Modelling and analysis of a genetic oscillator in E.coli

Abstract

This thesis presents the modelling and analysis of an engineered genetic oscillator in E.coli. Genetic oscillators composed of transcriptional feedback loops are the central components of circadian clocks [16]. Thus understanding small genetic oscillators is key for understanding the complex regulatory networks of circadian clocks. In order to monitor clock function, a new colony based imaging assay was set up, based on luminescent transcriptional reporter constructs, that allows for automated data collection over long time spans and for the screening of clock mutants. Clock runs produced damped oscillatory behaviour after starting the clock by removal of the lac inducer IPTG or by giving a metabolic stimulus by transferring cells onto fresh agar plates. A detailed mathematical model of the clock was constructed, taking into account discrete and stochastic regulatory binding events at the promoter sites. From this model, using the theory of heterogeneous systems [69, 66], deterministic equations were derived and analysed to yield conditions for the occurrence of stable oscillations based on the system's nullclines. To facilitate the modelling, an algorithm was devised and implemented, that allows for automated construction of Markov chain models of gene activity states based on DNA binding events. In sum, the work constitutes the establishment and analysis of an integrated experimental and modelling system, which opens possibilities for further investigation in order to yield insight into the properties of genetic oscillators