Multi‐equilibrium property of metabolic networks: Exclusion of multi‐stability for SSN metabolic modules
Multi‐equilibrium property of metabolic networks: Exclusion of multi‐stability for SSN metabolic modules
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DOI：
10.1002/rnc.1718
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发表时间：
2011-10
影响因子：
3.9
通讯作者：
Hong-Bo Lei;Ji-feng Zhang;Luonan Chen
中科院分区：
文献类型：
--
作者：
Hong-Bo Lei;Ji-feng Zhang;Luonan Chen
代谢网络能否容纳生物体内的多重平衡是一个基本而重要的问题。由于代谢网络的复杂性，从分析和数值的角度来研究整个问题通常是一项困难的任务。本文提出了一个面向结构的模块化研究框架来分析代谢网络的多稳定性。首先根据代谢网络结构的特殊性，将其分解为四种基本模块（称为代谢模块），然后针对其中一类基本模块--无抑制的单底物单产物（SSN）模块，推导了基于Hill动力学的非线性常微分方程（ODE）模型.我们证明了ODE模型的向量场的内射性等价于其雅可比矩阵的非奇异性，这使得我们能够等价地将SSN模块的多个平衡点不存在的不可验证的充分条件转换为可验证的充分条件。此外，我们证明了这一充分条件适用于生物体中的SSN模块。这样的理论结果不仅为代谢网络建模提供了一个通用框架，而且还表明活生物体中的SSN模块不可能是多稳态的。版权所有© 2011约翰威利父子有限公司.
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 © 2011 John Wiley & Sons, Ltd.