Multiple-quantum magic-angle spinning spectroscopy using nonlinear sampling

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.

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.

17O NMR studies of organic and biological molecules in aqueous solution and in the solid state

This review describes the latest developments in the field of ¹⁷O NMR spectroscopy of organic and biological molecules both in aqueous solution and in the solid state. In the first part of the review, a general theoretical description of the nuclear quadrupole relaxation process in isotropic liquids is presented at a mathematical level suitable for non-specialists. In addition to the first-order quadrupole interaction, the theory also includes additional relaxation mechanisms such as the second-order quadrupole interaction and its cross correlation with shielding anisotropy. This complete theoretical treatment allows one to assess the transverse relaxation rate (thus the line width) of NMR signals from half-integer quadrupolar nuclei in solution over the entire range of motion. On the basis of this theoretical framework, we discuss general features of quadrupole-central-transition (QCT) NMR, which is a particularly powerful method of studying biomolecules in the slow motion regime. Then we review recent advances in ¹⁷O QCT NMR studies of biological macromolecules in aqueous solution. The second part of the review is concerned with solid-state ¹⁷O NMR studies of organic and biological molecules. As a sequel to the previous review on the same subject [G. Wu, Prog. Nucl. Magn. Reson. Spectrosc. 52 (2008) 118-169], the current review provides a complete coverage of the literature published since 2008 in this area.

NMR of Macromolecular Assemblies and Machines at 1 GHz and Beyond: New Transformative Opportunities for Molecular Structural Biology

As a result of profound gains in sensitivity and resolution afforded by ultrahigh magnetic fields, transformative applications in the fields of structural biology and materials science are being realized. The development of dual low temperature superconducting (LTS)/high-temperature superconducting (HTS) magnets has enabled the achievement of magnetic fields above 1 GHz (23.5 T), which will open doors to an unprecedented new range of applications. In this contribution, we discuss the promise of ultrahigh field magnetic resonance. We highlight several methodological developments pertinent at high-magnetic fields including measurement of 1H-1H distances and 1H chemical shift anisotropy in the solid state as well as studies of quadrupolar nuclei such as 17O. Higher magnetic fields have advanced heteronuclear detection in solution NMR, valuable for applications including metabolomics and disordered proteins, as well as expanded use of proton detection in the solid state in conjunction with ultrafast magic angle spinning. We also present several recent applications to structural studies of the AP205 bacteriophage, the M2 channel from Influenza A, and biomaterials such as human bone. Gains in sensitivity and resolution from increased field strengths will enable advanced applications of NMR spectroscopy including in vivo studies of whole cells and intact virions.

Oxygen-17 NMR spectroscopy of water molecules in solid hydrates

17O solid-state NMR studies of waters of hydration in crystalline solids are presented. The 17O quadrupolar coupling and chemical shift (CS) tensors, and their relative orientations, are measured experimentally at room temperature for α-oxalic acid dihydrate, barium chlorate monohydrate, lithium sulfate monohydrate, potassium oxalate monohydrate, and sodium perchlorate monohydrate. The 17O quadrupolar coupling constants (CQ) range from 6.6 to 7.35 MHz and the isotropic chemical shifts range from –17 to 19.7 ppm. The oxygen CS tensor spans vary from 25 to 78 ppm. These represent the first complete CS and electric field gradient tensor measurements for water coordinated to metals in the solid state. Gauge-including projector-augmented wave density functional theory calculations overestimate the values of CQ, likely due to librational dynamics of the water molecules. Computed CS tensors only qualitatively match the experimental data. The lack of strong correlations between the experimental and computed data, and between these data and any single structural feature, is attributed to motion of the water molecules and to the relatively small overall range in the NMR parameters relative to their measurement precision. Nevertheless, the isotropic chemical shift, quadrupolar coupling constant, and CS tensor span clearly differentiate between the samples studied and establish a ‘fingerprint’ 17O spectral region for water coordinated to metals in solids.

Solid-State ¹⁷O NMR studies of organic and biological molecules: Recent advances and future directions

This Trends article highlights the recent advances published between 2012 and 2015 in solid-state (17)O NMR for organic and biological molecules. New developments in the following areas are described: (1) new oxygen-containing functional groups, (2) metal organic frameworks, (3) pharmaceuticals, (4) probing molecular motion in organic solids, (5) dynamic nuclear polarization, and (6) paramagnetic coordination compounds. For each of these areas, the author offers his personal views on important problems to be solved and possible future directions.

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

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

Sensitivity gains, linearity, and spectral reproducibility in nonuniformly sampled multidimensional MAS NMR spectra of high dynamic range

Recently, we have demonstrated that considerable inherent sensitivity gains are attained in MAS NMR spectra acquired by nonuniform sampling (NUS) and introduced maximum entropy interpolation (MINT) processing that assures the linearity of transformation between the time and frequency domains. In this report, we examine the utility of the NUS/MINT approach in multidimensional datasets possessing high dynamic range, such as homonuclear (13)C-(13)C correlation spectra. We demonstrate on model compounds and on 1-73-(U-(13)C,(15)N)/74-108-(U-(15)N) E. coli thioredoxin reassembly, that with appropriately constructed 50% NUS schedules inherent sensitivity gains of 1.7-2.1-fold are readily reached in such datasets. We show that both linearity and line width are retained under these experimental conditions throughout the entire dynamic range of the signals. Furthermore, we demonstrate that the reproducibility of the peak intensities is excellent in the NUS/MINT approach when experiments are repeated multiple times and identical experimental and processing conditions are employed. Finally, we discuss the principles for design and implementation of random exponentially biased NUS sampling schedules for homonuclear (13)C-(13)C MAS correlation experiments that yield high-quality artifact-free datasets.

Nonuniform sampling and maximum entropy reconstruction in multidimensional NMR

NMR spectroscopy is one of the most powerful and versatile analytic tools available to chemists. The discrete Fourier transform (DFT) played a seminal role in the development of modern NMR, including the multidimensional methods that are essential for characterizing complex biomolecules. However, it suffers from well-known limitations: chiefly the difficulty in obtaining high-resolution spectral estimates from short data records. Because the time required to perform an experiment is proportional to the number of data samples, this problem imposes a sampling burden for multidimensional NMR experiments. At high magnetic field, where spectral dispersion is greatest, the problem becomes particularly acute. Consequently multidimensional NMR experiments that rely on the DFT must either sacrifice resolution in order to be completed in reasonable time or use inordinate amounts of time to achieve the potential resolution afforded by high-field magnets. Maximum entropy (MaxEnt) reconstruction is a non-Fourier method of spectrum analysis that can provide high-resolution spectral estimates from short data records. It can also be used with nonuniformly sampled data sets. Since resolution is substantially determined by the largest evolution time sampled, nonuniform sampling enables high resolution while avoiding the need to uniformly sample at large numbers of evolution times. The Nyquist sampling theorem does not apply to nonuniformly sampled data, and artifacts that occur with the use of nonuniform sampling can be viewed as frequency-aliased signals. Strategies for suppressing nonuniform sampling artifacts include the careful design of the sampling scheme and special methods for computing the spectrum. Researchers now routinely report that they can complete an N-dimensional NMR experiment 3(N-1) times faster (a 3D experiment in one ninth of the time). As a result, high-resolution three- and four-dimensional experiments that were prohibitively time consuming are now practical. Conversely, tailored sampling in the indirect dimensions has led to improved sensitivity. Further advances in nonuniform sampling strategies could enable further reductions in sampling requirements for high resolution NMR spectra, and the combination of these strategies with robust non-Fourier methods of spectrum analysis (such as MaxEnt) represent a profound change in the way researchers conduct multidimensional experiments. The potential benefits will enable more advanced applications of multidimensional NMR spectroscopy to study biological macromolecules, metabolomics, natural products, dynamic systems, and other areas where resolution, sensitivity, or experiment time are limiting. Just as the development of multidimensional NMR methods presaged multidimensional methods in other areas of spectroscopy, we anticipate that nonuniform sampling approaches will find applications in other forms of spectroscopy.

A time-saving strategy for MAS NMR spectroscopy by combining nonuniform sampling and paramagnetic relaxation assisted condensed data collection

We present a time-saving strategy for acquiring 3D magic angle spinning NMR spectra for chemical shift assignments in proteins and protein assemblies in the solid state. By simultaneous application of nonuniform sampling (NUS) and paramagnetic-relaxation-assisted condensed data collection (PACC), we can attain 16-fold time reduction in the 3D experiments without sacrificing the signal-to-noise ratio or the resolution. We demonstrate that with appropriate concentration of paramagnetic dopant introduced into the sample the overwhelming majority of chemical shifts are not perturbed, with the exception of a limited number of shifts corresponding to residues located at the surface of the protein, which exhibit small perturbations. This approach enables multidimensional MAS spectroscopy in samples of intrinsically low sensitivity and/or high spectral congestion where traditional experiments fail, and is especially beneficial for structural and dynamics studies of large proteins and protein assemblies.

Enhanced sensitivity by nonuniform sampling enables multidimensional MAS NMR spectroscopy of protein assemblies

We report dramatic sensitivity enhancements in multidimensional MAS NMR spectra by the use of nonuniform sampling (NUS) and introduce maximum entropy interpolation (MINT) processing that assures the linearity between the time and frequency domains of the NUS acquired data sets. A systematic analysis of sensitivity and resolution in 2D and 3D NUS spectra reveals that with NUS, at least 1.5- to 2-fold sensitivity enhancement can be attained in each indirect dimension without compromising the spectral resolution. These enhancements are similar to or higher than those attained by the newest-generation commercial cryogenic probes. We explore the benefits of this NUS/MaxEnt approach in proteins and protein assemblies using 1-73-(U-(13)C,(15)N)/74-108-(U-(15)N) Escherichia coli thioredoxin reassembly. We demonstrate that in thioredoxin reassembly, NUS permits acquisition of high-quality 3D-NCACX spectra, which are inaccessible with conventional sampling due to prohibitively long experiment times. Of critical importance, issues that hinder NUS-based SNR enhancement in 3D-NMR of liquids are mitigated in the study of solid samples in which theoretical enhancements on the order of 3-4 fold are accessible by compounding the NUS-based SNR enhancement of each indirect dimension. NUS/MINT is anticipated to be widely applicable and advantageous for multidimensional heteronuclear MAS NMR spectroscopy of proteins, protein assemblies, and other biological systems.

Deterministic schedules for robust and reproducible non-uniform sampling in multidimensional NMR

We show that a simple, general, and easily reproducible method for generating non-uniform sampling (NUS) schedules preserves the benefits of random sampling, including inherently reduced sampling artifacts, while removing the pitfalls associated with choosing an arbitrary seed. Sampling schedules are generated from a discrete cumulative distribution function (CDF) that closely fits the continuous CDF of the desired probability density function. We compare random and deterministic sampling using a Gaussian probability density function applied to 2D HSQC spectra. Data are processed using the previously published method of Spectroscopy by Integration of Frequency and Time domain data (SIFT). NUS spectra from deterministic sampling schedules were found to be at least as good as those from random schedules at the SIFT critical sampling density, and significantly better at half that sampling density. The method can be applied to any probability density function and generalized to greater than two dimensions.

Sensitivity enhancement for maximally resolved two-dimensional NMR by nonuniform sampling

Resolving NMR signals which are separated in frequency on the order of their line widths requires obtaining the time domain free induction decay for a maximum time tmax = πT2 , where T2 is the transverse relaxation time of the given signals. Unfortunately, samples acquired beyond ∼1.26T2 contribute more noise than signal to the data; and samples in the range of about (0.75-1.26)× T2 have a negligible effect on the signal-to-noise ratio (SNR). Therefore, one must sacrifice SNR to reach evolution times of πT2 . One can preserve resolution in a shorter total experimental time by selecting a reduced set of samples from the Nyquist grid according to an exponential probability density which is on the order of the T2 of the signals. This practice is widely termed nonuniform sampling (NUS). We derive analytic theory for the enhancement of the intrinsic SNR of NUS time domain data compared with uniformly sampled data when the total experimental times are equivalent. This theory is general for any tmax and exponential weighting and is further carefully validated with simulations. Enhancements of SNR in the time domain on the order of twofold are routinely available when tmax ∼ πT2 and are reflected in the subsequent maximum entropy reconstructed spectra. SNR enhancement by NUS is demonstrated to be helpful in enabling the acquisition of HMQC spectra of dilute bile salts in which high resolution in the indirect carbon dimension is required.

Noise reduction by dynamic signal preemphasis

In this work we propose an approach to reduce the digitization noise for a given dynamic range, i.e., the number of bits, of an analog to digital converter used in an NMR receiver. In this approach, the receiver gain is dynamically increased so that the free induction decay is recorded in such an emphasized way that the decaying signal is digitized using as many number of bits as possible, and at the stage of data processing, the original signal profile is restored by applying the apodization that compensates the effect of the preemphasis. This approach, which we call APodization after Receiver gain InCrement during Ongoing sequence with Time (APRICOT), is performed in a solid-state system containing a pair of (13)C spins, one of which is fully isotopically labeled and the other is naturally abundant. It is demonstrated that the exceedingly smaller peak buried in the digitization noise in the conventional approach can be revealed by employing APRICOT.

Probing quadrupolar nuclei by solid-state NMR spectroscopy: recent advances

Solid-state nuclear magnetic resonance (NMR) of quadrupolar nuclei has recently undergone remarkable development of capabilities for obtaining structural and dynamic information at the molecular level. This review summarizes the key achievements attained during the last couple of decades in solid-state NMR of both integer spin and half-integer spin quadrupolar nuclei. We provide a concise description of the first- and second-order quadrupolar interactions, and their effect on the static and magic angle spinning (MAS) spectra. Methods are explained for efficient excitation of single- and multiple-quantum coherences, and acquisition of spectra under low- and high-resolution conditions. Most of all, we present a coherent, comparative description of the high-resolution methods for half-integer quadrupolar nuclei, including double rotation (DOR), dynamic angle spinning (DAS), multiple-quantum magic angle spinning (MQMAS), and satellite transition magic angle spinning (STMAS). Also highlighted are methods for processing and analysis of the spectra. Finally, we review methods for probing the heteronuclear and homonuclear correlations between the quadrupolar nuclei and their quadrupolar or spin-1/2 neighbors.

Boltzmann statistics rotational-echo double-resonance analysis

A new approach to rotational-echo double-resonance (REDOR) data analysis, analogous to Boltzmann maximum entropy statistics, is reported. This Boltzmann statistics REDOR (BS-REDOR) approach is useful for reconstructing an unbiased internuclear distance distribution for multiple internuclear distances from experimentally limited REDOR data sets on isolated spin pairs. The analysis is characterized by exploring reconstructions on model data and applied to both [1-(13)C,15N]-glycine and a long intramolecular distance in Abeta (16-22) peptide nanotubes. The approach also provides insight into the minimal number of REDOR data points required to allow faithful determination of dipolar couplings in systems with multiple internuclear distances.

Nonuniform sampling and maximum entropy reconstruction applied to the accurate measurement of residual dipolar couplings

Residual dipolar couplings (RDC) provide important global restraints for accurate structure determination by NMR. We show that nonuniform sampling in combination with maximum entropy reconstruction (MaxEnt) is a promising strategy for accelerating and potentially enhancing the acquisition of RDC spectra. Using MaxEnt-processed spectra of nonuniformly sampled data sets that are reduced up to one fifth relative to uniform sampling, accurate 13C'-13Calpha RDCs can be obtained that agree with an RMS of 0.67 Hz with those derived from uniformly sampled, Fourier transformed spectra. While confirming that frequency errors in MaxEnt spectra are very slight, an unexpected class of systematic errors was found to occur in the 6th significant figure of 13C' chemical shifts of doublets obtained by MaxEnt reconstruction. We show that this error stems from slight line shape perturbations and predict it should be encountered in other nonlinear spectral estimation algorithms. In the case of MaxEnt reconstruction, the error can easily be rendered systematic by straightforward optimization of MaxEnt reconstruction parameters and self-cancels in obtaining RDCs from nonuniformly sampled, MaxEnt reconstructed spectra.

Ultrafast Solid-State 2D NMR Experiments via Orientational Encoding

Among the methods proposed in recent years toward the acceleration of multidimensional NMR acquisitions is an "ultrafast" approach, capable of delivering arbitrary 2D correlations within a single scan. This scheme operates by parallelizing the indirect-domain temporal incrementation involved in 2D acquisitions, using as aid an ancillary inhomogeneous frequency broadening acting in combination with a train of frequency-shifted RF pulses. So far, all implementations of this frequency broadening have relied on magnetic field gradients; yet the practical performance of gradient-based approaches is sometimes inadequate-for instance when applied on solid samples subject to magic-angle spinning. In order to deal with these cases, an alternative encoding protocol is here introduced and experimentally exemplified, based on exploiting the intrinsic anisotropy that spin interactions exhibit in the solid state as the ancillary broadening in charge of encoding the interactions to be measured. Principles and preliminary examples of the new orientationally encoded ultrafast 2D NMR principle thus resulting are presented and discussed.

Application of Maximum Entropy reconstruction to PISEMA spectra

Maximum Entropy reconstruction is applied to two-dimensional PISEMA spectra of stationary samples of peptide crystals and proteins in magnetically aligned virus particles and membrane bilayers. Improvements in signal-to-noise ratios were observed with minimal distortion of the spectra when Maximum Entropy reconstruction was applied to non-linearly sampled data in the indirect dimension. Maximum Entropy reconstruction was also applied in the direct dimension by selecting sub-sets of data from the free induction decays. Because the noise is uncorrelated in the spectra obtained by Maximum Entropy reconstruction of data with different non-linear sampling schedules, it is possible to improve the signal-to-noise ratios by co-addition of multiple spectra derived from one experimental data set. The combined application of Maximum Entropy to data in the indirect and direct dimensions has the potential to lead to substantial reductions in the total amount of experimental time required for acquisition of data in multidimensional NMR experiments.

Fast acquisition of NMR spectra using Fourier transform of non-equispaced data

Rapid acquisition of high-resolution 2D and 3D NMR spectra is essential for studying biological macromolecules. In order to minimize the experimental time, a non-linear sampling scheme is proposed for the indirect dimensions of multidimensional experiments. These data can be processed using the algorithm proposed by Dutt and Rokhlin (Appl. Comp. Harm. Anal. 1995, 2, 85-100) for fast Fourier transforms of non equispaced data. Examples of 1H-(15)N HSQC spectra are shown, where crowded correlation peaks can be resolved using non-linear acquisition. Simulated data have been used to analyze the artefacts produced by the Lagrange interpolation. As compared to non-linear processing methods, this algorithm is simple and highly robust since no parameters need to be adjusted by the user.

Cancer promoted by the oncoprotein v-ErbA may be due to subcellular mislocalization of nuclear receptors

The retroviral v-ErbA oncoprotein is a highly mutated variant of the thyroid hormone receptor alpha (TRalpha), which is unable to bind T(3) and interferes with the action of TRalpha in mammalian and avian cancer cells. v-ErbA dominant-negative activity is attributed to competition with TRalpha for T(3)-responsive DNA elements and/or auxiliary factors involved in the transcriptional regulation of T(3)-responsive genes. However, competition models do not address the altered subcellular localization of v-ErbA and its possible implications in oncogenesis. Here, we report that v-ErbA dimerizes with TRalpha and the retinoid X receptor and sequesters a significant fraction of the two nuclear receptors in the cytoplasm. Recruitment of TRalpha to the cytoplasm by v-ErbA can be partially reversed in the presence of ligand and when chromatin is disrupted by the histone deacetylase inhibitor trichostatin A. These results define a new mode of action of v-ErbA and illustrate the importance of cellular compartmentalization in transcriptional regulation and oncogenesis.

High-resolution aliphatic side-chain assignments in 3D HCcoNH experiments with joint H-C evolution and non-uniform sampling

We describe an efficient NMR triple resonance approach that correlates, at high resolution, protein side-chain and backbone resonances. It relies on the combination of two strategies: joint evolution of aliphatic side-chain proton/carbon coherences using a backbone N-H based HCcoNH reduced dimensionality (RD) experiment and non-uniform sampling (NUS) in two indirect dimensions. A typical data set containing such correlation information can be acquired in 2 days, at very high resolution unfeasible for conventional 4D HCcoNH-TOCSY experiments. The resonances of the aliphatic side-chain protons are unambiguously assigned to their attached carbons through the analysis of the 'sum' and 'difference' spectra. This approach circumvents the tedious process of manual resonance assignments using HCcH-TOCSY data, while providing additional resolving power of backbone N-H signals. A simple peak-list based algorithm has been implemented in the IBIS software for rapid automated backbone and side-chain assignments.

Maximum entropy deconvolution of infrared spectra: use of a novel entropy expression without sign restriction

Absorbance and difference infrared spectra are often acquired aiming to characterize protein structure and structural changes of proteins upon ligand binding, as well as for many other chemical and biochemical studies. Their analysis requires as a first step the identification of the component bands (number, position, and area) and as a second step their assignment. The first step of the analysis is challenged by the habitually strong band overlap in infrared spectra. Therefore, it is useful to make use of a mathematical method able to narrow the component bands to the extent to eliminate, or at least reduce, the band overlap. Additionally, to be of general applicability this method should permit negative values for the solution. We present a maximum entropy deconvolution approach for the band-narrowing of absorbance and difference spectra showing the required characteristics, which uses the generalized negative Burg-entropy (Itakura-Saito discrepancy) generalized for difference spectra. We present results on synthetic noisy absorbance and difference spectra, as well as on experimental infrared spectra from the membrane protein bacteriorhodopsin.

3D NMR spectroscopy for resonance assignment and structure elucidation of proteins under MAS: novel pulse schemes and sensitivity considerations

Two types of 3D MAS NMR experiments are introduced, which combine standard (NC,CC) transfer schemes with (1H,1H) mixing to simultaneously detect connectivities and structural constraints of uniformly 15N,13C-labeled proteins with high spectral resolution. The homonuclear CCHHC and CCC experiments are recorded with one double-quantum evolution dimension in order to avoid a cubic diagonal in the spectrum. Depending on the second transfer step, spin systems or proton-proton contacts can be determined with reduced spectral overlap. The heteronuclear NHHCC experiment encodes NH-HC proton-proton interactions, which are indicative for the backbone conformation of the protein. The third dimension facilitates the identification of the amino acid spin system. Experimental results on U-[15N,13C]valine and U-[15N,13C]ubiquitin demonstrate their usefulness for resonance assignments and for the determination of structural constraints. Furthermore, we give a detailed analysis of alternative multidimensional sampling schemes and their effect on sensitivity and resolution.

Accelerated acquisition of high resolution triple-resonance spectra using non-uniform sampling and maximum entropy reconstruction

Non-uniform sampling is shown to provide significant time savings in the acquisition of a suite of three-dimensional NMR experiments utilized for obtaining backbone assignments of H, N, C', CA, and CB nuclei in proteins : HNCO, HN(CA)CO, HNCA, HN(CO)CA, HNCACB, and HN(CO)CACB. Non-uniform sampling means that data were collected for only a subset of all incremented evolution periods, according to a user-specified sampling schedule. When the suite of six 3D experiments was acquired in a uniform fashion for an 11 kDa cytoplasmic domain of a membrane protein at 1.5 mM concentration, a total of 146 h was consumed. With non-uniform sampling, the same experiments were acquired in 32 h and, through subsequent maximum entropy reconstruction, yielded spectra of similar quality to those obtained by conventional Fourier transform of the uniformly acquired data. The experimental time saved with this methodology can significantly accelerate protein structure determination by NMR, particularly when combined with the use of automated assignment software, and enable the study of samples with poor stability at room temperature. Since it is also possible to use the time savings to acquire a greater numbers of scans to increase sensitivity while maintaining high resolution, this methodology will help extend the size limit of proteins accessible to NMR studies, and open the way to studies of samples that suffer from solubility problems.

Field-cycling method with central transition readout for pure quadrupole resonance detection in dilute systems

We present a modification of a field-cycling method which uses the NMR signal of the central transition at high field to indirectly detect zero-field quadrupole transitions. The quadrupole transitions at zero-field are detected as changes in the overall intensity of the central transition signal after the field cycle, and the method is relatively immune to lineshape distortions of the central transition caused by receiver dead time, frequency response of the probe, longer pulse lengths, etc. Cross-polarization with protons is used to enhance the central-transition signal and to increase the recycling rate of the experiment. The technique is especially useful when mixtures of several species are present. In a frozen solution of phenylboronic acid, 11B quadrupole signals of the tetrahedral species at 600 kHz and planar-trigonal species at 1450 kHz are clearly resolved. The field-cycling approach allows high-sensitivity detection of low-frequency quadrupole transitions; the experiment is sensitive enough to study boronic-acid protease inhibitors bound to proteins and may possibly be extended to lower sensitivity nuclei. The experiments are performed using a low-temperature field-cycling apparatus, operated at 10-30 K, capable of pneumatically moving the sample from the high field of a commercial 500 MHz magnet to the area above the top of the magnet where the low field is controlled by a pair of Helmholz coils.