Non-uniform sampling of similar NMR spectra and its application to studies of the interaction between alpha-synuclein and liposomes.

The accelerated acquisition of multidimensional NMR spectra using sparse non-uniform sampling (NUS) has been widely adopted in recent years. The key concept in NUS is that a major part of the data is omitted during measurement, and then reconstructed using, for example, compressed sensing (CS) methods. CS requires spectra to be compressible, that is, they should contain relatively few "significant" points. The more compressible the spectrum, the fewer experimental NUS points needed in order for it to be accurately reconstructed. In this paper we show that the CS processing of similar spectra can be enhanced by reconstructing only the differences between them. Accurate reconstruction can be obtained at lower sampling levels as the difference is sparser than the spectrum itself. In many situations this method is superior to "conventional" compressed sensing. We exemplify the concept of "difference CS" with one such case-the study of alpha-synuclein binding to liposomes and its dependence on temperature. To obtain information on temperature-dependent transitions between different states, we need to acquire several dozen spectra at various temperatures, with and without the presence of liposomes. Our detailed investigation reveals that changes in the binding modes of the alpha-synuclein ensemble are not only temperature-dependent but also show non-linear behavior in their transitions. Our proposed CS processing approach dramatically reduces the number of NUS points required and thus significantly shortens the experimental time.

Enhanced Nuclear Magnetic Resonance Spectroscopy with Isotropic Mixing as a Pseudodimension.

Chemical analysis based on liquid-state nuclear magnetic resonance spectroscopy exploits numerous observables, mainly chemical shifts, relaxation rates, and internuclear coupling constants. Regarding the latter, the efficiencies of internuclear coherence transfers may be encoded in spectral peak intensities. The dependencies of these intensities on the experimental parameter that influences the transfer, for example, mixing time, are an important source of structural information. Yet, they are costly to measure and difficult to analyze. Here, we show that peak intensity build-up curves in two-dimensional total correlation spectroscopy (2D TOCSY) experiments may be quickly measured by employing nonuniform sampling and that their analysis can be effective if supported by quantum mechanical calculations. Thus, such curves can be used to form a new, third pseudodimension of the TOCSY spectrum. Similarly to the other two frequency dimensions, this one also resolves ambiguities and provides characteristic information. We show how the approach supports the analysis of a fragment of protein Tau Repeat-4 domain. Yet, its potential applications are far broader, including the analysis of complex mixtures or other polymers.

Accelerating quantitative 13C NMR spectra using an EXtended ACquisition Time (EXACT) method.

Accurate quantitative 13C NMR spectra can be accelerated by using EXACT (EXtended ACquisition Time) NMR methods which reduce Nuclear Overhauser Enhancement (NOE) during the FID. This allows 30-50% shorter experiment times to be used when achieving a given level of quantitative accuracy.

Temperature as an Extra Dimension in Multidimensional Protein NMR Spectroscopy.

NMR spectroscopy is a particularly informative method for studying protein structures and dynamics in solution; however, it is also one of the most time-consuming. Modern approaches to biomolecular NMR spectroscopy are based on lengthy multidimensional experiments, the duration of which grows exponentially with the number of dimensions. The experimental time may even be several days in the case of 3D and 4D spectra. Moreover, the experiment often has to be repeated under several different conditions, for example, to measure the temperature-dependent effects in a spectrum (temperature coefficients (TCs)). Herein, a new approach that involves joint sampling of indirect evolution times and temperature is proposed. This allows TCs to be measured through 3D spectra in even less time than that needed to acquire a single spectrum by using the conventional approach. Two signal processing methods that are complementary, in terms of sensitivity and resolution, 1) dividing data into overlapping subsets followed by compressed sensing reconstruction, and 2) treating the complete data set with a variant of the Radon transform, are proposed. The temperature-swept 3D HNCO spectra of two intrinsically disordered proteins, osteopontin and CD44 cytoplasmic tail, show that this new approach makes it possible to determine TCs and their non-linearities effectively. Non-linearities, which indicate the presence of a compact state, are particularly interesting. The complete package of data acquisition and processing software for this new approach are provided.

Non-Stationary Complementary Non-Uniform Sampling (NOSCO NUS) for Fast Acquisition of Serial 2D NMR Titration Data.

NMR spectroscopy offers unique benefits for ligand binding studies on isotopically labelled target proteins. These benefits include atomic resolution, direct distinction of binding sites and modes, a lowest detectable affinity limit, and function independent setup. Yet, retracing protein signal assignments from apo to holo states to derive exact dissociation constants and chemical shift perturbation amplitudes (for ligand docking and structure-based optimization) requires lengthy titration series of 2D heteronuclear correlation spectra at variable ligand concentration that may exceed the protein's lifetime and available spectrometer time. We present a novel method to overcome this critical limitation, based on non-stationary complementary non-uniform sampling (NOSCO NUS) combined with a robust particle swarm optimization algorithm. We illustrate its potential in two challenging studies with very distinct protein sizes and binding affinities, showing that NOSCO NUS can reduce measurement times by an order of magnitude to make such highly informative NMR titration studies more broadly feasible.

Accelerated acquisition in pure-shift spectra based on prior knowledge from 1H NMR.

Pure-shift NMR enhances spectral resolution, but the optimal resolution can only be obtained at the cost of acquisition time. We propose to accelerate pure-shift acquisition using optimised 'burst' non-uniform sampling schemes [I. E. Ndukwe, A. Shchukina, K. Kazimierczuk and C. P. Butts, Chem. Commun., 2016, 52, 12769] and then reconstruct the undersampled signal mathematically. Here, we focus on the reliability of this reconstruction depending on the sampling scheme and present a workflow for the sampling optimization. It is ready to be implemented in routine measurements and yields a great improvement in reconstruction of challenging cases.

TReNDS-Software for reaction monitoring with time-resolved non-uniform sampling.

NMR spectroscopy, used routinely for structure elucidation, has also become a widely applied tool for process and reaction monitoring. However, the most informative of NMR methods-correlation experiments-are often useless in this kind of applications. The traditional sampling of a multidimensional FID is usually time-consuming, and thus, the reaction-monitoring toolbox was practically limited to 1D experiments (with rare exceptions, e.g., single-scan or fast-sampling experiments). Recently, the technique of time-resolved non-uniform sampling (TR-NUS) has been proposed, which allows to use standard multidimensional pulse sequences preserving the temporal resolution close to that achievable in 1D experiments. However, the method existed only as a prototype and did not allow on-the-fly processing during the reaction. In this paper, we introduce TReNDS: free, user-friendly software kit for acquisition and processing of TR-NUS data. The program works on Bruker, Agilent, and Magritek spectrometers, allowing to carry out up to four experiments with interleaved TR-NUS. The performance of the program is demonstrated on the example of enzymatic hydrolysis of sucrose.

SCoT: Swept coherence transfer for quantitative heteronuclear 2D NMR.

Nuclear magnetic resonance (NMR) spectroscopy is frequently applied in quantitative chemical analysis (qNMR). It is easy to measure one-dimensional (1D) NMR spectra in a quantitative regime (with appropriately long relaxation delays and acquisition times); however, their applicability is limited in the case of complex samples with severe peak overlap. Two-dimensional (2D) NMR solves the overlap problem, but at the cost of biasing peak intensities and hence quantitativeness. This is partly due to the uneven coherence transfer between excited/detected 1H nuclei and the heteronuclei coupled to them (typically 13C). In the traditional approach, the transfer occurs via the evolution of a spin system state under the J-coupling Hamiltonian during a delay of a fixed length. The delay length is set on the basis of the predicted average coupling constant in the sample. This leads to disturbances for pairs of nuclei with coupling constants deviating from this average. Here, we present a novel approach based on non-standard processing of the data acquired in experiments, where the coherence transfer delay is co-incremented with non-uniformly sampled evolution time. This method allows us to obtain the optimal transfer for all resonances, which improves quantitativeness. We demonstrate the concept for the coherence transfer and multiplicity-edit delays in a heteronuclear single-quantum correlation experiment (HSQC).

Enabling Fast Pseudo-2D NMR Spectral Acquisition for Broadband Homonuclear Decoupling: The EXACT NMR Approach.

Pseudo-2D NMR spectroscopy provides a means of acquiring broadband homonuclear decoupled spectra useful for structural characterization of complex molecules. However, data points concatenated in the direct dimension in these experiments are acquired over incremented time periods-leading to long acquisition times with no sensitivity benefits due to the absence of signal averaging between scans. Herein, the concept of EXACT NMR spectroscopy ("burst" non-uniform sampling of data points) is explored in pseudo-2D experiments with results revealing little or no loss in spectral quality or signal intensity despite the acceleration of acquisition-up to 400 % in some cases.

Pitfalls in compressed sensing reconstruction and how to avoid them.

Multidimensional NMR can provide unmatched spectral resolution, which is crucial when dealing with samples of biological macromolecules. The resolution, however, comes at the high price of long experimental time. Non-uniform sampling (NUS) of the evolution time domain allows to suppress this limitation by sampling only a small fraction of the data, but requires sophisticated algorithms to reconstruct omitted data points. A significant group of such algorithms known as compressed sensing (CS) is based on the assumption of sparsity of a reconstructed spectrum. Several papers on the application of CS in multidimensional NMR have been published in the last years, and the developed methods have been implemented in most spectral processing software. However, the publications rarely show the cases when NUS reconstruction does not work perfectly or explain how to solve the problem. On the other hand, every-day users of NUS develop their rules-of-thumb, which help to set up the processing in an optimal way, but often without a deeper insight. In this paper, we discuss several sources of problems faced in CS reconstructions: low sampling level, missassumption of spectral sparsity, wrong stopping criterion and attempts to extrapolate the signal too much. As an appendix, we provide MATLAB codes of several CS algorithms used in NMR. We hope that this work will explain the mechanism of NUS reconstructions and help readers to set up acquisition and processing parameters. Also, we believe that it might be helpful for algorithm developers.

EXtended ACquisition Time (EXACT) NMR-A Case for 'Burst' Non-Uniform Sampling.

A strong case exists for the introduction of burst non-uniform sampling (NUS) in the direct dimension of NMR spectroscopy experiments. The resulting gaps in the NMR free induction decay can reduce the power demands of long experiments (by switching off broadband decoupling for example) and/or be used to introduce additional pulses (to refocus homonuclear coupling, for example). The final EXtended ACquisition Time (EXACT) spectra are accessed by algorithmic reconstruction of the missing data points and can provide higher resolution in the direct dimension than is achievable with existing non-NUS methods.