Revealing Structure via Dynamics: Biological Networks from Protein Folding to Food Webs

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A principal goal of biological theory is to understand complex living systems in terms of their parts and the interactions between their parts. In this project, an ecologist, a protein physiologist and a mathematician will collaborate to develop new ways of understanding how highly interconnected biological systems change through time. Specifically, these investigators aim to develop a general theory of linear dynamics on complex biological networks. Surprisingly, a great variety of critically important biological phenomena at a wide range of scales is captured by linear or approximately linear dynamics on complex networks. By applying novel methods for coarse graining biological networks, this project will answer questions such as: how many functionally distinct moving parts does a given system have? How do quantities of interest, such as nutrients or information, move through a highly interconnected network? Which nodes or edges in such a network are the most important for transmission? Can we identify nodes whose removal has the greatest or smallest effect on the performance of the network?Developing a framework for general linear dynamics on complex biological networks will have a broad and deep impact on our ability to understand, predict and control critically important biological processes at a wide range of scales. In addition, this project will contribute to training students at the undergraduate, graduate and postdoctoral level to work across disciplines such as ecology, physiology and mathematics to deepen our understanding of complex biological systems.