Mostly Biomathematics Lunchtime Seminar

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Biomass transfer on growing reaction networks: a delay differential equation formulation

Speaker: Wei-Hsiang Lin, Institute of Molecular Biology, Academia Sinica, Taiwan

Location: Warren Weaver Hall 1314

Date: Tuesday, April 22, 2025, 12:45 p.m.

Synopsis:

For a biological system to grow and expand, mass must be transferred from the environment to the system and be assimilated into its reaction network. Here, I characterize the biomass transfer process for growing autocatalytic systems. By tracking biomass along reaction pathways, an n-dimensional ordinary differential equation (ODE) of the reaction network can be reformulated into a one-dimensional delay differential equation (DDE) for its long-term dynamics. The kernel function of the DDE summarizes the overall amplification and transfer delay of the system and serves as a signature for autocatalysis dynamics. The DDE formulation allows reaction networks of various topologies and complexities to be compared and provides rigorous estimation scheme for growth rate upon dimensional reduction of reaction networks.