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dc.contributor.authorGedeon, Tomas
dc.contributor.authorPernarowski, Mark
dc.contributor.authorWilander, Adam
dc.identifier.citationGedeon, Tomas, Mark Pernarowski, and Adam Wilander. "Cyclic Feedback Systems with Quorum Sensing Coupling." Bulletin of Mathematical Biology. DOI:
dc.description.abstractSynchronization and desynchronization is of great interest in the study of circadian rhythms, metabolic oscillations and time-dependent cell aggregate behaviors. Several recent studies examine synchronization and other dynamics in models of repressilators coupled by a quorum sensing mechanism that uses a diffusive signal. Their numerical simulations have shown the complexity of the collective behavior depends sensitively on which protein upregulates diffusive signal. In this paper, we rigorously prove that the collective dynamics indeed strongly depends on how the signaling network integrates into the repressilator network. In fact we prove a general result for a class of negative cyclic feedback systems with signaling of which the repressilator is but one example. We show that if the feedback along the signaling loop is also negative, the resulting negative feedback, negative signaling (Nf-Ns) system admits either unique stable equilibrium, or a stable oscillation. When a positive signaling feedback is included, the system is no longer (Nf-Ns) and numerically exhibits multistable dynamics (Ullner et al. in Phys Rev Lett 99:148103, 2007; Phys Rev E 78:031904, 2008). We demonstrate that this multistability emerges through saddle node bifurcations of a sole cubic curve-as in generic bistable models.en_US
dc.subjectNegative cyclic feedback systemsen_US
dc.subjectQuorum sensingen_US
dc.titleCyclic Feedback Systems with Quorum Sensing Couplingen_US
mus.citation.journaltitleBulletin of Mathematical Biologyen_US
mus.identifier.categoryPhysics & Mathematicsen_US
mus.relation.collegeCollege of Letters & Scienceen_US
mus.relation.departmentMathematical Sciences.en_US
mus.relation.universityMontana State University - Bozemanen_US
mus.contributor.orcidGedeon, Tomas|0000-0001-5555-6741en_US

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