Complex metabolic network of glycerol fermentation by Klebsiella pneumoniae and its system identification via biological robustness

The bioconversion of glycerol to 1,3-propanediol (1,3-PD) by Klebsiella pneumoniae (K. pneumoniae) can be characterized by an intricate metabolic network of interactions among biochemical fluxes, metabolic compounds, key enzymes and genetic regulation. Since there are some uncertain factors in the fermentation, especially the transport mechanisms of substances across cell membrane, the metabolic network contains multiple possible metabolic systems. In this paper, we establish a complex metabolic network and the corresponding nonlinear hybrid dynamical system aiming to determine the most possible metabolic system. The existence, uniqueness and continuity of solutions are discussed. We quantitatively describe biological robustness and present a system identification model on the basis of robustness performance. The identification problem is decomposed into two subproblems and a procedure is constructed to solve them. Numerical results show that it is most possible that both glycerol and 1,3-PD pass the cell membrane by active transport coupling with passive diffusion under substrate-sufficient conditions, whereas, under substrate-limited conditions, glycerol passes cell membrane by active transport coupling with passive diffusion and 1,3-PD by active transport.