Theoretical analysis of the delay on the p53 micronetwork

Abstract

Time delay plays a crucial role in p53 dynamic. However, the theoretical understanding is still lower. Thus we construct a micro-differential equation model and introduce the time delay τ based on the regulation process. Firstly, we linearize the system and analyze the associated characteristic equation. We can conclude that there exists the delay threshold $\tau _{0}$ τ 0 such that when the delay τ is less than $\tau _{0}$ τ 0 , the system is asymptotically stable and otherwise stable oscillations occur. Secondly, we use the normal form method and the center manifold theorem to derive the direction and stability of the Hopf bifurcation. Finally, by numerical simulations we verify our theoretical results. We also find that the effect of noise on the amplitude is more severe than that of the period, which well agrees with the experimental results.

Mathematical Modelling of p53 Signalling during DNA Damage Response: A Survey

“…In recent years, a common extension when investigating the role of delays is to consider the extended model given in Figure 6 b. It has been shown that the delays in both negative feedback loops are important components to derive oscillatory behaviour [ 83 , 84 ]. One difficulty though is that in order to make analysis of the models tractable it has, so far, required that both delays are assumed to be equal, which may or may not be the case in the real biological system.…”

Stability and Hopf Bifurcation Analysis of a Fractional-order p53 Multiple Time Delays Model under PDα control

“…In the past research, great achievements have been made in establishing the stability of gene regulatory networks with time delays [10,11,12,13]. Mao et al analyzed that the time delay in the model is a necessary factor for the system to generate oscillation [14]; Xia et al pointed out that transcription delay can determine the vibration period of gene expression [15]; Wang et al found that the existence of time delay will lead to rich dynamic behavior of the system [16]. However, single time delay analysis is far from enough in gene regulation networks.…”