CAREER: Biochemical Reaction Systems: from Structure to Dynamics

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The project supported under this CAREER award will use the mathematics of networks to understand how living cells maintain a healthy balance of nutrients, like iron. In healthy cells, many chemical reactions take place all the time. Scientists think of these reactions as forming a network, like a wiring diagram, with connecting wires describing the movement of nutrients and metabolites through a cell's chemical reactions. Knowing the entire wiring diagram is not necessary for understanding the fate of individual nutrients, but the many interconnected circuits make it difficult to isolate only the part of the diagram important for certain activities, such as maintaining iron levels. This research will use mathematical techniques (specifically, algebraic geometry and dynamical systems) to find the simplest components in a reaction network that allow a cell to exhibit observed behaviors. Results will be tested using laboratory observations of how yeast cells manage and transport iron. Complementing the research projects will be educational activities centered around a Directed Reading Program in which undergraduate students will gain experience reading and presenting mathematics with the help of graduate-student mentors.The dynamics observed in living systems is much more than the sum of its parts. Systems biology, therefore, seeks to understand how biological components come together to generate emergent, systems-level behavior. A current bottleneck in systems biology is the lack of mathematical theory relating system structure to emergent behavior. Accordingly, this project will develop a theory of reaction systems tailored to biological networks. The investigator will build on her recent work that has helped clarify how bistability and other phenomena emerge in real-life systems. The aims here are to discover new criteria for multistationarity in reaction systems, and to answer the question of when Hopf bifurcations are preserved when new components are added to a network. These results will be used to answer important biological questions pertaining to how cells process information and how iron levels are maintained within cells. Specifically, the aims are to investigate the capacity for bistability and oscillations in phosphorylation networks, and to determine which components of iron-trafficking networks keep cellular-iron levels tightly regulated. Overall, the research will generate results well-suited to analyzing a large class of networks arising in living systems.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.