{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,11]],"date-time":"2026-07-11T21:42:23Z","timestamp":1783806143213,"version":"3.55.0"},"update-to":[{"DOI":"10.1371\/journal.pcbi.1009466","type":"new_version","label":"New version","source":"publisher","updated":{"date-parts":[[2021,12,21]],"date-time":"2021-12-21T00:00:00Z","timestamp":1640044800000}}],"reference-count":45,"publisher":"Public Library of Science (PLoS)","issue":"12","license":[{"start":{"date-parts":[[2021,12,3]],"date-time":"2021-12-03T00:00:00Z","timestamp":1638489600000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100005247","name":"University of British Columbia","doi-asserted-by":"crossref","id":[{"id":"10.13039\/501100005247","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/100000861","name":"Burroughs Wellcome Fund","doi-asserted-by":"crossref","id":[{"id":"10.13039\/100000861","id-type":"DOI","asserted-by":"crossref"}]},{"name":"New Frontiers in Research Fund"},{"DOI":"10.13039\/501100000038","name":"Natural Sciences and Engineering Research Council of Canada","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100000038","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                    Understanding how cells change their identity and behaviour in living systems is an important question in many fields of biology. The problem of inferring cell trajectories from single-cell measurements has been a major topic in the single-cell analysis community, with different methods developed for equilibrium and non-equilibrium systems (e.g. haematopoeisis vs. embryonic development). We show that optimal transport analysis, a technique originally designed for analysing time-courses, may also be applied to infer cellular trajectories from a single snapshot of a population in equilibrium. Therefore, optimal transport provides a unified approach to inferring trajectories that is applicable to both stationary and non-stationary systems. Our method, StationaryOT, is mathematically motivated in a natural way from the hypothesis of a Waddington\u2019s epigenetic landscape. We implement StationaryOT as a software package and demonstrate its efficacy in applications to simulated data as well as single-cell data from\n                    <jats:italic>Arabidopsis thaliana<\/jats:italic>\n                    root development.\n                  <\/jats:p>","DOI":"10.1371\/journal.pcbi.1009466","type":"journal-article","created":{"date-parts":[[2021,12,3]],"date-time":"2021-12-03T13:31:07Z","timestamp":1638538267000},"page":"e1009466","update-policy":"https:\/\/doi.org\/10.1371\/journal.pcbi.corrections_policy","source":"Crossref","is-referenced-by-count":39,"title":["Optimal transport analysis reveals trajectories in steady-state systems"],"prefix":"10.1371","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6775-0744","authenticated-orcid":true,"given":"Stephen","family":"Zhang","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2387-8783","authenticated-orcid":true,"given":"Anton","family":"Afanassiev","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Laura","family":"Greenstreet","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Tetsuya","family":"Matsumoto","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8290-7997","authenticated-orcid":true,"given":"Geoffrey","family":"Schiebinger","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"340","published-online":{"date-parts":[[2021,12,3]]},"reference":[{"key":"pcbi.1009466.ref001","author":"C. 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