Abstract
Based on a stochastic differential equation model for a single genetic regulatory system, we examine the dynamical effects of noisy fluctuations, arising in the synthesis reaction, on the evolution of the transcription factor activator in terms of its concentration. The fluctuations are modeled by Brownian motion and α-stable Lévy motion. Two deterministic quantities, the mean first exit time (MFET) and the first escape probability (FEP), are used to analyse the transitions from the low to high concentration states. A shorter MFET or higher FEP in the low concentration region facilitates such a transition. We have observed that higher noise intensities and larger jumps of the Lévy motion shortens the MFET and thus benefits transitions. The Lévy motion activates a transition from the low concentration region to the non-adjacent high concentration region, while Brownian motion can not induce this phenomenon. There are optimal proportions of Gaussian and non-Gaussian noises, which maximise the quantities MFET and FEP for each concentration, when the total sum of noise intensities are kept constant. Because a weaker stability indicates a higher transition probability, a new geometric concept is introduced to quantify the basin stability of the low concentration region, characterised by the escaping behaviour.
Highlights
Based on a stochastic differential equation model for a single genetic regulatory system, we examine the dynamical effects of noisy fluctuations, arising in the synthesis reaction, on the evolution of the transcription factor activator in terms of its concentration
The available experimental data are limited to certain specific parameters, and not all systems have a stationary distribution. We will fill this gap and employ tools of stochastic dynamical systems[26]. The advantage of this approach is that we study the dynamical behaviors of the transcription factors (TFs)-A monomer concentration under Lévy fluctuations by two deterministic quantities: the mean first exit time (MFET) and the first escape probability (FEP)
We focus on the impact of Gaussian Brownian motion and non-Gaussian α-stable Lévy motion on the mean first exit time, first escape probability and basin of attraction in transcription factor activator (TF-A) monomer concentration model
Summary
Based on a stochastic differential equation model for a single genetic regulatory system, we examine the dynamical effects of noisy fluctuations, arising in the synthesis reaction, on the evolution of the transcription factor activator in terms of its concentration. Previous investigations indicate that noise is a key factor for state transitions in genetic regulatory systems These stochastic fluctuations have been mostly considered under the usual assumption of Gaussian distribution[7,8,9]. It has been demonstrated that the noise intensity, the stability (Lévy) index of Lévy motion induces a switch process between distinct gene-expression states[11] It has been shown for a stochastic model that the average size of the bursts has an effect on the level of transcription factors[20]
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