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

The mammalian circadian clock plays a crucial role in regulating the 24-h 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...

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Bibliographic Details
Published in:Nonlinear dynamics 2024-05, Vol.112 (9), p.7527-7540
Main Authors: Wang, Conghua, Liu, Haihong, Zhang, Yuan
Format: Article
Language:English
Subjects:
Automotive Engineering
Bifurcation theory
Biological clocks
Circadian rhythm
Classical Mechanics
Constraint modelling
Control
Control theory
Dynamical Systems
Engineering
Feedback loops
Hopf bifurcation
Legislation
Mammals
Mechanical Engineering
Negative feedback
Original Paper
Oscillations
Robustness (mathematics)
Time lag
Vibration
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Summary:The mammalian circadian clock plays a crucial role in regulating the 24-h 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.
ISSN:0924-090X
1573-269X
DOI:10.1007/s11071-024-09416-y