{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,21]],"date-time":"2026-03-21T12:24:40Z","timestamp":1774095880853,"version":"3.50.1"},"reference-count":25,"publisher":"Oxford University Press (OUP)","issue":"4","license":[{"start":{"date-parts":[[2025,3,22]],"date-time":"2025-03-22T00:00:00Z","timestamp":1742601600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001665","name":"French National Research Agency","doi-asserted-by":"publisher","award":["ANR-16-CONV-0001"],"award-info":[{"award-number":["ANR-16-CONV-0001"]}],"id":[{"id":"10.13039\/501100001665","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2025,3,29]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:sec>\n                  <jats:title>Motivation<\/jats:title>\n                  <jats:p>In systems biology, modeling strategies aim to decode how molecular components interact to generate dynamical behavior. Boolean modeling is more and more used, but the description of the dynamics generated by discrete variables with only two values may be too limited to capture certain dynamical properties. Multivalued logical models can overcome this limitation by allowing more than two levels for each component. However, multivaluing a Boolean model is challenging.<\/jats:p>\n               <\/jats:sec>\n               <jats:sec>\n                  <jats:title>Results<\/jats:title>\n                  <jats:p>We present MRBM, a method for efficiently identifying the components of a Boolean model to be multivalued in order to capture specific fixed-point reachabilities in the asynchronous dynamics. To this goal, we defined a new updating scheme locating reachability properties in the most permissive dynamics. MRBM is supported by mathematical demonstrations and illustrated on a toy model and on two models of stem cell differentiation.<\/jats:p>\n               <\/jats:sec>\n               <jats:sec>\n                  <jats:title>Availability and implementation<\/jats:title>\n                  <jats:p>The MRBM method and the BMs used in this article are available on GitHub at: https:\/\/github.com\/NdnBnBn\/MRBM, and archived in Zenodo (doi: 10.5281\/ZENODO.14979798).<\/jats:p>\n               <\/jats:sec>","DOI":"10.1093\/bioinformatics\/btaf123","type":"journal-article","created":{"date-parts":[[2025,3,23]],"date-time":"2025-03-23T12:06:25Z","timestamp":1742731585000},"source":"Crossref","is-referenced-by-count":3,"title":["Refining Boolean models with the partial most permissive scheme"],"prefix":"10.1093","volume":"41","author":[{"given":"Nadine","family":"Ben Boina","sequence":"first","affiliation":[{"name":"Aix Marseille Univ, CNRS, I2M (UMR 7373), Turing Center for Living systems , Marseille,","place":["France"]},{"name":"Aix Marseille Univ, INSERM, MMG , Marseille,","place":["France"]}]},{"given":"Brigitte","family":"Moss\u00e9","sequence":"additional","affiliation":[{"name":"Aix Marseille Univ, CNRS, I2M (UMR 7373), Turing Center for Living systems , Marseille,","place":["France"]}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0885-7933","authenticated-orcid":false,"given":"Ana\u00efs","family":"Baudot","sequence":"additional","affiliation":[{"name":"Aix Marseille Univ, INSERM, MMG , Marseille,","place":["France"]},{"name":"CNRS , Marseille,","place":["France"]},{"name":"Barcelona Supercomputing Centre , Barcelona,","place":["Spain"]}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8560-8178","authenticated-orcid":false,"given":"Elisabeth","family":"Remy","sequence":"additional","affiliation":[{"name":"Aix Marseille Univ, CNRS, I2M (UMR 7373), Turing Center for Living systems , Marseille,","place":["France"]}]}],"member":"286","published-online":{"date-parts":[[2025,3,22]]},"reference":[{"key":"2025042501213119500_btaf123-B1","doi-asserted-by":"crossref","first-page":"137","DOI":"10.3109\/10409238.2011.556597","article-title":"Mathematical modeling of gene expression: a guide for the perplexed biologist","volume":"46","author":"Ay","year":"2011","journal-title":"Crit Rev Biochem Mol Biol"},{"key":"2025042501213119500_btaf123-B2","volume-title":"Principles of Model Checking","author":"Baier","year":"2008"},{"key":"2025042501213119500_btaf123-B3","doi-asserted-by":"crossref","first-page":"45","DOI":"10.1016\/j.tim.2006.11.003","article-title":"The nature of systems biology","volume":"15","author":"Bruggeman","year":"2007","journal-title":"Trends Microbiol"},{"key":"2025042501213119500_btaf123-B4","doi-asserted-by":"crossref","first-page":"e1461","DOI":"10.1002\/wsbm.1461","article-title":"Hybrid modeling frameworks of tumor development and treatment","volume":"12","author":"Chamseddine","year":"2020","journal-title":"Wiley Interdiscip Rev Syst Biol Med"},{"key":"2025042501213119500_btaf123-B5","doi-asserted-by":"crossref","first-page":"1861","DOI":"10.1101\/gad.1945410","article-title":"Classic and contemporary approaches to modeling biochemical reactions","volume":"24","author":"Chen","year":"2010","journal-title":"Genes Dev"},{"key":"2025042501213119500_btaf123-B6","doi-asserted-by":"crossref","first-page":"359","DOI":"10.1007\/3-540-45657-0_29","volume-title":"Computer Aided Verification, Lecture Notes in Computer Science","author":"Cimatti","year":"2002"},{"key":"2025042501213119500_btaf123-B7","doi-asserted-by":"crossref","first-page":"e1004426","DOI":"10.1371\/journal.pcbi.1004426","article-title":"Discovery of drug synergies in gastric cancer cells predicted by logical modeling","volume":"11","author":"Flobak","year":"2015","journal-title":"PLoS Comput Biol"},{"key":"2025042501213119500_btaf123-B8","doi-asserted-by":"crossref","first-page":"3525","DOI":"10.1038\/s41598-020-60251-8","article-title":"A system-level mechanistic explanation for asymmetric stem cell fates: Arabidopsis thaliana root niche as a study system","volume":"10","author":"Garc\u0131a-G\u00f3mez","year":"2020","journal-title":"Sci Rep"},{"key":"2025042501213119500_btaf123-B9","doi-asserted-by":"crossref","first-page":"1917","DOI":"10.1093\/bioinformatics\/btn336","article-title":"Synchronous versus asynchronous modeling of gene regulatory networks","volume":"24","author":"Garg","year":"2008","journal-title":"Bioinformatics"},{"key":"2025042501213119500_btaf123-B10","volume-title":"Answer Set Solving in Practice. 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