基于鲁棒性分析推断三羟基丙醛对两种酶的抑制作用
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摘要
本文以微生物歧化甘油生产1,3-丙二醇(1,3-PD)连续发酵过程为背景,研究三羟基丙醛(3-HPA)对甘油脱水酶(PDHt)和1,3-丙二醇氧化还原酶(PDOR)的活性抑制作用。在假设3-HPA对细胞比生长速率无抑制作用及甘油、1.3-PD跨膜运输方式为主被动结合运输的条件下,建立混杂非线性动力学模型,并研究了模型的基本性质。为了推断3-HPA对两种关键酶是否有抑制作用及抑制作用区域,提出了混杂非线性动力系统的定量鲁棒性分析方法。并基于鲁棒性指标,建立混杂非线性动力系统辨识模型,通过数值计算推断出了3-HPA对这两种酶的抑制作用区域。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。此项目研究将为实现1,3-PD的产业化生产提供理论指导,具有重要的理论意义与应用价值。本论文的研究内容与得到的主要结果可概括如下：
1.在甘油连续发酵生产1,3-PD过程中,针对3-HPA对两种关键酶活性抑制作用的不同情形,在假设3-HPA对细胞比生长速率无抑制作用及甘油、1.3-PD跨膜运输方式为主被动结合运输条件下,建立了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依赖性。
2.针对细胞内物质浓度无法测量问题,提出了生物系统鲁棒性的定量分析方法。以细胞外物质浓度的计算值与实验值的相对误差及生物鲁棒性作为性能指标,混杂非线性动力系统和系统的近似稳态性为主要约束,建立了具有离散和连续参量的混杂非线性动力系统辨识模型,并证明了该模型的可辨识性。最后构造优化算法,并通过数值计算推断出了3-HPA对PDHt酶和PDOR酶的抑制作用区域。
The 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. based on the different cases on the inhibitions of 3-hydroxypropionaldehyde (3-HPA) to the effect activities of two key enzymes (glycerol dehydratase (GDHt)and 1,3-propanediol oxydore-ductase (PDOR)), a nonlinear hybrid dynamical system is proposed on the hypothesis that the glycerol and 1,3-PD pass the cell membrane by both passive diffusion and active transport and that there is no inhibition of 3-HPA to the specific growth rate of cells. And the fundamental properties of the system are investigated. To infer the most rea-sonable case, a quantitative definition of biological robustness is presented. Taking the presented biological robustness as performance index, a system identification model is established. Finally, we obtain the most reasonable system to describe the inhibition of 3-HPA to the two key enzymes and compute the range of inhibition of 3-HPA to the two enzymes by numerical computation.This work was supported by National Natural Sci-ence 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 Pro-duction"(No.2007AA02Z208). The main results obtained in this dissertation may be summarized as follows:
1. During the continuous culture of glycerol bioconversion to 1.3-PD, based on the cases whether the inhibitions of 3-HPA to the effect activities of two key enzymes ( GDHt and PDOR), we propose a nonlinear hybrid dynamical system on the hypothesis that the glycerol and 1,3-PD pass the cell membrane by both passive diffusion and active transport and that there is no inhibition of 3-HPA to the specific growth rate of cells. And the fundamental properties of the system are investigated:the existence and uniqueness of the solution to the system and the continuous dependent with respect to parameters.
2. Because of the lack of intracellular information, we propose a quantitative defini-tion of biological robustness. taking the average relative error of extracellular substance concentrations and the biological robustness as performance index, we establish an iden-tification model containing discrete and continuous parameters, which is subject to some conditions including the proposed nonlinear hybrid dynamical systems and the approxi- matelv steady state of the dynamical system. Subsequently, we prove the identifiability of the model. Finally, we obtain the range of inhibition of 3-HPA to the two enzymes by numerical computation.
1.在甘油连续发酵生产1,3-PD过程中,针对3-HPA对两种关键酶活性抑制作用的不同情形,在假设3-HPA对细胞比生长速率无抑制作用及甘油、1.3-PD跨膜运输方式为主被动结合运输条件下,建立了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依赖性。
2.针对细胞内物质浓度无法测量问题,提出了生物系统鲁棒性的定量分析方法。以细胞外物质浓度的计算值与实验值的相对误差及生物鲁棒性作为性能指标,混杂非线性动力系统和系统的近似稳态性为主要约束,建立了具有离散和连续参量的混杂非线性动力系统辨识模型,并证明了该模型的可辨识性。最后构造优化算法,并通过数值计算推断出了3-HPA对PDHt酶和PDOR酶的抑制作用区域。
The 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. based on the different cases on the inhibitions of 3-hydroxypropionaldehyde (3-HPA) to the effect activities of two key enzymes (glycerol dehydratase (GDHt)and 1,3-propanediol oxydore-ductase (PDOR)), a nonlinear hybrid dynamical system is proposed on the hypothesis that the glycerol and 1,3-PD pass the cell membrane by both passive diffusion and active transport and that there is no inhibition of 3-HPA to the specific growth rate of cells. And the fundamental properties of the system are investigated. To infer the most rea-sonable case, a quantitative definition of biological robustness is presented. Taking the presented biological robustness as performance index, a system identification model is established. Finally, we obtain the most reasonable system to describe the inhibition of 3-HPA to the two key enzymes and compute the range of inhibition of 3-HPA to the two enzymes by numerical computation.This work was supported by National Natural Sci-ence 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 Pro-duction"(No.2007AA02Z208). The main results obtained in this dissertation may be summarized as follows:
1. During the continuous culture of glycerol bioconversion to 1.3-PD, based on the cases whether the inhibitions of 3-HPA to the effect activities of two key enzymes ( GDHt and PDOR), we propose a nonlinear hybrid dynamical system on the hypothesis that the glycerol and 1,3-PD pass the cell membrane by both passive diffusion and active transport and that there is no inhibition of 3-HPA to the specific growth rate of cells. And the fundamental properties of the system are investigated:the existence and uniqueness of the solution to the system and the continuous dependent with respect to parameters.
2. Because of the lack of intracellular information, we propose a quantitative defini-tion of biological robustness. taking the average relative error of extracellular substance concentrations and the biological robustness as performance index, we establish an iden-tification model containing discrete and continuous parameters, which is subject to some conditions including the proposed nonlinear hybrid dynamical systems and the approxi- matelv steady state of the dynamical system. Subsequently, we prove the identifiability of the model. Finally, we obtain the range of inhibition of 3-HPA to the two enzymes by numerical computation.
引文
[1]李卫东,刘曰锋.混杂系统研究综述.自动化技术与应用,2007年第27卷第1期.
[2]尹增山.混杂系统优化控制理论研究(博士学位论文).浙江：浙江大学,2001.
[3]Witsenhausen H S. A class of hybrid-state continuous-time dynamic systems[J]. IEEE Trans. on Automatic Control,1966,11(6):665-683.
[4]Tavernini L. Differential automata and their discrete simulators[J]. Nonlinear Analysis Theory. Methods and Applications,1987,11(6):665-683.
[5]Martin Buss, Markus Glocker, Nonlinear hybrid dynamical systems:modeling, optimal control, and applications. Modelling, Analysis and Design of Hybrid Systems,2002,279: 311-335.
[6]Ye H, Michel A N, Hou L. Stability theory for hybrid dynamical systems[C]. In Proc. of the 34th IEEE Conference on Decision and Control,1995:2679-2684.
[7]Ye H, Michel A N, Hou L. Sability theory for hybrid dynamical systems[J].Automatic Control. IEEE Transactions on,1998:461-474.
[8]Jun YONEYAMA, Robust Stability and Stabilization of Fuzzy Systems with Discrete and Distributed Time-Delay[J]. Intelligent Control, IEEE International Symposium on, 2006,(10):2372-2377.
[9]He K X, Lemmon M D. Lyapunov stability of continuous valued systems under the super-vision of discrete event transition systems[J]. LNCS, Springer-Verlag,1998,1386:175-189.
[10]Branicky M S, Borkar V, Mitter S. A unified framework for hybrid control:Model and optimal control theory [J]. IEEE Trans on Automatic Control,1998,43(1):31-45.
[11]AMADORI.AL, D'APICE. C, MANZO. R, PICCOLI. B, Hybridization of optimal control problems[J].2007,80(2):268-280.
[12]Hermann B G,PatelM.Today's and tomorrow's bio-based bulk chemicals from white bio-teehnology:a techno—eeonomic analysis[J]. Appl Bioehem Biotechnol,2007,136(3):361-388.
[13]Freund A. Uber die bildung and darstellung von trimethylenalkohol aus glycerin. Monat-shefte fur Chemie,1881,2:636-641.
[14]Yazdani S S,Gonzalez R.Anaerobic fermentation of glycerol:a path to eeonomic viability for the biofuels industry [J]. Curr Opin Biotechnol,2007,18(3):213-219.
[15]Deekwer W. Microbial conversion of glycerol into 1,3-propanediol[J]. FEMS Microbiol. Reviews.1995.16:143-149.
[16]Zeng A P. Rose A. Biebl H, Tag C, Guenzel B, Deckwer W D. Multiple product in-hibition and growth modeling of Clostridium butyricum and Klebsiella pneumoniae in ferentation[J]. Biotechnol Bioeng,1994,44(8):902-911.
[17]Zeng A P. A kinetic model for product formation of microbial and mammalian cells[J]. Biotechnol Bioeng,1995,46(4):314-324.
[18]修志龙,曾安平,安利佳.甘油生物连续歧化过程的过渡行为及数学模拟.高校化学工程学报,2000,14(1)：53-58.
[19]Caixia Gao, Enmin Feng. Zongtao Wang. Zhilong Xiu, Parameters identi-cation problem of the nonlinear dynamical system in microbial continuous cultures[J]. Applied Mathemat-ics and Computation,169(2005)476-484.
[20]Sun Y Q, Qi W T. Teng T, Xiu Z L, Zeng A P.Mathematical modeling of glycerol fermen-tation by Klebsiella pneumoniae:Concerning enzyme-catalytic reductive pathway and transport of glycerol and 1,3-propanediol across cell membrane[J]. Biochemical Engineer-ing Journal.2008.38(1).22-32.
[21]孙丽华,郭庆广,修志龙.一类具有时滞的生化模型和Hopf分叉研究.生物数学学报,2002,17(3)：286-292.
[22]马永峰.微生物连续培养模型中非线性行为的分析与模拟(博士学位论文).大连：大连理工大学,2004.
[23]Gao C X. Feng E M, Wang Z T, Xiu Z L. Nonlinear dynamical system of bio-dissimilation of glycerol to 1,3-propanediol and their optimal control[J]. Journal of Industrial and Man-agegent Optimization,2005,1(3):377-388.
[24]Gao C X, Li K Z, Feng E M. Nonlinear impulsive system of fed-batch culture in fermen-tative production and its properties. Chaos, Solitons & Fractals.2006,28(1):271-277
[25]Gao C X, Feng E M, Xiu Z L. Identification and optimization of the nonlinear impul-sive system in microbial fed-batch fermentation. Dynamics of Continuous Discrete and Impulsive systems-series A-Mathmatical Analysis,2006,13:625-632.
[26]Gao C X, Lang Y H et al. Nonlinear impulsive system of microbial production in fed-batch culture and its optimal control. Journal of Appllied Mathematics and Computing, 2005,19(1-2):203-214.
[27]Wang H Y, Feng E M, Xiu Z L. Optimality condition of the nonlinear impulsive system in fed-batch fermentation. Nonlinear Analysis:Theory. Mwthods & Applications,2008, 68(1):12-23.
[28]Wang G. Feng E M, Xiu Z L. Parameter identification of nonlinear hybrid dynamical system in fed-batch culture.
[29]Wang G, Feng E M, Xiu Z L. Optimal control problem of nonlinear hybrid dynamical system in fed-batch culture.
[30]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.工程数学学报,2006,23(1)：7-12.
[31]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.运筹学学报,2005,9(4)：89-96.
[32]李晓红,冯恩民,修志龙.微生物连续发酵稳定模型的算法与收敛性.清华大学学报(自然科学版).2007,47(s2)：1907-1909.
[33]李晓红,冯恩民,修志龙.微生物连续培养过程平衡点的稳定性.高校应用数学学报B辑.2005,,20(4)：377-383.
[34]宫召华,冯恩民.微生物批示流加发酵多阶段最优控制的最优性条件.运筹学学报,2009,12(4)：121-131.
[35]Gong Z H. Liu C Y. Feng E M, Xiu Z L. Modelling and parameter idntification of microbial biconversion in fed-batch cultures. Journal'of Process Control,2008,18(5):458-464.
[36]Wang L, Ye J X, Feng E M, Xiu Z L. An improved model for multistage simulation of glycerol fermentation in batch culture and its parameter identification. Nonlinear Analysis: Hybrid Systems,2009,3:455-462.
[37]Liu C Y, Gong Z H, Feng E M, Yin H C. Optimal switching control for microbial fed-batch culture. Nonlinear Analysis:Hybrid systems,2008,2(4):1168-1174.
[38]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.
[39]Kitano H. Biological robustness[J]. Nature review genetic,2004,5(11):826-837.
[40]Stelling J, Sauer U, Szallasi Z, et al. Robustness of cellular functions[J]. Cell,2004(118): 675-685
[41]McCann K S. The diversity stability debate[J]. Nature,2000,405:228-233.
[42]Kitano H. Towards a theory of biological robustness[J]. Molecular Systems Biology,2007, 3:137.
[43]Tian T H. Robustness of mathematical models for biological systems. Austral. Mathe-matical Soc.2004,45(E):565-577.
[44]Barkai N, Leibler S. Robustness in simple biochemical networks. Nature,1997,387: 913-917.
[45]Paolo E B, Marina S, Marc F, Angus C et al. A mathematical tool for exploring the dynamics of biological networks. PNAS,2007,104(49):19169-19174.
[46]陈国良,安虹：陈崚,郑启龙,单久龙.并行算法实践.高等教育出版社,2004.
[47]王鹏,吕爽,聂治：谢千河.并行计算应用及实战.北京：机械工业出版社,2008,10.
[48]马之恩,周义仓.常微分方程定性与稳定性方法.北京：科学出版社,2001.
[49]孙亚琴.甘油生物歧化过程酶催化和基因调控的非线性数学模拟与分析(博士学位论文).大连：大连理工大学,2010.
[50]修志龙,曾安平,安利佳.甘油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.
[51]Bibel H, Memzel K, Zeng A P, Deckwer W D, Microbialproduction of 1,3-propanediol[J]. Appl. Microbiol. Bio-technol.1999,52:289-297.
[52]Boenigk R, Bowien S, Gottschalk G. Fermentation of glycerol to 1,3-propanediol in con-tinuous cultures of Citrobacter freundii. Appl. Bicrobiol. Biotechnol,1993,38:453-457.
[53]Barbirato F, Grivet J P, Soucaille P, Bories A.3-Hydroxypropionaldehyde, an inhibitory metabolite of glycerol fermentation to 1,3-propanediol by enterobacterial species. Appl. Environ. Microbiol.1996,62:1448-1451.
[54]Barbirato F, Soucaille P, Bories A. Physiologic mechanisms involved in accumulation of 3-hydroxypropionaldehyde during fermentation of glycerol by Enterobacter agglomerans. Appl. Environ. Microbiol,1996,62:4405-4409.
[55]Sun J, van den Heuvel J, Soucaille P, et al. Comparative genomic snslysis of dha regulon and related genes for anaerobic glycerol metabolism in bacteria [J]. Biotechnol Prog,2003, 19(2):263-272.
[56]Richery D P, Lin E C. Importance of facilitated diffusion for effective utilization of glycerol by Escherichia coli. J.Bacteriol,1972,12:784-790.
[57]Heller K B, Lin E C, Wilson T H. Substrate specificity and transport properties of the glycerol facilitator of Escherichia coli. J.Bacteriol,1980,144:274-278.
[58]Daniel R, Boenigk R, Gottschalk G. Purification of 1,3-propanediol dehydrogenase from Citrobacter freundii and cloning, sequeneing, and over expression of the corresponding gene in Escherichia coli[J]. J. Bacteriol.,1995,177:2151-2156.
[59]Honda S, Toraya T, Fukui S. In situ reactivation of glycerol inactivated coenzyme-B12-dependent glycerol dehydratase and dioldehydratase[J]. J.Baeteriol.,1980,143:1458-1465.
[60]钱伟懿,徐恭贤,宫召华.最有控制理论及其应用.大连：大连理工大学出版社,2010.
[61]修志龙,微生物发酵法生产1,3-丙二醇的研究进展[J].微生物学通报,2000,27(4)：300-302
[62]Gao C X, Feng E M, Wang Z T, Xiu Z L. Parameters identification problem of the nonlinear dynamical system in microbial continuous cultures[J]. Applied Mathematics and Computation,2005,169(1):476-484.
[63]Li X H, Feng E M, Xiu Z L. Stability and optimal control of microorganisms in continuous culture[J]. Journal of Applied Mathematics and Computing,2006,22:435-440.
[64]Ralf Sleuer. Computational approaches to the topology, stability and dynamics of metabolic networks[J]. Phytochemistry.2007,68:2139-2151.
[65]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.生物工程学报：2007,23(2)：201-205.
[66]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.中国生物工程杂志,2003.23(2)：64-67.
[67]北野宏明编,周笔锋.周艳红等译,系统生物学基础.北京：化学工业出版社,2007.
[2]尹增山.混杂系统优化控制理论研究(博士学位论文).浙江：浙江大学,2001.
[3]Witsenhausen H S. A class of hybrid-state continuous-time dynamic systems[J]. IEEE Trans. on Automatic Control,1966,11(6):665-683.
[4]Tavernini L. Differential automata and their discrete simulators[J]. Nonlinear Analysis Theory. Methods and Applications,1987,11(6):665-683.
[5]Martin Buss, Markus Glocker, Nonlinear hybrid dynamical systems:modeling, optimal control, and applications. Modelling, Analysis and Design of Hybrid Systems,2002,279: 311-335.
[6]Ye H, Michel A N, Hou L. Stability theory for hybrid dynamical systems[C]. In Proc. of the 34th IEEE Conference on Decision and Control,1995:2679-2684.
[7]Ye H, Michel A N, Hou L. Sability theory for hybrid dynamical systems[J].Automatic Control. IEEE Transactions on,1998:461-474.
[8]Jun YONEYAMA, Robust Stability and Stabilization of Fuzzy Systems with Discrete and Distributed Time-Delay[J]. Intelligent Control, IEEE International Symposium on, 2006,(10):2372-2377.
[9]He K X, Lemmon M D. Lyapunov stability of continuous valued systems under the super-vision of discrete event transition systems[J]. LNCS, Springer-Verlag,1998,1386:175-189.
[10]Branicky M S, Borkar V, Mitter S. A unified framework for hybrid control:Model and optimal control theory [J]. IEEE Trans on Automatic Control,1998,43(1):31-45.
[11]AMADORI.AL, D'APICE. C, MANZO. R, PICCOLI. B, Hybridization of optimal control problems[J].2007,80(2):268-280.
[12]Hermann B G,PatelM.Today's and tomorrow's bio-based bulk chemicals from white bio-teehnology:a techno—eeonomic analysis[J]. Appl Bioehem Biotechnol,2007,136(3):361-388.
[13]Freund A. Uber die bildung and darstellung von trimethylenalkohol aus glycerin. Monat-shefte fur Chemie,1881,2:636-641.
[14]Yazdani S S,Gonzalez R.Anaerobic fermentation of glycerol:a path to eeonomic viability for the biofuels industry [J]. Curr Opin Biotechnol,2007,18(3):213-219.
[15]Deekwer W. Microbial conversion of glycerol into 1,3-propanediol[J]. FEMS Microbiol. Reviews.1995.16:143-149.
[16]Zeng A P. Rose A. Biebl H, Tag C, Guenzel B, Deckwer W D. Multiple product in-hibition and growth modeling of Clostridium butyricum and Klebsiella pneumoniae in ferentation[J]. Biotechnol Bioeng,1994,44(8):902-911.
[17]Zeng A P. A kinetic model for product formation of microbial and mammalian cells[J]. Biotechnol Bioeng,1995,46(4):314-324.
[18]修志龙,曾安平,安利佳.甘油生物连续歧化过程的过渡行为及数学模拟.高校化学工程学报,2000,14(1)：53-58.
[19]Caixia Gao, Enmin Feng. Zongtao Wang. Zhilong Xiu, Parameters identi-cation problem of the nonlinear dynamical system in microbial continuous cultures[J]. Applied Mathemat-ics and Computation,169(2005)476-484.
[20]Sun Y Q, Qi W T. Teng T, Xiu Z L, Zeng A P.Mathematical modeling of glycerol fermen-tation by Klebsiella pneumoniae:Concerning enzyme-catalytic reductive pathway and transport of glycerol and 1,3-propanediol across cell membrane[J]. Biochemical Engineer-ing Journal.2008.38(1).22-32.
[21]孙丽华,郭庆广,修志龙.一类具有时滞的生化模型和Hopf分叉研究.生物数学学报,2002,17(3)：286-292.
[22]马永峰.微生物连续培养模型中非线性行为的分析与模拟(博士学位论文).大连：大连理工大学,2004.
[23]Gao C X. Feng E M, Wang Z T, Xiu Z L. Nonlinear dynamical system of bio-dissimilation of glycerol to 1,3-propanediol and their optimal control[J]. Journal of Industrial and Man-agegent Optimization,2005,1(3):377-388.
[24]Gao C X, Li K Z, Feng E M. Nonlinear impulsive system of fed-batch culture in fermen-tative production and its properties. Chaos, Solitons & Fractals.2006,28(1):271-277
[25]Gao C X, Feng E M, Xiu Z L. Identification and optimization of the nonlinear impul-sive system in microbial fed-batch fermentation. Dynamics of Continuous Discrete and Impulsive systems-series A-Mathmatical Analysis,2006,13:625-632.
[26]Gao C X, Lang Y H et al. Nonlinear impulsive system of microbial production in fed-batch culture and its optimal control. Journal of Appllied Mathematics and Computing, 2005,19(1-2):203-214.
[27]Wang H Y, Feng E M, Xiu Z L. Optimality condition of the nonlinear impulsive system in fed-batch fermentation. Nonlinear Analysis:Theory. Mwthods & Applications,2008, 68(1):12-23.
[28]Wang G. Feng E M, Xiu Z L. Parameter identification of nonlinear hybrid dynamical system in fed-batch culture.
[29]Wang G, Feng E M, Xiu Z L. Optimal control problem of nonlinear hybrid dynamical system in fed-batch culture.
[30]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.工程数学学报,2006,23(1)：7-12.
[31]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.运筹学学报,2005,9(4)：89-96.
[32]李晓红,冯恩民,修志龙.微生物连续发酵稳定模型的算法与收敛性.清华大学学报(自然科学版).2007,47(s2)：1907-1909.
[33]李晓红,冯恩民,修志龙.微生物连续培养过程平衡点的稳定性.高校应用数学学报B辑.2005,,20(4)：377-383.
[34]宫召华,冯恩民.微生物批示流加发酵多阶段最优控制的最优性条件.运筹学学报,2009,12(4)：121-131.
[35]Gong Z H. Liu C Y. Feng E M, Xiu Z L. Modelling and parameter idntification of microbial biconversion in fed-batch cultures. Journal'of Process Control,2008,18(5):458-464.
[36]Wang L, Ye J X, Feng E M, Xiu Z L. An improved model for multistage simulation of glycerol fermentation in batch culture and its parameter identification. Nonlinear Analysis: Hybrid Systems,2009,3:455-462.
[37]Liu C Y, Gong Z H, Feng E M, Yin H C. Optimal switching control for microbial fed-batch culture. Nonlinear Analysis:Hybrid systems,2008,2(4):1168-1174.
[38]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.
[39]Kitano H. Biological robustness[J]. Nature review genetic,2004,5(11):826-837.
[40]Stelling J, Sauer U, Szallasi Z, et al. Robustness of cellular functions[J]. Cell,2004(118): 675-685
[41]McCann K S. The diversity stability debate[J]. Nature,2000,405:228-233.
[42]Kitano H. Towards a theory of biological robustness[J]. Molecular Systems Biology,2007, 3:137.
[43]Tian T H. Robustness of mathematical models for biological systems. Austral. Mathe-matical Soc.2004,45(E):565-577.
[44]Barkai N, Leibler S. Robustness in simple biochemical networks. Nature,1997,387: 913-917.
[45]Paolo E B, Marina S, Marc F, Angus C et al. A mathematical tool for exploring the dynamics of biological networks. PNAS,2007,104(49):19169-19174.
[46]陈国良,安虹：陈崚,郑启龙,单久龙.并行算法实践.高等教育出版社,2004.
[47]王鹏,吕爽,聂治：谢千河.并行计算应用及实战.北京：机械工业出版社,2008,10.
[48]马之恩,周义仓.常微分方程定性与稳定性方法.北京：科学出版社,2001.
[49]孙亚琴.甘油生物歧化过程酶催化和基因调控的非线性数学模拟与分析(博士学位论文).大连：大连理工大学,2010.
[50]修志龙,曾安平,安利佳.甘油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.
[51]Bibel H, Memzel K, Zeng A P, Deckwer W D, Microbialproduction of 1,3-propanediol[J]. Appl. Microbiol. Bio-technol.1999,52:289-297.
[52]Boenigk R, Bowien S, Gottschalk G. Fermentation of glycerol to 1,3-propanediol in con-tinuous cultures of Citrobacter freundii. Appl. Bicrobiol. Biotechnol,1993,38:453-457.
[53]Barbirato F, Grivet J P, Soucaille P, Bories A.3-Hydroxypropionaldehyde, an inhibitory metabolite of glycerol fermentation to 1,3-propanediol by enterobacterial species. Appl. Environ. Microbiol.1996,62:1448-1451.
[54]Barbirato F, Soucaille P, Bories A. Physiologic mechanisms involved in accumulation of 3-hydroxypropionaldehyde during fermentation of glycerol by Enterobacter agglomerans. Appl. Environ. Microbiol,1996,62:4405-4409.
[55]Sun J, van den Heuvel J, Soucaille P, et al. Comparative genomic snslysis of dha regulon and related genes for anaerobic glycerol metabolism in bacteria [J]. Biotechnol Prog,2003, 19(2):263-272.
[56]Richery D P, Lin E C. Importance of facilitated diffusion for effective utilization of glycerol by Escherichia coli. J.Bacteriol,1972,12:784-790.
[57]Heller K B, Lin E C, Wilson T H. Substrate specificity and transport properties of the glycerol facilitator of Escherichia coli. J.Bacteriol,1980,144:274-278.
[58]Daniel R, Boenigk R, Gottschalk G. Purification of 1,3-propanediol dehydrogenase from Citrobacter freundii and cloning, sequeneing, and over expression of the corresponding gene in Escherichia coli[J]. J. Bacteriol.,1995,177:2151-2156.
[59]Honda S, Toraya T, Fukui S. In situ reactivation of glycerol inactivated coenzyme-B12-dependent glycerol dehydratase and dioldehydratase[J]. J.Baeteriol.,1980,143:1458-1465.
[60]钱伟懿,徐恭贤,宫召华.最有控制理论及其应用.大连：大连理工大学出版社,2010.
[61]修志龙,微生物发酵法生产1,3-丙二醇的研究进展[J].微生物学通报,2000,27(4)：300-302
[62]Gao C X, Feng E M, Wang Z T, Xiu Z L. Parameters identification problem of the nonlinear dynamical system in microbial continuous cultures[J]. Applied Mathematics and Computation,2005,169(1):476-484.
[63]Li X H, Feng E M, Xiu Z L. Stability and optimal control of microorganisms in continuous culture[J]. Journal of Applied Mathematics and Computing,2006,22:435-440.
[64]Ralf Sleuer. Computational approaches to the topology, stability and dynamics of metabolic networks[J]. Phytochemistry.2007,68:2139-2151.
[65]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.生物工程学报：2007,23(2)：201-205.
[66]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.中国生物工程杂志,2003.23(2)：64-67.
[67]北野宏明编,周笔锋.周艳红等译,系统生物学基础.北京：化学工业出版社,2007.