Time-delayed intermittent oscillations and chaos in a transcriptional and post-transcriptional gene regulatory network for long-term memory

Noncoding RNAs play a crucial role in many biological processes ranging from gene expression regulation, genome defence to epigenetic inheritance. In this paper, a mathematical model with time delay is proposed to characterize gene regulation mediated by two small noncoding RNAs acting at transcriptional level and post-transcriptional level. Through bifurcation analysis of the model without time delay, complex dynamics such as monostability, bistability, excitability and oscillation are exhibited with changing parameters. Then, introducing the time delay in the monostable, bistable, excitable and oscillatory regions generates a variety of bifurcations, accompanied with intermittent oscillations, oscillations with discontinuously changing amplitudes and periods, and chaotic dynamics by quasi-periodic route or period-doubling cascade route. The abundant dynamical mechanism on bistable switches or oscillators accounts for many functional features of sncRNAs. As an application, the presented model can be used to qualitatively simulate experimental findings of long-term memory formation. The existence of bistability depending on appropriate time delay is critical for the sustained high state in the system, and the time delay may affect the number of repeated pulses of stimulation required for the establishment of long-term memory.