Effect of colored cross-correlated noise on the gene transcriptional regulatory system

Abstract

The transient properties (e.g., the mean first passage time T) of the gene transcriptional regulatory system driven by colored cross-correlated noise are investigated. The approximate Fokker-Planck equation is obtained based on the Novikov theorem and the Fox approach and the explicit expression of the mean first passage time is derived. The numerical computation results show that for the case of strong correlation intensity and short correlation time，a successive switch process (i.e.，“on”→“off”→“on”) occurs; for tha case of weak correlation intensity and long correlation time，only one switch process occurs (i.e.，“on”→“off”). The reentrance phenomena appear in the gene transcriptional regulatory system.

Stochastic resonance in the gene transcriptional regulatory system subjected to noises

“…[30] The coloured cross-correlated time can speed up the transition between the low concentration state and the high concentration state. [31] The time delay can also induce the two switches, etc. The SR phenomenon in the gene transcriptional regulatory system has been investigated in Ref.…”

Non-Markovian Effect on Gene Transcriptional Systems

“…where 𝜏 1 is the time delay in synthesis reactions of the TF, 𝜏 2 is the time delay in degradation reactions, 𝛼 = 0.4, 𝛽 = 6, 𝛾 = 1 and 𝑐 2 = 10 are selected as in Refs. [27,28,[30][31][32][33]. This transcriptional system has two stable states 𝑥 1 = 0.627, 𝑥 2 = 4.283, and an unstable state 𝑥 u = 1.490.…”