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

Abstract

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.

Optimal transport for automatic alignment of untargeted metabolomic data

“…Differences in experimental conditions can induce variations in RT between datasets that can be nonlinear and large in magnitude ( Zhou et al, 2012 ; Climaco Pinto et al, 2022 ; Habra et al, 2021 ). In the spirit of previous methods for LC-MS batch or dataset alignment ( Smith et al, 2006 ; Brunius et al, 2016 ; Liu et al, 2020 ; Vaughan et al, 2012 ; Habra et al, 2021 ; Climaco Pinto et al, 2022 ; Skoraczyński et al, 2022 ), the learned coupling is used to estimate a nonlinear map (drift function) between RTs of both datasets by weighted spline regression, which allows us to filter unlikely matches from the coupling matrix to obtain a refined coupling matrix ( Figure 1d , Materials and methods). An optional thresholding step removes matches with small weights from the coupling matrix.…”

“…The main technical innovation of GromovMatcher lies in its ability to incorporate the correlation information between metabolic feature intensities, building upon the powerful mathematical framework of computational optimal transport (OT; Peyré and Cuturi, 2019 ; Villani, 2021 ). OT has proven effective in solving various matching problems and has found applications in multiomics analysis ( Demetci et al, 2022 ), cell development ( Schiebinger et al, 2019 ; Yang et al, 2020 ), and chromatogram alignment ( Skoraczyński et al, 2022 ). Here, we leverage the Gromov-Wasserstein (GW) method ( Mémoli, 2011 ; Solomon et al, 2016 ), which matches datasets based on their distance structure and has been seminally applied to spatial reconstruction problems in genomics Nitzan et al, 2019 .…”

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

“…This opens the possibility to further develop computational methods for benchtop NMR instruments, which are readily available for many laboratories and useful for rapid screening of samples, but their low resolution poses a major obstacle in more complex analyses. Furthermore, the probabilistic paradigm is applicable for any kind of spectroscopy where the signal is non-negative and spectra can be approximated as linear combinations; in fact, computational methods based on the Wasserstein distance, including a simpler version of the Wasserstein regression, have already been shown to provide accurate results in mass spectrometry. ,, While each spectroscopic technique has its own specifics that need to be considered, Magnetstein has the potential to be a single tool that unifies the quantitative analyses of multiple kinds of spectroscopic data.…”

Novel Peak Shift Correction Method Based on the Retention Index for Peak Alignment in Untargeted Metabolomics

“…Metabolomics has emerged as a promising tool for elucidating the molecular phenotypes of organisms, providing comprehensive insights into the metabolic processes occurring within biological systems, and shedding light on regulatory mechanisms. − Liquid chromatography-mass spectrometry (LC-MS) has become the preferred platform for metabolomics research owing to its high sensitivity, selectivity, and coverage. − However, the complexity of biological matrices and the potential variability in analytical workflows often cause LC-MS data to exhibit drifts, shifts, and distortions that may impact the comparability and interpretation of metabolomics results. − Therefore, peak alignment is a fundamental and indispensable step in the LC-MS-based metabolomics workflows, responsible for integrating data on corresponding metabolites between different batches of LC-MS analysis and reducing the impact of such variations. ,− …”