Sensitivity of nonuniform sampling NMR

Enhancing Spectrometer Performance with Unsupervised Machine Learning

Solid-state NMR spectroscopy (SSNMR) is a powerful technique to probe structural and dynamic properties of biomolecules at an atomic level. Modern SSNMR methods employ multidimensional pulse sequences requiring data collection over a period of days to weeks. Variations in signal intensity or frequency due to environmental fluctuation introduce artifacts into the spectra. Therefore, it is critical to actively monitor instrumentation subject to fluctuations. Here, we demonstrate a method rooted in the unsupervised machine learning algorithm principal component analysis (PCA) to evaluate the impact of environmental parameters that affect sensitivity, resolution and peak positions (chemical shifts) in multidimensional SSNMR protein spectra. PCA loading spectra illustrate the unique features associated with each drifting parameter, while the PCA scores quantify the magnitude of parameter drift. This is demonstrated both for double (HC) and triple resonance (HCN) experiments. Furthermore, we apply this methodology to identify magnetic field B0 drift, and leverage PCA to "denoise" multidimensional SSNMR spectra of the membrane protein, EmrE, using several spectra collected over several days. Finally, we utilize PCA to identify changes in B1 (CP and decoupling) and B0 fields in a manner that we envision could be automated in the future. Overall, these approaches enable improved objectivity in monitoring NMR spectrometers, and are also applicable to other forms of spectroscopy.

Ultrafast Nuclear Magnetic Resonance as a Tool to Detect Rapid Chemical Change in Solution

Ultrafast nuclear magnetic resonance (NMR) uses spatial encoding to record an entire two-dimensional data set in just a single scan. The approach can be applied to either Fourier-transform or Laplace-transform NMR. In both cases, acquisition times are significantly shorter than traditional 2D/Laplace NMR experiments, which allows them to be used to monitor rapid chemical transformations. This Perspective outlines the principles of ultrafast NMR and focuses on examples of its use to detect fast molecular conversions in situ with high temporal resolution. We discuss how this valuable tool can be applied in the future to study a much wider variety of novel reactivity.

Solution Structure of Poly(UG) RNA

Poly(UG) or "pUG" RNAs are UG or GU dinucleotide repeat sequences which are highly abundant in eukaryotes. Post-transcriptional addition of pUGs to RNA 3' ends marks mRNAs as vectors for gene silencing in C. elegans. We previously determined the crystal structure of pUG RNA bound to the ligand N-methyl mesoporphyrin IX (NMM), but the structure of free pUG RNA is unknown. Here we report the solution structure of the free pUG RNA (GU)12, as determined by nuclear magnetic resonance spectroscopy and small and wide-angle x-ray scattering (NMR-SAXS-WAXS). The low complexity sequence and 4-fold symmetry of the structure result in overlapped NMR signals that complicate chemical shift assignment. We therefore utilized single site-specific deoxyribose modifications which did not perturb the structure and introduced well-resolved methylene signals that are easily identified in NMR spectra. The solution structure ensemble has a root mean squared deviation (RMSD) of 0.62 Å and is a compact, left-handed quadruplex with a Z-form backbone, or "pUG fold." Overall, the structure agrees with the crystal structure of (GU)12 bound to NMM, indicating the pUG fold is unaltered by docking of the NMM ligand. The solution structure reveals conformational details that could not be resolved by x-ray crystallography, which explain how the pUG fold can form within longer RNAs.

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.

Expanding the Limits of Structural Characterization of Marine Dissolved Organic Matter Using Nonuniform Sampling Frequency-Reversed Edited HSQC NMR

The multiplicity-edited heteronuclear single quantum correlation (ME-HSQC) NMR method is widely used for the structural characterization of marine dissolved organic matter (DOM), which is a complex molecular mixture comprising millions of individual compounds. However, the standard ME-HSQC suffers from significant signal cancellation and subsequent loss of crucial structural information due to the overlap between CH3/CH (positive) and CH2 (negative) cross-peaks in overcrowded regions. This study introduces nonuniform sampling in frequency-reversed ME-HSQC (NUS FR-ME-HSQC), highlighting its remarkable potential for the comprehensive structural characterization of marine DOM. By reversing the frequency of CH2 cross-peaks into an empty region, the FR-ME-HSQC method effectively simplifies the spectra and eliminates signal cancellation. We demonstrate that nonuniform sampling enables the acquisition of comparable spectra in half the time or significantly enhances the sensitivity in time-equivalent spectra. Comparative analysis also identifies vulnerable CH2 cross-peaks in the standard ME-HSQC that coincide with CH3 and CH cross-peaks, resulting in the loss of critical structural details. In contrast, the NUS FR-ME-HSQC retains these missing correlations, enabling in-depth characterization of marine DOM. These findings highlight the potential of NUS FR-ME-HSQC as an advanced NMR technique that effectively addresses challenges such as signal overcrowding and prolonged experimental times, enabling the thorough investigation of complex mixtures with implications in several fields, including chemistry, metabolomics, and environmental sciences. The advantages of NUS FR-ME-HSQC are experimentally demonstrated on two solid-phase-extracted DOM (SPE-DOM) samples from the surface and deep ocean. With this new technology, differences in the composition of DOM from various aquatic environments can be assigned to individual molecules.

nus-tool: A unified program for generating and analyzing sample schedules for nonuniformly sampled NMR experiments

Increases in digital resolution achieved by high-field NMR require increases in spectral width. Additionally, the ability to resolve two overlapping peaks requires a sufficiently long acquisition time. These constraints combine, so that achieving high resolution spectra on high-field magnets requires long experiment times when employing uniform sampling and Fourier Transform processing. These limitations may be addressed by using nonuniform sampling (NUS), but the complexity of the parameter space across the variety of available NUS schemes greatly hinders the establishment of optimal approaches and best practices. We address these challenges with nus-tool, which is a software package for generating and analyzing NUS schedules. The nus-tool software internally implements random sampling and exponentially biased sampling. Through pre-configured plug-ins, it also provides access to quantile sampling and Poisson gap sampling. The software computes the relative sensitivity, mean evolution time, point spread function, and peak-to-sidelobe ratio; all of which can be determined for a candidate sample schedule prior to running an experiment to verify expected sensitivity, resolution, and artifact suppression. The nus-tool package is freely available on the NMRbox platform through an interactive GUI and via the command line, which is especially useful for scripted workflows that investigate the effectiveness of various NUS schemes.

Sparse pseudocontact shift NMR data obtained from a non-canonical amino acid-linked lanthanide tag improves integral membrane protein structure prediction

A single experimental method alone often fails to provide the resolution, accuracy, and coverage needed to model integral membrane proteins (IMPs). Integrating computation with experimental data is a powerful approach to supplement missing structural information with atomic detail. We combine RosettaNMR with experimentally-derived paramagnetic NMR restraints to guide membrane protein structure prediction. We demonstrate this approach using the disulfide bond formation protein B (DsbB), an α-helical IMP. Here, we attached a cyclen-based paramagnetic lanthanide tag to an engineered non-canonical amino acid (ncAA) using a copper-catalyzed azide-alkyne cycloaddition (CuAAC) click chemistry reaction. Using this tagging strategy, we collected 203 backbone HN pseudocontact shifts (PCSs) for three different labeling sites and used these as input to guide de novo membrane protein structure prediction protocols in Rosetta. We find that this sparse PCS dataset combined with 44 long-range NOEs as restraints in our calculations improves structure prediction of DsbB by enhancements in model accuracy, sampling, and scoring. The inclusion of this PCS dataset improved the Cα-RMSD transmembrane segment values of the best-scoring and best-RMSD models from 9.57 Å and 3.06 Å (no NMR data) to 5.73 Å and 2.18 Å, respectively.

Primary Structure of Glycans by NMR Spectroscopy

Glycans, carbohydrate molecules in the realm of biology, are present as biomedically important glycoconjugates and a characteristic aspect is that their structures in many instances are branched. In determining the primary structure of a glycan, the sugar components including the absolute configuration and ring form, anomeric configuration, linkage(s), sequence, and substituents should be elucidated. Solution state NMR spectroscopy offers a unique opportunity to resolve all these aspects at atomic resolution. During the last two decades, advancement of both NMR experiments and spectrometer hardware have made it possible to unravel carbohydrate structure more efficiently. These developments applicable to glycans include, inter alia, NMR experiments that reduce spectral overlap, use selective excitations, record tilted projections of multidimensional spectra, acquire spectra by multiple receivers, utilize polarization by fast-pulsing techniques, concatenate pulse-sequence modules to acquire several spectra in a single measurement, acquire pure shift correlated spectra devoid of scalar couplings, employ stable isotope labeling to efficiently obtain homo- and/or heteronuclear correlations, as well as those that rely on dipolar cross-correlated interactions for sequential information. Refined computer programs for NMR spin simulation and chemical shift prediction aid the structural elucidation of glycans, which are notorious for their limited spectral dispersion. Hardware developments include cryogenically cold probes and dynamic nuclear polarization techniques, both resulting in enhanced sensitivity as well as ultrahigh field NMR spectrometers with a 1H NMR resonance frequency higher than 1 GHz, thus improving resolution of resonances. Taken together, the developments have made and will in the future make it possible to elucidate carbohydrate structure in great detail, thereby forming the basis for understanding of how glycans interact with other molecules.

Magic-angle-spinning NMR structure of the kinesin-1 motor domain assembled with microtubules reveals the elusive neck linker orientation

Microtubules (MTs) and their associated proteins play essential roles in maintaining cell structure, organelle transport, cell motility, and cell division. Two motors, kinesin and cytoplasmic dynein link the MT network to transported cargos using ATP for force generation. Here, we report an all-atom NMR structure of nucleotide-free kinesin-1 motor domain (apo-KIF5B) in complex with paclitaxel-stabilized microtubules using magic-angle-spinning (MAS) NMR spectroscopy. The structure reveals the position and orientation of the functionally important neck linker and how ADP induces structural and dynamic changes that ensue in the neck linker. These results demonstrate that the neck linker is in the undocked conformation and oriented in the direction opposite to the KIF5B movement. Chemical shift perturbations and intensity changes indicate that a significant portion of ADP-KIF5B is in the neck linker docked state. This study also highlights the unique capability of MAS NMR to provide atomic-level information on dynamic regions of biological assemblies.

Accelerating quantitative 13C NMR spectra using an EXtended ACquisition Time (EXACT) method

Accurate quantitative ¹³C NMR spectra can be accelerated by using EXACT (EXtended ACquisition Time) NMR methods which reduce Nuclear Overhauser Enhancement (NOE) during the FID. This allows 30-50% shorter experiment times to be used when achieving a given level of quantitative accuracy.

Spectroscopic signatures of bilayer ordering in native biological membranes

Membrane proteins and polycyclic lipids like cholesterol and hopanoids coordinate phospholipid bilayer ordering. This phenomenon manifests as partitioning of the liquid crystalline phase into liquid-ordered (Lo) and liquid-disordered (Ld) regions. In Eukaryotes, microdomains are rich in cholesterol and sphingolipids and serve as signal transduction scaffolds. In Prokaryotes, Lo microdomains increase pathogenicity and antimicrobial resistance. Previously, we identified spectroscopically distinct chemical shift signatures for all-trans (AT) and trans-gauche (TG) acyl chain conformations, cyclopropyl ring lipids (CPR), and hopanoids in prokaryotic lipid extracts and used Polarization Transfer (PT) SSNMR to investigate bilayer ordering. To investigate how these findings relate to native bilayer organization, we interrogate whole cell and whole membrane extract samples of Burkholderia thailendensis to investigate bilayer ordering in situ. In 13C-13C 2D SSNMR spectra, we assigned chemical shifts for lipid species in both samples, showing conservation of lipids of interest in our native membrane sample. A one-dimensional temperature series of PT SSNMR and transverse relaxation measurements of AT versus TG acyl conformations in the membrane sample confirm bilayer ordering and a broadened phase transition centered at a lower-than-expected temperature. Bulk protein backbone Cα dynamics and correlations consistent with lipid-protein contacts within are further indicative of microdomain formation and lipid ordering. In aggregate, these findings provide evidence for microdomain formation in vivo and provide insight into phase separation and transition mechanics in biological membranes.

High fidelity sampling schedules for NMR spectra of high dynamic range

The ability to reconstruct non-uniformly sampled (NUS) NMR spectra has mostly been accepted. Still a concern is lingering regarding artifacts from sampling non-uniformly. As experienced, some sampling schedules yield better results than others. Finding a useful schedule is relatively trivial for a low dynamic range spectrum and a conservative sparsity, but not so when the dynamic range is large and/or when extreme sparsity is used. High dynamic range is typically found in NOESY and spectra of metabolites, where quantification of peak heights is desired at high fidelity. Extreme sparsity is desired when high throughput is a goal. In all cases, selecting a poor sampling schedule can create unnecessary artifacts. Effectively, it is important to select a sampling schedule that provides a signal-to-artifact apex ratio (SAAR) value in par or better than the signal-to-noise ratio (SNR) value. Notably, by signal-to-artifact apex ratio we consider reconstruction fidelity as the apex intensity likeness, i.e., as the true signal to the tallest artifact. We show that the quality of reconstruction depends on the particular sampling schedule. We evaluate the reconstruction quality in the frequency domain following a matched Lorentz-to-Gauss transform plus common apodization and Fourier Transform. As the Lorentz-to-Gauss transform improves resolution and reduces ridges we include this when defining the Signal-to-Artifact Apex Ratio (SAAR) metric. This metric measures the ratio of simulated reconstructed peak height to the tallest artifact of reconstruction in a spectrum without noise. Once a NUS schedule is found with an optimal SAAR it will be satisfactory for all spectra recorded with the same parameter set. Tables with good seed values are provided in the supplement.

Rapid quantitative 1H-13C two-dimensional NMR with high precision

Two dimensional (2D) 1H-13C heteronuclear single-quantum correlation (HSQC) spectroscopy has recently been proposed for quantitative determination of typical linear low density polyethylene (LLDPE) with high accuracy. It requires highly precise measurement to achieve further reliable quantification. In this context, this paper aims at determining conditions that allow the achievement of high precision. On the basis of the optimized parameters, two time-saving strategies, nonuniform sampling (NUS) and band-selective HSQC are evaluated on model polyolefins in terms of repeatability. Precision better than 0.3% and 5% for ethylene content (E mol%) and 1-hexene content (H mol%) of the model poly(ethylene-co-1-hexene)s are obtained with 50% NUS or band-selective HSQC. Moreover, dramatic precision enhancements can be achieved with the combination of band-selective HSQC and 50% NUS, in which repeatabilities better than 0.15% and 2.5% for E mol% and H mol% are observed. The experiment times are reduced to about 0.5 h. These methods open important perspectives for rapid, precise and accurate quantitative analysis of complex polymers.

Lipid Nanodiscs for High-Resolution NMR Studies of Membrane Proteins

Membrane proteins (MPs) play essential roles in numerous cellular processes. Because around 70% of the currently marketed drugs target MPs, a detailed understanding of their structure, binding properties, and functional dynamics in a physiologically relevant environment is crucial for a more detailed understanding of this important protein class. We here summarize the benefits of using lipid nanodiscs for NMR structural investigations and provide a detailed overview of the currently used lipid nanodisc systems as well as their applications in solution-state NMR. Despite the increasing use of other structural methods for the structure determination of MPs in lipid nanodiscs, solution NMR turns out to be a versatile tool to probe a wide range of MP features, ranging from the structure determination of small to medium-sized MPs to probing ligand and partner protein binding as well as functionally relevant dynamical signatures in a lipid nanodisc setting. We will expand on these topics by discussing recent NMR studies with lipid nanodiscs and work out a key workflow for optimizing the nanodisc incorporation of an MP for subsequent NMR investigations. With this, we hope to provide a comprehensive background to enable an informed assessment of the applicability of lipid nanodiscs for NMR studies of a particular MP of interest.

Increasing sensitivity and versatility in NMR supersequences with new HSQC-based modules

The sensitivity-enhanced HSQC, as well as HSQC-TOCSY, experiments have been modified for incorporation into NOAH (NMR by Ordered Acquisition using ¹H detection) supersequences, adding diversity for ¹³C and ¹⁵N modules. Importantly, these heteronuclear modules have been specifically tailored to preserve the magnetisation required for subsequent acquisition of other heteronuclear or homonuclear modules in a supersequence. In addition, we present protocols for optimally combining HSQC and HSQC-TOCSY elements within the same supersequences, yielding high-quality 2D spectra suitable for structure characterisation but with greatly reduced experiment durations. We further demonstrate that these time savings can translate to increased detection sensitivity per unit time.

Non-uniform sampling in pulse dipolar spectroscopy by EPR: the redistribution of noise and the optimization of data acquisition

Pulse dipolar spectroscopy (PDS) in Electron Paramagnetic Resonance (EPR) is the method of choice for determining the distance distribution function for mono-, bi- or multi- spin-labeled macromolecules and nanostructures. PDS acquisition schemes conventionally use uniform sampling of the dipolar trace, but non-uniform sampling (NUS) schemes can decrease the total measurement time or increase the accuracy of the resulting distance distributions. NUS requires optimization of the data acquisition scheme, as well as changes in data processing algorithms to accommodate the non-uniformly sampled data. We investigate in silico the applicability of the NUS approach in PDS, considering its effect on random, truncation and sampling noise in the experimental data. Each type of noise in the time-domain data propagates differently and non-uniformly into the distance spectrum as errors in the distance distribution. NUS schemes seem to be a valid approach for increasing sensitivity and/or throughput in PDS by decreasing and redistributing noise in the distance spectrum so that it has less impact on the distance spectrum.

Software for reconstruction of nonuniformly sampled NMR data

Nonuniform sampling (NUS) of multidimensional NMR experiments is a powerful tool to obtain high-resolution spectra with less instrument time. With NUS, only a subset of the points needed for conventional Fourier transformation is recorded, and sophisticated algorithms are needed to reconstruct the missing data points. During the last decade, several software packages implementing the reconstruction algorithms have emerged and been refined and now result in spectra of almost similar quality as spectra from conventionally recorded and processed data. However, from the number of literature references to the reconstruction methods, many more multidimensional NMR spectra could presumably be recorded with NUS. To help researchers considering to start using NUS for their NMR experiments, we here review 13 different reconstruction methods found in five software packages (CambridgeCS, hmsIST, MddNMR, NESTA-NMR, and SMILE). We have compared how the methods run with the provided example scripts for reconstructing a nonuniform sampled three-dimensional ¹⁵ N-NOESY-HSQC at sampling densities from 5% to 50%. Overall, the spectra are all of similar quality above 20% sampling density. Thus, without any particular knowledge about the details of the reconstruction algorithms, significant reduction in the experiment time can be achieved. Below 20% sampling density, the intensities of particular weak peaks start being affected. MddNMR's IST with virtual echo and the SMILE algorithms still reproduced the spectra with the highest accuracy of peak intensities.

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.

Combining High-Pressure Perturbation with NMR Spectroscopy for a Structural and Dynamical Characterization of Protein Folding Pathways

High-hydrostatic pressure is an alternative perturbation method that can be used to destabilize globular proteins. Generally perfectly reversible, pressure exerts local effects on regions or domains of a protein containing internal voids, contrary to heat or chemical denaturant that destabilize protein structures uniformly. When combined with NMR spectroscopy, high pressure (HP) allows one to monitor at a residue-level resolution the structural transitions occurring upon unfolding and to determine the kinetic properties of the process. The use of HP-NMR has long been hampered by technical difficulties. Owing to the recent development of commercially available high-pressure sample cells, HP-NMR experiments can now be routinely performed. This review summarizes recent advances of HP-NMR techniques for the characterization at a quasi-atomic resolution of the protein folding energy landscape.

Developing nonuniform sampling strategies to improve sensitivity and resolution in 1,1-ADEQUATE experiments

Nonuniform sampling (NUS) strategies are developed for acquiring highly resolved 1,1-ADEQUATE spectra, in both conventional and homodecoupled (HD) variants with improved sensitivity. Specifically, the quantile-directed and Poisson gap methods were critically compared for distributing the samples nonuniformly, and the quantile schedules were further optimized for weighting. Both maximum entropy and iterative soft thresholding spectral estimation algorithms were evaluated. All NUS approaches were robust when the degree of data reduction is moderate, on the order of a 50% reduction of sampling points. Further sampling reduction by NUS is facilitated by using weighted schedules designed by the quantile method, which also suppresses sampling noise well. Seed independence and the ability to specify the sample weighting in quantile scheduling are important in optimizing NUS for 1,1-ADEQUATE data acquisition. Using NUS yields an improvement in sensitivity, while also making longer evolution times accessible that would be difficult or impractical to attain by uniform sampling. Theoretical predictions for the sensitivity enhancements in these experiments are in the range of 5-20%; NUS is shown to disambiguate weak signals, reveal some ⁿ J_CC correlations obscured by noise, and improve signal strength relative to uniform sampling in the same experimental time. This work presents sample schedule development for applying NUS to challenging experiments. The schedules developed here are made available for general use and should facilitate the broader utilization of ADEQUATE experiments (including 1,1-, 1,n-, and HD- variants) for challenging structure elucidation problems.

Maturation of the functional mouse CRES amyloid from globular form

The epididymal lumen contains a complex cystatin-rich nonpathological amyloid matrix with putative roles in sperm maturation and sperm protection. Given our growing understanding for the biological function of this and other functional amyloids, the problem still remains: how functional amyloids assemble including their initial transition to early oligomeric forms. To examine this, we developed a protocol for the purification of nondenatured mouse CRES, a component of the epididymal amyloid matrix, allowing us to examine its assembly to amyloid under conditions that may mimic those in vivo. Herein we use X-ray crystallography, solution-state NMR, and solid-state NMR to follow at the atomic level the assembly of the CRES amyloidogenic precursor as it progressed from monomeric folded protein to an advanced amyloid. We show the CRES monomer has a typical cystatin fold that assembles into highly branched amyloid matrices, comparable to those in vivo, by forming β-sheet assemblies that our data suggest occur via two distinct mechanisms: a unique conformational switch of a highly flexible disulfide-anchored loop to a rigid β-strand and by traditional cystatin domain swapping. Our results provide key insight into our understanding of functional amyloid assembly by revealing the earliest structural transitions from monomer to oligomer and by showing that some functional amyloid structures may be built by multiple and distinctive assembly mechanisms.

Non-Uniform Sampling in NMR Spectroscopy and the Preservation of Spectral Knowledge in the Time and Frequency Domains

The increased sensitivity under weighted non-uniform sampling (NUS) is demonstrated and quantified using Monte Carlo simulations of nuclear magnetic resonance (NMR) time- and frequency-domain signals. The concept of spectral knowledge is introduced and shown to be superior to the frequency-domain signal-to-noise ratio for assessing the quality of NMR data. Two methods for rigorously preserving spectral knowledge and the time-domain NUS knowledge enhancement upon transformation to the frequency domain are demonstrated, both theoretically and numerically. The first, non-uniform weighted sampling using consistent root-mean-square noise, is applicable to data sampled on the Nyquist grid, whereas the second, the block Fourier transform using consistent root-mean-square noise, can be used to transform time-domain data acquired with arbitrary, off-grid NUS.

How to measure long-range proton-carbon coupling constants from 1 H-selective HSQMBC experiments

Heteronuclear long-range scalar coupling constants (ⁿ J_CH ) are a valuable tool for solving problems in organic chemistry and are especially suited for stereochemical and configurational analyses of small molecules and natural products. This tutorial will focus on the step-by-step implementation of several 2D ¹ H frequency selective HSQMBC experiments for the easy and accurate measurement of either the magnitude or both the magnitude and the sign of long-range ⁿ J_CH couplings. The performance of these experiments will be showcased with several scenarios in a range of different experimental conditions.

Escherichia coli O176 LPS structure and dynamics: A NMR spectroscopy and MD simulation study

A lipopolysaccharide (LPS) molecule is a key component of the bacterial outer membrane used to protect the bacterium and to interact with the environment. To gain insight into its function, the study of the LPS conformation and dynamics at the molecular and cellular levels is necessary, but these highly diverse and dynamic membrane-LPS systems are difficult to study. In this work, by using NMR spectroscopy and molecular dynamics (MD) simulations, we determined the conformational preferences of an E. coli O176 O-antigen polysaccharide at the atomic level. Moreover, we analyzed the use of non-uniform sampling (NUS) for the acquisition of high dynamic range spectra, like ¹H,¹H-NOESY NMR experiments. A comparison of the effective transglycosidic distances derived from conventional uniformly sampled and NUS ¹H,¹H-NOESY data showed high similarity under equal measuring time conditions. Furthermore, the experimentally derived internuclear distances of the O-antigen polysaccharide with ten repeating units (RUs) showed very good agreement to those calculated from the MD simulations of the same O-antigen polysaccharide in solution. Analysis of the LPS bilayer simulations with five and with ten RUs revealed that, although similar with respect to populated states in solution, the O-antigen in LPS bilayers had more extended chains as a result of spatial limitations due to close packing. Additional MD simulations of O-antigen polysaccharides from E. coli O6 (branched repeating unit) and O91 (negatively charged linear repeating unit) in solution and LPS bilayers were performed and compared to those of O176 (linear polymer). For all three O-antigens, the ensemble of structures present for the polysaccharides in solution were consistent with the results from their ¹H,¹H-NOESY experiments. In addition, the similarities between the O-antigen on its own and as a constituent of the full LPS in bilayer environment makes it possible to realistically describe the LPS conformation and dynamics from the MD simulations.

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Uniform and non-uniform sampled NOESY NMR data yield similar internuclear distances.

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O-antigen internuclear distances from NMR and MD show excellent agreement.

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O-antigen ensemble structures from MD are consistent with NMR observations.

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O-antigen structures are more extended in LPS bilayers than in solution.

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MD simulations can describe realistic LPS conformation and dynamics.

Enhancing Compression Level for More Efficient Compressed Sensing and Other Lessons from NMR Spectroscopy

Modern nuclear magnetic resonance spectroscopy (NMR) is based on two- and higher-dimensional experiments that allow the solving of molecular structures, i.e., determine the relative positions of single atoms very precisely. However, rich chemical information comes at the price of long data acquisition times (up to several days). This problem can be alleviated by compressed sensing (CS)—a method that revolutionized many fields of technology. It is known that CS performs the most efficiently when measured objects feature a high level of compressibility, which in the case of NMR signal means that its frequency domain representation (spectrum) has a low number of significant points. However, many NMR spectroscopists are not aware of the fact that various well-known signal acquisition procedures enhance compressibility and thus should be used prior to CS reconstruction. In this study, we discuss such procedures and show to what extent they are complementary to CS approaches. We believe that the survey will be useful not only for NMR spectroscopists but also to inspire the broader signal processing community.

Sensitivity boosts by the CPMAS CryoProbe for challenging biological assemblies

Despite breakthroughs in MAS NMR hardware and experimental methodologies, sensitivity remains a major challenge for large and complex biological systems. Here, we report that 3-4 fold higher sensitivities can be obtained in heteronuclear-detected experiments, using a novel HCN CPMAS probe, where the sample coil and the electronics operate at cryogenic temperatures, while the sample is maintained at ambient temperatures (BioSolids CryoProbe™). Such intensity enhancements permit recording 2D and 3D experiments that are otherwise time-prohibitive, such as 2D ¹⁵N-¹⁵N proton-driven spin diffusion and ¹⁵N-¹³C double cross polarization to natural abundance carbon experiments. The benefits of CPMAS CryoProbe-based experiments are illustrated for assemblies of kinesin Kif5b with microtubules, HIV-1 capsid protein assemblies, and fibrils of human Y145Stop and fungal HET-s prion proteins - demanding systems for conventional MAS solid-state NMR and excellent reference systems in terms of spectral quality. We envision that this probe technology will be beneficial for a wide range of applications, especially for biological systems suffering from low intrinsic sensitivity and at physiological temperatures.

The influence of the probability density function on spectral quality in nonuniformly sampled multidimensional NMR

The goal of nonuniform sampling (NUS) is to select a subset of free induction decays (FIDs) from the conventional, uniform grid in a manner that sufficiently samples short evolution times needed for improved sensitivity and long evolution times needed for enhanced resolution. In addition to specifying the number of FIDs to be collected from a uniform grid, NUS schemes also specify the distribution of the selected FIDs, which directly impacts sampling-induced artifacts. Sampling schemes typically address these heuristic guidelines by utilizing a probability density function (PDF) to bias the distribution of sampled evolution times. Given this common approach, schemes differentiate themselves by how the evolution times are distributed within the envelope of the PDF. Here, we employ maximum entropy reconstruction and utilize in situ receiver operating characteristic (IROC) to conduct a critical comparison of the sensitivity and resolution that can be achieved by three types of biased sampling schemes: exponential (PDF is exponentially decaying), Poisson-gap (PDF derived from a sine function), and quantile-directed (PDF defined by simple polynomial decay). This methodology reveals practical insights and trends regarding how the sampling schemes and bias can provide the highest sensitivity and resolution for two nonuniformly sampled dimensions in a three-dimensional biomolecular NMR experiment. The IROC analysis circumvents the limitations of common metrics when used with nonlinear spectral estimation (a characteristic of all methods used with NUS) by quantifying the spectral quality via synthetic signals that are added to the empirical dataset. Recovery of these synthetic signals provides a proxy for the quality of the empirical portion of the spectrum. The central finding is that differences in spectral quality are primarily driven by the strength of bias in the PDF. In addition, a sampling coverage threshold is observed that appears to be connected to the dependence of each NUS method on its random seed. The differences between sampling schemes and biases are most relevant below 20% coverage where seed-dependence is high, whereas at higher coverages, the performance metrics for all of the sampling schemes begin to converge and approach a seed-independent regime. The results presented here show that aggressive sampling at low coverage can produce high-quality spectra by employing a sampling scheme that adheres to a decaying PDF with a bias to a broad range of short evolution times and includes relatively few FIDs at long evolution times.

Conformational changes upon gating of KirBac1.1 into an open-activated state revealed by solid-state NMR and functional assays

Inward rectifier K⁺ (Kir) channels play an important role in reestablishing the resting membrane state of the action potential of excitable cells in humans. KirBac1.1 is a prokaryotic Kir channel with a high degree of homology to human Kir channels and can be isotopically labeled in NMR quantities for structural studies. Functional assays and NMR assignments confirm that KirBac1.1 is in a constitutively conductive state. Solid-state NMR assignments further reveal alternate conformations at key sites in the protein that are well conserved through human Kir channels, hinting at a possible allosteric network between channels. These underlying sequential and structural motifs could explain abnormal conductive properties of these channels fundamental to their native gating processes.

The conformational changes required for activation and K⁺ conduction in inward-rectifier K⁺ (Kir) channels are still debated. These structural changes are brought about by lipid binding. It is unclear how this process relates to fast gating or if the intracellular and extracellular regions of the protein are coupled. Here, we examine the structural details of KirBac1.1 reconstituted into both POPC and an activating lipid mixture of 3:2 POPC:POPG (wt/wt). KirBac1.1 is a prokaryotic Kir channel that shares homology with human Kir channels. We establish that KirBac1.1 is in a constitutively active state in POPC:POPG bilayers through the use of real-time fluorescence quenching assays and Förster resonance energy transfer (FRET) distance measurements. Multidimensional solid-state NMR (SSNMR) spectroscopy experiments reveal two different conformers within the transmembrane regions of the protein in this activating lipid environment, which are distinct from the conformation of the channel in POPC bilayers. The differences between these three distinct channel states highlight conformational changes associated with an open activation gate and suggest a unique allosteric pathway that ties the selectivity filter to the activation gate through interactions between both transmembrane helices, the turret, selectivity filter loop, and the pore helix. We also identify specific residues involved in this conformational exchange that are highly conserved among human Kir channels.

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.

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.

Extreme Nonuniform Sampling for Protein NMR Dynamics Studies in Minimal Time

NMR spectroscopy is an extraordinarily rich source of quantitative dynamics of proteins in solution using spin relaxation or chemical exchange saturation transfer (CEST) experiments. However, ¹⁵N-CEST measurements require prolonged multidimensional, so-called pseudo-3D HSQC experiments where the pseudo dimension is a radio frequency offset Δω of a weak ¹⁵N saturation field. Nonuniform sampling (NUS) approaches have the potential to significantly speed up these measurements, but they also carry the risk of introducing serious artifacts and the systematic optimization of nonuniform sampling schedules has remained elusive. It is demonstrated here how this challenge can be addressed by using fitted cross-peaks of a reference 2D HSQC experiment as footprints, which are subsequently used to reconstruct cross-peak amplitudes of a pseudo-3D data set as a function of Δω by a linear least-squares fit. It is shown for protein Im7 how the approach can yield highly accurate CEST profiles based on an absolutely minimally sampled (AMS) data set allowing a speed-up of a factor 20-30. Spectrum-specific optimized nonuniform sampling (SONUS) schemes based on the Cramer-Rao lower bound metric were critical to achieve such a performance, revealing also more general properties of optimal sampling schedules. This is the first systematic exploration and optimization of NUS schedules for the dramatic speed-up of quantitative multidimensional NMR measurements that minimize unwanted errors.

Non-uniform HYSCORE: Measurement, processing and analysis with Hyscorean

Non-uniform sampling (NUS) provides a considerable reduction of measurement time especially for multi-dimensional experiments. This comes at the cost of additional signal processing steps to reconstruct the complete signal from the experimental data points. Despite being routinely employed in NMR for many experiments, EPR applications have not benefited from NUS due to the lack of a straightforward implementation to perform NUS in common commercial spectrometers. In this work we present a novel method to perform NUS HYSCORE experiments on commercial Bruker EPR spectrometers, along with a benchmark of modern reconstruction methods, and new processing software tools for NUS HYSCORE signals. All of this comes in the form of a free-software package: Hyscorean. Experimental NUS spectra are measured and processed with this package using different reconstruction methods and compared to their uniform sampled counterparts, thereby showcasing the method's potential for EPR spectroscopy.

Emerging solution NMR methods to illuminate the structural and dynamic properties of proteins

The first recognition of protein breathing was more than 50 years ago. Today, we are able to detect the multitude of interaction modes, structural polymorphisms, and binding-induced changes in protein structure that direct function. Solution-state NMR spectroscopy has proved to be a powerful technique, not only to obtain high-resolution structures of proteins, but also to provide unique insights into the functional dynamics of proteins. Here, we summarize recent technical landmarks in solution NMR that have enabled characterization of key biological macromolecular systems. These methods have been fundamental to atomic resolution structure determination and quantitative analysis of dynamics over a wide range of time scales by NMR. The ability of NMR to detect lowly populated protein conformations and transiently formed complexes plays a critical role in its ability to elucidate functionally important structural features of proteins and their dynamics.

Characterization by Empirical and Computational Methods of Dictyospiromide, an Intriguing Antioxidant Alkaloid from the Marine Alga Dictyota coriacea

The challenging structural motif of dictyospiromide (1), a spirosuccinimide alkaloid with antioxidant properties that are associated with activation of the Nrf2/ARE signaling pathway, was assigned using contemporary NMR experiments complemented with anisotropic NMR, chiroptical, and computational methodologies. Anisotropic NMR parameters provided critical orthogonal verification of the configuration of the difficult to assign spiro carbon and the other stereogenic centers in 1.

Importance of time-ordered non-uniform sampling of multi-dimensional NMR spectra of Aβ1-42 peptide under aggregating conditions

Although the order of the time steps in which the non-uniform sampling (NUS) schedule is implemented when acquiring multi-dimensional NMR spectra is of limited importance when sample conditions remain unchanged over the course of the experiment, it is shown to have major impact when samples are unstable. In the latter case, time-ordering of the NUS data points by the normalized radial length yields a reduction of sampling artifacts, regardless of the spectral reconstruction algorithm. The disadvantage of time-ordered NUS sampling is that halting the experiment prior to its completion will result in lower spectral resolution, rather than a sparser data matrix. Alternatively, digitally correcting for sample decay prior to reconstruction of randomly ordered NUS data points can mitigate reconstruction artifacts, at the cost of somewhat lower sensitivity. Application of these sampling schemes to the Alzheimer's amyloid beta (Aβ1-42) peptide at an elevated concentration, low temperature, and 3 kbar of pressure, where approximately 75% of the peptide reverts to an NMR-invisible state during the collection of a 3D 15N-separated NOESY spectrum, highlights the improvement in artifact suppression and reveals weak medium-range NOE contacts in several regions, including the C-terminal region of the peptide.

Selective Amino Acid-Only in Vivo NMR: A Powerful Tool To Follow Stress Processes

In vivo NMR of small 13C-enriched aquatic organisms is developing as a powerful tool to detect and explain toxic stress at the biochemical level. Amino acids are a very important category of metabolites for stress detection as they are involved in the vast majority of stress response pathways. As such, they are a useful proxy for stress detection in general, which could then be a trigger for more in-depth analysis of the metabolome. 1H-13C heteronuclear single quantum coherence (HSQC) is commonly used to provide additional spectral dispersion in vivo and permit metabolite assignment. While some amino acids can be assigned from HSQC, spectral overlap makes monitoring them in vivo challenging. Here, an experiment typically used to study protein structures is adapted for the selective detection of amino acids inside living Daphnia magna (water fleas). All 20 common amino acids can be selectively detected in both extracts and in vivo. By monitoring bisphenol-A exposure, the in vivo amino acid-only approach identified larger fluxes in a greater number of amino acids when compared to published works using extracts from whole organism homogenates. This suggests that amino acid-only NMR of living organisms may be a very sensitive tool in the detection of stress in vivo and is highly complementary to more traditional metabolomics-based methods. The ability of selective NMR experiments to help researchers to "look inside" living organisms and only detect specific molecules of interest is quite profound and paves the way for the future development of additional targeted experiments for in vivo research and monitoring.

Improving the sensitivity of FT-NMR spectroscopy by apodization weighted sampling

Apodization weighted acquisition is a simple approach to enhance the sensitivity of multidimensional NMR spectra by scaling the number of scans during acquisition of the indirect dimension(s). The signal content of the resulting spectra is identical to conventionally sampled data, yet the spectra show improved signal-to-noise ratios. There are no special requirements for data acquisition and processing: the time-domain data can be transformed with the same schemes used for conventionally recorded spectra, including Fourier transformation. The method is of general use in multidimensional liquid and solid state NMR experiments if the number of recorded transients per sampling point is bigger than the minimum required phase cycle of the pulse sequence.

Automatic Adaptive Gain for Magnetic Resonance Sensitivity Enhancement

The decaying nature of magnetic resonance (MR) signals results in a decreasing signal-to-quantization noise ratio (SQNR) over the acquisition time. Here we describe a method to enhance the SQNR, and thus the overall signal-to-noise ratio (SNR), by dynamically adapting the gain of the receiver before analog-to-digital conversion (ADC). This is in contrast to a standard experiment in which the gain is fixed for a single data acquisition and is thus adjusted only for the first points of the signal. The gain adjustment in our method is done automatically in a closed loop fashion by using the envelope of the MR signal as the control signal. Moreover, the method incorporates a robust mechanism that runs along with signal acquisition to monitor the gain modulation, enabling precise recovery of the signals. The automatic adaptive gain (AGAIN) method requires minimal additional hardware and is thus general and can be implemented in the signal path of any commercial spectrometer system. We demonstrate an SNR enhancement factor of 2.64 when applied to a custom spectrometer, while a factor of 1.4 was observed when applied to a commercial spectrometer.

TReNDS-Software for reaction monitoring with time-resolved non-uniform sampling

NMR spectroscopy, used routinely for structure elucidation, has also become a widely applied tool for process and reaction monitoring. However, the most informative of NMR methods-correlation experiments-are often useless in this kind of applications. The traditional sampling of a multidimensional FID is usually time-consuming, and thus, the reaction-monitoring toolbox was practically limited to 1D experiments (with rare exceptions, e.g., single-scan or fast-sampling experiments). Recently, the technique of time-resolved non-uniform sampling (TR-NUS) has been proposed, which allows to use standard multidimensional pulse sequences preserving the temporal resolution close to that achievable in 1D experiments. However, the method existed only as a prototype and did not allow on-the-fly processing during the reaction. In this paper, we introduce TReNDS: free, user-friendly software kit for acquisition and processing of TR-NUS data. The program works on Bruker, Agilent, and Magritek spectrometers, allowing to carry out up to four experiments with interleaved TR-NUS. The performance of the program is demonstrated on the example of enzymatic hydrolysis of sucrose.

Automated projection spectroscopy in solid-state NMR

Given that solid-state NMR is being used for protein samples of increasing molecular weight and complexity, higher-dimensionality methods are likely to be more and more indispensable for unambiguous chemical shift assignments in the near future. In addition, solid-state NMR spectral properties are increasingly comparable with solution NMR, allowing adaptation of more sophisticated solution NMR strategies for the solid state in addition to the conventional methodology. Assessing first principles, here we demonstrate the application of automated projection spectroscopy for a micro-crystalline protein in the solid state.

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.

Protons as Versatile Reporters in Solid-State NMR Spectroscopy

Solid-state nuclear magnetic resonance (ssNMR) is a spectroscopic technique that is used for characterization of molecular properties in the solid phase at atomic resolution. In particular, using the approach of magic-angle spinning (MAS), ssNMR has seen widespread applications for topics ranging from material sciences to catalysis, metabolomics, and structural biology, where both isotropic and anisotropic parameters can be exploited for a detailed assessment of molecular properties. High-resolution detection of protons long represented the holy grail of the field. With its high natural abundance and high gyromagnetic ratio, ¹H has naturally been the most important nucleus type for the solution counterpart of NMR spectroscopy. In the solid state, similar benefits are obtained over detection of heteronuclei, however, a rocky road led to its success as their high gyromagnetic ratio has also been associated with various detrimental effects. Two exciting approaches have been developed in recent years that enable proton detection: After partial deuteration of the sample to reduce the proton spin density, the exploitation of protons could begin. Also, faster MAS, nowadays using tiny rotors with frequencies up to 130 kHz, has relieved the need for expensive deuteration. Apart from the sheer gain in sensitivity from choosing protons as the detection nucleus, the proton chemical shift and several other useful aspects of protons have revolutionized the field. In this Account, we are describing the fundamentals of proton detection as well as the arising possibilities for characterization of biomolecules as associated with the developments in our own lab. In particular, we focus on facilitated chemical-shift assignment, structure calculation based on protons, and on assessment of dynamics in solid proteins. For example, the proton chemical-shift dimension adds additional information for resonance assignments in the protein backbone and side chains. Chemical shifts and high gyromagnetic ratio of protons enable direct readout of spatial information over large distances. Dynamics in the protein backbone or side chains can be characterized efficiently using protons as reporters. For all of this, the sample amounts necessary for a given signal-to-noise have drastically shrunk, and new methodology enables assessment of molecules with increasing monomer molecular weight and complexity. Taken together, protons are able to overcome previous limitations, by speeding up processes, enhancing accuracies, and increasing the accessible ranges of ssNMR spectroscopy, as we shall discuss in detail in the following. In particular, these methodological developments have been pushing solid-state NMR into a new regime of biological topics as they realistically allow access to complex cellular molecules, elucidating their functions and interactions in a multitude of ways.

Nonuniform sampling in multidimensional NMR for improving spectral sensitivity

The development of multidimensional NMR spectroscopy enabled an explosion of structural and dynamical investigations on proteins and other biomacromolecules. Practical limitations on data sampling, based on the Jeener paradigm of parametric sampling of indirect time domains, have long placed limits on resolution in the corresponding frequency dimensions. The emergence of nonuniform sampling (NUS) in indirect time dimensions circumvents those limitations, affording high resolution spectra from short data records collected in practically realized measurement times. In addition to substantially improved resolution, NUS can also be exploited to improve sensitivity, with gains comparable to those obtained using cryogenically cooled probes. We describe a general approach for acquiring and processing multidimensional NUS NMR data for improving sensitivity.

Nonuniform sampling by quantiles

A flexible strategy for choosing samples nonuniformly from a Nyquist grid using the concept of statistical quantiles is presented for broad classes of NMR experimentation. Quantile-directed scheduling is intuitive and flexible for any weighting function, promotes reproducibility and seed independence, and is generalizable to multiple dimensions. In brief, weighting functions are divided into regions of equal probability, which define the samples to be acquired. Quantile scheduling therefore achieves close adherence to a probability distribution function, thereby minimizing gaps for any given degree of subsampling of the Nyquist grid. A characteristic of quantile scheduling is that one-dimensional, weighted NUS schedules are deterministic, however higher dimensional schedules are similar within a user-specified jittering parameter. To develop unweighted sampling, we investigated the minimum jitter needed to disrupt subharmonic tracts, and show that this criterion can be met in many cases by jittering within 25-50% of the subharmonic gap. For nD-NUS, three supplemental components to choosing samples by quantiles are proposed in this work: (i) forcing the corner samples to ensure sampling to specified maximum values in indirect evolution times, (ii) providing an option to triangular backfill sampling schedules to promote dense/uniform tracts at the beginning of signal evolution periods, and (iii) providing an option to force the edges of nD-NUS schedules to be identical to the 1D quantiles. Quantile-directed scheduling meets the diverse needs of current NUS experimentation, but can also be used for future NUS implementations such as off-grid NUS and more. A computer program implementing these principles (a.k.a. QSched) in 1D- and 2D-NUS is available under the general public license.

Physical basis of amyloid fibril polymorphism

Polymorphism is a key feature of amyloid fibril structures but it remains challenging to explain these variations for a particular sample. Here, we report electron cryomicroscopy-based reconstructions from different fibril morphologies formed by a peptide fragment from an amyloidogenic immunoglobulin light chain. The observed fibril morphologies vary in the number and cross-sectional arrangement of a structurally conserved building block. A comparison with the theoretically possible constellations reveals the experimentally observed spectrum of fibril morphologies to be governed by opposing sets of forces that primarily arise from the β-sheet twist, as well as peptide-peptide interactions within the fibril cross-section. Our results provide a framework for rationalizing and predicting the structure and polymorphism of cross-β fibrils, and suggest that a small number of physical parameters control the observed fibril architectures.