Robust Persistence and Permanence in Biological Interaction Networks

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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.