Computational optimal transport for molecular spectra: The fully discrete case

Magnetstein: An Open-Source Tool for Quantitative NMR Mixture Analysis Robust to Low Resolution, Distorted Lineshapes, and Peak Shifts

1H NMR spectroscopy is a powerful tool for analyzing mixtures including determining the concentrations of individual components. When signals from multiple compounds overlap, this task requires computational solutions. They are typically based on peak-picking and the comparison of obtained peak lists with libraries of individual components. This can fail if peaks are not sufficiently resolved or when peak positions differ between the library and the mixture. In this paper, we present Magnetstein, a quantification algorithm rooted in the optimal transport theory that makes it robust to unexpected frequency shifts and overlapping signals. Thanks to this, Magnetstein can quantitatively analyze difficult spectra with the estimation trueness an order of magnitude higher than that of commercial tools. Furthermore, the method is easier to use than other approaches, having only two parameters with default values applicable to a broad range of experiments and requiring little to no preprocessing of the spectra.

Alignstein: Optimal transport for improved LC-MS retention time alignment

Background

Reproducibility of liquid chromatography separation is limited by retention time drift. As a result, measured signals lack correspondence over replicates of the liquid chromatography–mass spectrometry (LC-MS) experiments. Correction of these errors is named retention time alignment and needs to be performed before further quantitative analysis. Despite the availability of numerous alignment algorithms, their accuracy is limited (e.g., for retention time drift that swaps analytes’ elution order).

Results

We present the Alignstein, an algorithm for LC-MS retention time alignment. It correctly finds correspondence even for swapped signals. To achieve this, we implemented the generalization of the Wasserstein distance to compare multidimensional features without any reduction of the information or dimension of the analyzed data. Moreover, Alignstein by design requires neither a reference sample nor prior signal identification. We validate the algorithm on publicly available benchmark datasets obtaining competitive results. Finally, we show that it can detect the information contained in the tandem mass spectrum by the spatial properties of chromatograms.

Conclusions

We show that the use of optimal transport effectively overcomes the limitations of existing algorithms for statistical analysis of mass spectrometry datasets. The algorithm’s source code is available at https://github.com/grzsko/Alignstein.

Optimization of density fitting auxiliary Slater-type basis functions for time-dependent density functional theory

A new set of auxiliary basis function suitable to fit the induced electron density is presented. Such set has been optimized in order to furnish accurate absorption spectra using the complex polarizability algorithm of time-dependent density functional theory (TDDFT). An automatic procedure has been set up, able, thanks to the definition of suitable descriptors, to evaluate the resemblance of the auxiliary basis-dependent calculated spectra with respect to a reference. In this way, it has been possible to reduce the size of the basis set maximizing the basis set accuracy. Thanks to the choice to employ a collection of molecules for each element, such basis has proven transferable to molecules outside the collection. The final sets are therefore much more accurate and smaller than the previously optimized ones and have been already included in the database of the last release of the AMS suite of programs. The availability of the present new set will allow to improve drastically the applicability range of the polTDDFT method with higher accuracy and less computational effort.

Computational optimal transport for molecular spectra: The semi-discrete case

Comparing a discrete molecular spectrum to a continuous molecular spectrum in a quantitative manner is a challenging problem, for example, when attempting to fit a theoretical stick spectrum to a continuous spectrum. In this paper, the use of computational optimal transport is investigated for such a problem. In the optimal transport literature, the comparison of a discrete and a continuous spectrum is referred to as semi-discrete optimal transport and is a situation where a metric such as least-squares may be difficult to define except under special conditions. The merits of an optimal transport approach for this problem are investigated using the transport distance defined for the semi-discrete case. A tutorial on semi-discrete optimal transport for molecular spectra is included in this paper, and several well-chosen synthetic spectra are investigated to demonstrate the utility of computational optimal transport for the semi-discrete case. Among several types of investigations, we include calculations showing how the frequency resolution of the continuous spectrum affects the transport distance between a discrete and a continuous spectrum. We also use the transport distance to measure the distance between a continuous experimental electronic absorption spectrum of SO₂ and a theoretical stick spectrum for the same system. The comparison of the theoretical and experimental SO₂ spectra also allows us to suggest a theoretical value for the band origin that is closer to the observed band origin than previous theoretical values.