Stability and bifurcation analysis of a delayed genetic oscillator model

Gao, Chunyan; Chen, Fangqi

doi:10.1007/s11071-021-06968-1

Cited by 3 publications

(1 citation statement)

References 41 publications

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“…The robustness properties inherent in circadian clock architectures reflect the cell's capacity to adapt to external perturbations and tolerate an uncertain internal environment [22]. Previous investigations have emphasized the indispensability of time delays within negative feedback loops for sustaining oscillatory behavior while influencing characteristics such as amplitude, period, and robustness [7,16,28,27]. In mammalian circadian clocks, such delays arise from various processes encompassing transcription, translation, degradation, complex formation, as well as nuclear import and export [2].…”

Section: Introductionmentioning

confidence: 99%

Oscillatory dynamics of the mammalian circadian clock induced by the core delayed negative feedback loop

Wang,

Liu,

Zhang

2024

Nonlinear Dyn

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The mammalian circadian clock plays a crucial role in regulating the 24-hour physiological and behavioral processes. This work presents an improved model for the mammalian circadian clock by integrating physiologically plausible modifications into the Kim-Forger model, and investigates the oscillatory dynamics of the mammalian circadian clock induced by the core delayed negative feedback loop using bifurcation theory. The modifications involve introducing time delays in PER protein transcription, translation, and translocation, replacing the first-order law for PER degradation rate with the Michaelis-Menten law, and revising the transcription rate of P er genes. The modified model accurately captures circadian oscillations and overcomes the unrealistic constraints of the Kim-Forger model. In addition, by utilizing the time delay as a control parameter, the theoretical results reveal that the delay induces a supercritical Hopf bifurcation, leading to the emergence of circadian oscillations with enhanced robustness, longer periods, increased amplitudes, and phase delays. Finally, numerical simulations are presented toThe authors thank the anonymous reviewers for their valuable suggestions.

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Section: Introductionmentioning

confidence: 99%

Oscillatory dynamics of the mammalian circadian clock induced by the core delayed negative feedback loop

Wang,

Liu,

Zhang

2024

Nonlinear Dyn

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Oscillatory Dynamics Induced by Time Delays in the Quorum Sensing System of Pseudomonas Aeruginosa

Gao

Chen

2023

Int. J. Bifurcation Chaos

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In this work, a sufficiently simple quorum sensing model allows one to perform detailed analytic studies to gain insights into the dynamical mechanisms in Pseudomonas aeruginosa. It is shown that an optimal rate of model parameters is essential to induce oscillations without considering time delays. Theoretical analysis and numerical simulation reveal that the delays can induce subcritical Hopf bifurcation and oscillation hysteresis. By using the center manifold and normal form theory, the explicit formulas for determining the stability and direction of periodic solutions bifurcating from Hopf bifurcations are derived. Numerical results show that the global periodic solutions bifurcating from the equilibrium exist when the delay is faraway from the first critical value. Moreover, the length of the delay can determine the amplitudes and the periods of the oscillations. A two-parameter diagram of delays is given to illustrate their crucial roles in coordinating and regulating oscillatory dynamics of the system. These results may help to further understand the dynamics of quorum sensing system in Pseudomonas aeruginosa and provide beneficial guidelines in the process of bacterial delivery of drugs.

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Oscillatory dynamics of the mammalian circadian clock induced by the core delayed negative feedback loop

Wang

Liu

Yuan

2023

Preprint

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The mammalian circadian clock plays a crucial role in regulating the 24-hour physiological and behavioral processes. This work presents an improved model for the mammalian circadian clock by integrating physiologically plausible modifications into the Kim-Forger model, and investigates the oscillatory dynamics of the mammalian circadian clock induced by the core delayed negative feedback loop using bifurcation theory. The modifications involve introducing time delays in PER protein transcription, translation, and translocation, replacing the first-order law for PER degradation rate with the Michaelis-Menten law, and revising the transcription rate of $Per$ genes. The modified model accurately captures circadian oscillations and overcomes the unrealistic constraints of the Kim-Forger model. In addition, by utilizing the time delay as a control parameter, the theoretical results reveal that the delay induces a supercritical Hopf bifurcation, leading to the emergence of circadian oscillations with enhanced robustness, longer periods, increased amplitudes, and phase delays. Finally, numerical simulations are presented to assess the efficacy of the modified model and to validate the theoretical analysis.

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Stability and bifurcation analysis of a delayed genetic oscillator model

Cited by 3 publications

References 41 publications

Oscillatory dynamics of the mammalian circadian clock induced by the core delayed negative feedback loop

Oscillatory dynamics of the mammalian circadian clock induced by the core delayed negative feedback loop

Oscillatory Dynamics Induced by Time Delays in the Quorum Sensing System of Pseudomonas Aeruginosa

Oscillatory dynamics of the mammalian circadian clock induced by the core delayed negative feedback loop

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