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Mathematical Biosciences and Engineering (MBE)
 

Modeling transcriptional co-regulation of mammalian circadian clock

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

 
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Yanqin Wang - School of Mathematical Sciences, Soochow University, Suzhou 215006, Jiangsu, China (email)
Xin Ni - School of Mathematical Sciences, Soochow University, Suzhou 215006, Jiangsu, China (email)
Jie Yan - School of Mathematical Sciences, Soochow University, Suzhou 215006, Jiangsu, China (email)
Ling Yang - School of Mathematical Sciences, Soochow University, Suzhou 215006, Jiangsu, China (email)

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.

Keywords:  Circadian clock, delay differential equations, stability, Hopf bifurcation.
Mathematics Subject Classification:  Primary: 34D99; Secondary: 34C23.

Received: May 2016;      Accepted: January 2017;      Available Online: May 2017.

 References