Modeling transcriptional co-regulation of mammalian circadian clock

Yanqin Wang; Xin Ni; Jie Yan; Ling Yang; Yanqin Wang; Xin Ni; Jie Yan; Ling Yang

doi:10.3934/mbe.2017075

Mathematical Biosciences and Engineering

2017, Volume 14, Issue 5&6: 1447-1462. doi: 10.3934/mbe.2017075

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Modeling transcriptional co-regulation of mammalian circadian clock

1.
School of Mathematical Sciences, Soochow University, Suzhou 215006, Jiangsu, China
2.
School of Mathematics & Physics, Changzhou University, Changzhou 213164, Jiangsu, China

Received: 30 May 2016 Accepted: 20 January 2017 Published: 01 October 2017
MSC : Primary: 34D99; Secondary: 34C23

The circadian clock is a self-sustaining oscillator that has a period of about 24 hours at the molecular level. The oscillator is a transcription-translation feedback loop system composed of several genes. In this paper, a scalar nonlinear differential equation with two delays, modeling the transcriptional co-regulation in mammalian circadian clock, is proposed and analyzed. Sufficient conditions are established for the asymptotic stability of the unique nontrivial positive equilibrium point of the model by studying an exponential polynomial characteristic equation with delay-dependent coefficients. The existence of the Hopf bifurcations can be also obtained. Numerical simulations of the model with proper parameter values coincide with the theoretical result.
- Circadian clock,
- delay differential equations,
- stability,
- Hopf bifurcation
Citation: Yanqin Wang, Xin Ni, Jie Yan, Ling Yang. Modeling transcriptional co-regulation of mammalian circadian clock[J]. Mathematical Biosciences and Engineering, 2017, 14(5&6): 1447-1462. doi: 10.3934/mbe.2017075

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Abstract

The circadian clock is a self-sustaining oscillator that has a period of about 24 hours at the molecular level. The oscillator is a transcription-translation feedback loop system composed of several genes. In this paper, a scalar nonlinear differential equation with two delays, modeling the transcriptional co-regulation in mammalian circadian clock, is proposed and analyzed. Sufficient conditions are established for the asymptotic stability of the unique nontrivial positive equilibrium point of the model by studying an exponential polynomial characteristic equation with delay-dependent coefficients. The existence of the Hopf bifurcations can be also obtained. Numerical simulations of the model with proper parameter values coincide with the theoretical result.

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