Identification And Robustness Analysis Of Nonlinear Hybrid Dynamical System Concerning Glycerol Transport Mechanism

The fermentation of glycerol by Klebsiella pneumoniae is a complex bioprocess. In this pa-per, considering the uncertain factors that hard measured data of intracellular substances and unclear transport mechanism of substrate glycerol and product 1,3-PD, nonlinear hybrid dynamical models are proposed to describe this process under continuous culture. The main purpose of this paper is to infer the transport modes of glycerol and 1,3-PD across cell membrane. The main results obtained in this paper are summarized as follows:1) Suppose that 1,3-PD passes cell membrane by both passive diffusion and active transport, nonlinear hybrid dynamical system models are developed to describe the reductive pathway of glycerol dissimilation based on the three different trans-port modes of glycerol across cell membrane. In these models, the inhibitions of 3-hydroxypropionaldehyde (3-HPA) to the activities of two key enzymes (glycerol dehydratase (GDHt) and 1,3-propanediol oxydoreductase (PDOR)) and to the spe-cific cell growth rate are all taken into consideration. Subsequently, the Lipschitz and linear growth conditions are proved to make sure the properties of solutions to the system.2) Due to lacking data of intracellular substances, we present a new quantitative defini-tion of biological robustness to evaluate the effectiveness of parameter perturbation to the computational values of intracellular substances concentrations. Taking the presented biological robustness and the relative error between calculated values and experimental data as performance index, we establish a system identification model which contains both continuous variables (kinetic parameters) and discrete variables (three possible transport modes of glycerol).3) It is difficulty to solve the original identification problem for the reason that there are two kinds of parameter variables. In view of the independence of the two kinds of identification parameters, the original problem can be divided into identification sub-problem on continuous parameters and identification sub-problem on the discrete variables. An optimal algorithm is constructed. Numerical results show that it is most possible for glycerol to pass cell membrane by passive diffusion. We give the numerical simulation by software Origin 8 at the end. These results of this paper can not only develop the theory and the applications of nonlinear hybrid dynamical systems but also provide certain guidance for industrialization of 1,3-PD production. Therefore, this research is a essential foundation for numerical simulation and optimal control of the microbial conversion of glycerol to 1,3-PD.