Robust synchronization of genetic oscillators subjected to cell division and common entrainment

Hafiz Ahmed, Rosane Ushirobira, Denis Efimov

Research output: Chapter in Book/Report/Conference proceedingConference proceeding

Abstract

Cell division introduces discontinuities in the dynamics of genetic oscillators (circadian clocks, synthetic oscillators, etc.) causing phase drift. This paper considers the problem of phase synchronization for a population of genetic oscillators that undergoes cell division and with a common entraining input in the population. Inspired by stochastic simulation, this paper proposes analytical conditions that guarantee phase synchronization. This analytical conditions are derived based on Phase Response Curve (PRC) model of an oscillator (the first order reduced model obtained for the linearized system and inputs with sufficiently small amplitude). Cell division introduces state resetting in the model (or phase resetting in the case of phase model), placing it in the class of hybrid systems. It is shown through numerical experiments for a motivating example 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. Theoretical developments proposed in the paper are demonstrated through numerical simulations for two different genetic oscillator models (Goodwin oscillator and Van der Pol oscillator).
Original languageEnglish
Title of host publication2016 European Control Conference (ECC)
Place of PublicationAalborg, Denmark
PublisherIEEE
Pages1844-1849
Number of pages6
ISBN (Electronic)978-1-5090-2591-6, 978-1-5090-2590-9
ISBN (Print)978-1-5090-2592-3
DOIs
Publication statusPublished - 9 Jan 2017
Event2016 European Control Conference - Aalborg, Denmark
Duration: 29 Jun 20161 Jul 2016

Conference

Conference2016 European Control Conference
Abbreviated titleECC
CountryDenmark
CityAalborg
Period29/06/161/07/16

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