{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,7]],"date-time":"2026-05-07T05:00:15Z","timestamp":1778130015749,"version":"3.51.4"},"update-to":[{"DOI":"10.1371\/journal.pcbi.1013242","type":"new_version","label":"New version","source":"publisher","updated":{"date-parts":[[2025,8,18]],"date-time":"2025-08-18T00:00:00Z","timestamp":1755475200000}}],"reference-count":60,"publisher":"Public Library of Science (PLoS)","issue":"7","license":[{"start":{"date-parts":[[2025,7,24]],"date-time":"2025-07-24T00:00:00Z","timestamp":1753315200000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100000060","name":"National Institute of Allergy and Infectious Diseases","doi-asserted-by":"publisher","award":["U01 AI150680"],"award-info":[{"award-number":["U01 AI150680"]}],"id":[{"id":"10.13039\/100000060","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000060","name":"National Institute of Allergy and Infectious Diseases","doi-asserted-by":"publisher","award":["R01 AI093870"],"award-info":[{"award-number":["R01 AI093870"]}],"id":[{"id":"10.13039\/100000060","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["www.ploscompbiol.org"],"crossmark-restriction":false},"short-container-title":["PLoS Comput Biol"],"abstract":"<jats:p>\n                    Mechanistic models of dynamic, interacting cell populations have yielded many insights into the growth and resolution of immune responses. Historically these models have described the behavior of pre-defined cell types based on small numbers of phenotypic markers. The ubiquity of deep phenotyping therefore presents a new challenge; how do we confront tractable and interpretable mathematical models with high-dimensional data? To tackle this problem, we studied the development and persistence of lung tissue-resident memory CD4 and CD8 T cells (\n                    <jats:inline-formula id=\"pcbi.1013242.e001\">\n                      <jats:alternatives>\n                        <jats:graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" id=\"pcbi.1013242.e001g\" mimetype=\"image\" position=\"anchor\" xlink:href=\"info:doi\/10.1371\/journal.pcbi.1013242.e001\" xlink:type=\"simple\"\/>\n                        <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"inline\" id=\"M1\">\n                          <mml:mrow>\n                            <mml:msub>\n                              <mml:mtext>T<\/mml:mtext>\n                              <mml:mrow>\n                                <mml:mtext>RM<\/mml:mtext>\n                              <\/mml:mrow>\n                            <\/mml:msub>\n                          <\/mml:mrow>\n                        <\/mml:math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    ) in mice infected with influenza virus. We developed an approach in which dynamical model parameters and the population structure are inferred simultaneously. This method uses deep learning and stochastic variational inference and is trained on the single-cell flow-cytometry data directly, rather than on the kinetics of pre-identified clusters. We show that during the resolution phase of the immune response, memory CD4 and CD8 T cells within the lung are phenotypically diverse, with subsets exhibiting highly distinct and time-dependent dynamics.\n                    <jats:inline-formula id=\"pcbi.1013242.e002\">\n                      <jats:alternatives>\n                        <jats:graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" id=\"pcbi.1013242.e002g\" mimetype=\"image\" position=\"anchor\" xlink:href=\"info:doi\/10.1371\/journal.pcbi.1013242.e002\" xlink:type=\"simple\"\/>\n                        <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"inline\" id=\"M2\">\n                          <mml:mrow>\n                            <mml:msub>\n                              <mml:mtext>T<\/mml:mtext>\n                              <mml:mrow>\n                                <mml:mtext>RM<\/mml:mtext>\n                              <\/mml:mrow>\n                            <\/mml:msub>\n                          <\/mml:mrow>\n                        <\/mml:math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    heterogeneity is maintained long-term by ongoing differentiation of relatively persistent Bcl-2\n                    <jats:sup>hi<\/jats:sup>\n                    CD4 and CD8\n                    <jats:inline-formula id=\"pcbi.1013242.e004\">\n                      <jats:alternatives>\n                        <jats:graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" id=\"pcbi.1013242.e004g\" mimetype=\"image\" position=\"anchor\" xlink:href=\"info:doi\/10.1371\/journal.pcbi.1013242.e004\" xlink:type=\"simple\"\/>\n                        <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"inline\" id=\"M4\">\n                          <mml:mrow>\n                            <mml:msub>\n                              <mml:mtext>T<\/mml:mtext>\n                              <mml:mrow>\n                                <mml:mtext>RM<\/mml:mtext>\n                              <\/mml:mrow>\n                            <\/mml:msub>\n                          <\/mml:mrow>\n                        <\/mml:math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    subsets which resolve into distinct functional populations. Our approach yields new insights into the dynamics of tissue-localized immune memory, and is a novel basis for interpreting time series of high-dimensional data, broadly applicable to diverse biological systems.\n                  <\/jats:p>","DOI":"10.1371\/journal.pcbi.1013242","type":"journal-article","created":{"date-parts":[[2025,7,24]],"date-time":"2025-07-24T17:46:28Z","timestamp":1753379188000},"page":"e1013242","update-policy":"https:\/\/doi.org\/10.1371\/journal.pcbi.corrections_policy","source":"Crossref","is-referenced-by-count":4,"title":["A variational deep-learning approach to modeling memory T cell dynamics"],"prefix":"10.1371","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7504-9947","authenticated-orcid":true,"given":"Christiaan H.","family":"van Dorp","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Joshua I.","family":"Gray","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6644-4742","authenticated-orcid":true,"given":"Daniel H.","family":"Paik","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Donna L.","family":"Farber","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4606-4483","authenticated-orcid":true,"given":"Andrew J.","family":"Yates","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"340","published-online":{"date-parts":[[2025,7,24]]},"reference":[{"key":"pcbi.1013242.ref001","doi-asserted-by":"crossref","first-page":"52","DOI":"10.1016\/j.csda.2012.12.008","article-title":"Model-based clustering of high-dimensional data: a review","volume":"71","author":"C Bouveyron","year":"2014","journal-title":"Comput Statist Data Anal."},{"issue":"1","key":"pcbi.1013242.ref002","doi-asserted-by":"crossref","first-page":"393","DOI":"10.1093\/bib\/bbz170","article-title":"Deep learning-based clustering approaches for bioinformatics","volume":"22","author":"MR Karim","year":"2021","journal-title":"Brief Bioinform."},{"issue":"11","key":"pcbi.1013242.ref003","doi-asserted-by":"crossref","first-page":"810","DOI":"10.1038\/s41577-024-01040-6","article-title":"A guide to adaptive immune memory","volume":"24","author":"N Lam","year":"2024","journal-title":"Nat Rev Immunol."},{"issue":"25","key":"pcbi.1013242.ref004","doi-asserted-by":"crossref","first-page":"14926","DOI":"10.1073\/pnas.95.25.14926","article-title":"Models of immune memory: on the role of cross-reactive stimulation, competition, and homeostasis in maintaining immune memory","volume":"95","author":"R Antia","year":"1998","journal-title":"Proc Natl Acad Sci U S A."},{"issue":"8","key":"pcbi.1013242.ref005","doi-asserted-by":"crossref","first-page":"3928","DOI":"10.4049\/jimmunol.171.8.3928","article-title":"Different dynamics of CD4+ and CD8+ T cell responses during and after acute lymphocytic choriomeningitis virus infection","volume":"171","author":"RJ De Boer","year":"2003","journal-title":"J Immunol."},{"issue":"6","key":"pcbi.1013242.ref006","doi-asserted-by":"crossref","DOI":"10.1371\/journal.pbio.2005523","article-title":"Human TSCM cell dynamics in vivo are compatible with long-lived immunological memory and stemness","volume":"16","author":"P Costa Del Amo","year":"2018","journal-title":"PLoS Biol."},{"key":"pcbi.1013242.ref007","doi-asserted-by":"crossref","first-page":"947242","DOI":"10.3389\/fimmu.2022.947242","article-title":"Effect of cellular aging on memory T-cell homeostasis","volume":"13","author":"AC Swain","year":"2022","journal-title":"Front Immunol."},{"key":"pcbi.1013242.ref008","doi-asserted-by":"crossref","DOI":"10.7554\/eLife.23013","article-title":"Memory CD4 T cell subsets are kinetically heterogeneous and replenished from naive T cells at high levels","volume":"6","author":"G Gossel","year":"2017","journal-title":"Elife."},{"key":"pcbi.1013242.ref009","doi-asserted-by":"crossref","first-page":"20","DOI":"10.1016\/j.coviro.2020.09.006","article-title":"Anti-viral protective capacity of tissue resident memory T cells","volume":"46","author":"DH Paik","year":"2021","journal-title":"Curr Opin Virol."},{"issue":"10","key":"pcbi.1013242.ref010","doi-asserted-by":"crossref","first-page":"2561","DOI":"10.4049\/jimmunol.1900767","article-title":"Tissue-resident memory T cells in mice and humans: towards a quantitative ecology","volume":"203","author":"SE Morris","year":"2019","journal-title":"J Immunol."},{"issue":"34","key":"pcbi.1013242.ref011","doi-asserted-by":"crossref","DOI":"10.1126\/sciimmunol.aas9673","article-title":"Location, location, location: tissue resident memory T cells in mice and humans","volume":"4","author":"PA Szabo","year":"2019","journal-title":"Sci Immunol."},{"issue":"12","key":"pcbi.1013242.ref012","doi-asserted-by":"crossref","first-page":"2748","DOI":"10.1084\/jem.20181308","article-title":"CXCR6 regulates localization of tissue-resident memory CD8 T cells to the airways","volume":"216","author":"AN Wein","year":"2019","journal-title":"J Exp Med."},{"issue":"12","key":"pcbi.1013242.ref013","doi-asserted-by":"crossref","first-page":"2921","DOI":"10.1016\/j.celrep.2017.08.078","article-title":"Human tissue-resident memory T cells are defined by core transcriptional and functional signatures in lymphoid and mucosal sites","volume":"20","author":"BV Kumar","year":"2017","journal-title":"Cell Rep."},{"issue":"2","key":"pcbi.1013242.ref014","doi-asserted-by":"crossref","first-page":"374","DOI":"10.4049\/jimmunol.1800979","article-title":"Memory T cell dynamics in the lung during influenza virus infection","volume":"202","author":"A Pizzolla","year":"2019","journal-title":"J Immunol."},{"issue":"6","key":"pcbi.1013242.ref015","doi-asserted-by":"crossref","first-page":"109992","DOI":"10.1016\/j.celrep.2021.109992","article-title":"Mapping the evolution of T cell states during response and resistance to adoptive cellular therapy","volume":"37","author":"P Bachireddy","year":"2021","journal-title":"Cell Reports."},{"issue":"4","key":"pcbi.1013242.ref016","doi-asserted-by":"crossref","first-page":"307","DOI":"10.1561\/2200000056","article-title":"An introduction to variational autoencoders","volume":"12","author":"DP Kingma","year":"2019","journal-title":"FNT Mach Learn."},{"issue":"11","key":"pcbi.1013242.ref017","doi-asserted-by":"crossref","first-page":"5510","DOI":"10.4049\/jimmunol.1102243","article-title":"Cutting edge: tissue-retentive lung memory CD4 T cells mediate optimal protection to respiratory virus infection","volume":"187","author":"JR Teijaro","year":"2011","journal-title":"J Immunol."},{"issue":"2","key":"pcbi.1013242.ref018","doi-asserted-by":"crossref","first-page":"215","DOI":"10.1189\/jlb.0313180","article-title":"Lung-resident memory CD8 T cells (TRM) are indispensable for optimal cross-protection against pulmonary virus infection","volume":"95","author":"T Wu","year":"2014","journal-title":"J Leukoc Biol."},{"issue":"3","key":"pcbi.1013242.ref019","doi-asserted-by":"crossref","first-page":"501","DOI":"10.1038\/mi.2013.67","article-title":"Lung niches for the generation and maintenance of tissue-resident memory T cells","volume":"7","author":"DL Turner","year":"2014","journal-title":"Mucosal Immunol."},{"issue":"12","key":"pcbi.1013242.ref020","doi-asserted-by":"crossref","DOI":"10.1126\/sciimmunol.aam6970","article-title":"Resident memory CD8+ T cells in the upper respiratory tract prevent pulmonary influenza virus infection","volume":"2","author":"A Pizzolla","year":"2017","journal-title":"Sci Immunol."},{"issue":"4","key":"pcbi.1013242.ref021","doi-asserted-by":"crossref","first-page":"936","DOI":"10.4049\/jimmunol.1900093","article-title":"The impact of TCR signal strength on resident memory T cell formation during influenza virus infection","volume":"203","author":"JK Fiege","year":"2019","journal-title":"J Immunol."},{"issue":"1","key":"pcbi.1013242.ref022","doi-asserted-by":"crossref","first-page":"5233","DOI":"10.1038\/s41598-019-41695-z","article-title":"From Louvain to Leiden: guaranteeing well-connected communities","volume":"9","author":"VA Traag","year":"2019","journal-title":"Sci Rep."},{"key":"pcbi.1013242.ref023","doi-asserted-by":"crossref","first-page":"1","DOI":"10.18637\/jss.v076.i01","article-title":"Stan: a probabilistic programming language","volume":"76","author":"B Carpenter","year":"2017","journal-title":"J Stat Softw."},{"key":"pcbi.1013242.ref024","unstructured":"Team SD. Stan modeling language users guide and reference manual. 2024. https:\/\/mc-stan.org"},{"key":"pcbi.1013242.ref025","unstructured":"McInnes L, Healy J, Melville J. UMAP: uniform manifold approximation and projection for dimension reduction. 2020. http:\/\/arxiv.org\/abs\/1802.03426"},{"issue":"8","key":"pcbi.1013242.ref026","doi-asserted-by":"crossref","DOI":"10.1016\/j.immuni.2023.06.025","article-title":"Graded expression of the chemokine receptor CX3CR1 marks differentiation states of human and murine T cells and enables cross-species interpretation","volume":"56","author":"AJ Zwijnenburg","year":"2023","journal-title":"Immunity."},{"issue":"6","key":"pcbi.1013242.ref027","doi-asserted-by":"crossref","first-page":"1270","DOI":"10.1016\/j.immuni.2016.10.018","article-title":"The chemokine receptor CX3CR1 defines three antigen-experienced CD8 T cell subsets with distinct roles in immune surveillance and homeostasis","volume":"45","author":"C Gerlach","year":"2016","journal-title":"Immunity."},{"issue":"5","key":"pcbi.1013242.ref028","doi-asserted-by":"crossref","first-page":"1413","DOI":"10.1007\/s11222-016-9696-4","article-title":"Practical Bayesian model evaluation using leave-one-out cross-validation and WAIC","volume":"27","author":"A Vehtari","year":"2016","journal-title":"Stat Comput."},{"issue":"1","key":"pcbi.1013242.ref029","doi-asserted-by":"crossref","first-page":"267","DOI":"10.1111\/j.2517-6161.1996.tb02080.x","article-title":"Regression shrinkage and selection via the lasso","volume":"58","author":"R Tibshirani","year":"1996","journal-title":"J Roy Statist Soc Ser B (Methodol)."},{"issue":"3","key":"pcbi.1013242.ref030","article-title":"Using stacking to average Bayesian predictive distributions (with discussion)","volume":"13","author":"Y Yao","year":"2018","journal-title":"Bayesian Anal."},{"issue":"12","key":"pcbi.1013242.ref031","doi-asserted-by":"crossref","first-page":"1053","DOI":"10.1038\/s41592-018-0229-2","article-title":"Deep generative modeling for single-cell transcriptomics","volume":"15","author":"R Lopez","year":"2018","journal-title":"Nat Methods."},{"issue":"1","key":"pcbi.1013242.ref032","article-title":"Probabilistic harmonization and annotation of single-cell transcriptomics data with deep generative models","volume":"17","author":"C Xu","year":"2021","journal-title":"Mol Syst Biol."},{"key":"pcbi.1013242.ref033","doi-asserted-by":"crossref","unstructured":"Jiang Z, Zheng Y, Tan H, Tang B, Zhou H. Variational deep embedding: an unsupervised and generative approach to clustering. In: IJCAI2017. 2017. p. 1965\u201372.","DOI":"10.24963\/ijcai.2017\/273"},{"issue":"6","key":"pcbi.1013242.ref034","doi-asserted-by":"crossref","DOI":"10.1371\/journal.pcbi.1009086","article-title":"Mixture-of-experts variational autoencoder for clustering and generating from similarity-based representations on single cell data","volume":"17","author":"A Kopf","year":"2021","journal-title":"PLoS Comput Biol."},{"key":"pcbi.1013242.ref035","article-title":"Pyro: deep universal probabilistic programming","author":"E Bingham","year":"2018","journal-title":"J Mach Learn Res."},{"issue":"4","key":"pcbi.1013242.ref036","doi-asserted-by":"crossref","DOI":"10.1016\/j.cell.2019.01.006","article-title":"Optimal-transport analysis of single-cell gene expression identifies developmental trajectories in reprogramming","volume":"176","author":"G Schiebinger","year":"2019","journal-title":"Cell."},{"issue":"2","key":"pcbi.1013242.ref037","doi-asserted-by":"crossref","first-page":"159","DOI":"10.1038\/s41592-021-01346-6","article-title":"CellRank for directed single-cell fate mapping","volume":"19","author":"M Lange","year":"2022","journal-title":"Nat Methods."},{"key":"pcbi.1013242.ref038","unstructured":"Goodfellow I, Bengio Y, Courville A. Deep learning. MIT Press; 2016."},{"issue":"55","key":"pcbi.1013242.ref039","article-title":"Tissue-resident CD4+ T helper cells assist the development of protective respiratory B and CD8+ T cell memory responses","volume":"6","author":"YM Son","year":"2021","journal-title":"Sci Immunol."},{"issue":"3","key":"pcbi.1013242.ref040","doi-asserted-by":"crossref","first-page":"309","DOI":"10.1038\/s41590-019-0584-x","article-title":"Environmental cues regulate epigenetic reprogramming of airway-resident memory CD8+ T cells","volume":"21","author":"SL Hayward","year":"2020","journal-title":"Nat Immunol."},{"issue":"1","key":"pcbi.1013242.ref041","doi-asserted-by":"crossref","DOI":"10.1016\/j.immuni.2024.11.007","article-title":"Deep profiling deconstructs features associated with memory CD8+ T cell tissue residence","volume":"58","author":"MC Scott","year":"2025","journal-title":"Immunity."},{"key":"pcbi.1013242.ref042","unstructured":"Yao Y, Vehtari A, Simpson D, Gelman A. Yes, but did it work?: evaluating variational inference. In: Proceedings of the 35th International Conference on Machine Learning. 2018. p. 5581\u201390. https:\/\/proceedings.mlr.press\/v80\/yao18a.html"},{"issue":"8","key":"pcbi.1013242.ref043","doi-asserted-by":"crossref","DOI":"10.1371\/journal.pcbi.1011288","article-title":"The specious art of single-cell genomics","volume":"19","author":"T Chari","year":"2023","journal-title":"PLoS Comput Biol."},{"issue":"4","key":"pcbi.1013242.ref044","doi-asserted-by":"crossref","first-page":"585","DOI":"10.1006\/jtbi.2003.3208","article-title":"Models of CD8+ responses: 1. What is the antigen-independent proliferation program","volume":"221","author":"R Antia","year":"2003","journal-title":"J Theor Biol."},{"issue":"5","key":"pcbi.1013242.ref045","doi-asserted-by":"crossref","first-page":"791","DOI":"10.1038\/s41590-022-01171-9","article-title":"Replicative history marks transcriptional and functional disparity in the CD8+ T cell memory pool","volume":"23","author":"K Bresser","year":"2022","journal-title":"Nat Immunol."},{"key":"pcbi.1013242.ref046","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1186\/s12859-015-0862-z","article-title":"BayesFlow: latent modeling of flow cytometry cell populations","volume":"17","author":"K Johnsson","year":"2016","journal-title":"BMC Bioinformatics."},{"issue":"1","key":"pcbi.1013242.ref047","doi-asserted-by":"crossref","first-page":"390","DOI":"10.1038\/s41467-018-07931-2","article-title":"Single-cell RNA-seq denoising using a deep count autoencoder","volume":"10","author":"G Eraslan","year":"2019","journal-title":"Nat Commun."},{"key":"pcbi.1013242.ref048","doi-asserted-by":"crossref","unstructured":"Boyeau P, Hong J, Gayoso A, Jordan MI, Azizi E, Yosef N. Deep generative modeling for quantifying sample-level heterogeneity in single-cell omics; 2022. https:\/\/www.biorxiv.org\/content\/10.1101\/2022.10.04.510898v1","DOI":"10.1101\/2022.10.04.510898"},{"issue":"22","key":"pcbi.1013242.ref049","doi-asserted-by":"crossref","DOI":"10.1073\/pnas.2100293118","article-title":"Detection of differentially abundant cell subpopulations in scRNA-seq data","volume":"118","author":"J Zhao","year":"2021","journal-title":"Proc Natl Acad Sci U S A."},{"key":"pcbi.1013242.ref050","doi-asserted-by":"crossref","unstructured":"Chandler J, Bullock ME, Swain AC, Williams C, van Dorp CH, Seddon B, et al. Tissue resident memory CD4+ T cells are sustained by site-specific levels of self-renewal and replacement from precursors. eLife Sciences Publications, Ltd.; 2025. https:\/\/doi.org\/10.7554\/elife.104278.1","DOI":"10.7554\/eLife.104278.1"},{"issue":"8","key":"pcbi.1013242.ref051","doi-asserted-by":"crossref","DOI":"10.1371\/journal.pbio.3002380","article-title":"The dynamics and longevity of circulating CD4+ memory T cells depend on cell age and not the chronological age of the host","volume":"22","author":"ME Bullock","year":"2024","journal-title":"PLoS Biol."},{"issue":"8052","key":"pcbi.1013242.ref052","doi-asserted-by":"crossref","first-page":"1065","DOI":"10.1038\/s41586-024-08453-2","article-title":"Mapping cells through time and space with moscot","volume":"638","author":"D Klein","year":"2025","journal-title":"Nature."},{"issue":"1","key":"pcbi.1013242.ref053","doi-asserted-by":"crossref","first-page":"184","DOI":"10.1016\/j.cell.2015.05.047","article-title":"Data-driven phenotypic dissection of AML reveals progenitor-like cells that correlate with prognosis","volume":"162","author":"JH Levine","year":"2015","journal-title":"Cell."},{"issue":"10","key":"pcbi.1013242.ref054","doi-asserted-by":"crossref","DOI":"10.1088\/1742-5468\/2008\/10\/P10008","article-title":"Fast unfolding of communities in large networks","volume":"2008","author":"VD Blondel","year":"2008","journal-title":"J Stat Mech."},{"issue":"1","key":"pcbi.1013242.ref055","doi-asserted-by":"crossref","first-page":"15","DOI":"10.1186\/s13059-017-1382-0","article-title":"SCANPY: large-scale single-cell gene expression data analysis","volume":"19","author":"FA Wolf","year":"2018","journal-title":"Genome Biol."},{"key":"pcbi.1013242.ref056","unstructured":"Lienen M, G\u00fcnnemann S. Torchode: a parallel ODE solver for PyTorch. In: The symbiosis of deep learning and differential equations II, 2022. https:\/\/openreview.net\/forum?id=uiKVKTiUYB0"},{"issue":"33","key":"pcbi.1013242.ref057","doi-asserted-by":"crossref","first-page":"1143","DOI":"10.21105\/joss.01143","article-title":"ArviZ a unified library for exploratory analysis of Bayesian models in Python","volume":"4","author":"R Kumar","year":"2019","journal-title":"JOSS."},{"issue":"1","key":"pcbi.1013242.ref058","doi-asserted-by":"crossref","first-page":"194","DOI":"10.1137\/22M1469067","article-title":"Differential elimination for dynamical models via projections with applications to structural identifiability","volume":"7","author":"R Dong","year":"2023","journal-title":"SIAM J Appl Algebra Geometry."},{"issue":"6526","key":"pcbi.1013242.ref059","doi-asserted-by":"crossref","DOI":"10.1126\/science.aah6266","article-title":"Phylodynamics for cell biologists","volume":"371","author":"T Stadler","year":"2021","journal-title":"Science."},{"key":"pcbi.1013242.ref060","unstructured":"Kingma DP, Ba J. Adam: a method for stochastic optimization. arXiv preprint 2017. http:\/\/arxiv.org\/abs\/1412.6980"}],"updated-by":[{"DOI":"10.1371\/journal.pcbi.1013242","type":"new_version","label":"New version","source":"publisher","updated":{"date-parts":[[2025,8,18]],"date-time":"2025-08-18T00:00:00Z","timestamp":1755475200000}}],"container-title":["PLOS Computational Biology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dx.plos.org\/10.1371\/journal.pcbi.1013242","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,8,18]],"date-time":"2025-08-18T18:11:46Z","timestamp":1755540706000},"score":1,"resource":{"primary":{"URL":"https:\/\/dx.plos.org\/10.1371\/journal.pcbi.1013242"}},"subtitle":[],"editor":[{"given":"Rustom","family":"Antia","sequence":"first","affiliation":[],"role":[{"role":"editor","vocabulary":"crossref"}]}],"short-title":[],"issued":{"date-parts":[[2025,7,24]]},"references-count":60,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2025,7,24]]}},"URL":"https:\/\/doi.org\/10.1371\/journal.pcbi.1013242","relation":{"has-preprint":[{"id-type":"doi","id":"10.1101\/2024.07.08.602409","asserted-by":"object"}]},"ISSN":["1553-7358"],"issn-type":[{"value":"1553-7358","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,7,24]]}}}