Identification and robustness analysis of nonlinear multi-stage enzyme-catalytic dynamical system in batch culture

In this paper, based on biological phenomena of different characters at different stages, we propose a nonlinear multi-stage enzyme-catalytic dynamic system with unknown time and system parameters. Such system starts at different initial conditions for formulating batch culture process of glycerol bio-dissimilation to 1,3-propanediol. Some properties of the nonlinear system are discussed. In view of the difficulty in accurately measuring the concentration of intracellular substances and the absence of equilibrium points for the nonlinear system, we quantitatively define biological robustness for the entire process of batch culture instead of one for the approximately stable state of continuous culture. Taking the biological robustness of the intracellular substances together with the relative error between the experimental data and the computational values of the extracellular substances as the cost function, we formulate an identification problem subject to the nonlinear system, continuous state inequality constraints and parameter constraints. Analytical solution to system is not naturally available, therefore, a huge number of numerical computations of the proposed system and the proposed biological robustness make solving the identification problem by a serial computer a very complicated task. To improve computational efficiency, we develop an effective parallelized optimization algorithm, based on the constraint transcription and smoothing approximation techniques, for seeking the optimal time and system parameters. Compared with previous work, we assert that the optimal time and system parameters together with the corresponding nonlinear multi-stage dynamical system can reasonably describe batch fermentation at different initial conditions.