甘油生物歧化生产1，3-丙二醇的混杂非线性动力系统辨识
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摘要
本文以甘油为底物、采用微生物(克雷伯氏杆菌)歧化方法生产1,3-丙二醇(1,3-PD)的间歇发酵到连续发酵过程为背景,根据细胞外1,3-PD在还原路径中的三种不同的跨膜运输方式,建立了相应的混杂非线性动力系统,并研究了系统的基本性质。根据定量的鲁棒性分析建立混杂非线性动力系统辨识模型,构造了辨识问题的数值并行算法,通过数值并行计算对1,3-PD的跨膜运输方式进行分析和推断。该研究对深入理解克雷伯氏杆菌的甘油胞内代谢途径具有重要的参考价值,丰富与发展了混杂非线性动力系统的理论、系统辨识以及并行计算和并行优化算法的研究。本课题受国家自然科学基金项目“一类复杂网络上非光滑动力系统的优化理论与算法”(编号为10871033)和国家高技术研究发展计划(863计划)“生物柴油与1,3-丙二醇联产工艺优化研究”(编号为2007AA02Z208)的资助。本论文的研究内容与取得的主要结果可概括如下：
1.甘油通过克雷伯氏杆菌间歇发酵到连续发酵生产1,3-PD过程中,根据细胞外1,3-PD不同的跨膜运输方式建立相应的混杂非线性动力系统。本文基于甘油生物歧化过程还原途径酶催化动力学模型,考虑三羟基丙醛(3-HPA)对菌种生长的抑制作用,并在假设甘油的跨膜运输方式为主被动运输相结合的条件下,推断1,3-PD合理的跨膜运输方式。根据1,3-PD存在的不同跨膜运输方式(主动运输、被动运输、主被动运输相结合),建立相应的甘油间歇发酵到连续发酵生产1,3-PD的混杂非线性动力系统,并证明了动力系统解的存在唯一性及解关于参量的连续性。
2.针对细胞内物质浓度无法测试问题,提出了生物系统鲁棒性的定量定义。以细胞外物质浓度的计算值与实验值的平均相对误差及生物鲁棒性作为性能指标,及以混杂非线性动力系统和系统的近似稳态性等为主要约束,建立了关于离散和连续变量的混杂非线性动力系统辨识模型,并证明了辨识模型的可辨识性和最优解的存在性。
3.混杂非线性动力系统辨识问题的数值计算。由于混杂非线性动力系统辨识问题中性能指标和约束条件都是关于辨识参量的非线性泛函,无法得到关于参量的解析解,所以本文中采用求数值解的办法,依均匀分布从参量允许集中随机产生大量的参量样本。一方面构造了串行算法求解辨识问题,但计算量过大和计算时间长,且当样本个数较大时,计算效率更低；另一方面,为了提高计算效率,采用并行计算,构造了求解辨识问题的数值并行算法,编写基于消息传递的MPI并行程序,在大连理工大学数学科学学院部署的联想深腾集群1800上编译运行。通过数值并行计算更高效更快速的求解辨识问题,而且推断出1,3-PD的跨膜运输方式为主被动运输相结合更合理。
The batch and continuous fermentation of bio-dissimilation of glycerol to 1,3-propane-diol (1,3-PD) by Klebsiella pneumoniae(K.pneumoniae) are investigated in this paper. Basing on enzyme-catalytic kinetic model of glycerol metabolism in K.pneumoniae on the reductive pathway, we develop the nonlinear hybrid dynamical system to describe batch and continuous fermentation of glycerol according to different transport mechanisms of 1,3-PD, in which the inhibitory effect of 3-hydroxypropionaldehyde(3-HPA) on the growth of biomass was taken into consideration, and the properties of systems are studied. On the basis of the quantitative definition of biological robustness, we establish a nonlinear hybrid dynamical system identification model. Finally, we construct a parallel algorithm to solve the identification model, and infer the transport mechanism of 1,3-PD by numerical parallel computing. The research can not only develop the nonlinear hybrid dynamical system, parallel computing and parallel optimization algorithm, but also be helpful for deeply understanding metabolism pathways of glycerol fermentation by K.pneumoniae. In addition, this work is supported by National Natural Science Foundation "Optimization theory and algorithm of nonsmooth dynamic system in a class of complex networks" (No. 10871033) and the National High Technology Research and Development Program(863 Program) "Biodiesel and 1,3-Propanediol Integrated Production" (No.2007AA02Z208). The main results in this dissertation may be summarized as follows:
1. Basing on batch and continuous fermentation of bio-dissimilation of glycerol to 1,3-PD by K.pneumoniae, we propose the nonlinear hybrid dynamical systems on the basis of three transport mechanisms of 1,3-PD. In this dissertation, considering the inhibitory effect of 3-HPA on the growth of biomass and assuming that the glycerol transported by active transport coupled with passive diffusion, we aim to infer the most reasonable one from three possible transport mechanisms of 1,3-PD across the cell membrane (ac-tive transport, passive diffusion or active transport coupled with passive diffusion), and develop the corresponding nonlinear hybrid dynamical system to describe batch and con-tinuous fermentation of glycerol. It is proved that the solution to the system uniquely exists and is continuous with respect to parameters.
2. Because of lack of intracellular information, we propose a quantitative definition of biological robustness. Presenting a performance index on the basis of the average relative error of extracellular substance concentrations and the biological robustness, we establish an identification model containing discrete and continuous parameters, which is subject to some conditions including the proposed nonlinear hybrid dynamical systems, the ap-proximately steady state of the dynamical system. Finally, we prove the identifiability and existence of the optimal solution of the identification model.
3. A numerical computation algorithm is constructed to solve the nonlinear hybrid dynamical systems identification model. Because the performance index and constraint condition are nonlinear functional with respect to parameters, we cannot obtain analytic solutions for the identification model. The model is numerically solved by randomly generating large number of sample points from the admissible set of parameters. On the one hand, we construct a serial algorithm to solve the identification model, but the serial algorithm requires a large computation amount and time, and its computing is inefficient when the number of sample is larger. On the other hand, in order to improve computation efficiency, we present a parallel algorithm to solve the identification model by the parallel computing, and develop its parallel program using MPI which runs on the lenovo 1800 cluster of school of mathematical sciences from dalian university of technology. Numerical results show that it is most reasonable that 1,3-PD pass the cell membrane by active transport coupled with passive diffusion, and the identification problem is solved more quickly and efficiently by parallel computing.
1.甘油通过克雷伯氏杆菌间歇发酵到连续发酵生产1,3-PD过程中,根据细胞外1,3-PD不同的跨膜运输方式建立相应的混杂非线性动力系统。本文基于甘油生物歧化过程还原途径酶催化动力学模型,考虑三羟基丙醛(3-HPA)对菌种生长的抑制作用,并在假设甘油的跨膜运输方式为主被动运输相结合的条件下,推断1,3-PD合理的跨膜运输方式。根据1,3-PD存在的不同跨膜运输方式(主动运输、被动运输、主被动运输相结合),建立相应的甘油间歇发酵到连续发酵生产1,3-PD的混杂非线性动力系统,并证明了动力系统解的存在唯一性及解关于参量的连续性。
2.针对细胞内物质浓度无法测试问题,提出了生物系统鲁棒性的定量定义。以细胞外物质浓度的计算值与实验值的平均相对误差及生物鲁棒性作为性能指标,及以混杂非线性动力系统和系统的近似稳态性等为主要约束,建立了关于离散和连续变量的混杂非线性动力系统辨识模型,并证明了辨识模型的可辨识性和最优解的存在性。
3.混杂非线性动力系统辨识问题的数值计算。由于混杂非线性动力系统辨识问题中性能指标和约束条件都是关于辨识参量的非线性泛函,无法得到关于参量的解析解,所以本文中采用求数值解的办法,依均匀分布从参量允许集中随机产生大量的参量样本。一方面构造了串行算法求解辨识问题,但计算量过大和计算时间长,且当样本个数较大时,计算效率更低；另一方面,为了提高计算效率,采用并行计算,构造了求解辨识问题的数值并行算法,编写基于消息传递的MPI并行程序,在大连理工大学数学科学学院部署的联想深腾集群1800上编译运行。通过数值并行计算更高效更快速的求解辨识问题,而且推断出1,3-PD的跨膜运输方式为主被动运输相结合更合理。
The batch and continuous fermentation of bio-dissimilation of glycerol to 1,3-propane-diol (1,3-PD) by Klebsiella pneumoniae(K.pneumoniae) are investigated in this paper. Basing on enzyme-catalytic kinetic model of glycerol metabolism in K.pneumoniae on the reductive pathway, we develop the nonlinear hybrid dynamical system to describe batch and continuous fermentation of glycerol according to different transport mechanisms of 1,3-PD, in which the inhibitory effect of 3-hydroxypropionaldehyde(3-HPA) on the growth of biomass was taken into consideration, and the properties of systems are studied. On the basis of the quantitative definition of biological robustness, we establish a nonlinear hybrid dynamical system identification model. Finally, we construct a parallel algorithm to solve the identification model, and infer the transport mechanism of 1,3-PD by numerical parallel computing. The research can not only develop the nonlinear hybrid dynamical system, parallel computing and parallel optimization algorithm, but also be helpful for deeply understanding metabolism pathways of glycerol fermentation by K.pneumoniae. In addition, this work is supported by National Natural Science Foundation "Optimization theory and algorithm of nonsmooth dynamic system in a class of complex networks" (No. 10871033) and the National High Technology Research and Development Program(863 Program) "Biodiesel and 1,3-Propanediol Integrated Production" (No.2007AA02Z208). The main results in this dissertation may be summarized as follows:
1. Basing on batch and continuous fermentation of bio-dissimilation of glycerol to 1,3-PD by K.pneumoniae, we propose the nonlinear hybrid dynamical systems on the basis of three transport mechanisms of 1,3-PD. In this dissertation, considering the inhibitory effect of 3-HPA on the growth of biomass and assuming that the glycerol transported by active transport coupled with passive diffusion, we aim to infer the most reasonable one from three possible transport mechanisms of 1,3-PD across the cell membrane (ac-tive transport, passive diffusion or active transport coupled with passive diffusion), and develop the corresponding nonlinear hybrid dynamical system to describe batch and con-tinuous fermentation of glycerol. It is proved that the solution to the system uniquely exists and is continuous with respect to parameters.
2. Because of lack of intracellular information, we propose a quantitative definition of biological robustness. Presenting a performance index on the basis of the average relative error of extracellular substance concentrations and the biological robustness, we establish an identification model containing discrete and continuous parameters, which is subject to some conditions including the proposed nonlinear hybrid dynamical systems, the ap-proximately steady state of the dynamical system. Finally, we prove the identifiability and existence of the optimal solution of the identification model.
3. A numerical computation algorithm is constructed to solve the nonlinear hybrid dynamical systems identification model. Because the performance index and constraint condition are nonlinear functional with respect to parameters, we cannot obtain analytic solutions for the identification model. The model is numerically solved by randomly generating large number of sample points from the admissible set of parameters. On the one hand, we construct a serial algorithm to solve the identification model, but the serial algorithm requires a large computation amount and time, and its computing is inefficient when the number of sample is larger. On the other hand, in order to improve computation efficiency, we present a parallel algorithm to solve the identification model by the parallel computing, and develop its parallel program using MPI which runs on the lenovo 1800 cluster of school of mathematical sciences from dalian university of technology. Numerical results show that it is most reasonable that 1,3-PD pass the cell membrane by active transport coupled with passive diffusion, and the identification problem is solved more quickly and efficiently by parallel computing.
引文
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