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 paper, a generalized nonlinear hybrid dynamical system is proposed to describe this process under continuous culture based on three different transport modes of glycerol across cell membrane. In the system, the inhibitory effect of 3-hydroxypropionaldehyde to the activities of two key enzymes (glycerol dehydratase and 1,3-propanediol oxydoreductase) and to the specific cell growth rate are all taken into consideration. To infer the most reasonable transport mode of glycerol across cell membrane on the hypothesis that 1,3-propanediol passes cell membrane by both passive diffusion and active transport, a quantitative definition of biological robustness for intracellular substances is presented. Taking the presented biological robustness and relative error between experimental data and computational values as performance index, a system identification model is established. Numerical results show that it is most possible for glycerol to pass cell membrane by passive diffusion.

► We develop a nonlinear hybrid dynamical system to describe the continuous culture. ► We quantitatively formulate parametric robustness to infer the transport mode of glycerol. ► Based on the parametric robustness and relative error, we establish an identification model. ► Numerical algorithm is constructed to solve the identification problem.