Biomass transfer on autocatalytic reaction network: a delay differential equation formulation

Abstract

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 track 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.