Nonlinear Mathematical Simulation and Analysis of Dha Regulon for Glycerol Metabolism in Klebsiella pneumoniae

Complex metabolic network of 1,3-propanediol transport mechanisms 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 1,3-PD across cell membrane, the metabolic network contains multiple possible metabolic systems. Considering the genetic regulation of dha regulon and inhibition of 3-hydroxypropionaldehyde to the growth of cells, we establish a 14-dimensional nonlinear hybrid dynamical system aiming to determine the most possible metabolic system and the corresponding optimal parameter. The existence, uniqueness and continuity of solutions are discussed. Taking the robustness index of the intracellular substances together as a performance index, a system identification model is proposed, in which 1,395 continuous variables and 90 discrete variables are involved. The identification problem is decomposed into two subproblems and a parallel particle swarm optimization procedure is constructed to solve them. Numerical results show that it is most possible that 1,3-PD passes the cell membrane by active transport coupled with passive diffusion.