The properties of time-delay gene transcriptional regulation system

We introduce two deterministic models of time-delay gene transcriptional regulation system, and research the properties of the two systems by computational modeling. The time-delay positive feedback system has multistability, gene switch and staircases. The platform of staircases is narrower with shorter delay, in contrast, the platform is wider with longer delay. Moreover, the system has memory property and echo phenomena emerging. These properties are caused by stimulation responding to time delay. On the other hand, the time-delay positive-negative feedback system can elicit oscillations and staircases. Bifurcation diagram demonstrates oscillation region enlarging and amplitude increasing compare with no time delay system, furthermore, the transcription rate can adjust oscillation amplitude, and the platforms width are in accord with delay times. Oscillations and staircases can indicate that delay increases instability.