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 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

NUScon: a community-driven platform for quantitative evaluation of nonuniform sampling in NMR

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

Increasing the sensitivity of NMR diffusion measurements by paramagnetic longitudinal relaxation enhancement, with application to ribosome–nascent chain complexes

The translational diffusion of macromolecules can be examined non-invasively by stimulated echo (STE) NMR experiments to accurately determine their molecular sizes. These measurements can be important probes of intermolecular interactions and protein folding and unfolding, and are crucial in monitoring the integrity of large macromolecular assemblies such as ribosome–nascent chain complexes (RNCs). However, NMR studies of these complexes can be severely constrained by their slow tumbling, low solubility (with maximum concentrations of up to 10 μM), and short lifetimes resulting in weak signal, and therefore continuing improvements in experimental sensitivity are essential. Here we explore the use of the paramagnetic longitudinal relaxation enhancement (PLRE) agent NiDO2A on the sensitivity of 15N XSTE and SORDID heteronuclear STE experiments, which can be used to monitor the integrity of these unstable complexes. We exploit the dependence of the PLRE effect on the gyromagnetic ratio and electronic relaxation time to accelerate recovery of 1H magnetization without adversely affecting storage on N z during diffusion delays or introducing significant transverse relaxation line broadening. By applying the longitudinal relaxation-optimized SORDID pulse sequence together with NiDO2A to 70S Escherichia coli ribosomes and RNCs, NMR diffusion sensitivity enhancements of up to 4.5-fold relative to XSTE are achieved, alongside ~1.9-fold improvements in two-dimensional NMR sensitivity, without compromising the sample integrity. We anticipate these results will significantly advance the use of NMR to probe dynamic regions of ribosomes and other large, unstable macromolecular assemblies

Aqueous Metabolite Trends for the Progression of Nonalcoholic Fatty Liver Disease in Female Bariatric Surgery Patients by Targeted 1H-NMR Metabolomics

Determining biomarkers and better characterizing the biochemical progression of nonalcoholic fatty liver disease (NAFLD) remains a clinical challenge. A targeted 1H-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 (D2O) buffer (1H, 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

Methodology for Single Bee and Bee Brain 1H-NMR Metabolomics

The feasibility of metabolomic 1H NMR spectroscopy is demonstrated for its potential to help unravel the complex factors that are impacting honeybee health and behavior. Targeted and non-targeted 1H 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 1H 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 1H NMR more broadly in bees, native pollinators, and insects

Maintaining a high degree of research productivity at a predominately undergraduate institution as your career advances

In this perspective, two experienced academic administrators who are computational chemists discuss strategies for how to maintain an active research program at a predominately undergraduate institution as your career progresses. More responsibility equates to less time for research, so planning for research to remain a priority is essential. We all have the same amount of time, so figuring out how to use yours better is the key to remaining active. Professional organizations such as Council on Undergraduate Research, consortia of computational chemists such as Molecular Education and Research Consortium in computational chemistRY and Midwest Undergraduate Computational Chemistry Consortium, and attendance at professional conferences can help sustain your research program. Collaborations with faculty at other institutions provide a particularly effective accountability mechanism as well. Perhaps the best way to improve your productivity is to become a better mentor to your undergraduate students. Building a research group that is fun and exciting develops a culture that sustains itself and provides the momentum necessary to maintain progress toward scientific goals