~(13)C代谢通量分析及优化设计的应用与研究
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摘要
代谢通量分析是代谢工程中重要的量化分析工具,它们揭示基因改造及由此产生的结果变化间的因果关系,并在代谢活动中作为一个先决条件用于生物细胞催化剂的优化与设计。由于胞内通量无法直接测量,所以必须对其进行通量估计。碳同位素标记实验是目前最精确的通量分析方法,通过基板及碳标记状态分布的测量,依据同位素守恒测量代谢稳态平衡方程求解中间代谢物所产生的不可测通量。然而,通常情况下这些方程均为繁琐的代数操作,由于非线性和高维度,导致数值计算求解复杂。
本文的主要研究内容是探讨适合求解代谢通量的精确量化分析及生化途径模型仿真的优化算法,具体的研究工作如下:
(1)论文简要介绍了代谢通量分析应用的两种方法:化学计量矩阵和碳同位素标记实验,着重于同位素标记原理及其碳原子转移运算与数学模型的构建。本文将代谢通量估计问题归结为带约束条件的碳同位素富集度平衡的全局优化问题,而智能优化算法由于其高效性、收敛性和鲁棒性等特点,近年来被广泛应用于全局优化问题的求解。
(2)以环磷酸戍糖代谢网络为模型就几种智能优化算法进行~(13)C代谢通量分析,仿真实验中,量子粒子群算法相较于其他算法收敛迅速,存在较好的拟合效果。并利用算法的非线性逼近能力完成一个含5个代谢物的代谢途径模型的模拟仿真,将参数编码成算法的一组解向量,以实验值和预测值的误差平方加权和为目标优化函数。仿真试验表明用多样性指导量子粒子群算法求解较好,成功地完成了对已知模型的预测。
(3)QPSO虽然较好的求解代谢通量,但仍存在一定的误差,可见单一的智能算法并无法满足代谢通量精确量化分析的需求。论文提出多种优化算法相互结合取长补短进行通量估计。以模拟噪声环境下包含12个胞内代谢物共56维碳原子,16维通量的大肠杆菌代谢网络为研究对象进行求解。将量子粒子群算法与最小二乘相结合,分别用于通量分析及代谢物碳原子估计。仿真实验表明,LS用于代谢物碳原子分析、QPSO用于通量分析较好地完成了对代谢网络模型的拟合,较其他方法对非确定性网络的分析存在更小的均方误差及均方误差方差,适合通量精确量化分析。由此可见,对于不同的优化问题,单一的优化算法往往在执行速度或者优化精度方面无法达到平衡,因此综合考虑多种优化算法的优势,不同算法的混合对代谢通量估计有着广泛的应用前景。
Metabolic fluxes analysis has been regarded as an important quantity for metabolic engineering, they reveal cause-effect relationships between genetic modifications and resulting changes in metabolic activity. They are also used as a prerequisite for the design of optimal whole cell biocatalysts. The intracellular fluxes must be estimated due to the inability to measure them directly. A particular useful technique involves the use of 13C-enricbed substrates and the measurement of label distribution generated for each intermediate to uncover all unmeasured fluxes by solving the label balance equations, e.g. isotopomer balances, at steady state. However, the formation of these equations typically requires tedious algebraic manipulation and in many cases the resulting equations must be solved numerically, due to the nonlinearity and high dimensionality.
The purpose of our work is to find an intelligent algorithm which suit for the metabolic fluxes analysis and parameter estimation of the dynamic biochemical systems.
First, we introduce the main methods of metabolic flux analysis: stoichiometry matrix and carbon labeling experiments and isotope labeling experiments focus on theory and the transfer of carbon atoms in the basic operation and construction of a mathematical model. In this paper, flux estimation is formulated as a global optimization problem by carbon enrichment balances. Intelligent algorithms had been widely used in global optimization programming problems for the efficiency, convergency and robustness of the algorithms
Second, a case study considering the estimation of cyclic pentose phosphate pathway and 5 parameters of a nonlinear biochemical dynamic model have been taken as a benchmark. Several intelligent optimization algorithms have been explored to the problem. Experiments show that quantum-behaved particle swarm optimization algorithm can estimate the flux with high accuracy and successfully reconstruct the metabolic networks.
Third, the results show that a single optimization algorithm is ineffective. Combined with a variety of optimization algorithms to solve ~(13)CMFA will be a good method. The Quantum-behaved PSO algorithm performances are illustrated and compared with ordinary least squares estimation through simulation of the E. coli metabolic network in a noisy environment. The LS-QPSO algorithm has a better performance as showed by the comparative experiments. By the simulation shows, for different optimization problems, often in a single optimization algorithm optimization of execution speed or precision can not get satisfactory results, so considering the advantage of a variety of optimization algorithms to form a hybrid algorithm will bring metabolic flux estimation rapid development
本文的主要研究内容是探讨适合求解代谢通量的精确量化分析及生化途径模型仿真的优化算法,具体的研究工作如下:
(1)论文简要介绍了代谢通量分析应用的两种方法:化学计量矩阵和碳同位素标记实验,着重于同位素标记原理及其碳原子转移运算与数学模型的构建。本文将代谢通量估计问题归结为带约束条件的碳同位素富集度平衡的全局优化问题,而智能优化算法由于其高效性、收敛性和鲁棒性等特点,近年来被广泛应用于全局优化问题的求解。
(2)以环磷酸戍糖代谢网络为模型就几种智能优化算法进行~(13)C代谢通量分析,仿真实验中,量子粒子群算法相较于其他算法收敛迅速,存在较好的拟合效果。并利用算法的非线性逼近能力完成一个含5个代谢物的代谢途径模型的模拟仿真,将参数编码成算法的一组解向量,以实验值和预测值的误差平方加权和为目标优化函数。仿真试验表明用多样性指导量子粒子群算法求解较好,成功地完成了对已知模型的预测。
(3)QPSO虽然较好的求解代谢通量,但仍存在一定的误差,可见单一的智能算法并无法满足代谢通量精确量化分析的需求。论文提出多种优化算法相互结合取长补短进行通量估计。以模拟噪声环境下包含12个胞内代谢物共56维碳原子,16维通量的大肠杆菌代谢网络为研究对象进行求解。将量子粒子群算法与最小二乘相结合,分别用于通量分析及代谢物碳原子估计。仿真实验表明,LS用于代谢物碳原子分析、QPSO用于通量分析较好地完成了对代谢网络模型的拟合,较其他方法对非确定性网络的分析存在更小的均方误差及均方误差方差,适合通量精确量化分析。由此可见,对于不同的优化问题,单一的优化算法往往在执行速度或者优化精度方面无法达到平衡,因此综合考虑多种优化算法的优势,不同算法的混合对代谢通量估计有着广泛的应用前景。
Metabolic fluxes analysis has been regarded as an important quantity for metabolic engineering, they reveal cause-effect relationships between genetic modifications and resulting changes in metabolic activity. They are also used as a prerequisite for the design of optimal whole cell biocatalysts. The intracellular fluxes must be estimated due to the inability to measure them directly. A particular useful technique involves the use of 13C-enricbed substrates and the measurement of label distribution generated for each intermediate to uncover all unmeasured fluxes by solving the label balance equations, e.g. isotopomer balances, at steady state. However, the formation of these equations typically requires tedious algebraic manipulation and in many cases the resulting equations must be solved numerically, due to the nonlinearity and high dimensionality.
The purpose of our work is to find an intelligent algorithm which suit for the metabolic fluxes analysis and parameter estimation of the dynamic biochemical systems.
First, we introduce the main methods of metabolic flux analysis: stoichiometry matrix and carbon labeling experiments and isotope labeling experiments focus on theory and the transfer of carbon atoms in the basic operation and construction of a mathematical model. In this paper, flux estimation is formulated as a global optimization problem by carbon enrichment balances. Intelligent algorithms had been widely used in global optimization programming problems for the efficiency, convergency and robustness of the algorithms
Second, a case study considering the estimation of cyclic pentose phosphate pathway and 5 parameters of a nonlinear biochemical dynamic model have been taken as a benchmark. Several intelligent optimization algorithms have been explored to the problem. Experiments show that quantum-behaved particle swarm optimization algorithm can estimate the flux with high accuracy and successfully reconstruct the metabolic networks.
Third, the results show that a single optimization algorithm is ineffective. Combined with a variety of optimization algorithms to solve ~(13)CMFA will be a good method. The Quantum-behaved PSO algorithm performances are illustrated and compared with ordinary least squares estimation through simulation of the E. coli metabolic network in a noisy environment. The LS-QPSO algorithm has a better performance as showed by the comparative experiments. By the simulation shows, for different optimization problems, often in a single optimization algorithm optimization of execution speed or precision can not get satisfactory results, so considering the advantage of a variety of optimization algorithms to form a hybrid algorithm will bring metabolic flux estimation rapid development
引文
1. M.Mavrovouniotis and G.Stephanopoulos,Synthesis of biochemical production routes.Computers and Chemical Engineering,vol.16,no.6,PP.605-619,1992.
2. BaiLey J E,Toward a science of metabolic engineering. Science, 1991,252:1668-1675
3.张蓓编著代谢工程[M],天津:天津大学出版社2003.4 ISBN 7-5618-1759-2
4.内斯托儿,埃伯哈德著,休志龙等译.代谢工程的途径分析与优化[M].北京:化学工业出版社.2005
5.埃伯哈德著,储炬等译.生物化学系统的计算分析[M].北京:化学工业出版社.2006
6. A.Marx,A.A.de Graaf,W.Wiechert,L.Eggeling,and H.Sahm.,”Determination of the fluxes in central metabolism of corynebacterium glutamicum by nmr spectroscopy combined with metabolite balanc”Biotechnol.Bioeng.vol.49,PP.111-129,1996
7. Jong H D, Geiselmann J, Hernandez C et al. Genetic network analyzer: qualitative simulation of genetic regulatory networks[J]. Bioinformatics, 2003,19(3):336-344
8. Wiechert.W.13C Metabolic Flux Analysis.Metabolic Engineering,2001.3:l95-206
9. J. D.Fell and J.Small,“Fat synthesis in adipose tissue.an examination of stoichiometric constraints,”Biochem.Vol.238,no.3,PP.781—786,1986
10. Rankin Small,J.and D.A.Fell,The matrix method of metabolic control analysis: its validity for complex pathway structures,Journal of Theoretical Biology, 1989.136:181-197
11. Malloy,C.R.,A.D.Sherry,and F.M.Jeffrey,Evaluation of carbon flux and substrate selection through alternate pathways involving the citric acid cycle of the heart by 1 3C NMR spectroscopy.J Biol Chem,1988,263:6964-71
12. Savinell,J.M.and B.O.Paisson,Network analysis of intermediary metabolism using linear optimization.I.Development of mathematical formalism.J Biol Chem,1992,34:421-547
13. A.Vanv_a and B.Palsson,Metabolic capabilities of Escherichia coli:II.optimal growthpatterns,Journal of Theoretical Biology,vol.165,no.4,pp.503—522,1993
14. C.Zupke and G.Stephanopoulos,Intracellular flux analysis in hy’bridomasusing mass balances and in vitroC nlnr,Biotechnol Bioen9,vol.45.PP.292-303,1995
15. Wiechert and A.A.deGraaf,Bidirectional reaction steps in metabolic networks:I modeling and simulation of carbon isotope labeling experiments, Biotechn01.Bioeng.vol.55,no.1,PP.101—117,1997
16. K Sauer,U,et a1,Metabolic Flux Ratio Analysis of Genetic and Environmental Modulations of Escherichia coli Central Carbon Metabolism Biophysical Soc,1999.12:6679—6688.
17. A.de Graaf,K.Striegel,R.M.Wittig,B.Laufer,G.Schmitz,and W.Wiechert.“Metabolic state of zymomonas mobilis in glucose-,fructose-,and xylose-fed continuous cultures a 8 analysedby C-and 31p-nmr pectroscopy,
18. Schilling,C.H,et a1,Combining pathway analysis with flux balance analysis for the comprehensive study of metabolic systems.Biophysical Soc,2000,50:286-306
19. Petersen,S,et a1,In Vivo Quantification ofParallel and Bidirectional Fluxes inthe Anaplerosis of Corynebacterium glutamicum. ASBMB. 20005:35932.3594.
20. W.Wiechert,M.Mollney,S.Petersen,and A.A.de Graaf,A universal framework for 13C metabolic flux analysis,Metabolic Engineering,vol.3,no.3,PP.265-283,2001.
21. CovertM.w,C.H.Schilling,and B.Palsson,Regulation of gene expression in flux balance models ofmetabolism.Metabolic Engineering,2001,3:73-88.
22. van Winden,J.Heijnen,and P.Verheijen,Cumulative bondomers:A flew concept in flux analysis from 2d13C,1hl cosy nmr data,Biotechn01.Bioeng,vol.80,PP.731-745,2002
23. Beard,D.A,S.Liang,and H.Qian,Energy Balance for Analysis of Complex Metabolic Networks.Biophysical Soc.2002,7:79-86
24. G.John,1.Klimant C.Wittmann,and E.Heinzle,Integrated optical sensing of dissolved oxygen in microtiter plates:A novel tool for microbial cultivation,Biotechnology and Bioengineering,vol.81,no.7,PP.829—836,2003.
25. FA.Drysch,M.El Massaoudi,A.de Graaf,and H Sahm,Production process monitoring by serial mapping of microbial carbon flux distributions using a novel sensor reactor approach : 13c 1abeling-based metabolic flux analysis and 1-1ysine production.Metabolic Eng.Vol.5,no.2,pp.96—107,2003.
26. E.Fischer ,N.Zamboni,and U.Saner,High—throughput metabolic flux Analysis based on gas chromatography-mass spectrometry derived 13C constraints ,Anal.Biochem.vol.325,no.2,PP.308—316,2004
27. Kromer,J.O,et a1,In vivo quantification of intracellular amino acids and intermediates of the methionine pathway in Corynebacterium glutamicum Metabolic Engineering.2005,23:1 71-3.
28. Noh,K,A.Wahl,and w.Wiechert,Computational tools for isotopically instationary 13C labeling experiments under metabolic steady state conditions . Metabolic Engineering.2006,8:554—577
29. watani S,Yamada Y Metabolic flux analysis in biotechnology processes Biotechnol Lett.2008;30:79 .1799
30. Nanchen A,Schicker A,Sauer U.Cyclic AMP—dependent catabolite repression is the dominant control mechanism of metabolic fluxes under glucose limitation in Escherichia coli.J Baeteriol.2008;1 90:2323—2330
31.张惠展.途径工程—第三代基因工程[M].北京:中国轻工业出版社,2002.
32. Voit, E.O., Almeida, J. Decoupling dynamical systems for pathway identification from metabolic profiles[J]. Bioinformatics. 2004,20:1670-1681
33. Jiusheng Chen Improving metabolic flux estimation via evolution nary optimization for convex solution space Bionformatics Vol. 23 no. 9 2007, Pages 1115–1123
34. Kazuyuki Shimizu Metabolic Flux Analysis Based on ~(13)C -Labeling Experiments andIntegration of the Information with Gene and Protein Expression Patterns Adv Biochem Engin/Biotechnol 2004
35. Wolfgang Wiechert Bidirectional Reaction Steps in Metabolic NetworksExplicit Solution and Analysis of Isotopomer Labeling Systems BiotechnologyI And Bioengineering 1999
36.徐恭贤.一类生化过程的优化及控制方法研究[D].[博士学位论文].大连:大连理工大学,2008
37. Kimura.S, Hatakemana.M., Konagary A. Inference of S-system models of genetic networks using a genetic local search, 2003 [C]//Proceeding of the 2003 Congress on Evolutionary Computation. 2003:631-638
38.孙啸,陆祖宏,谢建明.生物信息学基础[M].北京:清华大学出版社,2005.
39. Schwefel, H P. Evolution and optimum seeking[M]. Wiley, New York,1995
40. Wolkenhauer O, Ullah M, Wellstead P, Cho K. The dynamic systems approach to control and regulation of intracellular networks[J]. FEBS Letters 2005, 579 (8): 1846-1853
41. J. Kennedy, R. C. Eberhart, Particle Swarm Optimization. Proc. IEEE Int’l Conference on Neural Networks, IV. Piscataway, NJ: IEEE Service Center, 1995, pp. 1942-1948
42. J. Sun, W.B Xu. A Global Search Strategy of Quantum-behaved Particle Swarm Optimization[A]. Proceedings of IEEE conference on Cybernetics and Intelligent Systems[C]. 2004. 111– 116
43. Kirkpatric S, Gelatt C D, Vecchi M P. Optimization by simulated annealing[J]. Science, 1983,220:671-680
44. Holland J H[M]. Adaptation in natural and artificial systems. Ann Arbor, MI: University of Michigan Press,1975
45.高隽.人工神经网络原理及仿真实例[M].北京:机械工业出版社,2007
46. J. Sun, B. Feng, W.B Xu. Particle Swarm Optimization with Particles Having Quantum Behavior, Proc. 2004 Congress on Evolutionary Computation, pp. 325-331.
47. Shi Y, Eberhart R C. A Modified Particle Swarm Optimizer. In: Proceedings of the IEEE International Conference on Evolutionary Computation. Piscataway, NJ: IEEE Press,1998, 69-73.
48. XU WENBO, SUN JUN, Adaptive parameter selection of quantum-behaved particle swarm optimization on global level[C], Springer Berlin / Heidelberg. D.S. Huang, X.P. Zhang,,G.B. huang (Eds.): ICIC 2005, LNCS 3644, 2005:420-428
49. Jing Yang, Sarawan Wongsa Differential Evolution and Its Application to Metabolic Flux Analysis EvoWorkshoPs 2005, lnsc 3449, PP. 115–124
50. Jing Yang Sarawan Wongsa Metabolic Flux Estimation A Self-AdaPtive Evolutionary Algorithm with Singular Value Decomposition Ieee Transactions on Computational 2007
51. Christo Phe H. Schilling Combining Pathway Analysis with Flux Balance Analysis for the ComPrehensive Study of Metabolic Systems, vol.71, No.4, 2000/2001
52. Thomas P. Runarsson and Xin Yao Stochastic Ranking for Constrained Evolutionary Optimization IEEE Transactions on Evolutionary Computational vol. 4, No. 3, 2000-9
53. Tobias Furch Comparative study on central metabolic fluxes of Bacillus megaterium strains in continuous culture using 13C labeled substrates Bioprocess Biosyst 2007
54. Nicola Zamboni Toward metabolome-based 13C flux analysis: auniversal tool for measuring in vivo metabolic activity ToPics in Current Genetics, Vol. 18 APril 2007
55. Carmen G. Moles, Pedro Mendes, Julio R.Banga. Parameter Estimation in Biochemical Pathways: A Comparison of Global Optimization Methods. Genome Res[J]. 2003:13:2467-2474
2. BaiLey J E,Toward a science of metabolic engineering. Science, 1991,252:1668-1675
3.张蓓编著代谢工程[M],天津:天津大学出版社2003.4 ISBN 7-5618-1759-2
4.内斯托儿,埃伯哈德著,休志龙等译.代谢工程的途径分析与优化[M].北京:化学工业出版社.2005
5.埃伯哈德著,储炬等译.生物化学系统的计算分析[M].北京:化学工业出版社.2006
6. A.Marx,A.A.de Graaf,W.Wiechert,L.Eggeling,and H.Sahm.,”Determination of the fluxes in central metabolism of corynebacterium glutamicum by nmr spectroscopy combined with metabolite balanc”Biotechnol.Bioeng.vol.49,PP.111-129,1996
7. Jong H D, Geiselmann J, Hernandez C et al. Genetic network analyzer: qualitative simulation of genetic regulatory networks[J]. Bioinformatics, 2003,19(3):336-344
8. Wiechert.W.13C Metabolic Flux Analysis.Metabolic Engineering,2001.3:l95-206
9. J. D.Fell and J.Small,“Fat synthesis in adipose tissue.an examination of stoichiometric constraints,”Biochem.Vol.238,no.3,PP.781—786,1986
10. Rankin Small,J.and D.A.Fell,The matrix method of metabolic control analysis: its validity for complex pathway structures,Journal of Theoretical Biology, 1989.136:181-197
11. Malloy,C.R.,A.D.Sherry,and F.M.Jeffrey,Evaluation of carbon flux and substrate selection through alternate pathways involving the citric acid cycle of the heart by 1 3C NMR spectroscopy.J Biol Chem,1988,263:6964-71
12. Savinell,J.M.and B.O.Paisson,Network analysis of intermediary metabolism using linear optimization.I.Development of mathematical formalism.J Biol Chem,1992,34:421-547
13. A.Vanv_a and B.Palsson,Metabolic capabilities of Escherichia coli:II.optimal growthpatterns,Journal of Theoretical Biology,vol.165,no.4,pp.503—522,1993
14. C.Zupke and G.Stephanopoulos,Intracellular flux analysis in hy’bridomasusing mass balances and in vitroC nlnr,Biotechnol Bioen9,vol.45.PP.292-303,1995
15. Wiechert and A.A.deGraaf,Bidirectional reaction steps in metabolic networks:I modeling and simulation of carbon isotope labeling experiments, Biotechn01.Bioeng.vol.55,no.1,PP.101—117,1997
16. K Sauer,U,et a1,Metabolic Flux Ratio Analysis of Genetic and Environmental Modulations of Escherichia coli Central Carbon Metabolism Biophysical Soc,1999.12:6679—6688.
17. A.de Graaf,K.Striegel,R.M.Wittig,B.Laufer,G.Schmitz,and W.Wiechert.“Metabolic state of zymomonas mobilis in glucose-,fructose-,and xylose-fed continuous cultures a 8 analysedby C-and 31p-nmr pectroscopy,
18. Schilling,C.H,et a1,Combining pathway analysis with flux balance analysis for the comprehensive study of metabolic systems.Biophysical Soc,2000,50:286-306
19. Petersen,S,et a1,In Vivo Quantification ofParallel and Bidirectional Fluxes inthe Anaplerosis of Corynebacterium glutamicum. ASBMB. 20005:35932.3594.
20. W.Wiechert,M.Mollney,S.Petersen,and A.A.de Graaf,A universal framework for 13C metabolic flux analysis,Metabolic Engineering,vol.3,no.3,PP.265-283,2001.
21. CovertM.w,C.H.Schilling,and B.Palsson,Regulation of gene expression in flux balance models ofmetabolism.Metabolic Engineering,2001,3:73-88.
22. van Winden,J.Heijnen,and P.Verheijen,Cumulative bondomers:A flew concept in flux analysis from 2d13C,1hl cosy nmr data,Biotechn01.Bioeng,vol.80,PP.731-745,2002
23. Beard,D.A,S.Liang,and H.Qian,Energy Balance for Analysis of Complex Metabolic Networks.Biophysical Soc.2002,7:79-86
24. G.John,1.Klimant C.Wittmann,and E.Heinzle,Integrated optical sensing of dissolved oxygen in microtiter plates:A novel tool for microbial cultivation,Biotechnology and Bioengineering,vol.81,no.7,PP.829—836,2003.
25. FA.Drysch,M.El Massaoudi,A.de Graaf,and H Sahm,Production process monitoring by serial mapping of microbial carbon flux distributions using a novel sensor reactor approach : 13c 1abeling-based metabolic flux analysis and 1-1ysine production.Metabolic Eng.Vol.5,no.2,pp.96—107,2003.
26. E.Fischer ,N.Zamboni,and U.Saner,High—throughput metabolic flux Analysis based on gas chromatography-mass spectrometry derived 13C constraints ,Anal.Biochem.vol.325,no.2,PP.308—316,2004
27. Kromer,J.O,et a1,In vivo quantification of intracellular amino acids and intermediates of the methionine pathway in Corynebacterium glutamicum Metabolic Engineering.2005,23:1 71-3.
28. Noh,K,A.Wahl,and w.Wiechert,Computational tools for isotopically instationary 13C labeling experiments under metabolic steady state conditions . Metabolic Engineering.2006,8:554—577
29. watani S,Yamada Y Metabolic flux analysis in biotechnology processes Biotechnol Lett.2008;30:79 .1799
30. Nanchen A,Schicker A,Sauer U.Cyclic AMP—dependent catabolite repression is the dominant control mechanism of metabolic fluxes under glucose limitation in Escherichia coli.J Baeteriol.2008;1 90:2323—2330
31.张惠展.途径工程—第三代基因工程[M].北京:中国轻工业出版社,2002.
32. Voit, E.O., Almeida, J. Decoupling dynamical systems for pathway identification from metabolic profiles[J]. Bioinformatics. 2004,20:1670-1681
33. Jiusheng Chen Improving metabolic flux estimation via evolution nary optimization for convex solution space Bionformatics Vol. 23 no. 9 2007, Pages 1115–1123
34. Kazuyuki Shimizu Metabolic Flux Analysis Based on ~(13)C -Labeling Experiments andIntegration of the Information with Gene and Protein Expression Patterns Adv Biochem Engin/Biotechnol 2004
35. Wolfgang Wiechert Bidirectional Reaction Steps in Metabolic NetworksExplicit Solution and Analysis of Isotopomer Labeling Systems BiotechnologyI And Bioengineering 1999
36.徐恭贤.一类生化过程的优化及控制方法研究[D].[博士学位论文].大连:大连理工大学,2008
37. Kimura.S, Hatakemana.M., Konagary A. Inference of S-system models of genetic networks using a genetic local search, 2003 [C]//Proceeding of the 2003 Congress on Evolutionary Computation. 2003:631-638
38.孙啸,陆祖宏,谢建明.生物信息学基础[M].北京:清华大学出版社,2005.
39. Schwefel, H P. Evolution and optimum seeking[M]. Wiley, New York,1995
40. Wolkenhauer O, Ullah M, Wellstead P, Cho K. The dynamic systems approach to control and regulation of intracellular networks[J]. FEBS Letters 2005, 579 (8): 1846-1853
41. J. Kennedy, R. C. Eberhart, Particle Swarm Optimization. Proc. IEEE Int’l Conference on Neural Networks, IV. Piscataway, NJ: IEEE Service Center, 1995, pp. 1942-1948
42. J. Sun, W.B Xu. A Global Search Strategy of Quantum-behaved Particle Swarm Optimization[A]. Proceedings of IEEE conference on Cybernetics and Intelligent Systems[C]. 2004. 111– 116
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