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Although the concepts of nonuniform sampling (NUS​​​​​​​) and non-Fourier spectral reconstruction in multidimensional NMR began to emerge 4 decades ago (Bodenhausen and Ernst, 1981; Barna and Laue, 1987), it is only relatively recently that NUS has become more commonplace. Advantages of NUS include the ability to tailor experiments to reduce data collection time and to improve spectral quality, whether through detection of closely spaced peaks (i.e., “resolution”) or peaks of weak intensity (i.e., “sensitivity”). Wider adoption of these methods is the result of improvements in computational performance, a growing abundance and flexibility of software, support from NMR spectrometer vendors, and the increased data sampling demands imposed by higher magnetic fields. However, the identification of best practices still remains a significant and unmet challenge. Unlike the discrete Fourier transform, non-Fourier methods used to reconstruct spectra from NUS data are nonlinear, depend on the complexity and nature of the signals, and lack quantitative or formal theory describing their performance. Seemingly subtle algorithmic differences may lead to significant variabilities in spectral qualities and artifacts. A community-based critical assessment of NUS challenge problems has been initiated, called the “Nonuniform Sampling Contest” (NUScon), with the objective of determining best practices for processing and analyzing NUS experiments. We address this objective by constructing challenges from NMR experiments that we inject with synthetic signals, and we process these challenges using workflows submitted by the community. In the initial rounds of NUScon our aim is to establish objective criteria for evaluating the quality of spectral reconstructions. We present here a software package for performing the quantitative analyses, and we present the results from the first two rounds of NUScon. We discuss the challenges that remain and present a roadmap for continued community-driven development with the ultimate aim of providing best practices in this rapidly evolving field. The NUScon software package and all data from evaluating the challenge problems are hosted on the NMRbox platform.

Recent global declines in bee health have elevated the need for a more complete understanding of the cellular stress mechanisms employed by diverse bee species. We recently uncovered the biomarker lethal (2) essential for life [l(2)efl] genes as part of a shared transcriptional program in response to a number of cell stressors in the western honey bee (Apis mellifera). Here, we describe another shared stress-responsive gene, glycine N-methyltransferase (Gnmt), which is known as a key metabolic switch controlling cellular methylation reactions. We observed Gnmt induction by both abiotic and biotic stressors. We also found increased levels of the GNMT reaction product sarcosine in the midgut after stress, linking metabolic changes with the observed changes in gene regulation. Prior to this study, Gnmt upregulation had not been associated with cellular stress responses in other organisms. To determine whether this novel stress-responsive gene would behave similarly in other bee species, we first characterized the cellular response to endoplasmic reticulum (ER) stress in lab-reared adults of the solitary alfalfa leafcutting bee (Megachile rotundata) and compared this with age-matched honey bees. The novel stress gene Gnmt was induced in addition to a number of canonical gene targets induced in both bee species upon unfolded protein response (UPR) activation, suggesting that stress-induced regulation of cellular methylation reactions is a common feature of bees. Therefore, this study suggests that the honey bee can serve as an important model for bee biology more broadly, although studies on diverse bee species will be required to fully understand global declines in bee populations., Competing Interests: Competing interests The authors declare no competing or financial interests., (© 2024. Published by The Company of Biologists Ltd.)

Hypothesis: Bile salts exhibit complex concentration-dependent micellization in aqueous solution, rooted in a long-standing hypothesis of increasing size in bile aggregation that has historically focused on the measurement of only one CMC detected by a given method, without resolving successive stepwise aggregates. Whether bile aggregation is continuous or discrete, at what concentration does the first aggregate form, and how many aggregation steps occur, all remain as open questions., Experiments: Bile salt critical micelle concentrations (CMCs) were investigated with NMR chemical shift titrations and a multi-CMC phase separation modeling approach developed herein. The proposed strategy is to establish a correspondence of the phase separation and mass action models to treat the first CMC; subsequent micellization steps, involving larger micelles, are then treated as phase separation events., Findings: The NMR data and the proposed multi-CMC model reveal and resolve multiple closely spaced sequential preliminary, primary, and secondary discrete CMCs in dihydroxy and trihydroxy bile salt systems in basic (pH 12) solutions with a single model of one NMR data set. Complex NMR data are closely explained by the model. Four CMCs are established in deoxycholate below 100 mM (298 K, pH 12): 3.8 ± 0.5 mM, 9.1 ± 0.3 mM, 27 ± 2 mM, and 57 ± 4 mM, while three CMCs were observed in multiple bile systems, also under basic conditions. Global fitting leverages the sensitivity of different protons to different aggregation stages. In resolving these closely spaced CMCs, the method also obtains chemical shifts of these spectroscopically inaccessible (aka dark) states of the distinct micelles., Competing Interests: Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2023 Elsevier Inc. All rights reserved.)

A continuing priority is to better understand and resolve the barriers to using nonuniform sampling (NUS) in challenging small molecule 2D NMR with subsampling of the Nyquist grid (a.k.a. coverage) below 50%. Possible causes for artifacts, often termed sampling noise, in 1D-NUS of 2D-NMR are revisited here, where weak aliasing artifacts are a growing concern as NUS becomes sparser. As NUS schedules become sparser, repeat sequences are shown to occur in the dense sampling regions early in the sampling schedule, causing aliasing artifacts in resulting spectra. An intuitive screening approach that detects patterns in sampling schedules based on a convolutional filter was implemented. Sampling schedules that have low proportions of repeat sequences show significantly reduced artifacts. Another route to remediate early repeat sequences is a short period of uniform sampling at the beginning of the schedule, which also leads to a significant suppression of unwanted sampling noise. Combining the repeat sequence filter with a survey of HSQC and LR-HSQMBC experiments, it is shown that very short initial uniform regions of about 2%-4% of the sampling space can ameliorate repeat sequences in sparser NUS and lead to robust spectral reconstructions by iterative soft thresholding (IST), even when the point spread function is unchanged. Using the principles developed here, a suite of 'one-click' schedules was developed for broader use., (© 2023 John Wiley & Sons Ltd.)

The feasibility of metabolomic 1 H NMR spectroscopy is demonstrated for its potential to help unravel the complex factors that are impacting honeybee health and behavior. Targeted and non-targeted 1 H NMR metabolic profiles of liquid and tissue samples of organisms could provide information on the pathology of infections and on environmentally induced stresses. This work reports on establishing extraction methods for NMR metabolic characterization of Apis mellifera , the European honeybee, describes the currently assignable aqueous metabolome, and gives examples of diverse samples (brain, head, body, whole bee) and biologically meaningful metabolic variation (drone, forager, day old, deformed wing virus). Both high-field (600 MHz) and low-field (80 MHz) methods are applicable, and 1 H NMR can observe a useful subset of the metabolome of single bees using accessible NMR instrumentation (600 MHz, inverse room temperature probe) in order to avoid pooling several bees. Metabolite levels and changes can be measured by NMR in the bee brain, where dysregulation of metabolic processes has been implicated in colony collapse. For a targeted study, the ability to recover 10-hydroxy-2-decenoic acid in mandibular glands is shown, as well as markers of interest in the bee brain such as GABA (4-aminobutyrate), proline, and arginine. The findings here support the growing use of 1 H NMR more broadly in bees, native pollinators, and insects.

Determining biomarkers and better characterizing the biochemical progression of nonalcoholic fatty liver disease (NAFLD) remains a clinical challenge. A targeted 1 H-NMR study of serum, combined with clinical variables, detected and localized biomarkers to stages of NAFLD in morbidly obese females. Pre-surgery serum samples from 100 middle-aged, morbidly obese female subjects, grouped on gold-standard liver wedge biopsies (non-NAFLD; steatosis; and fibrosis) were collected, extracted, and analyzed in aqueous (D 2 O) buffer ( 1 H, 600 MHz). Profiled concentrations were subjected to exploratory statistical analysis. Metabolites varying significantly between the non-NAFLD and steatosis groups included the ketone bodies 3-hydroxybutyrate (↓; p = 0.035) and acetone (↓; p = 0.012), and also alanine (↑; p = 0.004) and a putative pyruvate signal (↑; p = 0.003). In contrast, the steatosis and fibrosis groups were characterized by 2-hydroxyisovalerate (↑; p = 0.023), betaine (↓; p = 0.008), hypoxanthine (↓; p = 0.003), taurine (↓; p = 0.001), 2-hydroxybutyrate (↑; p = 0.045), 3-hydroxyisobutyrate (↑; p = 0.046), and increasing medium chain fatty acids. Exploratory classification models with and without clinical variables exhibited overall success rates ca. 75-85%. In the study conditions, inhibition of fatty acid oxidation and disruption of the hepatic urea cycle are supported as early features of NAFLD that continue in fibrosis. In fibrosis, markers support inflammation, hepatocyte damage, and decreased liver function. Complementarity of NMR concentrations and clinical information in classification models is shown. A broader hypothesis that standard-of-care sera can yield metabolomic information is supported.

Managed colonies of European honey bees ( Apis mellifera ) are under threat from Varroa destructor mite infestation and infection with viruses vectored by mites. In particular, deformed wing virus (DWV) is a common viral pathogen infecting honey bees worldwide that has been shown to induce behavioral changes including precocious foraging and reduced associative learning. We investigated how DWV infection of bees affects the transcriptomic response of the brain. The transcriptomes of individual brains were analyzed using RNA-Seq after experimental infection of newly emerged adult bees with DWV. Two analytical methods were used to identify differentially expressed genes from the ~15,000 genes in the Apis mellifera genome. The 269 genes that had increased expression in DWV infected brains included genes involved in innate immunity such as antimicrobial peptides (AMPs), Ago2, and Dicer. Single bee brain NMR metabolomics methodology was developed for this work and indicates that proline is strongly elevated in DWV infected brains, consistent with the increased presence of the AMPs abaecin and apidaecin. The 1361 genes with reduced expression levels includes genes involved in cellular communication including G-protein coupled, tyrosine kinase, and ion-channel regulated signaling pathways. The number and function of the downregulated genes suggest that DWV has a major impact on neuron signaling that could explain DWV related behavioral changes.

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., (© 2020 John Wiley & Sons, Ltd.)

The goal of nonuniform sampling (NUS) is to select a subset of free induction decays (FIDs) from the conventional, uniform grid in a manner that sufficiently samples short evolution times needed for improved sensitivity and long evolution times needed for enhanced resolution. In addition to specifying the number of FIDs to be collected from a uniform grid, NUS schemes also specify the distribution of the selected FIDs, which directly impacts sampling-induced artifacts. Sampling schemes typically address these heuristic guidelines by utilizing a probability density function (PDF) to bias the distribution of sampled evolution times. Given this common approach, schemes differentiate themselves by how the evolution times are distributed within the envelope of the PDF. Here, we employ maximum entropy reconstruction and utilize in situ receiver operating characteristic (IROC) to conduct a critical comparison of the sensitivity and resolution that can be achieved by three types of biased sampling schemes: exponential (PDF is exponentially decaying), Poisson-gap (PDF derived from a sine function), and quantile-directed (PDF defined by simple polynomial decay). This methodology reveals practical insights and trends regarding how the sampling schemes and bias can provide the highest sensitivity and resolution for two nonuniformly sampled dimensions in a three-dimensional biomolecular NMR experiment. The IROC analysis circumvents the limitations of common metrics when used with nonlinear spectral estimation (a characteristic of all methods used with NUS) by quantifying the spectral quality via synthetic signals that are added to the empirical dataset. Recovery of these synthetic signals provides a proxy for the quality of the empirical portion of the spectrum. The central finding is that differences in spectral quality are primarily driven by the strength of bias in the PDF. In addition, a sampling coverage threshold is observed that appears to be connected to the dependence of each NUS method on its random seed. The differences between sampling schemes and biases are most relevant below 20% coverage where seed-dependence is high, whereas at higher coverages, the performance metrics for all of the sampling schemes begin to converge and approach a seed-independent regime. The results presented here show that aggressive sampling at low coverage can produce high-quality spectra by employing a sampling scheme that adheres to a decaying PDF with a bias to a broad range of short evolution times and includes relatively few FIDs at long evolution times., Competing Interests: Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2019 Elsevier Inc. All rights reserved.)

Bile salts are facially amphiphilic, naturally occurring chemicals that aggregate to perform numerous biochemical processes. Because of their unique intermolecular properties, bile salts have also been employed as functional materials in medicine and separation science (e.g., drug delivery, chiral solubilization, purification of single-walled carbon nanotubes). Bile micelle formation is structurally complex, and it remains a topic of considerable study. Here, the exposed functionalities on the surface of cholate and deoxycholate micelles are shown to vary from one another and with the micelle aggregation state. Collectively, data from NMR and capillary electrophoresis reveal preliminary, primary, and secondary stepwise aggregation of the salts of cholic (CA) and deoxycholic (DC) acid in basic conditions (pH 12, 298 K), and address how the surface availability of chirally selective binding sites is dependent on these sequential stages of aggregation. Prior work has demonstrated sequential CA aggregation (pH 12, 298 K) including a preliminary CMC at ca. 7 mM (no chiral selection), followed by a primary CMC at ca. 14 mM that allows chiral selection of binaphthyl enantiomers. In this work, DC is also shown to form stepwise preliminary and primary aggregates (ca. 3 mM DC and 9 mM DC, respectively, pH 12, 298 K) but the preliminary 3 mM DC aggregate is capable of chirally selective solubilization of the binaphthyl enantiomers. Higher-order, secondary bile aggregates of each of CA and DC show significantly degraded chiral selectivity. Diffusion NMR reveals that secondary micelles of CA exclude the BNDHP guests, while secondary micelles of DC accommodate guests, but with a loss of chiral selectivity. These data lead to the hypothesis that secondary aggregates of DC have an exposed binding site, possibly the 7α-edge of a bile dimeric unit, while secondary CA micelles do not present binding edges to the solution, potentially instead exposing the three alcohol groups on the hydrophilic α-face to the solution.

A flexible strategy for choosing samples nonuniformly from a Nyquist grid using the concept of statistical quantiles is presented for broad classes of NMR experimentation. Quantile-directed scheduling is intuitive and flexible for any weighting function, promotes reproducibility and seed independence, and is generalizable to multiple dimensions. In brief, weighting functions are divided into regions of equal probability, which define the samples to be acquired. Quantile scheduling therefore achieves close adherence to a probability distribution function, thereby minimizing gaps for any given degree of subsampling of the Nyquist grid. A characteristic of quantile scheduling is that one-dimensional, weighted NUS schedules are deterministic, however higher dimensional schedules are similar within a user-specified jittering parameter. To develop unweighted sampling, we investigated the minimum jitter needed to disrupt subharmonic tracts, and show that this criterion can be met in many cases by jittering within 25-50% of the subharmonic gap. For nD-NUS, three supplemental components to choosing samples by quantiles are proposed in this work: (i) forcing the corner samples to ensure sampling to specified maximum values in indirect evolution times, (ii) providing an option to triangular backfill sampling schedules to promote dense/uniform tracts at the beginning of signal evolution periods, and (iii) providing an option to force the edges of nD-NUS schedules to be identical to the 1D quantiles. Quantile-directed scheduling meets the diverse needs of current NUS experimentation, but can also be used for future NUS implementations such as off-grid NUS and more. A computer program implementing these principles (a.k.a. QSched) in 1D- and 2D-NUS is available under the general public license., (Copyright © 2018 Elsevier Inc. All rights reserved.)

Combining micellar electrokinetic capillary chromatography (MEKC) and nuclear magnetic resonance (NMR) experimentation, we shed light on the structural basis for the chirally selective solubilization of atropisomeric binaphthyl compounds by bile salt micelles comprised of cholate (NaC) or deoxycholate (NaDC). The model binaphthyl analyte R,S-BNDHP exhibits chirally selective interactions with primary micellar aggregates of cholate and deoxycholate, as does the closely related analyte binaphthol (R,S-BN). Chiral selectivity was localized, by NMR chemical shift analysis, to the proton at the C12 position of these bile acids. Correspondingly, MEKC results show that the 12α-OH group of either NaC or NaDC is necessary for chirally selective resolution of these model binaphthyl analytes by bile micelles, and the S isomer is more highly retained by the micelles. With NMR, the chemical shift of 12β-H was perturbed more strongly in the presence of S-BNDHP than R-BNDHP. Intermolecular NOEs demonstrate that R,S-BNDHP and R,S-BN interact with a similar hydrophobic planar pocket lined with the methyl groups of the bile salts, and are best explained by the existence of an antiparallel dimeric unit of bile salts. Finally, chemical shift data and intermolecular NOEs support different interactions of the enantiomers with the edges of dimeric bile units, indicating that R,S-BNDHP enantiomers sample the same binding site preferentially from opposite edges of the dimeric bile unit. Chirality 28:525-533, 2016. © 2016 Wiley Periodicals, Inc., (© 2016 Wiley Periodicals, Inc.)

Isothermal titration calorimetry (ITC) is shown to be a sensitive reporter of bile salt micellization and chiral recognition. Detailed ITC characterization of bile micelle formation as well as the chiral recognition capabilities of sodium cholate (NaC), deoxycholate (NaDC), and taurodeoxycholate (NaTDC) micelle systems are reported. The ΔH(demic) of these bile salt micelle systems is directly observable and is strongly temperature-dependent, allowing also for the determination of ΔCp(demic). Using the pseudo-phase separation model, ΔG(demic) and TΔS(demic) were also calculated. Chirally selective guest-host binding of model racemic compounds 1,1'-bi-2-napthol (BN) and 1,1'-binaphthyl-2,2'-diylhydrogenphosphate (BNDHP) to bile salt micelles was then investigated. The S-isomer was shown to bind more tightly to the bile salt micelles in all cases. A model was developed that allows for the quantitative determination of the enthalpic difference in binding affinity that corresponds to chiral selectivity, which is on the order of 1 kJ mol(-1)., (© 2016 Wiley Periodicals, Inc.)

Routes to carbon-13 enrichment of bacterially expressed proteins include achieving uniform or positionally selective (e.g. ILV-Me, or (13)C', etc.) enrichment. We consider the potential for biosynthetically directed fractional enrichment (e.g. carbon-13 incorporation in the protein less than 100%) for performing routine n-(D)dimensional NMR spectroscopy of proteins. First, we demonstrate an approach to fractional isotope addition where the initial growth media containing natural abundance glucose is replenished at induction with a small amount (e.g. 10%(w/w)u-(13)C-glucose) of enriched nutrient. The approach considered here is to add 10% (e.g. 200mg for a 2g/L culture) u-(13)C-glucose at the induction time (OD600=0.8), resulting in a protein with enhanced (13)C incorporation that gives almost the same NMR signal levels as an exact 20% (13)C sample. Second, whereas fractional enrichment is used for obtaining stereospecific methyl assignments, we find that (13)C incorporation levels no greater than 20%(w/w) yield (13)C and (13)C-(13)C spin pair incorporation sufficient to conduct typical 3D-bioNMR backbone experiments on moderate instrumentation (600 MHz, RT probe). Typical 3D-bioNMR experiments of a fractionally enriched protein yield expected backbone connectivities, and did not show amino acid biases in this work, with one exception. When adding 10% u-(13)C glucose to expression media at induction, there is poor preservation of (13)Cα-(13)Cβ spin pairs in the amino acids ILV, leading to the absence of Cβ signals in HNCACB spectra for ILV, a potentially useful editing effect. Enhanced fractional carbon-13 enrichment provides lower-cost routes to high throughput protein NMR studies, and makes modern protein NMR more cost-accessible., (Copyright © 2015 Elsevier Inc. All rights reserved.)

Many information-rich multidimensional experiments in nuclear magnetic resonance spectroscopy can benefit from a signal-to-noise ratio (SNR) enhancement of up to about 2-fold if a decaying signal in an indirect dimension is sampled with nonconsecutive increments, termed nonuniform sampling (NUS). This work provides formal theoretical results and applications to resolve major questions about the scope of the NUS enhancement. First, we introduce the NUS Sensitivity Theorem in which any decreasing sampling density applied to any exponentially decaying signal always results in higher sensitivity (SNR per square root of measurement time) than uniform sampling (US). Several cases will illustrate this theorem and show that even conservative applications of NUS improve sensitivity by useful amounts. Next, we turn to a serious limitation of uniform sampling: the SNR by US decreases for extending evolution times, and thus total experimental times, beyond 1.26T2 (T2 = signal decay constant). Thus, SNR and resolution cannot be simultaneously improved by extending US beyond 1.26T2. We find that NUS can eliminate this constraint, and we introduce the matched NUS SNR Theorem: an exponential sampling density matched to the signal decay always improves the SNR with additional evolution time. Though proved for a specific case, broader classes of NUS densities also improve SNR with evolution time. Applications of these theoretical results are given for a soluble plant natural product and a solid tripeptide (u-(13)C,(15)N-MLF). These formal results clearly demonstrate the inadequacies of applying US to decaying signals in indirect nD-NMR dimensions, supporting a broader adoption of NUS.

Five spirocyclic acylphloroglucinol derivatives (1-5) have been isolated from a hexanes extract of the leaves of Hypericum pyramidatum. Pyramidatones A-D (1-3, 5) are new, and chipericumin C (4) has been previously reported. The acylphloroglucinols were characterized based on spectroscopic (NMR, IR, UV-VIS) and mass spectrometric data.

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.

Non-uniform sampling (NUS) has been established as a route to obtaining true sensitivity enhancements when recording indirect dimensions of decaying signals in the same total experimental time as traditional uniform incrementation of the indirect evolution period. Theory and experiments have shown that NUS can yield up to two-fold improvements in the intrinsic signal-to-noise ratio (SNR) of each dimension, while even conservative protocols can yield 20-40% improvements in the intrinsic SNR of NMR data. Applications of biological NMR that can benefit from these improvements are emerging, and in this work we develop some practical aspects of applying NUS nD-NMR to studies that approach the traditional detection limit of nD-NMR spectroscopy. Conditions for obtaining high NUS sensitivity enhancements are considered here in the context of enabling (1)H,(15)N-HSQC experiments on natural abundance protein samples and (1)H,(13)C-HMBC experiments on a challenging natural product. Through systematic studies we arrive at more precise guidelines to contrast sensitivity enhancements with reduced line shape constraints, and report an alternative sampling density based on a quarter-wave sinusoidal distribution that returns the highest fidelity we have seen to date in line shapes obtained by maximum entropy processing of non-uniformly sampled data.

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.

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., (Copyright © 2011 John Wiley & Sons, Ltd.)

Competition between nutation (r.f. driven) and adiabatic (rotor-driven) multi-quantum coherence transfer mechanisms in spin 3/2 systems results in diminished performance of rotation induced adiabatic coherence transfer (RIACT) in isotropic multiple-quantum magic-angle spinning (MQMAS) experiments for small e(2)qQ/h (<2 MHz) and high radio-frequency powers. We present a simple shaped RIACT pulse consisting of a truncated sine wave (spanning 0-0.8pi) that corrects the sensitivity losses, phase twist and relative intensity errors that can arise in MQMAS spectra utilizing constant-amplitude RIACT pulses. The shaped RIACT pulse may enhance the study of metals in biomolecules where quadrupole couplings of S=3/2 nuclei such as (23)Na tend to be small.

Bile salt micelles can be employed as a pseudostationary phase in micellar electrokinetic capillary chromatography (MEKC) separations of chiral analytes. To improve MEKC separations of chiral analytes, a molecular level understanding of micelle aggregation in the presence of analyte is needed. Here, aggregation of sodium cholate has been observed by exploiting the presence of a model analyte molecule. The 31P and 1H nuclear magnetic resonance spectroscopy (NMR) chemical shifts of (R,S)-1,1'-binaphthyl-2,2'-diylhydrogenphosphate ((R,S)-BNDHP), a model analyte in chiral MEKC separations, are demonstrated to be very sensitive to the aggregation state of the bile salt sodium cholate. In addition to probing micellar aggregation, the NMR spectral resolution of enantiomeric species is also stronglycorrelated with chiral separations in MEKC. In this work, the aggregation of sodium cholate in basic solutions (pH 12) has been observed over the concentration range 0-100 mM. The primary critical micelle concentration (cmc) was found to be 14 +/- 1 mM for basic solutions of sodium cholate. In addition, a primitive aggregate is clearly observed to form at 7 +/- 1 mM sodium cholate. The data also show pseudo-cmc behavior for secondary aggregation observed in the regime of 50-60 mM cholate. Finally, the H5-H7 edge of BNDHP is shown to be sensitive to chirally selective interactions with primary cholate micelles.

The title complex, [Zn(C(2)H(3)O(3))(2)(H(2)O)(2)], was prepared and the crystal structure determined as part of a (67)Zn solid state nuclear magnetic resonance study. In the title complex, the Zn atom has a disorted octa-hedral coordination comprising two bidentate glycolate ligands and two water mol-ecules. The water mol-ecules are cis to each other; one is trans to a carboxyl-ate O atom and the other trans to an alcohol O atom. The crystal structure has an extensive O-H⋯O hydrogen-bond network.

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.

We report proton chemical shifts for two model chiral analytes that are commonly used in the study of micellar electrokinetic capillary chromatography (MEKC), R,S-1,1'-binaphthol (1, BN) and R,S-1,1'-binaphthyl-2,2'-diyl hydrogen phosphate (2, BNDHP), in the absence and presence of monomers and micelles of sodium cholate and sodium deoxycholate. The analytes undergo fast exchange in and out of the micelles, which perturbs the analytes' chemical shifts, and which we use to resolve some resonances that are degenerate at both 300 and 600 MHz. Although BN and BNDHP are simple molecules, the proton assignments are only unambiguously established with the aid of the exchange with micelles, an attractive alternative to other methodologies such as the use of paramagnetic shift reagents which may also cause spectral distortions. We rely also upon 2D-NOE spectra of samples in the presence of micelles to perform these assignments. Recently published assignments, which were based upon 2D-COSY spectroscopy, appear to be in error and are corrected here. Finally, we note that these shifts are information-rich reporters on the nature of the interactions of these model analytes with the micelles., (Copyright (c) 2006 John Wiley & Sons, Ltd.)

We have recently developed and implemented two experiments in biomolecular NMR for an undergraduate-level biophysical chemistry laboratory with commercially available (15) N-enriched human ubiquitin. These experiments take advantage of (15) N direct detection of the NMR signal. The first experiment develops skills in acquiring and interpreting one-dimensional and two-dimensional NMR data of an aqueous protein sample (D. Rovnyak, L. E. Thompson (2005) An accessible two-dimensional solution nuclear magnetic resonance experiment on human ubiquitin, Biochem. Mol. Biol. Educ. 33, 117-122). In the second experiment, discussed here, students examine the overall dynamics of a protein in solution. Students measure spin relaxation times T(1) and T(2) and use these data to estimate a rotational correlation time, τ(c) , and the diameter of ubiquitin using the Stokes-Einstein relation. This is a fast and simple experiment, requiring about 1 h of instrument time, and a valuable opportunity to provide a hands-on experience in studying macromolecular size and dynamics. This experiment is conducted in synchrony with lecture material on hydrodynamics and sedimentation., (Copyright © 2007 International Union of Biochemistry and Molecular Biology, Inc.)

The dsRNA-dependent protein kinase (PKR) is a key mediator of the anti-viral and anti-proliferative effects of interferon. Unphosphorylated PKR is characterized by inhibitory interactions between the kinase and RNA binding domains (RBDs), but the structural details of the latent state and its unraveling during activation are not well understood. To study PKR regulation by NMR we assigned a large portion of the backbone resonances of the catalytically inactive K296R kinase domain, and performed (15)N-heteronuclear single quantum coherence (HSQC) titrations of this kinase domain with the RBDs. Chemical shift perturbations in the kinase indicate that RBD2 binds to the substrate eIF2alpha docking site in the kinase C-lobe. Consistent with these results, a mutation in the eIF2alpha docking site, F495A, displays weaker interactions with the RBD. The full-length RBD1+2 binds more strongly to the kinase domain than RBD2 alone. The observed chemical shift changes extend from the eIF2alpha binding site into the kinase N-lobe and inside the active site, consistent with weak interactions between the N-terminal part of the RBD and the kinase.

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.

Solution-state nuclear magnetic resonance (NMR) is an invaluable tool in structural and molecular biology research, but may be underutilized in undergraduate laboratories because instrumentation for performing structural studies of macromolecules in aqueous solutions is not yet widely available for use in undergraduate laboratories. We have implemented an experiment that is ideal for more commonly available 4.8-7.0 Tesla, double-channel NMR instruments that would not usually be used for biomolecular NMR work. We analyzed a commercially available, (15) N-enriched human ubiquitin sample with a two-dimensional correlation experiment using indirect (1) H evolution and direct (15) N detection, which produced spectra with high resolution on a spectrometer operating at 7.0 Tesla (300 MHz (1) H resonance frequency). The simplicity of the experiment makes it possible to be configured by undergraduate students with minimal supervision from the instructor. Students gain experience in acquiring multidimensional biomolecular NMR experiments, confirm that ubiquitin is stably folded, and observe the correspondence between specific signals and individual amino acids in ubiquitin., (Copyright © 2005 International Union of Biochemistry and Molecular Biology, Inc.)

The arrival of very high field magnets and cryogenic circuitries, and the development of relaxation-optimized pulse sequences have added powerful tools for increasing sensitivity and resolution in NMR studies of biomacromolecules. The potential of these advances is not fully realized in practice, however, since current experimental protocols do not permit sufficient data sampling for optimal resolution in the indirect dimensions. Here we analyze quantitatively how increasing resolution in indirect dimensions affects the S/N ratio and compare this with currently used sampling routines. Optimal resolution would require sampling up to approximately 3 R (2)(-1), and the S/N reaches a maximum at approximately 1.2 R (2)(-1). Currently used data acquisition protocols rarely sample beyond 0.4 R (2)(-1), and extending evolution times would result in prohibitively long experiments. We show that a general solution to this problem is to use non-uniform sampling, where only a small subset of data points in the indirect sampling space are measured, and possibly different numbers of transients are collected for different evolution times. Coupled with modern methods of spectrum analysis, this strategy delivers substantially improved resolution and/or reduced measuring times compared to uniform sampling, without compromising sensitivity. Higher resolution in the indirect dimensions will facilitate the use of automated assignment programs.

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.

NMR spectroscopy is a relatively insensitive technique and many biomolecular applications operate near the limits of sensitivity and resolution. A particularly challenging example is detection of the quadrupolar nucleus 17O, due to its low natural abundance, large quadrupole couplings, and low gyromagnetic ratio. Yet the chemical shift of 17O spans almost 1000 ppm in organic molecules and it serves as a potentially unique reporter of hydrogen bonding in peptides, nucleic acids, and water, and as a valuable complement to 13C and 15N NMR. Recent developments including the multiple-quantum magic-angle spinning (MQMAS) experiment have enabled the detection of 17O in biological solids, but very long data acquisitions are required to achieve sufficient sensitivity and resolution. Here, we perform nonlinear sampling in the indirect dimension of MQMAS experiments to substantially reduce the total acquisition time and improve sensitivity and resolution. Nonlinear sampling prevents the use of the discrete Fourier transform; instead, we employ maximum entropy (MaxEnt) reconstruction. Nonlinearly sampled MQMAS spectra are shown to provide high resolution and sensitivity in several systems, including lithium sulfate monohydrate (LiSO(4)-H(2)17O) and L-asparagine monohydrate (H(2)17O). The combination of nonlinear sampling and MaxEnt reconstruction promises to make the application of 17O MQMAS practical in a wider range of biological systems.

We describe the concept of multiple-quantum cross polarization (CP) between an I = 32 and an I = 12 spin during magic-angle spinning. Experimental and theoretical results for (23)Na-(1)H pairs are presented that elucidate the transfer mechanism and the beneficial effect of adiabatic amplitude modulations of the CP field. The multiple-quantum CP approach is shown to be beneficial for improving the sensitivity of CP-MQMAS experiments and for detecting dipolar correlations., (Copyright 2000 Academic Press.)