Non-uniform sampling to enhance the performance of compact NMR for characterizing new psychoactive substances.

Efficient and robust analytical methods are needed to improve the identification and subsequent regulation of new psychoactive substances (NPS). NMR spectroscopy is a unique method able to determine the structure of small molecules such as NPS even in mixtures. However, high-field NMR analysis is associated with expensive purchase and maintenance costs. For more than a decade, compact NMR spectrometers have changed this paradigm. It was recently shown that a dedicated analytical workflow combining compact NMR and databases could identify the molecular structure of NPS, in spite of the lower spectral dispersion and sensitivity of compact spectrometers. This approach relies on 1H-13C HSQC to both recognize NPS and elucidate the structure of unknown substances. Still, its performance is limited by the need to compromise between resolution and experiment time. Here, we show that this strategy can be significantly improved by implementing non-uniform sampling (NUS) to improve spectral resolution in the 13C dimension of HSQC at no cost in terms of experiment time. Gains in the range of 3 to 4 in resolution are achieved for pure NPS and for a mixture. Finally, 2D HSQC with NUS was applied to improve the identification of NPS with the assistance of databases. The resulting method appears as a useful tool for the characterization of NPS in mixtures, which is essential for forensic laboratories.

A Recursive Non-Uniform Sampling Estimator for Asynchronous Nonlinear Systems.

In this paper, we consider the problem of asynchronous estimation in the presence of packet losses for the randomly sampling nonlinear system. Packet losses occur at the control input and at the measurement side. Firstly, the synchronization of the asynchronous sampling system is realized by weighting the state of the adjacent state update points. Secondly, the projection theorem is used to estimate the system state at the sampling time. Due to modeling errors and unmodeled dynamics, obtaining an accurate dynamic model is challenging. Therefore, observation inference based on interpolation techniques is proposed to solve the asynchronous estimation problem. Furthermore, the algorithm is extended to multi-sensor systems to obtain a distributed fusion estimator. Finally, simulation experiments are conducted to validate the effectiveness of the algorithm.

Non-uniform sampling of similar NMR spectra and its application to studies of the interaction between alpha-synuclein and liposomes.

The accelerated acquisition of multidimensional NMR spectra using sparse non-uniform sampling (NUS) has been widely adopted in recent years. The key concept in NUS is that a major part of the data is omitted during measurement, and then reconstructed using, for example, compressed sensing (CS) methods. CS requires spectra to be compressible, that is, they should contain relatively few "significant" points. The more compressible the spectrum, the fewer experimental NUS points needed in order for it to be accurately reconstructed. In this paper we show that the CS processing of similar spectra can be enhanced by reconstructing only the differences between them. Accurate reconstruction can be obtained at lower sampling levels as the difference is sparser than the spectrum itself. In many situations this method is superior to "conventional" compressed sensing. We exemplify the concept of "difference CS" with one such case-the study of alpha-synuclein binding to liposomes and its dependence on temperature. To obtain information on temperature-dependent transitions between different states, we need to acquire several dozen spectra at various temperatures, with and without the presence of liposomes. Our detailed investigation reveals that changes in the binding modes of the alpha-synuclein ensemble are not only temperature-dependent but also show non-linear behavior in their transitions. Our proposed CS processing approach dramatically reduces the number of NUS points required and thus significantly shortens the experimental time.

5D solid-state NMR spectroscopy for facilitated resonance assignment.

1H-detected solid-state NMR spectroscopy has been becoming increasingly popular for the characterization of protein structure, dynamics, and function. Recently, we showed that higher-dimensionality solid-state NMR spectroscopy can aid resonance assignments in large micro-crystalline protein targets to combat ambiguity (Klein et al., Proc. Natl. Acad. Sci. U.S.A. 2022). However, assignments represent both, a time-limiting factor and one of the major practical disadvantages within solid-state NMR studies compared to other structural-biology techniques from a very general perspective. Here, we show that 5D solid-state NMR spectroscopy is not only justified for high-molecular-weight targets but will also be a realistic and practicable method to streamline resonance assignment in small to medium-sized protein targets, which such methodology might not have been expected to be of advantage for. Using a combination of non-uniform sampling and the signal separating algorithm for spectral reconstruction on a deuterated and proton back-exchanged micro-crystalline protein at fast magic-angle spinning, direct amide-to-amide correlations in five dimensions are obtained with competitive sensitivity compatible with common hardware and measurement time commitments. The self-sufficient backbone walks enable efficient assignment with very high confidence and can be combined with higher-dimensionality sidechain-to-backbone correlations from protonated preparations into minimal sets of experiments to be acquired for simultaneous backbone and sidechain assignment. The strategies present themselves as potent alternatives for efficient assignment compared to the traditional assignment approaches in 3D, avoiding user misassignments derived from ambiguity or loss of overview and facilitating automation. This will ease future access to NMR-based characterization for the typical solid-state NMR targets at fast MAS.

Application of accelerated heteronuclear single quantum coherence experiments to the rapid quantification of monosaccharides and disaccharides in dairy products.

Monosaccharides and disaccharides are important dietary components, but if insufficiently metabolized by some population subgroups, they are also linked to disease patterns. Thus, the correct analytical identification, quantification, and labeling of these food components are crucial to inform and potentially protect consumers. Enzymatic assays and high-performance anion-exchange chromatography with pulsed amperometric detection are established methods for the quantification of monosaccharides and disaccharides that, however, require long measuring times (60-180 min). Accelerated methods for the identification and quantification of the nutritionally relevant monosaccharides and disaccharides d-glucose, d-galactose, d-fructose, sucrose, lactose, and maltose were therefore developed. To realize this goal, the NMR experiments HSQC (heteronuclear single quantum coherence) and acceleration by sharing adjacent polarization (ASAP)-HSQC were applied. Measurement times were reduced to 27 and 6 min, respectively, by optimizing the interscan delay and applying non-uniform sampling. The optimized methods were used to quantify d-glucose, d-galactose, d-fructose, sucrose, and lactose in various dairy products. Results of the HSQC and ASAP-HSQC methods are equivalent to the results of the reference methods in terms of both precision and accuracy, demonstrating that these methods can be used to correctly analyze nutritionally relevant monosaccharides and disaccharides in short times.

The rise of the machines in chemistry.

The use of artificial intelligence and, more specifically, deep learning methods in chemistry is becoming increasingly common. Applications in informatics fields, such as cheminformatics and proteomics, structural biology, and spectroscopy, including NMR, are on the rise. Recent developments in model architectures, such as graph convolutional neural networks and transformers, have been enabled by advancements in computational hardware and software. However, model architectures with more predictive power often require larger amounts of training data, which can be challenging to acquire, but this requirement can be mitigated through techniques like pretraining and fine-tuning. In spite of these successes, challenges remain, such as normalization and scaling of data, availability of experimentally acquired data, and model explainability.

Distorted Acquisition of Dynamic Events Sensed by Frequency-Scanning Fiber-Optic Interrogators and a Mitigation Strategy.

Fiber-optic dynamic interrogators, which use periodic frequency scanning, actually sample a time-varying measurand on a non-uniform time grid. Commonly, however, the sampled values are reported on a uniform time grid, synchronized with the periodic scanning. It is the novel and noteworthy message of this paper that this artificial assignment may give rise to significant distortions in the recovered signal. These distortions increase with both the signal frequency and measurand dynamic range for a given sampling rate and frequency scanning span of the interrogator. They may reach disturbing values in dynamic interrogators, which trade-off scanning speed with scanning span. The paper also calls for manufacturers of such interrogators to report the sampled values along with their instants of acquisition, allowing interpolation algorithms to substantially reduce the distortion. Experimental verification of a simulative analysis includes: (i) a commercial dynamic interrogator of 'continuous' FBG fibers that attributes the measurand values to a uniform time grid; as well as (ii) a dynamic Brillouin Optical time Domain (BOTDA) laboratory setup, which provides the sampled measurand values together with the sampling instants. Here, using the available measurand-dependent sampling instants, we demonstrate a significantly cleaner signal recovery using spline interpolation.

A simple approach for reconstruction of non-uniformly sampled pseudo-3D NMR data for accurate measurement of spin relaxation parameters.

We explain how to conduct a pseudo-3D relaxation series NUS measurement so that it can be reconstructed by existing 3D NUS reconstruction methods to give accurate relaxation values. We demonstrate using reconstruction algorithms IST and SMILE that this 3D approach allows lower sampling densities than for independent 2D reconstructions. This is in keeping with the common finding that higher dimensionality increases signal sparsity, enabling lower sampling density. The approach treats the relaxation series as ordinary 3D time-domain data whose imaginary part in the pseudo-dimension is zero, and applies any suitably linear 3D NUS reconstruction method accordingly. Best results on measured and simulated data were achieved using acquisitions with 9 to 12 planes and exponential spacing in the pseudo-dimension out to ~ 2 times the inverse decay time. Given these criteria, in typical cases where 2D reconstructions require 50% sampling, the new 3D approach generates spectra reliably at sampling densities of 25%.

FID-Net: A versatile deep neural network architecture for NMR spectral reconstruction and virtual decoupling.

In recent years, the transformative potential of deep neural networks (DNNs) for analysing and interpreting NMR data has clearly been recognised. However, most applications of DNNs in NMR to date either struggle to outperform existing methodologies or are limited in scope to a narrow range of data that closely resemble the data that the network was trained on. These limitations have prevented a widescale uptake of DNNs in NMR. Addressing this, we introduce FID-Net, a deep neural network architecture inspired by WaveNet, for performing analyses on time domain NMR data. We first demonstrate the effectiveness of this architecture in reconstructing non-uniformly sampled (NUS) biomolecular NMR spectra. It is shown that a single network is able to reconstruct a diverse range of 2D NUS spectra that have been obtained with arbitrary sampling schedules, with a range of sweep widths, and a variety of other acquisition parameters. The performance of the trained FID-Net in this case exceeds or matches existing methods currently used for the reconstruction of NUS NMR spectra. Secondly, we present a network based on the FID-Net architecture that can efficiently virtually decouple 13Cα-13Cß couplings in HNCA protein NMR spectra in a single shot analysis, while at the same time leaving glycine residues unmodulated. The ability for these DNNs to work effectively in a wide range of scenarios, without retraining, paves the way for their widespread usage in analysing NMR data.

Clustered sparsity and Poisson-gap sampling.

Non-uniform sampling (NUS) is a popular way of reducing the amount of time taken by multidimensional NMR experiments. Among the various non-uniform sampling schemes that exist, the Poisson-gap (PG) schedules are particularly popular, especially when combined with compressed-sensing (CS) reconstruction of missing data points. However, the use of PG is based mainly on practical experience and has not, as yet, been explained in terms of CS theory. Moreover, an apparent contradiction exists between the reported effectiveness of PG and CS theory, which states that a "flat" pseudo-random generator is the best way to generate sampling schedules in order to reconstruct sparse spectra. In this paper we explain how, and in what situations, PG reveals its superior features in NMR spectroscopy. We support our theoretical considerations with simulations and analyses of experimental data from the Biological Magnetic Resonance Bank (BMRB). Our analyses reveal a previously unnoticed feature of many NMR spectra that explains the success of "blue-noise" schedules, such as PG. We call this feature "clustered sparsity". This refers to the fact that the peaks in NMR spectra are not just sparse but often form clusters in the indirect dimension, and PG is particularly suited to deal with such situations. Additionally, we discuss why denser sampling in the initial and final parts of the clustered signal may be useful.

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.

Staring Spotlight SAR with Nonlinear Frequency Modulation Signal and Azimuth Non-Uniform Sampling for Low Sidelobe Imaging.

In synthetic aperture radar (SAR) imaging, geometric resolution, sidelobe level (SLL) and signal-to-noise ratio (SNR) are the most important parameters for measuring the SAR image quality. The staring spotlight mode continuously transmits signals to a fixed area by steering the azimuth beam to acquire azimuth high geometric resolution, and its two-dimensional (2D) impulse response with the low SLL is usually obtained from the 2D weighted power spectral density (PSD) by the selected weighting window function. However, this results in the SNR reduction due to 2D amplitude window weighting. In this paper, the staring spotlight SAR with nonlinear frequency modulation (NLFM) signal and azimuth non-uniform sampling (ANUS) is proposed to obtain high geometric resolution SAR images with the low SLL and almost without any SNR reduction. The NLFM signal obtains non-equal interval frequency sampling points under uniform time sampling by adjusting the instantaneous chirp rate. Its corresponding PSD is similar to the weighting window function, and its pulse compression result without amplitude window weighting has low sidelobes. To obtain a similar Doppler frequency distribution for low sidelobe imaging in azimuth, the received SAR echoes are designed to be non-uniformly sampled in azimuth, in which the sampling sequence is dense in middle and sparse in both ends, and azimuth compression result with window weighting would also have low sidelobes. According to the echo model of the proposed imaging mode, both the back projection algorithm (BPA) and range migration algorithm (RMA) are modified and presented to handle the raw data of the proposed imaging mode. Both imaging results on simulated targets and experimental real SAR data processing results of a ground-based radar validate the proposed low sidelobe imaging mode.

Toward an Estimation of the Optical Feedback Factor C on the Fly for Displacement Sensing.

In this paper, a method based on the inherent event-based sampling capability of laser optical feedback interferometry (OFI) is proposed to assess the optical feedback factor C when the laser operates in the moderate and strong feedback regimes. Most of the phase unwrapping open-loop OFI algorithms rely on the estimation of C to retrieve the displacement with nanometric precision. Here, the proposed method operates in open-loop configuration and relies only on OFI's fringe detection, thereby improving its robustness and ease of use. The proposed method is able to estimate C with a precision of <5%. The obtained performances are compared to three different approaches previously published and the impacts of phase noise and sampling frequency are reported. We also show that this method can assess C on the fly even when C is varying due to speckle. To the best of the authors' knowledge, these are the first reported results of time-varying C estimation. In addition, through C estimation over time, it could pave the way not only to higher performance phase unwrapping algorithms but also to a better control of the optical feedback level via the use of an adaptive lens and thus to better displacement retrieval performances.

Remaining Useful Life Estimation for Engineered Systems Operating under Uncertainty with Causal GraphNets.

In this work, a novel approach, termed GNN-tCNN, is presented for the construction and training of Remaining Useful Life (RUL) models. The method exploits Graph Neural Networks (GNNs) and deals with the problem of efficiently learning from time series with non-equidistant observations, which may span multiple temporal scales. The efficacy of the method is demonstrated on a simulated stochastic degradation dataset and on a real-world accelerated life testing dataset for ball-bearings. The proposed method learns a model that describes the evolution of the system implicitly rather than at the raw observation level and is based on message-passing neural networks, which encode the irregularly sampled causal structure. The proposed approach is compared to a recurrent network with a temporal convolutional feature extractor head (LSTM-tCNN), which forms a viable alternative for the problem considered. Finally, by taking advantage of recent advances in the computation of reparametrization gradients for learning probability distributions, a simple, yet efficient, technique is employed for representing prediction uncertainty as a gamma distribution over RUL predictions.

Diagnostic Interpretation of Non-Uniformly Sampled Electrocardiogram.

We present a set of three fundamental methods for electrocardiogram (ECG) diagnostic interpretation adapted to process non-uniformly sampled signal. The growing volume of ECGs recorded daily all over the world (roughly estimated to be 600 TB) and the expectance of long persistence of these data (on the order of 40 years) motivated us to challenge the feasibility of medical-grade diagnostics directly based on arbitrary non-uniform (i.e., storage-efficient) ECG representation. We used a refined time-independent QRS detection method based on a moving shape matching technique. We applied a graph data representation to quantify the similarity of asynchronously sampled heartbeats. Finally, we applied a correlation-based non-uniform to time-scale transform to get a multiresolution ECG representation on a regular dyadic grid and to find precise P, QRS and T wave delimitation points. The whole processing chain was implemented and tested with MIT-BIH Database (probably the most referenced cardiac database) and CSE Multilead Database (used for conformance testing of medical instruments) signals arbitrarily sampled accordingly to a perceptual model (set for variable sampling frequency of 100-500 Hz, compression ratio 3.1). The QRS detection shows an accuracy of 99.93% with false detection ratio of only 0.18%. The classification shows an accuracy of 99.27% for 14 most frequent MIT-BIH beat types and 99.37% according to AAMI beat labels. The wave delineation shows cumulative (i.e., sampling model and non-uniform processing) errors of: 9.7 ms for P wave duration, 3.4 ms for QRS, 6.7 ms for P-Q segment and 17.7 ms for Q-T segment, all the values being acceptable for medical-grade interpretive software.

Reducing the measurement time of exact NOEs by non-uniform sampling.

We have previously reported on the measurement of exact NOEs (eNOEs), which yield a wealth of additional information in comparison to conventional NOEs. We have used these eNOEs in a variety of applications, including calculating high-resolution structures of proteins and RNA molecules. The collection of eNOEs is challenging, however, due to the need to measure a NOESY buildup series consisting of typically four NOESY spectra with varying mixing times in a single measurement session. While the 2D version can be completed in a few days, a fully sampled 3D-NOESY buildup series can take 10 days or more to acquire. This can be both expensive as well as problematic in the case of samples that are not stable over such a long period of time. One potential method to significantly decrease the required measurement time of eNOEs is to use non-uniform sampling (NUS) to decrease the number of points measured in the indirect dimensions. The effect of NUS on the extremely tight distance restraints extracted from eNOEs may be very pronounced. Therefore, we investigated the fidelity of eNOEs measured from three test cases at decreasing NUS densities: the 18.4 kDa protein human Pin1, the 4.1 kDa WW domain of Pin1 (both in 3D), and a 4.6 kDa 14mer RNA UUCG tetraloop (2D). Our results show that NUS imparted negligible error on the eNOE distances derived from good quality data down to 10% sampling for all three cases, but there is a noticeable decrease in the eNOE yield that is dependent upon the underlying sparsity, and thus complexity, of the sample. For Pin1, this transition occurred at roughly 40% while for the WW domain and the UUCG tetraloop it occurred at lower NUS densities of 20% and 10%, respectively. We rationalized these numbers through reconstruction simulations under various conditions. The extent of this loss depends upon the number of scans taken as well as the number of peaks to be reconstructed. Based on these findings, we have created guidelines for choosing an optimal NUS density depending on the number of peaks needed to be reconstructed in the densest region of a 2D or 3D NOESY spectrum.

Non-uniform sampling in quantitative assessment of heterogeneous solid-state NMR line shapes.

Non-uniform sampling has been successfully used for solution and solid-state NMR of homogeneous samples. In the solid state, protein samples are often dominated by inhomogeneous contributions to the homogeneous line widths. In spite of different technical strategies for peak reconstruction by different methods, we validate that NUS can generally be used also for such situations where spectra are made up of complex peak shapes rather than Lorentian lines. Using the RMSD between subsampled and reconstructed data and those spectra obtained with uniform sampling for a sample comprising a wide conformational distribution, we quantitatively evaluate the identity of inhomogeneous peak patterns. The evaluation comprises Iterative Soft Thresholding (hmsIST implementation) as a method explicitly not assuming Lorentian lineshapes, as well as Sparse Multidimensional Iterative Lineshape Enhanced (SMILE) algorithm and Signal Separation Algorithm (SSA) reconstruction, which do work on the basis of Lorentian lineshape models, with different sampling densities. Even though individual peculiarities are apparent, all methods turn out principally viable to reconstruct the heterogeneously broadened peak shapes.

Boosting the resolution of low-field [Formula: see text] relaxation experiments on intrinsically disordered proteins with triple-resonance NMR.

Improving our understanding of nanosecond motions in disordered proteins requires the enhanced sampling of the spectral density function obtained from relaxation at low magnetic fields. High-resolution relaxometry and two-field NMR measurements of relaxation have, so far, only been based on the recording of one- or two-dimensional spectra, which provide insufficient resolution for challenging disordered proteins. Here, we introduce a 3D-HNCO-based two-field NMR experiment for measurements of protein backbone [Formula: see text] amide longitudinal relaxation rates. The experiment provides accurate longitudinal relaxation rates at low field (0.33 T in our case) preserving the resolution and sensitivity typical for high-field NMR spectroscopy. Radiofrequency pulses applied on six different radiofrequency channels are used to manipulate the spin system at both fields. The experiment was demonstrated on the C-terminal domain of [Formula: see text] subunit of RNA polymerase from Bacillus subtilis, a protein with highly repetitive amino-acid sequence and very low dispersion of backbone chemical shifts.

Sensitivity-enhanced three-dimensional and carbon-detected two-dimensional NMR of proteins using hyperpolarized water.

Signal enhancements of up to two orders of magnitude in protein NMR can be achieved by employing HDO as a vector to introduce hyperpolarization into folded or intrinsically disordered proteins. In this approach, hyperpolarized HDO produced by dissolution-dynamic nuclear polarization (D-DNP) is mixed with a protein solution waiting in a high-field NMR spectrometer, whereupon amide proton exchange and nuclear Overhauser effects (NOE) transfer hyperpolarization to the protein and enable acquisition of a signal-enhanced high-resolution spectrum. To date, the use of this strategy has been limited to 1D and 1H-15N 2D correlation experiments. Here we introduce 2D 13C-detected D-DNP, to reduce exchange-induced broadening and other relaxation penalties that can adversely affect proton-detected D-DNP experiments. We also introduce hyperpolarized 3D spectroscopy, opening the possibility of D-DNP studies of larger proteins and IDPs, where assignment and residue-specific investigation may be impeded by spectral crowding. The signal enhancements obtained depend in particular on the rates of chemical and magnetic exchange of the observed residues, thus resulting in non-uniform 'hyperpolarization-selective' signal enhancements. The resulting spectral sparsity, however, makes it possible to resolve and monitor individual amino acids in IDPs of over 200 residues at acquisition times of just over a minute. We apply the proposed experiments to two model systems: the compactly folded protein ubiquitin, and the intrinsically disordered protein (IDP) osteopontin (OPN).

Amino-acid selective isotope labeling enables simultaneous overlapping signal decomposition and information extraction from NMR spectra.

Signal overlapping is a major bottleneck for protein NMR analysis. We propose a new method, stable-isotope-assisted parameter extraction (SiPex), to resolve overlapping signals by a combination of amino-acid selective isotope labeling (AASIL) and tensor decomposition. The basic idea of Sipex is that overlapping signals can be decomposed with the help of intensity patterns derived from quantitative fractional AASIL, which also provides amino-acid information. In SiPex, spectra for protein characterization, such as 15N relaxation measurements, are assembled with those for amino-acid information to form a four-order tensor, where the intensity patterns from AASIL contribute to high decomposition performance even if the signals share similar chemical shift values or characterization profiles, such as relaxation curves. The loading vectors of each decomposed component, corresponding to an amide group, represent both the amino-acid and relaxation information. This information link provides an alternative protein analysis method that does not require "assignments" in a general sense; i.e., chemical shift determinations, since the amino-acid information for some of the residues allows unambiguous assignment according to the dual selective labeling. SiPex can also decompose signals in time-domain raw data without Fourier transform, even in non-uniformly sampled data without spectral reconstruction. These features of SiPex should expand biological NMR applications by overcoming their overlapping and assignment problems.