{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,9]],"date-time":"2026-01-09T12:52:51Z","timestamp":1767963171669,"version":"3.49.0"},"reference-count":38,"publisher":"Public Library of Science (PLoS)","issue":"6","license":[{"start":{"date-parts":[[2012,6,28]],"date-time":"2012-06-28T00:00:00Z","timestamp":1340841600000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["www.ploscompbiol.org"],"crossmark-restriction":false},"short-container-title":["PLoS Comput Biol"],"DOI":"10.1371\/journal.pcbi.1002396","type":"journal-article","created":{"date-parts":[[2012,6,28]],"date-time":"2012-06-28T16:46:38Z","timestamp":1340901998000},"page":"e1002396","update-policy":"https:\/\/doi.org\/10.1371\/journal.pcbi.corrections_policy","source":"Crossref","is-referenced-by-count":8,"title":["Equation-Free Analysis of Two-Component System Signalling Model Reveals the Emergence of Co-Existing Phenotypes in the Absence of Multistationarity"],"prefix":"10.1371","volume":"8","author":[{"given":"Rebecca B.","family":"Hoyle","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Daniele","family":"Avitabile","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Andrzej M.","family":"Kierzek","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"340","published-online":{"date-parts":[[2012,6,28]]},"reference":[{"key":"ref1","doi-asserted-by":"crossref","first-page":"564","DOI":"10.1111\/j.1365-2958.2006.05249.x","article-title":"Bistability in bacteria.","volume":"61","author":"D Dubnau","year":"2006","journal-title":"Mol Microbiol"},{"key":"ref2","doi-asserted-by":"crossref","first-page":"1622","DOI":"10.1126\/science.1099390","article-title":"Bacterial persistence as a phenotypic switch.","volume":"305","author":"N Balaban","year":"2004","journal-title":"Science"},{"key":"ref3","doi-asserted-by":"crossref","first-page":"e1771","DOI":"10.1371\/journal.pone.0001771","article-title":"Positive feedback and noise activate the stringent response regulator Rel in mycobacteria.","volume":"3","author":"K Sureka","year":"2008","journal-title":"PLoS ONE"},{"key":"ref4","doi-asserted-by":"crossref","first-page":"4889","DOI":"10.1128\/JB.182.17.4889-4898.2000","article-title":"The stringent response of <italic>Mycobacterium tuberculosis<\/italic> is required for long-term survival.","volume":"182","author":"T Primm","year":"2000","journal-title":"J Bacteriol"},{"key":"ref5","doi-asserted-by":"crossref","first-page":"10026","DOI":"10.1073\/pnas.1631248100","article-title":"The role of RelMtb-mediated adaptation to stationary phase in long-term persistence of <italic>Mycobacterium tuberculosis<\/italic> in mice.","volume":"100","author":"J Dahl","year":"2003","journal-title":"Proc Natl Acad Sci U S A"},{"key":"ref6","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 K\u00e6rn","year":"2005","journal-title":"Nat Rev Genet"},{"key":"ref7","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1515\/jib-2005-11","article-title":"Stochastic activation of the response regulator PhoB by noncognate histidine kinases.","volume":"2","author":"L Zhou","year":"2005","journal-title":"J Integrative Bioinformatics"},{"key":"ref8","doi-asserted-by":"crossref","first-page":"259","DOI":"10.1038\/nrmicro1381","article-title":"Phenotypic variation in bacteria: the role of feedback regulation.","volume":"4","author":"W Smits","year":"2006","journal-title":"Nat Rev Microbiol"},{"key":"ref9","doi-asserted-by":"crossref","first-page":"140","DOI":"10.1016\/S0955-0674(02)00314-9","article-title":"Self-perpetuating states in signal transduction: positive feedback, double-negative feedback and bistability.","volume":"14","author":"J Ferrell","year":"2002","journal-title":"Curr Opin Cell Biol"},{"key":"ref10","doi-asserted-by":"crossref","first-page":"526","DOI":"10.1126\/science.1140818","article-title":"Noise in gene expression determines cell fate in <italic>Bacillus subtilis<\/italic>.","volume":"317","author":"H Maamar","year":"2007","journal-title":"Science"},{"key":"ref11","doi-asserted-by":"crossref","first-page":"1716","DOI":"10.1126\/science.1137455","article-title":"Tunability and noise dependence in differentiation dynamics.","volume":"315","author":"G S\u00fcel","year":"2007","journal-title":"Science"},{"key":"ref12","doi-asserted-by":"crossref","first-page":"169","DOI":"10.1016\/j.cell.2005.06.006","article-title":"Stochastic gene expression in a lentiviral positive-feedback loop: HIV-1 Tat fluctuations drive phenotypic diversity.","volume":"122","author":"L Weinberger","year":"2005","journal-title":"Cell"},{"key":"ref13","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1088\/1478-3975\/4\/1\/004","article-title":"Positive feedback, stochasticity and genetic competence.","volume":"4","author":"R Karmakar","year":"2007","journal-title":"Phys Biol"},{"key":"ref14","doi-asserted-by":"crossref","first-page":"3116","DOI":"10.1016\/S0006-3495(01)75949-8","article-title":"Stochasticity in transcriptional regulation: origins, consequences, and mathematical representations.","volume":"81","author":"T Kepler","year":"2001","journal-title":"Biophys J"},{"key":"ref15","doi-asserted-by":"crossref","first-page":"531","DOI":"10.1039\/B906951H","article-title":"Stochastic kinetic model of two component system signalling reveals all-or-none, graded and mixed mode stochastic switching responses.","volume":"6","author":"A Kierzek","year":"2009","journal-title":"Mol BioSyst"},{"key":"ref16","doi-asserted-by":"crossref","first-page":"084106","DOI":"10.1063\/1.2149854","article-title":"Gene regulatory networks: A coarse-grained, equation-free approach to multiscale computation.","volume":"124","author":"R Erban","year":"2006","journal-title":"J Chem Phys"},{"key":"ref17","doi-asserted-by":"crossref","first-page":"155103","DOI":"10.1063\/1.2718529","article-title":"Variable-free exploration of stochastic models: a gene regulatory network example.","volume":"126","author":"R Erban","year":"2007","journal-title":"J Chem Phys"},{"key":"ref18","doi-asserted-by":"crossref","first-page":"214106","DOI":"10.1063\/1.2131050","article-title":"An equation-free probabilistic steady-state approximation: Dynamic application to the stochastic simulation of biochemical reaction networks.","volume":"123","author":"H Salis","year":"2005","journal-title":"J Chem Phys"},{"key":"ref19","doi-asserted-by":"crossref","first-page":"331","DOI":"10.1007\/s00285-007-0086-6","article-title":"An equation-free approach to analyzing heterogeneous cell population dynamics.","volume":"55","author":"K Bold","year":"2007","journal-title":"J Math Biol"},{"key":"ref20","doi-asserted-by":"crossref","first-page":"2759","DOI":"10.3934\/dcds.2012.32.2759","article-title":"Stability and stabilization of the constrained runs schemes for equation-free projection to a slow manifold.","volume":"32","author":"A Zagaris","year":"2012","journal-title":"DCDS-A"},{"key":"ref21","doi-asserted-by":"crossref","first-page":"211","DOI":"10.1016\/0022-2836(85)90086-5","article-title":"The OR control system of bacteriophage lambda* 1: A physical-chemical model for gene regulation.","volume":"181","author":"M Shea","year":"1985","journal-title":"J Mol Biol"},{"key":"ref22","doi-asserted-by":"crossref","first-page":"691","DOI":"10.1073\/pnas.0234782100","article-title":"Robustness and the cycle of phosphorylation and dephosphorylation in a two-component regulatory system.","volume":"100","author":"E Batchelor","year":"2003","journal-title":"Proc Natl Acad Sci U S A"},{"key":"ref23","doi-asserted-by":"crossref","first-page":"2340","DOI":"10.1021\/j100540a008","article-title":"Exact stochastic simulation of coupled chemical reactions.","volume":"81","author":"D Gillespie","year":"1977","journal-title":"J Phys Chem"},{"key":"ref24","doi-asserted-by":"crossref","first-page":"347","DOI":"10.1137\/060666457","article-title":"Modeling and simulating chemical reactions.","volume":"50","author":"D Higham","year":"2008","journal-title":"SIAM Rev"},{"key":"ref25","first-page":"290","article-title":"Simulating, analyzing, and animating dynamical systems: a guide to XPPAUT for researchers and students","author":"B Ermentrout","year":"2002","journal-title":"Society for Industrial Mathematics"},{"key":"ref26","doi-asserted-by":"crossref","first-page":"715","DOI":"10.4310\/CMS.2003.v1.n4.a5","article-title":"Equation-free, coarse-grained multiscale computation: enabling microscopic simulators to perform system-level analysis.","volume":"1","author":"IG Kevrekidis","year":"2003","journal-title":"Comm Math Sci"},{"key":"ref27","doi-asserted-by":"crossref","first-page":"321","DOI":"10.1146\/annurev.physchem.59.032607.093610","article-title":"Equation-free multiscale computation: Algorithms and applications.","volume":"60","author":"I Kevrekidis","year":"2009","journal-title":"Annu Rev Phys Chem"},{"key":"ref28","doi-asserted-by":"crossref","first-page":"403","DOI":"10.1137\/050638667","article-title":"The moment map: nonlinear dynamics of density evolution via a few moments.","volume":"5","author":"D Barkley","year":"2006","journal-title":"SIAM J Appl Dyn Syst"},{"key":"ref29","doi-asserted-by":"crossref","first-page":"204108","DOI":"10.1063\/1.2372492","article-title":"Spatially distributed stochastic systems: Equation-free and equation-assisted preconditioned computations.","volume":"125","author":"L Qiao","year":"2006","journal-title":"J Chem Phys"},{"key":"ref30","doi-asserted-by":"crossref","first-page":"984","DOI":"10.1137\/080731360","article-title":"Analysis of a stochastic chemical system close to a SNIPER bifurcation of its mean-field model.","volume":"70","author":"R Erban","year":"2009","journal-title":"SIAM J Appl Math"},{"key":"ref31","doi-asserted-by":"crossref","first-page":"103","DOI":"10.1007\/s11071-011-9962-0","article-title":"Detection of coarse-grained unstable states of microscopic\/stochastic systems: a timestepper-based iterative protocol.","volume":"67","author":"AC Tsoumanis","year":"2012","journal-title":"Nonlinear Dyn"},{"key":"ref32","doi-asserted-by":"crossref","first-page":"10083","DOI":"10.1063\/1.1476929","article-title":"Coarse stability and bifurcation analysis using stochastic simulators: kinetic Monte Carlo examples.","volume":"116","author":"A Makeev","year":"2002","journal-title":"J Chem Phys"},{"key":"ref33","first-page":"165","article-title":"Two-component and phosphorelay signal transduction.","volume":"3","author":"J Hoch","year":"2000","journal-title":"Curr Opin Cell Biol"},{"key":"ref34","doi-asserted-by":"crossref","first-page":"e1001065","DOI":"10.1371\/journal.pbio.1001065","article-title":"Metabolic regulation of mycobacterial growth and antibiotic sensitivity.","volume":"9","author":"S Baek","year":"2011","journal-title":"PLoS Biol"},{"key":"ref35","doi-asserted-by":"crossref","first-page":"492","DOI":"10.1128\/jb.174.2.492-498.1992","article-title":"Molecular analysis of the <italic>Escherichia coli<\/italic> PhoP-PhoQ operon.","volume":"174","author":"M Kasahara","year":"1992","journal-title":"J Bacteriol"},{"key":"ref36","doi-asserted-by":"crossref","first-page":"955","DOI":"10.1111\/j.1365-2958.1994.tb00374.x","article-title":"Anaerobic activation of arcA transcription in <italic>Escherichia coli<\/italic>: roles of Fnr and ArcA.","volume":"11","author":"I Compan","year":"1994","journal-title":"Mol Microbiol"},{"key":"ref37","doi-asserted-by":"crossref","first-page":"24155","DOI":"10.1074\/jbc.M110715200","article-title":"EnvZ-OmpR interaction and osmoregulation in <italic>Escherichia coli<\/italic>.","volume":"277","author":"S Cai","year":"2002","journal-title":"J Biol Chem"},{"key":"ref38","doi-asserted-by":"crossref","first-page":"054104","DOI":"10.1063\/1.1992473","article-title":"Avoiding negative populations in explicit Poisson tau-leaping.","volume":"123","author":"Y Cao","year":"2005","journal-title":"J Chem Phys"}],"container-title":["PLoS Computational Biology"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/dx.plos.org\/10.1371\/journal.pcbi.1002396","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,30]],"date-time":"2019-06-30T07:01:43Z","timestamp":1561878103000},"score":1,"resource":{"primary":{"URL":"https:\/\/dx.plos.org\/10.1371\/journal.pcbi.1002396"}},"subtitle":[],"editor":[{"given":"Jennifer L.","family":"Reed","sequence":"first","affiliation":[],"role":[{"role":"editor","vocabulary":"crossref"}]}],"short-title":[],"issued":{"date-parts":[[2012,6,28]]},"references-count":38,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2012,6,28]]}},"URL":"https:\/\/doi.org\/10.1371\/journal.pcbi.1002396","relation":{},"ISSN":["1553-7358"],"issn-type":[{"value":"1553-7358","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,6,28]]}}}