Pathway identification using parallel optimization for a complex metabolic system in microbial continuous culture

The bio-dissimilation of glycerol to 1,3-propanediol (1,3-PD) by Klebsiella pneumoniae (K. pneumoniae) is a complex bioprocess due to the multiple inhibitions of substrate and products onto the cell growth. In consideration of the fact that both the inhibition mechanisms of 3-hydroxypropionaldehyde (3-HPA) onto the cell growth and the transport systems of glycerol and 1,3-PD across the cell membrane are still unclear, we consider 72 possible metabolic pathways, and establish a novel mathematical model which is represented by an eight-dimensional nonlinear dynamical system. The existence, uniqueness, continuous dependence of solutions to the system and the compactness of the solution set are explored. On the basis of biological robustness, we give a quantitative definition of robustness index of the intracellular substances. Taking the robustness index of the intracellular substances together with the relative error between the experimental data and the computational values of the extracellular substances as a performance index, a parameter identification model is proposed for the nonlinear dynamical system, in which 43848 continuous variables and 1152 discrete variables are involved. A parallel particle swarm optimization — pathways identification algorithm (PPSO-PIA) is constructed to find the optimal pathway and parameters under various experiments conditions. Numerical results show that the optimal pathway and the corresponding dynamical system can describe the continuous fermentation reasonably.