Pathway And Parameter Identification Of A Complex Metabolic System Via Biological Robustness

The bioconversion of glycerol to1,3-propanediol (1,3-PD) by Klebsiella pneumoniae can be characterized by a complex biological engineering, in which exist some uncertain factors, especially the transport mechanisms of glycerol and1,3-PD across cell membrane. In this paper, we identify transport mechanism of glycerol and1,3-PD according to a fourteen-dimensional nonlinear enzyme-catalytic and genetie regulation hybrid dynamical system. Some basic properties of the dynamical system are discussed. On the basis of biological properties, we give a quantitative definition of robustness of the intracellular substances and robustness analysis for each system. Then, we propose a identification model and a parallel algorithm to solve it. Numerical results show that it is most possible that both glycerol and1,3-PD pass the cell membrane by active transport and passive diffusion. We make a serious investigate for the nonlinear enzyme-catalytic and genetie regulation hybrid system of continuous fermentation. The main contributions are sum-marized as follows:1) on the basis of model of Sun, consider not only the inhibition of3-HPA to the growth of cells and dha regulon gene expression, but also the genetie regulation and nine possible transport mechanisms of glycerol and1,3-PD across cell membrane, we propose a nonlinear hybrid dynamical system to describe the microbial continuous cultures. The existence, uniqueness and continuity of solutions for the system are discussed.2) For transport mechanism of glycerol and1,3-PD is not clear, we define the relative error of the extracellular concentrations. Meanwhile robustness analysis of system with respect to parameter to intracellular concentrations. Taking the robustness index of the intracellular substances and the relative error of extracellular substances as a performance index and the hybrid dynamical system as the constraint condition, a system identification model is proposed. The existence of optimal solution of the model is proved.3) Because the identification model IP includes135hybrid dynamical systems,4050continuous variables,540discrete variables and contains a huge number of numerical com-putations, we decompose the problem IP into two subproblems and prove decomposition identification problem is equivalent to the identification problem IP. Then, proposed a parallel algorithm to solve it and obtain the optimal pathway and parameters. Finally, we give the simulated results and simulated diagrams of a set of experimental data, re- spectively.