Multi-equilibrium property of metabolic networks: Exclusion of multi-stability for SSN metabolic modules

doi:10.1002/rnc.1718

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	Multi-equilibrium property of metabolic networks: Exclusion of multi-stability for SSN metabolic modules
	Lei, Hong-Bo 1; Zhang, Ji-Feng1 ; Chen, Luonan 2
刊名	INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL
	2011-10-01
卷号	21 期号:15 页码:1791-1806
关键词	metabolic network multiple equilibria multi-stability SSN module
ISSN号	1049-8923
DOI	10.1002/rnc.1718
英文摘要	It is a fundamental and important problem whether or not a metabolic network can admit multiple equilibria in a living organism. Due to the complexity of the metabolic network, it is generally a difficult task to study the problem as a whole from both analytical and numerical viewpoints. In this paper, a structure-oriented modularization research framework is proposed to analyze the multi-stability of metabolic networks. We first decompose a metabolic network into four types of basic building blocks (called metabolic modules) according to the particularity of its structure, and then focus on one type of these basic building blocks-the single substrate and single product with no inhibition (SSN) module, by deriving a nonlinear ordinary differential equation (ODE) model based on the Hill kinetics. We show that the injectivity of the vector field of the ODE model is equivalent to the nonsingularity of its Jacobian matrix, which enables us equivalently to convert an unverifiable sufficient condition for the absence of multiple equilibria of an SSN module into a verifiable one. Moreover, we prove that this sufficient condition holds for the SSN module in a living organism. Such a theoretical result not only provides a general framework for modeling metabolic networks, but also shows that the SSN module in a living organism cannot be multi-stable. Copyright (C) 2011 John Wiley & Sons, Ltd.
资助项目	National Natural Science Foundation of China[60821091] ; National Natural Science Foundation of China[61072149] ; National Natural Science Foundation of China[91029301]
WOS研究方向	Automation & Control Systems ; Engineering ; Mathematics
语种	英语
出版者	WILEY-BLACKWELL
WOS记录号	WOS:000295374100006
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/11329]
专题	系统科学研究所
通讯作者	Zhang, Ji-Feng
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, Key Lab Syst & Control, Beijing 100190, Peoples R China 2.Chinese Acad Sci, Shanghai Inst Biol Sci, Key Lab Syst Biol, Shanghai 200031, Peoples R China
推荐引用方式 GB/T 7714	Lei, Hong-Bo,Zhang, Ji-Feng,Chen, Luonan. Multi-equilibrium property of metabolic networks: Exclusion of multi-stability for SSN metabolic modules[J]. INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL,2011,21(15):1791-1806.
APA	Lei, Hong-Bo,Zhang, Ji-Feng,&Chen, Luonan.(2011).Multi-equilibrium property of metabolic networks: Exclusion of multi-stability for SSN metabolic modules.INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL,21(15),1791-1806.
MLA	Lei, Hong-Bo,et al."Multi-equilibrium property of metabolic networks: Exclusion of multi-stability for SSN metabolic modules".INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL 21.15(2011):1791-1806.