Generalized indirect covariance NMR formalism for establishment of multidimensional spin correlations

Minimizing Pervasive Artifacts in 4D Covariance Maps for Protein Side Chain NMR Assignments

Nuclear magnetic resonance (NMR) is a mainstay of biophysical studies that provides atomic level readouts to formulate molecular mechanisms. Side chains are particularly important to derive mechanisms involving proteins as they carry functional groups, but NMR studies of side chains are often limited by challenges in assigning their signals. Here, we designed a novel computational method that combines spectral derivatives and matrix square-rooting to produce reliable 4D covariance maps from routinely acquired 3D spectra and facilitates side chain resonance assignments. Thus, we generate two 4D maps from 3D-HcccoNH and 3D-HCcH-TOCSY spectra that each help overcome signal overlap or sensitivity losses. These 4D maps feature HC-HSQCs of individual side chains that can be paired to assigned backbone amide resonances of individual aliphatic signals, and both are obtained from a single modified covariance calculation. Further, we present 4D maps produced using conventional triple resonance experiments to easily assign asparagine side chain amide resonances. The 4D covariance maps encapsulate the lengthy manual pattern recognition used in traditional assignment methods and distill the information as correlations that can be easily visualized. We showcase the utility of the 4D covariance maps with a 10 kDa peptidyl carrier protein and a 52 kDa cyclization domain from a nonribosomal peptide synthetase.

Covariance NMR: Theoretical concerns, practical considerations, contemporary applications and related techniques

The family of resolution enhancement and spectral reconstruction techniques collectively known as covariance NMR continues to expand, along with the list of applications for these techniques. Recent advances in covariance NMR include the utilization of covariance to reconstruct pure shift NMR spectra, and the growing use of covariance NMR in processing non-uniformly sampled data, especially in solid state NMR and metabolomics. This review describes theoretical and practical considerations for direct and indirect covariance NMR techniques, and summarizes recent additions to the covariance NMR family. The review also outlines some of the applications of covariance NMR, and places covariance NMR in the larger context of methods that use statistical and algebraic approaches to enhance and combine various kinds of spectroscopic data, including tensor-based approaches for multidimensional NMR and heterocovariance spectroscopy.

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.

Covariance NMR Processing and Analysis for Protein Assignment

During NMR resonance assignment it is often necessary to relate nuclei to one another indirectly, through their common correlations to other nuclei. Covariance NMR has emerged as a powerful technique to correlate such nuclei without relying on error-prone peak peaking. However, false-positive artifacts in covariance spectra have impeded a general application to proteins. We recently introduced pre- and postprocessing steps to reduce the prevalence of artifacts in covariance spectra, allowing for the calculation of a variety of 4D covariance maps obtained from diverse combinations of pairs of 3D spectra, and we have employed them to assign backbone and sidechain resonances in two large and challenging proteins. In this chapter, we present a detailed protocol describing how to (1) properly prepare existing 3D spectra for covariance, (2) understand and apply our processing script, and (3) navigate and interpret the resulting 4D spectra. We also provide solutions to a number of errors that may occur when using our script, and we offer practical advice when assigning difficult signals. We believe such 4D spectra, and covariance NMR in general, can play an integral role in the assignment of NMR signals.

Covariance nuclear magnetic resonance methods for obtaining protein assignments and novel correlations

Protein NMR resonance assignment can be a tedious and error prone process, and it is often a limiting factor in biomolecular NMR studies. Challenges are exacerbated in larger proteins, disordered proteins, and often alpha-helical proteins, owing to an increase in spectral complexity and frequency degeneracies. Here, several multi-dimensional spectra must be inspected and compared in an iterative manner before resonances can be assigned with confidence. Over the last two decades, covariance NMR has evolved to become applicable to protein multi-dimensional spectra. The method, previously used to generate new correlations from spectra of small organic molecules, can now be used to recast assignment procedures as mathematical operations on NMR spectra. These operations result in multidimensional correlation maps combining all information from input spectra and providing direct correlations between moieties that would otherwise be compared indirectly through reporter nuclei. Thus, resonances of sequential residues can be identified and side-chain signals can be assigned by visual inspection of 4D arrays. This review highlights advances in covariance NMR that permitted to generate reliable 4D arrays and describes how these arrays can be obtained from conventional NMR spectra.

Ultra-high resolution in low field tabletop NMR spectrometers

An approach for resolution enhancement is proposed, for data acquired on low field tabletop NMR spectrometers by employing processing-based (generalized indirect covariance) advancements in pure shift NMR.

Access to experimentally infeasible spectra by pure-shift NMR covariance

Covariance processing is a versatile processing tool to generate synthetic NMR spectral representations without the need to acquire time-consuming experimental datasets. Here we show that even experimentally prohibited NMR spectra can be reconstructed by introducing key features of a reference 1D CHn-edited spectrum into standard 2D spectra. This general procedure is illustrated with the calculation of experimentally infeasible multiplicity-edited pure-shift NMR spectra of some very popular homonuclear (ME-psCOSY and ME-psTOCSY) and heteronuclear (ME-psHSQC-TOCSY and ME-psHMBC) experiments.

Exploring the use of Generalized Indirect Covariance to reconstruct pure shift NMR spectra: Current Pros and Cons

The current Pros and Cons of a processing protocol to generate pure chemical shift NMR spectra using Generalized Indirect Covariance are presented and discussed. The transformation of any standard 2D homonuclear and heteronuclear spectrum to its pure shift counterpart by using a reference DIAG spectrum is described. Reconstructed pure shift NMR spectra of NOESY, HSQC, HSQC-TOCSY and HSQMBC experiments are reported for the target molecule strychnine.

Applications of high dimensionality experiments to biomolecular NMR

High dimensionality NMR experiments facilitate resonance assignment and precise determination of spectral parameters such as coupling constants. Sparse non-uniform sampling enables acquisition of experiments of high dimensionality with high resolution in acceptable time. In this review we present and compare some significant applications of NMR experiments of dimensionality higher than three in the field of biomolecular studies in solution.

Effortless assignment with 4D covariance sequential correlation maps

Traditional Nuclear Magnetic Resonance (NMR) assignment procedures for proteins rely on preliminary peak-picking to identify and label NMR signals. However, such an approach has severe limitations when signals are erroneously labeled or completely neglected. The consequences are especially grave for proteins with substantial peak overlap, and mistakes can often thwart entire projects. To overcome these limitations, we previously introduced an assignment technique that bypasses traditional pick peaking altogether. Covariance Sequential Correlation Maps (COSCOMs) transform the indirect connectivity information provided by multiple 3D backbone spectra into direct (H, N) to (H, N) correlations. Here, we present an updated method that utilizes a single four-dimensional spectrum rather than a suite of three-dimensional spectra. We demonstrate the advantages of 4D-COSCOMs relative to their 3D counterparts. We introduce improvements accelerating their calculation. We discuss practical considerations affecting their quality. And finally we showcase their utility in the context of a 52 kDa cyclization domain from a non-ribosomal peptide synthetase.

Assignment of methyl NMR resonances of a 52 kDa protein with residue-specific 4D correlation maps

Methyl groups have become key probes for structural and functional studies by nuclear magnetic resonance. However, their NMR signals cluster in a small spectral region and assigning their resonances can be a tedious process. Here, we present a method that facilitates assignment of methyl resonances from assigned amide groups. Calculating the covariance between sensitive methyl and amide 3D spectra, each providing correlations to C(α) and C(β) separately, produces 4D correlation maps directly correlating methyl groups to amide groups. Optimal correlation maps are obtained by extracting residue-specific regions, applying derivative to the dimensions subject to covariance, and multiplying 4D maps stemming from different 3D spectra. The latter procedure rescues weak signals that may be missed in traditional assignment procedures. Using these covariance correlation maps, nearly all assigned isoleucine, leucine, and valine amide resonances of a 52 kDa nonribosomal peptide synthetase cyclization domain were paired with their corresponding methyl groups.

Nonuniform sampling and non-Fourier signal processing methods in multidimensional NMR

Beginning with the introduction of Fourier Transform NMR by Ernst and Anderson in 1966, time domain measurement of the impulse response (the free induction decay, FID) consisted of sampling the signal at a series of discrete intervals. For compatibility with the discrete Fourier transform (DFT), the intervals are kept uniform, and the Nyquist theorem dictates the largest value of the interval sufficient to avoid aliasing. With the proposal by Jeener of parametric sampling along an indirect time dimension, extension to multidimensional experiments employed the same sampling techniques used in one dimension, similarly subject to the Nyquist condition and suitable for processing via the discrete Fourier transform. The challenges of obtaining high-resolution spectral estimates from short data records using the DFT were already well understood, however. Despite techniques such as linear prediction extrapolation, the achievable resolution in the indirect dimensions is limited by practical constraints on measuring time. The advent of non-Fourier methods of spectrum analysis capable of processing nonuniformly sampled data has led to an explosion in the development of novel sampling strategies that avoid the limits on resolution and measurement time imposed by uniform sampling. The first part of this review discusses the many approaches to data sampling in multidimensional NMR, the second part highlights commonly used methods for signal processing of such data, and the review concludes with a discussion of other approaches to speeding up data acquisition in NMR.

Nonuniform sampling and non-Fourier signal processing methods in multidimensional NMR

Beginning with the introduction of Fourier Transform NMR by Ernst and Anderson in 1966, time domain measurement of the impulse response (the free induction decay, FID) consisted of sampling the signal at a series of discrete intervals. For compatibility with the discrete Fourier transform (DFT), the intervals are kept uniform, and the Nyquist theorem dictates the largest value of the interval sufficient to avoid aliasing. With the proposal by Jeener of parametric sampling along an indirect time dimension, extension to multidimensional experiments employed the same sampling techniques used in one dimension, similarly subject to the Nyquist condition and suitable for processing via the discrete Fourier transform. The challenges of obtaining high-resolution spectral estimates from short data records using the DFT were already well understood, however. Despite techniques such as linear prediction extrapolation, the achievable resolution in the indirect dimensions is limited by practical constraints on measuring time. The advent of non-Fourier methods of spectrum analysis capable of processing nonuniformly sampled data has led to an explosion in the development of novel sampling strategies that avoid the limits on resolution and measurement time imposed by uniform sampling. The first part of this review discusses the many approaches to data sampling in multidimensional NMR, the second part highlights commonly used methods for signal processing of such data, and the review concludes with a discussion of other approaches to speeding up data acquisition in NMR.

Facilitated assignment of large protein NMR signals with covariance sequential spectra using spectral derivatives

Nuclear magnetic resonance (NMR) studies of larger proteins are hampered by difficulties in assigning NMR resonances. Human intervention is typically required to identify NMR signals in 3D spectra, and subsequent procedures depend on the accuracy of this so-called peak picking. We present a method that provides sequential connectivities through correlation maps constructed with covariance NMR, bypassing the need for preliminary peak picking. We introduce two novel techniques to minimize false correlations and merge the information from all original 3D spectra. First, we take spectral derivatives prior to performing covariance to emphasize coincident peak maxima. Second, we multiply covariance maps calculated with different 3D spectra to destroy erroneous sequential correlations. The maps are easy to use and can readily be generated from conventional triple-resonance experiments. Advantages of the method are demonstrated on a 37 kDa nonribosomal peptide synthetase domain subject to spectral overlap.

A review of blind source separation in NMR spectroscopy

Fourier transform is the data processing naturally associated to most NMR experiments. Notable exceptions are Pulse Field Gradient and relaxation analysis, the structure of which is only partially suitable for FT. With the revamp of NMR of complex mixtures, fueled by analytical challenges such as metabolomics, alternative and more apt mathematical methods for data processing have been sought, with the aim of decomposing the NMR signal into simpler bits. Blind source separation is a very broad definition regrouping several classes of mathematical methods for complex signal decomposition that use no hypothesis on the form of the data. Developed outside NMR, these algorithms have been increasingly tested on spectra of mixtures. In this review, we shall provide an historical overview of the application of blind source separation methodologies to NMR, including methods specifically designed for the specificity of this spectroscopy.

Coniothyrione: anatomy of a structure revision

Coniothyrione is a xanthone-derived antibiotic reported several years ago by researchers at Merck & Co. Inc. Revision of the position of the chloro substitution was recently proposed on the basis of empirical reinterpretation of the carbon chemical shift data and a hypothetical biosynthetic argument without the acquisition of any new spectral data to support the postulated change in substituent location. The originally published HMBC data lead to an equivocal assignment of the structure and do not provide a solid basis of support for either structure. Neural network (13)C chemical shift calculations and density functional theory calculations also led to undifferentiated structures. Definitive confirmation of the structure of coniothyrione based on the acquisition and interpretation of 1,1-ADEQUATE and inverted (1)J(CC) 1,n-ADEQUATE data is now reported.

Using NMR to identify and characterize natural products

Over the past 28 years there have been several thousand publications describing the use of 2D NMR to identify and characterize natural products. During this time period, the amount of sample needed for this purpose has decreased from the 20-50 mg range to under 1 mg. This has been due to both improvements in NMR hardware and methodology. This review will focus on mainly methodology improvements, particularly in pulse sequences, acquisition and processing methods which are particularly relevant to natural product research, with lesser discussion of hardware improvements.

HMBC-1,n-ADEQUATE spectra calculated from HMBC and 1,n-ADEQUATE spectra

Unsymmetrical and generalized indirect covariance processing methods provide a means of mathematically combining pairs of 2D NMR spectra that share a common frequency domain to facilitate the extraction of correlation information. Previous reports have focused on the combination of HSQC spectra with 1,1-, 1,n-, and inverted (1)J(CC) 1,n-ADEQUATE spectra to afford carbon-carbon correlation spectra that allow the extraction of direct ((1)J(CC)), long-range ((n)J(CC), where n ≥ 2), and (1)J(CC)-edited long-range correlation data, respectively. Covariance processing of HMBC and 1,1-ADEQUATE spectra has also recently been reported, allowing convenient, high-sensitivity access to (n)J(CC) correlation data equivalent to the much lower sensitivity n,1-ADEQUATE experiment. Furthermore, HMBC-1,1-ADEQUATE correlations are observed in the F1 frequency domain at the intrinsic chemical shift of the (13)C resonance in question rather than at the double-quantum frequency of the pair of correlated carbons, as visualized by the n,1, and m,n-ADEQUATE experiments, greatly simplifying data interpretation. In an extension of previous work, the covariance processing of HMBC and 1,n-ADEQUATE spectra is now reported. The resulting HMBC-1,n-ADEQUATE spectrum affords long-range carbon-carbon correlation data equivalent to the very low sensitivity m,n-ADEQUATE experiment. In addition to the significantly higher sensitivity of the covariance calculated spectrum, correlations in the HMBC-1,n-ADEQUATE spectrum are again detected at the intrinsic (13)C chemical shifts of the correlated carbons rather than at the double-quantum frequency of the pair of correlated carbons. HMBC-1,n-ADEQUATE spectra can provide correlations ranging from diagonal ((0)J(CC) or diagonal correlations) to (4)J(CC) under normal circumstances to as much as (6)J(CC) in rare instances. The experiment affords the potential means of establishing the structures of severely proton-deficient molecules.

1J(CC)-edited HSQC-1,n-ADEQUATE: a new paradigm for simultaneous direct and long-range carbon-carbon correlation

Establishing the carbon skeleton of a molecule greatly facilitates the process of structure elucidation, leaving only heteroatoms to be inserted, heterocyclic rings to be closed, and stereochemical features to be defined. INADEQUATE, and more recently PANACEA, have been the only means of coming close to the goal of totally defining the carbon skeleton of a molecule. Unfortunately, the extremely low sensitivity and prodigious sample requirements of these experiments and the multiple receiver requirement for the latter experiment have severely restricted the usage of these experiments. Proton-detected ADEQUATE experiments, in contrast, have considerably higher sensitivity and more modest sample requirements. By combining experiments such as 1,1-ADEQUATE and 1,n-ADEQUATE with higher sensitivity experiments such as GHSQC through covariance processing, sample requirements can be further reduced with a commensurate improvement in the s/n ratio and F(1) resolution of the covariance processed spectrum. We now wish to report the covariance processing of an inverted (1)J(CC) 1,n-ADEQUATE experiment with a non-edited GHSQC spectrum to afford a spectrum that can trace the carbon skeleton of a molecule with the exception of correlations between quaternary carbons.

HMBC-1,1-ADEQUATE via generalized indirect covariance: a high sensitivity alternative to n,1-ADEQUATE

1,1-ADEQUATE and the related long-range 1,n- and n,1-ADEQUATE variants were developed to provide an unequivocal means of establishing (2)J(CH) and the equivalent of (n)J(CH) correlations where n = 3,4. Whereas the 1,1- and 1,n-ADEQUATE experiments have two simultaneous evolution periods that refocus the chemical shift and afford net single quantum evolution for the carbon spins, the n,1-variant has a single evolution period that leaves the carbon spin to be observed at the double quantum frequency. The n,1-ADEQUATE experiment begins with an HMBC-type (n)J(CH) magnetization transfer, which leads to inherently lower sensitivity than the 1,1- and 1,n-ADEQUATE experiments that begin with a (1)J(CH) transfer. These attributes, in tandem, serve to render the n,1-ADEQUATE experiment less generally applicable and more difficult to interpret than the 1,n-ADEQUATE experiment, which can in principle afford the same structural information. Unsymmetrical and generalized indirect covariance processing methods can complement and enhance the structural information encoded in combinations of experiments e.g. HSQC-1,1- or -1,n-ADEQUATE. Another benefit is that covariance processing methods offer the possibility of mathematically combining a higher sensitivity 2D NMR spectrum with for example 1,1- or 1,n-ADEQUATE to improve access to the information content of lower sensitivity congeners. The covariance spectrum also provides a significant enhancement in the F(1) digital resolution. The combination of HMBC and 1,1-ADEQUATE spectra is shown here using strychnine as a model compound to derive structural information inherent to an n,1-ADEQUATE spectrum with higher sensitivity and in a more convenient to interpret single quantum presentation.

HSQC-1,1-ADEQUATE and HSQC-1,n-ADEQUATE: enhanced methods for establishing adjacent and long-range 13C-13C connectivity networks

1H-13C GHSQC and GHMBC spectra are irrefutably among the most valuable 2D NMR experiments for the establishment of unknown chemical structures. However, the indeterminate nature of the length of the long-range coupling(s) observed via the (n)J(CH)-optimized delay of the GHMBC experiment can complicate the interpretation of the data when dealing with novel chemical structures. A priori there is no way to differentiate 2J(CH) from (n)J(CH) correlations, where n ≥ 3. Access to high-field spectrometers with cryogenic NMR probes brings 1,1- and 1,n-ADEQUATE experiments into range for modest samples. Subjecting ADEQUATE spectra to covariance processing with high sensitivity experiments such as multiplicity-edited GHSQC affords a diagonally symmetric 13C-13C correlation spectrum in which correlation data are observed with the apparent sensitivity of the GHSQC spectrum. HSQC-1,1-ADEQUATE covariance spectra derived by co-processing of GHSQC and 1,1-ADEQUATE spectra allow the carbon skeleton of molecules to be conveniently traced. HSQC-1,n-ADEQUATE spectra provide enhanced access to correlations equivalent to 4J(CH) correlations in a GHMBC spectrum. When these data are used to supplement GHMBC data, a powerfully synergistic set of heteronuclear correlations are available. The methods discussed are illustrated using retrorsine (1) as a model compound.

The use of 1H-31P GHMBC and covariance NMR to unambiguously determine phosphate ester linkages in complex polysaccharide mixtures

Poly- and oligo-saccharides are commonly employed as antigens in many vaccines. These antigens contain phosphoester structural elements that are crucial to the antigenicity, and hence the effectiveness of the vaccine. Nuclear Magnetic Resonance (NMR) is a powerful tool for the site-specific identification of phosphoesters in saccharides. We describe here two advances in the characterization of phosphoesters in saccharides: (1) the use of (1)H-(31)P GHMBC to determine the site-specific identity of phosphoester moieties in heterogeneous mixtures and (2) the use of Unsymmetrical/Generalized Indirect Covariance (U/GIC) to calculate a carbon-phosphorus 2D spectrum. The sensitivity of the (1)H-(31)P GHMBC is far greater than the "standard" (1)H-(31)P GHSQC and allows long-range (3-5)J(HP) couplings to be readily detected. This is the first example to be reported of using U/GIC to calculate a carbon-phosphorus spectrum. The U/GIC processing affords, in many cases, a fivefold to tenfold or greater increase in signal-to-noise ratios in the calculated spectrum. When coupled with the high sensitivity of (1)H-(31)P HMBC, U/GIC processing allows the complete and unambiguous assignments of phosphoester moieties present in heterogeneous samples at levels of ~5% (or less) of the total sample, expanding the breadth of samples that NMR can be used to analyze. This new analytical technique is generally applicable to any NMR-observable phosphoester.

HSQC-1,n-ADEQUATE: a new approach to long-range 13C-13C correlation by covariance processing

Long-range, two-dimensional heteronuclear shift correlation NMR methods play a pivotal role in the assembly of novel molecular structures. The well-established GHMBC method is a high-sensitivity mainstay technique, affording connectivity information via (n)J(CH) coupling pathways. Unfortunately, there is no simple way of determining the value of n and hence no way of differentiating two-bond from three- and occasionally four-bond correlations. Three-bond correlations, however, generally predominate. Recent work has shown that the unsymmetrical indirect covariance or generalized indirect covariance processing of multiplicity edited GHSQC and 1,1-ADEQUATE spectra provides high-sensitivity access to a (13)C-(13) C connectivity map in the form of an HSQC-1,1-ADEQUATE spectrum. Covariance processing of these data allows the 1,1-ADEQUATE connectivity information to be exploited with the inherent sensitivity of the GHSQC spectrum rather than the intrinsically lower sensitivity of the 1,1-ADEQUATE spectrum itself. Data acquisition times and/or sample size can be substantially reduced when covariance processing is to be employed. In an extension of that work, 1,n-ADEQUATE spectra can likewise be subjected to covariance processing to afford high-sensitivity access to the equivalent of (4)J(CH) GHMBC connectivity information. The method is illustrated using strychnine as a model compound.

Using indirect covariance processing for structure elucidation of small molecules in cases of spectral crowding

Indirect and unsymmetrical indirect covariance NMR provide powerful tools to compute and visualize correlation information by transforming component spectra into combined spectral data matrices. Sensitive component spectra such as TOCSY, HSQC and NOESY can be quickly converted into experimentally insensitive or time-consuming correlation spectra such as HSQC-NOESY. The comparison of illustrative series of spectra from four steroids, dexamethasone, testosterone, allylestrenol and tibolone, renders the effects of resonance overlap on the ease of interpretation visible. The compounds are selected such that signal overlap increases systematically in the proton and carbon domain. Spectra are defined as light, moderate and heavy signal overlap, based on signal density. The investigation suggests that moderate spectral congestion in either proton or carbon domain leads to a number of artifacts that does not hamper signal assignment but lowers the level of confidence on de novo structure elucidation. Since the number of correlations usually increases through covariance processing, component spectra with severe spectral congestion in both dimensions are not suitable for covariance processing and the resulting spectra do not support structure confirmation or structure elucidation. The calculated spectra are compared with the corresponding experimental spectra with respect to their application in structure elucidation laboratory environments.

HSQC-ADEQUATE: an investigation of data requirements

Utilizing (13)C-(13)C connectivity networks for the assembly of carbon skeletons from HSQC-ADEQUATE spectra was recently reported. HSQC-ADEQUATE data retain the resonance multiplicity information of the multiplicity-edited GHSQC spectrum and afford a significant improvement in the signal-to-noise (s/n) ratio relative to the 1,1-ADEQUATE data used in the calculation of the HSQC-ADEQUATE spectrum by unsymmetrical indirect covariance (UIC) processing methods. The initial investigation into the computation of HSQC-ADEQUATE correlation plots utilized overnight acquisition of the 1,1-ADEQUATE data used for the calculation. In this communication, we report the results of an investigation of the reduction in acquisition time for the 1,1-ADEQUATE data to take advantage of the s/n gain during the UIC processing to afford the final HSQC-ADEQUATE correlation plot. Data acquisition times for the 1,1-ADEQUATE spectrum can be reduced to as little as a few hours, while retaining excellent s/n ratios and all responses contained in spectra computed from overnight data acquisitions. Concatenation of multiplicity-edited GHSQC and 1,1-ADEQUATE data also allows the interrogation of submilligram samples with 1,1-ADEQUATE data when using spectrometers equipped with 1.7-mm Micro CryoProbes ™.

HSQC-ADEQUATE correlation: a new paradigm for establishing a molecular skeleton

Various experimental methods have been developed to unequivocally identify vicinal neighbor carbon atoms. Variants of the HMBC experiment intended for this purpose have included 2J3J-HMBC and H2BC. The 1,1-ADEQUATE experiment, in contrast, was developed to accomplish the same goal but relies on the (1) J(CC) coupling between a proton-carbon resonant pair and the adjacent neighbor carbon. Hence, 1,1-ADEQUATE can identify non-protonated adjacent neighbor carbons, whereas the 2J3J-HMBC and H2BC experiments require both neighbor carbons to be protonated to operate. Since 1,1-ADEQUATE data are normally interpreted with close reference to an HSQC spectrum of the molecule in question, we were interested in exploring the unsymmetrical indirect covariance processing of multiplicity-edited GHSQC and 1,1-ADEQUATE spectra to afford an HSQC-ADEQUATE correlation spectrum that facilitates the extraction of carbon-carbon connectivity information. The HSQC-ADEQUATE spectrum of strychnine is shown and the means by which the carbon skeleton can be conveniently traced is discussed.

A covariance NMR toolbox for MATLAB and OCTAVE

The Covariance NMR Toolbox is a new software suite that provides a streamlined implementation of covariance-based analysis of multi-dimensional NMR data. The Covariance NMR Toolbox uses the MATLAB or, alternatively, the freely available GNU OCTAVE computer language, providing a user-friendly environment in which to apply and explore covariance techniques. Covariance methods implemented in the toolbox described here include direct and indirect covariance processing, 4D covariance, generalized indirect covariance (GIC), and Z-matrix transform. In order to provide compatibility with a wide variety of spectrometer and spectral analysis platforms, the Covariance NMR Toolbox uses the NMRPipe format for both input and output files. Additionally, datasets small enough to fit in memory are stored as arrays that can be displayed and further manipulated in a versatile manner within MATLAB or OCTAVE.

A practical implementation of cross-spectrum in protein backbone resonance assignment

The concept of cross-spectrum is applied in protein NMR spectroscopy to assist in the backbone sequential resonance assignment. Cross-spectrum analysis is used routinely to reveal correlations in frequency domains as a means to reveal common features contained in multiple time series. Here the cross-spectrum between related NMR spectra, for example HNCO and HN(CA)CO, can be calculated with point-by-point multiplications along their common C' carbon axis. In the resulting higher order cross-spectrum, an enhanced correlation signal occurs at every common i-1 carbon frequency allowing the amide proton H(N) (and nitrogen N) resonances from residues i and i-1 to be identified. The cross-spectrum approach is demonstrated using 2D spectra H(N)CO, H(NCA)CO, H(NCO)CACB, and H(N)CACB measured on a 15N/13C double-labeled Ubiquitin sample. These 2D spectra are used to calculate two pseudo-3D cross-spectra, H(i)-H(i)(-1)-C'(i)(-1) and H(i)-H(i)(-1)-CA(i)(-1)CB(i)(-1). We show using this approach, backbone resonances of H, C', CA, and CB can be fully assigned without ambiguity. The cross-spectrum principle is expected to offer an easy, practical, and more quantitative approach for heteronuclear backbone resonance assignment.