The structure of infinitesimal homeostasis in input-output networks.
The structure of infinitesimal homeostasis in input-output networks.
复制标题
输入输出网络中无穷小稳态的结构。
DOI：
10.1007/s00285-021-01614-1
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发表时间：
2021-05-21
影响因子：
1.9
通讯作者：
Golubitsky M
中科院分区：
文献类型：
--
作者：
Wang Y;Huang Z;Antoneli F;Golubitsky M
动态平衡是指系统的输出随输入的变化而大致不变的现象。动态平衡经常发生在生化网络和其他相互作用的元素网络中，在这些网络中，数学模型基于与网络相关的微分方程。这些网络可以抽象为具有不同的输入节点、不同的输出节点和多个调节节点的有向图。在这些模型中，投入产出图由一个稳定的平衡点定义。稳定性意味着每一个近处都有一个稳定的平衡，而无穷小的动态平衡发生在什么时候。我们证明了存在一个动态阵，当且仅当。我们注意到H中的项是线性化耦合，并且是这些项中的齐次多项式。我们使用组合矩阵理论来分解多项式，从而确定与每个有向图相关联的不同类型的可能的自稳的菜单。具体地说，我们证明了每个因子对应于的一个子网络。这些因素分为两个组合定义的类别：结构性和附着性。结构因素对应于前馈主旨，附件因素对应于反馈主旨。最后，我们发现了一种算法，可以在不对模型方程进行数值模拟的情况下确定与每个因素对应的动态子网络基序。该算法允许我们对低度因素进行分类。有两种类型的一阶动态平衡(负反馈环路和动力学或霍尔丹模体)和两种类型的二阶动态平衡(前馈环路和一个二阶附属物模体)。
Homeostasis refers to a phenomenon whereby the output of a system is approximately constant on variation of an input . Homeostasis occurs frequently in biochemical networks and in other networks of interacting elements where mathematical models are based on differential equations associated to the network. These networks can be abstracted as digraphs with a distinguished input node , a different distinguished output node o, and a number of regulatory nodes . In these models the input–output map is defined by a stable equilibrium at . Stability implies that there is a stable equilibrium for each near and infinitesimal homeostasis occurs at when . We show that there is an homeostasis matrix for which if and only if . We note that the entries in H are linearized couplings and is a homogeneous polynomial of degree in these entries. We use combinatorial matrix theory to factor the polynomial and thereby determine a menu of different types of possible homeostasis associated with each digraph . Specifically, we prove that each factor corresponds to a subnetwork of . The factors divide into two combinatorially defined classes: structural and appendage. Structural factors correspond to feedforward motifs and appendage factors correspond to feedback motifs. Finally, we discover an algorithm for determining the homeostasis subnetwork motif corresponding to each factor of without performing numerical simulations on model equations. The algorithm allows us to classify low degree factors of . There are two types of degree 1 homeostasis (negative feedback loops and kinetic or Haldane motifs) and there are two types of degree 2 homeostasis (feedforward loops and a degree two appendage motif).
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影响因子：
5.4
作者：
Nijhout HF;Best JA;Reed MC
通讯作者：
Reed MC
DOI：
10.1090/s0273-0979-06-01108-6
发表时间：
2006-01-01
影响因子：
1.3
作者：
Golubitsky, Martin;Stewart, Ian
通讯作者：
Stewart, Ian
影响因子：
64.8
作者：
Aoki, Stephanie K.;Lillacci, Gabriele;Khammash, Mustafa
通讯作者：
Khammash, Mustafa
影响因子：
4.3
作者：
Nijhout, H. Frederik;Best, Janet;Reed, Michael C.
通讯作者：
Reed, Michael C.
影响因子：
64.5
作者：
Ma W;Trusina A;El-Samad H;Lim WA;Tang C
通讯作者：
Tang C