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| Steady-state Analysis of the Gene Transcriptional Regulation System Under the Double-noise Excitation |
| ZHANG Meng, GUO Yongfeng, LIU Qianru
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| School of Mathematical Sciences, Tiangong University, Tianjin 300387, China |
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Abstract Noise is playing an important role in the regulation of gene transcription in biological systems. This paper studies the dynamics of gene transcription regulation system under the effects of multiplicative Gaussian white noise and additive Lévy noise. Firstly, the Lévy noise is simulated with the Janicki-Weron algorithm, and then the fourth-order Runge-Kutta algorithm is used to calculate the steady-state probability density(SPD) function of the protein concentration, then the steady state analysis of the gene transcriptional regulation system is carried out by the SPD figures. The study found that Gaussian noise intensity, Lévy noise intensity, stability index, and skewness parameter all can induce phase transitions in the gene transcription regulation system; At the same time, the increase of these parameters will cause the gene transcription regulation system to gradually the " on" state changes to the "off" state.
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Received: 17 September 2021
Published: 21 July 2023
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