输入-输出网络中的平衡:结构、分类和应用

Fernando Antoneli, Martin Golubitsky, Jiaxin Jin, Ian Stewart
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引用次数: 0

摘要

稳态与生物系统中存在的调节机制有关,在这种机制下,当某种外部干扰影响系统时,某些特定变量会保持在接近设定值的范围内。在数学上,"稳态 "的概念可以用输入-输出函数来正式表述,该函数将代表外部干扰的参数映射到输出变量,而输出变量必须保持在一个相当窄的范围内。这一观察结果启发了无穷小平衡概念的引入,即输入-输出函数的导数在一个孤立点为零。从这个角度出发,我们可以应用奇点理论的方法来描述无穷小平衡点(即输入-输出函数的临界点)。在本文中,我们回顾了研究输入-输出网络中的恒定点的无限小方法。输入-输出网络是一个具有两个不同节点 "输入 "和 "输出 "的网络,网络的动态决定了系统相应的输入-输出功能。此外,这种方法与组合矩阵理论中的图论思想相结合,为从网络拓扑角度对输入-输出网络中不同类型的稳态(稳态机制)进行分类提供了系统的方法。反过来,这又产生了新的数学概念,如同态子网络、同态模式、同态模式交互。我们以生化网络、化学反应网络 (CRN)、基因调控网络 (GRN)、细胞内金属离子调控等几个生物学实例说明了这一理论的实用性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Homeostasis in Input-Output Networks: Structure, Classification and Applications
Homeostasis is concerned with regulatory mechanisms, present in biological systems, where some specific variable is kept close to a set value as some external disturbance affects the system. Mathematically, the notion of homeostasis can be formalized in terms of an input-output function that maps the parameter representing the external disturbance to the output variable that must be kept within a fairly narrow range. This observation inspired the introduction of the notion of infinitesimal homeostasis, namely, the derivative of the input-output function is zero at an isolated point. This point of view allows for the application of methods from singularity theory to characterize infinitesimal homeostasis points (i.e. critical points of the input-output function). In this paper we review the infinitesimal approach to the study of homeostasis in input-output networks. An input-output network is a network with two distinguished nodes `input' and `output', and the dynamics of the network determines the corresponding input-output function of the system. This class of dynamical systems provides an appropriate framework to study homeostasis and several important biological systems can be formulated in this context. Moreover, this approach, coupled to graph-theoretic ideas from combinatorial matrix theory, provides a systematic way for classifying different types of homeostasis (homeostatic mechanisms) in input-output networks, in terms of the network topology. In turn, this leads to new mathematical concepts, such as, homeostasis subnetworks, homeostasis patterns, homeostasis mode interaction. We illustrate the usefulness of this theory with several biological examples: biochemical networks, chemical reaction networks (CRN), gene regulatory networks (GRN), Intracellular metal ion regulation and so on.
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