Robust Persistence and Permanence in Biological Interaction Networks

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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.