Abstract：
:Synchronization 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.
journal_name
Bull Math Bioljournal_title
Bulletin of mathematical biologyauthors
Gedeon T,Pernarowski M,Wilander Adoi
10.1007/s11538-016-0187-8subject
Has Abstractpub_date
2016-06-01 00:00:00pages
1291-317issue
6eissn
0092-8240issn
1522-9602pii
10.1007/s11538-016-0187-8journal_volume
78pub_type
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