Modelling And Optimization Of Several Nonlinear Dynamical Systems In A Class Of Microbial Bioconversion Processes

This dissertation investigates the modelling, analysis and parameter identification of the microbial production of 1,3-propanediol from glycerol. In terms of process kinetics and com-putational system biology, we apply nonlinear hybrid systems, S system theory and structural kinetic modelling to simulating the fermentation process and providing theoretical analysis for genetic engineering of the strains. The main contributions obtained in this dissertation are sum-marized as follows.1. A fed-batch fermentation of glycerol with open loop substrate input and pH logic control is considered. According to the factual experiments, we divide the whole fermentation process into four different modes and propose a hybrid vector field to describe them. A switching rule among various modes is constructed based on the control principles of the flows of substrate and neutralizing agent. A hybrid system is formulated by combing the hybrid vector field and the switching rule. The non-Zenoness and well-posedness of the hybrid system are discussed. Numerical simulation of a factual fed-batch fermentation is carried out.2. Based on the proposed hybrid system, a parameter identification model is built, which is a problem of semi-infinite nonsmooth programming. The parametric sensitivity functions for the hybrid system are given by a set of impulsive differential equations and the one-sided directional differentiability of the constraint functions are proved in terms of the calculus of variation of piecewise-smooth curves. On this basis, the optimality conditions of the parameter identification problem are derived. Two algorithms are constructed to reduce the number of parameters to be optimized and to solve the identification problem, respectively.3. In the context that the transport mechanisms of glycerol and 1,3-propanediol across cell membrane in glycerol metabolic system are still unclear, we develop dynamical systems for various possible metabolic systems, which are presented in the form of S systems. The parameters of the systems are identified based on extracellular data. In the absence of intracellular data, we take the robustness property of biological system into consid-eration and propose a quantitative definition of biological robustness. The robustness performance is used to measure the plausibility of the possible systems and to determine the most reasonable transport systems of glycerol and 1,3-propanediol from all possible ones. Parameter sensitivity and Log gain of the steady states with respect to the inde-pendent variables are also estimated. Numerical results reveal that the steady states of the system are relatively insensitive to the independent variables and the rate constants, which show the validity of the determined system again.4. A structural kinetic model is proposed to describe the dynamics of the reductive path-way of glycerol metabolism. Without the intracellular data, the feasible ranges of the parameters in the model still can be given based on the structure of the metabolic net-work and the knowledge of the reaction mechanisms. We then estimate the influence of over-expression of the genes encoding glycerol dehydratase and 1,3-propanediol oxidore-ductase on the stability of the system. The existence of instability and Hopf bifurcation are proved and some previously experimental phenomena are explained by our numerical results.The results of this dissertation can not only develop the theory and the applications of nonlinear hybrid dynamical systems and computational system biology, but also reduce exper-imental cost and provide certain guidance for industrialization of 1,3-propanediol production. Therefore, this research is quite interesting in both theory and practice.