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Analysis of complex reacting mixtures by time-resolved 2D NMR Rupashree Dass, Wiktor Ko#mi#ski, and Krzysztof Kazimierczuk Anal. Chem., Just Accepted Manuscript • Publication Date (Web): 15 Dec 2014 Downloaded from http://pubs.acs.org on December 16, 2014
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Analytical Chemistry
Analysis of complex reacting mixtures by time-resolved 2D NMR Rupashree Dass1, Wiktor Koźmiński1, and Krzysztof Kazimierczuk2,* 1
Faculty of Chemistry, Biological and Chemical Research Centre, University of Warsaw, Żwirki i Wigury 101, 02-089 Warsaw, Poland 2 Centre of New Technologies, University of Warsaw, Banacha 2C, 02-097 Warsaw, Poland Nuclear magnetic resonance (NMR) spectroscopy is a versatile tool for chemical analysis. Besides the most straightforward application to study a stable sample containing a single compound, NMR has been also used for the analysis of mixtures. In particular, the analyzed mixtures can undergo changes caused by chemical reactions. The multi-dimensional NMR techniques are especially effective in a case of samples containing many components. Unfortunately, they are usually too lengthy to be applied in timeresolved experiments performed to study mentioned changes in a series of spectral “snapshots”. Recently, time-resolved nonuniform sampling (NUS) has been proposed as a straightforward solution to the problem. In this paper we discuss the features of time-resolved NUS and give practical recommendations regarding the temporal resolution and use of the time pseudo-dimension to resolve the components. The theoretical considerations are exemplified by the application in challenging cases of fermenting samples of wheat flour and milk.
Introduction A variety of analytical techniques to monitor chemical reactions have been developed over the years, finding applications in numerous branches of industry, such as food or pharmaceutical processing. They help to determine mechanisms of various processes: biochemical reactions, organic synthesis, phase transitions, photocatalytic reactions etc. Techniques such as chromatography and mass spectrometry1,2 , nuclear magnetic resonance (NMR) spectroscopy3,4, Raman spectroscopy5, infrared spectroscopy6, and electrochemical techniques7 have been proven useful for this purpose. NMR provides precise structural information and is noninvasive in nature. It can also be used to monitor reactions in situ, sometimes with the use of specialized sensors8, or benchtop spectrometers9. Traditionally, to monitor an ongoing reaction series of one-dimensional (1D) 1H NMR spectra are taken at discrete intervals of time. However, 1D measurements may not provide sufficient resolution in a case of complicated mixture, where tens or even hundreds of spectral peaks are present in a region of few ppm. The monitoring is possible if at least one peak of the compound of interest is well separated in a spectrum. Though, this requirement often cannot be fulfilled. The problem of peak overlap in 1D can be circumvented by introducing additional spectral dimensions.10 The resolution, however, comes at the high price of the extended acquisition time required to sample the data points in the indirect spectral dimensions. The sampling is time-consuming because of two reasons. Firstly, its rate is proportional to a spectral window as described by Nyquist-Shannon theorem11,12. Secondly, mini-
mum spectral linewidth is inversely proportional to the evolution time reached.13 Thus, to obtain optimal resolution (linewidth) at a given sampling rate, one has to acquire large amount of sampling points, each taking a few seconds of experimental time. Non-uniform sampling (NUS) solves this problem by collecting only a fraction of the data. The omitted points are reconstructed using various algorithms differing in the assumption about the property of the reconstructed spectrum. The assumptions include: maximum entropy14, maximum sparsity15,16 or presence of the dark regions17. The compressed sensing (CS) method, exploiting the fact that NMR spectrum is sparse (“mostly empty”) has been proven useful in challenging cases of NMR spectra, such as NOESY with high dynamic range of signal intensities.18 The use of NUS allows to reduce the time needed to acquire single spectrum in a sequential (time-resolved) experiment19. However, it does not allow to reduce timescale of a single “snapshot” to the one achievable with 1D (1-2 seconds). The fast-sampling20 or single-scan methods21 are an important alternative, but require the use of advanced pulse sequences. The current work presents a methodological approach to study reactions occurring in complex mixtures with 2D NMR spectra of significantly improved resolution in time dimension, i.e. the number of “snapshots” per unit of time similar to the one in serial 1D measurement. We use both time-resolved variant of NUS and CS processing. Time resolved spectroscopy combined with NUS has been introduced by Orekhov and coworkers.22 In the original paper, the non-uniformly sampled data was collected in parallel to reaction occurring in the sample and then divided into subsets co-processed with multidimensional decomposition (importantly, the peak positions did not change). The approach exploiting CS processing and
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Analytical Chemistry
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adapted to the case of spectra where peak positions may vary was discussed in our recent paper23. The idea behind time-resolved CS is to process overlapping subsets of NUS dataset, where sampling is performed in parallel to reactions occurring in a sample. The result is a stack of two-dimensional (2D) spectra forming a third dimension corresponding to time or reaction progress (see Figure 1). If a studied process affects peak positions, intensities or linewidths, then the effect will be averaged over acquisition time of a single subset. Importantly, because of non-regular sampling, the lineshapes are not affected by the increase or decrease in the signal intensity. Such effect, observed and described by Balbach et al 24 occurs only, if evolution time incrementation is correlated with the change of concentration. Shuffled NUS removes this correlation, perhaps changing regular lineshape disturbance into “noise”. In the current paper we discuss in details the properties of time-resolved CS on the example of complex, reacting mixtures i.e. fermentation processes of milk and wheat in situ. In particular, the approaches to process the time pseudodimension are described, as the use of it to resolve components of a mixture or the reduction of mentioned time averaging. The advantages of the approach comparing to traditional sequential 1D experiment are also shown, as well as details of CS processing and spectral analysis.
Experimental Methods The experimental setup In the first example ethanol fermentation of wheat flour by yeasts (Saccharomyces Cerevisiae) was studied. There is a variety of different metabolic pathways that can contribute to the process, with the main substrates and products including: maltose, glucose, acetic acid, ethanol, glycerol. The fermentation can be performed in situ inside NMR magnet, as shown previously25 The sample was prepared by mixing 50 mg of wheat flour (type 480 from “Polskie Młyny”, www.polskiemlyny.pl) and 550 µl of solvent (250 µl of water, 50 µl of D2O, 250 µl of pH 7.0 phosphate buffer) in a standard 5 mm NMR tube. 30 mg of yeasts was added to the mixture. The measurement was started after 40 minutes from the addition of yeasts. The main reaction during the fermentation of wheat flour is (roughly): 2Hexose → 2glycerol + ethanol + acetic acid + 2CO2 + 2H2O where “hexose” is usually glucose or maltose. In our study we monitored glycerol, ethanol, acetic acid and glucose. In the second example fermentation of milk by kefir grains was studied. In monitored process of heterolactic fermentation lactic acid, ethanol and carbon dioxide are formed. The fermentation was performed in situ inside NMR magnet without any preprocessing of the sample (like centrifugation) usually required26. The main reaction during the fermentation of milk is (roughly):
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Sugars → lactic acid + ethanol + CO2 Where “sugars” can be either mono- or disaccharides (glucose and lactose). In our study we monitored ethanol. The sample was prepared by mixing 500 µl of 3.2 % of ultra high temperature processed commercially available cow milk (“Łaciate” from Mlekpol, www.mlekpol.com.pl) and 50 µl of D2O. 200µg of kefir grains (Vital Kefir from Agrovis, www.agrovis.eu) were added. The measurement started after 60 minutes from the addition of the kefir grains. The experiments were performed on an Agilent 600 MHz DDR2 NMR spectrometer equipped with a Penta probe. All of the measurements were performed at 298K. The serial 1D 1H NMR measurement was performed by acquiring a spectra at equal intervals of 30 minutes for the first sample and 10 minutes for the second. The 2D time-resolved NUS experiments were performed using conventional HSQC pulse sequence with multiplicity editing for the second sample. Pairs of adiabatic wideband uniform rate and smooth truncation (WURST) pulses (300ms, maximum γB/2π 13.8kHz) were used for broadband refocusing of 13C evolution. Hard pulses of 8 µs (1H) and 18.1 µs (13C) were used. Spectral widths were equal to 40221 Hz (13C) and 12755 (1H). Inter-scan delay was set to 1.3 s for the first sample and 1 s for the second sample. For the first sample, sampling was performed with 27 000 randomly chosen from the full grid of 200 points (repetitions were allowed) with 8 scans per point. For the second sample 18000 points were used with 2 scans per point.
Time-resolved compressed sensing The CS processing of individual subsets (“frames”) of the time-resolved NUS dataset follows the rules for single NUS dataset described elsewhere23. According to the theory27, if a subset contains n NUS data points taken from the Nyquist grid of N points, then the minimum number of points to be sampled is: ≈
(1)
and thus is related mostly to the number of significant (“nonzero”) spectral points K and so to the number of peaks. Importantly, in case of time-resolved NUS n can be optimized after acquisition. The spectrum is found by minimizing the function: ‖ ∙ − ‖ + ||
(2)
where iFT corresponds to inverse Fourier transform matrix, S is spectrum and s is a measured signal. Second term corre"
sponds to || = + ⋯ + !# and represents the sparsity constraint28. In the present study, the minimum was found using Iteratively Re-weighted Least Squares (IRLS) algorithm implemented in mddnmr 2.4 software29 with default parameters (10 iterations, p iteratively changed from 1 to 0). The subsets of 128 points were used, which corresponds to 50 minutes (first sample) and 10 minutes (second sample).
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Analytical Chemistry
The spectral analysis
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Traditionally, the analysis of an NMR spectrum starts with a peak-picking and integration of the peaks found. The peakpicking is often implemented as a search for a local maxima higher than certain threshold. The integration can be performed in many ways, for example by curve fitting (e.g. Lorentzian), or directly (e.g. with rectangle or Simpsons method)30. The approach, although effective for a single spectrum, does not seem feasible in a case of large stack of 2D spectra obtained from time-resolved NUS experiment. To allow easy analysis of changes of a particular peak, the peak has to be easily identified in a peak list. The list should contain the same number of elements for all spectra in a stack and a peak position in a list should not change. Thus, we propose the following automatic approach to obtain peak list from a timeresolved NUS spectrum:
The modern hardware, however, makes the latter obstacle less significant. Cryogenically cooled probes32, high-field magnets and signal enhancement by dynamic nuclear polarization33 allow to reach sufficient SNR in few sampling points for growing number of experimental cases. Thus, the need for the down-scaling of CS requirements is becoming important. Previously, it was shown, that application of non-convex compressed sensing based on lp-norm (0
