Mathematical Biosciences and Engineering (Oct 2020)
Optimal bacterial resource allocation: metabolite production in continuous bioreactors
Abstract
We show novel results addressing the problem of synthesizing a metabolite of interest in continuous bioreactors through resource allocation control. Our approach is based on a coarse-grained self-replicator dynamical model that accounts for microbial culture growth inside the bioreactor, and incorporates a synthetic growth switch that allows to externally modify the RNA polymerase concentration of the bacterial population, thus disrupting the natural process of allocation of available resources in bacteria. Further on, we study its asymptotic behavior using dynamical systems theory, and we provide conditions for the persistence of the bacterial population. We aim to maximize the synthesis of the metabolite of interest during a fixed interval of time in terms of the resource allocation decision. The latter is formulated as an Optimal Control Problem which is then explored using Pontryagin's Maximum Principle. We analyze the solution of the problem and propose a sub-optimal control strategy given by a constant allocation decision, which eventually takes the system to the optimal steady-state production regime. On this basis, we study and compare the two most significant steadystate production objectives in continuous bioreactors: biomass production and metabolite production. For this last purpose, and in addition to the allocation parameter, we control the dilution rate of the bioreactor, and we analyze the results through a numerical approach. The resulting two-dimensional optimization problem is defined in terms of Michaelis-Menten kinetics, and takes into account the constraints for the existence of the equilibrium of interest.
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