Hybrid System,Stability And Robustness Identification Of Continuous Culture With Inhibitory Effects

The biocatalytic conversion of 1,3-propanediol from glycerol in continuous culture is considered in this thesis.Based on a kinetic model of enzyme-catalysis reactions,an improved hybrid dynamic system was proposed so as to describe the considered process,in which the problem of some unclear inhibitory mechanisms of the key metabolites onto the metabolic reactions was fully considered.The inhibitory mechanisms and the involved kinetic parameters of the proposed model were identified via biological robustness.Meanwhile,the stability of the enzyme-catalysis model was explored.This study is supported by China National Natural Science Foundation(Grant Nos.10471014,10671126,10871033,11171050),"973" plan project(2007CB714304)and "863" plan project(2007AA02Z208).The results of this thesis will on one hand enhance the theory of nonlinear hybrid dynamical system and computational biology,and on the other serve as a reference for the industrialized production of 1,3-propanediol.The major work and main results of this thesis are summarized as follows.1.The equilibria of an eight-dimensional nonlinear dynamical system which described the dynamic behavior of microbial reductive pathway from extracellular environment to intracellular environment was numerically computed,and the stability of the equilibria was analyzed.The eight-dimensional nonlinear steady equations were firstly decoupled by elimination method,resulting in two univariate equations of rational functions.The symbolic real root isolation method was applied to solve the transformed univariate rational equations and the equilibria of the original steady equations were obtained by subsitituting the roots into the equations.The stability of the equilibria was analyzed,the results of which numerically verify the existence of multi-steady states of the microbial fermentation of glycerol in continuous culture.2.A novel nonlinear hybrid dynamical system is developed,in which the consumption of extracellular substrate,the formation of extracellular products,the metabolic reactions in cells,the transformation of glycerol and 1,3-propanediol between extracellular and intracellular environments as well as the inhitory effect of the intermediate metabolite 3-HP A to two key enzymes(GDHt and PDOR)were all taken into consideration.Existence and uniqueness of solutions to the proposed system was inferred,and continuous dependence of solutions with respect to parameters as well as compactness of solution set was also obtained.3.To overcome the problem that the traditional parameter identification technique is invalid due to the absence of intracellular data,we proposed a quantitative definition of biological robustness,which is one of the fundamental traits of biological systems.A parameter identification model was developed,in which biological robustness was used as performance index and the hybrid dynamical system was taken as constraints.The identifiability of the model was proved.Numerical algorithm was constructed based on discretization technique,which is applied to solving the identification model.Consequently,the inhibitory zone of 3-HPA and the values of the involved parameters were identified.