title: Synchronization of degrade-and-fire oscillations via a common activator.
abstract: The development of synthetic gene oscillators has not only demonstrated our ability to forward engineer reliable circuits in living cells, but it has also proven to be an excellent testing ground for the statistical behavior of coupled noisy oscillators. Previous experimental studies demonstrated that a shared positive feedback can reliably synchronize such oscillators, though the theoretical mechanism was not studied in detail. In the present work, we examine an experimentally motivated stochastic model for coupled degrade-and-fire gene oscillators, where a core delayed negative feedback establishes oscillations within each cell, and a shared delayed positive feedback couples all cells. We use analytic and numerical techniques to investigate conditions for one cluster and multicluster synchrony. A nonzero delay in the shared positive feedback, as expected for the experimental systems, is found to be important for synchrony to occur.
authors.affiliation: Department of Physics, Virginia Tech, 850 West Campus Drive, Blacksburg, Virginia 24061-0435, USA and Department of Biological Sciences, Virginia Tech, 1405 Perry Street, Blacksburg, Virginia 24061-0406, USA.
authors.forename: William
authors.initials: W
authors.lastname: Mather
authors.affiliation: Department of Bioengineering, UCSD, 9500 Gilman Drive, La Jolla, California 92093-0412, USA and Molecular Biology Section, Division of Biology, UCSD, 9500 Gilman Drive, La Jolla, California 92093-0368, USA and BioCircuits Institute, UCSD, 9500 Gilman Drive, La Jolla, California 92093-0328, USA.
authors.forename: Jeff
authors.initials: J
authors.lastname: Hasty
authors.affiliation: BioCircuits Institute, UCSD, 9500 Gilman Drive, La Jolla, California 92093-0328, USA.
authors.forename: Lev S
authors.initials: LS
authors.lastname: Tsimring
mesh_terms: D001683:Biological Clocks / Q000235:genetics*; D025461:Feedback, Physiological; D005813:Genes, Synthetic; D008957:Models, Genetic; D013269:Stochastic Processes