Sensitivity analysis and parameter identification of nonlinear hybrid systems for glycerol transport mechanisms in continuous culture

In this paper, we establish a modified fourteen-dimensional nonlinear hybrid dynamic system with genetic regulation to describe the microbial continuous culture, in which we consider that there are three possible ways for glycerol to pass the cell's membrane and one way for 1,3-PD (passive diffusion and active transport). Then we discuss the existence, uniqueness, continuous dependence of solutions and the compactness of the solution set. We construct a global sensitivity analysis approach to reduce the number of kinetic parameters. In order to infer the most reasonable transport mechanism of glycerol, we propose a parameter identification model aiming at identifying the parameter with higher sensitivity and transport of glycerol, which takes the robustness index of the intracellular substance together with the relative error between the experimental data and the computational values of the extracellular substance as a performance index. Finally, a parallel algorithm is applied to find the optimal transport of glycerol and parameters.