Abstract
Biological systems are governed by coupled interactions between intracellular metabolism and bioreactor operation that span multiple time scales. Constraint-based metabolic models are widely used to describe intracellular metabolism, but repeatedly solving the optimization problem at each time step in dynamic models introduces numerical challenges related to infeasibility and computational efficiency. This work presents a multi-scale modeling framework that integrates genome-scale, constraint-based metabolic models with dynamic bioreactor simulations. Intracellular metabolism is described using positive flux variables in a parsimonious flux balance analysis, and the resulting embedded optimization problem is replaced by a neural network surrogate. The surrogate provides a smooth approximation of the embedded optimization mapping and eliminates repeated linear program solves during simulation. The approach is demonstrated for fed-batch fermentation of Escherichia coli, in which the surrogate model yields intracellular fluxes under substrate-limited conditions, whereas the underlying linear program would otherwise be infeasible. The framework provides a continuous representation of intracellular metabolism suitable for dynamic simulation of genome-scale models in bioreactor configurations.