{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,25]],"date-time":"2026-05-25T15:04:21Z","timestamp":1779721461852,"version":"3.53.1"},"reference-count":35,"publisher":"Oxford University Press (OUP)","issue":"3","license":[{"start":{"date-parts":[[2026,5,25]],"date-time":"2026-05-25T00:00:00Z","timestamp":1779667200000},"content-version":"vor","delay-in-days":24,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100004281","name":"National Science Centre","doi-asserted-by":"publisher","award":["2024\/53\/B\/ST6\/03852"],"award-info":[{"award-number":["2024\/53\/B\/ST6\/03852"]}],"id":[{"id":"10.13039\/501100004281","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2026,5,4]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>Liquid chromatography\u2013mass spectrometry (LC\u2013MS) and nuclear magnetic resonance (NMR) spectroscopy are complementary analytical techniques widely used in proteomics, metabolomics, and structural biology. Both generate high-dimensional, noisy spectra where overlapping peaks complicate interpretation. LC\u2013MS relies on retention time (RT) separation before mass analysis, while multidimensional NMR spreads information across chemical-shift axes to reduce congestion. However, comparative or replicate experiments often introduce RT shifts in LC\u2013MS or frequency shifts in NMR, hindering accurate matching of corresponding features. In some experiments, such as variable-temperature NMR, the shifts are intentionally triggered, and frequency tracking provides important information. In any case, a robust, scalable alignment across runs is critical for reliable compound identification, quantification, and structural analysis. We propose a truncated Wasserstein distance-based algorithm for aligning LC\u2013MS and NMR spectra. By constraining maximum transport distance and formulating alignment as a minimum-cost flow problem solved via the Network Simplex algorithm, our method accelerates computation, suppresses spurious matches, and improves robustness to noise. On benchmark LC\u2013MS datasets, it achieved 0.97 precision, 0.96 recall, and a 0.6-s runtime, outperforming OpenMS and DeepRTAlign tools. For NMR data, the algorithm proved effective in 2D, 4D, and even 7D analyses. The algorithm is implemented in wnetalign with supporting modules wnet and pylmcf, available on PyPI and GitHub under permissive licenses: https:\/\/github.com\/michalsta\/pylmcf, https:\/\/github.com\/michalsta\/wnet, https:\/\/github.com\/michalsta\/wnetalign.<\/jats:p>","DOI":"10.1093\/bib\/bbag247","type":"journal-article","created":{"date-parts":[[2026,5,8]],"date-time":"2026-05-08T11:45:42Z","timestamp":1778240742000},"source":"Crossref","is-referenced-by-count":0,"title":["WNetAlign: fast and accurate spectra alignment using truncated Wasserstein distance and network simplex"],"prefix":"10.1093","volume":"27","author":[{"ORCID":"https:\/\/orcid.org\/0009-0009-6782-8412","authenticated-orcid":false,"given":"Justyna","family":"Kr\u00f3l","sequence":"first","affiliation":[{"name":"Faculty of Mathematics, Informatics and Mechanics, University of Warsaw , Banacha 2, 02-097 Warsaw,","place":["Poland"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0009-8284-2554","authenticated-orcid":false,"given":"Maria","family":"Bochenek","sequence":"additional","affiliation":[{"name":"Faculty of Mathematics, Informatics and Mechanics, University of Warsaw , Banacha 2, 02-097 Warsaw,","place":["Poland"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7380-4673","authenticated-orcid":false,"given":"Sylwia","family":"Jopa","sequence":"additional","affiliation":[{"name":"Centre of New Technologies, University of Warsaw , Banacha 2C, 02-097 Warsaw,","place":["Poland"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9585-1737","authenticated-orcid":false,"given":"Krzysztof","family":"Kazimierczuk","sequence":"additional","affiliation":[{"name":"Centre of New Technologies, University of Warsaw , Banacha 2C, 02-097 Warsaw,","place":["Poland"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3476-3017","authenticated-orcid":false,"given":"Anna","family":"Gambin","sequence":"additional","affiliation":[{"name":"Faculty of Mathematics, Informatics and Mechanics, University of Warsaw , Banacha 2, 02-097 Warsaw,","place":["Poland"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5227-3447","authenticated-orcid":false,"given":"Micha\u0142 Piotr","family":"Startek","sequence":"additional","affiliation":[{"name":"Faculty of Mathematics, Informatics and Mechanics, University of Warsaw , Banacha 2, 02-097 Warsaw,","place":["Poland"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2026,5,25]]},"reference":[{"key":"2026052510355706000_ref1","doi-asserted-by":"crossref","first-page":"104","DOI":"10.1093\/bib\/bbt080","article-title":"LC\u2013MS alignment in theory and practice: a comprehensive algorithmic review","volume":"16","author":"Smith","year":"2015","journal-title":"Brief Bioinform"},{"key":"2026052510355706000_ref2","doi-asserted-by":"crossref","first-page":"375","DOI":"10.1186\/1471-2105-9-375","article-title":"Critical assessment of alignment procedures for LC\u2013MS proteomics and metabolomics measurements","volume":"9","author":"Lange","year":"2008","journal-title":"BMC Bioinformatics"},{"key":"2026052510355706000_ref3","doi-asserted-by":"crossref","first-page":"161","DOI":"10.1016\/0022-2836(88)90446-9","article-title":"Folding of immunogenic peptide fragments of proteins in water solution. I. Sequence requirements for the formation of a reverse turn","volume":"201","author":"Jane Dyson","year":"1988","journal-title":"J Mol Biol"},{"key":"2026052510355706000_ref4","doi-asserted-by":"crossref","first-page":"201","DOI":"10.1016\/0022-2836(88)90447-0","article-title":"Folding of immunogenic peptide fragments of proteins in water solution. II. The nascent helix","volume":"201","author":"Jane Dyson","year":"1988","journal-title":"J Mol Biol"},{"key":"2026052510355706000_ref5","doi-asserted-by":"crossref","first-page":"1821","DOI":"10.1002\/pro.3485","article-title":"Using ${}^1$H${}^N$ amide temperature coefficients to define intrinsically disordered regions: an alternative NMR method","volume":"27","author":"Okazaki","year":"2018","journal-title":"Protein Sci"},{"key":"2026052510355706000_ref6","doi-asserted-by":"crossref","first-page":"1625","DOI":"10.1006\/jmbi.1998.2265","article-title":"Characterisation of low free-energy excited states of folded proteins","volume":"284","author":"Baxter","year":"1998","journal-title":"J Mol Biol"},{"key":"2026052510355706000_ref7","doi-asserted-by":"crossref","first-page":"1753","DOI":"10.1002\/chem.202003678","article-title":"Temperature as an extra dimension in multidimensional protein NMR spectroscopy","volume":"27","author":"Shchukina","year":"2021","journal-title":"Chem Eur J"},{"key":"2026052510355706000_ref8","doi-asserted-by":"crossref","first-page":"306","DOI":"10.1002\/pro.3785","article-title":"Temperature dependence of NMR chemical shifts: tracking and statistical analysis","volume":"29","author":"Trainor","year":"2020","journal-title":"Protein Sci"},{"key":"2026052510355706000_ref9","doi-asserted-by":"crossref","first-page":"e8956","DOI":"10.1002\/rcm.8956","article-title":"Masserstein: linear regression of mass spectra by optimal transport","volume":"39","author":"Ciach","year":"2025;","journal-title":"Rapid Commun Mass Spectrom"},{"key":"2026052510355706000_ref10","doi-asserted-by":"crossref","first-page":"giac101","DOI":"10.1093\/gigascience\/giac101","article-title":"Alignstein: optimal transport for improved LC\u2013MS retention time alignment","volume":"11","author":"Skoraczy\u0144ski","year":"2022","journal-title":"GigaScience"},{"key":"2026052510355706000_ref11","doi-asserted-by":"crossref","first-page":"163","DOI":"10.1186\/1471-2105-9-163","article-title":"Openms \u2013 an open-source software framework for mass spectrometry","volume":"9","author":"Sturm","year":"2008","journal-title":"BMC Bioinformatics"},{"key":"2026052510355706000_ref12","first-page":"i273","article-title":"A geometric approach for the alignment of liquid chromatography-mass spectrometry data","volume-title":"Bioinformatics","author":"Lange","year":"2007"},{"key":"2026052510355706000_ref13","doi-asserted-by":"crossref","first-page":"1902","DOI":"10.1093\/bioinformatics\/btl276","article-title":"A suite of algorithms for the comprehensive analysis of complex protein mixtures using high-resolution LC-MS","volume":"22","author":"Bellew","year":"2006","journal-title":"Bioinformatics"},{"key":"2026052510355706000_ref14","doi-asserted-by":"crossref","first-page":"1328","DOI":"10.1074\/mcp.M500141-MCP200","article-title":"A software suite for the generation and comparison of peptide arrays from sets of data collected by liquid chromatography-mass spectrometry","volume":"4","author":"Li","year":"2005","journal-title":"Mol Cell Proteomics"},{"key":"2026052510355706000_ref15","doi-asserted-by":"crossref","first-page":"4054","DOI":"10.1093\/bioinformatics\/bti660","article-title":"Data pre-processing in liquid chromatography-mass spectrometry-based proteomics","volume":"21","author":"Zhang","year":"2005","journal-title":"Bioinformatics"},{"key":"2026052510355706000_ref16","doi-asserted-by":"crossref","first-page":"779","DOI":"10.1021\/ac051437y","article-title":"XCMS: processing mass spectrometry data for metabolite profiling using nonlinear peak alignment, matching, and identification","volume":"78","author":"Smith","year":"2006","journal-title":"Anal Chem"},{"key":"2026052510355706000_ref17","doi-asserted-by":"crossref","first-page":"634","DOI":"10.1093\/bioinformatics\/btk039","article-title":"MZmine: toolbox for processing and visualization of mass spectrometry based molecular profile data","volume":"22","author":"Katajamaa","year":"2006","journal-title":"Bioinformatics"},{"key":"2026052510355706000_ref18","doi-asserted-by":"crossref","first-page":"190","DOI":"10.1016\/j.jmr.2009.11.012","article-title":"icoshift: a versatile tool for the rapid alignment of 1D NMR spectra","volume":"202","author":"Savorani","year":"2010","journal-title":"J Magn Reson"},{"key":"2026052510355706000_ref19","doi-asserted-by":"crossref","first-page":"405","DOI":"10.1186\/1471-2105-12-405","article-title":"An integrated workflow for robust alignment and simplified quantitative analysis of NMR spectrometry data","volume":"12","author":"Thuy-Nga","year":"2011","journal-title":"BMC Bioinformatics"},{"key":"2026052510355706000_ref20","doi-asserted-by":"crossref","first-page":"e1006018","DOI":"10.1371\/journal.pcbi.1006018","article-title":"speaq 2.0: a complete workflow for high-throughput 1D NMR spectra processing and quantification","volume":"14","author":"Beirnaert","year":"2018","journal-title":"PLoS Comput Biol"},{"key":"2026052510355706000_ref21","first-page":"2331","article-title":"Global intensity-guided peak matching and alignment for 2D HSQC spectra in metabolomics","volume":"95","author":"Zhou","year":"2023","journal-title":"Anal Chem"},{"key":"2026052510355706000_ref22","doi-asserted-by":"crossref","first-page":"188","DOI":"10.1021\/acs.analchem.3c03594","article-title":"Magnetstein: an open-source tool for quantitative NMR mixture analysis robust to low resolution, distorted lineshapes, and peak shifts","volume":"96","author":"Dom\u017ca\u0142","year":"2024","journal-title":"Anal Chem"},{"key":"2026052510355706000_ref23","first-page":"1","volume-title":"A User\u2019s Guide to Optimal Transport","author":"Ambrosio","year":"2013"},{"key":"2026052510355706000_ref24","doi-asserted-by":"crossref","first-page":"355","DOI":"10.1561\/2200000073","article-title":"Computational optimal transport: with applications to data science","volume":"11","author":"Peyr\u00e9","year":"2019","journal-title":"Found Trends Mach Learn"},{"key":"2026052510355706000_ref25","doi-asserted-by":"crossref","first-page":"4832","DOI":"10.1021\/acs.analchem.4c01652","article-title":"Network flow methods for NMR-based compound identification","volume":"97","author":"L\u00fccken","year":"2025","journal-title":"Anal Chem"},{"key":"2026052510355706000_ref26","volume-title":"Network Flows: Theory, Algorithms and Applications","author":"Ahuja","year":"1994"},{"key":"2026052510355706000_ref27","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1016\/j.entcs.2011.06.003","article-title":"Lemon \u2013 An open source C++ graph template library","volume":"264","author":"Dezso\u030b","year":"2011","journal-title":"Electronic Notes in Theoretical Computer Science"},{"key":"2026052510355706000_ref28","doi-asserted-by":"crossref","first-page":"377","DOI":"10.1145\/62212.62249","article-title":"A faster strongly polynomial minimum cost flow algorithm","volume-title":"Proceedings of the Twentieth annual ACM symposium on Theory of Computing","author":"Orlin","year":"1988"},{"key":"2026052510355706000_ref29","doi-asserted-by":"crossref","first-page":"24","DOI":"10.1016\/j.molonc.2015.07.004","article-title":"4-protein signature predicting tamoxifen treatment outcome in recurrent breast cancer","volume":"10","author":"De Marchi","year":"2016","journal-title":"Mol Oncol"},{"key":"2026052510355706000_ref30","doi-asserted-by":"crossref","first-page":"D368","DOI":"10.1093\/nar\/gkac1050","article-title":"Biological magnetic resonance data bank","volume":"51","author":"Hoch","year":"2022","journal-title":"Nucleic Acids Res"},{"key":"2026052510355706000_ref31","doi-asserted-by":"crossref","first-page":"1432","DOI":"10.1002\/prot.21832","article-title":"Pressure-induced changes in the solution structure of the GB1 domain of protein G","volume":"71","author":"Wilton","year":"2008","journal-title":"Proteins: Struct Funct Bioinf"},{"key":"2026052510355706000_ref32","first-page":"277","article-title":"NMRPipe: a multidimensional spectral processing system based on UNIX pipes","volume-title":"J Biomol NMR","author":"Delaglio"},{"key":"2026052510355706000_ref33","doi-asserted-by":"crossref","first-page":"30","DOI":"10.1038\/s41597-023-02879-5","article-title":"The 100-protein NMR spectra dataset: a resource for biomolecular NMR data analysis","volume":"11","author":"Klukowski","year":"2024","journal-title":"Sci Data"},{"key":"2026052510355706000_ref34","doi-asserted-by":"crossref","first-page":"e1010258","DOI":"10.1371\/journal.pcbi.1010258","article-title":"Linear discriminant analysis reveals hidden patterns in NMR chemical shifts of intrinsically disordered proteins","volume":"18","author":"Romero","year":"2022","journal-title":"PLoS Comput Biol"},{"key":"2026052510355706000_ref35","doi-asserted-by":"crossref","first-page":"8188","DOI":"10.1038\/s41467-023-43909-5","article-title":"DeepRTAlign: toward accurate retention time alignment for large cohort mass spectrometry data analysis","volume":"14","author":"Liu","year":"2023","journal-title":"Nat Commun"}],"container-title":["Briefings in Bioinformatics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/academic.oup.com\/bib\/article-pdf\/27\/3\/bbag247\/68381874\/bbag247.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/bib\/article-pdf\/27\/3\/bbag247\/68381874\/bbag247.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,5,25]],"date-time":"2026-05-25T14:36:08Z","timestamp":1779719768000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/bib\/article\/doi\/10.1093\/bib\/bbag247\/8692742"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,5]]},"references-count":35,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2026,5,4]]}},"URL":"https:\/\/doi.org\/10.1093\/bib\/bbag247","relation":{},"ISSN":["1467-5463","1477-4054"],"issn-type":[{"value":"1467-5463","type":"print"},{"value":"1477-4054","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2026,5]]},"published":{"date-parts":[[2026,5]]},"article-number":"bbag247"}}