Theory of covariance nuclear magnetic resonance spectroscopy

Covariance nuclear magnetic resonance (NMR) spectroscopy provides an effective way for establishing nuclear spin connectivities in molecular systems. The method, which identifies correlated spin dynamics in terms of covariances between 1D spectra, benefits from a high spectral resolution along the indirect dimension without requiring apodization and Fourier transformation along this dimension. The theoretical treatment of covariance NMR spectroscopy is given for NOESY and TOCSY experiments. It is shown that for a large class of 2D NMR experiments the covariance spectrum and the 2D Fourier transform spectrum can be related to each other by means of Parseval's theorem. A general procedure is presented for the construction of a symmetric spectrum with improved resolution along the indirect frequency domain as compared to the 2D FT spectrum.     

Solid-state NMR covariance of homonuclear correlation spectra

Direct covariance NMR spectroscopy, which does not involve a Fourier transformation along the indirect dimension, is demonstrated to obtain homonuclear correlation two-dimensional (2D) spectra in the solid state. In contrast to the usual 2D Fourier transform (2D-FT) NMR, in a 2D covariance (2D-Cov) spectrum the spectral resolution in the indirect dimension is determined by the resolution along the detection dimension, thereby largely reducing the time-consuming indirect sampling requirement. The covariance method does not need any separate phase correction or apodization along the indirect dimension because it uses those applied in the detection dimension. We compare in detail the specifications obtained with 2D-FT and 2D-Cov, for narrow and broad resonances. The efficiency of the covariance data treatment is demonstrated in organic and inorganic samples that are both well crystallized and amorphous, for spin -1/2 nuclei with 13C, 29Si, and 31P through-space or through-bond homonuclear 2D correlation spectra. In all cases, the experimental time has been reduced by at least a factor of 10, without any loss of resolution and signal to noise ratio, with respect to what is necessary with the 2D-FT NMR. According to this method, we have been able to study the silicate network of glasses by 2D NMR within reasonable experimental time despite the very long relaxation time of the 29Si nucleus. The main limitation of the 2D-Cov data treatment is related to the introduction of autocorrelated peaks onto the diagonal, which does not represent any actual connectivity.     

Homo- and heteronuclear two-dimensional covariance solid-state NMR spectroscopy with a dual-receiver system

Two-dimensional (2D) covariance NMR spectroscopy, which has originally been established to extract homonuclear correlations (HOMCOR), is extended to include heteronuclear correlations (HETCOR). In a (13)C/(15)N 2D chemical shift correlation experiment, (13)C and (15)N signals of a polycrystalline sample of (13)C, (15)N-labeled amino acid are acquired simultaneously using a dual-receiver NMR system. The data sets are rearranged for the covariance data processing, and the (13)C-(15)N heteronuclear correlations are obtained together with the (13)C-(13)C and (15)N-(15)N homonuclear correlations. The present approach retains the favorable feature of the original covariance HOMCOR that the spectral resolution along the indirect dimension is given by that of the detection dimension. As a result, much fewer amounts of data are required to obtain a well-resolved 2D spectrum compared to the case of the conventional 2D Fourier-Transformation (FT) scheme. Hence, one can significantly save the experimental time, or enhance the sensitivity by increasing the number of signal averaging within a given measurement time.     

A double‐Fourier approach to enhance the efficiency of the indirect domain sampling in 2D NMR

The relatively long times that may be involved in high‐resolution two‐dimensional nuclear magnetic resonance (2D NMR) have stimulated the search for alternative schemes to collect these data. Particularly onerous situations arise when both high‐resolution and large spectral widths are sought along the indirect domain. Strategies proposed for dealing with such cases include folding‐over procedures, Hadamard encoding, and nonlinear data sampling. This communication discusses an alternative strategy, which exploits a partial prior knowledge regarding the position of the NMR resonances along the indirect domain together with customized excitations for every particular t₁ increment, to achieve an optimal sampling in terms of resolution and bandwidth. On the basis of such optimized encoding of the indirect‐domain evolution, which can easily be coped with by modern spectrometers, it becomes possible to maximize the resolution of fine structures without compromising on the spectral bandwidths. The processing of the resulting data along the indirect domain is based on the use of two serially applied discrete Fourier transforms; one to distinguish the main bands in the spectrum and the other to resolve the latter's fine features. A number of simple heteronuclear correlation experiments illustrating the significant acquisition time savings and simultaneous improvements in resolution that can be achieved with the resulting double‐Fourier encoding procedure are illustrated. Copyright © 2011 John Wiley & Sons, Ltd.     

Application of the forward linear prediction on high-resolution NMR spectra in inhomogeneous fields

In homogeneous fields, the advantages of forward linear prediction (LP) for processing 2D NMR data sets have long been recognized. In this paper, the forward LP method was employed to obtain high-resolution NMR spectra in inhomogeneous fields. Intermolecular multiple-quantum coherence (iMQC) signals are caused by intermolecular dipolar interactions and can be used to obtain 1D high-resolution NMR spectra from the 2D iMQC spectra acquired in inhomogeneous fields. However, when the 2D spectra are acquired with insufficient increments to save experimental time, wiggles around strong peaks and bad resolution will occur. Extending the data set by forward LP in the indirect dimension is a good way to improve spectral resolution. Compared to normal discrete Fourier transform, the forward LP method can shorten experimental time by a factor of four or more at the same level of sensitivity and resolution.     

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.     

Homonuclear long-range correlation spectra from HMBC experiments by covariance processing

We present a new application of covariance nuclear magnetic resonance processing based on 1H--13C-HMBC experiments which provides an effective way for establishing indirect 1H--1H and 13C--13C nuclear spin connectivity at natural isotope abundance. The method, which identifies correlated spin networks in terms of covariance between one-dimensional traces from a single decoupled HMBC experiment, derives 13C--13C as well as 1H--1H spin connectivity maps from the two-dimensional frequency domain heteronuclear long-range correlation data matrix. The potential and limitations of this novel covariance NMR application are demonstrated on two compounds: eugenyl-beta-D-glucopyranoside and an emodin-derivative.     

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.     

Fast and high-resolution stereochemical analysis by nonuniform sampling and covariance processing of anisotropic natural abundance 2D 2H NMR datasets

Natural abundance deuterium (NAD) 2D NMR spectroscopy using chiral or achiral liquid crystals is an efficient analytical tool for the stereochemical analysis of enantio- or diastereomers by the virtue of proton-to-deuterium substitution. In particular, it allows the measurement of enantiopurity of organic synthetic molecules or the determination of the natural isotopic (1)H/(2)H fractionation in biological molecules, such as fatty acid methyl esters (FAME). So far, the NAD 2D spectra of solutes were acquired by using uniform sampling (US) and processed by conventional 2D Fourier transform (FT), which could result in long measurement times for medium-sized analytes or low solute concentrations. Herein, we demonstrate that this conventional approach can be advantageously replaced by nonuniform sampling (NUS) processed by covariance (Cov) transform. This original spectral reconstruction provides a significant enhancement of spectral resolution, as well as a reduction of measurement times. The application of Cov to NUS data has required the introduction of a regularization procedure in the time domain for the indirect dimension. The analytical potential of combining Cov and NUS is demonstrated by measuring the enantiomeric excess of a scalemic mixture of 2-ethyloxirane and by determining the diastereomeric excess of methyl vernoleate, a natural FAME. These two organic compounds were aligned in a polypeptide (poly(γ-benzyl-L-glutamate)) mesophase. In the case of NAD 2D NMR spectroscopy, we show that Cov and NUS methods allow a decrease in measurement time by a factor of two compared with Cov applied to US data and a factor of four compared with FT applied to US 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 t ₁. 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 t ₁ 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 t ₁ 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.     

Optimizing sensitivity and resolution in time-shared NMR experiments

An improved approach to optimize the overall sensitivity and the resolution requirements in the indirect dimension of (13)C/(15)N time-shared (TS) NMR experiments is presented. A different data sampling acquisition procedure is applied for (13)C and (15)N in the indirect dimension, and a proper data recombination before conventional data processing allows a customized adjustment of spectral widths, number of scans and number of increments individually for (13)C and (15)N. The major benefit is an important improvement on the detection limits of the TS experiment that overcomes the lower sensitivity of (15)N over (13)C at natural abundance. We evaluate such enhancements from 2D TS-HMBC experiments recorded on a nitrogen-containing synthetic azole derivative of pharmaceutical interest.     

Enhanced covariance spectroscopy from minimal datasets

A novel approach is described for the determination of reliable high-resolution homonuclear NMR covariance spectra from minimal datasets. It uses a sparse sampling scheme along the indirect dimension together with a comprehensive analysis of finite sampling effects that eliminates spurious correlations. The scheme, which is demonstrated for TOCSY and COSY, offers a substantial speed up over current methods, rendering it suitable for high-throughput screening applications.     

Using indirect covariance spectra to identify artifact responses in unsymmetrical indirect covariance calculated spectra

Several groups of authors have reported studies in the areas of indirect and unsymmetrical indirect covariance NMR processing methods. Efforts have recently focused on the use of unsymmetrical indirect covariance processing methods to combine various discrete two-dimensional NMR spectra to afford the equivalent of the much less sensitive hyphenated 2D NMR experiments, for example indirect covariance (icv)-heteronuclear single quantum coherence (HSQC)-COSY and icv-HSQC-nuclear Overhauser effect spectroscopy (NOESY). Alternatively, unsymmetrical indirect covariance processing methods can be used to combine multiple heteronuclear 2D spectra to afford icv-13C-15N HSQC-HMBC correlation spectra. We now report the use of responses contained in indirect covariance processed HSQC spectra as a means for the identification of artifacts in both indirect covariance and unsymmetrical indirect covariance processed 2D NMR spectra.     

High resolution 1H detected 1H,13C correlation spectra in MAS solid-state NMR using deuterated proteins with selective 1H,2H isotopic labeling of methyl groups

MAS solid-state NMR experiments applied to biological solids are still hampered by low sensitivity and resolution. In this work, we employ a deuteration scheme in which individual methyl groups are selectively protonated. This labeling scheme allows the acquisition of proton carbon correlation spectra with a resolution comparable to that in solution-state NMR experiments. We observe an increase in resolution by a factor of 10-15 compared to standard heteronuclear correlation experiments using PMLG for 1H,1H dipolar decoupling in the indirect dimension. At the same time, the full sensitivity of the proton-based experiment is retained. In comparison to the heteronuclear detected version of the experiment, a gain in sensitivity of a factor of approximately 4.7 is achieved.     

Disentangling Complex Mixtures of Compounds with Near‐Identical 1H and 13C NMR Spectra using Pure Shift NMR Spectroscopy

The thorough analysis of highly complex NMR spectra using pure shift NMR experiments is described. The enhanced spectral resolution obtained from modern 2D HOBS experiments incorporating spectral aliasing in the ¹³C indirect dimension enables the distinction of similar compounds exhibiting near‐identical ¹H and ¹³C NMR spectra. It is shown that a complete set of extremely small Δδ(¹H) and Δδ(¹³C) values, even below the natural line width (1 and 5 ppb, respectively), can be simultaneously determined and assigned.     

New developments in the spatial encoding of spin interactions for single‐scan 2D NMR

Single‐scan 2D NMR relies on a spatial axis for encoding the indirect‐domain internal spin interactions. Various strategies have been demonstrated for fulfilling the needs underlying this procedure. All such schemes use gradient‐echoed sequences that leave at their conclusion solely the effects of the internal interactions along the indirect domain; they also include a real‐time scheme that though simple, yields in general mixed‐phase line shapes. The present paper introduces two new proposals geared up for easing the spatial encoding underlying single‐scan 2D NMR methodologies. One of these is capable of delivering dispersive‐free peaks along the indirect domain, and thereby purely‐absorptive 2D line shapes, in amplitude‐encoded experiments. The other demonstrates for the first time, the possibility to obtain single‐scan 2D spectra without echoing the effects of the encoding gradient–simply by applying a single‐pulse frequency sweep to encode the interactions. Both of these modes are compatible with homo‐ and heteronuclear correlations, and exhibit a number of complementary features vis‐à‐vis encoding alternatives that have so far been presented. The overall principles underlying these new spatially encoding protocols are derived, and their performance demonstrated with single‐scan 2D NMR TOCSY and HSQC experiments on model compounds. Copyright © 2009 John Wiley & Sons, Ltd.     

Electron spin echo envelope modulation spectroscopy with g-value and orientation filters

Two new electron spin echo envelope modulation (ESEEM) experiments, electron-Zeeman (EZ) ESEEM and right-angle wiggling (RAW) ESEEM, are introduced. The experiments are based on the combination of a one- or two-dimensional ESEEM sequence with an EZ-EPR or RAW-EPR detection scheme. The approaches provide considerably enhanced g-value and orientation filters as compared to the standard ESEEM experiments. EZ-ESEEM facilitates the disentangling of overlapping nuclear frequencies along a g-value dimension for systems with anisotropic g-matrices, whereas with RAW-ESEEM overlapping frequency components along a dimension that is related to the change in resonance frequency when the orientation is varied, can be separated. The underlying concepts are outlined and the new experiments are illustrated by numerical simulations and examples of applications.     

Indirect covariance NMR spectroscopy

A novel NMR scheme is presented that establishes homonuclear spin correlations without requiring direct detection of the spin species. This covariance NMR method is experimentally demonstrated for a mixture of amino acids and for the uniformly 13C-labeled cyclic decapeptide antamanide using a 13C-edited TOCSY experiment. The method opens up new avenues for the experimental analysis of molecules containing insensitive spins encountered in biomolecular NMR and analytical chemistry including metabolomics.     

J-GFT NMR for precise measurement of mutually correlated nuclear spin-spin couplings

G-matrix Fourier transform (GFT) NMR spectroscopy is presented for accurate and precise measurement of chemical shifts and nuclear spin-spin couplings correlated according to spin system. The new approach, named "J-GFT NMR", is based on a largely extended GFT NMR formalism and promises to have a broad impact on projection NMR spectroscopy. Specifically, constant-time J-GFT (6,2)D (HA-CA-CO)-N-HN was implemented for simultaneous measurement of five mutually correlated NMR parameters, that is, 15N backbone chemical shifts and the four one-bond spin-spin couplings 13Calpha-1Halpha, 13Calpha-13C', 15N-13C', and 15N-1HNu. The experiment was applied for measuring residual dipolar couplings (RDCs) in an 8 kDa protein Z-domain aligned with Pf1 phages. Comparison with RDC values extracted from conventional NMR experiments reveals that RDCs are measured with high precision and accuracy, which is attributable to the facts that (i) the use of constant time evolution ensures that signals do not broaden whenever multiple RDCs are jointly measured in a single dimension and (ii) RDCs are multiply encoded in the multiplets arising from the joint sampling. This corresponds to measuring the couplings multiple times in a statistically independent manner. A key feature of J-GFT NMR, i.e., the correlation of couplings according to spin systems without reference to sequential resonance assignments, promises to be particularly valuable for rapid identification of backbone conformation and classification of protein fold families on the basis of statistical analysis of dipolar couplings.     

Single-scan NMR spectroscopy at arbitrary dimensions

Multidimensional nuclear magnetic resonance (NMR) provides one of the foremost analytical tools available to elucidate the structure and dynamics of complex molecules in their native states. Executing this kind of experiment generally requires collecting an n-dimensional time-domain signal S, from which the spectrum arises via an appropriate Fourier analysis of its various time variables. This time-domain signal is actually measured directly only along one of the time axes, while the effects introduced by the remaining time variables are monitored via a parametric incrementation of their values throughout independent experiments. Two-dimensional (2D) NMR experiments thus usually require longer acquisition times than unidimensional experiments, 3D NMR is orders-of-magnitude more time consuming than 2D spectroscopy, etc. Very recently, we proposed and demonstrated an approach whereby data acquisition in 2D NMR can be parallelized, enabling the collection of complete 2D spectral sets within a single transient. The present paper discusses the extension of this 2D NMR methodology to an arbitrary number of dimensions. The principles of the ensuing ultrafast n-dimensional NMR approach are described, and a variety of homo- and heteronuclear 3D and 4D NMR spectra collected within a fraction of a second are presented.