Accelerated NMR Spectroscopy by Using Compressed Sensing

Disease-linked mutations cause exposure of a protein quality control degron

More than half of disease-causing missense variants are thought to lead to protein degradation, but the molecular mechanism of how these variants are recognized by the cell remains enigmatic. Degrons are stretches of amino acids that help mediate recognition by E3 ligases and thus confer protein degradation via the ubiquitin-proteasome system. While degrons that mediate controlled degradation of, for example, signaling components and cell-cycle regulators are well described, so-called protein-quality-control degrons that mediate the degradation of destabilized proteins are poorly understood. Here, we show that disease-linked dihydrofolate reductase (DHFR) missense variants are structurally destabilized and chaperone-dependent proteasome targets. We find two regions in DHFR that act as degrons, and the proteasomal turnover of one of these was dependent on the molecular chaperone Hsp70. Structural analyses by nuclear magnetic resonance (NMR) and hydrogen/deuterium exchange revealed that this degron is buried in wild-type DHFR but becomes transiently exposed in the disease-linked missense variants.

A General Reconstruction Method for Multidimensional Sparse Sampling Nuclear Magnetic Resonance Spectroscopy

Multidimensional NMR spectroscopy provides a powerful tool for structure elucidation and dynamic analysis of complex samples, particularly for biological macromolecules. Multidimensional sparse sampling effectively accelerates NMR experiments while an efficient reconstruction method is generally required for unraveling spectra. Various reconstruction methods were proposed for pure Fourier NMR (only involving chemical shifts and J couplings detection). However, reconstruction concerned with Laplace-related NMR (i.e., involving relaxation or diffusion detection) is more challenging due to its ill-posed property. The existing Laplace-related NMR sparse sampling reconstruction methods suffer from poor resolution and possible artifacts in the resulting spectra owing to the pitfalls of the optimization algorithms. Herein, we propose a general approach for fast high-resolution reconstruction of multidimensional sparse sampling NMR, including pure Fourier, mixed Fourier-Laplace, and pure Laplace NMR, benefiting from the comprehensive sparse constraint and effective optimization algorithm and thus showing the promising prospects of multidimensional NMR.

Definition of the immune evasion-replication interface of rabies virus P protein

Rabies virus phosphoprotein (P protein) is a multifunctional protein that plays key roles in replication as the polymerase cofactor that binds to the complex of viral genomic RNA and the nucleoprotein (N protein), and in evading the innate immune response by binding to STAT transcription factors. These interactions are mediated by the C-terminal domain of P (P_CTD). The colocation of these binding sites in the small globular P_CTD raises the question of how these interactions underlying replication and immune evasion, central to viral infection, are coordinated and, potentially, coregulated. While direct data on the binding interface of the P_CTD for STAT1 is available, the lack of direct structural data on the sites that bind N protein limits our understanding of this interaction hub. The P_CTD was proposed to bind via two sites to a flexible loop of N protein (N_pep) that is not visible in crystal structures, but no direct analysis of this interaction has been reported. Here we use Nuclear Magnetic Resonance, and molecular modelling to show N protein residues, Leu381, Asp383, Asp384 and phosphor-Ser389, are likely to bind to a ‘positive patch’ of the P_CTD formed by Lys211, Lys214 and Arg260. Furthermore, in contrast to previous predictions we identify a single site of interaction on the P_CTD by this N_pep. Intriguingly, this site is proximal to the defined STAT1 binding site that includes Ile201 to Phe209. However, cell-based assays indicate that STAT1 and N protein do not compete for P protein. Thus, it appears that interactions critical to replication and immune evasion can occur simultaneously with the same molecules of P protein so that the binding of P protein to activated STAT1 can potentially occur without interrupting interactions involved in replication. These data suggest that replication complexes might be directly involved in STAT1 antagonism.

For viruses to infect cells and generate progeny, they must be able to mediate replication, while simultaneously evading the innate immune system. Viruses with small genomes often achieve this through multifunctional proteins that have roles in both replication and immune evasion, such as the phosphoprotein (P protein) of rabies virus. P protein is an essential cofactor in genome replication and transcription, dependent on the well-folded C-terminal domain (P_CTD), which binds to the nucleoprotein (N protein) when complexed with RNA. The P_CTD can also bind and antagonize signal transducers and activators of transcription (STAT) proteins, that are essential for activating antiviral mechanisms. Here we show using Nuclear Magnetic Resonance spectroscopy and cell-based assays, that the STAT1-binding and N-binding interfaces are proximal but, nevertheless, it appears that the same molecule of P_CTD can simultaneously bind STAT1 and N protein. These data suggest that P-protein-STAT1 interaction, critical to immune evasion, can occur without interrupting interactions underlying replication, and so replication complexes might be directly involved in STAT1 antagonism.

Temperature as an Extra Dimension in Multidimensional Protein NMR Spectroscopy

NMR spectroscopy is a particularly informative method for studying protein structures and dynamics in solution; however, it is also one of the most time-consuming. Modern approaches to biomolecular NMR spectroscopy are based on lengthy multidimensional experiments, the duration of which grows exponentially with the number of dimensions. The experimental time may even be several days in the case of 3D and 4D spectra. Moreover, the experiment often has to be repeated under several different conditions, for example, to measure the temperature-dependent effects in a spectrum (temperature coefficients (TCs)). Herein, a new approach that involves joint sampling of indirect evolution times and temperature is proposed. This allows TCs to be measured through 3D spectra in even less time than that needed to acquire a single spectrum by using the conventional approach. Two signal processing methods that are complementary, in terms of sensitivity and resolution, 1) dividing data into overlapping subsets followed by compressed sensing reconstruction, and 2) treating the complete data set with a variant of the Radon transform, are proposed. The temperature-swept 3D HNCO spectra of two intrinsically disordered proteins, osteopontin and CD44 cytoplasmic tail, show that this new approach makes it possible to determine TCs and their non-linearities effectively. Non-linearities, which indicate the presence of a compact state, are particularly interesting. The complete package of data acquisition and processing software for this new approach are provided.

Non-Stationary Complementary Non-Uniform Sampling (NOSCO NUS) for Fast Acquisition of Serial 2D NMR Titration Data

NMR spectroscopy offers unique benefits for ligand binding studies on isotopically labelled target proteins. These benefits include atomic resolution, direct distinction of binding sites and modes, a lowest detectable affinity limit, and function independent setup. Yet, retracing protein signal assignments from apo to holo states to derive exact dissociation constants and chemical shift perturbation amplitudes (for ligand docking and structure‐based optimization) requires lengthy titration series of 2D heteronuclear correlation spectra at variable ligand concentration that may exceed the protein's lifetime and available spectrometer time. We present a novel method to overcome this critical limitation, based on non‐stationary complementary non‐uniform sampling (NOSCO NUS) combined with a robust particle swarm optimization algorithm. We illustrate its potential in two challenging studies with very distinct protein sizes and binding affinities, showing that NOSCO NUS can reduce measurement times by an order of magnitude to make such highly informative NMR titration studies more broadly feasible.

Review and Prospect: Deep Learning in Nuclear Magnetic Resonance Spectroscopy

Since the concept of deep learning (DL) was formally proposed in 2006, it has had a major impact on academic research and industry. Nowadays, DL provides an unprecedented way to analyze and process data with demonstrated great results in computer vision, medical imaging, natural language processing, and so forth. Herein, applications of DL in NMR spectroscopy are summarized, and a perspective for DL as an entirely new approach that is likely to transform NMR spectroscopy into a much more efficient and powerful technique in chemistry and life sciences is outlined.

Accelerated Nuclear Magnetic Resonance Spectroscopy with Deep Learning

Nuclear magnetic resonance (NMR) spectroscopy serves as an indispensable tool in chemistry and biology but often suffers from long experimental times. We present a proof-of-concept of the application of deep learning and neural networks for high-quality, reliable, and very fast NMR spectra reconstruction from limited experimental data. We show that the neural network training can be achieved using solely synthetic NMR signals, which lifts the prohibiting demand for a large volume of realistic training data usually required for a deep learning approach.

Combining rapid 2D NMR experiments with novel pre-processing workflows and MIC quality measures for metabolomics

INTRODUCTION

The use of 2D NMR data sources (COSY in this paper) allows to reach general metabolomics results which are at least as good as the results obtained with 1D NMR data, and this with a less advanced and less complex level of pre-processing. But a major issue still exists and can largely slow down a generalized use of 2D data sources in metabolomics: the experiment duration.

OBJECTIVE

The goal of this paper is to overcome the experiment duration issue in our recently published MIC strategy by considering faster 2D COSY acquisition techniques: a conventional COSY with a reduced number of transients and the use of the Non-Uniform Sampling (NUS) method. These faster alternatives are all submitted to novel 2D pre-processing workflows and to Metabolomic Informative Content analyses. Eventually, results are compared to those obtained with conventional COSY spectra.

METHODS

To pre-process the 2D data sources, the Global Peak List (GPL) workflow and the Vectorization workflow are used. To compare this data sources and to detect the more informative one(s), MIC (Metabolomic Informative Content) indexes are used, based on clustering and inertia measures of quality.

RESULTS

Results are discussed according to a multi-factor experimental design (which is unsupervised and based on human urine samples). Descriptive PCA results and MIC indexes are shown, leading to the direct and objective comparison of the different data sets.

CONCLUSION

In conclusion, it is demonstrated that conventional COSY spectra recorded with only one transient per increment and COSY spectra recorded with 50% of non-uniform sampling provide very similar MIC results as the initial COSY recorded with four transients, but in a much shorter time. Consequently, using techniques like the reduction of the number of transients or NUS can really open the door to a potential high-throughput use of 2D COSY spectra in metabolomics.

Accelerating 2D NMR relaxation dispersion experiments using iterated maps

NMR relaxation dispersion experiments play a central role in exploring molecular motion over an important range of timescales, and are an example of a broader class of multidimensional NMR experiments that probe important biomolecules. However, resolving the spectral features of these experiments using the Fourier transform requires sampling the full Nyquist grid of data, making these experiments very costly in time. Practitioners often reduce the experiment time by omitting 1D experiments in the indirectly observed dimensions, and reconstructing the spectra using one of a variety of post-processing algorithms. In prior work, we described a fast, Fourier-based reconstruction method using iterated maps according to the Difference Map algorithm of Veit Elser (DiffMap). Here we describe coDiffMap, a new reconstruction method that is based on DiffMap, but which exploits the strong correlations between 2D data slices in a pseudo-3D experiment. We apply coDiffMap to reconstruct dispersion curves from an [Formula: see text] relaxation dispersion experiment, and demonstrate that the method provides fast reconstructions and accurate relaxation curves down to very low numbers of sparsely-sampled data points.

Reaching the sparse-sampling limit for reconstructing a single peak in a 2D NMR spectrum using iterated maps

Many of the ubiquitous experiments of biomolecular NMR, including [Formula: see text], [Formula: see text], and CEST, involve acquiring repeated 2D spectra under slightly different conditions. Such experiments are amenable to acceleration using non-uniform sampling spectral reconstruction methods that take advantage of prior information. We previously developed one such technique, an iterated maps method (DiffMap) that we successfully applied to 2D NMR spectra, including [Formula: see text] relaxation dispersion data. In that prior work, we took a top-down approach to reconstructing the 2D spectrum with a minimal number of sparse samples, reaching an undersampling fraction that appeared to leave some room for improvement. In this study, we develop an in-depth understanding of the action of the DiffMap algorithm, identifying the factors that cause reconstruction errors for different undersampling fractions. This improved understanding allows us to formulate a bottom-up approach to finding the lowest number of sparse samples required to accurately reconstruct individual spectral features with DiffMap. We also discuss the difficulty of extending this method to reconstructing many peaks at once, and suggest a way forward.

XLSY: Extra-Large NMR Spectroscopy

NMR studies of intrinsically disordered proteins and other complex biomolecular systems require spectra with the highest resolution and dimensionality. An efficient approach, extra‐large NMR spectroscopy, is presented for experimental data collection, reconstruction, and handling of very large NMR spectra by a combination of the radial and non‐uniform sampling, a new processing algorithm, and rigorous statistical validation. We demonstrate the first high‐quality reconstruction of a full seven‐dimensional HNCOCACONH and two five‐dimensional HACACONH and HN(CA)CONH experiments for a representative intrinsically disordered protein α‐synuclein. XLSY will significantly enhance the NMR toolbox in challenging biomolecular studies.

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.

Bacteriophage Tail-Tube Assembly Studied by Proton-Detected 4D Solid-State NMR

Obtaining unambiguous resonance assignments remains a major bottleneck in solid-state NMR studies of protein structure and dynamics. Particularly for supramolecular assemblies with large subunits (>150 residues), the analysis of crowded spectral data presents a challenge, even if three-dimensional (3D) spectra are used. Here, we present a proton-detected 4D solid-state NMR assignment procedure that is tailored for large assemblies. The key to recording 4D spectra with three indirect carbon or nitrogen dimensions with their inherently large chemical shift dispersion lies in the use of sparse non-uniform sampling (as low as 2 %). As a proof of principle, we acquired 4D (H)COCANH, (H)CACONH, and (H)CBCANH spectra of the 20 kDa bacteriophage tail-tube protein gp17.1 in a total time of two and a half weeks. These spectra were sufficient to obtain complete resonance assignments in a straightforward manner without use of previous solution NMR data.

Absolute Minimal Sampling of Homonuclear 2D NMR TOCSY Spectra for High-Throughput Applications of Complex Mixtures

Modern applications of 2D NMR spectroscopy to diagnostic screening, metabolomics, quality control, and other high-throughput applications are often limited by the time-consuming sampling requirements along the indirect time domain t1 . 2D total correlation spectroscopy (TOCSY) provides unique spin connectivity information for the analysis of a large number of compounds in complex mixtures, but standard methods typically require >100 t1 increments for an accurate spectral reconstruction, rendering these experiments ineffective for high-throughput applications. For a complex metabolite mixture it is demonstrated that absolute minimal sampling (AMS), based on direct fitting of resonance frequencies and amplitudes in the time domain, yields an accurate spectral reconstruction of TOCSY spectra using as few as 16 t1 points. This permits the rapid collection of homonuclear 2D NMR experiments at high resolution with measurement times that previously were only the realm of 1D experiments.

Pitfalls in compressed sensing reconstruction and how to avoid them

Multidimensional NMR can provide unmatched spectral resolution, which is crucial when dealing with samples of biological macromolecules. The resolution, however, comes at the high price of long experimental time. Non-uniform sampling (NUS) of the evolution time domain allows to suppress this limitation by sampling only a small fraction of the data, but requires sophisticated algorithms to reconstruct omitted data points. A significant group of such algorithms known as compressed sensing (CS) is based on the assumption of sparsity of a reconstructed spectrum. Several papers on the application of CS in multidimensional NMR have been published in the last years, and the developed methods have been implemented in most spectral processing software. However, the publications rarely show the cases when NUS reconstruction does not work perfectly or explain how to solve the problem. On the other hand, every-day users of NUS develop their rules-of-thumb, which help to set up the processing in an optimal way, but often without a deeper insight. In this paper, we discuss several sources of problems faced in CS reconstructions: low sampling level, missassumption of spectral sparsity, wrong stopping criterion and attempts to extrapolate the signal too much. As an appendix, we provide MATLAB codes of several CS algorithms used in NMR. We hope that this work will explain the mechanism of NUS reconstructions and help readers to set up acquisition and processing parameters. Also, we believe that it might be helpful for algorithm developers.

Absolute Minimal Sampling in High-Dimensional NMR Spectroscopy

Standard three-dimensional Fourier transform (FT) NMR experiments of molecular systems often involve prolonged measurement times due to extensive sampling required along the indirect time domains to obtain adequate spectral resolution. In recent years, a wealth of alternative sampling methods has been proposed to ease this bottleneck. However, due to their algorithmic complexity, for a given sample and experiment it is often hard to determine the minimal sampling requirement, and hence the maximal achievable experimental speed up. Herein we introduce an absolute minimal sampling (AMS) method that can be applied to common 3D NMR experiments. We show for the proteins ubiquitin and arginine kinase that for widely used experiments, such as 3D HNCO, accurate carbon frequencies can be obtained with a single time increment, while for others, such as 3D HN(CA)CO, all relevant information is obtained with as few as 6 increments amounting to a speed up of a factor 7-50.

A Set of Efficient nD NMR Protocols for Resonance Assignments of Intrinsically Disordered Proteins

The RF pulse scheme RN[N-CA HEHAHA]NH, which provides a convenient approach to the acquisition of different multidimensional chemical shift correlation NMR spectra leading to backbone resonance assignments, including those of the proline residues of intrinsically disordered proteins (IDPs), is experimentally demonstrated. Depending on the type of correlation data required, the method involves the generation of in-phase ((15) N)(x) magnetisation via different magnetisation transfer pathways such as H→N→CO→N, HA→CA→CO→N, H→N→CA→N and H→CA→N, the subsequent application of (15) N-(13) C(α) heteronuclear Hartmann-Hahn mixing over a period of ≈100 ms, chemical-shift labelling of relevant nuclei before and after the heteronuclear mixing step and amide proton detection in the acquisition dimension. It makes use of the favourable relaxation properties of IDPs and the presence of (1) JCαN and (2) JCαN couplings to achieve efficient correlation of the backbone resonances of each amino acid residue "i" with the backbone amide resonances of residues "i-1" and "i+1". It can be implemented in a straightforward way through simple modifications of the RF pulse schemes commonly employed in protein NMR studies. The efficacy of the approach is demonstrated using a uniformly ((15) N,(13) C) labelled sample of α-synuclein. The different possibilities for obtaining the amino-acid-type information, simultaneously with the connectivity data between the backbone resonances of sequentially neighbouring residues, have also been outlined.

Artifacts in time-resolved NUS: A case study of NOE build-up curves from 2D NOESY

Multidimensional NMR spectroscopy requires time-consuming sampling of indirect dimensions and so is usually used to study stable samples. However, dynamically changing compounds or their mixtures commonly occur in problems of natural science. Monitoring them requires the use multidimensional NMR in a time-resolved manner - in other words, a series of quick spectra must be acquired at different points in time. Among the many solutions that have been proposed to achieve this goal, time-resolved non-uniform sampling (TR-NUS) is one of the simplest. In a TR-NUS experiment, the signal is sampled using a shuffled random schedule and then divided into overlapping subsets. These subsets are then processed using one of the NUS reconstruction methods, for example compressed sensing (CS). The resulting stack of spectra forms a temporal "pseudo-dimension" that shows the changes caused by the process occurring in the sample. CS enables the use of small subsets of data, which minimizes the averaging of the effects studied. Yet, even within these limited timeframes, the sample undergoes certain changes. In this paper we discuss the effect of varying signal amplitude in a TR-NUS experiment. Our theoretical calculations show that the variations within the subsets lead to t1-noise, which is dependent on the rate of change of the signal amplitude. We verify these predictions experimentally. As a model case we choose a novel 2D TR-NOESY experiment in which mixing time is varied in parallel with shuffled NUS in the indirect dimension. The experiment, performed on a sample of strychnine, provides a near-continuous NOE build-up curve, whose shape closely reflects the t1-noise level. 2D TR-NOESY reduces the measurement time compared to the conventional approach and makes it possible to verify the theoretical predictions about signal variations during TR-NUS.

Fast acquisition of multidimensional NMR spectra of solids and mesophases using alternative sampling methods

Unique information about the atom-level structure and dynamics of solids and mesophases can be obtained by the use of multidimensional nuclear magnetic resonance (NMR) experiments. Nevertheless, the acquisition of these experiments often requires long acquisition times. We review here alternative sampling methods, which have been proposed to circumvent this issue in the case of solids and mesophases. Compared to the spectra of solutions, those of solids and mesophases present some specificities because they usually display lower signal-to-noise ratios, non-Lorentzian line shapes, lower spectral resolutions and wider spectral widths. We highlight herein the advantages and limitations of these alternative sampling methods. A first route to accelerate the acquisition time of multidimensional NMR spectra consists in the use of sparse sampling schemes, such as truncated, radial or random sampling ones. These sparsely sampled datasets are generally processed by reconstruction methods differing from the Discrete Fourier Transform (DFT). A host of non-DFT methods have been applied for solids and mesophases, including the G-matrix Fourier transform, the linear least-square procedures, the covariance transform, the maximum entropy and the compressed sensing. A second class of alternative sampling consists in departing from the Jeener paradigm for multidimensional NMR experiments. These non-Jeener methods include Hadamard spectroscopy as well as spatial or orientational encoding of the evolution frequencies. The increasing number of high field NMR magnets and the development of techniques to enhance NMR sensitivity will contribute to widen the use of these alternative sampling methods for the study of solids and mesophases in the coming years.

Non-Uniform Sampling and J-UNIO Automation for Efficient Protein NMR Structure Determination

High-resolution structure determination of small proteins in solution is one of the big assets of NMR spectroscopy in structural biology. Improvements in the efficiency of NMR structure determination by advances in NMR experiments and automation of data handling therefore attracts continued interest. Here, non-uniform sampling (NUS) of 3D heteronuclear-resolved [(1)H,(1)H]-NOESY data yielded two- to three-fold savings of instrument time for structure determinations of soluble proteins. With the 152-residue protein NP_372339.1 from Staphylococcus aureus and the 71-residue protein NP_346341.1 from Streptococcus pneumonia we show that high-quality structures can be obtained with NUS NMR data, which are equally well amenable to robust automated analysis as the corresponding uniformly sampled data.

Accelerated NMR spectroscopy with low-rank reconstruction

Accelerated multi-dimensional NMR spectroscopy is a prerequisite for high-throughput applications, studying short-lived molecular systems and monitoring chemical reactions in real time. Non-uniform sampling is a common approach to reduce the measurement time. Here, a new method for high-quality spectra reconstruction from non-uniformly sampled data is introduced, which is based on recent developments in the field of signal processing theory and uses the so far unexploited general property of the NMR signal, its low rank. Using experimental and simulated data, we demonstrate that the low-rank reconstruction is a viable alternative to the current state-of-the-art technique compressed sensing. In particular, the low-rank approach is good in preserving of low-intensity broad peaks, and thus increases the effective sensitivity in the reconstructed spectra.

Multi-phosphorylation of the intrinsically disordered unique domain of c-Src studied by in-cell and real-time NMR spectroscopy

Intrinsically disordered regions (IDRs) are preferred sites for post-translational modifications essential for regulating protein function. The enhanced local mobility of IDRs facilitates their observation by NMR spectroscopy in vivo. Phosphorylation events can occur at multiple sites and respond dynamically to changes in kinase-phosphatase networks. Here we used real-time NMR spectroscopy to study the effect of kinases and phosphatases present in Xenopus oocytes and egg extracts on the phosphorylation state of the "unique domain" of c-Src. We followed the phosphorylation of S17 in oocytes, and of S17, S69, and S75 in egg extracts by NMR spectroscopy, MS, and western blotting. Addition of specific kinase inhibitors showed that S75 and S69 are phosphorylated by CDKs (cyclin-dependent kinases) differently from Cdk1. Moreover, although PKA (cAMP-dependent protein kinase) can phosphorylate S17 in vitro, this was not the major S17 kinase in egg extracts. Changes in PKA activity affected the phosphorylation levels of CDK-dependent sites, thus suggesting indirect effects of kinase-phosphatase networks. This study provides a proof-of-concept of the use of real-time in vivo NMR spectroscopy to characterize kinase/phosphatase effects on intrinsically disordered regulatory domains.