Hierarchical MPC applied to bacterial resource allocation and metabolite synthesis

Microorganisms have evolved submitted to a continuous optimisation process that has improved their capacity to proliferate in nature, developing highly optimized distribution mechanisms of their resources. Considering the microbial selfreplication process as a resource allocation problem is a novel approach that has motivated numerous applications to the artificial production of metabolites of interest. Model-based optimal control studies are essential in understanding these naturally-evolved allocation strategies, but they are usually represented by open-loop control laws. In this context, we introduce a hierarchical shrinking-horizon non-linear MPC scheme that aims to maximise the production of a metabolite of interest. The control loop acts on an external signal that is able to disrupt the natural allocation process. The approach uses an optimal control-based input parametrisation that takes into account the structure of the open-loop natural allocation strategy of the cell, to emulate a closed-loop control law. We provide examples of the open-loop control strategies, and simulations of the hierarchical scheme.