Optimal allocation of bacterial resources in fed-batch reactors

In bacteria, the mechanisms behind the allocation of resources to different cellular functions (i.e. growth or nutrient uptake) have been tuned to optimally adjust cell composition to changing environments. Simple dynamical models of bacterial growth have been key in predicting these mechanisms through a resource allocation perspective. This approach has also been applied to the production of added-value compounds, to determine how to externally adjust the cellular composition in order to maximize metabolite over biomass synthesis. This paper presents a resource allocation perspective of a fed-batch process, based on a multi-scale mechanistic model considering intracellular concentrations of the main cellular components, as well as the dynamics of the bioreactor. The model presented here is a simple coarse-grained self-replicator model of E. coli, accounting for empirical cellular trade-offs observed in previous experimental works. The problem of maximizing an added-value metabolite of interest is written as an Optimal Control problem, in terms of the internal resource allocation parameter and the feeding rate of the bioreactor. Numerical results are provided to better understand the role of cellular composition in fed-batch processing.