Knowledge-based nonuniform sampling in multidimensional NMR

The full resolution afforded by high-field magnets is rarely realized in the indirect dimensions of multidimensional NMR experiments because of the time cost of uniformly sampling to long evolution times. Emerging methods utilizing nonuniform sampling (NUS) enable high resolution along indirect dimensions by sampling long evolution times without sampling at every multiple of the Nyquist sampling interval. While the earliest NUS approaches matched the decay of sampling density to the decay of the signal envelope, recent approaches based on coupled evolution times attempt to optimize sampling by choosing projection angles that increase the likelihood of resolving closely-spaced resonances. These approaches employ knowledge about chemical shifts to predict optimal projection angles, whereas prior applications of tailored sampling employed only knowledge of the decay rate. In this work we adapt the matched filter approach as a general strategy for knowledge-based nonuniform sampling that can exploit prior knowledge about chemical shifts and is not restricted to sampling projections. Based on several measures of performance, we find that exponentially weighted random sampling (envelope matched sampling) performs better than shift-based sampling (beat matched sampling). While shift-based sampling can yield small advantages in sensitivity, the gains are generally outweighed by diminished robustness. Our observation that more robust sampling schemes are only slightly less sensitive than schemes highly optimized using prior knowledge about chemical shifts has broad implications for any multidimensional NMR study employing NUS. The results derived from simulated data are demonstrated with a sample application to PfPMT, the phosphoethanolamine methyltransferase of the human malaria parasite Plasmodium falciparum.     

Performance tuning non-uniform sampling for sensitivity enhancement of signal-limited biological NMR

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 ¹H,¹⁵N-HSQC experiments on natural abundance protein samples and ¹H,¹³C-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.     

Time-resolved NMR studies of RNA folding

The application of real-time NMR experiments to the study of RNA folding, as reviewed in this article, is relatively new. For many RNA folding events, current investigations suggest that the time scales are in the second to minute regime. In addition, the initial investigations suggest that different folding rates are observed for one structural transition may be due to the hierarchical folding units of RNA. Many of the experiments developed in the field of NMR of protein folding cannot directly be transferred to RNA: hydrogen exchange experiments outside the spectrometer cannot be applied since the intrinsic exchange rates are too fast in RNA, relaxation dispersion experiments on the other require faster structural transitions than those observed in RNA. On the other hand, information derived from time-resolved NMR experiments, namely the acquisition of native chemical shifts, can be readily interpreted in light of formation of a single long-range hydrogen bonding interaction. Together with mutational data that can readily be obtained for RNA and new ligation technologies that enhance site resolution even further, time-resolved NMR may become a powerful tool to decipher RNA folding. Such understanding will be of importance to understand the functions of coding and non-coding RNAs in cells.     

Comprehensive simulation of metagenomic sequencing data with non-uniform sampling distribution

Background: Metagenomic sequencing is a complex sampling procedure from unknown mixtures of many genomes. Having metagenome data with known genome compositions is essential for both benchmarking bioinformatics software and for investigating influences of various factors on the data. Compared to data from real microbiome samples or from defined microbial mock community, simulated data with proper computational models are better for the purpose as they provide more flexibility for controlling multiple factors. Methods: We developed a non-uniform metagenomic sequencing simulation system (nuMetaSim) that is capable of mimicking various factors in real metagenomic sequencing to reflect multiple properties of real data with customizable parameter settings. Results: We generated 9 comprehensive metagenomic datasets with different composition complexity from of 203 bacterial genomes and 2 archaeal genomes related with human intestine system. Conclusion: The data can serve as benchmarks for comparing performance of different methods at different situations, and the software package allows users to generate simulation data that can better reflect the specific properties in their scenarios.     

New methods for fast multidimensional NMR

Considerable excitement has been aroused by recent new methods for speeding up multidimensional NMR experiments by radically modifying the normal time-domain sampling protocols. These new schemes include the filter diagonalization method, GFT-NMR, the single-scan two-dimensional technique, Hadamard spectroscopy, and a proposal based on projection-reconstruction of three-dimensional spectra. All these methods deliver appreciable improvements in the speed of data acquisition and show promise for speeding up multidimensional NMR of proteins. This perspective aims to describe these important new procedures in simple terms and to comment on their advantages and possible limitations.     

Optimizing resolution in multidimensional NMR by three-way decomposition

Resolution depends on the number of points sampled in a FID; in indirectly detected dimensions it is an important determinant of the total experiment time. Based on the high redundancy present in NMR data, we propose the following timesaving scheme for three-dimensional spectra. An extensive grid of discrete t1- and t2-values is used, which increases resolution while preserving the spectral width. Total experiment time is reduced by avoiding the recording of t3-FIDs for selected pairs of t1 and t2; typically the recording is omitted for about 75% of the (t1,t2) combinations. These data sets are referred to as sparse, and post-experimental processing making optimal use of spectral redundancy provides the missing, non-recorded data. We have previously shown that three-way decomposition (TWD) within the MUNIN approach provides a practical way to process dense NMR data sets. Here, a novel TWD algorithm [Ibraghimov, (2002) Numer. Linear Algebra Appl. 9, 551–565] is used to complement a sparselyrecorded time-domain data set by providing the missing FIDs for all (t1,t2) combinations omitted in the experiment. A necessary condition is that for each t1-value at least a few FIDs are recorded, and similar for each t2-value. The method is demonstrated on non-uniformly sampled ¹⁵N-NOESY-HSQC data sets recorded for the 14 kD protein azurin. The spectra obtained by TWD, reconstruction and ordinary transform to frequency-domain are, in spite of the large number of signals and the high dynamic range typical for NOESYs, highly similar to a corresponding reference spectrum, for which all (t1,t2) combinations were recorded.     

Peak picking multidimensional NMR spectra with the contour geometry based algorithm CYPICK

The automated identification of signals in multidimensional NMR spectra is a challenging task, complicated by signal overlap, noise, and spectral artifacts, for which no universally accepted method is available. Here, we present a new peak picking algorithm, CYPICK, that follows, as far as possible, the manual approach taken by a spectroscopist who analyzes peak patterns in contour plots of the spectrum, but is fully automated. Human visual inspection is replaced by the evaluation of geometric criteria applied to contour lines, such as local extremality, approximate circularity (after appropriate scaling of the spectrum axes), and convexity. The performance of CYPICK was evaluated for a variety of spectra from different proteins by systematic comparison with peak lists obtained by other, manual or automated, peak picking methods, as well as by analyzing the results of automated chemical shift assignment and structure calculation based on input peak lists from CYPICK. The results show that CYPICK yielded peak lists that compare in most cases favorably to those obtained by other automated peak pickers with respect to the criteria of finding a maximal number of real signals, a minimal number of artifact peaks, and maximal correctness of the chemical shift assignments and the three-dimensional structure obtained by fully automated assignment and structure calculation.     

Time-resolved NMR: extracting the topology of complex enzyme networks

The use of nondestructive NMR spectroscopy for enzymatic studies offers unique opportunities to identify nearly all enzymatic byproducts and detect unstable short-lived products or intermediates at the molecular level; however, numerous challenges must be overcome before it can become a widely used tool. The biosynthesis of acetyl-coenzyme A (acetyl-CoA) by acetyl-CoA synthetase is used here as a case study for the development of an analytical NMR-based time-course assay platform. We describe an algorithm to deconvolve superimposed spectra into spectra for individual molecules, and further develop a model to simulate the acetyl-CoA synthetase enzyme reaction network using the data derived from time-course NMR. Simulation shows indirectly that synthesis of acetyl-CoA is mediated via an enzyme-bound intermediate (possibly acetyl-AMP) and is accompanied by a nonproductive loss from an intermediate. The ability to predict enzyme function based on partial knowledge of the enzymatic pathway topology is also discussed.     

A non-uniform sampling approach enables studies of dilute and unstable proteins

NMR spectroscopy is a powerful method in structural and functional analysis of macromolecules and has become particularly prevalent in studies of protein structure, function and dynamics. Unique to NMR spectroscopy is the relatively low constraints on sample preparation and the high level of control of sample conditions. Proteins can be studied in a wide range of buffer conditions, e.g. different pHs and variable temperatures, allowing studies of proteins under conditions that are closer to their native environment compared to other structural methods such as X-ray crystallography and electron microscopy. The key disadvantage of NMR is the relatively low sensitivity of the method, requiring either concentrated samples or very lengthy data-acquisition times. Thus, proteins that are unstable or can only be studied in dilute solutions are often considered practically unfeasible for NMR studies. Here, we describe a general method, where non-uniform sampling (NUS) allows for signal averaging to be monitored in an iterative manner, enabling efficient use of spectrometer time, ultimately leading to savings in costs associated with instrument and isotope-labelled protein use. The method requires preparation of multiple aliquots of the protein sample that are flash-frozen and thawed just before acquisition of a short NMR experiments carried out while the protein is stable (12 h in the presented case). Non-uniform sampling enables sufficient resolution to be acquired for each short experiment. Identical NMR datasets are acquired and sensitivity is monitored after each co-added spectrum is reconstructed. The procedure is repeated until sufficient signal-to-noise is obtained. We discuss how maximum entropy reconstruction is used to process the data, and propose a variation on the previously described method of automated parameter selection. We conclude that combining NUS with iterative co-addition is a general approach, and particularly powerful when applied to unstable proteins.     

Improving resolution in multidimensional NMR using random quadrature detection with compressed sensing reconstruction

NMR spectroscopy is central to atomic resolution studies in biology and chemistry. Key to this approach are multidimensional experiments. Obtaining such experiments with sufficient resolution, however, is a slow process, in part since each time increment in every indirect dimension needs to be recorded twice, in quadrature. We introduce a modified compressed sensing (CS) algorithm enabling reconstruction of data acquired with random acquisition of quadrature components in gradient-selection NMR. We name this approach random quadrature detection (RQD). Gradient-selection experiments are essential to the success of modern NMR and with RQD, a 50 % reduction in the number of data points per indirect dimension is possible, by only acquiring one quadrature component per time point. Using our algorithm (CS_RQD), high quality reconstructions are achieved. RQD is modular and combined with non-uniform sampling we show that this provides increased flexibility in designing sampling schedules leading to improved resolution with increasing benefits as dimensionality of experiments increases, with particular advantages for 4- and higher dimensional experiments.     

Chemical shift optimization in multidimensional NMR spectra by AUREMOL-SHIFTOPT

A problem often encountered in multidimensional NMR-spectroscopy is that an existing chemical shift list of a protein has to be used to assign an experimental spectrum but does not fit sufficiently well for a safe assignment. A similar problem occurs when temperature or pressure series of n-dimensional spectra are to be evaluated automatically. We have developed two different algorithms, AUREMOL-SHIFTOPT1 and AUREMOL-SHIFTOPT2 that fulfill this task. In the present contribution their performance is analyzed employing a set of simulated and experimental two-dimensional and three-dimensional spectra obtained from three different proteins. A new z-score based on atom and amino acid specific chemical shift distributions is introduced to weight the chemical shift contributions in different dimensions properly.     

Knowns and unknowns in metabolomics identified by multidimensional NMR and hybrid MS/NMR methods

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Removal of a time barrier for high-resolution multidimensional NMR spectroscopy

We introduce the recursive multidimensional decomposition (R-MDD) method to speed recording of high-resolution NMR spectra. The measurement time is logarithmically dependent on the sizes of indirect spectral dimensions. R-MDD has the sensitivity and resolution advantages of optimized nonuniform acquisition schemes and is applicable to all types of biomolecular spectra. We demonstrated it for triple resonance experiments on three globular proteins (ubiquitin, azurin and the barstar-barnase complex) of 8-22 kDa.     

Minimizing the effects of radio-frequency heating in multidimensional NMR experiments

Summary Application of radio-frequency power in multidimensional NMR experiments can significantly increase the sample temperature compared to that of the surrounding gas flow. Radio-frequency heating effects become more severe at higher magnetic field strengths and ionic strengths. The effects are particularly noticeable for experiments that utilize ¹H and/or ¹³C isotropic mixing and broadband decoupling. If radio-frequency power is applied during the systematically increasing evolution period t₁, the sample temperature can change with t₁ and thereby cause line-shape distortions. Such distortions are easily avoided by ensuring that the average radio-frequency power remains constant during the entire experiment.     

Analytical solution to the coupled evolution of multidimensional NMR data

A substantial time savings in the collection of multidimensional NMR data can be achieved by coupling the evolution of nuclei in the indirect dimensions. In order to save time, the sampling of the indirect dimensions is inherently incomplete. Therefore, many algorithms and samplings schemes have been developed aimed at separating the coevolved frequencies into analyzable data with limited artifacts. This paper extends the use of circulant matrices to describe coupled evolution with convolutions. By understanding the data in terms of convolutions, there is an exact solution to the inversion problem of extracting the orthogonal vectors from the coupled dimensions. Previously, this inversion problem has been solved using peak coordinates extracted from spectra. In contrast, the method described here uses spectra directly. This solution suggests a simple sampling scheme of collecting N orthogonal spectra, and N + 1 projections at specific projection angles, however, the theory developed can be extended generally to arbitrary projection angles. The circulant matrix methodology is demonstrated for simulated and real data. Further, an algorithm for separating overlapped signals in the detected dimension is presented. The algorithm involves the forward calculation of the coupled spectra from the orthogonal spectra, followed by back calculation of the orthogonal spectra from the coupled spectra, thus permitting rigorous cross-validation. This algorithm is shown to be robust in that erroneous solutions give rise to large artifacts. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Al NMR: a novel NMR data processing program optimized for sparse sampling

Sparse sampling in biomolecular multidimensional NMR offers increased acquisition speed and resolution and, if appropriate conditions are met, an increase in sensitivity. Sparse sampling of indirectly detected time domains combined with the direct truly multidimensional Fourier transform has elicited particular attention because of the ability to generate a final spectrum amenable to traditional analysis techniques. A number of sparse sampling schemes have been described including radial sampling, random sampling, concentric sampling and variations thereof. A fundamental feature of these sampling schemes is that the resulting time domain data array is not amenable to traditional Fourier transform based processing and phasing correction techniques. In addition, radial sampling approaches offer a number of advantages and capabilities that are also not accessible using standard NMR processing techniques. These include sensitivity enhancement, sub-matrix processing and determination of minimal sets of sampling angles. Here we describe a new software package (Al NMR) that enables these capabilities in the context of a general NMR data processing environment.