多输入节点网络的稳态与细菌趋化性中的鲁棒性
Homeostasis in Networks with Multiple Input Nodes and Robustness in Bacterial Chemotaxis
AI总结：
本文将输入-输出网络的稳态分析理论扩展至多输入节点情形，发现新的输入配重稳态机制，并应用于大肠杆菌趋化性模型，同时基于通有性定义了稳态鲁棒性。
摘要：
当生物系统中存在一个被调控的量维持在狭窄数值范围内时，该系统即实现了稳态。本文将稳态视为一种网络动力学现象。在此背景下，我们改进了一种用于分析具有明确输入和输出节点的网络动力系统（称为“输入-输出网络”）中稳态的通用理论。该理论能够以“模型无关”的方式定义给定网络的“稳态类型”，即分类取决于网络拓扑而非具体的模型方程。每种“稳态类型”代表一种产生稳态的可能机制，并与原始网络的一个特定“子网基序”相关联。本文的贡献是将该理论扩展到多输入节点的网络情况。为展示我们的理论，我们将其应用于细菌趋化性——这是生化系统中稳态的典型范例。通过研究大肠杆菌（Escherichia coli）趋化性的一个代表性模型，我们验证了其对应的抽象网络具有多个输入节点。这表明我们对理论的扩展能够纳入此前无法覆盖的一类重要模型。此外，从我们的抽象视角来看，所研究模型中稳态的出现由一种新机制引起，我们称之为输入配重稳态（input counterweight homeostasis）。这种新的稳态机制是在我们的研究过程中发现的，由网络多个输入节点之间的平衡作用产生——因此，它的发生需要至少存在两个输入节点。最后，本文建立的框架能够基于动力系统理论中的“通有性”概念，形式化定义稳态的“鲁棒性”概念。我们讨论了这种稳态鲁棒性在趋化性模型中的表现形式。
英文摘要：
A biological system achieve homeostasis when there is a regulated quantity that is maintained within a narrow range of values. Here we consider homeostasis as a phenomenon of network dynamics. In this context, we improve a general theory for the analysis of homeostasis in network dynamical systems with distinguished input and output nodes, called `input-output networks'. The theory allows one to define `homeostasis types' of a given network in a `model independent' fashion, in the sense that the classification depends on the network topology rather than on the specific model equations. Each `homeostasis type' represents a possible mechanism for generating homeostasis and is associated with a suitable `subnetwork motif' of the original network. Our contribution is an extension of the theory to the case of networks with multiple input nodes. To showcase our theory, we apply it to bacterial chemotaxis, a paradigm for homeostasis in biochemical systems. By considering a representative model of Escherichia coli chemotaxis, we verify that the corresponding abstract network has multiple input nodes. Thus showing that our extension of the theory allows for the inclusion of an important class of models that were previously out of reach. Moreover, from our abstract point of view, the occurrence of homeostasis in the studied model is caused by a new mechanism, called input counterweight homeostasis. This new homeostasis mechanism was discovered in the course of our investigation and is generated by a balancing between the several input nodes of the network -- therefore, it requires the existence of at least two input nodes to occur. Finally, the framework developed here allows one to formalize a notion of `robustness' of homeostasis based on the concept of `genericity' from the theory dynamical systems. We discuss how this kind of robustness of homeostasis appears in the chemotaxis model.
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