Extraction of Weak Spectroscopic Signals with High Fidelity: Examples from ESR

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

Two-dimensional electron spin resonance (2D ESR) spectroscopy is a unique experimental technique for probing protein structure and dynamics, including processes that occur at the microsecond time scale. While it provides significant resolution enhancement over the one-dimensional experimental setup, spectral broadening and noise make extraction of spectral information highly challenging. Traditionally, two-dimensional Fourier transform (2D FT) is applied for the analysis of 2D ESR signals, although its efficiency is limited to stationary signals. In addition, it often fails to resolve overlapping peaks in 2D ESR. In this work, we propose a time-frequency analysis of 2D time-domain signals, which identifies all frequency peaks by decoupling a signal into its distinct constituent components via projection on the time-frequency plane. The method utilizes 2D undecimated discrete wavelet transform (2D UDWT) as an intermediate step in the analysis, followed by signal reconstruction and 2D FT. We have applied the method to a simulated 2D double quantum coherence (DQC) signal for validation and a set of experimental 2D ESR signals, demonstrating its efficiency in resolving overlapping peaks in the frequency domain, while displaying frequency evolution with time in case of non-stationary data.

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

The accurate analysis of continuous-wave electron spin resonance (cw ESR) spectra of biological or organic free-radicals and paramagnetic metal complexes is key to understanding their structure-function relationships and electrochemical properties. The current methods of analysis based on simulations often fail to extract the spectral information accurately. In addition, such analyses are highly sensitive to spectral resolution and artifacts, users' defined input parameters and spectral complexity. We introduce a simulation-independent spectral analysis approach that enables broader application of ESR. We use a wavelet packet transform-based method for extracting g values and hyperfine (A) constants directly from cw ESR spectra. We show that our method overcomes the challenges associated with simulation-based methods for analyzing poorly/partially resolved and unresolved spectra, which is common in most cases. The accuracy and consistency of the method are demonstrated on a series of experimental spectra of organic radicals and copper-nitrogen complexes. We showed that for a two-component system, the method identifies their individual spectral features even at a relative concentration of 5% for the minor component.

DESPERATE: A Python library for processing and denoising NMR spectra

NMR spectroscopy is an inherently insensitive technique with respect to the amount of observable signal. A common element in all NMR spectra is random thermal noise that is often characterized by a signal-to-noise ratio (SNR). SNR can be generically improved experimentally with repetitive signal averaging or during post-processing with apodization; the former of which often results in long experimental times and the latter results in the loss of spectral resolution. Denoising techniques can instead be used during post-processing to enhance SNR without compromising resolution. The most common approach relies on the singular-value decomposition (SVD) to discard noisy components of NMR data. SVD-based approaches work well, such as Cadzow and PCA, but are computationally expensive when used for large datasets that are often encountered in NMR (e.g., Carr-Purcell/Meiboom-Gill and nD datasets). Herein, we describe the implementation of a new wavelet transform (WT) routine for the fast and robust denoising of 1D and 2D NMR spectra. Several simulated and experimental datasets are denoised with both SVD-based Cadzow or PCA and WT's, and the resulting SNR enhancements and spectral uniformity are compared. WT denoising offers similar and improved denoising compared with SVD and operates faster by several orders-of-magnitude in some cases. All denoising and processing routines used in this work are included in a free and open-source Python library called DESPERATE.

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

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.

Hyperfine Decoupling of ESR Spectra Using Wavelet Transform

The objective of spectral analysis is to resolve and extract relevant features from experimental data in an optimal fashion. In continuous-wave (cw) electron spin resonance (ESR) spectroscopy, both g values of a paramagnetic center and hyperfine splitting (A) caused by its interaction with neighboring magnetic nuclei in a molecule provide important structural and electronic information. However, in the presence of g- and/or A-anisotropy and/or large number of resonance lines, spectral analysis becomes highly challenging. Either high-resolution experimental techniques are employed to resolve the spectra in those cases or a range of suitable ESR frequencies are used in combination with simulations to identify the corresponding g and A values. In this work, we present a wavelet transform technique in resolving both simulated and experimental cw-ESR spectra by separating the hyperfine and super-hyperfine components. We exploit the multiresolution property of wavelet transforms that allow the separation of distinct features of a spectrum based on simultaneous analysis of spectrum and its varying frequency. We retain the wavelet components that stored the hyperfine and/or super-hyperfine features, while eliminating the wavelet components representing the remaining spectrum. We tested the method on simulated cases of metal–ligand adducts at L-, S-, and X-band frequencies, and showed that extracted g values, hyperfine and super-hyperfine coupling constants from simulated spectra, were in excellent agreement with the values of those parameters used in the simulations. For the experimental case of a copper(II) complex with distorted octahedral geometry, the method was able to extract g and hyperfine coupling constant values, and revealed features that were buried in the overlapped spectra.