Denoising NMR time-domain signal by singular-value decomposition accelerated by graphics processing units

Stationary wavelet denoising of solid-state NMR spectra using multiple similar measurements

Accumulating several scans of free induction decays is always needed to improve the signal-to-noise ratio of NMR spectra, especially for the low gyromagnetic ratio solid-state NMR. In this study, we present a new denoising approach based on the correlations between multiple similar NMR spectra. Contrary to the simple averaging of multiple scans or denoising the final averaged spectrum, we propose a Wavelet-based Denoising technique for Multiple Similar scans(WDMS). Firstly, the stationary wavelet transform is applied to decompose every spectrum into approximation coefficients and detail coefficients. Then, the detail coefficients are multiplied by weights calculated based on Pearson's correlation coefficient and structural similarity index between approximation coefficients of different spectra. Finally, the average of these detailed components is used to denoise the spectra. The proposed method is carried on the assumption that noise between multiple spectra is uncorrelated while peak signal information is similar between different spectra, thus preserving the possibility of applying further processing to the data. As a demonstration, the standard wavelet denoise is applied to the WDMS-processed spectra, achieving a further increase in the S/N ratio. We confirm the reliability of the denoising approach based on multiple scans on 1D/2D solid-state MAS/static NMR spectra. In addition, we also show that this method can be used to deal with a single Car-Purcell-Meiboom-Gill (CPMG) echo train.

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.

Solid-state NMR methods for the characterization of bioconjugations and protein-material interactions

Protein solid-state NMR has evolved dramatically over the last two decades, with the development of new hardware and sample preparation methodologies. This technique is now ripe for complex applications, among which one can count bioconjugation, protein chemistry and functional biomaterials. In this review, we provide our account on this aspect of protein solid-state NMR.

A denoising method for multidimensional magnetic resonance spectroscopy and imaging based on compressed sensing

Both in spectroscopy and imaging, t₁-noise arising from instabilities such as temperature alterations, field-related frequency drifts, electronic and sample-spinning instabilities, or motions in in vivo experiments, affects many 2D Magnetic Resonance experiments. This work introduces a post-processing method that aims to attenuate t₁-noise, by suitably averaging multiple signals/representations that have been reconstructed from the sampled data. The ensuing Compressed Sensing Multiplicative (CoSeM) denoising starts from a fully sampled 2D MR data set, discards random indirect-domain points, and makes up for these missing, masked data, by a compressed sensing reconstruction of the now incompletely sampled 2D data set. This procedure is repeated for multiple renditions of the masked data -some of which will have been more strongly affected by t₁-noise than others. This leads to a large set of 2D NMR spectra/images compatible with the collected data; CoSeM chooses out of these those renditions that reduce the noise according to a suitable criterion, and then sums up their spectra/images leading to a reduction in t₁-noise. The performance of the method was assessed in synthetic data, as well as in numerous different experiments: 2D solid and solution state NMR, 2D localized MRS of live brains, and 2D abdominal MRI. Throughout all these data, CoSeM processing evidenced 2-3 fold increases in SNR, without introducing biases, false peaks, or spectral/image blurring. CoSeM also retains a quantitative linearity in the information -allowing, for instance, reliable T₁ inversion-recovery MRI mapping experiments.

In-Cell Structural Biology by NMR: The Benefits of the Atomic Scale

In-cell structural biology aims at extracting structural information about proteins or nucleic acids in their native, cellular environment. This emerging field holds great promise and is already providing new facts and outlooks of interest at both fundamental and applied levels. NMR spectroscopy has important contributions on this stage: It brings information on a broad variety of nuclei at the atomic scale, which ensures its great versatility and uniqueness. Here, we detail the methods, the fundamental knowledge, and the applications in biomedical engineering related to in-cell structural biology by NMR. We finally propose a brief overview of the main other techniques in the field (EPR, smFRET, cryo-ET, etc.) to draw some advisable developments for in-cell NMR. In the era of large-scale screenings and deep learning, both accurate and qualitative experimental evidence are as essential as ever to understand the interior life of cells. In-cell structural biology by NMR spectroscopy can generate such a knowledge, and it does so at the atomic scale. This review is meant to deliver comprehensive but accessible information, with advanced technical details and reflections on the methods, the nature of the results, and the future of the field.

The exposome paradigm to predict environmental health in terms of systemic homeostasis and resource balance based on NMR data science

The environment, from microbial ecosystems to recycled resources, fluctuates dynamically due to many physical, chemical and biological factors, the profile of which reflects changes in overall state, such as environmental illness caused by a collapse of homeostasis. To evaluate and predict environmental health in terms of systemic homeostasis and resource balance, a comprehensive understanding of these factors requires an approach based on the "exposome paradigm", namely the totality of exposure to all substances. Furthermore, in considering sustainable development to meet global population growth, it is important to gain an understanding of both the circulation of biological resources and waste recycling in human society. From this perspective, natural environment, agriculture, aquaculture, wastewater treatment in industry, biomass degradation and biodegradable materials design are at the forefront of current research. In this respect, nuclear magnetic resonance (NMR) offers tremendous advantages in the analysis of samples of molecular complexity, such as crude bio-extracts, intact cells and tissues, fibres, foods, feeds, fertilizers and environmental samples. Here we outline examples to promote an understanding of recent applications of solution-state, solid-state, time-domain NMR and magnetic resonance imaging (MRI) to the complex evaluation of organisms, materials and the environment. We also describe useful databases and informatics tools, as well as machine learning techniques for NMR analysis, demonstrating that NMR data science can be used to evaluate the exposome in both the natural environment and human society towards a sustainable future.

Multivariate Curve Resolution for 2D Solid-State NMR spectra

We present a processing method, based on the multivariate curve resolution approach (MCR), to denoise 2D solid-state NMR spectra, yielding a substantial S/N ratio increase while preserving the lineshapes and relative signal intensities. These spectral features are particularly important in the quantification of silicon species, where sensitivity is limited by the low natural abundance of the ²⁹Si nuclei and by the dilution of the intrinsic protons of silica, but can be of interest also when dealing with other intermediate-to-low receptivity nuclei. This method also offers the possibility of coprocessing multiple 2D spectra that have the signals at the same frequencies but with different intensities (e.g.: as a result of a variation in the mixing time). The processing can be carried out on the time-domain data, thus preserving the possibility of applying further processing to the data. As a demonstration, we have applied Cadzow denoising on the MCR-processed FIDs, achieving a further increase in the S/N ratio and more effective denoising also on the transients at longer indirect evolution times. We have applied the combined denoising on a set of experimental data from a lysozyme-silica composite.

Optimized reconstructions of compressively sampled two-dimensional infrared spectra

Compressive sampling has the potential to dramatically accelerate the pace of data collection in two-dimensional infrared (2D IR) spectroscopy. We have previously introduced the Generic Iteratively Reweighted Annihilating Filter (GIRAF) reconstruction algorithm to solve the reconstruction in 2D IR compressive sampling. Here, we report a thorough assessment of this method and comparison to our earlier efforts using the Total Variation (TV) algorithm. We show that the GIRAF algorithm has some distinct advantages over TV. Although it is no better or worse in terms of ameliorating the impacts of compressive sampling on the measured 2D IR line shape, we find that the nature of those effects is different for GIRAF than they were for TV. In addition to assessing the impacts on the line shape of a single oscillator, we also test the ability of the algorithm to reconstruct spectra that have transitions from more than one oscillator, such as the coupled carbonyl oscillators in rhodium dicarbonyl. Finally, and perhaps most importantly, we show that the GIRAF algorithm has a distinct denoising effect on the signal-to-noise ratio (SNR) of the 2D IR spectra that can increase the SNR by as much as 4× without any additional signal averaging and collecting fewer data points, which should further enhance the acceleration of data collection that can be achieved using compressive sampling and enable even more challenging experimental measurements.

Interactions of Plutonium with Pseudomonas sp. Strain EPS-1W and Its Extracellular Polymeric Substances

Safe and effective nuclear waste disposal, as well as accidental radionuclide releases, necessitates our understanding of the fate of radionuclides in the environment, including their interaction with microorganisms. We examined the sorption of Pu(IV) and Pu(V) to Pseudomonas sp. strain EPS-1W, an aerobic bacterium isolated from plutonium (Pu)-contaminated groundwater collected in the United States at the Nevada National Security Site (NNSS) in Nevada. We compared Pu sorption to cells with and without bound extracellular polymeric substances (EPS). Wild-type cells with intact EPS sorbed Pu(V) more effectively than cells with EPS removed. In contrast, cells with and without EPS showed the same sorption affinity for Pu(IV). In vitro experiments with extracted EPS revealed rapid reduction of Pu(V) to Pu(IV). Transmission electron microscopy indicated that 2- to 3-nm nanocrystalline Pu(IV)O₂ formed on cells equilibrated with high concentrations of Pu(IV) but not Pu(V). Thus, EPS, while facilitating Pu(V) reduction, inhibit the formation of nanocrystalline Pu(IV) precipitates.

IMPORTANCE

Our results indicate that EPS are an effective reductant for Pu(V) and sorbent for Pu(IV) and may impact Pu redox cycling and mobility in the environment. Additionally, the resulting Pu morphology associated with EPS will depend on the concentration and initial Pu oxidation state. While our results are not directly applicable to the Pu transport situation at the NNSS, the results suggest that, in general, stationary microorganisms and biofilms will tend to limit the migration of Pu and provide an important Pu retardation mechanism in the environment. In a broader sense, our results, along with a growing body of literature, highlight the important role of microorganisms as producers of redox-active organic ligands and therefore as modulators of radionuclide redox transformations and complexation in the subsurface.

Comprehensive multiphase NMR applied to a living organism

Comprehensive multiphase (CMP) NMR is a novel technology that integrates all the hardware from solution-, gel- and solid-state into a single NMR probe, permitting all phases to be studied in intact samples. Here comprehensive multiphase (CMP) NMR is used to study all components in a living organism for the first time. This work describes 4 new scientific accomplishments summarized as: (1) CMP-NMR is applied to a living animal, (2) an effective method to deliver oxygen to the organisms is described which permits longer studies essential for in-depth NMR analysis in general, (3) a range of spectral editing approaches are applied to fully differentiate the various phases solutions (metabolites) through to solids (shell) (4) 13C isotopic labelling and multidimensional NMR are combined to provide detailed assignment of metabolites and structural components in vivo. While not explicitly studied here the multiphase capabilities of the technique offer future possibilities to study kinetic transfer between phases (e.g. nutrient assimilation, contaminant sequestration), molecular binding at interfaces (e.g. drug or contaminant binding) and bonding across and between phases (e.g. muscle to bone) in vivo. Future work will need to focus on decreasing the spinning speed to reduce organism stress during analysis.

Methods for analysis of size-exclusion chromatography-small-angle X-ray scattering and reconstruction of protein scattering

Size-exclusion chromatography in line with small-angle X-ray scattering (SEC-SAXS) has emerged as an important method for investigation of heterogeneous and self-associating systems, but presents specific challenges for data processing including buffer subtraction and analysis of overlapping peaks. This paper presents novel methods based on singular value decomposition (SVD) and Guinier-optimized linear combination (LC) to facilitate analysis of SEC-SAXS data sets and high-quality reconstruction of protein scattering directly from peak regions. It is shown that Guinier-optimized buffer subtraction can reduce common subtraction artifacts and that Guinier-optimized linear combination of significant SVD basis components improves signal-to-noise and allows reconstruction of protein scattering, even in the absence of matching buffer regions. In test cases with conventional SAXS data sets for cytochrome c and SEC-SAXS data sets for the small GTPase Arf6 and the Arf GTPase exchange factors Grp1 and cytohesin-1, SVD-LC consistently provided higher quality reconstruction of protein scattering than either direct or Guinier-optimized buffer subtraction. These methods have been implemented in the context of a Python-extensible Mac OS X application known as Data Evaluation and Likelihood Analysis (DELA), which provides convenient tools for data-set selection, beam intensity normalization, SVD, and other relevant processing and analytical procedures, as well as automated Python scripts for common SAXS analyses and Guinier-optimized reconstruction of protein scattering.