Mathematical analysis of robustness of oscillations in models of the mammalian circadian clock

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dc.contributor.authorYao, Xiangyuen
dc.contributor.authorHeidebrecht, Benjamin L.en
dc.contributor.authorChen, Jingen
dc.contributor.authorTyson, John J.en
dc.date.accessioned2024-02-13T13:50:06Zen
dc.date.available2024-02-13T13:50:06Zen
dc.date.issued2022-03-18en
dc.description.abstractCircadian rhythms in a wide range of organisms are mediated by molecular mechanisms based on transcription-translation feedback. In this paper, we use bifurcation theory to explore mathematical models of genetic oscillators, based on Kim & Forger’s interpretation of the circadian clock in mammals. At the core of their models is a negative feedback loop whereby PER proteins (PER1 and PER2) bind to and inhibit their transcriptional activator, BMAL1. For oscillations to occur, the dissociation constant of the PER:BMAL1 complex, Kbd, must be ≤ 0.04 nM, which is orders of magnitude smaller than a reasonable expectation of 1–10 nM for this protein complex. We relax this constraint by two modifications to Kim & Forger’s ‘single negative feedback’ (SNF) model: first, by introducing a multistep reaction chain for posttranscriptional modifications of Per mRNA and posttranslational phosphorylations of PER, and second, by replacing the first-order rate law for degradation of PER in the nucleus by a Michaelis-Menten rate law. These modifications increase the maximum allowable Kbd to ~2 nM. In a third modification, we consider an alternative rate law for gene transcription to resolve an unrealistically large rate of Per2 transcription at very low concentrations of BMAL1. Additionally, we studied extensions of the SNF model to include a second negative feedback loop (involving REV-ERB) and a supplementary positive feedback loop (involving ROR). Contrary to Kim & Forger’s observations of these extended models, we find that, with our modifications, the supplementary positive feedback loop makes the oscillations more robust than observed in the models with one or two negative feedback loops. However, all three models are similarly robust when accounting for circadian rhythms (~24 h period) with Kbd ≥ 1 nM. Our results provide testable predictions for future experimental studies.en
dc.description.versionPublished versionen
dc.format.extent23 page(s)en
dc.format.mimetypeapplication/pdfen
dc.identifierARTN e1008340 (Article number)en
dc.identifier.doihttps://doi.org/10.1371/journal.pcbi.1008340en
dc.identifier.eissn1553-7358en
dc.identifier.issn1553-734Xen
dc.identifier.issue3en
dc.identifier.orcidChen, Jing [0000-0001-6321-0505]en
dc.identifier.otherPCOMPBIOL-D-20-01637 (PII)en
dc.identifier.pmid35302984en
dc.identifier.urihttps://hdl.handle.net/10919/117968en
dc.identifier.volume18en
dc.language.isoenen
dc.publisherPublic Library of Scienceen
dc.relation.urihttps://www.ncbi.nlm.nih.gov/pubmed/35302984en
dc.rightsCreative Commons Attribution 4.0 Internationalen
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/en
dc.subject.meshAnimalsen
dc.subject.meshMammalsen
dc.subject.meshTranscription Factorsen
dc.subject.meshRNA, Messengeren
dc.subject.meshCircadian Rhythmen
dc.subject.meshCLOCK Proteinsen
dc.subject.meshARNTL Transcription Factorsen
dc.subject.meshCircadian Clocksen
dc.titleMathematical analysis of robustness of oscillations in models of the mammalian circadian clocken
dc.title.serialPlos Computational Biologyen
dc.typeArticle - Refereeden
dc.type.dcmitypeTexten
dc.type.otherArticleen
dc.type.otherJournalen
dcterms.dateAccepted2022-02-25en
pubs.organisational-group/Virginia Techen
pubs.organisational-group/Virginia Tech/Scienceen
pubs.organisational-group/Virginia Tech/Science/Biological Sciencesen
pubs.organisational-group/Virginia Tech/Faculty of Health Sciencesen
pubs.organisational-group/Virginia Tech/All T&R Facultyen
pubs.organisational-group/Virginia Tech/Science/COS T&R Facultyen

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