Masserstein: Linear regression of mass spectra by optimal transport

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.

Envemind: Accurate Monoisotopic Mass Determination Based On Isotopic Envelope

Nowadays, monoisotopic mass is used as an important feature in top-down proteomics. Knowing the exact monoisotopic mass is helpful for precise and quick protein identification in large protein databases. However, only in spectra of small molecules the monoisotopic peak is visible. For bigger molecules like proteins, it is hidden in noise or undetected at all, and therefore its position has to be predicted. By improving the prediction of the peak, we contribute to a more accurate identification of molecules, which is crucial in fields such as chemistry and medicine. In this work, we present the envemind algorithm, which is a two-step procedure to predict monoisotopic masses of proteins. The prediction is based on an isotopic envelope. Therefore, envemind is dedicated to spectra where we are able to resolve the one dalton separated isotopic variants. Furthermore, only single-molecule spectra are allowed, that is, spectra that do not require prior deconvolution. The algorithm deals with the problem of off-by-one dalton errors, which are common in monoisotopic mass prediction. A novel aspect of this work is a mathematical exploration of the space of molecules, where we equate chemical formulas and their theoretical spectrum. Since the space of molecules consists of all possible chemical formulas, this approach is not limited to known substances only. This makes optimization processes faster and enables to approximate theoretical spectrum for a given experimental one. The algorithm is available as a Python package envemind on our GitHub page https://github.com/PiotrRadzinski/envemind.

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.

Computational optimal transport for molecular spectra: The fully discrete case

The use of computational optimal transport is investigated as a tool for comparing two molecular spectra. Unlike other techniques for comparing molecular spectra in a pattern-recognition framework, transport distances simultaneously encode information about line positions and intensities. In addition, it is shown that transport distances are a useful alternative to Euclidean distances as Euclidean distances are based on line-by-line comparisons, while transport distances reflect broader features of molecular spectra and adequately compare spectra with different resolutions. This paper includes a tutorial on the use of optimal transport and investigates several well-chosen examples to illustrate the utility of computational optimal transport for comparing molecular spectra.