Open AccessModeling transcriptional co-regulation of mammalian circadian clock
Author(s) -
Yanqin Wang,
Xin Ni,
Jie Yan,
Ling Yang
Publication year - 2017
Publication title -
mathematical biosciences and engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.451
H-Index - 45
eISSN - 1551-0018
pISSN - 1547-1063
DOI - 10.3934/mbe.2017075
Subject(s) - circadian clock , scalar (mathematics) , control theory (sociology) , negative feedback , mathematics , nonlinear system , equilibrium point , exponential stability , differential equation , van der pol oscillator , polynomial , delay differential equation , circadian rhythm , mathematical analysis , physics , biology , computer science , neuroscience , quantum mechanics , geometry , control (management) , voltage , artificial intelligence
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.