title: On robustness of phase resetting to cell division under entrainment.
abstract: The problem of phase synchronization for a population of genetic oscillators (circadian clocks, synthetic oscillators, etc.) is considered in this paper, taking into account a cell division process and a common entrainment input in the population. The proposed analysis approach is based on the Phase Response Curve (PRC) model of an oscillator (the first order reduced model obtained for the linearized system and inputs with infinitesimal amplitude). The occurrence of cell division introduces state resetting in the model, placing it in the class of hybrid systems. It is shown that without common entraining input in all oscillators, the cell division acts as a disturbance causing phase drift, while the presence of entrainment guarantees boundedness of synchronization phase errors in the population. The performance of the obtained solutions is demonstrated via computer experiments for two different models of circadian/genetic oscillators (Neurospora׳s circadian oscillation model and the repressilator).
authors.affiliation: Non-A project @ Inria, Parc Scientifique de la Haute Borne, 40 avenue Halley, 59650 Villeneuve d׳Ascq, France. Electronic address: hafiz.ahmed@inria.fr.
authors.forename: Hafiz
authors.initials: H
authors.lastname: Ahmed
authors.affiliation: Non-A project @ Inria, Parc Scientifique de la Haute Borne, 40 avenue Halley, 59650 Villeneuve d׳Ascq, France.
authors.forename: Rosane
authors.initials: R
authors.lastname: Ushirobira
authors.affiliation: Non-A project @ Inria, Parc Scientifique de la Haute Borne, 40 avenue Halley, 59650 Villeneuve d׳Ascq, France; CRIStAL (UMR-CNRS 9189) Ecole Centrale de Lille, Avenue Paul Langevin, 59651 Villeneuve d׳Ascq, France; Department of Control Systems and Informatics, University ITMO, 49 avenue Kronverkskiy, 197101 Saint Petersburg, Russia.
authors.forename: Denis
authors.initials: D
authors.lastname: Efimov
mesh_terms: D002455:Cell Division; D002940:Circadian Rhythm / Q000502:physiology*; D008954:Models, Biological; D009491:Neurospora / Q000166:cytology* / Q000502:physiology*
keywords: Cell division; Oscillation control; Phase resetting