JAMC

Article http://dx.doi.org/10.26855/jamc.2026.03.002

Dynamic Characteristics and Synergistic Effect of Gaussian White Noise and Color Noise in Gene Transcription Regulation System

TOTAL VIEWS: 217

Yan Fu¹, Yu Gao¹, Shujun Bi¹, Juan Zeng¹, Wenjing Wang¹, Yumeng Zhang¹, Guowei Wang^2,3,*

¹School of Computer and Mathematics, Yuzhang Normal University, Nanchang 330103, Jiangxi, China.

²School of Aeronautical Mechanical and Electrical Engineering, Jiangxi Flight University, Nanchang 330024, Jiangxi, China.

³School of Education, Nanchang Institute of Science and Technology, Nanchang 330044, Jiangxi, China.

*Corresponding author:Guowei Wang

This work was supported by the College Student Innovation Training Program Project of Jiangxi Provincial (S202413774018), Natural Science Foundation of Jiangxi Provincial (20232BAB201048), and Senior Talent In-troduction Project of Jiangxi Flight University.

Published: March 4,2026

Abstract

This research employs the Fox approximation method and Novikov’s theorem to derive the Fokker-Planck equation of gene transcriptional regulatory systems, thus random dynamical characteristics and synergistic effect of cross-correlated Gaussian colored noise and white noise on the system are investigated. Specifically, the effects of noise intensity and correlation time on the steady-state probability distribution and the mean first passage time of the system are analyzed through numerical simulation. The obtained results indicate that auto-correlation time and cross-correlation time can serve as crucial parameters in regulating gene switching states. Noise intensity, correlation time, and correlation strength can exert significant regulatory effects on the steady-state probability distribution function of the gene transcription regulatory system. Meanwhile, a study on the mean first passage time reveals that correlation strength and correlation time play complex roles in gene transcription, sometimes exhibiting equivalent effects, while other times acting in opposition. Under different correlation conditions, protein concentration transitions display intricate dynamical behaviors, such as re-recording phenomena. This research proposes regulating gene states through changes in protein concentration, providing new insights for the design of genetic drugs.

Keywords

Gene transcriptional; Regulatory system; Cross-correlated; Steady-state probability distribution; Mean first passage time

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How to cite this paper

Dynamic Characteristics and Synergistic Effect of Gaussian White Noise and Color Noise in Gene Transcription Regulation System

How to cite this paper: Yan Fu, Yu Gao, Shujun Bi, Juan Zeng, Wenjing Wang, Yumeng Zhang, Guowei Wang. (2026) Dynamic Characteristics and Synergistic Effect of Gaussian White Noise and Color Noise in Gene Transcription Regulation System. Journal of Applied Mathematics and Computation, 10(1), 7-20.

DOI: http://dx.doi.org/10.26855/jamc.2026.03.002