[C04] Systems Biology

[C04-01] Analyzing biomass transfer in autocatalytic reaction networks with delay differential equations

*Wei-Hsiang Lin¹ (1. Academia Sinica (Taiwan))

Keywords:

reaction network,delay differential equation,biomass,dynamical system,growth rate

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. To track biomass along reaction pathways, I have reformulated the n-dimensional ordinary differential equation (ODE) of the reaction network into a one-dimensional delay differential equation (DDE) encompassing 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 a rigorous estimate of growth rate upon dimensional reduction of reaction networks.