{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,15]],"date-time":"2026-06-15T17:53:03Z","timestamp":1781545983078,"version":"3.54.5"},"reference-count":44,"publisher":"Oxford University Press (OUP)","issue":"3","license":[{"start":{"date-parts":[[2026,6,15]],"date-time":"2026-06-15T00:00:00Z","timestamp":1781481600000},"content-version":"vor","delay-in-days":45,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc\/4.0\/"}],"funder":[{"name":"National Institute of General Medical Sciences of the National Institutes of Health","award":["R35GM151089"],"award-info":[{"award-number":["R35GM151089"]}]},{"name":"National Institute of General Medical Sciences of the National Institutes of Health","award":["R35GM128753"],"award-info":[{"award-number":["R35GM128753"]}]},{"DOI":"10.13039\/100000002","name":"National Institutes of Health","doi-asserted-by":"publisher","award":["R00HG011490"],"award-info":[{"award-number":["R00HG011490"]}],"id":[{"id":"10.13039\/100000002","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>Most RNA molecules adopt multiple alternative structures, forming dynamic ensembles that cannot be captured by single-structure prediction. Recent advances in chemical probing methods (e.g. DMS-MaPseq and SHAPE-MaP sequencing) now provide single-molecule signals that reflect this structural heterogeneity, enabling computational reconstruction of RNA conformational states. However, existing ensemble-inference approaches based on expectation\u2013maximization (EM) often suffer from instability, convergence to suboptimal local optima, and poor scalability on high-dimensional, sparse mutation matrices, particularly for complex or modification-dependent RNA ensembles. To address these limitations, we developed VIRSE, a variational Bayesian framework that uses coordinate ascent variational inference to achieve efficient, scalable, and noise-robust reconstruction of RNA conformational mixtures from chemical probing data. We evaluated VIRSE using extensive simulations, including mechanism-informed mutation simulations that mimic realistic DMS-MaP-seq behavior (A\/C mutation bias, context-dependent dropouts, position-specific mutation rates) and idealized Bernoulli-mixture datasets without experimental artifacts. Across all conditions, especially in high-dimensional and long RNA regimes, VIRSE achieved superior ensemble separation and improved cluster identifiability compared with EM, while maintaining stable posteriors, resolving low-abundance states, and scaling to thousands of nucleotide positions. Applied to experimental datasets, including the human immunodeficiency virus-1 Rev response element, SARS-CoV-2 SHAPE-MaP measurements, and the Escherichia coli mgtL Mg2+-responsive riboswitch, VIRSE successfully recovered biologically meaningful and physically plausible RNA conformational ensembles. VIRSE is freely available at https:\/\/github.com\/QSong-github\/VIRSE.<\/jats:p>","DOI":"10.1093\/bib\/bbag301","type":"journal-article","created":{"date-parts":[[2026,5,20]],"date-time":"2026-05-20T11:45:20Z","timestamp":1779277520000},"source":"Crossref","is-referenced-by-count":0,"title":["VIRSE: a variational Bayesian framework for RNA structural ensemble inference"],"prefix":"10.1093","volume":"27","author":[{"given":"Jialu","family":"Liang","sequence":"first","affiliation":[{"name":"Department of Health Outcomes and Biomedical Informatics, University of Florida , 1889 Museum Rd, Suite 7000, Gainesville, FL 32611 ,","place":["United States"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yanfei","family":"Wang","sequence":"additional","affiliation":[{"name":"Department of Health Outcomes and Biomedical Informatics, University of Florida , 1889 Museum Rd, Suite 7000, Gainesville, FL 32611 ,","place":["United States"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xiao","family":"Fan","sequence":"additional","affiliation":[{"name":"J. Crayton Pruitt Family Department of Biomedical Engineering, University of Florida , 1275 Center Drive, Biomedical Sciences Building, JG56 P.O. Box 116131, Gainesville, FL 32611 ,","place":["United States"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7955-197X","authenticated-orcid":false,"given":"Mingyi","family":"Xie","sequence":"additional","affiliation":[{"name":"Department of Biochemistry and Molecular Biology, University of Florida , Gainesville, 1200 Newell Drive, FL 32610 ,","place":["United States"]},{"name":"UF Health Cancer Institute, University of Florida , 2033 Mowry Rd, Suite 145, Gainesville, FL 32610 ,","place":["United States"]},{"name":"UF Genetics Institute, University of Florida , 2033 Mowry Road, Gainesville, FL 32610 ,","place":["United States"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4455-5302","authenticated-orcid":false,"given":"Qianqian","family":"Song","sequence":"additional","affiliation":[{"name":"Department of Health Outcomes and Biomedical Informatics, University of Florida , 1889 Museum Rd, Suite 7000, Gainesville, FL 32611 ,","place":["United States"]},{"name":"UF Health Cancer Institute, University of Florida , 2033 Mowry Rd, Suite 145, Gainesville, FL 32610 ,","place":["United States"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2026,6,15]]},"reference":[{"key":"2026061513073030400_ref1","doi-asserted-by":"publisher","first-page":"77","DOI":"10.1016\/j.cell.2014.03.008","article-title":"The noncoding RNA revolution-trashing old rules to forge new ones","volume":"157","author":"Cech","year":"2014","journal-title":"Cell"},{"key":"2026061513073030400_ref2","doi-asserted-by":"publisher","first-page":"784","DOI":"10.1038\/s41580-024-00748-6","article-title":"Identification of RNA structures and their roles in RNA functions","volume":"25","author":"Cao","year":"2024","journal-title":"Nat Rev Mol Cell Biol"},{"key":"2026061513073030400_ref3","doi-asserted-by":"publisher","first-page":"469","DOI":"10.1038\/nrg3681","article-title":"Insights into RNA structure and function from genome-wide studies","volume":"15","author":"Mortimer","year":"2014","journal-title":"Nat Rev Genet"},{"key":"2026061513073030400_ref4","doi-asserted-by":"publisher","first-page":"1128","DOI":"10.1038\/s41467-022-28603-2","article-title":"Secondary structural ensembles of the SARS-CoV-2 RNA genome in infected cells","volume":"13","author":"Lan","year":"2022","journal-title":"Nat Commun"},{"key":"2026061513073030400_ref5","doi-asserted-by":"publisher","first-page":"1708","DOI":"10.1016\/j.molcel.2022.02.009","article-title":"Discovery of a large-scale, cell-state-responsive allosteric switch in the 7SK RNA using DANCE-MaP","volume":"82","author":"Olson","year":"2022","journal-title":"Mol Cell"},{"key":"2026061513073030400_ref6","doi-asserted-by":"publisher","first-page":"394","DOI":"10.1038\/s41586-022-05135-9","article-title":"In vivo single-molecule analysis reveals COOLAIR RNA structural diversity","volume":"609","author":"Yang","year":"2022","journal-title":"Nature"},{"key":"2026061513073030400_ref7","doi-asserted-by":"publisher","first-page":"925","DOI":"10.1038\/s41467-025-56149-6","article-title":"Telomerase RNA structural heterogeneity in living human cells detected by DMS-MaPseq","volume":"16","author":"Forino","year":"2025","journal-title":"Nat Commun"},{"key":"2026061513073030400_ref8","doi-asserted-by":"publisher","first-page":"941","DOI":"10.1038\/s41467-021-21194-4","article-title":"RNA secondary structure prediction using deep learning with thermodynamic integration","volume":"12","author":"Sato","year":"2021","journal-title":"Nat Commun"},{"key":"2026061513073030400_ref9","doi-asserted-by":"publisher","first-page":"3314","DOI":"10.1093\/nar\/gkt1291","article-title":"The influence of viral RNA secondary structure on interactions with innate host cell defences","volume":"42","author":"Witteveldt","year":"2014","journal-title":"Nucleic Acids Res"},{"key":"2026061513073030400_ref10","doi-asserted-by":"publisher","first-page":"314","DOI":"10.1093\/nar\/gkx1057","article-title":"Modeling RNA secondary structure folding ensembles using SHAPE mapping data","volume":"46","author":"Spasic","year":"2018","journal-title":"Nucleic Acids Res"},{"key":"2026061513073030400_ref11","doi-asserted-by":"publisher","first-page":"438","DOI":"10.1038\/s41586-020-2253-5","article-title":"Determination of RNA structural diversity and its role in HIV-1 RNA splicing","volume":"582","author":"Tomezsko","year":"2020","journal-title":"Nature"},{"key":"2026061513073030400_ref12","doi-asserted-by":"publisher","first-page":"367","DOI":"10.1093\/bioinformatics\/btm591","article-title":"Rfold: an exact algorithm for computing local base pairing probabilities","volume":"24","author":"Kiryu","year":"2008","journal-title":"Bioinformatics"},{"key":"2026061513073030400_ref13","doi-asserted-by":"publisher","first-page":"e7","DOI":"10.1093\/nar\/gkac1029","article-title":"LazySampling and LinearSampling: fast stochastic sampling of RNA secondary structure with applications to SARS-CoV-2","volume":"51","author":"Zhang","year":"2008","journal-title":"Nucleic Acids Res"},{"key":"2026061513073030400_ref14","doi-asserted-by":"publisher","first-page":"75","DOI":"10.1038\/nmeth.4057","article-title":"DMS-MaPseq for genome-wide or targeted RNA structure probing in vivo","volume":"14","author":"Zubradt","year":"2017","journal-title":"Nat Methods"},{"key":"2026061513073030400_ref15","doi-asserted-by":"publisher","first-page":"219","DOI":"10.1007\/978-1-0716-1158-6_13","article-title":"DMS-MaPseq for genome-wide or targeted RNA structure probing in vitro and in vivo","volume":"2254","author":"Tomezsko","year":"2021","journal-title":"Methods Mol Biol"},{"key":"2026061513073030400_ref16","doi-asserted-by":"publisher","first-page":"959","DOI":"10.1038\/nmeth.3029","article-title":"RNA motif discovery by SHAPE and mutational profiling (SHAPE-MaP)","volume":"11","author":"Siegfried","year":"2014","journal-title":"Nat Methods"},{"key":"2026061513073030400_ref17","doi-asserted-by":"publisher","first-page":"1181","DOI":"10.1038\/nprot.2018.010","article-title":"In-cell RNA structure probing with SHAPE-MaP","volume":"13","author":"Smola","year":"2018","journal-title":"Nat Protoc"},{"key":"2026061513073030400_ref18","doi-asserted-by":"publisher","first-page":"249","DOI":"10.1016\/j.ymeth.2022.05.001","article-title":"Using DMS-MaPseq to uncover the roles of DEAD-box proteins in ribosome assembly","volume":"204","author":"Liu","year":"2022","journal-title":"Methods"},{"key":"2026061513073030400_ref19","volume-title":"Pattern recognition and machine learning","author":"Bishop","year":"2006"},{"key":"2026061513073030400_ref20","doi-asserted-by":"publisher","first-page":"5222","DOI":"10.1080\/03610918.2020.1764034","article-title":"Beyond the EM algorithm: constrained optimization methods for latent class model","volume":"51","author":"Chen","year":"2022","journal-title":"Commun Stat Simul Comput"},{"key":"2026061513073030400_ref21","doi-asserted-by":"publisher","first-page":"129","DOI":"10.1162\/neco.1996.8.1.129","article-title":"On convergence properties of the EM algorithm for Gaussian mixtures","volume":"8","author":"Xu","year":"1996","journal-title":"Neural Comput"},{"key":"2026061513073030400_ref22","doi-asserted-by":"publisher","first-page":"859","DOI":"10.1080\/01621459.2017.1285773","article-title":"Variational inference: a review for statisticians","volume":"112","author":"Blei","year":"2017","journal-title":"J Am Stat Assoc"},{"key":"2026061513073030400_ref23","doi-asserted-by":"publisher","first-page":"183","DOI":"10.1023\/A:1007665907178","article-title":"An introduction to variational methods for graphical models","volume":"37","author":"Jordan","year":"1999","journal-title":"Mach Learn"},{"key":"2026061513073030400_ref24","doi-asserted-by":"publisher","first-page":"711","DOI":"10.1038\/nature08237","article-title":"Architecture and secondary structure of an entire HIV-1 RNA genome","volume":"460","author":"Watts","year":"2009","journal-title":"Nature"},{"key":"2026061513073030400_ref25","doi-asserted-by":"publisher","first-page":"4676","DOI":"10.1093\/nar\/gkv313","article-title":"The HIV-1 rev response element (RRE) adopts alternative conformations that promote different rates of virus replication","volume":"43","author":"Sherpa","year":"2015","journal-title":"Nucleic Acids Res"},{"key":"2026061513073030400_ref26","doi-asserted-by":"publisher","first-page":"143","DOI":"10.1017\/S1355838201001881","article-title":"Two alternating structures of the HIV-1 leader RNA","volume":"7","author":"Huthoff","year":"2001","journal-title":"RNA"},{"key":"2026061513073030400_ref27","doi-asserted-by":"publisher","first-page":"12436","DOI":"10.1093\/nar\/gkaa1053","article-title":"Genome-wide mapping of SARS-CoV-2 RNA structures identifies therapeutically-relevant elements","volume":"48","author":"Manfredonia","year":"2020","journal-title":"Nucleic Acids Res"},{"key":"2026061513073030400_ref28","doi-asserted-by":"publisher","DOI":"10.1101\/2020.06","article-title":"Structure of the full SARS-CoV-2 RNA genome in infected cells","volume":"29","author":"","year":"2020","journal-title":"bioRxiv"},{"key":"2026061513073030400_ref29","doi-asserted-by":"publisher","first-page":"e03656","DOI":"10.7554\/eLife.03656","article-title":"RNA-guided assembly of rev-RRE nuclear export complexes","volume":"3","author":"Bai","year":"2014","journal-title":"Elife"},{"key":"2026061513073030400_ref30","doi-asserted-by":"publisher","first-page":"594","DOI":"10.1016\/j.cell.2013.10.008","article-title":"An unusual topological structure of the HIV-1 rev response element","volume":"155","author":"Fang","year":"2013","journal-title":"Cell"},{"key":"2026061513073030400_ref31","doi-asserted-by":"crossref","first-page":"785","DOI":"10.1038\/s41592-018-0121-0","article-title":"COMRADES determines in vivo RNA structures and interactions","volume":"15","author":"","year":"2018","journal-title":"Nat Methods"},{"key":"2026061513073030400_ref32","doi-asserted-by":"publisher","first-page":"249","DOI":"10.1038\/s41592-021-01075-w","article-title":"Genome-scale deconvolution of RNA structure ensembles","volume":"18","author":"Morandi","year":"2021","journal-title":"Nat Methods"},{"key":"2026061513073030400_ref44","doi-asserted-by":"publisher","DOI":"10.1038\/s41587-025-02739-0","article-title":"Identification of conserved RNA regulatory switches in living cells using RNA secondary structure ensemble mapping and covariation analysis","volume-title":"Nature Biotechnology","author":"Borovsk\u00e1","year":"2025"},{"key":"2026061513073030400_ref33","doi-asserted-by":"publisher","first-page":"188","DOI":"10.1177\/0049124103262065","article-title":"AIC and BIC: comparisons of assumptions and performance","volume":"33","author":"Kuha","year":"2004","journal-title":"Sociol Methods Res"},{"key":"2026061513073030400_ref34","doi-asserted-by":"publisher","first-page":"e97","DOI":"10.1093\/nar\/gky486","article-title":"RNA framework: an all-in-one toolkit for the analysis of RNA structures and post-transcriptional modifications","volume":"46","author":"Incarnato","year":"2018","journal-title":"Nucleic Acids Res"},{"key":"2026061513073030400_ref35","doi-asserted-by":"publisher","first-page":"487","DOI":"10.1007\/s00357-022-09413-z","article-title":"Understanding the adjusted Rand index and other partition comparison indices based on counting object pairs","volume":"39","author":"Warrens","year":"2022","journal-title":"J Classif"},{"key":"2026061513073030400_ref36","doi-asserted-by":"publisher","first-page":"79","DOI":"10.1214\/aoms\/1177729694","article-title":"On information and sufficiency","volume":"22","author":"Kullback","year":"1951","journal-title":"Ann Math Stat"},{"key":"2026061513073030400_ref37","doi-asserted-by":"publisher","first-page":"e0279774","DOI":"10.1371\/journal.pone.0279774","article-title":"Decomposition of the mean absolute error (MAE) into systematic and unsystematic components","volume":"18","author":"Robeson","year":"2023","journal-title":"PLoS One"},{"key":"2026061513073030400_ref38","first-page":"2796","volume":"7","author":"Kurihara","year":"2007","journal-title":"IJCAI"},{"key":"2026061513073030400_ref39","article-title":"Rotated mean-field variational inference and iterative Gaussianization","author":"Chen","year":"2025"},{"key":"2026061513073030400_ref40","doi-asserted-by":"publisher","first-page":"118","DOI":"10.1007\/s11222-024-10430-8","article-title":"Spike and slab Bayesian sparse principal component analysis","volume":"34","author":"Ning","year":"2024","journal-title":"Stat Comput"},{"key":"2026061513073030400_ref41","doi-asserted-by":"publisher","first-page":"679","DOI":"10.3390\/e26080679","article-title":"GAD-PVI: a general accelerated dynamic-weight particle-based variational inference framework","volume":"26","author":"Wang","year":"2024","journal-title":"Entropy"},{"key":"2026061513073030400_ref42","article-title":"Sparse variational inference: Bayesian coresets from scratch","volume":"32","author":"Campbell","year":"2019","journal-title":"Adv Neural Inf Proces Syst"},{"key":"2026061513073030400_ref43","author":"","year":"2024"}],"container-title":["Briefings in Bioinformatics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/academic.oup.com\/bib\/article-pdf\/27\/3\/bbag301\/68529322\/bbag301.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/bib\/article-pdf\/27\/3\/bbag301\/68529322\/bbag301.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,6,15]],"date-time":"2026-06-15T17:07:40Z","timestamp":1781543260000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/bib\/article\/doi\/10.1093\/bib\/bbag301\/8708247"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,5]]},"references-count":44,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2026,5,4]]}},"URL":"https:\/\/doi.org\/10.1093\/bib\/bbag301","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":"bbag301"}}