Effective Processing of Pulse Field Gradient NMR of Mixtures by Blind Source Separation

Speedy Component Resolution Using Spatially Encoded Diffusion NMR Data

Diffusion-ordered NMR spectroscopy (DOSY) is a powerful tool to analyse mixtures. Spatially encoded (SPEN) DOSY enables recording a full DOSY dataset in just one scan by performing spatial parallelisation of the gradient dimension. The simplest and most widely used approach to processing DOSY data is to fit each peak in the spectrum with a single or multiple exponential decay. However, when there is peak overlap, and/or when the diffusion decays of the contributing components are too similar, this method has limitations. Multivariate analysis of DOSY data, which is an attractive alternative, consists of decomposing the experimental data, into compound-specific diffusion decays and 1D NMR spectra. Multivariate analysis has been very successfully used for conventional DOSY data, but its use for SPEN DOSY data has only recently been reported. Here, we present a comparison, for SPEN DOSY data, of two widely used algorithms, SCORE and OUTSCORE, that aim at unmixing the spectra of overlapped species through a least square fit or a cross-talk minimisation, respectively. Data processing was performed with the General NMR Analysis Toolbox (GNAT), with custom-written code elements that now expands the capabilities, and makes it possible to import and process SPEN DOSY data. This comparison is demonstrated on three different two-component mixtures, each with different characteristics in terms of signal overlap, diffusion coefficient similarity, and component concentration.

NMR methods for the analysis of mixtures

NMR spectroscopy is a powerful approach for the analysis of mixtures. Its usefulness arises in large part from the vast landscape of methods, and corresponding pulse sequences, that have been and are being designed to tackle the specific properties of mixtures of small molecules. This feature article describes a selection of methods that aim to address the complexity, the low concentrations, and the changing nature that mixtures can display. These notably include pure-shift and diffusion NMR methods, hyperpolarisation methods, and fast 2D NMR methods such as ultrafast 2D NMR and non-uniform sampling. Examples or applications are also described, in fields such as reaction monitoring and metabolomics, to illustrate the relevance and limitations of different methods.

Use of Diethanolamine as a Viscous Solvent for Mixture Analysis by Multidimensional Heteronuclear ViscY NMR Experiments

Diethanolamine/DMSO-d₆ as a viscous binary solvent is first reported for the individualization of low-polarity mixture components by multidimensional heteronuclear ViscY NMR experiments under spin diffusion conditions. Solvent viscosity induces the slowing down of molecular tumbling, hence promoting magnetization transfer by dipolar longitudinal cross-relaxation. As a result, all ¹H nuclei resonances within the same molecule may correlate in a 2D nuclear Overhauser effect spectroscopy (NOESY) spectrum, giving access to mixture analysis. We offer a new way to analyze mixtures by considering 3D heteronuclear heteronuclear single-quantum coherence-NOESY (HSQC-NOESY) experiments under viscous conditions. We state the individualization of four low-polarity chemical compounds dissolved in the diethanolamine/DMSO-d₆ solvent blend using homonuclear selective 1D, 2D ¹H-¹H NOESY experiments and heteronuclear 1D, 2D ¹H-¹⁹F heteronuclear Overhauser effect spectroscopy, 2D ¹H-¹⁹F, ¹H-³¹P HSQC-NOESY, and 3D ¹H-¹⁹F-¹H, ¹H-³¹P-¹H HSQC-NOESY experiments by taking profit from spin diffusion.

Data-driven separation of MRI signal components for tissue characterization

PURPOSE

MRI can be utilized for quantitative characterization of tissue. To assess e.g. water fractions or diffusion coefficients for compartments in the brain, a decomposition of the signal is necessary. Imposing standard models carries the risk of estimating biased parameters if model assumptions are violated. This work introduces a data-driven multicomponent analysis, the monotonous slope non-negative matrix factorization (msNMF), tailored to extract data features expected in MR signals.

METHODS

The msNMF was implemented by extending the standard NMF with monotonicity constraints on the signal profiles and their first derivatives. The method was validated using simulated data, and subsequently applied to both ex vivo DWI data and in vivo relaxometry data. Reproducibility of the method was tested using the latter.

RESULTS

The msNMF recovered the multi-exponential signals in the simulated data and showed superiority to standard NMF (based on the explained variance, area under the ROC curve, and coefficient of variation). Diffusion components extracted from the DWI data reflected the cell density of the underlying tissue. The relaxometry analysis resulted in estimates of edema water fractions (EWF) highly correlated with published results, and demonstrated acceptable reproducibility.

CONCLUSION

The msNMF can robustly separate MR signals into components with relation to the underlying tissue composition, and may potentially be useful for e.g. tumor tissue characterization.

Ultrafast diffusion-based unmixing of 1H NMR spectra

We show that the NMR spectra of components in a mixture can be separated using 2D data acquired in less than one second, and an algorithm that is executed in just a few seconds. This NMR unmixing method is based on spatial encoding of the translational diffusion coefficients of the mixture's components, with multivariate processing of the data. This requires a new frequency swept pulse, which is designed and implemented to obtain quadratic spacing of the spatially parallelised gradient dimension. Ultrafast NMR unmixing may help in the analysis of mixtures that evolve in time.

Accurate estimation of diffusion coefficient for molecular identification in a complex background

To eliminate the effects of complex background signals and to enhance the accuracy of the diffusion coefficient measurement, derivative NMR spectroscopy with negligible loss of the spectral quality is introduced based on the customized Savitzky-Golay method and used to construct diffusion-ordered NMR spectroscopy (DOSY). The criterion of the method was established by simulations. The application of this method on mouse urine and serum showed that the accuracy and precision of diffusion coefficient measurements in a complex background were improved to enhance the identification of molecules. Graphical abstract Diffusion-ordered NMR spectroscopy is a powerful tool for analyzing complex mixtures. To improve the accuracy of diffusion coefficient measurement, the magnitude of complex derivative spectra is introduced as a post-processing method to eliminate the effects of background signals, broad signals, or distorted baseline. And thus, accurate estimate of the diffusion coefficient is ensured to enhance the molecule identification.

The interpretation of small molecule diffusion coefficients: Quantitative use of diffusion-ordered NMR spectroscopy

Measuring accurate molecular self-diffusion coefficients, D, by nuclear magnetic resonance (NMR) techniques has become routine as hardware, software and experimental methodologies have all improved. However, the quantitative interpretation of such data remains difficult, particularly for small molecules. This review article first provides a description of, and explanation for, the failure of the Stokes-Einstein equation to accurately predict small molecule diffusion coefficients, before moving on to three broadly complementary methods for their quantitative interpretation. Two are based on power laws, but differ in the nature of the reference molecules used. The third addresses the uncertainties in the Stokes-Einstein equation directly. For all three methods, a wide range of examples are used to show the range of chemistry to which diffusion NMR can be applied, and how best to implement the different methods to obtain quantitative information from the chemical systems studied.

Multivariate Curve Resolution for 2D Solid-State NMR spectra

We present a processing method, based on the multivariate curve resolution approach (MCR), to denoise 2D solid-state NMR spectra, yielding a substantial S/N ratio increase while preserving the lineshapes and relative signal intensities. These spectral features are particularly important in the quantification of silicon species, where sensitivity is limited by the low natural abundance of the ²⁹Si nuclei and by the dilution of the intrinsic protons of silica, but can be of interest also when dealing with other intermediate-to-low receptivity nuclei. This method also offers the possibility of coprocessing multiple 2D spectra that have the signals at the same frequencies but with different intensities (e.g.: as a result of a variation in the mixing time). The processing can be carried out on the time-domain data, thus preserving the possibility of applying further processing to the data. As a demonstration, we have applied Cadzow denoising on the MCR-processed FIDs, achieving a further increase in the S/N ratio and more effective denoising also on the transients at longer indirect evolution times. We have applied the combined denoising on a set of experimental data from a lysozyme-silica composite.

Challenges in the decomposition of 2D NMR spectra of mixtures of small molecules

Analytical methods for mixtures of small molecules require specificity (is a certain molecule present in the mix?) and speciation capabilities. NMR spectroscopy has been a tool of choice for both of these issues since its early days, due to its quantitative (linear) response, sufficiently high resolving power and capabilities of inferring molecular structures from spectral features (even in the absence of a reference database). However, the analytical performances of NMR spectroscopy are being stretched by the increased complexity of the samples, the dynamic range of the components, and the need for a reasonable turnover time. One approach that has been actively pursued for disentangling the composition complexity is the use of 2D NMR spectroscopy. While any of the many experiments from this family will increase the spectral resolution, some are more apt for mixtures, as they are capable of unveiling signals belonging to whole molecules or fragments of it. Among the most popular ones, one can enumerate HSQC-TOCSY, DOSY and Maximum-Quantum (MaxQ) NMR spectroscopy. For multicomponent samples, the development of robust mathematical methods of signal decomposition would provide a clear edge towards identification. We have been pursuing, along these lines, Blind Source Separation (BSS). Here, the un-mixing of the spectra is achieved relying on correlations detected on a series of datasets. The series could be associated with samples of different relative composition or in a classically acquired 2D experiment by the mathematical laws underlying the construction of the indirect dimension, the one not recorded by the spectrometer. Many algorithms have been proposed for BSS in NMR spectroscopy since the seminal work of Nuzillard. In this paper, we use rather standard algorithms in BSS in order to disentangle NMR spectra. We show on simulated data (both 1D and 2D HSQC) that these approaches enable us to accurately disentangle multiple components, and provide good estimates for the concentrations of compounds. Furthermore, we show that after proper realignment of the signals, the same algorithms are able to disentangle real 1D NMR spectra. We obtain similar results on 2D HSQC spectra, where the BSS algorithms are able to successfully disentangle components, and provide even better estimates for concentrations.

InterSpin: Integrated Supportive Webtools for Low- and High-Field NMR Analyses Toward Molecular Complexity

InterSpin (http://dmar.riken.jp/interspin/) comprises integrated, supportive, and freely accessible preprocessing webtools and a database to advance signal assignment in low- and high-field NMR analyses of molecular complexities ranging from small molecules to macromolecules for food, material, and environmental applications. To support handling of the broad spectra obtained from solid-state NMR or low-field benchtop NMR, we have developed and evaluated two preprocessing tools: sensitivity improvement with spectral integration, which enhances the signal-to-noise ratio by spectral integration, and peaks separation, which separates overlapping peaks by several algorithms, such as non-negative sparse coding. In addition, the InterSpin Laboratory Information Management System (SpinLIMS) database stores numerous standard spectra ranging from small molecules to macromolecules in solid and solution states (dissolved in polar/nonpolar solvents), and can be searched under various conditions using the following molecular assignment tools. SpinMacro supports easy assignment of macromolecules in natural mixtures via solid-state ¹³C peaks and dimethyl sulfoxide-dissolved ¹H-¹³C correlation peaks. InterAnalysis improves the accuracy of molecular assignment by integrated analysis of ¹H-¹³C correlation peaks and ¹H-J correlation peaks of small molecules dissolved in D₂O or deuterated methanol, which supports easy narrowing down of metabolite candidates. Finally, by enabling database interoperability, SpinLIMS's client software will ultimately support scientific discovery by facilitating sharing and reusing of NMR data.

The GNAT: A new tool for processing NMR data

The GNAT (General NMR Analysis Toolbox) is a free and open-source software package for processing, visualising, and analysing NMR data. It supersedes the popular DOSY Toolbox, which has a narrower focus on diffusion NMR. Data import of most common formats from the major NMR platforms is supported, as well as a GNAT generic format. Key basic processing of NMR data (e.g., Fourier transformation, baseline correction, and phasing) is catered for within the program, as well as more advanced techniques (e.g., reference deconvolution and pure shift FID reconstruction). Analysis tools include DOSY and SCORE for diffusion data, ROSY T₁ /T₂ estimation for relaxation data, and PARAFAC for multilinear analysis. The GNAT is written for the MATLAB® language and comes with a user-friendly graphical user interface. The standard version is intended to run with a MATLAB installation, but completely free-standing compiled versions for Windows, Mac, and Linux are also freely available.

Reconstructing diffusion ordered NMR spectroscopy by simultaneous inversion of Laplace transform

2D diffusion-ordered NMR spectroscopy (DOSY) has been widely recognized as a powerful tool for analyzing mixtures and probing inter-molecular interactions in situ. But it is difficult to differentiate molecules with similar diffusion coefficients in presence of overlapped spectra. Its performance is susceptible to the number of chemical components, and usually gets worse when the number of components increases. Here, to alleviate the problem, numerical simultaneous inversion of Laplace transform (SILT) of many related variables is proposed for reconstructing DOSY spectrum (SILT-DOSY). The advantage of the proposed method in comparison to other methods is that it is capable of estimating the number of analytes more accurately and deriving corresponding component spectra, which in turn leads to the more reliable identification of the components.

19 F NMR matrix-assisted DOSY: a versatile tool for differentiating fluorinated species in mixtures

NMR is the most versatile tool for the analysis of organic compounds and, in combination with Diffusion-Ordered Spectroscopy ('DOSY'), can give information on compounds in complex mixtures without the need for physical separation. In mixtures where the components' diffusion coefficients are nearly identical, for example because of similar sizes, Matrix-Assisted DOSY ('MAD') can help separate the signals of different constituents, resolving their spectra. Unfortunately, DOSY (including MAD) typically fails where signals overlap, as is common in ¹ H NMR. Using ¹⁹ F NMR avoids such problems, because the great sensitivity of the ¹⁹ F chemical shift to local environment leads to very well-dispersed spectra. Another advantage is the absence of any ¹⁹ F background signals from the matrices typically used, avoiding interference with the analyte signals. In this study, differentiation among fluorophenol and fluoroaniline isomers was evaluated using normal and reverse micelles-of sodium dodecyl sulfate (SDS), cetyltrimethylammonium bromide (CTAB) and dioctyl sodium sulfosuccinate (AOT)-as matrices. These surfactants provide useful diffusion separation in these difficult mixtures, with all the solutes interacting with the matrices to different extents, in some cases leading to differences in diffusion coefficient of more than 30%. The best matrices for separating the signals of both acid and basic species were shown to be AOT and CTAB, which are useful over a wide range of surfactant concentration. Copyright © 2016 John Wiley & Sons, Ltd.

Spatially encoded 2D and 3D diffusion-ordered NMR spectroscopy

The separation of 2D spectra of components in mixtures is accelerated with spatial encoding.

Pulsed-field gradient nuclear magnetic resonance measurements (PFG NMR) for diffusion ordered spectroscopy (DOSY) mapping

The advent of Diffusion Ordered SpectroscopY (DOSY) NMR has enabled diffusion coefficients to be routinely measured and used to characterize chemical systems in solution. Indeed, DOSY NMR allows the separation of the chemical entities present in multicomponent systems and provides information on their intermolecular interactions as well as on their size and shape.

PALMA, an improved algorithm for DOSY signal processing

NMR is a tool of choice for the measurement of diffusion coefficients of species in solution.

Silica sol assisted chromatographic NMR spectroscopy for resolution of trans- and cis-isomers

Chromatographic NMR spectroscopy can separate the mixtures of species with significantly different molecular size, but generally fails for isomeric species. Herein, we reported the resolution of trans- and cis-isomers and their structural analogue, which are different in molecular shapes, but similar in mass, were greatly enhanced in the presence of silica sol. The mixtures of maleic acid, fumaric acid and succinic acid, and the mixtures of trans- and cis-1,2-cyclohexanedicarboxylic acids, were distinguished by virtue of their different degrees of interaction with silica sol. Moreover, we found mixed solvents could improve the spectral resolution of DOSY spectra of mixtures.

Development of polycarbonate-containing block copolymers for thin film self-assembly applications

High quality block copolymers are needed for thin film self-assembly and directed self-assembly applications.

Monitoring polydispersity by NMR diffusometry with tailored norm regularisation and moving-frame processing

A new way of processing diffusion NMR data is proposed that exploits _p-norm regularization of the inverse Laplace transform tailored to polydisperse macromolecular samples.

A review of blind source separation in NMR spectroscopy

Fourier transform is the data processing naturally associated to most NMR experiments. Notable exceptions are Pulse Field Gradient and relaxation analysis, the structure of which is only partially suitable for FT. With the revamp of NMR of complex mixtures, fueled by analytical challenges such as metabolomics, alternative and more apt mathematical methods for data processing have been sought, with the aim of decomposing the NMR signal into simpler bits. Blind source separation is a very broad definition regrouping several classes of mathematical methods for complex signal decomposition that use no hypothesis on the form of the data. Developed outside NMR, these algorithms have been increasingly tested on spectra of mixtures. In this review, we shall provide an historical overview of the application of blind source separation methodologies to NMR, including methods specifically designed for the specificity of this spectroscopy.