Robust Persistence and Permanence in Biological Interaction Networks

持久性和持久性指的是系统以稳健的方式将其所有变量保持在固定范围内的能力。这一现象是许多现代生物学和生物医学研究的焦点，从分子和细胞到组织、有机体、种群和生态系统，都有这种现象。例如，在细胞水平上，基因和蛋白质网络的持续性在建立动态平衡方面起着关键作用，动态平衡是细胞调节关键变量的能力，从而使内部条件保持相对恒定。例如，在人口动态层面上的持久性在传染病的传播中发挥了作用。该项目旨在开发用于分析持续性的新的数学方法和计算算法。这将使生物学家和生物医学科学家能够更好地研究感兴趣的各种生物网络的持久性属性。对持久系统进行更全面的描述，将有助于我们更好地了解传染病成为地方性疾病的条件，以及可能导致其灭绝的变化。该项目通过参与研究来培养本科生和研究生。持久性是生物相互作用网络最重要的特征之一。由于网络节点之间的正负反馈、非线性相互作用和其他复杂的信号传递，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)可能是具有挑战性的。这些挑战是由于非线性系统动力学的内在复杂性造成的。这个项目将分析持久性作为一个基本的理论概念，它遍历了生物复杂性的水平，并将开发数学和计算工具来理解一般生物相互作用网络中的持久性。该项目将特别关注种群动力学模型，目的是提供数学和计算工具，以绘制种群之间相互作用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智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

Persistence and permanence refer to the capacity of a system to maintain all its variables within fixed limits in a robust way. The phenomenon 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. Persistence at the population-dynamics level plays a role, for example, in the spread of infectious disease. This project aims to develop new mathematical methods and computational algorithms for analyzing persistence. This will allow biologists and biomedical scientists to better investigate persistence properties of diverse biological networks of interest. A more complete characterization of persistent systems will improve our understanding of the conditions that allow an infectious disease to become endemic and of the changes that may drive it to extinction. The project involves training of undergraduate and graduate students through involvement in the research.Persistence is one of the most important features of biological interaction networks. 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) can be challenging due to positive and negative feedbacks, nonlinear interactions, and other complex signaling between the nodes of the network. These challenges are due to the inherent complexity of the dynamics of nonlinear systems. This project will analyze persistence as a fundamental theoretical concept that traverses levels of biological complexity and will develop mathematical and computational tools to understand persistence in general biological interaction networks. The project will especially focus on population dynamics models, with the aim to provide mathematical and computational tools for drawing precise connections between the structure of the network of interactions between populations 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.