{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,31]],"date-time":"2025-12-31T10:48:13Z","timestamp":1767178093325,"version":"build-2238731810"},"update-to":[{"DOI":"10.1371\/journal.pcbi.1006051","type":"new_version","label":"New version","source":"publisher","updated":{"date-parts":[[2018,3,22]],"date-time":"2018-03-22T00:00:00Z","timestamp":1521676800000}}],"reference-count":61,"publisher":"Public Library of Science (PLoS)","issue":"3","license":[{"start":{"date-parts":[[2018,3,12]],"date-time":"2018-03-12T00:00:00Z","timestamp":1520812800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11622101"],"award-info":[{"award-number":["11622101"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"National Natural Science Foundation of China (CN)","award":["21373021"],"award-info":[{"award-number":["21373021"]}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["1DP1OD000277"],"award-info":[{"award-number":["1DP1OD000277"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["www.ploscompbiol.org"],"crossmark-restriction":false},"short-container-title":["PLoS Comput Biol"],"DOI":"10.1371\/journal.pcbi.1006051","type":"journal-article","created":{"date-parts":[[2018,3,12]],"date-time":"2018-03-12T13:25:44Z","timestamp":1520861144000},"page":"e1006051","update-policy":"https:\/\/doi.org\/10.1371\/journal.pcbi.corrections_policy","source":"Crossref","is-referenced-by-count":12,"title":["Relatively slow stochastic gene-state switching in the presence of positive feedback significantly broadens the region of bimodality through stabilizing the uninduced phenotypic state"],"prefix":"10.1371","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0404-5268","authenticated-orcid":true,"given":"Hao","family":"Ge","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Pingping","family":"Wu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5466-8650","authenticated-orcid":true,"given":"Hong","family":"Qian","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiaoliang Sunney","family":"Xie","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"340","published-online":{"date-parts":[[2018,3,12]]},"reference":[{"key":"ref1","doi-asserted-by":"crossref","first-page":"128701","DOI":"10.1103\/PhysRevLett.94.128701","article-title":"Cell fates as high-dimensional attractor states of a complex gene regulatory network","volume":"94","author":"S Huang","year":"2005","journal-title":"Phys. Rev. Lett"},{"key":"ref2","doi-asserted-by":"crossref","first-page":"2672","DOI":"10.1073\/pnas.1519210113","article-title":"Dynamics inside the cancer cell attractor reveal cell heterogeneity, limits of stability and escape","volume":"113","author":"Q Li","year":"2016","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref3","doi-asserted-by":"crossref","first-page":"442","DOI":"10.1126\/science.1161427","article-title":"A stochastic single-molecule event triggers phenotype switching of a Bacteria cell","volume":"322","author":"PJ Choi","year":"2008","journal-title":"Science"},{"key":"ref4","doi-asserted-by":"crossref","first-page":"737","DOI":"10.1038\/nature02298","article-title":"Multistability in the lactose utilization network of Escherichia coli","volume":"427","author":"EM Ozbudak","year":"2004","journal-title":"Nature"},{"key":"ref5","doi-asserted-by":"crossref","first-page":"544","DOI":"10.1038\/nature06965","article-title":"Transcriptome-wide noise controls lineage choice in mammalian progenitor cells","volume":"453","author":"HH Chang","year":"2006","journal-title":"Nature"},{"key":"ref6","doi-asserted-by":"crossref","first-page":"633","DOI":"10.1016\/j.cell.2011.07.026","article-title":"Stochastic state transitions give rise to phenotypic equilibrium in populations of cancer cells","volume":"146","author":"PB Gupta","year":"2011","journal-title":"Cell"},{"key":"ref7","doi-asserted-by":"crossref","first-page":"471","DOI":"10.1038\/ng.110","article-title":"Stochastic switching as a survival strategy in fluctuating environments","volume":"40","author":"M. Acar","year":"2008","journal-title":"Nat. Genetics"},{"key":"ref8","article-title":"The Plausibility of Life: Resolving Darwin\u2019s Dilemma","author":"MW Kirschner","year":"2005"},{"key":"ref9","doi-asserted-by":"crossref","first-page":"2075","DOI":"10.1126\/science.1114383","article-title":"Phenotypic diversity, population growth, and information in fluctuating environments","volume":"309","author":"E Kussell","year":"2005","journal-title":"Science"},{"key":"ref10","doi-asserted-by":"crossref","first-page":"308","DOI":"10.1038\/nature10315","article-title":"Central dogma at the single-molecule level in living cells","volume":"475","author":"GW Li","year":"2011","journal-title":"Nature"},{"key":"ref11","doi-asserted-by":"crossref","first-page":"533","DOI":"10.1126\/science.1188308","article-title":"Quantifying E. coli proteome and transcriptome with single-molecule sensitivity in single cells","volume":"329","author":"Y Taniguchi","year":"2010","journal-title":"Science"},{"key":"ref12","doi-asserted-by":"crossref","first-page":"587","DOI":"10.1016\/0022-5193(78)90326-0","article-title":"A model for the statistical fluctuations of protein numbers in a microbial population","volume":"71","author":"O Berg","year":"1978","journal-title":"J. Theor. Biol"},{"key":"ref13","article-title":"What makes the lac-pathway switch: identifying the fluctuations that trigger phenotype switching in gene regulatory systems","author":"P Bhogale","year":"2014","journal-title":"Nucl. Acids Res"},{"key":"ref14","doi-asserted-by":"crossref","first-page":"358","DOI":"10.1038\/nature04599","article-title":"Stochastic protein expression in individual cells at the single molecule level","volume":"440","author":"L Cai","year":"2006","journal-title":"Nature"},{"key":"ref15","doi-asserted-by":"crossref","first-page":"167","DOI":"10.1038\/nature09326","article-title":"Functional roles for noise in genetic circuits","volume":"467","author":"A Eldar","year":"2010","journal-title":"Nature"},{"issue":"23","key":"ref16","doi-asserted-by":"crossref","first-page":"5447","DOI":"10.1103\/PhysRevLett.84.5447","article-title":"Random signal fluctuations can reduce random fluctuations in regulated components of chemical regulatory networks","volume":"84","author":"J Paulsson","year":"2000","journal-title":"Phys. Rev. Lett"},{"key":"ref17","doi-asserted-by":"crossref","first-page":"247","DOI":"10.1016\/0022-5193(79)90250-9","article-title":"Note on the kinetics and stochastics of induced protein synthesis as influenced by various models for messenger RNA degradation","volume":"79","author":"D Rigney","year":"1979","journal-title":"J. Theoret. Biol"},{"key":"ref18","doi-asserted-by":"crossref","first-page":"1218","DOI":"10.1126\/science.aad0635","article-title":"Measurements of gene regulation in individual cells reveals rapid switching between propomter states","volume":"351","author":"LA Sep\u00falveda","year":"2016","journal-title":"Science"},{"key":"ref19","doi-asserted-by":"crossref","first-page":"472","DOI":"10.1126\/science.1198817","article-title":"Mammalian genes are transcribed with widely different bursting kinetics","volume":"332","author":"D Suter","year":"2011","journal-title":"Science"},{"key":"ref20","doi-asserted-by":"crossref","first-page":"1600","DOI":"10.1126\/science.1119623","article-title":"Probing gene expression in live cells, one protein molecule at a time","volume":"311","author":"J Yu","year":"2006","journal-title":"Science"},{"key":"ref21","doi-asserted-by":"crossref","first-page":"120","DOI":"10.1063\/1.1750549","article-title":"Statistical fluctuations in autocatalytic reactions","volume":"8","author":"M Delbr\u00fcck","year":"1940","journal-title":"J. Chem. Phys"},{"key":"ref22","doi-asserted-by":"crossref","first-page":"078101","DOI":"10.1103\/PhysRevLett.114.078101","article-title":"Stochastic phenotype transition of a single cell in an intermediate region of gene-state switching","volume":"114","author":"H Ge","year":"2015","journal-title":"Phys. Rev. Lett"},{"key":"ref23","doi-asserted-by":"crossref","first-page":"259","DOI":"10.1007\/s10955-009-9850-x","article-title":"Non-equilibrium thermodynamics of piecewise deterministic Markov Processes","volume":"137","author":"A Faggionato","year":"2009","journal-title":"J. Stat. Phys"},{"key":"ref24","doi-asserted-by":"crossref","first-page":"1333","DOI":"10.1016\/j.jmb.2007.04.021","article-title":"Distinctive topologies of partner-switching signaling networks correlate with their physiological roles","volume":"369","author":"OA Igoshin","year":"2007","journal-title":"J. Mol. Biol"},{"key":"ref25","doi-asserted-by":"crossref","first-page":"976","DOI":"10.1016\/j.celrep.2012.08.038","article-title":"Consecutive positive feedback loops create a bistable switch that controls preadipocyte-to-adipocyte conversion","volume":"2","author":"BO Park","year":"2012","journal-title":"Cell Rep"},{"key":"ref26","doi-asserted-by":"crossref","first-page":"1384","DOI":"10.1126\/science.1252079","article-title":"Controlling low rates of cell differentiation through noise and ultrahigh feedback","volume":"344","author":"R Ahrends","year":"2014","journal-title":"Science"},{"key":"ref27","doi-asserted-by":"crossref","first-page":"18926","DOI":"10.1073\/pnas.0509547102","article-title":"Absolute rate theories of epigenetic stability","volume":"102","author":"AM Walczak","year":"2005","journal-title":"Proc. Natl. Acad. Sci"},{"key":"ref28","doi-asserted-by":"crossref","first-page":"1129","DOI":"10.1073\/pnas.79.4.1129","article-title":"Qualitative model for gene regulation by <italic>\u03bb<\/italic> phage repressor","volume":"79","author":"GK Ackers","year":"1982","journal-title":"Proc. Natl. Acad. Sci"},{"key":"ref29","doi-asserted-by":"crossref","first-page":"7304","DOI":"10.1073\/pnas.0509874103","article-title":"Predicting stochastic gene expression dynamics in single cells","volume":"103","author":"T Mettetal","year":"2006","journal-title":"Proc. Natl. Acad. U.S.A"},{"key":"ref30","doi-asserted-by":"crossref","first-page":"3830","DOI":"10.1529\/biophysj.106.101717","article-title":"Origin of bistability in the <italic>lac<\/italic> operon","volume":"92","author":"M Santill\u00e1n","year":"2007","journal-title":"Biophys. J"},{"key":"ref31","doi-asserted-by":"crossref","first-page":"1700","DOI":"10.1021\/bi00679a024","article-title":"Interaction of effecting ligands with lac repressor and repressor-operator complex","volume":"14","author":"MD Barkley","year":"1975","journal-title":"Biochemistry"},{"key":"ref32","doi-asserted-by":"crossref","first-page":"10115","DOI":"10.1016\/S0021-9258(19)70435-9","article-title":"Kinetic studies of inducer binding to <italic>lac<\/italic> repressor operator complex","volume":"255","author":"M Dunaway","year":"1980","journal-title":"J. Biol. Chem"},{"key":"ref33","doi-asserted-by":"crossref","first-page":"197","DOI":"10.1088\/1478-3967\/1\/4\/001","article-title":"Graded and binary responses in stochastic gene expression","volume":"1","author":"R Karmakar","year":"2004","journal-title":"Phys. Biol"},{"key":"ref34","doi-asserted-by":"crossref","first-page":"227","DOI":"10.1063\/1.1349894","article-title":"Bistability in cell signaling: How to make continuous processes discontinuous, and reversible processes irreversible","volume":"11","author":"J Ferrell","year":"2001","journal-title":"Chaos"},{"key":"ref35","doi-asserted-by":"crossref","first-page":"028101","DOI":"10.1103\/PhysRevLett.94.028101","article-title":"Nonequilibrium thermodynamics and nonlinear kinetics in a cellular signaling switch","volume":"94","author":"TC Reluga","year":"2005","journal-title":"Phys. Rev. Lett"},{"key":"ref36","doi-asserted-by":"crossref","first-page":"34","DOI":"10.1038\/nphys2819","article-title":"Spontaneous recovery in dynamical networks","volume":"10","author":"A Majdandzic","year":"2014","journal-title":"Nat. Phys"},{"key":"ref37","year":"1977","unstructured":"Zeeman EC. Catastrophe Theory-Selected Papers 1972-1977. Reading, MA: Addison-Wesley; <year>1977<\/year>."},{"key":"ref38","doi-asserted-by":"crossref","first-page":"18958","DOI":"10.1073\/pnas.0706110104","article-title":"Purely stochastic binary decisions in cell signaling models without underlying deterministic bistabilities","volume":"104","author":"MN Artyomov","year":"2007","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref39","doi-asserted-by":"crossref","first-page":"1254","DOI":"10.1021\/jp109036y","article-title":"Adiabatic and non-adiabatic non-equilibrium stochastic dynamics of single regulating genes","volume":"115","author":"H Feng","year":"2011","journal-title":"J. Phys. Chem. B"},{"key":"ref40","doi-asserted-by":"crossref","first-page":"051907","DOI":"10.1103\/PhysRevE.72.051907","article-title":"Self-regulating gene: an exact solution","volume":"72","author":"JEM Hornos","year":"2005","journal-title":"Phys. Rev. E"},{"key":"ref41","doi-asserted-by":"crossref","first-page":"451","DOI":"10.1038\/nrg1615","article-title":"Stochasticity in gene expression:from theories to phenotypes","volume":"6","author":"M Kaern","year":"2005","journal-title":"Nat Rev Genet"},{"key":"ref42","doi-asserted-by":"crossref","first-page":"065104","DOI":"10.1063\/1.3535561","article-title":"A perturbation analysis of rate theory of self-regulating genes and signaling networks","volume":"134","author":"PZ Shi","year":"2011","journal-title":"J. Chem. Phys"},{"key":"ref43","doi-asserted-by":"crossref","first-page":"1142","DOI":"10.1126\/science.1178962","article-title":"Noise can induce bimodality in positive transcriptional feedback loops without bistability","volume":"327","author":"T To","year":"2010","journal-title":"Science"},{"key":"ref44","doi-asserted-by":"crossref","first-page":"20093","DOI":"10.1021\/jp065187g","article-title":"When does the Michaelis-Menten equation hold for fluctuating enzymes?","volume":"110","author":"W Min","year":"2006","journal-title":"J. Phys. Chem. B"},{"key":"ref45","doi-asserted-by":"crossref","first-page":"248102","DOI":"10.1103\/PhysRevLett.106.248102","article-title":"Determining the stability of genetic switches: explicitly accounting for mRNA noise","volume":"106","author":"M Assaf","year":"2011","journal-title":"Phys. Rev. Lett"},{"key":"ref46","doi-asserted-by":"crossref","first-page":"048101","DOI":"10.1103\/PhysRevLett.88.048101","article-title":"Epigenetics as a first exit problem","volume":"88","author":"E Aurell","year":"2002","journal-title":"Phys. Rev. Lett"},{"key":"ref47","doi-asserted-by":"crossref","first-page":"148103","DOI":"10.1103\/PhysRevLett.103.148103","article-title":"Thermodynamic limit of a nonequilibrium steady state: Maxwell-type construction for a bistable biochemical system","volume":"103","author":"H Ge","year":"2009","journal-title":"Phys. Rev. Lett"},{"issue":"2","key":"ref48","doi-asserted-by":"crossref","first-page":"e88167","DOI":"10.1371\/journal.pone.0088167","article-title":"Constructing the energy landscape for genetic switching system driven by intrinsic noise","volume":"9","author":"C Lv","year":"2014","journal-title":"Plos One"},{"key":"ref49","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1016\/j.bpj.2010.03.058","article-title":"The potential landscape of genetic circuits imposes the arrow of time in stem cell differentiation","volume":"99","author":"J Wang","year":"2010","journal-title":"Biophys. J"},{"key":"ref50","doi-asserted-by":"crossref","first-page":"3539","DOI":"10.1098\/rsif.2012.0434","article-title":"Quasi-potential landscape in complex multi-stable systems","volume":"9","author":"JX Zhou","year":"2012","journal-title":"J. R. Soc. Interface"},{"key":"ref51","doi-asserted-by":"crossref","first-page":"094109","DOI":"10.1063\/1.4943096","article-title":"Construction of the landscape for multi-stable systems: Potential landscape, quasi- potential, A-type integral and beyond","volume":"144","author":"PJ Zhou","year":"2016","journal-title":"J. Chem. Phys"},{"key":"ref52","first-page":"188","article-title":"Calculating biological behaviors of epigenetic states in the phage <italic>\u03bb<\/italic> life cycle","volume":"4","author":"XM Zhu","year":"2004","journal-title":"Funct. Integr. Genomics"},{"key":"ref53","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-0611-8","article-title":"Random Perturbations of Dynamical Systems","author":"MI Freidlin","year":"1998"},{"issue":"10","key":"ref54","doi-asserted-by":"crossref","first-page":"e2000841","DOI":"10.1371\/journal.pbio.2000841","article-title":"Nonlatching positive feedback enables robust bimodality by decoupling expression noise from the mean","volume":"15","author":"BS Razooky","year":"2017","journal-title":"PLOS Biol"},{"key":"ref55","doi-asserted-by":"crossref","first-page":"990","DOI":"10.1007\/s10955-010-0093-7","article-title":"Cellular biology in terms of stochastic nonlinear biochemical dynamics: Emergent properties, isogenetic variations and chemical system inheritability","volume":"141","author":"H Qian","year":"2010","journal-title":"J. Stat. Phys"},{"key":"ref56","first-page":"1","article-title":"Mesoscopic biochemical basis of isogenetic inheritance and canalization: Stochasticity, nonlinearity, and emergent landscape","volume":"9","author":"H Qian","year":"2012","journal-title":"Mol Cell Biomech"},{"key":"ref57","doi-asserted-by":"crossref","first-page":"553","DOI":"10.1073\/pnas.43.7.553","article-title":"Enzyme induction as an all-or-none phenomenon","volume":"43","author":"A Novick","year":"1957","journal-title":"Proc. Natl. Acad. Sci. U.S.A"},{"key":"ref58","doi-asserted-by":"crossref","first-page":"10","DOI":"10.1016\/0021-9991(75)90060-1","article-title":"A new algorithm for Monte Carlo simulation of Ising spin systems","volume":"17","author":"AB Bortz","year":"1975","journal-title":"J. Comput. Phys"},{"issue":"3","key":"ref59","doi-asserted-by":"crossref","first-page":"455","DOI":"10.2307\/1990339","article-title":"Markoff chains-Denumerable case. Trans","volume":"58","author":"JL Doob","year":"1945","journal-title":"Amer. Math. Soc"},{"issue":"4","key":"ref60","doi-asserted-by":"crossref","first-page":"403","DOI":"10.1016\/0021-9991(76)90041-3","article-title":"A general method for numerically simulating the stochastic time evolution of coupled chemical reactions","volume":"22","author":"DT Gillespie","year":"1976","journal-title":"J. Comput. Phys"},{"issue":"25","key":"ref61","doi-asserted-by":"crossref","first-page":"2340","DOI":"10.1021\/j100540a008","article-title":"Exact stochastic simulation of coupled chemical reactions","volume":"81","author":"DT Gillespie","year":"1977","journal-title":"J. Phys. Chem"}],"updated-by":[{"DOI":"10.1371\/journal.pcbi.1006051","type":"new_version","label":"New version","source":"publisher","updated":{"date-parts":[[2018,3,22]],"date-time":"2018-03-22T00:00:00Z","timestamp":1521676800000}}],"container-title":["PLOS Computational Biology"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/dx.plos.org\/10.1371\/journal.pcbi.1006051","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,8,15]],"date-time":"2022-08-15T17:59:27Z","timestamp":1660586367000},"score":1,"resource":{"primary":{"URL":"https:\/\/dx.plos.org\/10.1371\/journal.pcbi.1006051"}},"subtitle":[],"editor":[{"given":"Daniel A","family":"Beard","sequence":"first","affiliation":[],"role":[{"role":"editor","vocabulary":"crossref"}]}],"short-title":[],"issued":{"date-parts":[[2018,3,12]]},"references-count":61,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2018,3,12]]}},"URL":"https:\/\/doi.org\/10.1371\/journal.pcbi.1006051","relation":{},"ISSN":["1553-7358"],"issn-type":[{"value":"1553-7358","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,3,12]]}}}