Theoretical investigation on models of circadian rhythms based on dimerization and proteolysis of PER and TIM
Circadian rhythms of physiology and behavior are widespread\break mechanisms in many organisms. The internal biological rhythms are driven by molecular clocks, which oscillate with a period nearly but not exactly $24$ hours. Many classic models of circadian rhythms are based on a time-delayed negati...
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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.2017064 |
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| author | Jifa Jiang Qiang Liu Lei Niu |
| author_facet | Jifa Jiang Qiang Liu Lei Niu |
| author_sort | Jifa Jiang |
| collection | DOAJ |
| description | Circadian rhythms of physiology and behavior are widespread\break mechanisms in many organisms. The internal biological rhythms are driven by molecular clocks, which oscillate with a period nearly but not exactly $24$ hours. Many classic models of circadian rhythms are based on a time-delayed negative feedback, suggested by the protein products inhibiting transcription of their own genes. In 1999, based on stabilization of PER upon dimerization, Tyson et al. [J. J. Tyson, C. I. Hong, C. D. Thron, B. Novak, Biophys. J. 77 (1999) 2411-2417] proposed a crucial positive feedback to the circadian oscillator. This idea was mathematically expressed in a three-dimensional model. By imposing assumptions that the dimerization reactions were fast and dimeric proteins were in rapid equilibrium, they reduced the model to a pair of nonlinear ordinary differential equations of mRNA and total protein concentrations. Then they used phase plane analysis tools to investigate circadian rhythms. In this paper, the original three-dimensional model is studied. We explore the existence of oscillations and their periods. Much attention is paid to investigate how the periods depend on model parameters. The numerical simulations are in good agreement with their reduced work. |
| format | Article |
| id | doaj-art-83d18bbedb6f4cbeb943075b3d1b5aa0 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2017-09-01 |
| publisher | AIMS Press |
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| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-83d18bbedb6f4cbeb943075b3d1b5aa02025-01-24T02:40:31ZengAIMS PressMathematical Biosciences and Engineering1551-00182017-09-01145&61247125910.3934/mbe.2017064Theoretical investigation on models of circadian rhythms based on dimerization and proteolysis of PER and TIMJifa Jiang0Qiang Liu1Lei Niu2Mathematics and Science College, Shanghai Normal University, Shanghai 200234, ChinaDepartment of Mathematics, University of Science and Technology of China, Hefei 230026, ChinaMathematics and Science College, Shanghai Normal University, Shanghai 200234, ChinaCircadian rhythms of physiology and behavior are widespread\break mechanisms in many organisms. The internal biological rhythms are driven by molecular clocks, which oscillate with a period nearly but not exactly $24$ hours. Many classic models of circadian rhythms are based on a time-delayed negative feedback, suggested by the protein products inhibiting transcription of their own genes. In 1999, based on stabilization of PER upon dimerization, Tyson et al. [J. J. Tyson, C. I. Hong, C. D. Thron, B. Novak, Biophys. J. 77 (1999) 2411-2417] proposed a crucial positive feedback to the circadian oscillator. This idea was mathematically expressed in a three-dimensional model. By imposing assumptions that the dimerization reactions were fast and dimeric proteins were in rapid equilibrium, they reduced the model to a pair of nonlinear ordinary differential equations of mRNA and total protein concentrations. Then they used phase plane analysis tools to investigate circadian rhythms. In this paper, the original three-dimensional model is studied. We explore the existence of oscillations and their periods. Much attention is paid to investigate how the periods depend on model parameters. The numerical simulations are in good agreement with their reduced work.https://www.aimspress.com/article/doi/10.3934/mbe.2017064circadian rhythmpositive feedbacksteady statelimit cycleperiod |
| spellingShingle | Jifa Jiang Qiang Liu Lei Niu Theoretical investigation on models of circadian rhythms based on dimerization and proteolysis of PER and TIM Mathematical Biosciences and Engineering circadian rhythm positive feedback steady state limit cycle period |
| title | Theoretical investigation on models of circadian rhythms based on dimerization and proteolysis of PER and TIM |
| title_full | Theoretical investigation on models of circadian rhythms based on dimerization and proteolysis of PER and TIM |
| title_fullStr | Theoretical investigation on models of circadian rhythms based on dimerization and proteolysis of PER and TIM |
| title_full_unstemmed | Theoretical investigation on models of circadian rhythms based on dimerization and proteolysis of PER and TIM |
| title_short | Theoretical investigation on models of circadian rhythms based on dimerization and proteolysis of PER and TIM |
| title_sort | theoretical investigation on models of circadian rhythms based on dimerization and proteolysis of per and tim |
| topic | circadian rhythm positive feedback steady state limit cycle period |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2017064 |
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