~（13）C标记技术测定Escherichia coli TUQ2厌氧中心碳代谢途径通量分布
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摘要
本文拟采用气质联用(GC-MS)的定量分析手段,通过对~(13)C标记的中间代谢产物标记状态的定量分析,对Escherichia coli TUQ2的中心碳代谢网络通量进行确定,为今后分析确定大肠杆菌生产琥珀酸新的基因改造靶点提供指导依据。本文通过实验确定GC-MS实验前期的恒化操作条件参数和步骤,并建立起实验前期的标记策略、实验后期的GC-MS谱图解析和数据处理的一整套比较完整的分析方法。
由于GC-MS底物定量选取策略的复杂性,本文主要采用定性的方法对底物标记方法进行确定。GC-MS的样品取自大肠杆菌添加了~(13)C标记底物的恒化培养经过3个停留时间所得到的中间代谢物的水解产物,为后期中心代谢网络通量的计算提供可靠的实验数据基础。
FiatFlux是一款定量研究胞内代谢通量的软件,对于不熟悉数学方法和同位素示踪实验的用户也可以进行胞内通量计算。该软件面向非专业用户,可以满足他们进行特殊研究的要求,包括用~(13)C标记底物、混合物以及生物体。
本文中心代谢网络通量的计算可分为四个步骤,首先建立适合该菌体的模型,用MATLAB对模型进行适当的修正。然后是对实验得出的GC-MS谱图的各氨基酸峰进行手动标记,选取一种合适的标记方案,再根据液相色谱测得的胞外通量和反应网络中各步反应的是否发生和其可逆性结合计算,最后以模拟计算和实验数据拟合的最小平方估计F值为优化目标,计算得到大肠杆菌中心代谢网络的通量值。
This paper adopts the ~(13)C labeling technique combined with Gas Chromalography-Mass Spectrum (GC-MS) measurement technique as quantitive analysis method to identify the central metabolic flux distributions of Escherichia coli TUQ2 under anaerobic enviroment. This project will provide a more accurate bird’s view about metabolic flux distributions under ptsG gene knockout condition and will help to locate more protential gene manipulation point for strain production improvement of succinic acid. Due to the limited time, unavailability of equipments and chemicals, this paper only covers preliminary experiments to figure out the procedures and culture parameters of the prophase GC-MS chemostat experiment. Problems such as substrates labeling strategy, GC-MS spectrum analysis, etc. are theoretically analyzed and settled properly.
Considering the complexisity of determinating substrate labeling stragety, the selection of labeling pattern in this paper is qualitively decided under the guidance of combined optimization of high GC-MS spectrum resolution and strong signal intensity.
The GC-MS samples are prepared from the intermediate metabolite hydrolyzed residues. The intermediate metabolites are derived from the chemostat E. coli culture, after adding ~(13)C labeling substrate and waiting for 3 resident times. FiatFlux, which is an intuitive tool for quantitative investigations of intracellular metabolism by users that are not familiar with numerical methods or isotopic tracer experiments. The aim of this open source software is to enable non-specialists to adapt the software to their specific scientific interests, including other ~(13)C-substrates, labeling mixtures, and organisms.
The calculation of the central metabolic flux distribution in this paper can be devided into four steps. First of all, a model which is suitable for Escherichia coli TUQ2 is founded,and a correction could be made with MATLAB if needed. Secondly, manually assign TBDMS-derivatized proteinogenic amino acids analyzed by GC-MS,and choose a proper assignment.Thirdly,determin the extracellular flux by HPLC and the activity and reversibility of all reactions in the reaction network must be considered during the calculation process.Finally,use least square estimation F between simulation calculation and experiment data as the optimization objective to solve the central metabolic flux distribution of Escherichia coli TUQ2 under anaerobic enviroment.
由于GC-MS底物定量选取策略的复杂性,本文主要采用定性的方法对底物标记方法进行确定。GC-MS的样品取自大肠杆菌添加了~(13)C标记底物的恒化培养经过3个停留时间所得到的中间代谢物的水解产物,为后期中心代谢网络通量的计算提供可靠的实验数据基础。
FiatFlux是一款定量研究胞内代谢通量的软件,对于不熟悉数学方法和同位素示踪实验的用户也可以进行胞内通量计算。该软件面向非专业用户,可以满足他们进行特殊研究的要求,包括用~(13)C标记底物、混合物以及生物体。
本文中心代谢网络通量的计算可分为四个步骤,首先建立适合该菌体的模型,用MATLAB对模型进行适当的修正。然后是对实验得出的GC-MS谱图的各氨基酸峰进行手动标记,选取一种合适的标记方案,再根据液相色谱测得的胞外通量和反应网络中各步反应的是否发生和其可逆性结合计算,最后以模拟计算和实验数据拟合的最小平方估计F值为优化目标,计算得到大肠杆菌中心代谢网络的通量值。
This paper adopts the ~(13)C labeling technique combined with Gas Chromalography-Mass Spectrum (GC-MS) measurement technique as quantitive analysis method to identify the central metabolic flux distributions of Escherichia coli TUQ2 under anaerobic enviroment. This project will provide a more accurate bird’s view about metabolic flux distributions under ptsG gene knockout condition and will help to locate more protential gene manipulation point for strain production improvement of succinic acid. Due to the limited time, unavailability of equipments and chemicals, this paper only covers preliminary experiments to figure out the procedures and culture parameters of the prophase GC-MS chemostat experiment. Problems such as substrates labeling strategy, GC-MS spectrum analysis, etc. are theoretically analyzed and settled properly.
Considering the complexisity of determinating substrate labeling stragety, the selection of labeling pattern in this paper is qualitively decided under the guidance of combined optimization of high GC-MS spectrum resolution and strong signal intensity.
The GC-MS samples are prepared from the intermediate metabolite hydrolyzed residues. The intermediate metabolites are derived from the chemostat E. coli culture, after adding ~(13)C labeling substrate and waiting for 3 resident times. FiatFlux, which is an intuitive tool for quantitative investigations of intracellular metabolism by users that are not familiar with numerical methods or isotopic tracer experiments. The aim of this open source software is to enable non-specialists to adapt the software to their specific scientific interests, including other ~(13)C-substrates, labeling mixtures, and organisms.
The calculation of the central metabolic flux distribution in this paper can be devided into four steps. First of all, a model which is suitable for Escherichia coli TUQ2 is founded,and a correction could be made with MATLAB if needed. Secondly, manually assign TBDMS-derivatized proteinogenic amino acids analyzed by GC-MS,and choose a proper assignment.Thirdly,determin the extracellular flux by HPLC and the activity and reversibility of all reactions in the reaction network must be considered during the calculation process.Finally,use least square estimation F between simulation calculation and experiment data as the optimization objective to solve the central metabolic flux distribution of Escherichia coli TUQ2 under anaerobic enviroment.
引文
[1]Lee SY, Hong SH, Moon SY. In silico metabolic pathway analysis and design: succinic acid production by metabolically engineered Escherichia coli as an example.Genome Inform. 2002;13:214-223
[2]Adachi K, Cruz NF, Sokoloff L, et al. Labeling of metabolic pools by [6-14C]glucose during K(+)-induced stimulation of glucose utilization in rat brain. J Cereb Blood Flow Metab. 1995;15:97-110
[3]Zamboni N, Fischer E, Sauer U.Transient expression and flux changes during a shift from high to low riboflavin production in continuous cultures of Bacillus subtilis.Biotechnol Bioeng. 2005;89:219-232
[4]Franzen CJ. Metabolic flux analysis of RQ-controlled microaerobic ethanol production by Saccharomyces cerevisiae. Yeast. 2003;20:117-132
[5]Wiechert W. 13C Metabolic Flux Analysis. Metabolic Engineering. 2001;3: 195-206
[6]Allwood JW, Ellis DI, Heald JK, et al. Metabolomic approaches reveal that phosphatidic and phosphatidyl glycerol phospholipids are major discriminatory non-polar metabolites in responses by Brachypodium distachyon to challenge by Magnaporthe grisea. Plant J. 2006;46:351-368
[7]Wiback SJ, Mahadevan R, Palsson B. Using metabolic flux data to further constrain the metabolic solution space and predict internal flux patterns:the Escherichia coli spectrum. Biotechnol Bioeng. 2004;86:317-331.
[8]F?rster J, Gombert AK, Nielsen J. A functional genomics approach using metabolomics and in silico pathway analysis. Biotechnol Bioeng. 2002;79:703-712
[9]Stephanopulos GN, Aristidou AA, Nielsen J. Metabolic Engineering Principle and methodologies.NEW YORK: Academic Press, 1998, 235-246
[10]Wiechert W, M?llney M, Petersen S, et al. A universal framework for 13C metabolic flux analysis. Metab Eng. 2001;3:265-283
[11]Vallino JJ, Stephanopoulos G. Metabolic flux distributions in Corynebacterium glutamicum during growth and lysine overproduction. Reprinted from Biotechnology and Bioengineering. 1993;41:633-646
[12]Pantel J, Schr?der J, Sauer H,et al. Quantitative magnetic resonance imaging and neuropsychological functions in dementia of the Alzheimer type. Psychol Med. 1997;27:221-229
[13]De Graaf AA, Striegel K, Wittig RM,et al. Metabolic state of Zymomonas mobilis in glucose-, fructose-, and xylose-fed continuous cultures as analysed by 13C- and 31P-NMR spectroscopy.Arch Microbiol. 1999;171:371-85
[14]Christensen B, Nielsen J. Isotopomer Analysis Using GC-MS. Metabolic Engineering.1999;1:282-290
[15]Dauner M, Sauer U. GC-MS analysis of amino acids rapidly provides rich information for isotopomer balancing. Biotechnol Prog. 2000;16:642-649
[16]Beard DA., Liang S, and Qian H. Energy Balance for Analysis of Complex Metabolic Networks. Biophysical Soc. 2002;7:79-86
[17]Isermann N, Wiechert W. Metabolic isotopomer labeling systems. Part II: structural flux identifiability analysis. Math Biosci. 2003;183:175-214
[18]Martin GE, Zektzer AS. Two-dimensional NMR methods for establishing molecular connectivity: a chemist's guide to experiment selection, performance, and interpretation. Metabolic Engineering. 1988;4:125-142
[19]Zhao J, Shimizu K. Metabolic flux analysis of Escherichia coli K12 grown on 13C-labeled acetate and glucose using GC-MS and powerful flux calculation method. Journal of Biotechnology. 2003;101:101-117
[20]Fischer E, Sauer U. Metabolic flux profiling of Escherichia coli mutants in central carbon metabolism using GC-MS. FEBS. 2003;3:100-109
[21]Wiechert W. Bidirectional reaction steps in metabolic networks: III. Explicit solution and analysis of isotopomer labeling systems. Biotechnology and Bioengineering. 1999;66:69-85
[22]Mollney M. Bidirectional reaction steps in metabolic networks: IV. Optimal design of isotopomer labeling experiments. Biotechnology and Bioengineering. 1999; 66:86-103
[23]Sriram G., Shanks JV. Improvements in metabolic flux analysis using carbon bond labeling experiments: Bondomer balancing and Boolean function mapping. Metabolic Engineering. 2004, 6:116-132.
[24]Van Winden. Metabolic flux and metabolic network analysis of Penicillium chrysogenum using 2D [C-13, H-1] COSYNMR measurements and cumulative Bondomer simulation. Biotechnology and Bioengineering. 2003;83:75-92
[25]Mendes P. Biochemistry by numbers: simulation of biochemical pathways with Gepasi 3. Metabolic Engineering. 1997;14:361-370
[26]Pfeiffer T. METATOOL: for studying metabolic networks. Bioinformatics 1999;15:251-257
[27] Wiechert W. A universal framework for 13C metabolic flux analysis. Metabolic Engineering. 2001;3:265-283
[28]Zhu T. Convex analysis of metabolic network for optimal cell design & flux validation by GC-MS or NMR. Metabolic Engineering. 2002;20:458-467
[29]Nanchen A, Fuhrer T, Sauer U. Determination of metabolic flux ratios from 13C-experiments and gas chromatography-mass spectrometry data: protocol and principles. Methods Mol Biol. 2007;358:177-97.
[30]Zamboni N, Fischer E, Sauer U. FiatFlux--a software for metabolic flux analysis from 13C-glucose experiments. BMC Bioinformatics. 2005;6:209
[31]Blum JJ, Stein RB. On the analysis of metabolic networks.In“Biological Regulation and Development”. New York: Plenum Press, 1982, 99-124
[32]Rankin SJ, Fell DA. The matrix method of metabolic control analysis: its validity for complex pathway structures. Journal of Theoretical Biology. 1989;136:181-197
[33]Malloy CR, Sherry AD, Jeffrey FM. Evaluation of carbon flux and substrate selection through alternate pathways involving the citric acid cycle of the heart by 13C NMR spectroscopy. J Biol Chem.1988;263:6964-6971
[34]Majewski RA, Domach MM. Simple Constrained-Optimization View of Acetate Overflow in Escherichia coli. J Biol Chem.1990;12:732-738
[35]Savinell JM, Palsson BO. Network analysis of intermediary metabolism using linear optimization. I. Development of mathematical formalism. J Biol Chem.1992; 34:421-454
[36]Savinell JM, Palsson BO. Network analysis of intermediary metabolism using linear optimization. II. Interpretation of hybridoma cell metabolism. J Biol Chem. 1992;9:455-473
[37]Savinell JM, Palsson BO. Optimal selection of metabolic fluxes for in vivo measurement. I. Development of mathematical methods. Am Soc Microbiol. 1992; 20:201-214
[38]Savinell JM, Palsson BO. Optimal selection of metabolic fluxes for in vivo measurement. II. Application to Escherichia coli and hybridoma cell metabolism. Am Soc Microbiol.1992;47:215-242
[39]Katz J, Wals P, Lee WN. Isotopomer studies of gluconeogenesis and the Krebs cycle with 13C-labeled lactate. ASBMB.1993;2:25509-25521.
[40]Wiechert W. Bidirectional reaction steps in metabolic networks: II. Flux estimation and statistical analysis. Journal of Biotechnology.1997;30:118-135
[41]Schmidt K, Nielsen J, Villadsen J. Quantitative analysis of metabolic fluxes in Escherichia coli, using two-dimensional NMR spectroscopy and complete isotopomer models. Journal of Biotechnology. 1999;71:175-189
[42]Sauer U. Metabolic Flux Ratio Analysis of Genetic and Environmental Modulations of Escherichia coli Central Carbon Metabolism. Biophysical Soc.1999; 12:6679-6688
[43]Schilling CH. Combining pathway analysis with flux balance analysis for the comprehensive study of metabolic systems. Biophysical Soc. 2000;50:286-306
[44]Petersen S. In Vivo Quantification of Parallel and Bidirectional Fluxes in the Anaplerosis of Corynebacterium glutamicum. ASBMB. 2000;5:35932-35941
[45]Covert MW, Schilling CH, Palsson B. Regulation of gene expression in flux balance models of metabolism. Metabolic Engineering. 2001;3:73-88
[46]Mahadevan R, Edwards JS, Doyle FJ. Dynamic Flux Balance Analysis of Diauxic Growth in Escherichia coli. Biophysical Soc. 2002;23:1331-1340
[47]Beard DA, Liang S, Qian H. Energy Balance for Analysis of Complex Metabolic Networks. Biophysical Soc. 2002;7:79-86
[48]Massaoudi E. Production process monitoring by serial mapping of microbial carbon flux distributions using a novel sensor reactor approach: I--Sensor reactor system. Metabolic Engineering. 2003;37:86-95
[49]Drysch A. Production process monitoring by serial mapping of microbial carbon flux distributions using a novel Sensor Reactor approach: II--(13) C-labeling-based metabolic flux analysis and L-lysine production. Metabolic Engineering. 2003;9:96-107
[50]Kromer JO.In-Depth Profiling of Lysine-Producing Corynebacterium glutamicum by Combined Analysis of the Transcriptome, Metabolome, and Fluxome. Am Soc Microbiol. 2004;45:1769-1784
[51]Wiechert W, N?h K. From stationary to instationary metabolic flux analysis.Adv Biochem Eng Biotechnol. 2005;92:145-72
[52]Noh K, Wahl A, Wiechert W. Computational tools for isotopically instationary 13C labeling experiments under metabolic steady state conditions. Metabolic Engineering. 2006;8:554-577
[53]Iwatani S, Yamada Y. Metabolic flux analysis in biotechnology processes. Biotechnol Lett. 2008;30:791-799
[54]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 Bacteriol.2008;190:2323-2330
[55]Grotkjaer T, Akesson M, Nielsen J, et al. Impact of transamination reactions and protein turnover on labeling dynamics in (13)C-labeling experiments.Biotechnol Bioeng. 2004;86:209-216
[56]van Winden WA, van Dam JC, Ras C, et al. Metabolic-flux analysis of Saccharomyces cerevisiae CEN.PK113-7D based on mass isotopomer measurements of (13)C-labeled primary metabolites. FEMS Yeast Res. 2005;5:559-568
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[60]Nanchen A, Fuhrer T, Sauer U. Determination of metabolic flux ratios from 13C-experiments and gas chromatography-mass spectrometry data: protocol and principles. Methods Mol Biol.2007;358:177-197
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[2]Adachi K, Cruz NF, Sokoloff L, et al. Labeling of metabolic pools by [6-14C]glucose during K(+)-induced stimulation of glucose utilization in rat brain. J Cereb Blood Flow Metab. 1995;15:97-110
[3]Zamboni N, Fischer E, Sauer U.Transient expression and flux changes during a shift from high to low riboflavin production in continuous cultures of Bacillus subtilis.Biotechnol Bioeng. 2005;89:219-232
[4]Franzen CJ. Metabolic flux analysis of RQ-controlled microaerobic ethanol production by Saccharomyces cerevisiae. Yeast. 2003;20:117-132
[5]Wiechert W. 13C Metabolic Flux Analysis. Metabolic Engineering. 2001;3: 195-206
[6]Allwood JW, Ellis DI, Heald JK, et al. Metabolomic approaches reveal that phosphatidic and phosphatidyl glycerol phospholipids are major discriminatory non-polar metabolites in responses by Brachypodium distachyon to challenge by Magnaporthe grisea. Plant J. 2006;46:351-368
[7]Wiback SJ, Mahadevan R, Palsson B. Using metabolic flux data to further constrain the metabolic solution space and predict internal flux patterns:the Escherichia coli spectrum. Biotechnol Bioeng. 2004;86:317-331.
[8]F?rster J, Gombert AK, Nielsen J. A functional genomics approach using metabolomics and in silico pathway analysis. Biotechnol Bioeng. 2002;79:703-712
[9]Stephanopulos GN, Aristidou AA, Nielsen J. Metabolic Engineering Principle and methodologies.NEW YORK: Academic Press, 1998, 235-246
[10]Wiechert W, M?llney M, Petersen S, et al. A universal framework for 13C metabolic flux analysis. Metab Eng. 2001;3:265-283
[11]Vallino JJ, Stephanopoulos G. Metabolic flux distributions in Corynebacterium glutamicum during growth and lysine overproduction. Reprinted from Biotechnology and Bioengineering. 1993;41:633-646
[12]Pantel J, Schr?der J, Sauer H,et al. Quantitative magnetic resonance imaging and neuropsychological functions in dementia of the Alzheimer type. Psychol Med. 1997;27:221-229
[13]De Graaf AA, Striegel K, Wittig RM,et al. Metabolic state of Zymomonas mobilis in glucose-, fructose-, and xylose-fed continuous cultures as analysed by 13C- and 31P-NMR spectroscopy.Arch Microbiol. 1999;171:371-85
[14]Christensen B, Nielsen J. Isotopomer Analysis Using GC-MS. Metabolic Engineering.1999;1:282-290
[15]Dauner M, Sauer U. GC-MS analysis of amino acids rapidly provides rich information for isotopomer balancing. Biotechnol Prog. 2000;16:642-649
[16]Beard DA., Liang S, and Qian H. Energy Balance for Analysis of Complex Metabolic Networks. Biophysical Soc. 2002;7:79-86
[17]Isermann N, Wiechert W. Metabolic isotopomer labeling systems. Part II: structural flux identifiability analysis. Math Biosci. 2003;183:175-214
[18]Martin GE, Zektzer AS. Two-dimensional NMR methods for establishing molecular connectivity: a chemist's guide to experiment selection, performance, and interpretation. Metabolic Engineering. 1988;4:125-142
[19]Zhao J, Shimizu K. Metabolic flux analysis of Escherichia coli K12 grown on 13C-labeled acetate and glucose using GC-MS and powerful flux calculation method. Journal of Biotechnology. 2003;101:101-117
[20]Fischer E, Sauer U. Metabolic flux profiling of Escherichia coli mutants in central carbon metabolism using GC-MS. FEBS. 2003;3:100-109
[21]Wiechert W. Bidirectional reaction steps in metabolic networks: III. Explicit solution and analysis of isotopomer labeling systems. Biotechnology and Bioengineering. 1999;66:69-85
[22]Mollney M. Bidirectional reaction steps in metabolic networks: IV. Optimal design of isotopomer labeling experiments. Biotechnology and Bioengineering. 1999; 66:86-103
[23]Sriram G., Shanks JV. Improvements in metabolic flux analysis using carbon bond labeling experiments: Bondomer balancing and Boolean function mapping. Metabolic Engineering. 2004, 6:116-132.
[24]Van Winden. Metabolic flux and metabolic network analysis of Penicillium chrysogenum using 2D [C-13, H-1] COSYNMR measurements and cumulative Bondomer simulation. Biotechnology and Bioengineering. 2003;83:75-92
[25]Mendes P. Biochemistry by numbers: simulation of biochemical pathways with Gepasi 3. Metabolic Engineering. 1997;14:361-370
[26]Pfeiffer T. METATOOL: for studying metabolic networks. Bioinformatics 1999;15:251-257
[27] Wiechert W. A universal framework for 13C metabolic flux analysis. Metabolic Engineering. 2001;3:265-283
[28]Zhu T. Convex analysis of metabolic network for optimal cell design & flux validation by GC-MS or NMR. Metabolic Engineering. 2002;20:458-467
[29]Nanchen A, Fuhrer T, Sauer U. Determination of metabolic flux ratios from 13C-experiments and gas chromatography-mass spectrometry data: protocol and principles. Methods Mol Biol. 2007;358:177-97.
[30]Zamboni N, Fischer E, Sauer U. FiatFlux--a software for metabolic flux analysis from 13C-glucose experiments. BMC Bioinformatics. 2005;6:209
[31]Blum JJ, Stein RB. On the analysis of metabolic networks.In“Biological Regulation and Development”. New York: Plenum Press, 1982, 99-124
[32]Rankin SJ, Fell DA. The matrix method of metabolic control analysis: its validity for complex pathway structures. Journal of Theoretical Biology. 1989;136:181-197
[33]Malloy CR, Sherry AD, Jeffrey FM. Evaluation of carbon flux and substrate selection through alternate pathways involving the citric acid cycle of the heart by 13C NMR spectroscopy. J Biol Chem.1988;263:6964-6971
[34]Majewski RA, Domach MM. Simple Constrained-Optimization View of Acetate Overflow in Escherichia coli. J Biol Chem.1990;12:732-738
[35]Savinell JM, Palsson BO. Network analysis of intermediary metabolism using linear optimization. I. Development of mathematical formalism. J Biol Chem.1992; 34:421-454
[36]Savinell JM, Palsson BO. Network analysis of intermediary metabolism using linear optimization. II. Interpretation of hybridoma cell metabolism. J Biol Chem. 1992;9:455-473
[37]Savinell JM, Palsson BO. Optimal selection of metabolic fluxes for in vivo measurement. I. Development of mathematical methods. Am Soc Microbiol. 1992; 20:201-214
[38]Savinell JM, Palsson BO. Optimal selection of metabolic fluxes for in vivo measurement. II. Application to Escherichia coli and hybridoma cell metabolism. Am Soc Microbiol.1992;47:215-242
[39]Katz J, Wals P, Lee WN. Isotopomer studies of gluconeogenesis and the Krebs cycle with 13C-labeled lactate. ASBMB.1993;2:25509-25521.
[40]Wiechert W. Bidirectional reaction steps in metabolic networks: II. Flux estimation and statistical analysis. Journal of Biotechnology.1997;30:118-135
[41]Schmidt K, Nielsen J, Villadsen J. Quantitative analysis of metabolic fluxes in Escherichia coli, using two-dimensional NMR spectroscopy and complete isotopomer models. Journal of Biotechnology. 1999;71:175-189
[42]Sauer U. Metabolic Flux Ratio Analysis of Genetic and Environmental Modulations of Escherichia coli Central Carbon Metabolism. Biophysical Soc.1999; 12:6679-6688
[43]Schilling CH. Combining pathway analysis with flux balance analysis for the comprehensive study of metabolic systems. Biophysical Soc. 2000;50:286-306
[44]Petersen S. In Vivo Quantification of Parallel and Bidirectional Fluxes in the Anaplerosis of Corynebacterium glutamicum. ASBMB. 2000;5:35932-35941
[45]Covert MW, Schilling CH, Palsson B. Regulation of gene expression in flux balance models of metabolism. Metabolic Engineering. 2001;3:73-88
[46]Mahadevan R, Edwards JS, Doyle FJ. Dynamic Flux Balance Analysis of Diauxic Growth in Escherichia coli. Biophysical Soc. 2002;23:1331-1340
[47]Beard DA, Liang S, Qian H. Energy Balance for Analysis of Complex Metabolic Networks. Biophysical Soc. 2002;7:79-86
[48]Massaoudi E. Production process monitoring by serial mapping of microbial carbon flux distributions using a novel sensor reactor approach: I--Sensor reactor system. Metabolic Engineering. 2003;37:86-95
[49]Drysch A. Production process monitoring by serial mapping of microbial carbon flux distributions using a novel Sensor Reactor approach: II--(13) C-labeling-based metabolic flux analysis and L-lysine production. Metabolic Engineering. 2003;9:96-107
[50]Kromer JO.In-Depth Profiling of Lysine-Producing Corynebacterium glutamicum by Combined Analysis of the Transcriptome, Metabolome, and Fluxome. Am Soc Microbiol. 2004;45:1769-1784
[51]Wiechert W, N?h K. From stationary to instationary metabolic flux analysis.Adv Biochem Eng Biotechnol. 2005;92:145-72
[52]Noh K, Wahl A, Wiechert W. Computational tools for isotopically instationary 13C labeling experiments under metabolic steady state conditions. Metabolic Engineering. 2006;8:554-577
[53]Iwatani S, Yamada Y. Metabolic flux analysis in biotechnology processes. Biotechnol Lett. 2008;30:791-799
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