External Noise and External Signal Induced Transition of Gene Switch and Coherence Resonance in the Genetic Regulatory S
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External Noise and External Signal Induced Transition of Gene Switch and Coherence Resonance in the Genetic Regulatory System Jian-Cheng Shi1 • Min Luo1 • Tao Dong1 Chu-Sheng Huang1
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Received: 14 October 2015 / Accepted: 10 March 2017 Springer Science+Business Media Dordrecht 2017
Abstract The transition of gene switch induced by external noises (multiplicative external noise and additive external noise) and external signals is investigated in the genetic regulatory system. Results show that the state-to-state transition of gene switch as well as resonant behaviors, such as the explicit coherence resonance (ECR), implicit coherence resonance (ICR) and control parameter coherence biresonance (CPCBR), can appear when noises are injected into the genetic regulatory system. The ECR is increased with the increase of the control parameter value when starting from the supercritical Hopf bifurcation parameter point, and there exists a critical control parameter value for the occurrence of ECR. However, the ICR is decreased as the control parameter value is increased when starting from the subcritical Hopf bifurcation point. In particular, the coherence of ECR is higher and more sensitive to noise than that of ICR. When an external signal is introduced into the system, the enhancement or suppression of the CPCBR and the number of peaks strongly depend on the frequency and amplitude of the external signal. Furthermore, the gene regulation system can selectively enhance or decrease the noise-induced oscillation signals at preferred frequency and amplitude of an external signal.
& Chu-Sheng Huang [email protected] Jian-Cheng Shi [email protected] Min Luo [email protected] Tao Dong [email protected] 1
College of Chemistry and Material Science, Guangxi Teachers Education University, Nanning 530001, China
123
J.-C. Shi et al.
Keywords External noise External signal Transition of gene switch Coherence resonance Genetic regulatory system
1 Introduction In recent years, plenty of researches have shown that noises can be acknowledged for their potentially constructive and functional role in many biological processes (Yi et al. 2006; Yu et al. 2009; Wang et al. 2012; Chen and Hsu 2012; Strelkowa 2014; de Franciscis et al. 2014). Up to now several resonance phenomena have been intensively studied in a large variety of physical, chemical, and biological systems (Hou et al. 1999; Li and Li 2006; Pikovsky and Kurths 1997; Li and Lang 2006; Yi et al. 2006; Yu et al. 2009). Among these are stochastic resonance (SR), which is the name coined for the rather counterintuitive fact that the response of a nonlinear system to an external periodic signal may be enhanced through an optimal amount of noise (Hou et al. 1999; Li and Li 2006; Yi et al. 2006), and coherence resonance (CR), which is the phenomenon in which external noise alone (without any external periodic signal) induces coherent oscillations in a nonlinear system in such a way that the coherence displays resonent-like behavior with the variation of noise intensity (
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