Effects of noise and time delay on E2F's expression level in a bistable Rb‐E2F gene’s regulatory network

Abstract

The bistable Rb-E2F gene regulatory network plays a central role in regulating cellular proliferation-quiescence transition. Based on Gillespie's chemical Langevin method, the stochastic bistable Rb-E2F gene's regulatory network with time delays is proposed. It is found that under the moderate intensity of internal noise, delay in the Cyclin E synthesis rate can greatly increase the average concentration value of E2F. When the delay is considered in both E2F-related positive feedback loops, within a specific range of delay (3-13)hr, the average expression of E2F is significantly increased. Also, this range is in the scope with that experimentally given by Dong et al. [65]. By analysing the quasi-potential curves at different delay times, simulation results show that delay regulates the dynamic behaviour of the system in the following way: small delay stabilises the bistable system; the medium delay is conducive to a high steady-state, making the system fluctuate near the high steady-state; large delay induces approximately periodic transitions between high and low steady-state. Therefore, by regulating noise and time delay, the cell itself can control the expression level of E2F to respond to different situations. These findings may provide an explanation of some experimental result intricacies related to the cell cycle.This is an open access article under the terms of the Creative Commons Attribution-NonCommercial License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited and is not used for commercial purposes.

Escape by jumps and diffusion by 𝛼-stable noise across the barrier in a double well potential

“…This makes possible to find potentials such that the weak noise threshold is very different in the two wells, leaving an interval of noise intensities for which the response of the system to a change in the noise intensity follows qualitatively different laws. This could affect systems with very asymmetrical potentials, such as in [21]. Also similar phenomena could appear if the system approaches a saddle-node bifurcation, and the parameters of the well change in a way such that the weak noise threshold is crossed, giving a change of diffusive mode but in time instead of space.…”

“…Noise induced transitions between different stable states occur in many types of simple or complex systems: chemical reactions [14], geophysics and climate modelling [3,9], gene regulatory networks [2,21], just to mention a few.…”