Modeling transcriptional co-regulation of mammalian circadian clock
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 transcri...
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| Language: | English |
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AIMS Press
2017-09-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2017075 |
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| _version_ | 1832590027790483456 |
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| author | Yanqin Wang Xin Ni Jie Yan Ling Yang |
| author_facet | Yanqin Wang Xin Ni Jie Yan Ling Yang |
| author_sort | Yanqin Wang |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-15e7da0f157c462ab18f572b7ea4c0be |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2017-09-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-15e7da0f157c462ab18f572b7ea4c0be2025-01-24T02:40:31ZengAIMS PressMathematical Biosciences and Engineering1551-00182017-09-01145&61447146210.3934/mbe.2017075Modeling transcriptional co-regulation of mammalian circadian clockYanqin Wang0Xin Ni1Jie Yan2Ling Yang3School of Mathematical Sciences, Soochow University, Suzhou 215006, Jiangsu, ChinaSchool of Mathematical Sciences, Soochow University, Suzhou 215006, Jiangsu, ChinaSchool of Mathematical Sciences, Soochow University, Suzhou 215006, Jiangsu, ChinaSchool of Mathematical Sciences, Soochow University, Suzhou 215006, Jiangsu, ChinaThe 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.https://www.aimspress.com/article/doi/10.3934/mbe.2017075circadian clockdelay differential equationsstabilityhopf bifurcation |
| spellingShingle | Yanqin Wang Xin Ni Jie Yan Ling Yang Modeling transcriptional co-regulation of mammalian circadian clock Mathematical Biosciences and Engineering circadian clock delay differential equations stability hopf bifurcation |
| title | Modeling transcriptional co-regulation of mammalian circadian clock |
| title_full | Modeling transcriptional co-regulation of mammalian circadian clock |
| title_fullStr | Modeling transcriptional co-regulation of mammalian circadian clock |
| title_full_unstemmed | Modeling transcriptional co-regulation of mammalian circadian clock |
| title_short | Modeling transcriptional co-regulation of mammalian circadian clock |
| title_sort | modeling transcriptional co regulation of mammalian circadian clock |
| topic | circadian clock delay differential equations stability hopf bifurcation |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2017075 |
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