{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T10:03:04Z","timestamp":1777629784026,"version":"3.51.4"},"update-to":[{"DOI":"10.1371\/journal.pcbi.1012393","type":"new_version","label":"New version","source":"publisher","updated":{"date-parts":[[2024,9,16]],"date-time":"2024-09-16T00:00:00Z","timestamp":1726444800000}}],"reference-count":52,"publisher":"Public Library of Science (PLoS)","issue":"9","license":[{"start":{"date-parts":[[2024,9,4]],"date-time":"2024-09-04T00:00:00Z","timestamp":1725408000000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100019180","name":"HORIZON EUROPE European Research Council","doi-asserted-by":"publisher","award":["805046"],"award-info":[{"award-number":["805046"]}],"id":[{"id":"10.13039\/100019180","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100016190","name":"Trond Mohn stiftelse","doi-asserted-by":"publisher","award":["TMS2021TMT09"],"award-info":[{"award-number":["TMS2021TMT09"]}],"id":[{"id":"10.13039\/100016190","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004837","name":"Ministerio de Ciencia e Innovaci\u00f3n","doi-asserted-by":"publisher","award":["PID2019-111256RB-I00"],"award-info":[{"award-number":["PID2019-111256RB-I00"]}],"id":[{"id":"10.13039\/501100004837","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["www.ploscompbiol.org"],"crossmark-restriction":false},"short-container-title":["PLoS Comput Biol"],"abstract":"<jats:p>Accumulation processes, where many potentially coupled features are acquired over time, occur throughout the sciences from evolutionary biology to disease progression, and particularly in the study of cancer progression. Existing methods for learning the dynamics of such systems typically assume limited (often pairwise) relationships between feature subsets, cross-sectional or untimed observations, small feature sets, or discrete orderings of events. Here we introduce HyperTraPS-CT (Hypercubic Transition Path Sampling in Continuous Time) to compute posterior distributions on continuous-time dynamics of many, arbitrarily coupled, traits in unrestricted state spaces, accounting for uncertainty in observations and their timings. We demonstrate the capacity of HyperTraPS-CT to deal with cross-sectional, longitudinal, and phylogenetic data, which may have no, uncertain, or precisely specified sampling times. HyperTraPS-CT allows positive and negative interactions between arbitrary subsets of features (not limited to pairwise interactions), supporting Bayesian and maximum-likelihood inference approaches to identify these interactions, consequent pathways, and predictions of future and unobserved features. We also introduce a range of visualisations for the inferred outputs of these processes and demonstrate model selection and regularisation for feature interactions. We apply this approach to case studies on the accumulation of mutations in cancer progression and the acquisition of anti-microbial resistance genes in tuberculosis, demonstrating its flexibility and capacity to produce predictions aligned with applied priorities.<\/jats:p>","DOI":"10.1371\/journal.pcbi.1012393","type":"journal-article","created":{"date-parts":[[2024,9,4]],"date-time":"2024-09-04T13:49:04Z","timestamp":1725457744000},"page":"e1012393","update-policy":"https:\/\/doi.org\/10.1371\/journal.pcbi.corrections_policy","source":"Crossref","is-referenced-by-count":10,"title":["HyperTraPS-CT: Inference and prediction for accumulation pathways with flexible data and model structures"],"prefix":"10.1371","volume":"20","author":[{"ORCID":"https:\/\/orcid.org\/0009-0004-1610-9403","authenticated-orcid":true,"given":"Olav N. L.","family":"Aga","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2860-8272","authenticated-orcid":true,"given":"Morten","family":"Brun","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4392-8592","authenticated-orcid":true,"given":"Kazeem A.","family":"Dauda","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6637-9039","authenticated-orcid":true,"given":"Ramon","family":"Diaz-Uriarte","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4199-6708","authenticated-orcid":true,"given":"Konstantinos","family":"Giannakis","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8559-3519","authenticated-orcid":true,"given":"Iain G.","family":"Johnston","sequence":"additional","affiliation":[]}],"member":"340","published-online":{"date-parts":[[2024,9,4]]},"reference":[{"issue":"24","key":"pcbi.1012393.ref001","doi-asserted-by":"crossref","first-page":"5457","DOI":"10.1093\/bioinformatics\/btac710","article-title":"EvAM-Tools: tools for evolutionary accumulation and cancer progression models","volume":"38","author":"R Diaz-Uriarte","year":"2022","journal-title":"Bioinformatics"},{"key":"pcbi.1012393.ref002","unstructured":"Diaz-Uriarte R, Johnston IG. A picture guide to cancer progression and monotonic accumulation models: evolutionary assumptions, plausible interpretations, and alternative uses. arXiv preprint arXiv:231206824. 2024;."},{"key":"pcbi.1012393.ref003","doi-asserted-by":"crossref","first-page":"267","DOI":"10.1146\/annurev-ecolsys-110411-160331","article-title":"Evolutionary inferences from phylogenies: a review of methods","volume":"43","author":"B O\u2019Meara","year":"2012","journal-title":"Annual Review Of Ecology, Evolution, And Systematics"},{"issue":"2","key":"pcbi.1012393.ref004","doi-asserted-by":"crossref","first-page":"101","DOI":"10.1016\/j.cels.2016.01.013","article-title":"Evolutionary inference across eukaryotes identifies specific pressures favoring mitochondrial gene retention","volume":"2","author":"IG Johnston","year":"2016","journal-title":"Cell systems"},{"key":"pcbi.1012393.ref005","doi-asserted-by":"crossref","DOI":"10.7554\/eLife.00961","article-title":"Phenotypic landscape inference reveals multiple evolutionary paths to C4 photosynthesis","volume":"2","author":"B Williams","year":"2013","journal-title":"Elife"},{"key":"pcbi.1012393.ref006","first-page":"1","article-title":"Reconstructing Disease Histories in Huge Discrete State Spaces","author":"R Schill","year":"2024","journal-title":"KI-K\u00fcnstliche Intelligenz"},{"key":"pcbi.1012393.ref007","doi-asserted-by":"crossref","first-page":"e1","DOI":"10.1093\/sysbio\/syu081","article-title":"Cancer evolution: mathematical models and computational inference","volume":"64","author":"N Beerenwinkel","year":"2015","journal-title":"Systematic Biology"},{"key":"pcbi.1012393.ref008","article-title":"Towards precision healthcare: context and mathematical challenges","author":"C Colijn","year":"2017","journal-title":"Frontiers in Physiology"},{"issue":"1","key":"pcbi.1012393.ref009","doi-asserted-by":"crossref","first-page":"63","DOI":"10.1038\/s41746-019-0140-y","article-title":"Precision identification of high-risk phenotypes and progression pathways in severe malaria without requiring longitudinal data","volume":"2","author":"IG Johnston","year":"2019","journal-title":"NPJ digital medicine"},{"issue":"12","key":"pcbi.1012393.ref010","doi-asserted-by":"crossref","first-page":"e1009055","DOI":"10.1371\/journal.pcbi.1009055","article-title":"Conditional prediction of consecutive tumor evolution using cancer progression models: What genotype comes next?","volume":"17","author":"J Diaz-Colunga","year":"2021","journal-title":"PLoS computational biology"},{"issue":"8","key":"pcbi.1012393.ref011","doi-asserted-by":"crossref","first-page":"e1007246","DOI":"10.1371\/journal.pcbi.1007246","article-title":"Every which way? On predicting tumor evolution using cancer progression models","volume":"15","author":"R Diaz-Uriarte","year":"2019","journal-title":"PLoS computational biology"},{"issue":"1","key":"pcbi.1012393.ref012","doi-asserted-by":"crossref","first-page":"3676","DOI":"10.1038\/s41467-023-39400-w","article-title":"Joint inference of exclusivity patterns and recurrent trajectories from tumor mutation trees","volume":"14","author":"XG Luo","year":"2023","journal-title":"Nature Communications"},{"issue":"6","key":"pcbi.1012393.ref013","doi-asserted-by":"crossref","DOI":"10.1016\/j.isci.2020.101245","article-title":"Data-driven inference reveals distinct and conserved dynamic pathways of tool use emergence across animal taxa","volume":"23","author":"IG Johnston","year":"2020","journal-title":"Iscience"},{"key":"pcbi.1012393.ref014","volume-title":"Phylogenetic comparative methods in R","author":"LJ Revell","year":"2022"},{"key":"pcbi.1012393.ref015","doi-asserted-by":"crossref","first-page":"217","DOI":"10.1111\/j.2041-210X.2011.00169.x","article-title":"phytools: an R package for phylogenetic comparative biology (and other things)","volume":"3","author":"L Revell","year":"2012","journal-title":"Methods In Ecology And Evolution"},{"issue":"3","key":"pcbi.1012393.ref016","doi-asserted-by":"crossref","first-page":"468","DOI":"10.1111\/2041-210X.13534","article-title":"Generalized hidden Markov models for phylogenetic comparative datasets","volume":"12","author":"JD Boyko","year":"2021","journal-title":"Methods in Ecology and Evolution"},{"key":"pcbi.1012393.ref017","doi-asserted-by":"crossref","first-page":"853","DOI":"10.1089\/cmb.2006.13.853","article-title":"New probabilistic network models and algorithms for oncogenesis","volume":"13","author":"M Hjelm","year":"2006","journal-title":"Journal Of Computational Biology"},{"key":"pcbi.1012393.ref018","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.jocs.2018.10.009","article-title":"Efficient computational strategies to learn the structure of probabilistic graphical models of cumulative phenomena","volume":"30","author":"D Ramazzotti","year":"2019","journal-title":"Journal of computational science"},{"issue":"10","key":"pcbi.1012393.ref019","doi-asserted-by":"crossref","first-page":"e108358","DOI":"10.1371\/journal.pone.0108358","article-title":"Inferring tree causal models of cancer progression with probability raising","volume":"9","author":"LO Loohuis","year":"2014","journal-title":"PloS one"},{"issue":"18","key":"pcbi.1012393.ref020","doi-asserted-by":"crossref","first-page":"3016","DOI":"10.1093\/bioinformatics\/btv296","article-title":"CAPRI: efficient inference of cancer progression models from cross-sectional data","volume":"31","author":"D Ramazzotti","year":"2015","journal-title":"Bioinformatics"},{"issue":"1","key":"pcbi.1012393.ref021","first-page":"1","article-title":"OncoNEM: inferring tumor evolution from single-cell sequencing data","volume":"17","author":"EM Ross","year":"2016","journal-title":"Genome biology"},{"issue":"17","key":"pcbi.1012393.ref022","doi-asserted-by":"crossref","first-page":"i727","DOI":"10.1093\/bioinformatics\/btw459","article-title":"Large-scale inference of conjunctive Bayesian networks","volume":"32","author":"H Montazeri","year":"2016","journal-title":"Bioinformatics"},{"issue":"2","key":"pcbi.1012393.ref023","doi-asserted-by":"crossref","first-page":"219","DOI":"10.1016\/S0025-5564(02)00086-X","article-title":"Estimating an oncogenetic tree when false negatives and positives are present","volume":"176","author":"A Szabo","year":"2002","journal-title":"Mathematical biosciences"},{"issue":"1","key":"pcbi.1012393.ref024","doi-asserted-by":"crossref","first-page":"39","DOI":"10.1016\/j.cels.2019.10.009","article-title":"HyperTraPS: inferring probabilistic patterns of trait acquisition in evolutionary and disease progression pathways","volume":"10","author":"SF Greenbury","year":"2020","journal-title":"Cell systems"},{"key":"pcbi.1012393.ref025","first-page":"463102","article-title":"Forward flux sampling for rare event simulations","volume":"21","author":"R Allen","year":"2009","journal-title":"Journal Of Physics: Condensed Matter"},{"issue":"1","key":"pcbi.1012393.ref026","doi-asserted-by":"crossref","first-page":"btac803","DOI":"10.1093\/bioinformatics\/btac803","article-title":"HyperHMM: efficient inference of evolutionary and progressive dynamics on hypercubic transition graphs","volume":"39","author":"MT Moen","year":"2023","journal-title":"Bioinformatics"},{"issue":"2","key":"pcbi.1012393.ref027","doi-asserted-by":"crossref","first-page":"70","DOI":"10.1016\/j.cels.2016.02.007","article-title":"Why have organelles retained genomes?","volume":"2","author":"JF Allen","year":"2016","journal-title":"Cell systems"},{"key":"pcbi.1012393.ref028","doi-asserted-by":"crossref","first-page":"81030","DOI":"10.1109\/ACCESS.2024.3410327","article-title":"Comparing Structure and Dynamics of Transition Graphs by the Symmetric Difference Metric Over an Edge-Filtration","volume":"12","author":"B. Garc\u00eda Pascual","year":"2024","journal-title":"IEEE Access"},{"key":"pcbi.1012393.ref029","doi-asserted-by":"crossref","first-page":"e01403","DOI":"10.7554\/eLife.01403","article-title":"Shining fresh light on the evolution of photosynthesis","volume":"2","author":"A Samal","year":"2013","journal-title":"eLife"},{"issue":"1","key":"pcbi.1012393.ref030","doi-asserted-by":"crossref","first-page":"2823","DOI":"10.1038\/s41598-021-81709-3","article-title":"Understanding learner behaviour in online courses with Bayesian modelling and time series characterisation","volume":"11","author":"RL Peach","year":"2021","journal-title":"Scientific reports"},{"issue":"1","key":"pcbi.1012393.ref031","doi-asserted-by":"crossref","first-page":"53","DOI":"10.1093\/biostatistics\/kxj033","article-title":"A mutagenetic tree hidden Markov model for longitudinal clonal HIV sequence data","volume":"8","author":"N Beerenwinkel","year":"2007","journal-title":"Biostatistics"},{"issue":"9","key":"pcbi.1012393.ref032","doi-asserted-by":"crossref","first-page":"e1008363","DOI":"10.1371\/journal.pcbi.1008363","article-title":"Comparing mutational pathways to lopinavir resistance in HIV-1 subtypes B versus C","volume":"17","author":"S Posada-C\u00e9spedes","year":"2021","journal-title":"PLoS Computational Biology"},{"issue":"1","key":"pcbi.1012393.ref033","doi-asserted-by":"crossref","first-page":"241","DOI":"10.1093\/bioinformatics\/btz513","article-title":"Modelling cancer progression using mutual hazard networks","volume":"36","author":"R Schill","year":"2020","journal-title":"Bioinformatics"},{"issue":"2","key":"pcbi.1012393.ref034","doi-asserted-by":"crossref","first-page":"e1027","DOI":"10.1002\/cso2.1027","article-title":"Oncogenetic network estimation with disjunctive Bayesian networks","volume":"1","author":"PB Nicol","year":"2021","journal-title":"Computational and Systems Oncology"},{"issue":"3","key":"pcbi.1012393.ref035","doi-asserted-by":"crossref","first-page":"754","DOI":"10.1093\/bioinformatics\/btab717","article-title":"PMCE: efficient inference of expressive models of cancer evolution with high prognostic power","volume":"38","author":"F Angaroni","year":"2022","journal-title":"Bioinformatics"},{"issue":"4","key":"pcbi.1012393.ref036","doi-asserted-by":"crossref","first-page":"e00277","DOI":"10.1016\/j.heliyon.2017.e00277","article-title":"Progression inference for somatic mutations in cancer","volume":"3","author":"LE Peterson","year":"2017","journal-title":"Heliyon"},{"key":"pcbi.1012393.ref037","doi-asserted-by":"crossref","first-page":"22889","DOI":"10.1109\/ACCESS.2018.2827024","article-title":"Inference of cancer progression with probabilistic graphical model from cross-sectional mutation data","volume":"6","author":"W Zhang","year":"2018","journal-title":"IEEE Access"},{"issue":"4","key":"pcbi.1012393.ref038","doi-asserted-by":"crossref","first-page":"213","DOI":"10.1038\/nrg.2016.170","article-title":"The evolution of tumour phylogenetics: principles and practice","volume":"18","author":"R Schwartz","year":"2017","journal-title":"Nature Reviews Genetics"},{"key":"pcbi.1012393.ref039","first-page":"14580","article-title":"Scaling up continuous-time Markov chains helps resolve underspecification","volume":"34","author":"A Gotovos","year":"2021","journal-title":"Advances in Neural Information Processing Systems"},{"key":"pcbi.1012393.ref040","doi-asserted-by":"crossref","first-page":"311","DOI":"10.2307\/2406441","article-title":"A method for deducing branching sequences in phylogeny","author":"JH Camin","year":"1965","journal-title":"Evolution"},{"issue":"3720","key":"pcbi.1012393.ref041","doi-asserted-by":"crossref","first-page":"363","DOI":"10.1126\/science.152.3720.363","article-title":"Evolution of the structure of ferredoxin based on living relics of primitive amino acid sequences","volume":"152","author":"RV Eck","year":"1966","journal-title":"Science"},{"issue":"1","key":"pcbi.1012393.ref042","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1093\/sysbio\/18.1.1","article-title":"Quantitative phyletics and the evolution of anurans","volume":"18","author":"AG Kluge","year":"1969","journal-title":"Systematic Biology"},{"key":"pcbi.1012393.ref043","first-page":"911","volume-title":"Artificial Intelligence and Statistics","author":"I Murray","year":"2016"},{"issue":"1","key":"pcbi.1012393.ref044","doi-asserted-by":"crossref","first-page":"5327","DOI":"10.1038\/s41467-020-19119-8","article-title":"Clonal evolution of acute myeloid leukemia revealed by high-throughput single-cell genomics","volume":"11","author":"K Morita","year":"2020","journal-title":"Nature communications"},{"issue":"3","key":"pcbi.1012393.ref045","doi-asserted-by":"crossref","first-page":"279","DOI":"10.1038\/ng.2878","article-title":"Evolution and transmission of drug-resistant tuberculosis in a Russian population","volume":"46","author":"N Casali","year":"2014","journal-title":"Nature genetics"},{"issue":"6","key":"pcbi.1012393.ref046","doi-asserted-by":"crossref","first-page":"895","DOI":"10.1038\/s41588-018-0128-6","article-title":"Quantification of subclonal selection in cancer from bulk sequencing data","volume":"50","author":"MJ Williams","year":"2018","journal-title":"Nature genetics"},{"issue":"7","key":"pcbi.1012393.ref047","doi-asserted-by":"crossref","first-page":"404","DOI":"10.1038\/s41576-019-0114-6","article-title":"Resolving genetic heterogeneity in cancer","volume":"20","author":"S Turajlic","year":"2019","journal-title":"Nature Reviews Genetics"},{"key":"pcbi.1012393.ref048","doi-asserted-by":"crossref","unstructured":"Schill R, Klever M, L\u00f6sch A, Hu YL, Vocht S, Rupp K, et al. Overcoming Observation Bias for Cancer Progression Modeling. In: International Conference on Research in Computational Molecular Biology. Springer; 2024. p. 217\u2013234.","DOI":"10.1007\/978-1-0716-3989-4_14"},{"issue":"1342","key":"pcbi.1012393.ref049","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1098\/rspb.1994.0006","article-title":"Detecting correlated evolution on phylogenies: a general method for the comparative analysis of discrete characters","volume":"255","author":"M Pagel","year":"1994","journal-title":"Proceedings of the Royal Society of London Series B: Biological Sciences"},{"issue":"6","key":"pcbi.1012393.ref050","doi-asserted-by":"crossref","first-page":"913","DOI":"10.1080\/106351501753462876","article-title":"A likelihood approach to estimating phylogeny from discrete morphological character data","volume":"50","author":"PO Lewis","year":"2001","journal-title":"Systematic biology"},{"key":"pcbi.1012393.ref051","first-page":"4486","article-title":"Phylogenetic comparative methods: learning from trees","author":"L Harmon","year":"2019","journal-title":"EcoEvoRxiv preprint"},{"key":"pcbi.1012393.ref052","article-title":"A hypercubic Mk model framework for capturing reversibility in disease, cancer, and evolutionary accumulation modelling","author":"I Johnston","year":"2024","journal-title":"bioRxiv"}],"updated-by":[{"DOI":"10.1371\/journal.pcbi.1012393","type":"new_version","label":"New version","source":"publisher","updated":{"date-parts":[[2024,9,16]],"date-time":"2024-09-16T00:00:00Z","timestamp":1726444800000}}],"container-title":["PLOS Computational Biology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dx.plos.org\/10.1371\/journal.pcbi.1012393","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,9,16]],"date-time":"2024-09-16T14:06:37Z","timestamp":1726495597000},"score":1,"resource":{"primary":{"URL":"https:\/\/dx.plos.org\/10.1371\/journal.pcbi.1012393"}},"subtitle":[],"editor":[{"given":"Alison","family":"Marsden","sequence":"first","affiliation":[]}],"short-title":[],"issued":{"date-parts":[[2024,9,4]]},"references-count":52,"journal-issue":{"issue":"9","published-online":{"date-parts":[[2024,9,4]]}},"URL":"https:\/\/doi.org\/10.1371\/journal.pcbi.1012393","relation":{"has-preprint":[{"id-type":"doi","id":"10.1101\/2024.03.07.583841","asserted-by":"object"}]},"ISSN":["1553-7358"],"issn-type":[{"value":"1553-7358","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,9,4]]}}}