Unsupervised Analysis of Small Molecule Mixtures by Wavelet-Based Super-Resolved NMR

Abstract

Resolving small molecule mixtures by nuclear magnetic resonance (NMR) spectroscopy has been of great interest for a long time for its precision, reproducibility, and efficiency. However, spectral analyses for such mixtures are often highly challenging due to overlapping resonance lines and limited chemical shift windows. The existing experimental and theoretical methods to produce shift NMR spectra in dealing with the problem have limited applicability owing to sensitivity issues, inconsistency, and/or the requirement of prior knowledge. Recently, we resolved the problem by decoupling multiplet structures in NMR spectra by the wavelet packet transform (WPT) technique. In this work, we developed a scheme for deploying the method in generating highly resolved WPT NMR spectra and predicting the composition of the corresponding molecular mixtures from their 1H NMR spectra in an automated fashion. The four-step spectral analysis scheme consists of calculating the WPT spectrum, peak matching with a WPT shift NMR library, followed by two optimization steps in producing the predicted molecular composition of a mixture. The robustness of the method was tested on an augmented dataset of 1000 molecular mixtures, each containing 3 to 7 molecules. The method successfully predicted the constituent molecules with a median true positive rate of 1.0 against the varying compositions, while a median false positive rate of 0.04 was obtained. The approach can be scaled easily for much larger datasets.

A Simulation Independent Analysis of Single- and Multi-Component cw ESR Spectra

“…The capability of the wavelet transform in picking periodic hyperfine pattern from poorly resolved ESR spectra was highlighted previously [25]. In a series of recent publications [26][27][28], we have presented an improved version of the wavelet transform based spectral analysis, which can decouple different frequency components in an ESR or nuclear magnetic resonance (NMR) spectrum, enhancing the resolution and providing an opportunity to extract spectral information or parameters in a selective and objective manner. We have modified the Noise Elimination and Reduction via Denoising (NERD) method [25,29], which is based on the discrete wavelet transform (DWT) method, for separation of the hyperfine lines in cw ESR spectra and extraction of spectral parameters initially [26].…”

“…We have modified the Noise Elimination and Reduction via Denoising (NERD) method [25,29], which is based on the discrete wavelet transform (DWT) method, for separation of the hyperfine lines in cw ESR spectra and extraction of spectral parameters initially [26]. Later, in analyzing 1 H NMR spectra of molecular mixtures, which features highly overlapped resonance lines due to the presence of scalar coupling between intramolecular protons, we recognized that spectral decomposition by the wavelet packet transform (WPT) is superior to DWT in separating the central frequencies from the multiplet structures encompassing them [27,28]. Using the same concept, a cw ESR spectrum is decomposed into its different frequency components by WPT and at an optimum level of decomposition, a detail component in the wavelet domain is used in extracting the hyperfine and/or superhyperfine structure, if any.…”

Review on NMR as a tool to analyse natural products extract directly: Molecular structure elucidation and biological activity analysis

“…For example, pure shift NMR combined with wavelet packet transform (WPT) technique can offer super-resolved pure shift spectra and eliminate phase distortion. 55,56 Artificial intelligence combined with NMR technology is in the ascendant, such as MADByTE for natural products dereplication, 57 small molecule accurate recognition technology (SMART), 58,59 2D NMR barcoding and differential analysis technology, 60 and so forth. These can improve the accuracy of structural analysis and accelerate the utilisation efficiency of natural products, and they also deserve attention as promising NMR technologies to analyse natural products mixture directly.…”

“…However, data post‐processing and artificial intelligence technologies combined with NMR acquisitions can also contribute to cost‐effective natural products mixture analysis. For example, pure shift NMR combined with wavelet packet transform (WPT) technique can offer super‐resolved pure shift spectra and eliminate phase distortion 55,56 . Artificial intelligence combined with NMR technology is in the ascendant, such as MADByTE for natural products dereplication, 57 small molecule accurate recognition technology (SMART), 58,59 2D NMR barcoding and differential analysis technology, 60 and so forth.…”

Time-Frequency Analysis of Two-Dimensional Electron Spin Resonance Signals

“…Wavelet transforms are powerful methods for time-frequency analysis due to their flexible window length and applicability to multi-dimensional signals. The advantages of using wavelet-based spectral analysis in both ESR and nuclear magnetic resonance (NMR) spectroscopic studies in one-dimensional experiments have been established, − where one can reliably decouple different spectral components, including noise, in separating individual peaks. In this work, we present a 2D undecimated discrete wavelet transform , (UDWT)-based approach that can effectively identify and separate overlapping peaks in 2D ESR signals.…”