Dynamic Behavior of p53 Driven by Delay and a Microrna-34a-Mediated Feedback Loop

Abstract

The tumor suppressor protein p53 is a critical hub in the comprehensive transcriptional network that inhibits the growth of cells after acute stress stimulation. In this paper, an integrated model of the p53 signaling pathway in response to DNA damage is proposed and the p53 stability and oscillatory dynamics are analyzed. Through theoretical analysis and numerical simulation, we find that the delay as a bifurcation parameter can drive the p53-Mdm2 module to undergo a supercritical Hopf bifurcation, thereby producing oscillation behavior. Moreover, we demonstrate how the positive feedback loop formed by p53* and microRNA-34a (miR-34a) with the feature of double-negative regulation produces limit-cycle oscillations. Further, we find that miR-34a can affect the critical value of Hopf bifurcation in delay-induced p53 networks. In addition, we show that ATM, once activated by DNA damage, makes p53* undergo two Hopf bifurcations. These results revealed that both time delay and miR-34a can have tumor suppressing roles by promoting p53 oscillation or high level expression, which will provide a perspective for promoting the development of anti-cancer drugs by targeting miR-34a and time delay.

Keywords: feedback loops; miR-34a; p53-Mdm2 pathway; time delay.

Figure 1

The p53 signal network. ATM* relays the DNA damage signal and induces activation of p53 from the inactive state to the active state (p53*). P53* is a transcriptional factor that can effectively promote the production of Mdm2; during that process there are inevitably time delays. Here, the time delay covers the time needed during both Mdm2 transcription and translation, which is recorded as τ. In turn, Mdm2 can bind to p53 and p53*, resulting in enhanced degradation of p53 and p53*. On the other hand, p53* can also activate miR-34a. Subsequently, miR-34a inhibits SIRT1 by promoting the degradation of sirt1 mRNA, which leads to an increase of acetylated p53. In addition, Mdm2 protein is degraded by a mechanism stimulated by ATM*.

Figure 2

A simplified relationship containing the main components of the p53 signal network. The central node p53* connects two feedback loops. One is a negative feedback loop formed by p53* and Mdm2 with time delay, and the other is a positive feedback loop formed by p53* and miR-34a with the feature of double-negative regulation.

Figure 3

The bifurcation diagram of p53* concentration and model parameters. (A), (B), (C) and (D) correspond to the parameters ATM*, k_on2, k_smi1 and k_smi2, respectively.

Figure 4

The bifurcation diagram of the k_on2 versus ATM* concentration.

Figure 5

The effects of time delay τ on the p53-Mdm2 system of model (1) when there is no expression of miR34-a. (A) The positive equilibrium is asymptotically stable whenτ = 0. (B) The positive equilibrium is asymptotically stable when τ = 3 < τ₀ = 5.1038. (C,D) The positive equilibrium is unstable when τ = 6 > τ₀ = 5.1038.

Figure 6

The effects of time delay τ on the p53-Mdm2 system of model (1) when there is certain expression of miR34-a. (A) The positive equilibrium is asymptotically stable when τ = 0. (B) The positive equilibrium is asymptotically stable when τ = 1.5 < τ₀ = 3.5578. (C,D) The positive equilibrium is unstable when τ = 4.5 > τ₀ = 3.5578.

Figure 7

The effect of time delay on the dynamics of the p53-mdm2 system. (A) The time evolution process of the p53* concentration when ATM* = 0.5. (B) The time evolution process of the Mdm2 concentration when ATM* = 0.5. (C) The time evolution process of the p53* concentration when ATM* = 1. (D) The time evolution process of the Mdm2 concentration when ATM* = 1.

Figure 8

The bifurcation diagram of p53* concentration corresponds to the parameter k_smd2.

Figure 9

The bifurcation diagram of p53* concentration corresponds to the parameter k_fp.