Developing nonuniform sampling strategies to improve sensitivity and resolution in 1,1-ADEQUATE experiments

The Finally Rewarding Search for A Cytotoxic Isosteviol Derivative

Acid hydrolysis of stevioside resulted in a 63% yield of isosteviol (1), which served as a starting material for the preparation of numerous amides. These compounds were tested for cytotoxic activity, employing a panel of human tumor cell lines, and almost all amides were found to be non-cytotoxic. Only the combination of isosteviol, a (homo)-piperazinyl spacer and rhodamine B or rhodamine 101 unit proved to be particularly suitable. These spacered rhodamine conjugates exhibited cytotoxic activity in the sub-micromolar concentration range. In this regard, the homopiperazinyl-spacered derivatives were found to be better than those compounds with piperazinyl spacers, and rhodamine 101 conjugates were more cytotoxic than rhodamine B hybrids.

Revisiting aliasing noise to build more robust sparsity in nonuniform sampling 2D-NMR

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.

High fidelity sampling schedules for NMR spectra of high dynamic range

The ability to reconstruct non-uniformly sampled (NUS) NMR spectra has mostly been accepted. Still a concern is lingering regarding artifacts from sampling non-uniformly. As experienced, some sampling schedules yield better results than others. Finding a useful schedule is relatively trivial for a low dynamic range spectrum and a conservative sparsity, but not so when the dynamic range is large and/or when extreme sparsity is used. High dynamic range is typically found in NOESY and spectra of metabolites, where quantification of peak heights is desired at high fidelity. Extreme sparsity is desired when high throughput is a goal. In all cases, selecting a poor sampling schedule can create unnecessary artifacts. Effectively, it is important to select a sampling schedule that provides a signal-to-artifact apex ratio (SAAR) value in par or better than the signal-to-noise ratio (SNR) value. Notably, by signal-to-artifact apex ratio we consider reconstruction fidelity as the apex intensity likeness, i.e., as the true signal to the tallest artifact. We show that the quality of reconstruction depends on the particular sampling schedule. We evaluate the reconstruction quality in the frequency domain following a matched Lorentz-to-Gauss transform plus common apodization and Fourier Transform. As the Lorentz-to-Gauss transform improves resolution and reduces ridges we include this when defining the Signal-to-Artifact Apex Ratio (SAAR) metric. This metric measures the ratio of simulated reconstructed peak height to the tallest artifact of reconstruction in a spectrum without noise. Once a NUS schedule is found with an optimal SAAR it will be satisfactory for all spectra recorded with the same parameter set. Tables with good seed values are provided in the supplement.

More than ADEQUATE: doubling the sensitivity of 13CH–13CH correlations in double-quantum NMR experiments

Tracing the connectivity of CH–CHx moieties of organic compounds in an overnight cryoprobe NMR experiment using milligrams of material.

Clustered sparsity and Poisson-gap sampling

Non-uniform sampling (NUS) is a popular way of reducing the amount of time taken by multidimensional NMR experiments. Among the various non-uniform sampling schemes that exist, the Poisson-gap (PG) schedules are particularly popular, especially when combined with compressed-sensing (CS) reconstruction of missing data points. However, the use of PG is based mainly on practical experience and has not, as yet, been explained in terms of CS theory. Moreover, an apparent contradiction exists between the reported effectiveness of PG and CS theory, which states that a "flat" pseudo-random generator is the best way to generate sampling schedules in order to reconstruct sparse spectra. In this paper we explain how, and in what situations, PG reveals its superior features in NMR spectroscopy. We support our theoretical considerations with simulations and analyses of experimental data from the Biological Magnetic Resonance Bank (BMRB). Our analyses reveal a previously unnoticed feature of many NMR spectra that explains the success of "blue-noise" schedules, such as PG. We call this feature "clustered sparsity". This refers to the fact that the peaks in NMR spectra are not just sparse but often form clusters in the indirect dimension, and PG is particularly suited to deal with such situations. Additionally, we discuss why denser sampling in the initial and final parts of the clustered signal may be useful.

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 , 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.

Non-uniform sampling for NOESY? A case study on spiramycin

To date, most nuclear magnetic resonance (NMR)-based 3-D structure determinations of both small molecules and of biopolymers utilize the nuclear Overhauser effect (NOE) via NOESY spectra. The acquisition of high-quality NOESY spectra is a prerequisite for quantitative analysis providing accurate interatomic distances. As the acquisition of NOE build-ups is time-consuming, acceleration of the process by the use of non-uniform sampling (NUS) may seem beneficial; however, the quantitativity of NOESY spectra acquired with NUS has not yet been validated. Herein, NOESY spectra with various extents of NUS have been recorded, artificial NUS spectra with two different sampling schemes created, and by using two different NUS reconstruction algorithms the influence of NUS on the data quality was evaluated. Using statistical analyses, NUS is demonstrated to influence the accuracy of quantitative NOE experiments. The NOE-based distances show an increased error as the sampling density decreases. Weak NOE signals are affected more severely by NUS than more intense ones. The application of NUS with NOESY comes at two major costs: the interatomic distances are determined with lower accuracy and long-range correlations are lost.

Development of 19 F-detected 1,1-ADEQUATE for the characterization of polyfluorinated and perfluorinated compounds

Polyfluorinated and perfluorinated compounds in the environment are a growing health concern. ¹⁹ F-detected variants of commonly employed heteronuclear shift correlation experiments such as heteronuclear single quantum correlation (HSQC) and heteronuclear multiple bond correlation (HMBC) are available; ¹⁹ F-detected experiments that employ carbon-carbon homonuclear coupling, in contrast, have never been reported. Herein, we report the measurement of the ¹ J_CC and ⁿ J_CC coupling constants of a simple perfluorinated phthalonitrile and the first demonstration of a ¹⁹ F-detected 1,1-ADEQUATE experiment.

Application of INADEQUATE NMR techniques for directly tracing out the carbon skeleton of a natural product

INTRODUCTION

Nuclear magnetic resonance (NMR) measurement of ¹ J_CC coupling by two-dimensional (2D) INADEQUATE (incredible natural abundance double quantum transfer experiment), which is a special case of double-quantum (DQ) spectroscopy that offers unambiguous determination of ¹³ C-¹³ C spin-spin connectivities through the DQ transitions of the spin system, is especially suited to solving structures rich in quaternary carbons and poor in hydrogen content (Crews rule).

OBJECTIVE

To review published literature on the application of NMR methods to determine structure in the liquid-state, which specifically considers the interaction of a pair of carbon-13 (¹³ C) nuclei adjacent to one another, to allow direct tracing out of contiguous carbon connectivity using 2D INADEQUATE.

METHODOLOGY

A comprehensive literature search was implemented with various databases: Web of Knowledge, PubMed and SciFinder, and other relevant published materials including published monographs. The keywords used, in various combinations, with INADEQUATE being present in all combinations, in the search were 2D NMR, ¹ J_CC coupling, natural product, structure elucidation, ¹³ C-¹³ C connectivity, cryoprobe and CASE (computer-assisted structure elucidation)/PANACEA (protons and nitrogen and carbon et alia).

RESULTS

The 2D INADEQUATE continues to solve "intractable" problems in natural product chemistry, and using milligram quantities with cryoprobe techniques combined with CASE/PANACEA experiments can increase machine time efficiency. The ¹³ C-¹³ C-based structural elucidation by dissolution single-scan dynamic nuclear polarisation NMR can overcome disadvantages of ¹³ C insensitivity at natural abundance. Selected examples have demonstrated the trajectory of INADEQUATE spectroscopy from structural determination to clarification of metabolomics analysis and use of DFT (density functional theory) and coupling constants to clarify the connectivity, hybridisation and stereochemistry within natural products.

CONCLUSIONS

Somewhat neglected over the years because of perceived lack of sensitivity, the 2D INADEQUATE NMR technique has re-emerged as a useful tool for solving natural products structures, which are rich in quaternary carbons and poor in hydrogen content.

The influence of the probability density function on spectral quality in nonuniformly sampled multidimensional NMR

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.