Complex role of time delay in dynamical coordination of neural progenitor fate decisions mediated by Notch pathway

Although the oscillation and bistability in Notch signaling pathway are essential for neural development, the precise regulation mechanism and biological significance underlying these dynamics have so far remained elusive. In this work, we proposed a specific delayed computational model to qualitatively explore the dynamical coordination of neural progenitor fate decisions. We found that the double -negative feedback loop formed by Hes1 and miR-9 can give rise to bistability that possesses the potential to create two coexisting stable steady states of high and low levels of Hes1, thereby resulting in two distinct fates: quiescent progenitors and differentiated neurons. Furthermore, we theoretically revealed that the time delay resulting from Hes1 protein production can induce stable sustained oscillations through a supercritical Hopf bifurcation, which facilitates the neural progenitor maintenance and proliferation. Uniquely, we discovered an emerging role of the time delay that has ability to trigger spontaneous switches between bistable states without any modification of model parameters and initial conditions, and established the corresponding basins of attraction to illustrate the principle of this time -delay -based switches. Moreover, we observed delay -induced transient chaos phenomenon in our work. Our results are consistent with several experimental observations and theoretical results, which may provide a new clue for exploring the complex regulatory mechanism of neural development.