连续发酵复杂动力系统参数辨识与鲁棒性分析
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摘要
本文以甘油为底物、采用微生物歧化方法生产1,3-丙二醇的连续发酵过程为背景,基于连续发酵酶催化动力学模型,考虑胞外甘油在还原路径中的三种不同的跨膜运输方式,建立连续发酵酶催化复杂动力系统,并研究系统的基本性质。基因调控连续发酵动力系统的建立和研究为实验上采用基因敲除等技术培养高产量新菌种提供理论指导。本课题受到国家“十五”科技攻关计划项目“发酵工程生产1,3-丙二醇”(编号为2001BA708801-04)和国家高技术研究发展计划(863计划)“生物柴油与1,3-丙二醇的联产工艺”(编号为2007AA022208)的资助。此项研究将为实现1,3-丙二醇的产业化生产提供理论指导,因此,该项目研究具有重要的理论意义与应用价值。本论文的研究内容与取得的主要结果可概括如下:
1、对还原路径中克雷伯氏菌胞外甘油和胞内1,3-丙二醇的跨膜运输机理进行分析和推断。在假设胞内1,3-丙二醇的跨膜运输方式为主被动结合的条件下,分别考虑胞外甘油的三种不同的跨膜运输方式(主动、被动、主被动结合),根据米氏方程建立连续发酵酶催化复杂动力系统及其参数辨识模型,证明了系统的基本性质(解的存在性和唯一性)和辨识模型的可辨识性。构造优化算法,依实验数据求得最优辨识参数。辨识后的模型中1,3-丙二醇的计算值与实验值之间的相对误差为30%左右,根据实际问题可知建立的模型适合描述连续发酵过程。
2、提出生物鲁棒性分析方法。根据模型的稳定性严格依赖于动力系统敏感参数的精确数值,从对参数进行扰动的角度,建立定量的鲁棒性能指标及其优化算法。对连续发酵酶催化复杂动力系统中的三个模型分别进行鲁棒性分析,依照目标函数值,选取合理的模型去更好地反映胞外甘油的跨膜运输机理。复杂动力系统中的三个模型的鲁棒数值结果表明,参数辨识性能指标作为选取合理系统的唯一标准是不完善的,因而对模型进行鲁棒性分析是非常必要的。
The enzyme-catalytic complex dynamical systems of bio-dissimilation of glycerol to 1,3-propanediol by Klebsiella pneumoniae are investigated in this paper.Basing on enzyme-catalytic kinetic model of continuous fermentation,considering the different transport ways of extracellular glycerol on the reductive pathway,the complex dynamical systems including three models are established and the properties of solutions are studied.The study of the new model can not only be helpful for deeply understanding metabolic and genetic regulation of dha regulon of glycerol metabolism,but also provide certain reference for genetic modification of Klebsiella pneumoniae.This work was supported by the tenth 5 years' projects of Science and Technology Administration of China "Microbial Production of 1,3-Propanediol"(No.2001BA708 B01-04) and National High Technology Research and Development Program of China(863 Program)" Biodiesel and 1,3-Propanediol Integrated Production"(No.2007AA02Z208).The main results obtained in this dissertation may be summarized as follows:
1.The transport mechanism of glycerol and 1,3-PD across cell membrane on the reductive pathway is analyzed and discussed.Under the assumption that 1,3-PD passes the cell membrane by both passive diffusion and active transport,considering three different transport ways of extracellular glycerol separately which are active transport,passive transport as well as active and passive transport,the enzyme-catalytic complex dynamical systems are developed by Michalis-Menten kinetics.We prove some basic properties of the systems,such as existence and uniqueness of the solution.Moreover,parameter identification models of complex dynamical systems are established and the identifiability of models is proved.The feasible optimization algorithm is constructed to find the optimal parameters for the models in accordance with the experimental data.The numerical simulation show that the relative errors between experimental and computational values of 1,3-PD is 30%or so.According to the actual biological system,the models presented in this paper are fit for formulating the factual fermentation.
2.A new analysis method of biological robustness is proposed.As the stability of model depends crucially on the precise numerical values of sensitive kinetic parameters,from the perspective of a change in these parameters,a quantitative performance index of robustness and its optimization algorithm are established,then the robustness of each model in complex dynamical systems is analyzed.According to the value of objective function,we can select a reasonable system to reflect the transport mechanism of glycerol.The numerical results of robustness indicate that performance index of parameter identification is not perfect to be the unique standard to select a reasonable model,so robust analysis for each model is necessary.
1、对还原路径中克雷伯氏菌胞外甘油和胞内1,3-丙二醇的跨膜运输机理进行分析和推断。在假设胞内1,3-丙二醇的跨膜运输方式为主被动结合的条件下,分别考虑胞外甘油的三种不同的跨膜运输方式(主动、被动、主被动结合),根据米氏方程建立连续发酵酶催化复杂动力系统及其参数辨识模型,证明了系统的基本性质(解的存在性和唯一性)和辨识模型的可辨识性。构造优化算法,依实验数据求得最优辨识参数。辨识后的模型中1,3-丙二醇的计算值与实验值之间的相对误差为30%左右,根据实际问题可知建立的模型适合描述连续发酵过程。
2、提出生物鲁棒性分析方法。根据模型的稳定性严格依赖于动力系统敏感参数的精确数值,从对参数进行扰动的角度,建立定量的鲁棒性能指标及其优化算法。对连续发酵酶催化复杂动力系统中的三个模型分别进行鲁棒性分析,依照目标函数值,选取合理的模型去更好地反映胞外甘油的跨膜运输机理。复杂动力系统中的三个模型的鲁棒数值结果表明,参数辨识性能指标作为选取合理系统的唯一标准是不完善的,因而对模型进行鲁棒性分析是非常必要的。
The enzyme-catalytic complex dynamical systems of bio-dissimilation of glycerol to 1,3-propanediol by Klebsiella pneumoniae are investigated in this paper.Basing on enzyme-catalytic kinetic model of continuous fermentation,considering the different transport ways of extracellular glycerol on the reductive pathway,the complex dynamical systems including three models are established and the properties of solutions are studied.The study of the new model can not only be helpful for deeply understanding metabolic and genetic regulation of dha regulon of glycerol metabolism,but also provide certain reference for genetic modification of Klebsiella pneumoniae.This work was supported by the tenth 5 years' projects of Science and Technology Administration of China "Microbial Production of 1,3-Propanediol"(No.2001BA708 B01-04) and National High Technology Research and Development Program of China(863 Program)" Biodiesel and 1,3-Propanediol Integrated Production"(No.2007AA02Z208).The main results obtained in this dissertation may be summarized as follows:
1.The transport mechanism of glycerol and 1,3-PD across cell membrane on the reductive pathway is analyzed and discussed.Under the assumption that 1,3-PD passes the cell membrane by both passive diffusion and active transport,considering three different transport ways of extracellular glycerol separately which are active transport,passive transport as well as active and passive transport,the enzyme-catalytic complex dynamical systems are developed by Michalis-Menten kinetics.We prove some basic properties of the systems,such as existence and uniqueness of the solution.Moreover,parameter identification models of complex dynamical systems are established and the identifiability of models is proved.The feasible optimization algorithm is constructed to find the optimal parameters for the models in accordance with the experimental data.The numerical simulation show that the relative errors between experimental and computational values of 1,3-PD is 30%or so.According to the actual biological system,the models presented in this paper are fit for formulating the factual fermentation.
2.A new analysis method of biological robustness is proposed.As the stability of model depends crucially on the precise numerical values of sensitive kinetic parameters,from the perspective of a change in these parameters,a quantitative performance index of robustness and its optimization algorithm are established,then the robustness of each model in complex dynamical systems is analyzed.According to the value of objective function,we can select a reasonable system to reflect the transport mechanism of glycerol.The numerical results of robustness indicate that performance index of parameter identification is not perfect to be the unique standard to select a reasonable model,so robust analysis for each model is necessary.
引文
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[5]田平芳,谭天伟.甘油歧化为1,3-丙二醇的代谢及关键酶研究进展[J].生物工程报,2007,23(2):201-205.
[6]张青瑞,修志龙,曾安平.克雷伯氏杆菌发酵生产1,3-丙二醇的代谢通量优化分析[J].化工学报,2006,57(6):1403-1409.
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[8]迟乃玉,刘长江,刘英吴,张庆芳,郑学仿.编码1,3-丙二醇氧化还原酶基因的克隆和表达[J].微生物学报,2003,43(6):717-721.
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[23]李晓红,冯恩民,修志龙.微生物间歇发酵非线性动力系统的性质和最优控制[J].运筹学学报,2005,9(4):89-96.
[24]Li Xiaohong,Feng Enmin,Xiu Zhilong.Stability and optimal control of Microorganisms in continuous culture[J].J.of Appl.Math.And Comp.,2006,22(i):425-434.
[25]Wolpert,D.H.and MAcredy,W.G.No free lunch theorems for optimization[M].Transactions on Evolutionary Computation,1997,1:67-82.
[26]朱炳,包家立,应磊.生物鲁棒性的研究进展[J].生物物理学报,2007,5:357-362.
[27]Kitano H.Biological robustness[J].Nature review genetic,2004,5(11):826-837.
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[30]张昊,吴捷.一种新型的系统参数鲁棒性综合方法[J].华南理工大学学,1999,01:120-125.
[31]孙世岩,邱志明,王航宇.基于鲁棒性分析的PROMETHEE参数推断方法[J].武汉理工大学学报,2007,29(6):60-64.
[33]Biebl H,Menzel K,Zeng A P.Microbial production of 1,3-propanediol Appl.Microbiol.Biotech,1999,52:289-297.
[34]Boenigk R,Bowien S,Gottschalk G.Fermentation of glycerol to 1,3-propanediol in continuous cultures od Citrobacter freundii.Appl.Biocechol,1993,38:453-457.
[35]F.Barbirato,J.P.Grivet,P.Soucaille,A.Bories.3-Hydroxypropionaldehyde,an inhibitory metabolite of glycerol fermentation to 1,3-propanediol by enterobacterial species.Appl.Environ.Microbiol,1996,62:1448-1451.
[36]F.Barbirato,P.Soucaille,A.Bories.Physiologic mechanisms involved in accumulation of 3-hydroxypropionaldehyde during fermentation of glycerol by Enterobacter agglomerans.Appl.Environ.Microbiol,1996,62:4405-4409.
[37]戚以政,汪叔雄.生化反映动力学与反应器[M].北京:化学工业出版社,1995.
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[39]Z.Xiu,A.Zeng,L.An.Mathematical modelling of kinetics and research on multiplicity of glycerol bioconversion to 1,3-propanediol by Klebsiella pneumoniae under microaerobic conditionss[J].Enzyme Microbial Technol,2003,33:386-394.
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[2]修志龙.微生物发酵法生产1,3-丙二醇的研究进展[N].微生物学通报,2000,27(4):300-302
[3]綦文涛,修志龙.甘油歧化生产1,3-丙二醇过程的代谢和基因调控机理研究进展[J].中国生物工程杂志,2003,23(2)..
[4]A.Nemeth,B.Kupcsulik,B.Sevella.1,3-Propanediol oxidoreductase production with Klebsiella pneumoniae DSM2026[J].World Journal of Microbiology Biotechnology,2003,19,659-663.
[5]田平芳,谭天伟.甘油歧化为1,3-丙二醇的代谢及关键酶研究进展[J].生物工程报,2007,23(2):201-205.
[6]张青瑞,修志龙,曾安平.克雷伯氏杆菌发酵生产1,3-丙二醇的代谢通量优化分析[J].化工学报,2006,57(6):1403-1409.
[7]蔡忠贞,刘宏娟,张建安,刘德华,张富春.基因工程技术在1,3-丙二醇生产中的应用及研究进展[J].现代化工,2007,S(2):48-51.
[8]迟乃玉,刘长江,刘英吴,张庆芳,郑学仿.编码1,3-丙二醇氧化还原酶基因的克隆和表达[J].微生物学报,2003,43(6):717-721.
[9]Y.Q.Sun et al.Mathematical modeling of glycerol fermentation by Klebsiella pneumoniae:Concerning enzyme-catalytic reductive pathway and transport of glycerol and 1,3-propanediol across cell membrane[J].Biochem.Eng.J.,2008,38(1):22-32.
[10]曲荟锦,王凤寰,田平芳,谭天伟.克雷伯肺炎杆菌1,3-丙二醇氧化还原酶基因克隆及表达条件研究[J].工业微生物,2007,37(1):25-29.
[11]田平芳,谭天伟.遗传改造Klebsiella pneumoniae提高1,3-丙二醇产量的研究进展[J].化工进展,2008,27(3):322-325.
[12]A.P.Zeng,A.ROSE,H.Biebl,et al.Multiple product inhibition and growth modeling of Clostridium butyricum and Klebsiella pneumoniae in fermentation[J].Biotechnol Bioeng,1994,44:902-911.
[13]A.P.Zeng,W.D.Deckwer.A kinetic model for substrate and energy comsumption of microbial growth under substrate-sufficient conditions[J].Biotechnol Prog,1995,11:71-79.
[14]A.P.Zeng.A kinetic model for product formation of microbial and mammalian cells[J].Biotechnol Bioeng,1995,46:314-324.
[15]K.Menzel,A.P.Zeng,W.D.Deckwer.High concentration and productivity of 1,3-propanediol from continuous fermentation of glycerol by Klebsiella pneumoniae[J].Enzyme Microb.Technol,1997,20:82-86.
[16]Z.L.Xiu,A.P.Zeng,W.D.Deckwer.Multiplicty and Stablity Analysis of Microorganisms in Continuous Culture:Effects of Mutabolic Overflow and Growth Inhibition[J].Biotechnol Bioeng,1998,57:251-261.
[17]修志龙,曾安平,安佳利.甘油生物歧化过程动力学数学模拟和多稳态研究[J].大连理工大学学报,2000,40(4):428-433.
[18]L.H.Sun,Z.L.Xiu,Y.F.Ma.Model analysis of multiplicity and bifurcation in continuous cultures of microorganisms[J].Journal of Dalian University of Technology,2003,41(3):300-304.
[19]Y.F.Ma,L.H.Sun,Z.L.Xiu.Microbial Theoretical Analysis of Oscillatory Behavior in Process of Microbial Continuous Culture[J].Chinese Journal of Engineering Mathematics,2003,20(1):1-6.
[20]C.X.GaG,Z.T.Wang,E.M.Feng,Z.L.Xiu.Parameters identification problem of the nonlinear dynamical system in microbial continuous cultures[J].Appl.Math.Comput.,2005,169:476-484.
[21]C.X.G,E.M.Feng,Z.T.Wang,Z.L.Xiu.Nonlinear dynamical system of bio-dissimilation of glycerol to 1.,3-propanediol and their optimal control[J].J.of Industrial and Managegent Optimization,2005,1(3):377-388.
[22]李晓红,冯恩民,修志龙.微生物连续培养非线性动力系统的性质和最优性条件[J].工程数学学报,2006,23(1):7-12.
[23]李晓红,冯恩民,修志龙.微生物间歇发酵非线性动力系统的性质和最优控制[J].运筹学学报,2005,9(4):89-96.
[24]Li Xiaohong,Feng Enmin,Xiu Zhilong.Stability and optimal control of Microorganisms in continuous culture[J].J.of Appl.Math.And Comp.,2006,22(i):425-434.
[25]Wolpert,D.H.and MAcredy,W.G.No free lunch theorems for optimization[M].Transactions on Evolutionary Computation,1997,1:67-82.
[26]朱炳,包家立,应磊.生物鲁棒性的研究进展[J].生物物理学报,2007,5:357-362.
[27]Kitano H.Biological robustness[J].Nature review genetic,2004,5(11):826-837.
[28]Stelling,J.,Sauer,U.,Szallasi,Z.,Doyle Ⅲ.,F.J.,Doyle,J..Robustness of cellular function[J].Cell,2004(l18):675-685.
[29]McCann,K.S.The diversity stability debate[J].Nature,2000,405:228-233.
[30]张昊,吴捷.一种新型的系统参数鲁棒性综合方法[J].华南理工大学学,1999,01:120-125.
[31]孙世岩,邱志明,王航宇.基于鲁棒性分析的PROMETHEE参数推断方法[J].武汉理工大学学报,2007,29(6):60-64.
[33]Biebl H,Menzel K,Zeng A P.Microbial production of 1,3-propanediol Appl.Microbiol.Biotech,1999,52:289-297.
[34]Boenigk R,Bowien S,Gottschalk G.Fermentation of glycerol to 1,3-propanediol in continuous cultures od Citrobacter freundii.Appl.Biocechol,1993,38:453-457.
[35]F.Barbirato,J.P.Grivet,P.Soucaille,A.Bories.3-Hydroxypropionaldehyde,an inhibitory metabolite of glycerol fermentation to 1,3-propanediol by enterobacterial species.Appl.Environ.Microbiol,1996,62:1448-1451.
[36]F.Barbirato,P.Soucaille,A.Bories.Physiologic mechanisms involved in accumulation of 3-hydroxypropionaldehyde during fermentation of glycerol by Enterobacter agglomerans.Appl.Environ.Microbiol,1996,62:4405-4409.
[37]戚以政,汪叔雄.生化反映动力学与反应器[M].北京:化学工业出版社,1995.
[38]Menzel K,Zeng A P,Bieblh,et al.Kinetic,dynamics,and pathway studies of glycerol metabolism by Klebsiella pneumonia in anaerobic continuous culture:Ⅰ,the phenomena and characterization of osciallations and hysteresis[J].Biochnol Bioeng,1996,52:549-560.
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