Analysis of Small-Molecule Mixtures by Super-Resolved ¹H NMR Spectroscopy

Abstract

Analysis of small molecules is essential to metabolomics, natural products, drug discovery, food technology, and many other areas of interest. Current barriers preclude from identifying the constituent molecules in a mixture as overlapping clusters of NMR lines pose a major challenge in resolving signature frequencies for individual molecules. While homonuclear decoupling techniques produce much simplified pure shift spectra, they often affect sensitivity. Conversion of typical NMR spectra to pure shift spectra by signal processing without a priori knowledge about the coupling patterns is essential for accurate analysis. We developed a super-resolved wavelet packet transform based ¹H NMR spectroscopy that can be used in high-throughput studies to reliably decouple individual constituents of small molecule mixtures. We demonstrate the efficacy of the method on the model mixtures of saccharides and amino acids in the presence of significant noise.

Graphical Abstract

INTRODUCTION

Analysis of small molecules across a wide range of studies of metabolites, organic and natural products, food, potential drug molecules rely heavily on nuclear magnetic resonance (NMR) spectroscopy, along with mass spectrometry (MS) and liquid chromatography (LC).^1–9 Out of the three methods, NMR is ideal for identification of novel molecules and large-scale studies, given the ease of sample preparation, its non-destructive nature, access to instruments and high reproducibility.¹⁰ However, ¹H NMR spectroscopy, which is the most widely used version, suffers from limited resolution in analyzing small-molecule mixtures.^11,12 In recent years, sensitivity of NMR has been improved greatly,^13–15 but resolution enhancement efforts have faced an immovable barrier due to the presence of overlapping multiplets, originating from the relatively small chemical shift windows and scalar couplings between protons. While multidimensional NMR can enhance resolution, these are often not feasible because of the long signal acquisition time associated with those. Collapsing the multiplets in a typical ¹H NMR spectrum into singlets produces a pure shift spectrum,^16,17 which can greatly improve resolution for analysis of small molecule mixtures. Homonuclear decoupled ¹H NMR yields pure shift spectra,^16,18–21 but the resolution increment in those experiments often comes at the price of reduced sensitivity and spectral artifacts.^16,22 However, deconvolution of NMR spectra to shift spectra, which includes the maximum entropy method, can only be applied successfully when the scalar coupling patterns and the coupling constants are known.^23,24 Many other sampling, spectral editing, and fingerprint matching techniques have been developed for both 1D and 2D NMR spectroscopic analysis,^25–29 but those have either limited applicability or limited reliability, especially for highly complex or novel molecular mixtures. In that regard, NMR shift spectroscopy provides more control to the users in spectral interpretation and error analysis. Therefore, our objective was to propose a signal processing technique that can be applied to any ¹H NMR spectrum of a mixture of small molecules without a priori knowledge and convert it to a shift spectrum for accurate identification of the constituting molecules.

Magnetic resonance spectra are made of multiple components corresponding to different types of interactions among nuclear and/or electronic spins. A multilevel filtration technique is required to separate the components by their frequency and timestamps. Wavelet transform is such a technique that decomposes a spectrum into a pair of approximation and detail components, which corresponds to the low- and high-frequency spectral components, respectively. In converting NMR spectra to shift spectra, we used successive wavelet decomposition of the original spectra to produce an approximation component which provides the overall envelope encompassing a multiplet, essentially converting it to a singlet. Previously, we applied the wavelet transform based algorithm³⁰ to continuous wave electron spin resonance (cw-ESR) spectra, in order to enhance the resolution and extract hidden features.³¹ Its applications in removing spectral noise^30,32–34 and isolating weak signal components in ESR³⁵ have been extremely successful.

In the discrete form of wavelet transform (DWT), the approximation component from a decomposition level is passed through to the next level of decomposition, providing a coarse filtering of the original signal into sub-bands of unequal frequency ranges. In wavelet packet transform (WPT), both the approximation and detail components are decomposed at each level, resulting in a much finer filtering over 2^K equal-width sub-bands at a decomposition level of K. That has been our motivation to use WPT for conversion of NMR to shift spectra without any loss of information. In this regard, we should note that detail components extract both high-frequency spectral features as well as noise. That is why wavelet transform based conversion of NMR to shift spectra is practically insensitive to noise.

THEORETICAL METHODS

A high level summary of the process of generating shift spectra from NMR using WPT is shown in Figure 1 using glutathione ¹H NMR as an example. In the first step, the input NMR spectrum was decomposed by WPT, producing an approximation component that is virtually the original spectrum, while most of the spectral noise showed up in the detail component. The decomposition was continued until all multiplets in the spectrum were converted to singlets in the resultant approximation component (A^K). For this particular example, K was equal to 7. The second step in the analysis poses two sets of challenges: (i) identifying artifacts and (ii) locating peak positions. We figured that the artifacts can be separated from actual peaks by comparing the final approximation component to the original spectrum as well as the approximation components from the previous decomposition levels. In the second step of Figure 1, the relevant regions are highlighted (light purple), while peaks showing up outside those regions were identified as artifacts and those are highlighted in yellow circles. The peaks in the relevant regions are pointed out by downward triangles (blue). Consequently the stick spectrum is produced combining the peak positions and heights. In this work, we selected the peaks by visual inspection, however one can develop an automated method based on well-justified criteria.³⁶ The details of the WPT theory is provided in the Supporting Information.

Figure 1.

Conversion of ¹H NMR spectra to WPT shift spectra. Glutathione ¹H NMR recorded at 500 MHz in H₂O is shown in the left. In the first step, all multiplets in the spectrum are collapsed to singlets in the approximation component (blue boxed) at WPT decomposition level K. The peaks are separated from artifacts (yellow circles) of WPT in the second step. The peak positions (blue colored triangles) and heights are used to produce the stick spectrum. The maximum intensity of the original NMR spectrum was ~1, and the maximum intensities of each of the components are printed next to the spectra in blue for comparison.

RESULTS AND DISCUSSION

Model Data Preparation.

Quantitative analysis of carbohydrates is an essential step in food and pharmaceutical industries,^37–41 while identification of amino acids in biological samples is crucial in probing various disease pathophysiology.^42–46 We analyzed two model mixtures of (I) saccharides and (II) amino acids in this work. An equal mixture of cellobiose, fructose and sucrose was used in (I). In our second model (II), we used a mixture of six amino acids, namely, glutamine, glycine, isoleucine, leucine, threonine, and valine. Two different varieties of (II) were prepared by mixing the individual amino acid spectra in different proportions.

All the NMR spectra in this work were obtained from the Human Metabolome Database (HMDB).⁴⁷ Impurity peaks at chemical shifts values smaller than 2.4 ppm in the cellobiose spectrum were removed. Normalization of individual spectra was carried out by dividing each data set by the sum of the NMR intensities. We concatenated individual components’ spectra to create the NMR spectra for the model mixtures. The process of concatenation increased the number of spectral data points compared to the individual spectra or artificially enhanced spectral resolution. In order to resolve the issue, the resultant spectral domain size was reduced to the mean length of the individual spectra by binning of the NMR frequencies into discrete intervals. For mixture (I), the noisy spectra was obtained by adding 2.5% random noise to the noise-free version, and 10% random noise was added in case of mixture (II).

Spectral Analysis.

In analyzing a model mixture of saccharides (I), WPT shift spectra for each of the components, cellobiose, fructose, and sucrose, were obtained first from the corresponding experimental ¹H NMR spectra, recorded at 500 MHz. Cellobiose is a disaccharide and is an excellent test case given that its NMR spectrum is highly overlapped in the region of 3.2–4.0 ppm. The WPT spectra were obtained from the corresponding ¹H NMR spectra by using Daubechies (Db9) wavelet at the decomposition levels of 7 (cellobiose), 7 (fructose), and 8 (sucrose), respectively. For all the three molecules, the ¹H NMR multiplet midpoints and the WPT shift peaks are given in Table S1. It can be seen that each of the peaks were replicated in the WPT shift spectra except for the peak at 3.89 ppm for sucrose. The NMR spectrum of sucrose has two double doublets centered at 3.87 and 3.89 ppm. The WPT analysis in this case treated the two closely spaced clusters as a single multiplet and yielded a peak at 3.87 ppm. The original NMR and the WPT shift spectra for the three saccharides are shown in Figure 2. Next, the individual NMR spectra were mixed in an appropriate fashion to create the NMR spectra for a mixture of the saccharides. Figure 3 shows the conversion and analysis of the mixed NMR spectra. The key takeaways were the replication of the signature NMR peaks for all three components in the highly overlapped region of 3.5 ppm < chemical shift ≤ 4.2 ppm and the exact match between the WPT shift spectra for the noise-free (A) and noisy (B) cases. Comparing with the original spectra, we inferred that the peak at 3.81 ppm was resulted from unresolved peaks centered around 3.81 ppm (fructose), 3.82 ppm (sucrose), and 3.83 ppm (cellobiose). A separate analysis of the region between 3.78 and 3.94 ppm at a wavelet decomposition level of 7 resolved the cellobiose peak at 3.83 ppm and previously unresolved peaks at 3.87 ppm (sucrose) and 3.90 ppm (fructose).

Figure 2.

Conversions of ¹H NMR spectra of cellobiose, fructose, and sucrose to WPT shift spectra. The WPT shift spectra were produced from the approximation components at levels 7 (A), 7 (B), and 8 (C) of wavelet decomposition of the respective NMR spectra by using Db9 wavelet.

Figure 3.

Analysis of model mixtures of cellobiose, fructose, and sucrose using Db9 wavelet at a wavelet decomposition level of 8 are illustrated for the noise-free (A) and noisy (B) data sets. The resolved peaks corresponding to cellobiose (light blue), fructose (violet), and sucrose (navy) are color-coded, while the line at 3.81 ppm is marked unresolved (gray). Analysis of the spectral slice between 3.78 and 3.94 ppm at a decomposition level of 7 resolved the peaks at 3.83 ppm (cellobiose), 3.87 ppm (sucrose) and 3.90 ppm (fructose).

Two sets of NMR spectra for model mixture (II) were produced by mixing the spectra of glutamine, glycine, isoleucine, leucine, threonine, and valine at equal (II.A) and varying proportions (II.B), given in Figure 4. The noise level was set to 10% compared to the highest NMR peak intensity in both the cases. The area under an NMR peak is proportional to the number of associated protons and in a mixed spectra, separated constituent peaks can be used in quantification of the composition of the mixture. Given that the area under a peak is proportional to both its height and width, we compared the WPT shift spectra of (II.A) and (II.B) for correlation with the compositions of the mixtures. Glancing through the two WPT shift spectra shown in Figure 4A,B, we can notice significant changes in the peak intensities for glycine, threonine and valine, which correlates to the change in the compositions of the two mixtures. By comparing the peak heights in the second mixture with the first, we calculated the amount of those three amino acids to be 13% (absolute error = +3), 24% (−6), and 14% (+4), respectively. For glutamine, isoleucine and leucine, the calculated concentrations from WPT spectra were 18% (−2), 17% (+2), and 15% (0). While the calculated relative concentrations were significantly off from the actual values given that peak heights were used instead of peak areas, the changes in peak intensities in the two model mixtures correlated with the changes in their compositions. This property of WPT shift spectra can be useful in semiquantitative analysis of small molecule mixtures and probing relative changes in their compositions. WPT shift peaks for the individual amino acids, obtained at a wavelet decomposition level of 7, are tabulated in Table S2.

Figure 4.

Analysis of the NMR spectra of two different compositions of model mixture (II) of six amino acids at 10% noise are illustrated. Conversion of the NMR spectra using Db9 wavelet at a decomposition level of 8 are shown (A, B). The peaks corresponding to glutamine (red), glycine (blue), isoleucine (green), leucine (orange), threonine (cyan), and valine (magenta) were resolved in both the WPT shift spectra. The compositions of the mixtures and the resolved lines in the WPT shift spectra are tabulated on the left.

CONCLUSIONS

In summary, we showed that wavelet transform or more specifically wavelet packet transform produces highly resolved shift spectra from ¹H NMR spectra of small molecule mixtures in a reliable fashion. Our method extracted the signature NMR lines for the constituent molecules in two model mixtures of saccharides and amino acids, even in the presence of 10% noise. Additionally, correlation between the composition of a mixture and its WPT shift peak intensities revealed the quantitative nature of the method. It should be noted that WPT analysis resolves NMR spectra fully where the multiplets are not indistinguishably overlapped.

Data Availability Statement

Data used in this work have been stored in the public github repository (https://github.com/Signal-Science-Lab), and the software is available at https://denoising.cornell.edu.