Auto-Regulation of Transcription and Translation: Oscillations, Excitability and Intermittency.

Several members of the Hes/Her family, conserved targets of the Notch signalling pathway, encode transcriptional repressors that dimerise, bind DNA and self-repress. Such autoinhibition of transcription can yield homeostasis and, in the presence of delays that account for processes such as transcription, splicing and transport, oscillations. Whilst previous models of autoinhibition of transcription have tended to treat processes such as translation as being unregulated (and hence linear), here we develop and explore a mathematical model that considers autoinhibition of transcription together with nonlinear regulation of translation. It is demonstrated that such a model can yield, in the absence of delays, nonlinear dynamical behaviours such as excitability, homeostasis, oscillations and intermittency. These results indicate that regulation of translation as well as transcription allows for a much richer range of behaviours than is possible with autoregulation of transcription alone. A number of experiments are suggested that would that allow for the signature of autoregulation of translation as well as transcription to be experimentally detected in a Notch signalling system.