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.

PALMA, an improved algorithm for DOSY signal processing.

NMR is a tool of choice for the measurement of diffusion coefficients of species in solution. The DOSY experiment, a 2D implementation of this measurement, has been proven to be particularly useful for the study of complex mixtures, molecular interactions, polymers, etc. However, DOSY data analysis requires to resort to the inverse Laplace transform, in particular for polydisperse samples. This is a known difficult numerical task for which we present here a novel approach. A new algorithm based on a splitting scheme and on the use of proximity operators is introduced. Used in conjunction with a Maximum Entropy and hybrid regularisation, this algorithm converges rapidly and produces results robust against experimental noise. This method has been called PALMA. It is able to reproduce faithfully monodisperse as well as polydisperse systems, and numerous simulated and experimental examples are presented. It has been implemented on the server where users can have their datasets processed automatically.