEL results for a mixture of glucose, glucose-6-phosphate and maltose, in D2O. Data were acquired using the sequence of Figure 2 with TOCSY-t1 evolution and diffusion encoding, using a doubly frequency modulated selective pulse. (a) Selective TOCSY 1H spectrum obtained by exciting the anomeric region around 4.65 ppm, (b) PARAFAC evolution modes for all three components, (c) PARAFAC diffusion modes, (d-f) PARAFAC spectral modes for the terminal β-glucose components of free glucose, maltose and glucose-6-phosphate, respectively. For (b) and (c) plots, glucose points are represented with yellow filled



balls, glucose-6-phosphate with orange inverted triangles, and maltose with blue filled stars. The difference in diffusion coefficient between glucose-6-phosphate and maltose, which is less than 1 %, is too small to be resolved in plot (c). Full experimental details are given in the ESI. dependence on the additional dimensions. This is demonstrated in Figure 3, which shows the results of PARAFAC decomposition of a SCALPEL dataset acquired using diffusion and TOCSY-t1 evolution encoding for a model mixture of glucose, glucose-6-phosphate and maltose. From the three diffusion modes for the different mixture components it is straightforward to determine their diffusion coefficients, but it is evident that the values for glucose-6phosphate and maltose are very similar (within about 1%, as measured using a DESTO experiment, see Figure ESI6). Here CSSF-TOCSY would not be able to resolve glucose and glucose-6-phosphate, as their anomeric chemical shifts are indistinguishable (for conventional 2D TOCSY, see Figure ESI7). Neither diffusion encoding nor TOCSY-t1 evolution variation alone is sufficient to allow the contributions of the three different mixture components to be disentangled. There is no prior knowledge of the analytical form of the TOCSY-t1 time evolution that would allow it to be used alone, and the difference in diffusion coefficient is far too small for diffusion alone to be used. The subspectra of Figure 1 could potentially have been extracted using CSSF-TOCSY, because the three overlapping anomeric doublets in Figure 1a each have different chemical shifts, but this is not the case in Figure 3, where the glucose and glucose-6-phosphate shifts are indistinguishable. The question of the number of points that need to be sampled in the labelling dimensions of experiments of the form of Figure 2 is an interesting one. The absolute minimum number of measurements needed is not currently well-defined,32 but is usually less than conservative minimum of acquiring as many points in each dimension as there are components. With adequate signal-to-noise ratio the latter will always over-

determine the problem, and should always allow analysis. However the most practical strategy is to acquire an excess of data points, since this reduces the impact of systematic experimental errors and imperfections, so the data for Figures 1 and 3 used: 8 x 4 (TOCSY-t1 and diffusion) points and 32 x 8 points, respectively. In SCALPEL we can easily replace the diffusion labelling with transverse relaxation, using the same pulse sequence (Figure 2) but incrementing the delay τ instead of the gradient amplitude G4. The actual magnitude of T2 is not important for SCALPEL, as the relaxation is used only to provide statistical leverage in discriminating between the signals of different species. The use of SCALPEL with T2 and TOCSY-t1 evolution encoding is illustrated in Figure 4 for a mixture of the disaccharides lactose and melibiose. Here the spectra from 6 spin systems can be extracted from the intact sample, significantly beyond what is possible with previous methods (for iREST2 ROSY see Figure ESI9), in a single experiment. (The use of relaxation encoding can be complicated by crosscorrelated relaxation in some spin systems, but this was not a problem here. Different T2 weighting sequences such as CPMG38 and PROJECT39 will give different values for T2, but as noted above this is not a problem provided that there is sufficient difference between the T2s of different species.)

CONCLUSION The introduction of the SCALPEL class of experiments represents a step function improvement in our ability to analyse difficult mixtures by NMR. Provided that the experimental data have sufficient signal-to-noise ratio and that there is no

Figure 4. All six PARAFAC spectral modes, one for each non-reducing sugar and two each for the terminal reducing sugars, obtained from a single SCALPEL experiment, for a mixture of lactose and melibiose in D2O. Data were acquired using the sequence of Figure 2 with T2 relaxation and TOCSY-t1 evolution encoding, using a triply frequency modulated selective pulse. Relaxation time constants were measured from the first TOCSY-t1 increment experiment, and are respectively: a) 0.78-0.83 s; b) 1.09 s; c) 1.03 s; d) 0.61 s; e) 1.06 s and; f) 0.96 s. Full experimental details are given in the ESI.


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Journal of the American Chemical Society degeneracy, neither severe spectral overlap nor high dynamic range (up to 100:1) should impede SCALPEL analysis. There is ample scope for further developments, exploring the space of NMR parameters and going beyond three dimensions. Here we use the multilinear PARAFAC decomposition, but in other circumstances, e.g. with perfectly degenerate modes, the use of alternative algorithms such as PARALIND would be more appropriate.40 With the pulse sequence code provided in the ESI and the processing tools offered by the GNAT, these new experiments should be immediately accessible to the general chemist.

ASSOCIATED CONTENT Supporting Information The Supporting Information is available free of charge on the ACS Publications website. The processing of SCALPEL experimental data is straightforward using the free and open source software package GNAT (downloadable at https://www.nmr.chemistry.manchester.ac.uk),41 which is a graphical user interface (GUI) for analysis of NMR data from the major NMR manufacturers’ instruments. Data acquired using the Bruker pulse programme for the sequence of Figure 2 (downloadable, together with all experimental data, at DOI: 10.17632/tbhmz5396m.1), can be directly imported and analysed in the GNAT, which includes an interface to the NWAY Toolbox for analysis of multiway data,42 together with useful tools for statistical analysis. Additional figures as noted in the text, full NMR pulse sequence, experimental parameters, processing protocol, pulse program codes and AU macros for Bruker spectrometers. (PDF)

AUTHOR INFORMATION Corresponding Author * Email: [email protected].

Author Contributions All authors have given approval to the final version of the manuscript.

Notes The authors declare no competing financial interests.

ACKNOWLEDGMENT This work was supported by the Engineering and Physical Sciences Research Council (grant number EP/N033949/1 and EP/R018790/1) and by a studentship to GDP from Science Without Borders – Brazil (CNPq reference number 233163/2014-0). The authors gratefully acknowledge helpful discussions with Dr Mohammadali Foroozandeh.

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