David Rovnyak

The statistical mechanical description of molecular rotation employs the concept of the symmetry number (σ), which classically is the number of identical configurations of a molecule accessible through rotations (IUPAC; Compendium of Chemical Terminology, fifth ed. International Union of Pure and Applied Chemistry; 2025). However, a meta-analysis of physical chemistry source materials finds that the IUPAC definition is not widely presented, nor is a formal method for determining σ always identified to readers. Materials tend to use informal reasoning or treat σ as self-evident. For example, it is common to justify the symmetry number of methane (CH4, σ = 12) by invoking successive C3 operations around each bond. Such an approach can overcount the initial position or cause confusion by overlooking the C2 axes and does not constitute a general method for determining σ. This Viewpoint supports wider adoption of the canonical IUPAC definition of σ in physical chemistry disciplinary materials and then reviews three formal methods for determining it in rigid molecules: (i) using the proper rotational subgroup to count all proper rotational symmetry operations (Cn, Cn–1) and the identity (E), (ii) using combinatorics to count label-superimposable configurations, and (iii) using a group theoretical method, the Schreier-Sims algorithm. The method used should be identified and presented in sufficient detail to be applied to other rigid molecules. The method of determining the order of the proper rotational subgroup merits greater use since it is most closely associated with the IUPAC standard and is widely accessible.

Nonuniform sampling (NUS) NMR is a potent method for enabling diverse multidimensional NMR spectroscopies, but it depends on the quality of the sampling schedule, particularly for one-dimensional NUS (i.e., for 2D-NMR) and for sparser sampling where noise-like artifacts (aka sampling noise) are commonly observed. Current NUS scheduling algorithms, while generally effective, can also allow flaws that lead to increased artifactual noise in spectral reconstructions. Computation or expert user curation can improve such schedules but are not easily reproduced at the spectrometer. This work builds on lessons that reducing patterns in NUS schedules can reduce artifacts and aid sparser NUS. It is proposed here that patterns in a sampling schedule be treated sequentially at local and global scales. First, a localized decoherence filter is presented that leverages the properties of the binary Thue-Morse (TM) sequence to remediate patterned subsequences in the schedule. Next, an approach to polishing the point-spread-function (PSF) by an iterative thresholding method was developed, where improving the PSF treats the schedule globally. These algorithms are implemented in a hands-free scheduler for one-dimensional NUS and tested with both iterative soft thresholding (IST) and iterative line shape (SMILE) reconstructions. While varying degrees of sampling noise are still expected, particularly in sparser NUS conditions, these methods reduce larger spectral artifacts and perform more consistent design of schedules for broader use, as illustrated with sodium naproxen, strychnine, and u-¹³C,¹⁵N-ubiquitin for weighted (e.g., quantile, Poisson gap, exponential), and random unweighted (RU) NUS, though limitations of sparse RU-NUS should be considered.

Metabolomics is a rapidly growing multidisciplinary field with ever increasing demand and usability, which is attracting a surge of new researchers. While their varied skill sets, scientific questions, and approaches enrich the field with fresh perspectives and innovation, individual investigators also bring wide-ranging levels of metabolomics-specific experience and diverse areas of interest. These factors introduce considerable variability and inconsistency in both the methodology and reporting. A recent comparative literature review of nuclear magnetic resonance (NMR) metabolomics from studies published in 2010 and 2020 revealed significant shortcomings in the reporting of experimental details necessary for evaluating both the scientific rigor and the reproducibility of NMR-based metabolomics experiments. Each stage of metabolomics research contains multiple methodological choices and various optimization parameters, all of which can introduce experimental bias and alter the study results. This emphasizes the need for proper reporting to enhance reproducibility, data reusability, and study comparability. To address these concerns, the NMR Special Interest Group within the Metabolomics Association of North America presents reporting recommendations focused on fundamental aspects of NMR metabolomics research identified from the detailed literature review report. These include specifics with respect to study design, sample preparation, data acquisition, data processing and analysis, data accessibility, and comparability to previous studies. Also presented is a complementary list of seminal papers in the field to guide the study design and implementation of NMR metabolomics experiments. This initiative seeks to enhance the long-term impact of NMR metabolomics by supporting high-quality, reproducible, and impactful data collected from well-executed and thoroughly reported studies.

The honey bee (Apis mellifera) is of paramount importance to human activities through the pollination services they provide in agricultural settings. Honey bee colonies in the United States have suffered from an increased rate of annual die-off in recent years, stemming from a complex set of interacting stressors that remain poorly described. Defining the cellular responses that are perturbed by divergent stressors represents a key step in understanding these synergies. We found that multiple model stressors induce upregulated expression of the lactate dehydrogenase (Ldh) gene in the midgut of the eusocial honey bee and that the Ldh gene family is expanded in diverse bee species. Alterations in Ldh expression were concomitant with changes in the expression of other genes involved in cellular respiration and genes encoding insulin/insulin-like growth factor signaling (IIS) pathway components. Additionally, changes in metabolites in the midgut after stress, including increased levels of lactate, linked metabolic changes with the observed changes in gene expression. Select transcriptional changes in response to stress were similarly observed in the solitary alfalfa leafcutting bee (Megachile rotundata). Thus, increased Ldh expression may be part of a core stress response remodeling cellular respiration and insulin signaling. These findings suggest that a conserved cellular response that regulates metabolic demands under diverse stressful conditions may play a protective role in bees regardless of life history.

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.

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.

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.

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 ⁿJ_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.