Robust analysis of hybrid dynamical systems for 1, 3-propanediol transport mechanisms in microbial continuous fermentation

A better understanding of the biological phenomena observed in cells requires the creation and analysis of mathematical models of cellular metabolism and physiology. In the study of the glycerol continuous bioconversion to 1, 3-propanediol by Klebsiella pneumoniae, there are some uncertain factors such as the mechanism about the transports of substances across cell membrane. In this paper, a nonlinear hybrid system which describes the intracellular reductive pathway is presented, according to the possible transport mechanisms of 1, 3-propanediol across cell membrane. The existence, uniqueness, and continuity of the solutions for the nonlinear hybrid system are discussed. It is difficult to measure the concentrations of intracellular substances; so, a quantitative robustness analysis method is proposed. Taking the robustness of intracellular substance concentrations as the performance index, an identification model is proposed, which is subjected to the constraint of nonlinear hybrid dynamical system. Finally, an algorithm procedure is constructed to solve the parameter identification model, and the most possible transport mechanism of 1, 3-propanediol and the optimal parameters of the corresponding system are also given.