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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Main Authors: Maria Conceição A. Leite, Yunjiao Wang
Format: Article
Language:English
Published: AIMS Press 2009-12-01
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.
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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