Sparse sampling methods in multidimensional NMR

Although the discrete Fourier transform played an enabling role in the development of modern NMR spectroscopy, it suffers from a well-known difficulty providing high-resolution spectra from short data records. In multidimensional NMR experiments, so-called indirect time dimensions are sampled parametrically, with each instance of evolution times along the indirect dimensions sampled via separate one-dimensional experiments. The time required to conduct multidimensional experiments is directly proportional to the number of indirect evolution times sampled. Despite remarkable advances in resolution with increasing magnetic field strength, multiple dimensions remain essential for resolving individual resonances in NMR spectra of biological macromolecues. Conventional Fourier-based methods of spectrum analysis limit the resolution that can be practically achieved in the indirect dimensions. Nonuniform or sparse data collection strategies, together with suitable non-Fourier methods of spectrum analysis, enable high-resolution multidimensional spectra to be obtained. Although some of these approaches were first employed in NMR more than two decades ago, it is only relatively recently that they have been widely adopted. Here we describe the current practice of sparse sampling methods and prospects for further development of the approach to improve resolution and sensitivity and shorten experiment time in multidimensional NMR. While sparse sampling is particularly promising for multidimensional NMR, the basic principles could apply to other forms of multidimensional spectroscopy.     

Complete 1H and 13C signal assignment of prenol‐10 with 3D NMR spectroscopy

The complete assignment of ¹H and ¹³C chemical shifts of natural abundance prenol‐10 is reported for the first time. It was achieved using 3D NMR experiments, which were based on random sampling of the evolution time space followed by multidimensional Fourier transform. This approach makes it possible to acquire 3D NMR spectra in a reasonable time and preserves high resolution in indirectly detected dimensions. It is shown that the interpretation of 3D COSY–HMBC and 3D TOCSY–HSQC spectra is crucial in the structural analysis of prenol‐10. Copyright © 2009 John Wiley & Sons, Ltd.     

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.     

Determination of spin-spin couplings from ultrahigh resolution 3D NMR spectra obtained by optimized random sampling and multidimensional Fourier transformation

An example of precise evaluation of backbone scalar J couplings using random sampling of evolution time space in 3D NMR experiments is presented. The recorded spectrum, due to violation of the Nyquist theorem limitation, exhibits ultrahigh resolution in indirect dimensions compared to standard NMR experiment acquired at the same time. The obtained results enable simple and accurate evaluation of scalar and residual dipolar couplings from a single multidimensional NMR experiment.     

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.     

Ultrafast Multidimensional Laplace NMR Using a Single‐Sided Magnet

Laplace NMR (LNMR) consists of relaxation and diffusion measurements providing detailed information about molecular motion and interaction. Here we demonstrate that ultrafast single‐ and multidimensional LNMR experiments, based on spatial encoding, are viable with low‐field, single‐sided magnets with an inhomogeneous magnetic field. This approach shortens the experiment time by one to two orders of magnitude relative to traditional experiments, and increases the sensitivity per unit time by a factor of three. The reduction of time required to collect multidimensional data opens significant prospects for mobile chemical analysis using NMR. Particularly tantalizing is future use of hyperpolarization to increase sensitivity by orders of magnitude, allowed by single‐scan approach.     

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.     

Recovering Invisible Signals by Two‐Field NMR Spectroscopy

Nuclear magnetic resonance (NMR) studies have benefited tremendously from the steady increase in the strength of magnetic fields. Spectacular improvements in both sensitivity and resolution have enabled the investigation of molecular systems of rising complexity. At very high fields, this progress may be jeopardized by line broadening, which is due to chemical exchange or relaxation by chemical shift anisotropy. In this work, we introduce a two‐field NMR spectrometer designed for both excitation and observation of nuclear spins in two distinct magnetic fields in a single experiment. NMR spectra of several small molecules as well as a protein were obtained, with two dimensions acquired at vastly different magnetic fields. Resonances of exchanging groups that are broadened beyond recognition at high field can be sharpened to narrow peaks in the low‐field dimension. Two‐field NMR spectroscopy enables the measurement of chemical shifts at optimal fields and the study of molecular systems that suffer from internal dynamics, and opens new avenues for NMR spectroscopy at very high magnetic fields.     

Determination of Complex Small‐Molecule Structures Using Molecular Alignment Simulation

Correct structural assignment of small molecules and natural products is critical for drug discovery and organic chemistry. Anisotropy‐based NMR spectroscopy is a powerful tool for the structural assignment of organic molecules, but it relies on the utilization of a medium that disrupts the isotropic motion of molecules in organic solvents. Here, we establish a quantitative correlation between the atomic structure of the alignment medium, the molecular structure of the small molecule, and molecule‐specific anisotropic NMR parameters. The quantitative correlation uses an accurate three‐dimensional molecular alignment model that predicts residual dipolar couplings of small molecules aligned by poly(γ‐benzyl‐l ‐glutamate). The technique facilitates reliable determination of the correct stereoisomer and enables unequivocal, rapid determination of complex molecular structures from extremely sparse NMR data.     

High-resolution four-dimensional 1H-13C NOE spectroscopy using methyl-TROSY, sparse data acquisition, and multidimensional decomposition

An approach for recording four-dimensional (4D) methyl (1)H-(13)C-(13)C-(1)H NOESY spectra with high resolution and sensitivity is presented and applied to Malate Synthase G (723 residues, 82 kDa). Sensitivity and resolution have been optimized using a highly deuterated, methyl-protonated sample in concert with methyl-TROSY, sparse data sampling in the three indirect dimensions, and 4D spectral reconstruction using multidimensional decomposition (MDD). A sparse data acquisition protocol is introduced that ensures that sufficiently long indirect acquisition times can be employed to exploit the decreased relaxation rates associated with methyl-TROSY, without increasing the duration of the 4D experiment beyond acceptable measurement times. In this manner, only a fraction ( approximately 30%) of the experimental data that would normally be needed to achieve a spectrum of high resolution is acquired. The reconstructed 4D spectrum is of similar resolution and sensitivity to three-dimensional (3D) (13)C-edited NOE spectra, is straightforward to analyze, and resolves ambiguities that emerge when 3D data sets only are considered.     

Partial‐Homogeneity‐Based Two‐Dimensional High‐Resolution Nuclear Magnetic Resonance Spectroscopy under Inhomogeneous Magnetic Fields

High‐resolution multidimensional nuclear magnetic resonance (NMR) spectroscopy serves as an irreplaceable and versatile tool in various chemical investigations. In this study, a method based on the concept of partial homogeneity is developed to offer two‐dimensional (2D) high‐resolution NMR spectra under inhomogeneous fields. Oscillating gradients are exerted to encode the high‐resolution information, and a field‐inhomogeneity correction algorithm based on pattern recognition is designed to recover high‐resolution spectra. Under fields where inhomogeneity primarily distributes along a single orientation, the proposed method will improve performances of 2D NMR spectroscopy without increasing the experimental duration or significant loss in sensitivity, and thus may open important perspectives for studies of inhomogeneous chemical systems.     

Study of the self‐diffusion of poly(ethylene glycol)s in poly(vinyl alcohol) aqueous systems

We have measured the self‐diffusion coefficients of a series of oligo‐ and poly(ethylene glycol)s with molecular weights ranging from 150 to 10,000, in aqueous solutions and gels of poly(vinyl alcohol) (PVA), using the pulsed‐gradient spin‐echo NMR techniques. The PVA concentrations varied from 0 to 0.38 g/mL which ranged from dilute solutions to polymer gels. Effects of the diffusant size and polymer concentration on the self‐diffusion coefficients have been investigated. The temperature dependence of the self‐diffusion coefficients has also been studied for poly(ethylene glycol)s with molecular weights of 600 and 2,000. Several theoretical models based on different physical concepts are used to fit the experimental data. The suitability of these models in the interpretation of the self‐diffusion data is discussed. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 2396–2403, 1999     

Detection of Potential TNA and RNA Nucleoside Precursors in a Prebiotic Mixture by Pure Shift Diffusion‐Ordered NMR Spectroscopy

In the context of prebiotic chemistry, one of the characteristics of mixed nitrogenous‐oxygenous chemistry is its propensity to give rise to highly complex reaction mixtures. There is therefore an urgent need to develop improved spectroscopic techniques if onerous chromatographic separations are to be avoided. One potential avenue is the combination of pure shift methodology, in which NMR spectra are measured with greatly improved resolution by suppressing multiplet structure, with diffusion‐ordered spectroscopy, in which NMR signals from different species are distinguished through their different rates of diffusion. Such a combination has the added advantage of working with intact mixtures, allowing analyses to be carried out without perturbing mixtures in which chemical entities are part of a network of reactions in equilibrium. As part of a systems chemistry approach towards investigating the self‐assembly of potentially prebiotic small molecules, we have analysed the complex mixture arising from mixing glycolaldehyde and cyanamide, in a first application of pure shift DOSY NMR to the characterisation of a partially unknown reaction composition. The work presented illustrates the potential of pure shift DOSY to be applied to chemistries that give rise to mixtures of compounds in which the NMR signal resolution is poor. The direct formation of potential RNA and TNA nucleoside precursors, amongst other adducts, was observed. These preliminary observations may have implications for the potentially prebiotic assembly chemistry of pyrimidine threonucleotides, and therefore of TNA, by using recently reported chemistries that yield the activated pyridimidine ribonucleotides.     

Solvent Effect and Reactivity Trend in the Aerobic Oxidation of 1,3‐Propanediols over Gold Supported on Titania: NMR Diffusion and Relaxation Studies

In recent work, it was reported that changes in solvent composition, precisely the addition of water, significantly inhibits the catalytic activity of Au/TiO₂ catalyst in the aerobic oxidation of 1,4‐butanediol in methanol due to changes in diffusion and adsorption properties of the reactant. In order to understand whether the inhibition mechanism of water on diol oxidation in methanol is generally valid, the solvent effect on the aerobic catalytic oxidation of 1,3‐propanediol and its two methyl‐substituted homologues, 2‐methyl‐1,3‐propanediol and 2,2‐dimethyl‐1,3‐propanediol, over a Au/TiO₂ catalyst has been studied here using conventional catalytic reaction monitoring in combination with pulsed‐field gradient nuclear magnetic resonance (PFG‐NMR) diffusion and NMR relaxation time measurements. Diol conversion is significantly lower when water is present in the initial diol/methanol mixture. A reactivity trend within the group of diols was also observed. Combined NMR diffusion and relaxation time measurements suggest that molecular diffusion and, in particular, the relative strength of diol adsorption, are important factors in determining the conversion. These results highlight NMR diffusion and relaxation techniques as novel, non‐invasive characterisation tools for catalytic materials, which complement conventional reaction data.     

Ion Dynamics in a Mixed‐Cation Alkoxy‐Ammonium Ionic Liquid Electrolyte for Sodium Device Applications

The ion dynamics in a novel sodium‐containing room‐temperature ionic liquid (IL) consisting of an ether‐functionalised quaternary ammonium cation and bis(trifluoromethylsulfonyl)amide [NTf₂] anion with various concentrations of Na[NTf₂] have been characterised using differential scanning calorimetry, impedance spectroscopy, diffusometry and NMR relaxation measurements. The IL studied has been specifically designed to dissolve a relatively large concentration of Na[NTf₂] salt (over 2 mol kg^?1) as this has been shown to improve ion transport and conductivity. Consistent with other studies, the measured ionic conductivity and diffusion coefficients show that the overall ionic mobility decreases with decreasing temperature and increasing salt content. NMR relaxation measurements provide evidence for correlated dynamics between the ether‐functionalised ammonium and Na cations, possibly with the latter species acting as cross‐links between multiple ammonium cations. Finally, preliminary cyclic voltammetry experiments show that this IL can undergo stable electrochemical cycling and could therefore be potentially useful as an electrolyte in a Na‐based device.     

Two‐Dimensional NMR Spectroscopy with Temperature‐Sweep

Two‐dimensional nuclear magnetic resonance (NMR) spectroscopy is useful for studying temperature‐dependent effects on molecular structure. However, experimental time is usually long, because sampling is repeated at several temperatures. A novel solution to the problem is proposed, in which signal sampling is performed in parallel to the linear temperature‐sweep.     

Study of liquid–liquid interfaces by an easily implemented localized NMR sequence

To selectively extract heavy metals from solutions containing fission products, it is essential to optimize the liquid–liquid extraction processes. Such an objective requires improving the fundamental knowledge of the different mechanisms that are involved in these processes. In that respect, we propose a localized NMR sequence named LOCSY to assess the concentration profiles of different species involved in these processes. One of the goals of this sequence is to study the products as close as possible to the liquid–liquid interface with the help of a standard NMR spectrometer of chemistry labs. The one‐dimensional spatial localization along the NMR tube is obtained by a discrete stepping of the frequency‐selective excitation pulses under a pulsed field gradient. Specific data processing has been developed to obtain the 1D NMR spectra as a function of the vertical position in the NMR tube. The LOCSY sequence has been tested and evaluated on three different systems: (i) a cylindrical phantom inserted in the NMR tube containing 4‐methylsalicylic acid solution, (ii) D₂O/olive oil biphasic system, and (iii) the dissolution of solid saccharose in D₂O. These examples illustrate potential applications of the LOCSY sequence, particularly the possibility to measure concentration profiles and to study phenomena such as diffusion, provided the dynamic range is compatible with NMR timescale and sensitivity. Copyright © 2010 John Wiley & Sons, Ltd.     

Fast multidimensional localized parallel NMR spectroscopy for the analysis of samples

A parallel localized spectroscopy (PALSY) method is presented to speed up the acquisition of multidimensional NMR (nD) spectra. The sample is virtually divided into a discrete number of nonoverlapping slices that relax independently during consecutive scans of the experiment, affording a substantial reduction in the interscan relaxation delay and the total experiment time. PALSY was tested for the acquisition of three experiments 2D COSY, 2D DQF‐COSY and 2D TQF‐COSY in parallel, affording a time‐saving factor of 3–4. Some unique advantages are that the achievable resolution in any dimension is not compromised in any way: it uses conventional NMR data processing, it is not prone to generate spectral artifacts, and once calibrated, it can be used routinely with these and other combinations of NMR spectra. Copyright © 2010 John Wiley & Sons, Ltd.     

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.     

Two‐Dimensional Infrared Spectroscopy Reveals the Structure of an Evans Auxiliary Derivative and Its SnCl4 Lewis Acid Complex

Determining the structure of reactive intermediates is the key to understanding reaction mechanisms. To access these structures, a method combining structural sensitivity and high time resolution is required. Here ultrafast polarization‐dependent two‐dimensional infrared (P2D‐IR) spectroscopy is shown to be an excellent complement to commonly used methods such as one‐dimensional IR and multidimensional NMR spectroscopy for investigating intermediates. P2D‐IR spectroscopy allows structure determination by measuring the angles between vibrational transition dipole moments. The high time resolution makes P2D‐IR spectroscopy an attractive method for structure determination in the presence of fast exchange and for short‐lived intermediates. The ubiquity of vibrations in molecules ensures broad applicability of the method, particularly in cases in which NMR spectroscopy is challenging due to a low density of active nuclei. Here we illustrate the strengths of P2D‐IR by determining the conformation of a Diels–Alder dienophile that carries the Evans auxiliary and its conformational change induced by the complexation with the Lewis acid SnCl₄, which is a catalyst for stereoselective Diels–Alder reactions. We show that P2D‐IR in combination with DFT computations can discriminate between the various conformers of the free dienophile N‐crotonyloxazolidinone that have been debated before, proving antiperiplanar orientation of the carbonyl groups and s‐cis conformation of the crotonyl moiety. P2D‐IR unequivocally identifies the coordination and conformation in the catalyst–substrate complex with SnCl₄, even in the presence of exchange that is fast on the NMR time scale. It resolves a chelate with the carbonyl orientation flipped to synperiplanar and s‐cis crotonyl configuration as the main species. This work sets the stage for future studies of other catalyst–substrate complexes and intermediates using a combination of P2D‐IR spectroscopy and DFT computations.