https://doi.org/10.1140/epjp/s13360-025-06521-8
Regular Article
Dichotomous noise-induced switching in the synergistic toggle switch
1
School of Mathematics and Statistics, Hainan University, 570228, Haikou, Hainan, People’s Republic of China
2
School of Cyberspace Security, Hainan University, 570228, Haikou, Hainan, People’s Republic of China
3
Key Laboratory of Engineering Modeling and Statistical Computation of Hainan Province, Hainan University, 570228, Haikou, Hainan, People’s Republic of China
4
School of Mathematics and Statistics, Xuzhou University of Technology, 221111, Xuzhou, China
Received:
17
March
2025
Accepted:
4
June
2025
Published online:
18
June
2025
The accurate capture of transcription factor signals by receptors is key to achieving a toggle switch. However, this process is limited by the embedded tissue environment that impedes the diffusion of ligand molecules to form a stochastic oscillatory rather than a constant signal. Here, we try to decipher the regulated mechanism of dichotomous noise-induced switching in the classical toggle switch to elucidate how the noise strength and molecular memory can regulate the phenotype switch and affect the significant dynamic characteristic. Different from the traditional chemical master equation, we introduce dichotomous noise to illustrate the dynamic occupancy mode of the transcription factor on the binding site to yield a more accurate model for demonstrating the process of the toggle switch. The findings reveal that toggle switch systems are highly sensitive to fluctuations in noise intensity. Minor tweaks in noise levels can substantially boost the likelihood of system switching, thereby profoundly affecting the system’s dynamic behavior and long-term stability. Furthermore, changes in autocorrelation time length demonstrate a distinct threshold effect on system switching. Once this threshold is surpassed, the system’s responsiveness to autocorrelation time undergoes a significant enhancement. This threshold effect is the principal driver behind the phase transitions in regulatory systems and directly governs the sharp reductions in the mean first passage time. Concurrently, the mean residence time of the system in each steady state exhibits an extreme value effect. These findings offer novel insights for the construction of more complex regulatory elements within the synergistic toggle switch, enabling enhanced control and performance in synthetic model organisms.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2025
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
