Quick, sensitive serial NMR experiments with Radon transform

Supporting the assignment of NMR spectra with variable-temperature experiments

Nuclear magnetic resonance (NMR) spectroscopy is one of the most powerful tools in analytical chemistry. An important step in the analysis of NMR data is the assignment of resonance frequencies to the corresponding atoms in the molecule being investigated. The traditional approach considers the spectrum's characteristic parameters: chemical shift values, internuclear couplings, and peak intensities. In this paper, we show how to support the process of assigning a series of spectra of similar organic compounds by using temperature coefficients, that is, the rates of change in chemical shift values associated with given changes in temperature.

Optimizing measurements of linear changes of NMR signal parameters

Serial NMR experiments are commonly applied in variable-temperature studies, reaction monitoring, and other tasks. The resonance frequencies often shift linearly over the series, and the shift rates help to characterize the studied system. They can be determined using a classical fitting of peak positions or a more advanced method of Radon transform. However, the optimal procedure for data collection remains to be determined. In this paper, we discuss how to invest experimental time, i.e., whether to measure more scans at the expense of the number of spectra or vice versa. The results indicate that classical fitting provides slightly less error than the Radon transform, although the latter can be the method of choice for a low signal-to-noise ratio. We demonstrate this fact through theoretical consideration, simulations, and an experiment. Finally, we extend our considerations to the linear fitting of peak amplitudes. Interestingly, the optimal setup for measuring peak height changes differs from the one for resonance frequency changes - fewer spectra with more scans provide better results.

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.

Variable-temperature NMR spectroscopy for metabolite identification in biological materials

Nuclear magnetic resonance is a "workhorse technique" used in metabolomics, complementary to mass spectrometry. Unfortunately, only the most basic NMR methods are sensitive enough to allow fast medical screening. The most common of them, a simple 1H NMR, suffers from low dispersion of resonance frequencies, which often hampers the identification of metabolites. In this article we show that 1H NMR spectra contain previously overlooked parameters potentially helpful in metabolite identification, namely the rates of temperature-induced changes of chemical shifts. We prove that they are reproducible between various metabolite mixtures and can be determined quickly when Radon transform is used to process the data.

Benefits of time-resolved nonuniform sampling in reaction monitoring: The case of aza-Michael addition of benzylamine and acrylamide

Monitoring of chemical reactions is best carried out using methods that sample the test object at a rate greater than the time scale of the processes taking place. The recently proposed time-resolved nonuniform sampling (TR-NUS) method allows the use of two-dimensional (2D) nuclear magnetic resonance (NMR) spectra for this purpose and provides a time resolution equivalent to that achievable using one-dimensional spectra. Herein, we show that TR-NUS acquired data eliminates 2D spectral line disturbances and enables more accurate signal integration and kinetics conclusions. The considerations are exemplified with a seemingly simple aza-Michael reaction of benzylamine and acrylamide. Surprisingly, the product identification is possible only using 2D spectra, although credible monitoring requires TR-NUS.

High-resolution 2-D NMR spectroscopy based on the Radon transform and pure shift technique for studying chemical shifts perturbations

Chemical shift plays an important role in molecular analysis. However, chemical shifts are influenced by temperature, solvent concentration, pressure, and so forth. Therefore, measuring chemical shift perturbations caused by these factors is helpful to molecular studies. A new form of 2-D spectroscopy (projection spectroscopy) has been introduced whose indirect dimension is derived by implementing the Radon transform on a series of conventional 1-D proton spectra and indicates such perturbations. However, signal overlap may exist in the conventional 1-D spectra and hence in the resulting projection spectra, hampering clear multiplet analysis and accurate extraction of perturbations. Here, the pure shift decoupling technique is employed to obtain clearer projection spectrum with higher spectral resolution. The combination of pure shift technique and the Radon transform is helpful to accurately extract chemical shift perturbations. It is believed that this application will open up a vast prospect for molecular analysis.

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.

Fast time-resolved NMR with non-uniform sampling

NMR spectroscopy is a versatile tool for studying time-dependent processes: chemical reactions, phase transitions or macromolecular structure changes. However, time-resolved NMR is usually based on the simplest among available techniques - one-dimensional spectra serving as "snapshots" of the studied process. One of the reasons is that multidimensional experiments are very time-expensive due to costly sampling of evolution time space. In this review we summarize efforts to alleviate the problem of limited applicability of multidimensional NMR in time-resolved studies. We focus on techniques based on sparse or non-uniform sampling (NUS), which lead to experimental time reduction by omitting a significant part of the data during measurement and reconstructing it mathematically, adopting certain assumptions about the spectrum. NUS spectra are faster to acquire than conventional ones and thus better suited to the role of "snapshots", but still suffer from non-stationarity of the signal i.e. amplitude and frequency variations within a dataset. We discuss in detail how these instabilities affect the spectra, and what are the optimal ways of sampling the non-stationary FID signal. Finally, we discuss related areas of NMR where serial experiments are exploited and how they can benefit from the same NUS-based approaches.

Nonstationary Two-Dimensional Nuclear Magnetic Resonance: A Method for Studying Reaction Mechanisms in Situ

Nuclear magnetic resonance spectroscopy (NMR) is a versatile tool of chemical analysis allowing one to determine structures of molecules with atomic resolution. Particularly informative are two-dimensional (2D) experiments that directly identify atoms coupled by chemical bonds or a through-space interaction. Thus, NMR could potentially be powerful tool to study reactions in situ and explain their mechanisms. Unfortunately, 2D NMR is very time-consuming and thus often cannot serve as a "snapshot" technique for in situ reaction monitoring. Particularly difficult is the case of spectra, in which resonance frequencies vary in the course of reaction. This leads to resolution and sensitivity loss, often hindering the detection of transient products. In this paper we introduce a novel approach to correct such nonstationary 2D NMR signals and raise the detection limits over 10 times. We demonstrate success of its application for studying the mechanism of the reaction of AgSO₄-induced synthesis of diphenylmethane-type compounds. Several reactions occur in the studied mixture of benzene and toluene, all with rather low yield and leading to compounds with similar chemical shifts. Nevertheless, with the use of a proposed 2D NMR approach we were able to describe complex mechanisms of diphenylmethane formation involving AgSO₄-induced toluene deprotonation and formation of benzyl carbocation, followed by nucleophilic attacks.

Quick temperature-sweep pure-shift NMR: the case of solvent effects in atorvastatin

Quick and sensitive serial pseudo-2D pure-shift NMR experiments provide novel insight into the temperature-dependent solvent distribution.

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.