CRAFT (complete reduction to amplitude frequency table)--robust and time-efficient Bayesian approach for quantitative mixture analysis by NMR

New analytical methods focusing on polar metabolite analysis in mass spectrometry and NMR-based metabolomics

Following in the footsteps of genomics and proteomics, metabolomics has revolutionised the way we investigate and understand biological systems. Rapid development in the last 25 years has been driven largely by technical innovations in mass spectrometry and nuclear magnetic resonance spectroscopy. However, despite the modest size of metabolomes relative to proteomes and genomes, methodological capabilities for robust, comprehensive metabolite analysis remain a major challenge. Therefore, development of new methods and techniques remains vital for progress in the field. Here, we review developments in LC-MS, GC-MS and NMR methods in the last few years that have enhanced quantitative and comprehensive metabolome coverage, highlighting the techniques involved, their technical capabilities, relative performance, and potential impact.

Quantification of Biopharmaceutically Relevant Nonionic Surfactant Excipients Using Benchtop qNMR

Nonionic surfactant excipients (NISEs) are commonly added to biologics formulations to mitigate the effects of stress incurred by the active biotherapeutic during manufacturing, transport, and storage. During manufacturing, NISEs are added by dilution of a stock solution directly into a protein formulation, and their accurate addition is critical in maintaining the quality and integrity of the drug product and thus ensuring patient safety. This is especially true for the common NISEs, polysorbates 20 and 80 (PS20 and PS80, respectively) and poloxamer 188 (P188). With the increasing diversity of biologic modalities within modern pharmaceutical pipelines, there is thus a critical need to develop and deploy convenient and user-accessible analytical techniques that can rapidly and reliably quantify these NISEs under biopharmaceutically relevant conditions. We thus pursued 60 MHz benchtop quantitative NMR (qNMR) as a nondestructive and user-friendly analytical technique for the quantification of PS20, PS80, and P188 under such conditions. We demonstrated the ability of benchtop qNMR (1) to quantify simulated PS20, PS80, and P188 stock solutions representative of those used during the drug substance (DS) formulation step in biomanufacturing and (2) to quantify these NISEs at and below their target concentrations (≤0.025% w/v) directly in biologics formulations containing histidine, sucrose, and one of three biotherapeutic modalities (monoclonal antibody, antibody-drug conjugate, and Fc-fusion protein). Our results demonstrate that benchtop qNMR offers a fit-for-purpose, reliable, user-friendly, and green analytical route by which NISE of interest to the biopharmaceutical industry may be readily and reliably quantified. We conclude that benchtop qNMR has the potential to be applied to other excipient formulation components in the presence of various biological modalities as well as the potential for routine integration within analytical and QC laboratories across pharmaceutical development and manufacturing sites.

Reaction monitoring via benchtop nuclear magnetic resonance spectroscopy: A practical comparison of on-line stopped-flow and continuous-flow sampling methods

The ability for nuclear magnetic resonance (NMR) spectroscopy to provide quantitative, structurally rich information makes this spectroscopic technique an attractive reaction monitoring tool. The practicality of NMR for this type of analysis has only increased in the recent years with the influx of commercially available benchtop NMR instruments and compatible flow systems. In this study, we aim to compare 19F NMR reaction profiles acquired under both on-line continuous-flow and stopped-flow sampling methods, with modern benchtop NMR instrumentation, and two reaction systems: a homogeneous imination reaction and a biphasic activation of a carboxylic acid to acyl fluoride. Reaction trends with higher data density can be acquired with on-line continuous-flow analyses, and this work highlights that representative reaction trends can be acquired without any correction when monitoring resonances with a shorter spin-lattice relaxation time (T1), and with the used flow conditions. On-line stopped-flow analyses resulted in representative reaction trends in all cases, including the monitoring of resonances with a long T1, without the need of any correction factors. The benefit of easier data analysis, however, comes with the cost of time, as the fresh reaction solution must be flowed into the NMR system, halted, and time must be provided for spins to become polarized in the instrument's external magnetic field prior to spectral measurement. Results for one of the reactions were additionally compared with the use of a high-field NMR.

SAND: Automated Time-Domain Modeling of NMR Spectra Applied to Metabolite Quantification

Developments in untargeted nuclear magnetic resonance (NMR) metabolomics enable the profiling of thousands of biological samples. The exploitation of this rich source of information requires a detailed quantification of spectral features. However, the development of a consistent and automatic workflow has been challenging because of extensive signal overlap. To address this challenge, we introduce the software Spectral Automated NMR Decomposition (SAND). SAND follows on from the previous success of time-domain modeling and automatically quantifies entire spectra without manual interaction. The SAND approach uses hybrid optimization with Markov chain Monte Carlo methods, employing subsampling in both time and frequency domains. In particular, SAND randomly divides the time-domain data into training and validation sets to help avoid overfitting. We demonstrate the accuracy of SAND, which provides a correlation of ∼0.9 with ground truth on cases including highly overlapped simulated data sets, a two-compound mixture, and a urine sample spiked with different amounts of a four-compound mixture. We further demonstrate an automated annotation using correlation networks derived from SAND decomposed peaks, and on average, 74% of peaks for each compound can be recovered in single clusters. SAND is available in NMRbox, the cloud computing environment for NMR software hosted by the Network for Advanced NMR (NAN). Since the SAND method uses time-domain subsampling (i.e., random subset of time-domain points), it has the potential to be extended to a higher dimensionality and nonuniformly sampled data.

Magnetstein: An Open-Source Tool for Quantitative NMR Mixture Analysis Robust to Low Resolution, Distorted Lineshapes, and Peak Shifts

1H NMR spectroscopy is a powerful tool for analyzing mixtures including determining the concentrations of individual components. When signals from multiple compounds overlap, this task requires computational solutions. They are typically based on peak-picking and the comparison of obtained peak lists with libraries of individual components. This can fail if peaks are not sufficiently resolved or when peak positions differ between the library and the mixture. In this paper, we present Magnetstein, a quantification algorithm rooted in the optimal transport theory that makes it robust to unexpected frequency shifts and overlapping signals. Thanks to this, Magnetstein can quantitatively analyze difficult spectra with the estimation trueness an order of magnitude higher than that of commercial tools. Furthermore, the method is easier to use than other approaches, having only two parameters with default values applicable to a broad range of experiments and requiring little to no preprocessing of the spectra.

Rapid and automated lipid profiling by nuclear magnetic resonance spectroscopy using neural networks

Nuclear magnetic resonance (NMR) spectroscopy is a powerful tool for quantitative metabolomics; however, quantification of metabolites from NMR data is often a slow and tedious process requiring user input and expertise. In this study, we propose a neural network approach for rapid, automated lipid identification and quantification from NMR data. Multilayered perceptron (MLP) networks were developed with NMR spectra as the input and lipid concentrations as output. Three large synthetic datasets were generated, each with 55,000 spectra from an original 30 scans of reference standards, by using linear combinations of standards and simulating experimental-like modifications (line broadening, noise, peak shifts, baseline shifts) and common interference signals (water, tetramethylsilane, extraction solvent), and were used to train MLPs for robust prediction of lipid concentrations. The performances of MLPS were first validated on various synthetic datasets to assess the effect of incorporating different modifications on their accuracy. The MLPs were then evaluated on experimentally acquired data from complex lipid mixtures. The MLP-derived lipid concentrations showed high correlations and slopes close to unity for most of the quantified lipid metabolites in experimental mixtures compared with ground-truth concentrations. The most accurate, robust MLP was used to profile lipids in lipophilic hepatic extracts from a rat metabolomics study. The MLP lipid results analyzed by two-way ANOVA for dietary and sex differences were similar to those obtained with a conventional NMR quantification method. In conclusion, this study demonstrates the potential and feasibility of a neural network approach for improving speed and automation in NMR lipid profiling and this approach can be easily tailored to other quantitative, targeted spectroscopic analyses in academia or industry.

Deconvolution of 1D NMR spectra: A deep learning-based approach

The analysis of nuclear magnetic resonance (NMR) spectra to detect peaks and characterize their parameters, often referred to as deconvolution, is a crucial step in the quantification, elucidation, and verification of the structure of molecular systems. However, deconvolution of 1D NMR spectra is a challenge for both experts and machines. We propose a robust, expert-level quality deep learning-based deconvolution algorithm for 1D experimental NMR spectra. The algorithm is based on a neural network trained on synthetic spectra. Our customized pre-processing and labeling of the synthetic spectra enable the estimation of critical peak parameters. Furthermore, the neural network model transfers well to the experimental spectra and demonstrates low fitting errors and sparse peak lists in challenging scenarios such as crowded, high dynamic range, shoulder peak regions as well as broad peaks. We demonstrate in challenging spectra that the proposed algorithm is superior to expert results.

Quantitative nuclear magnetic resonance of chloride by an accurate internal standard approach

Chloride is the most common counterion used to improve aqueous solubility and enhance stability of small molecule active pharmaceutical ingredients. While several analytical techniques, such as titration, HPLC with charged aerosol detection, and ion chromatography, are currently utilized to assay the level of chloride, they have notable limitations, and these instruments may not be readily available. Here, we present a generally applicable ³⁵ Cl solution NMR method to assay the level of chloride in pharmaceutical compounds. The method uses KClO₄ as an internal standard for improved accuracy in comparison with external standard methods, and it was found to be robust, linear over three orders of magnitude, precise (<3% RSD), and accurate (<0.5% absolute error).

Metabolomics and NMR

The purpose of this manuscript will be to convince the reader to dive deeper into NMR spectroscopy and prevent the technique from being just another "black-box" in the lab. We will try to concisely highlight interesting topics and supply additional references for further exploration at each stage. The advantages of delving into the technique will be shown. The secondary objective, i.e., avoiding common problems before starting, will hopefully then become clear. Lastly, we will emphasize the spectrometer information needed for manuscript reporting to allow reproduction of results and confirm findings.

Problems, principles and progress in computational annotation of NMR metabolomics data

BACKGROUND

Compound identification remains a critical bottleneck in the process of exploiting Nuclear Magnetic Resonance (NMR) metabolomics data, especially for ¹H 1-dimensional (¹H 1D) data. As databases of reference compound spectra have grown, workflows have evolved to rely heavily on their search functions to facilitate this process by generating lists of potential metabolites found in complex mixture data, facilitating annotation and identification. However, approaches for validating and communicating annotations are most often guided by expert knowledge, and therefore are highly variable despite repeated efforts to align practices and define community standards.

AIM OF REVIEW

This review is aimed at broadening the application of automated annotation tools by discussing the key ideas of spectral matching and beginning to describe a set of terms to classify this information, thus advancing standards for communicating annotation confidence. Additionally, we hope that this review will facilitate the growing collaboration between chemical data scientists, software developers and the NMR metabolomics community aiding development of long-term software solutions.

KEY SCIENTIFIC CONCEPTS OF REVIEW

We begin with a brief discussion of the typical untargeted NMR identification workflow. We differentiate between annotation (hypothesis generation, filtering), and identification (hypothesis testing, verification), and note the utility of different NMR data features for annotation. We then touch on three parts of annotation: (1) generation of queries, (2) matching queries to reference data, and (3) scoring and confidence estimation of potential matches for verification. In doing so, we highlight existing approaches to automated and semi-automated annotation from the perspective of the structural information they utilize, as well as how this information can be represented computationally.

Computational simulation of 1 H NMR profiles of complex biofluid analyte mixtures at differential operating frequencies: Applications to low-field benchtop spectra

Estimations of accurate and reliable NMR chemical shift values, coupling patterns and constants within a reasonable timeframe remain significantly challenging, and the unavailability of reliable software strategies for the prediction of low-field (e.g., 60 MHz) spectra from those acquired at higher operating frequencies hampers their direct comparison. Hence, this study explored the applications of accessible software options for predicting these parameters in the ¹ H NMR profiles of analytes as a function of magnetic field strength; this was performed for individual analytes and also for complex biofluid matrices featured in metabolomics investigations. For this purpose, results from the very first successful experimental acquisition and simulation of the ¹ H NMR profiles of intact human salivary supernatant samples on a 60 MHz benchtop spectrometer were evaluated. Using salivary metabolite concentrations determined at 400 MHz, it was demonstrated that simulation of the low-field spectra of five biomolecules with the most prominent ¹ H resonances detectable allowed multiple component fits to be applied to experimental spectra. Hence, these salivary ¹ H NMR profiles could be successfully predicted throughout the 45-600 MHz operating frequency range. With the exception of propionate resonance multiplets, which revealed more complex coupling patterns at low field and required more astute computational and fitting options, valuable quantitative metabolomics data on salivary acetate, formate, methanol and glycine could be attained from low-field spectrometres. These studies are both timely and pertinent in view of the recent advancement of low-field benchtop NMR facilities for diagnostically significant biomarker tracking in biofluids. Experiments performed with added ammonium chloride to facilitate the release of salivary metabolites from biopolymer binding sites provided evidence that a small but nevertheless significant proportion of propionate, but not lactate, was bound to such sites, an observation of much relevance to biomolecule quantification in salivary metabolomics investigations.

Bucket Fuser: Statistical Signal Extraction for 1D 1H NMR Metabolomic Data

Untargeted metabolomics is a promising tool for identifying novel disease biomarkers and unraveling underlying pathomechanisms. Nuclear magnetic resonance (NMR) spectroscopy is particularly suited for large-scale untargeted metabolomics studies due to its high reproducibility and cost effectiveness. Here, one-dimensional (1D) 1H NMR experiments offer good sensitivity at reasonable measurement times. Their subsequent data analysis requires sophisticated data preprocessing steps, including the extraction of NMR features corresponding to specific metabolites. We developed a novel 1D NMR feature extraction procedure, called Bucket Fuser (BF), which is based on a regularized regression framework with fused group LASSO terms. The performance of the BF procedure was demonstrated using three independent NMR datasets and was benchmarked against existing state-of-the-art NMR feature extraction methods. BF dynamically constructs NMR metabolite features, the widths of which can be adjusted via a regularization parameter. BF consistently improved metabolite signal extraction, as demonstrated by our correlation analyses with absolutely quantified metabolites. It also yielded a higher proportion of statistically significant metabolite features in our differential metabolite analyses. The BF algorithm is computationally efficient and it can deal with small sample sizes. In summary, the Bucket Fuser algorithm, which is available as a supplementary python code, facilitates the fast and dynamic extraction of 1D NMR signals for the improved detection of metabolic biomarkers.

Multi-Tissue Time-Domain NMR Metabolomics Investigation of Time-Restricted Feeding in Male and Female Nile Grass Rats

Metabolic disease resulting from overnutrition is prevalent and rapidly increasing in incidence in modern society. Time restricted feeding (TRF) dietary regimens have recently shown promise in attenuating some of the negative metabolic effects associated with chronic nutrient stress. The purpose of this study is to utilize a multi-tissue metabolomics approach using nuclear magnetic resonance (NMR) spectroscopy to investigate TRF and sex-specific effects of high-fat diet in a diurnal Nile grass rat model. Animals followed a six-week dietary protocol on one of four diets: chow ad libitum, high-fat ad libitum (HF-AD), high-fat early TRF (HF-AM), or high-fat late TRF (HF-PM), and their liver, heart, and white adipose tissues were harvested at the end of the study and were analyzed by NMR. Time-domain complete reduction to amplitude–frequency table (CRAFT) was used to semi-automate and systematically quantify metabolites in liver, heart, and adipose tissues while minimizing operator bias. Metabolite profiling and statistical analysis revealed lipid remodeling in all three tissues and ectopic accumulation of cardiac and hepatic lipids for HF-AD feeding compared to a standard chow diet. Animals on TRF high-fat diet had lower lipid levels in the heart and liver compared to the ad libitum group; however, no significant differences were noted for adipose tissue. Regardless of diet, females exhibited greater amounts of hepatic lipids compared to males, while no consistent differences were shown in adipose and heart. In conclusion, this study demonstrates the feasibility of performing systematic and time-efficient multi-tissue NMR metabolomics to elucidate metabolites involved in the crosstalk between different metabolic tissues and provides a more holistic approach to better understand the etiology of metabolic disease and the effects of TRF on metabolic profiles.

Time-Domain-Based Methyl Proton NMR with Absolute Quantitation Ability for Targeted Metabolomics

In high-throughput scenarios of targeted metabolomics, it is a significant challenge to process complex NMR spectra with severely overlapping signals produced by metabolites with similar chemical structures. Traditional frequency-domain NMR is ineffective to some degree due to the low sensitivity and poor resolution, and the precision of quantitation is usually affected by poorly or inconsistently phased and baselined spectra. Here, we established a strategy based on time-domain NMR focusing on methyl protons for targeted metabolomics. The targeted metabolomics focusing on bufadienolides for varietal discrimination of three toad venoms was conducted to demonstrate the practicability of time-domain-based methyl proton NMR. It revealed that the signals could be precisely identified and quantitated with an signal-to-noise ratio (SNR) of about 10 and a resolution of about 1.0 Hz. The sensitivity and resolution improvement make it particularly applicable in targeted metabolomics. The precise and absolute quantitation ability confirmed by triple-quadrupole mass spectrometry (QqQ-MS) could further extend its application range. Importantly, the methyl group is common in metabolites with a relatively wide chemical shift range. Time-domain analysis could be conducted in common NMR software. This technique is very easy and convenient for general researchers when employed as a complementary alternative to traditional frequency-domain NMR, especially in the field of targeted metabolomics.

Deep Learning-Based Method for Compound Identification in NMR Spectra of Mixtures

Nuclear magnetic resonance (NMR) spectroscopy is highly unbiased and reproducible, which provides us a powerful tool to analyze mixtures consisting of small molecules. However, the compound identification in NMR spectra of mixtures is highly challenging because of chemical shift variations of the same compound in different mixtures and peak overlapping among molecules. Here, we present a pseudo-Siamese convolutional neural network method (pSCNN) to identify compounds in mixtures for NMR spectroscopy. A data augmentation method was implemented for the superposition of several NMR spectra sampled from a spectral database with random noises. The augmented dataset was split and used to train, validate and test the pSCNN model. Two experimental NMR datasets (flavor mixtures and additional flavor mixture) were acquired to benchmark its performance in real applications. The results show that the proposed method can achieve good performances in the augmented test set (ACC = 99.80%, TPR = 99.70% and FPR = 0.10%), the flavor mixtures dataset (ACC = 97.62%, TPR = 96.44% and FPR = 2.29%) and the additional flavor mixture dataset (ACC = 91.67%, TPR = 100.00% and FPR = 10.53%). We have demonstrated that the translational invariance of convolutional neural networks can solve the chemical shift variation problem in NMR spectra. In summary, pSCNN is an off-the-shelf method to identify compounds in mixtures for NMR spectroscopy because of its accuracy in compound identification and robustness to chemical shift variation.

Fundamental and practical aspects of machine learning for the peak picking of biomolecular NMR spectra

Rapid progress in machine learning offers new opportunities for the automated analysis of multidimensional NMR spectra ranging from protein NMR to metabolomics applications. Most recently, it has been demonstrated how deep neural networks (DNN) designed for spectral peak picking are capable of deconvoluting highly crowded NMR spectra rivaling the facilities of human experts. Superior DNN-based peak picking is one of a series of critical steps during NMR spectral processing, analysis, and interpretation where machine learning is expected to have a major impact. In this perspective, we lay out some of the unique strengths as well as challenges of machine learning approaches in this new era of automated NMR spectral analysis. Such a discussion seems timely and should help define common goals for the NMR community, the sharing of software tools, standardization of protocols, and calibrate expectations. It will also help prepare for an NMR future where machine learning and artificial intelligence tools will be common place.

Newton meets Ockham: Parameter estimation and model selection of NMR data with NMR-EsPy

We present NMR-EsPy (NMR Estimation in Python), a versatile, simple-to-use Python package for estimating the signal parameters that describe one-dimensional time-domain NMR data. The software is fully integrated into Topspin, a widely used NMR platform, and comes with a Graphical User Interface, allowing users unfamiliar with the underlying theory and/or Python programming to access the full functionality of the software package. NMR-EsPy utilises Newton's method, an iterative non-linear programming technique. By including the variance of oscillator phases in the optimization, NMR-EsPy can generate parsimonious parameter estimates, giving NMR users access to meaningful quantitative information. This principle is easily extendable to study specific regions of an NMR spectrum to reduce computational cost. The complete mathematical treatment along with examples of the implementation of the estimation routine are presented.

Early Time-Restricted Feeding Amends Circadian Clock Function and Improves Metabolic Health in Male and Female Nile Grass Rats

Lengthening the daily eating period contributes to the onset of obesity and metabolic syndrome. Dietary approaches, including energy restriction and time-restricted feeding, are promising methods to combat metabolic disorders. This study explored the effect of early and late time-restricted feeding (TRF) on weight and adiposity, food consumption, glycemic control, clock gene expression, and liver metabolite composition in diurnal Nile grass rats (NGRs). Adult male and female Nile grass rats were randomly assigned to one of three groups: (1) access to a 60% high-fat (HF) diet ad-libitum (HF-AD), (2) time-restricted access to the HF diet for the first 6 h of the 12 h light/active phase (HF-AM) or (3) the second 6 h of the 12 h light/active phase (HF-PM). Animals remained on their respective protocols for six weeks. TRF reduced total energy consumption and weight gain, and early TRF (HF-AM) reduced fasting blood glucose, restored Per1 expression, and reduced liver lipid levels. Although sex-dependent differences were observed for fat storage and lipid composition, TRF improved metabolic parameters in both male and female NGRs. In conclusion, this study demonstrated that early TRF protocol benefits weight management, improves lipid and glycemic control, and restores clock gene expression in NGRs.

Quantitative and convenient real-time reaction monitoring using stopped-flow benchtop NMR

We present a stopped-flow benchtop NMR system (composed of commercially available hardware components) that allows for quantitative reaction monitoring to be completed with relative ease, even with experimentally complex reaction systems.

Standardization and Control of Grignard Reactions in a Universal Chemical Synthesis Machine using online NMR

A big problem with the chemistry literature is that it is not standardized with respect to precise operational parameters, and real time corrections are hard to make without expert knowledge. This lack of context means difficult reproducibility because many steps are ambiguous, and hence depend on tacit knowledge. Here we present the integration of online NMR into an automated chemical synthesis machine (CSM aka. "Chemputer" which is capable of small-molecule synthesis using a universal programming language) to allow automated analysis and adjustment of reactions on the fly. The system was validated and benchmarked by using Grignard reactions which were chosen due to their importance in synthesis. The system was monitored in real time using online-NMR, and spectra were measured continuously during the reactions. This shows that the synthesis being done in the Chemputer can be dynamically controlled in response to feedback optimizing the reaction conditions according to the user requirements.

The qNMR Summit 5.0: Proceedings and Status of qNMR Technology

The goal of the qNMR Summit is to take stock of the status quo and the recent developments in qNMR research and applications in a timely and accurate manner. It provides a platform for both advanced and novice qNMR practitioners to receive a well-rounded update and discuss potential qNMR-related applications and collaborations. For over a decade, scientists from academia, industry, nonprofit institutions, and governmental bodies have focused on the standardization of qNMR methodology, as well as its metrological and pharmacopeial utility. This paper reviews key content of qNMR Summits 1.0 to 4.0 and puts into perspective the outcomes and available transcripts of the October 2019 Summit 5.0, with attendees from the United States, Canada, Japan, Korea, and several European countries. Summit presentations focused on qNMR methodology in the pharmaceutical industry, advanced quantitation algorithms, and promising developments.

Complete Reduction to Amplitude Frequency Table (CRAFT)-A perspective

The CRAFT (Complete Reduction to Amplitude Frequency Table) technique, based on Bayesian analysis approach, converts FID and/or interferogram (time domain) to a frequency-amplitude table (tabular domain) in a robust, automated, and time-efficient fashion. This mini review/perspective presents an introduction to CRAFT as a processing workflow followed by a discussion of several practical 1D and 2D examples of its applicability and associated benefit. CRAFT provides high quality quantitative results for complex systems without any need for conventional preprocessing steps, such as phase and baseline corrections. Two-dimensional time domain data are typically truncated, particularly in the evolution dimension, and conventional processing after zero-filling and t_1max -matched apodization masks potentially available peak resolution. The line broadening introduced by extensive zero-filling and severe apodization functions leads to the lack of clear resolution of cross peaks. CRAFT decimation of interferograms, on the other hand, requires minimal or no apodization prior to extraction of the NMR parameters and significantly improves the spectral linewidth of the cross peaks along F₁ dimension compared to conventional (FT) processing. The tabular representation of the CRAFT2d cross peaks information can be visualized in a variety of frequency domain formats for conventional spectral interpretation as well as quantitative applications. A simple workflow to generate in silico oversampled interferogram (iSOS) is presented, and its potential benefit in CRAFT decimation of highly crowded 2D NMR is demonstrated. This report is meant as a collective thesis to present a potentially new paradigm in data processing that questions the need for hitherto unchallenged preprocessing steps, such as phase and baseline correction in 1D and zero-fill/severe apodization in 2D.

A Monte Carlo Method for Analyzing Systematic and Random Uncertainty in Quantitative Nuclear Magnetic Resonance Measurements

Quantitative nuclear magnetic resonance (qNMR) is a powerful analytical technology that is capable of quantifying the concentration of any analyte with exquisite accuracy and precision so long as it contains at least one nonlabile nuclear magnetic resonance (NMR)-active nucleus. Unlike with traditional analytical technologies, the concentrations of analytes do not directly influence the uncertainty in the quantification of NMR signals because an ideal NMR response depends only on the nature and amount of the nucleus being observed. Rather, in the absence of spectral artifacts and under favorable experimental conditions, the measurement uncertainty may be influenced by the following factors: (1) spectroscopic parameters such as the spectral width, number of time domain points, and acquisition time; (2) postacquisition data processing, such as apodization and zero-filling; (3) the signal-to-noise ratios (SNRs) and lineshapes of the two signals being used in a qNMR measurement; and (4) the method of signal quantification employed, such as numerical integration or lineshape fitting (LF). Here, a general Monte Carlo (MC) method that considers these factors is presented, with which the random and systematic contributions to qNMR measurement uncertainty may be calculated. Autocorrelation analysis of synthetic and experimental noise is used in a fingerprint-like approach to demonstrate the validity of the simulations. The MC method allows for a general quantitative assessment of measurement uncertainty without the need to acquire spectral replicates and without reference to the molecular structures and concentrations of analytes. Representative examples of qNMR measurement uncertainty simulations are provided in which the metrological performances of integration and LF are contrasted for signal pairs obtained using various acquisition and processing schemes in the low-SNR regime-an area where application of the proposed MC method may prove to be particularly salient.

RTExtract: time-series NMR spectra quantification based on 3D surface ridge tracking

MOTIVATION

Time-series nuclear magnetic resonance (NMR) has advanced our knowledge about metabolic dynamics. Before analyzing compounds through modeling or statistical methods, chemical features need to be tracked and quantified. However, because of peak overlap and peak shifting, the available protocols are time consuming at best or even impossible for some regions in NMR spectra.

RESULTS

We introduce Ridge Tracking-based Extract (RTExtract), a computer vision-based algorithm, to quantify time-series NMR spectra. The NMR spectra of multiple time points were formulated as a 3D surface. Candidate points were first filtered using local curvature and optima, then connected into ridges by a greedy algorithm. Interactive steps were implemented to refine results. Among 173 simulated ridges, 115 can be tracked (RMSD < 0.001). For reproducing previous results, RTExtract took less than 2 h instead of ∼48 h, and two instead of seven parameters need tuning. Multiple regions with overlapping and changing chemical shifts are accurately tracked.

AVAILABILITY AND IMPLEMENTATION

Source code is freely available within Metabolomics toolbox GitHub repository (https://github.com/artedison/Edison_Lab_Shared_Metabolomics_UGA/tree/master/metabolomics_toolbox/code/ridge_tracking) and is implemented in MATLAB and R.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

A comparison of non-uniform sampling and model-based analysis of NMR spectra for reaction monitoring

Nuclear magnetic resonance (NMR) spectroscopy is widely used for applications in the field of reaction and process monitoring. When complex reaction mixtures are studied, NMR spectra often suffer from low resolution and overlapping peaks, which places high demands on the method used to acquire or to analyse the NMR spectra. This work presents two NMR methods that help overcome these challenges: 2D non-uniform sampling (NUS) and a recently proposed model-based fitting approach for the analysis of 1D NMR spectra. We use the reaction of glycerol with acetic acid as it produces five reaction products that are all chemically similar and, hence, challenging to distinguish. The reaction was measured on a high-field 400 MHz NMR spectrometer with a 2D NUS-heteronuclear single quantum coherence (HSQC) and a conventional 1D ¹ H NMR sequence. We show that comparable results can be obtained using both 2D and 1D methods, if the 2D volume integrals of the 2D NUS-HSQC NMR spectra are calibrated. Further, we monitor the same reaction on a low-field 43 MHz benchtop NMR spectrometer and analyse the acquired 1D ¹ H NMR spectra with the model-based approach and with partial least-squares regression (PLS-R), both trained using a single, calibrated data set. Both methods achieve results that are in good quantitative agreement with the high-field data. However, the model-based method was found to be less sensitive to the training data set used than PLS-R and, hence, was more robust when the reaction conditions differed from that of the training data.

CRAFT for NMR lipidomics: Targeting lipid metabolism in leucine-supplemented tumor-bearing mice

Lipid profiling by 1 H-NMR has gained increasing utility in many fields because of its intrinsically quantitative, nondestructive nature and the ability to differentiate small molecules based on their spectral location. Most nuclear magnetic resonance (NMR) techniques for metabolite quantification use frequency domain analysis that involves many user-dependent steps such as phase and baseline correction and quantification by either manual integration or peak fitting. Recently, Bayesian analysis of time-domain NMR data has been shown to reduce operator bias and increase automation in NMR spectroscopy. In this study, we demonstrate the use of CRAFT (complete reduction to amplitude-frequency table), a Bayesian-based approach to automate processing in NMR-based lipidomics using lipid standards and tissue samples of healthy and tumor-bearing mice supplemented with leucine. Complex mixtures of lipid standards were prepared and examined using CRAFT to validate it against conventional Fourier transform (FT)-NMR and derive a fingerprint to be used for analyzing lipid profiles of serum and liver samples. CRAFT and FT-NMR were comparable in accuracy, with CRAFT achieving higher correlation in quantifying several lipid species. Analysis of the serum lipidome of tumor-bearing mice revealed hyperlipidemia and no signs of hepatic triglyceride accumulation compared with that of the healthy group demonstrating that the tumor-bearing mice were in a state of precachexia. Leucine-supplementation was associated with minimal changes in the lipid profile in both tissues. In conclusion, our study demonstrates that the CRAFT method can accurately identify and quantify lipids in complex lipid mixtures and murine tissue samples and, hence, will increase automation and reproducibility in NMR-based lipidomics.

NMR spectroscopy goes mobile: Using NMR as process analytical technology at the fume hood

Nuclear magnetic resonance (NMR) is potentially a very powerful process analytical technology (PAT) tool as it gives an atomic resolution picture of the reaction mixture without the need for chromatography. NMR is well suited for interrogating transient intermediates, providing kinetic information via NMR active nuclei, and most importantly provides universally quantitative information for all species in solution. This contrasts with commonly used PAT instruments, such as Raman or Flow-infrared (IR), which requires a separate calibration curve for every component of the reaction mixture. To date, the large footprint of high-field (≥400 MHz) NMR spectrometers and the immobility of superconducting magnets, coupled with strict requirements for the architecture for the room it is to be installed, have been a major obstacle to using this technology right next to fume hoods where chemists perform synthetic work. Here, we describe the use of a small, lightweight 60 MHz Benchtop NMR system (Nanalysis Pro-60) located on a mobile platform, that was used to monitor both small and intermediate scale Grignard formation and coupling reactions. We also show how low field NMR can provide a deceptively simple yes/no answer (for a system that would otherwise require laborious off-line testing) in the enrichment of one component versus another in a kilogram scale distillation. Benchtop NMR was also used to derive molecule specific information from Flow-IR, a technology found in most manufacturing sites, and compare the ease at which the concentrations of the reaction mixtures can be derived by NMR versus IR.

Quantitative analysis of cannabinoids using benchtop NMR instruments

The quantification of cannabinoids is an essential part of cannabis profiling and testing, whether for medical or recreational use. As regulatory bodies continue to increase testing requirements for these products, it is crucial that alternative and effective analytical methods be developed. Herein, we describe the use of benchtop NMR instruments for the quantification of Δ9-tetrahydrocannabinol (THC) and cannabidiol (CBD) in a variety of cannabis concentrates and compare the values to those obtained using HPLC, the most common approach for the quantification of cannabinoids. Based on the discrepancies observed in test values from different laboratories using only HPLC, the value of orthogonal testing methods has been identified and is increasingly desired.

Bayesian approach for automated quantitative analysis of benchtop NMR data

Low-cost, user-friendly benchtop NMR instruments are often touted as a "one-click" solution for data acquisition, however insufficient peak dispersion in their spectra often reduces the accuracy of quantification and requires user expertise with sophisticated processing tools. Our work aims to facilitate the wide acceptance of benchtop NMR instruments as a viable and effective substitute for cryogenic magnets. We propose an algorithmic approach that completely automates the routine analysis of sets of samples with similar compositions - the problem that often underlies many industrial applications concerned with reaction and process monitoring and quality control. Our solution is rooted in the idea of parametric modelling formulated in terms of Bayesian statistics, which effectively incorporates prior knowledge about the studied system (such as concentration-dependent chemical shift changes) that is usually available in industrial applications. Furthermore, the use of quantum mechanical models for chemical species makes our approach invariant to the spectrometer field strength - a necessary prerequisite for the successful analysis of benchtop data. We demonstrate the performance of our method with two representative sets of samples: mixtures of alcohols and acetates, and aqueous mixtures of biologically relevant species. In these examples, our fully automated analysis of benchtop spectra achieves average errors in concentrations of 0.01 mol/mol and 0.02 mol/mol respectively. Our method is competitive with the traditional processing approaches of well resolved high-field data and has the potential to bring the benefits of NMR even to a small chemistry laboratory.

Improving the accuracy of model-based quantitative nuclear magnetic resonance

Low spectral resolution and extensive peak overlap are the common challenges that preclude quantitative analysis of nuclear magnetic resonance (NMR) data with the established peak integration method. While numerous model-based approaches overcome these obstacles and enable quantification, they intrinsically rely on rigid assumptions about functional forms for peaks, which are often insufficient to account for all unforeseen imperfections in experimental data. Indeed, even in spectra with well-separated peaks whose integration is possible, model-based methods often achieve suboptimal results, which in turn raises the question of their validity for more challenging datasets. We address this problem with a simple model adjustment procedure, which draws its inspiration directly from the peak integration approach that is almost invariant to lineshape deviations. Specifically, we assume that the number of mixture components along with their ideal spectral responses are known; we then aim to recover all useful signals left in the residual after model fitting and use it to adjust the intensity estimates of modelled peaks. We propose an alternative objective function, which we found particularly effective for correcting imperfect phasing of the data - a critical step in the processing pipeline. Application of our method to the analysis of experimental data shows the accuracy improvement of 20 %-40 % compared to the simple least-squares model fitting.

Signal Deconvolution and Noise Factor Analysis Based on a Combination of Time-Frequency Analysis and Probabilistic Sparse Matrix Factorization

Nuclear magnetic resonance (NMR) spectroscopy is commonly used to characterize molecular complexity because it produces informative atomic-resolution data on the chemical structure and molecular mobility of samples non-invasively by means of various acquisition parameters and pulse programs. However, analyzing the accumulated NMR data of mixtures is challenging due to noise and signal overlap. Therefore, data-cleansing steps, such as quality checking, noise reduction, and signal deconvolution, are important processes before spectrum analysis. Here, we have developed an NMR measurement informatics tool for data cleansing that combines short-time Fourier transform (STFT; a time-frequency analytical method) and probabilistic sparse matrix factorization (PSMF) for signal deconvolution and noise factor analysis. Our tool can be applied to the original free induction decay (FID) signals of a one-dimensional NMR spectrum. We show that the signal deconvolution method reduces the noise of FID signals, increasing the signal-to-noise ratio (SNR) about tenfold, and its application to diffusion-edited spectra allows signals of macromolecules and unsuppressed small molecules to be separated by the length of the T₂* relaxation time. Noise factor analysis of NMR datasets identified correlations between SNR and acquisition parameters, identifying major experimental factors that can lower SNR.

Effects of the vat pasteurization process and refrigerated storage on the bovine milk metabolome

This study is the first to investigate the evolution of cow milk metabolites throughout the vat pasteurization process and storage using untargeted metabolomics based on a multiplatform approach. Nuclear magnetic resonance and ultraperformance liquid chromatography-quadrupole time-of-flight mass spectrometry were used for fingerprinting water-soluble nutritional compounds, and headspace gas chromatography-mass spectrometry was used to fingerprint the volatile organic compounds. This study demonstrated that vat pasteurization was an efficient and mild means of milk preservation resulting in only minor changes to the metabolites. The pasteurized milk samples exhibited a stable metabolome during the first 8 d of refrigerated storage. However, at the latter stage of storage, the concentrations of pantothenic acid and butyrylcarnitine decreased, whereas some fatty acids, organic acids, α-AA, peptides, and ketones increased. These selected metabolites that changed during milk storage could be used as potential biomarkers to track the storage conditions of pasteurized cow milk.

Searching for Small Molecules with an Atomic Sort

The discovery of biologically active small molecules requires sifting through large amounts of data to identify unique or unusual arrangements of atoms. Here, we develop, test and evaluate an atom-based sort to identify novel features of secondary metabolites and demonstrate its use to evaluate novelty in marine microbial and sponge extracts. This study outlines an important ongoing advance towards the translation of autonomous systems to identify, and ultimately elucidate, atomic novelty within a complex mixture of small molecules.

Two-dimensional subband Steiglitz-McBride algorithm for automatic analysis of two-dimensional nuclear magnetic resonance data

Rapid, accurate, and automatic quantitation of two-dimensional nuclear magnetic resonance(2D-NMR) data is a challenging problem. Recently, a Bayesian information criterion based subband Steiglitz-McBride algorithm has been shown to exhibit superior performance on all three fronts when applied to the quantitation of one-dimensional NMR free induction decay data. In this paper, we demonstrate that the 2D Steiglitz-McBride algorithm, in conjunction with 2D subband decomposition and the 2D Bayesian information criterion, also achieves excellent results for 2D-NMR data in terms of speed, accuracy, and automation-especially when compared in these respects to the previously published analysis techniques for 2D-NMR data.

Enhancing benchtop NMR spectroscopy by means of sample shifting

Benchtop NMR sensitivity enhancement by cyclic, mechanical shifting of a sample to preserve high nuclear spin polarization.

Analysis of NMR Metabolomics Data

In this chapter, we summarize data preprocessing and data analysis strategies used for analysis of NMR data for metabolomics studies. Metabolomics consists of the analysis of the low molecular weight compounds in cells, tissues, or biological fluids, and has been used to reveal biomarkers for early disease detection and diagnosis, to monitor interventions, and to provide information on pathway perturbations to inform mechanisms and identifying targets. Metabolic profiling (also termed metabotyping) involves the analysis of hundreds to thousands of molecules using mainly state-of-the-art mass spectrometry (MS) and nuclear magnetic resonance (NMR) spectroscopy technologies. While NMR is less sensitive than mass spectrometry, NMR does provide a wealth of complex and information rich metabolite data. NMR data together with the use of conventional statistics, modeling methods, and bioinformatics tools reveals biomarker and mechanistic information. A typical NMR spectrum, with up to 64k data points, of a complex biological fluid or an extract of cells and tissues consists of thousands of sharp signals that are mainly derived from small molecules. In addition, a number of advanced NMR spectroscopic methods are available for extracting information on high molecular weight compounds such as lipids or lipoproteins. There are numerous data preprocessing, data reduction, and analysis methods developed and evolving in the field of NMR metabolomics. Our goal is to provide an extensive summary of NMR data preprocessing and analysis strategies by providing examples and open source and commercially available analysis software and bioinformatics tools.

Band-selective excitation NMR spectroscopy and quantitative time-domain analysis using Complete Reduction to Amplitude-Frequency Table (CRAFT) to determine distribution coefficients during drug development

A sensitive quantitative ¹ H NMR method for determining distribution or partition coefficients has been developed that is applicable to early drug discovery. After partitioning and equilibration, aliquots from each layer are analyzed using band-selective excitation ¹ H NMR spectroscopy in regions that are free of 1-octanol and water solvent signals. Signals are quantitated directly using CRAFT software, and their amplitudes are adjusted to correct for nonuniformity within the excitation band. Using this approach, the distribution coefficients for 20 drugs present at low concentrations were determined giving values that were in excellent agreement with literature values.

31P NMR-Based Phospholipid Fingerprinting of Powdered Infant Formula

Infant formula (IF), regarded as the optimal substitute for human breast milk, is very important for infant growth and development. Phospholipids (PLs) are ubiquitous components of infant formula as they have good emulsifier properties in addition to their nutritional and biological functions. In this study, the PL contents in four different commercial IF brands (indicated as A, M, O, and W) were characterized and quantified using optimized ³¹P NMR spectroscopy. PLs (nine) were identified and quantified, and among these, phosphatidylethanolamine and sphingomyelin occurred at lower concentrations (5.72 and 8.89 mg/100 g, respectively) in IFs from brand O, whereas phosphatidic acid was higher (2.83 mg/100 g) in IFs from brand W. In summary, ³¹P NMR spectroscopy, combined with the multivariate data analysis, proved to be an effective analytical toolbox for evaluating the PL contents in IF and the comparative differences between IF brands.

Time-domain signal modelling in multidimensional NMR experiments for estimation of relaxation parameters

We present a model-based method for estimation of relaxation parameters from time-domain NMR data specifically suitable for processing data in popular 2D phase-sensitive experiments. Our model is formulated in terms of commutative bicomplex algebra, which allows us to use the complete information available in an NMR signal acquired with principles of quadrature detection without disregarding any of its dimensions. Compared to the traditional intensity-analysis method, our model-based approach offers an important advantage for the analysis of overlapping peaks and is robust over a wide range of signal-to-noise ratios. We assess its performance with simulated experiments and then apply it for determination of [Formula: see text], [Formula: see text], and [Formula: see text] relaxation rates in datasets of a protein with more than 100 cross peaks.

Measuring Protein Concentration by Diffusion-Filtered Quantitative Nuclear Magnetic Resonance Spectroscopy

The concentration of macromolecules in solution is a crucial property in many areas of research, including the development and commercialization of biological therapeutics. For proteins in particular, none of the reported methods for measuring concentration detect a molecular property that is known a priori; rather, they rely on ligand binding, degradation and derivitization, or an intrinsic property that must be determined experimentally. The purpose of this report is to describe (1) a diffusion-filtered qNMR experiment (DF-qNMR) for quantitating macromolecules in complex matrices and (2) an overall method for measuring absolute protein concentration based on this DF-qNMR experiment. This method combines protein denaturation with the diffusion filter to produce clean spectra of the protein with well-resolved resonances, regardless of the matrix complexity. The concentration is then obtained by comparing the peak area of the valine/isoleucine/leucine methyl groups to an external, certified, small-molecule quantitation standard. The method, which is referred to as VILMHA (valine isoleucine leucine methyl hydrogen analysis), was tested on three proteins of various sizes. In all cases, the measured concentration was within 1.8% of the labeled value for the undiluted standard reference material evaluated. In addition, the RSD's were less than 1.25% in all cases and less than 1% in most cases. The accuracy, precision, and ease of use make this method superior to existing absolute protein concentration methods. Furthermore, VILMHA is ideally suited to serve as the basis for converting the relative protein concentration methods into absolute methods or establishing molecular-specific parameters. Finally, DF-qNMR has the potential to quantitate other types of macromolecules (e.g., such as polymers, surfactants, etc.) in the presence of small-molecule contaminants.

A field-invariant method for quantitative analysis with benchtop NMR

Recently developed benchtop instruments have the potential of bringing the benefits of NMR spectroscopy to the wide variety of industrial applications. Unfortunately, their low spectral resolution poses significant challenges for traditional quantification approach. Here we present a novel model-based method designed to overcome these challenges. By defining our models in terms of quantum mechanical properties of the underlying spin system, we make our approach invariant to the spectrometer field strength and especially suitable for analyzing benchtop data. Our experimental results on prepared samples and natural fruit juices confirm the applicability of our method for quantitative analysis of medium-field ¹H NMR spectra. The developed method succeeds in accurately separating the spectra of glucose anomers and even monitoring their interconversion in non-deuterated water. Furthermore, the compositions of unbuffered natural fruit juices estimated using data from 43 MHz to 400 MHz spectrometers are in good agreement with each other and with the reference values from nutrition databases.

Robust 1D NMR lineshape fitting using real and imaginary data in the frequency domain

Quantitative NMR is intrinsically dependent on precise, accurate, and robust peak area calculation. In this work, we demonstrate how the use of complex-valued peak descriptions can improve peak fitting in the frequency domain - incorporating phase and baseline correction as well as apodization while working with commonly used Fourier-transformed data. The method has been implemented in an open source R package called rnmrfit that is available for download on GitHub (https://github.com/ssokolen/rnmrfit). Application to real data suggests that this approach can also result in dramatically higher precision than can be achieved with existing software. Simulation data indicates that coefficients of variation below 0.1% can be readily achieved at signal to noise (SNR) ratios of approximately 100. The use of complex-valued data in the frequency domain is demonstrated as a relatively simple and effective means of improving peak fitting for quantitative NMR analysis.

Non-Uniform and Absolute Minimal Sampling for High-Throughput Multidimensional NMR Applications

Many biomolecular NMR applications can benefit from the faster acquisition of multidimensional NMR data with high resolution and their automated analysis and interpretation. In recent years, a number of non-uniform sampling (NUS) approaches have been introduced for the reconstruction of multidimensional NMR spectra, such as compressed sensing, thereby bypassing traditional Fourier-transform processing. Such approaches are applicable to both biomacromolecules and small molecules and their complex mixtures and can be combined with homonuclear decoupling (pure shift) and covariance processing. For homonuclear 2D TOCSY experiments, absolute minimal sampling (AMS) permits the drastic shortening of measurement times necessary for high-throughput applications for identification and quantification of components in complex biological mixtures in the field of metabolomics. Such TOCSY spectra can be comprehensively represented by graphic theoretical maximal cliques for the identification of entire spin systems and their subsequent query against NMR databases. Integration of these methods in webservers permits the rapid and reliable identification of mixture components. Recent progress is reviewed in this Minireview.

A subband Steiglitz-McBride algorithm for automatic analysis of FID data

Fast, accurate, and automatic extraction of parameters of nuclear magnetic resonance free induction decay (FID) signal for chemical spectroscopy is a challenging problem. Recently, the Steiglitz-McBride algorithm has been shown to exhibit superior performance in terms of speed, accuracy, and automation when applied to the extraction of T₂ relaxation parameters for myelin water imaging of brain. Applying it to FID data reveals that it falls short of the second objective, the accuracy. Especially, it struggles with the issue of missed spectral peaks when applied to chemical samples with relatively dense frequency spectra. To overcome this issue, a preprocessing stage of subband decomposition is proposed before the application of Steiglitz-McBride algorithm to the FID signal. It is demonstrated that by doing so, a considerable improvement in accuracy is achieved. But this is not gained at the cost of the first objective, the speed. An adaptive subband decomposition is employed in conjunction with the Bayesian information criteria to carry out an efficient decomposition according to spectral content of the signal under investigation. Furthermore, adaptive subband decomposition and the Bayesian information criteria also serve to make the resulting algorithm independent of user input, which also fulfills the third objective, the automation. This makes the proposed algorithm favorable for fast, accurate, and automatic extraction of FID signal parameters.

Application of CRAFT (complete reduction to amplitude frequency table) in nonuniformly sampled (NUS) 2D NMR data processing

The recently published CRAFT (complete reduction to amplitude frequency table) technique converts the raw FID data (i.e., time domain data) into a table of frequencies, amplitudes, decay rate constants, and phases. It offers an alternate approach to decimate time-domain data, with minimal preprocessing step. It has been shown that application of CRAFT technique to process the t₁ dimension of the 2D data significantly improved the detectable resolution by its ability to analyze without the use of ubiquitous apodization of extensively zero-filled data. It was noted earlier that CRAFT did not resolve sinusoids that were not already resolvable in time-domain (i.e., t₁ max dependent resolution). We present a combined NUS-IST-CRAFT approach wherein the NUS acquisition technique (sparse sampling technique) increases the intrinsic resolution in time-domain (by increasing t₁ max), IST fills the gap in the sparse sampling, and CRAFT processing extracts the information without loss due to any severe apodization. NUS and CRAFT are thus complementary techniques to improve intrinsic and usable resolution. We show that significant improvement can be achieved with this combination over conventional NUS-IST processing. With reasonable sensitivity, the models can be extended to significantly higher t₁ max to generate an indirect-DEPT spectrum that rivals the direct observe counterpart.