Chaotic motifs in gene regulatory networks.

Chaos should occur often in gene regulatory networks (GRNs) which have been widely described by nonlinear coupled ordinary differential equations, if their dimensions are no less than 3. It is therefore puzzling that chaos has never been reported in GRNs in nature and is also extremely rare in model...

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Autores principales:	Zhaoyang Zhang, Weiming Ye, Yu Qian, Zhigang Zheng, Xuhui Huang, Gang Hu
Formato:	article
Lenguaje:	EN
Publicado:	Public Library of Science (PLoS) 2012
Materias:	Medicine R Science Q
Acceso en línea:	https://doaj.org/article/ce7a3c1897a54395a1dc40669623fd02
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spelling	oai:doaj.org-article:ce7a3c1897a54395a1dc40669623fd022021-11-18T07:13:18ZChaotic motifs in gene regulatory networks.1932-620310.1371/journal.pone.0039355https://doaj.org/article/ce7a3c1897a54395a1dc40669623fd022012-01-01T00:00:00Zhttps://www.ncbi.nlm.nih.gov/pmc/articles/pmid/22792171/pdf/?tool=EBIhttps://doaj.org/toc/1932-6203Chaos should occur often in gene regulatory networks (GRNs) which have been widely described by nonlinear coupled ordinary differential equations, if their dimensions are no less than 3. It is therefore puzzling that chaos has never been reported in GRNs in nature and is also extremely rare in models of GRNs. On the other hand, the topic of motifs has attracted great attention in studying biological networks, and network motifs are suggested to be elementary building blocks that carry out some key functions in the network. In this paper, chaotic motifs (subnetworks with chaos) in GRNs are systematically investigated. The conclusion is that: (i) chaos can only appear through competitions between different oscillatory modes with rivaling intensities. Conditions required for chaotic GRNs are found to be very strict, which make chaotic GRNs extremely rare. (ii) Chaotic motifs are explored as the simplest few-node structures capable of producing chaos, and serve as the intrinsic source of chaos of random few-node GRNs. Several optimal motifs causing chaos with atypically high probability are figured out. (iii) Moreover, we discovered that a number of special oscillators can never produce chaos. These structures bring some advantages on rhythmic functions and may help us understand the robustness of diverse biological rhythms. (iv) The methods of dominant phase-advanced driving (DPAD) and DPAD time fraction are proposed to quantitatively identify chaotic motifs and to explain the origin of chaotic behaviors in GRNs.Zhaoyang ZhangWeiming YeYu QianZhigang ZhengXuhui HuangGang HuPublic Library of Science (PLoS)articleMedicineRScienceQENPLoS ONE, Vol 7, Iss 7, p e39355 (2012)
institution	DOAJ
collection	DOAJ
language	EN
topic	Medicine R Science Q
spellingShingle	Medicine R Science Q Zhaoyang Zhang Weiming Ye Yu Qian Zhigang Zheng Xuhui Huang Gang Hu Chaotic motifs in gene regulatory networks.
description	Chaos should occur often in gene regulatory networks (GRNs) which have been widely described by nonlinear coupled ordinary differential equations, if their dimensions are no less than 3. It is therefore puzzling that chaos has never been reported in GRNs in nature and is also extremely rare in models of GRNs. On the other hand, the topic of motifs has attracted great attention in studying biological networks, and network motifs are suggested to be elementary building blocks that carry out some key functions in the network. In this paper, chaotic motifs (subnetworks with chaos) in GRNs are systematically investigated. The conclusion is that: (i) chaos can only appear through competitions between different oscillatory modes with rivaling intensities. Conditions required for chaotic GRNs are found to be very strict, which make chaotic GRNs extremely rare. (ii) Chaotic motifs are explored as the simplest few-node structures capable of producing chaos, and serve as the intrinsic source of chaos of random few-node GRNs. Several optimal motifs causing chaos with atypically high probability are figured out. (iii) Moreover, we discovered that a number of special oscillators can never produce chaos. These structures bring some advantages on rhythmic functions and may help us understand the robustness of diverse biological rhythms. (iv) The methods of dominant phase-advanced driving (DPAD) and DPAD time fraction are proposed to quantitatively identify chaotic motifs and to explain the origin of chaotic behaviors in GRNs.
format	article
author	Zhaoyang Zhang Weiming Ye Yu Qian Zhigang Zheng Xuhui Huang Gang Hu
author_facet	Zhaoyang Zhang Weiming Ye Yu Qian Zhigang Zheng Xuhui Huang Gang Hu
author_sort	Zhaoyang Zhang
title	Chaotic motifs in gene regulatory networks.
title_short	Chaotic motifs in gene regulatory networks.
title_full	Chaotic motifs in gene regulatory networks.
title_fullStr	Chaotic motifs in gene regulatory networks.
title_full_unstemmed	Chaotic motifs in gene regulatory networks.
title_sort	chaotic motifs in gene regulatory networks.
publisher	Public Library of Science (PLoS)
publishDate	2012
url	https://doaj.org/article/ce7a3c1897a54395a1dc40669623fd02
work_keys_str_mv	AT zhaoyangzhang chaoticmotifsingeneregulatorynetworks AT weimingye chaoticmotifsingeneregulatorynetworks AT yuqian chaoticmotifsingeneregulatorynetworks AT zhigangzheng chaoticmotifsingeneregulatorynetworks AT xuhuihuang chaoticmotifsingeneregulatorynetworks AT ganghu chaoticmotifsingeneregulatorynetworks
_version_	1718423817534046208

Chaotic motifs in gene regulatory networks.

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