{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,7]],"date-time":"2025-06-07T20:27:59Z","timestamp":1749328079673,"version":"3.37.3"},"reference-count":26,"publisher":"Oxford University Press (OUP)","issue":"6","license":[{"start":{"date-parts":[[2019,11,14]],"date-time":"2019-11-14T00:00:00Z","timestamp":1573689600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"funder":[{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]},{"name":"DFG, German Research Foundation","award":["390939984"],"award-info":[{"award-number":["390939984"]}]},{"DOI":"10.13039\/501100001659","name":"German Research Foundation","doi-asserted-by":"crossref","award":["INST 35\/1134-1 FUGG"],"award-info":[{"award-number":["INST 35\/1134-1 FUGG"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2020,3,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:sec>\n                  <jats:title>Motivation<\/jats:title>\n                  <jats:p>Apparent time delays in partly observed, biochemical reaction networks can be modelled by lumping a more complex reaction into a series of linear reactions often referred to as the linear chain trick. Since most delays in biochemical reactions are no true, hard delays but a consequence of complex unobserved processes, this approach often more closely represents the true system compared with delay differential equations. In this paper, we address the question of how to select the optimal number of additional equations, i.e. the chain length (CL).<\/jats:p>\n               <\/jats:sec>\n               <jats:sec>\n                  <jats:title>Results<\/jats:title>\n                  <jats:p>We derive a criterion based on parameter identifiability to infer CLs and compare this method to choosing the model with a CL that leads to the best fit in a maximum likelihood sense, which corresponds to optimizing the Bayesian information criterion. We evaluate performance with simulated data as well as with measured biological data for a model of JAK2\/STAT5 signalling and access the influence of different model structures and data characteristics. Our analysis revealed that the proposed method features a superior performance when applied to biological models and data compared with choosing the model that maximizes the likelihood.<\/jats:p>\n               <\/jats:sec>\n               <jats:sec>\n                  <jats:title>Availability and implementation<\/jats:title>\n                  <jats:p>Models and data used for simulations are available at https:\/\/github.com\/Data2Dynamics\/d2d and http:\/\/jeti.uni-freiburg.de\/PNAS_Swameye_Data.<\/jats:p>\n               <\/jats:sec>\n               <jats:sec>\n                  <jats:title>Supplementary information<\/jats:title>\n                  <jats:p>Supplementary data are available at Bioinformatics online.<\/jats:p>\n               <\/jats:sec>","DOI":"10.1093\/bioinformatics\/btz838","type":"journal-article","created":{"date-parts":[[2019,11,13]],"date-time":"2019-11-13T20:11:13Z","timestamp":1573675873000},"page":"1848-1854","source":"Crossref","is-referenced-by-count":1,"title":["Estimating chain length for time delays in dynamical systems using profile likelihood"],"prefix":"10.1093","volume":"36","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3053-5124","authenticated-orcid":false,"given":"Adrian L","family":"Hauber","sequence":"first","affiliation":[{"name":"Institute of Physics, University of Freiburg , Freiburg 79104, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Raphael","family":"Engesser","sequence":"additional","affiliation":[{"name":"Institute of Physics, University of Freiburg , Freiburg 79104, Germany"},{"name":"Signalling Research Centres BIOSS and CIBSS, University of Freiburg , Freiburg 79104, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Joep","family":"Vanlier","sequence":"additional","affiliation":[{"name":"Institute of Physics, University of Freiburg , Freiburg 79104, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jens","family":"Timmer","sequence":"additional","affiliation":[{"name":"Institute of Physics, University of Freiburg , Freiburg 79104, Germany"},{"name":"Signalling Research Centres BIOSS and CIBSS, University of Freiburg , Freiburg 79104, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2019,11,14]]},"reference":[{"key":"2023060911585998900_btz838-B1","doi-asserted-by":"crossref","first-page":"516","DOI":"10.1038\/msb.2011.50","article-title":"Division of labor by dual feedback regulators controls JAK2\/STAT5 signaling over broad ligand range","volume":"7","author":"Bachmann","year":"2011","journal-title":"Mol. 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