Optimal control for the metabolic activity of microbial cells through the metabolic flux parameterization

During microbial fermentation, the metabolic fluxes reflect the growth and reproduction rate of microbial cells. By adjusting the metabolic fluxes, the desired production target can be achieved. It is highly necessary to ensure that the fermentation process meets the production constraints because the metabolic fluxes are regulated by various enzymatic reactions. However, previous studies cannot guarantee that the production constraints are satisfied over the course of the process. In this paper, constraints are designed at the microscopic flux level for the E. coli cell fermentation process. A control variable parameterization method, which discretizes the control variables while the state variables remain continuous, is used to optimize the E. coli cell growth activity, where the time domain is divided into several subintervals. In each subinterval, the metabolic fluxes are approximated by a series of parameters to be optimized. Then, the E. coli metabolic activity is transformed into a dynamic optimization problem, and the optimal trajectories of metabolic fluxes are obtained by solving the problem. Finally, the simulation results of the E. coli fermentation process verify the effectiveness of the method.