On Robustness of Phase Resetting to Cell Division under Entrainment

Hafiz Ahmed 1 Rosane Ushirobira 1 Denis Efimov 2, 1
1 NON-A - Non-Asymptotic estimation for online systems
CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille (CRIStAL) - UMR 9189, Inria Lille - Nord Europe
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).
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Hafiz Ahmed, Rosane Ushirobira, Denis Efimov. On Robustness of Phase Resetting to Cell Division under Entrainment. Journal of Theoretical Biology, Elsevier, 2015. ⟨hal-01211491⟩

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