Robust 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，在所有尺度上都可以发现，从分子和细胞到组织，有机体，种群和生态系统。 例如，在细胞水平上，基因和蛋白质网络的持久性在稳态的建立中起着关键作用，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。在这个项目中，研究人员的目标是创建算法，实现分析持久性的数学方法，这将使生物学家和生物医学科学家能够研究各种感兴趣的生物网络的持久性。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将提高我们对这些疾病的理解。持久性和永久性是指系统以稳健的方式将所有变量保持在某些固定限制内的能力;它们是生物相互作用网络的关键特征之一。在理解特定生物相互作用所起的作用（例如，细胞中信号通路的作用，或在生态系统中引入外来物种的影响）时，通常很难解释正反馈和负反馈的影响，非线性相互作用，以及网络节点之间的其他复杂信号。这些困难是由于非线性系统的动力学固有的复杂性。该项目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，旨在开发数学和计算工具，以了解一般生物相互作用网络中的持久性。作为这一方向的具体步骤，研究人员将专注于生物化学网络，目的是提供数学工具，用于绘制反应网络的结构与其相关动力系统的持久性属性之间的精确联系。该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

The phenomenon of persistence is the focus of much modern biological and biomedical research, and is found at all scales, from the molecular and cellular, to tissues, organisms, populations, and ecosystems. For example, 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. In this project, the investigator aims to create algorithms that implement mathematical methods for analyzing persistence, which will allow biologists and biomedical scientists to investigate persistence properties of diverse biological networks of interest. 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 will improve our understanding of these diseases. Persistence and permanence refer to the capacity of a system to maintain all its variables within some fixed limits in a robust way; they are among the key features of biological interaction networks. In understanding the role played by specific biological interactions (for example, the role of a signaling pathway in a cell, or the effect of introducing a foreign species in an ecosystem), there are often difficulties in interpreting 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. This project analyzes persistence as a fundamental theoretical concept that traverses levels of biological complexity and aims to develop mathematical and computational tools to understand persistence in general biological interaction networks. As a concrete step in that direction, the investigator will focus on biochemical networks, with the aim to provide mathematical tools for drawing precise connections between the structure of a reaction network and the persistence properties of its associated dynamical system.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.