一类微生物发酵的多种非线性动力系统建模与优化
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摘要
本文以甘油生物转化生产1,3-丙二醇为研究背景,针对提高发酵生产强度和目标产物转化率的两种途径——发酵工艺优化和菌种基因改造,分别从过程动力学和计算系统生物学的角度,利用了非线性混杂系统建模与优化、S系统理论和结构动力学建模等方法,对该发酵过程进行了研究,主要工作可概括如下：
1.考虑非耦联批式流加发酵,根据实际发酵实验,把整个发酵过程分为不同的发酵模式,提出了一个能够描述所有发酵模式的混杂速率向量场,再依据底物和中和剂流加控制方式的不同,建立了描述发酵模式之间切换的规则,与混杂向量场共同构成了非耦联批式流加发酵的非线性混杂动力系统,研究了该系统的非齐诺性和适定性等问题,并对具体实验进行了数值模拟.
2.针对所提出的非耦联批式流加发酵的混杂动力系统,建立了具有非光滑连续状态约束的参数辨识模型,并以脉冲微分方程的形式给出了混杂动力系统的参数灵敏度函数,利用曲线变分等数学工具,证明了约束函数关于参数单边方向可导,给出了辨识问题的最优性条件,分别构造算法估计参数的灵敏度并对灵敏度较高的参数进行辨识.
3.针对甘油连续发酵的代谢还原途径上底物甘油和产物1,3-丙二醇跨膜运输机理不清等问题,以S系统的形式给出了描述胞外主要物质和胞内还原途径上关键代谢物的变化的多种可能动力学模型,并基于胞外数据对各个模型进行了参数辨识.在缺乏胞内实验数据的情况下,基于生物系统的鲁棒性特征,给出了甘油代谢系统鲁棒性的定量定义,利用这一指标衡量各种可能系统的鲁棒性,从而推断出甘油和1,3-丙二醇的最有可能的跨膜运输方式.此外,针对推断后的S系统,分析了系统状态关于独立变量的对数增益以及参数的灵敏度,数值结果表明系统的对数增益和参数灵敏度均比较平稳,进一步验证了系统的合理性.
4.建立了甘油代谢还原途径的结构动力学模型,并根据代谢网络的结构给出了模型参数的范围(称为参数空间),在参数空间上从各个角度分析了过量表达克雷伯氏菌的甘油脱水酶和1,3-丙二醇氧化还原酶的编码来降低3-羟基丙醛的抑制强度这一基因改造过程可能对甘油代谢还原途径的动力学产生的影响,验证了不稳定性和分岔的存在性,并通过数值结果对以往的一些实验现象进行了解释.
本文的工作不仅可以丰富非线性混杂系统与计算系统生物学的理论,而且可以为1,3-丙二醇的产业化生产提供参考.因此该项研究具有重要的理论意义与应用价值.
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.
1.考虑非耦联批式流加发酵,根据实际发酵实验,把整个发酵过程分为不同的发酵模式,提出了一个能够描述所有发酵模式的混杂速率向量场,再依据底物和中和剂流加控制方式的不同,建立了描述发酵模式之间切换的规则,与混杂向量场共同构成了非耦联批式流加发酵的非线性混杂动力系统,研究了该系统的非齐诺性和适定性等问题,并对具体实验进行了数值模拟.
2.针对所提出的非耦联批式流加发酵的混杂动力系统,建立了具有非光滑连续状态约束的参数辨识模型,并以脉冲微分方程的形式给出了混杂动力系统的参数灵敏度函数,利用曲线变分等数学工具,证明了约束函数关于参数单边方向可导,给出了辨识问题的最优性条件,分别构造算法估计参数的灵敏度并对灵敏度较高的参数进行辨识.
3.针对甘油连续发酵的代谢还原途径上底物甘油和产物1,3-丙二醇跨膜运输机理不清等问题,以S系统的形式给出了描述胞外主要物质和胞内还原途径上关键代谢物的变化的多种可能动力学模型,并基于胞外数据对各个模型进行了参数辨识.在缺乏胞内实验数据的情况下,基于生物系统的鲁棒性特征,给出了甘油代谢系统鲁棒性的定量定义,利用这一指标衡量各种可能系统的鲁棒性,从而推断出甘油和1,3-丙二醇的最有可能的跨膜运输方式.此外,针对推断后的S系统,分析了系统状态关于独立变量的对数增益以及参数的灵敏度,数值结果表明系统的对数增益和参数灵敏度均比较平稳,进一步验证了系统的合理性.
4.建立了甘油代谢还原途径的结构动力学模型,并根据代谢网络的结构给出了模型参数的范围(称为参数空间),在参数空间上从各个角度分析了过量表达克雷伯氏菌的甘油脱水酶和1,3-丙二醇氧化还原酶的编码来降低3-羟基丙醛的抑制强度这一基因改造过程可能对甘油代谢还原途径的动力学产生的影响,验证了不稳定性和分岔的存在性,并通过数值结果对以往的一些实验现象进行了解释.
本文的工作不仅可以丰富非线性混杂系统与计算系统生物学的理论,而且可以为1,3-丙二醇的产业化生产提供参考.因此该项研究具有重要的理论意义与应用价值.
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.
引文
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