Persistence and Permanence in Biological Interaction Networks

持久性现象是现代生物学和生物医学研究的焦点。 持久性存在于所有尺度，从分子和细胞到组织、生物体、种群和生态系统。 在细胞水平上，基因和蛋白质网络的持久性在建立稳态中起着关键作用，稳态是细胞调节关键变量的能力，因此内部条件保持相对恒定。 在细胞内水平，这些相互作用网络的节点可以是信号分子、基因和基因产物;在生态系统水平，这些节点可以是各种物种和能源。 许多疾病涉及特定类型细胞的稳态紊乱，这对应于相关相互作用网络的持续性丧失。 持久性系统的更完整的表征可能会提高对这些疾病的理解。 该项目将创建实现理解持久性的数学方法的软件，并将允许生物学家和生物医学科学家分析各种感兴趣的生物网络的持久性特性。持久性和持久性是指系统以稳健的方式将其所有变量保持在一定范围内的能力，这种能力是生物相互作用网络的最重要特征之一。为了理解特定生物相互作用所起的作用（例如，细胞中的信号传导途径），人们在试图解释正反馈和负反馈、非线性相互作用以及网络节点之间的其他复杂信号传导的影响时常常面临很大的困难。这些困难是由于非线性系统的动力学固有的复杂性。有重大的数学挑战需要克服，其研究将导致丰富的新领域的生物学洞察力以及数学理论。这个项目将分析持久性作为一个基本的理论概念，贯穿生物复杂性的水平。数学和计算工具将被开发来理解一般生物相互作用网络中的持久性。作为这方面的一个具体步骤，该项目将侧重于生物化学网络，目的是提供数学工具，用于绘制反应网络结构与其持久性之间的精确联系。这些工具将适用于复杂的网络，并将能够区分非常相似的网络，但具有相当不同的持久性能力。

The phenomenon of persistence is the focus of much modern biological and biomedical research. Persistence is found at all scales, from the molecular and cellular, to tissues, organisms, populations, and ecosystems. At the cellular level, persistence in gene and protein networks plays a key role in the establishment of homeostasis, which is the ability of the cell to regulate key variables, so that internal conditions remain relatively constant. At the intracellular level, the nodes of these interaction networks could be signaling molecules, genes, and gene products; at the ecosystem level, the nodes could be the various species and energy resources. Many diseases involve a disturbance of homeostasis in specific types of cells, which corresponds to a loss of persistence in the associated interaction networks. A more complete characterization of persistent systems may improve the understanding of these diseases. This project will create software that implements mathematical methods for understanding persistence, and will allow biologists and biomedical scientists to analyze persistence properties of diverse biological networks of interest. Persistence and permanence refer to the capacity of a system to maintain all of its variables within some fixed limits in a robust way, and this capacity is one of the most important features of biological interaction networks. In order to understand the role played by specific biological interactions (e.g., a signaling pathway in a cell), one often faces great difficulties in trying to interpret the effect of positive and negative feedbacks, nonlinear interactions, and other complex signaling between the nodes of the network. These difficulties are due to the inherent complexity of the dynamics of nonlinear systems. There are significant mathematical challenges to be overcome, whose study will lead to rich new areas of biological insight as well as mathematical theory. This project will analyze persistence as a fundamental theoretical concept that traverses levels of biological complexity. Mathematical and computational tools will be developed to understand persistence in general biological interaction networks. As a concrete step in that direction, this project will focus on biochemical networks, with the aim to provide mathematical tools for drawing precise connections between reaction network structure and its persistence properties. These tools will be applicable to complex networks, and will be able to distinguish between very similar networks having rather different capacities for persistence.