Multistability, oscillations and bifurcations in feedback loops
Feedback loops are found to be important network structures inregulatory networks of biological signaling systems because they areresponsible for maintaining normal cellular activity. Recently,the functions of feedback loops have received extensive attention.The existing results in the literature...
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| Format: | Article |
| Language: | English |
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AIMS Press
2009-12-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2010.7.83 |
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| author | Maria Conceição A. Leite Yunjiao Wang |
| author_facet | Maria Conceição A. Leite Yunjiao Wang |
| author_sort | Maria Conceição A. Leite |
| collection | DOAJ |
| description | Feedback loops are found to be important network structures inregulatory networks of biological signaling systems because they areresponsible for maintaining normal cellular activity. Recently,the functions of feedback loops have received extensive attention.The existing results in the literature mainly focus on verifyingthat negative feedback loops are responsible for oscillations,positive feedback loops for multistability, and coupled feedbackloops for the combined dynamics observed in their individual loops.In this work, we develop a general framework for studying systematicallyfunctions of feedback loops networks. We investigate the generaldynamics of all networks with one to three nodes and one to two feedback loops. Interestingly, our results are consistent with Thomas' conjectures although we assume each node in the network undergoes a decay, which corresponds to a negative loop in Thomas' setting. Besides studying how network structures influence dynamics at the linear level, we explore thepossibility of network structures having impact on the nonlineardynamical behavior by using Lyapunov-Schmidt reduction and singularity theory. |
| format | Article |
| id | doaj-art-2c0934e0c2be421790337132b3219e4c |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2009-12-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-2c0934e0c2be421790337132b3219e4c2025-01-24T02:00:16ZengAIMS PressMathematical Biosciences and Engineering1551-00182009-12-0171839710.3934/mbe.2010.7.83Multistability, oscillations and bifurcations in feedback loopsMaria Conceição A. Leite0Yunjiao Wang1Department of Mathematics, University of Oklahoma, Norman, OK 73019-0315Department of Mathematics, University of Oklahoma, Norman, OK 73019-0315Feedback loops are found to be important network structures inregulatory networks of biological signaling systems because they areresponsible for maintaining normal cellular activity. Recently,the functions of feedback loops have received extensive attention.The existing results in the literature mainly focus on verifyingthat negative feedback loops are responsible for oscillations,positive feedback loops for multistability, and coupled feedbackloops for the combined dynamics observed in their individual loops.In this work, we develop a general framework for studying systematicallyfunctions of feedback loops networks. We investigate the generaldynamics of all networks with one to three nodes and one to two feedback loops. Interestingly, our results are consistent with Thomas' conjectures although we assume each node in the network undergoes a decay, which corresponds to a negative loop in Thomas' setting. Besides studying how network structures influence dynamics at the linear level, we explore thepossibility of network structures having impact on the nonlineardynamical behavior by using Lyapunov-Schmidt reduction and singularity theory.https://www.aimspress.com/article/doi/10.3934/mbe.2010.7.83oscillationscoupled feedback loopstranscriptional regulatory networksbifurcation.multistability |
| spellingShingle | Maria Conceição A. Leite Yunjiao Wang Multistability, oscillations and bifurcations in feedback loops Mathematical Biosciences and Engineering oscillations coupled feedback loops transcriptional regulatory networks bifurcation. multistability |
| title | Multistability, oscillations and bifurcations in feedback loops |
| title_full | Multistability, oscillations and bifurcations in feedback loops |
| title_fullStr | Multistability, oscillations and bifurcations in feedback loops |
| title_full_unstemmed | Multistability, oscillations and bifurcations in feedback loops |
| title_short | Multistability, oscillations and bifurcations in feedback loops |
| title_sort | multistability oscillations and bifurcations in feedback loops |
| topic | oscillations coupled feedback loops transcriptional regulatory networks bifurcation. multistability |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2010.7.83 |
| work_keys_str_mv | AT mariaconceicaoaleite multistabilityoscillationsandbifurcationsinfeedbackloops AT yunjiaowang multistabilityoscillationsandbifurcationsinfeedbackloops |