Modeling with a view to target identification in metabolic engineering: A critical evaluation of the available tools

The state of the art tools for modeling metabolism, typically used in the domain of metabolic engineering, were reviewed. The tools considered are stoichiometric network analysis (elementary modes and extreme pathways), stoichiometric modeling (metabolic flux analysis, flux balance analysis, and carbon modeling), mechanistic and approximative modeling, cybernetic modeling, and multivariate statistics. In the context of metabolic engineering, one should be aware that the usefulness of these tools to optimize microbial metabolism for overproducing a target compound depends predominantly on the characteristic properties of that compound. Because of their shortcomings not all tools are suitable for every kind of optimization; issues like the dependence of the target compound's synthesis on severe (redox) constraints, the characteristics of its formation pathway, and the achievable/desired flux towards the target compound should play a role when choosing the optimization strategy. © 2010 American Institute of Chemical Engineers Biotechnol. Prog., 2010

[1]  B. Wanner,et al.  One-step inactivation of chromosomal genes in Escherichia coli K-12 using PCR products. , 2000, Proceedings of the National Academy of Sciences of the United States of America.

[2]  Jochen Förster,et al.  Modeling Lactococcus lactis using a genome-scale flux model , 2005, BMC Microbiology.

[3]  D. Ramkrishna,et al.  Cybernetic modeling of bacterial cultures at low growth rates: Mixed‐substrate systems , 1988, Biotechnology and bioengineering.

[4]  P. R. Jensen,et al.  Synthetic promoter libraries--tuning of gene expression. , 2006, Trends in biotechnology.

[5]  D. Kell Metabolomics and systems biology: making sense of the soup. , 2004, Current opinion in microbiology.

[6]  S. Lee,et al.  Systems metabolic engineering of Escherichia coli for L-threonine production , 2007, Molecular systems biology.

[7]  H. Kacser,et al.  The control of flux. , 1995, Biochemical Society transactions.

[8]  M. Matsumura,et al.  Separation of dilute aqueous butanol and acetone solutions by pervaporation through liquid membranes , 1987, Biotechnology and bioengineering.

[9]  M. Reuss,et al.  In vivo dynamics of the pentose phosphate pathway in Saccharomyces cerevisiae. , 1999, Metabolic engineering.

[10]  S. Panke,et al.  Putative regulatory sites unraveled by network-embedded thermodynamic analysis of metabolome data , 2006, Molecular systems biology.

[11]  J. Heijnen,et al.  Dynamic simulation and metabolic re-design of a branched pathway using linlog kinetics. , 2003, Metabolic engineering.

[12]  E. Ruppin,et al.  Regulatory on/off minimization of metabolic flux changes after genetic perturbations. , 2005, Proceedings of the National Academy of Sciences of the United States of America.

[13]  M. J. van der Werf,et al.  Towards replacing closed with open target selection strategies. , 2005, Trends in biotechnology.

[14]  U. Sauer,et al.  Metabolic flux response to phosphoglucose isomerase knock-out in Escherichia coli and impact of overexpression of the soluble transhydrogenase UdhA. , 2001, FEMS Microbiology Letters.

[15]  Vladimír Kvasnička,et al.  A hybrid of simplex method and simulated annealing , 1997 .

[16]  G. Stephanopoulos,et al.  Flux amplification in complex metabolic networks , 1997 .

[17]  Jamey Dale Young A system-level mathematical description of metabolic regulation combining aspects of elementary mode analysis with cybernetic control laws , 2005 .

[18]  F. Doyle,et al.  Dynamic flux balance analysis of diauxic growth in Escherichia coli. , 2002, Biophysical journal.

[19]  S. Wold,et al.  PLS-regression: a basic tool of chemometrics , 2001 .

[20]  D Ramkrishna,et al.  Cybernetic modeling of bacteriol cultures at low growth rates: Single‐substrate systems , 1989, Biotechnology and bioengineering.

[21]  U. Sauer,et al.  Systematic evaluation of objective functions for predicting intracellular fluxes in Escherichia coli , 2007, Molecular systems biology.

[22]  W. Dunn,et al.  Measuring the metabolome: current analytical technologies. , 2005, The Analyst.

[23]  David M. Holloway,et al.  Spatial Bistability Generates hunchback Expression Sharpness in the Drosophila Embryo , 2008, PLoS Comput. Biol..

[24]  B O Palsson,et al.  Flux-balance analysis of mitochondrial energy metabolism: consequences of systemic stoichiometric constraints. , 2001, American journal of physiology. Regulatory, integrative and comparative physiology.

[25]  S. Lee,et al.  In silico metabolic pathway analysis and design: succinic acid production by metabolically engineered Escherichia coli as an example. , 2002, Genome informatics. International Conference on Genome Informatics.

[26]  B. Palsson,et al.  Transcriptional regulation in constraints-based metabolic models of Escherichia coli Covert , 2002 .

[27]  G. Bennett,et al.  A kinetic model of oxygen regulation of cytochrome production in Escherichia coli. , 2006, Journal of theoretical biology.

[28]  J. Pronk,et al.  When transcriptome meets metabolome: fast cellular responses of yeast to sudden relief of glucose limitation , 2006, Molecular systems biology.

[29]  P R Patnaik,et al.  Are microbes intelligent beings?: An assessment of cybernetic modeling. , 2000, Biotechnology advances.

[30]  J. Villadsen,et al.  Modeling isotopomer distributions in biochemical networks using isotopomer mapping matrices. , 1997, Biotechnology and bioengineering.

[31]  M. Koffas,et al.  Evolutionary metabolic engineering , 2005 .

[32]  M. Hirai,et al.  Integration of transcriptomics and metabolomics for understanding of global responses to nutritional stresses in Arabidopsis thaliana. , 2004, Proceedings of the National Academy of Sciences of the United States of America.

[33]  Steven J Cox,et al.  Development of a metabolic network design and optimization framework incorporating implementation constraints: a succinate production case study. , 2006, Metabolic engineering.

[34]  M. Boguski,et al.  Functional genomics: it's all how you read it. , 1997, Science.

[35]  Varner,et al.  Application of cybernetic models to metabolic engineering: investigation of storage pathways , 1998, Biotechnology and bioengineering.

[36]  J. Heijnen Approximative kinetic formats used in metabolic network modeling , 2005, Biotechnology and bioengineering.

[37]  J. Nielsen,et al.  Thermodynamics of Metabolic Pathways for Penicillin Production: Analysis of Thermodynamic Feasibility and Free Energy Changes During Fed‐Batch Cultivation , 1997 .

[38]  Peter D. Karp,et al.  EcoCyc: a comprehensive database resource for Escherichia coli , 2004, Nucleic Acids Res..

[39]  Hengkun Xie,et al.  Combined use of partial least-squares regression and neural network for residual life estimation of large generator stator insulation , 2007 .

[40]  L Yang,et al.  Incorporating qualitative knowledge in enzyme kinetic models using fuzzy logic. , 1999, Biotechnology and bioengineering.

[41]  H. Westerhoff,et al.  Thermodynamics and Control of Biological Free-Energy Transduction , 1987 .

[42]  John Gould,et al.  Toward the automated generation of genome-scale metabolic networks in the SEED , 2007, BMC Bioinformatics.

[43]  Jianying Gao,et al.  Dynamic Metabolic Modeling for a MAB Bioprocess , 2007, Biotechnology progress.

[44]  Doraiswami Ramkrishna,et al.  Cybernetic Modeling and Regulation of Metabolic Pathways. Growth on Complementary Nutrients , 1994 .

[45]  G. Church,et al.  Genome-Scale Metabolic Model of Helicobacter pylori 26695 , 2002, Journal of bacteriology.

[46]  L. Quek,et al.  OpenFLUX: efficient modelling software for 13C-based metabolic flux analysis , 2009, Microbial cell factories.

[47]  Erwin P. Gianchandani,et al.  Flux balance analysis in the era of metabolomics , 2006, Briefings Bioinform..

[48]  Stefan Schuster,et al.  Systems biology Metatool 5.0: fast and flexible elementary modes analysis , 2006 .

[49]  P. Verheijen,et al.  Possible pitfalls of flux calculations based on (13)C-labeling. , 2001, Metabolic engineering.

[50]  S Wold,et al.  Quantitative sequence-activity models (QSAM)--tools for sequence design. , 1993, Nucleic acids research.

[51]  Johannes Tramper,et al.  Modeling Neisseria meningitidis metabolism: from genome to metabolic fluxes , 2007, Genome Biology.

[52]  J. Nielsen,et al.  Mathematical modelling of metabolism. , 2000, Current opinion in biotechnology.

[53]  D. Ramkrishna,et al.  Metabolic engineering from a cybernetic perspective: aspartate family of amino acids. , 1999, Metabolic engineering.

[54]  Ralf Takors,et al.  Sensitivity analysis for the reduction of complex metabolism models , 2004 .

[55]  M. Reuss,et al.  In vivo analysis of glucose-induced fast changes in yeast adenine nucleotide pool applying a rapid sampling technique. , 1993, Analytical biochemistry.

[56]  Susumu Goto,et al.  KEGG: Kyoto Encyclopedia of Genes and Genomes , 2000, Nucleic Acids Res..

[57]  V. Hatzimanikatis,et al.  Thermodynamics-based metabolic flux analysis. , 2007, Biophysical journal.

[58]  Annik Nanchen,et al.  Nonlinear Dependency of Intracellular Fluxes on Growth Rate in Miniaturized Continuous Cultures of Escherichia coli , 2006, Applied and Environmental Microbiology.

[59]  Jason A. Papin,et al.  Extreme pathway lengths and reaction participation in genome-scale metabolic networks. , 2002, Genome research.

[60]  H. Qian,et al.  Energy balance for analysis of complex metabolic networks. , 2002, Biophysical journal.

[61]  R. Carlson,et al.  Fundamental Escherichia coli biochemical pathways for biomass and energy production: creation of overall flux states , 2004, Biotechnology and bioengineering.

[62]  R Ramakrishna,et al.  Cybernetic modeling of growth in mixed, substitutable substrate environments: Preferential and simultaneous utilization. , 1996, Biotechnology and bioengineering.

[63]  Rishi Jain,et al.  Bayesian-based selection of metabolic objective functions , 2007 .

[64]  D. Ramkrishna,et al.  Metabolic Engineering from a Cybernetic Perspective. 1. Theoretical Preliminaries , 1999, Biotechnology progress.

[65]  J. Heijnen,et al.  Metabolome dynamic responses of Saccharomyces cerevisiae to simultaneous rapid perturbations in external electron acceptor and electron donor. , 2007, FEMS yeast research.

[66]  M. Tomita Whole-cell simulation: a grand challenge of the 21st century. , 2001, Trends in biotechnology.

[67]  Adam Powell,et al.  The Origins of Lactase Persistence in Europe , 2009, PLoS Comput. Biol..

[68]  Bernhard O Palsson,et al.  Extreme pathway analysis of human red blood cell metabolism. , 2002, Biophysical journal.

[69]  K. Shimizu,et al.  Effect of poxB gene knockout on metabolism in Escherichia coli based on growth characteristics and enzyme activities , 2007 .

[70]  Bernhard Palsson,et al.  In silico biology through “omics” , 2002, Nature Biotechnology.

[71]  José Iborra,et al.  Role of Wet Experiment Design in Data Generation: From in Vivo to in Silico and Back , 2007, Silico Biol..

[72]  S. Schuster,et al.  Metabolic network structure determines key aspects of functionality and regulation , 2002, Nature.

[73]  W Wiechert,et al.  Bidirectional reaction steps in metabolic networks: IV. Optimal design of isotopomer labeling experiments. , 1999, Biotechnology and bioengineering.

[74]  T. Kudo,et al.  Formation of a chiral acetoinic compound from diacetyl by Escherichia coli expressing meso‐2,3‐butanediol dehydrogenase , 1999, Letters in applied microbiology.

[75]  Mariët J. van der Werf,et al.  Towards replacing closed with open target selection strategies , 2005 .

[76]  D. Fell Metabolic control analysis: a survey of its theoretical and experimental development. , 1992, The Biochemical journal.

[77]  B. Palsson,et al.  Parallel adaptive evolution cultures of Escherichia coli lead to convergent growth phenotypes with different gene expression states. , 2005, Genome research.

[78]  B. Palsson,et al.  Constraints-based models: regulation of gene expression reduces the steady-state solution space. , 2003, Journal of theoretical biology.

[79]  Masaru Tomita,et al.  E-CELL: software environment for whole-cell simulation , 1999, Bioinform..

[80]  U. Sauer,et al.  YtsJ Has the Major Physiological Role of the Four Paralogous Malic Enzyme Isoforms in Bacillus subtilis , 2006, Journal of bacteriology.

[81]  M. Reuss,et al.  In VivoDynamics of the Pentose Phosphate Pathway inSaccharomyces cerevisiae , 1999 .

[82]  J. Nielsen,et al.  Uncovering transcriptional regulation of metabolism by using metabolic network topology. , 2005, Proceedings of the National Academy of Sciences of the United States of America.

[83]  C. Wittmann,et al.  Application of MALDI-TOF MS to lysine-producing Corynebacterium glutamicum: a novel approach for metabolic flux analysis. , 2001, European journal of biochemistry.

[84]  S. Wold,et al.  Some recent developments in PLS modeling , 2001 .

[85]  Nagasuma R. Chandra,et al.  Flux Balance Analysis of Mycolic Acid Pathway: Targets for Anti-Tubercular Drugs , 2005, PLoS Comput. Biol..

[86]  M. De Mey,et al.  Comparison of DNA and RNA quantification methods suitable for parameter estimation in metabolic modeling of microorganisms. , 2006, Analytical biochemistry.

[87]  P. Vanrolleghem,et al.  MFA for Overdetermined Systems Reviewed and Compared with RNA Expression Data to Elucidate the Difference in Shikimate Yield between Carbon‐ and Phosphate‐Limited Continuous Cultures of E. coli W3110.shik1 , 2006, Biotechnology progress.

[88]  Achille Messac,et al.  Integrated Energy and Flux Balance Based Multiobjective Framework for Large-Scale Metabolic Networks , 2007, Annals of Biomedical Engineering.

[89]  T. Hankemeier,et al.  Microbial metabolomics: replacing trial-and-error by the unbiased selection and ranking of targets , 2005, Journal of Industrial Microbiology and Biotechnology.

[90]  M. Kanehisa,et al.  Observing metabolic functions at the genome scale , 2007, Genome Biology.

[91]  H. Martens,et al.  Modified Jack-knife estimation of parameter uncertainty in bilinear modelling by partial least squares regression (PLSR) , 2000 .

[92]  P. Bruheim,et al.  Cold glycerol-saline: the promising quenching solution for accurate intracellular metabolite analysis of microbial cells. , 2007, Analytical biochemistry.

[93]  Paul Christakopoulos,et al.  Comparative metabolic network analysis of two xylose fermenting recombinant Saccharomyces cerevisiae strains. , 2005, Metabolic engineering.

[94]  J. Heijnen,et al.  Linear constraint relations in biochemical reaction systems: II. Diagnosis and estimation of gross errors , 1994, Biotechnology and bioengineering.

[95]  H. Mishima,et al.  Milbemycins, a new family of macrolide antibiotics: fermentation, isolation and physico-chemical properties. , 1980, The Journal of antibiotics.

[96]  Matthias Reuss,et al.  Dynamic sensitivity analysis for metabolic systems , 1997 .

[97]  B. Palsson,et al.  Genome-scale reconstruction of the Saccharomyces cerevisiae metabolic network. , 2003, Genome research.

[98]  Jens Nielsen,et al.  Effect of carbon source perturbations on transcriptional regulation of metabolic fluxes in Saccharomyces cerevisiae , 2007, BMC Systems Biology.

[99]  Wim Soetaert,et al.  Microbial metabolomics: past, present and future methodologies , 2006, Biotechnology Letters.

[100]  Eberhard O Voit,et al.  Analysis of dynamic labeling data. , 2004, Mathematical biosciences.

[101]  Joseph J. Heijnen,et al.  Metabolic flux analysis of a glycerol‐overproducing Saccharomyces cerevisiae strain based on GC‐MS, LC‐MS and NMR‐derived 13C‐labelling data , 2007 .

[102]  R. Takors,et al.  Quantification of intracellular metabolites in Escherichia coli K12 using liquid chromatographic-electrospray ionization tandem mass spectrometric techniques. , 2001, Analytical biochemistry.

[103]  H. Garoff Using recombinant DNA techniques to study protein targeting in the eucaryotic cell. , 1985, Annual review of cell biology.

[104]  J. Heijnen,et al.  Changes in the metabolome of Saccharomyces cerevisiae associated with evolution in aerobic glucose-limited chemostats. , 2005, FEMS yeast research.

[105]  Jens Nielsen,et al.  Impact of transamination reactions and protein turnover on labeling dynamics in 13C‐labeling experiments , 2004, Biotechnology and bioengineering.

[106]  B. Imperiali,et al.  Optimal Sox-based fluorescent chemosensor design for serine/threonine protein kinases. , 2006, Analytical biochemistry.

[107]  Uwe Sauer,et al.  The PEP-pyruvate-oxaloacetate node as the switch point for carbon flux distribution in bacteria. , 2005, FEMS microbiology reviews.

[108]  Hiroaki Kitano,et al.  The systems biology markup language (SBML): a medium for representation and exchange of biochemical network models , 2003, Bioinform..

[109]  J. Bailey,et al.  Effects of spatiotemporal variations on metabolic control: approximate analysis using (log)linear kinetic models. , 1997, Biotechnology and bioengineering.

[110]  S. Lee,et al.  Metabolic engineering of Escherichia coli for the production of l-valine based on transcriptome analysis and in silico gene knockout simulation , 2007, Proceedings of the National Academy of Sciences.

[111]  Klaus Mauch,et al.  Model of central and trimethylammonium metabolism for optimizing L-carnitine production by E. coli. , 2005, Metabolic engineering.

[112]  B. Palsson,et al.  The Escherichia coli MG1655 in silico metabolic genotype: its definition, characteristics, and capabilities. , 2000, Proceedings of the National Academy of Sciences of the United States of America.

[113]  C. Chassagnole,et al.  Dynamic modeling of the central carbon metabolism of Escherichia coli. , 2002, Biotechnology and bioengineering.

[114]  D. Ramkrishna,et al.  Metabolic regulation in bacterial continuous cultures: I , 1991, Biotechnology and bioengineering.

[115]  J E Bailey,et al.  MCA has more to say. , 1996, Journal of theoretical biology.

[116]  Wolfgang Wiechert,et al.  13C labeling experiments at metabolic nonstationary conditions: An exploratory study , 2008, BMC Bioinformatics.

[117]  Sahm,et al.  13C tracer experiments and metabolite balancing for metabolic flux analysis: comparing two approaches , 1998, Biotechnology and bioengineering.

[118]  Zheng Zhao,et al.  Isotopic non-stationary 13C gluconate tracer method for accurate determination of the pentose phosphate pathway split-ratio in Penicillium chrysogenum. , 2008, Metabolic engineering.

[119]  João A. Lopes,et al.  Chemometrics in bioprocess engineering: process analytical technology (PAT) applications , 2004 .

[120]  Marco Oldiges,et al.  Metabolomics: current state and evolving methodologies and tools , 2007, Applied Microbiology and Biotechnology.

[121]  Jo Maertens,et al.  Construction and model-based analysis of a promoter library for E. coli: an indispensable tool for metabolic engineering , 2007, BMC biotechnology.

[122]  R. A. van den Berg,et al.  Centering, scaling, and transformations: improving the biological information content of metabolomics data , 2006, BMC Genomics.

[123]  G. Stephanopoulos CHAPTER 1 – The Essence of Metabolic Engineering , 1998 .

[124]  Achim Kienle,et al.  Steady-state multiplicity in bioreactors : bifurcation analysis of cybernetic models , 2003 .

[125]  Erwin P. Gianchandani,et al.  Correction: Dynamic Analysis of Integrated Signaling, Metabolic, and Regulatory Networks , 2008, PLoS Computational Biology.

[126]  Friedrich Srienc,et al.  Metabolic pathway analysis of a recombinant yeast for rational strain development. , 2002, Biotechnology and bioengineering.

[127]  Peter A Vanrolleghem,et al.  Parallel hybrid modeling methods for a full-scale cokes wastewater treatment plant. , 2005, Journal of biotechnology.

[128]  John A. Nelder,et al.  A Simplex Method for Function Minimization , 1965, Comput. J..

[129]  P. Minkkinen,et al.  Partial least squares modeling of an activated sludge plant: A case study , 1997 .

[130]  R. Sharan,et al.  A genome-scale computational study of the interplay between transcriptional regulation and metabolism , 2007, Molecular systems biology.

[131]  J. Heijnen,et al.  Metabolic-flux analysis of Saccharomyces cerevisiae CEN.PK113-7D based on mass isotopomer measurements of (13)C-labeled primary metabolites. , 2005, FEMS yeast research.

[132]  Wolfgang Wiechert,et al.  Computational tools for isotopically instationary 13C labeling experiments under metabolic steady state conditions. , 2006, Metabolic engineering.

[133]  G. Stephanopoulos,et al.  Identifying gene targets for the metabolic engineering of lycopene biosynthesis in Escherichia coli. , 2005, Metabolic engineering.

[134]  M. Reuss,et al.  In vivo analysis of metabolic dynamics in Saccharomyces cerevisiae: II. Mathematical model. , 1997, Biotechnology and bioengineering.

[135]  D. Schomburg,et al.  Enzyme data and metabolic information: BRENDA, a resource for research in biology, biochemistry, and medicine , 2000 .

[136]  Jason A. Papin,et al.  Comparison of network-based pathway analysis methods. , 2004, Trends in biotechnology.

[137]  C. Francke,et al.  Reconstructing the metabolic network of a bacterium from its genome. , 2005, Trends in microbiology.

[138]  Lalit M. Patnaik,et al.  Genetic algorithms: a survey , 1994, Computer.

[139]  M. Reuss,et al.  In vivo analysis of metabolic dynamics in Saccharomyces cerevisiae : I. Experimental observations. , 1997, Biotechnology and bioengineering.

[140]  Keith Beven,et al.  A manifesto for the equifinality thesis , 2006 .

[141]  J E Bailey,et al.  Metabolic flux analysis with a comprehensive isotopomer model in Bacillus subtilis. , 2001, Biotechnology and bioengineering.

[142]  Jens Nielsen,et al.  Evolutionary programming as a platform for in silico metabolic engineering , 2005, BMC Bioinformatics.

[143]  J. Nielsen,et al.  Quantitative analysis of metabolic fluxes in Escherichia coli, using two-dimensional NMR spectroscopy and complete isotopomer models. , 1999, Journal of biotechnology.

[144]  J. Guest,et al.  Pyruvate oxidase contributes to the aerobic growth efficiency of Escherichia coli. , 2001, Microbiology.

[145]  Intawat Nookaew,et al.  Identification of flux regulation coefficients from elementary flux modes: A systems biology tool for analysis of metabolic networks , 2007, Biotechnology and bioengineering.

[146]  J. Nielsen,et al.  Integration of gene expression data into genome-scale metabolic models. , 2004, Metabolic engineering.

[147]  Jörg Stelling,et al.  Large-scale computation of elementary flux modes with bit pattern trees , 2008, Bioinform..

[148]  D. Fell,et al.  The role of multiple enzyme activation in metabolic flux control. , 1998, Advances in enzyme regulation.

[149]  B. Palsson,et al.  Theory for the systemic definition of metabolic pathways and their use in interpreting metabolic function from a pathway-oriented perspective. , 2000, Journal of theoretical biology.

[150]  D. Fell,et al.  A general definition of metabolic pathways useful for systematic organization and analysis of complex metabolic networks , 2000, Nature Biotechnology.

[151]  Vinay Satish Kumar,et al.  A Genome-Scale Metabolic Reconstruction of Mycoplasma genitalium, iPS189 , 2009, PLoS Comput. Biol..

[152]  Hiroyuki Ogata,et al.  KEGG: Kyoto Encyclopedia of Genes and Genomes , 1999, Nucleic Acids Res..

[153]  J. Heijnen,et al.  Analysis of in vivo kinetics of glycolysis in aerobic Saccharomyces cerevisiae by application of glucose and ethanol pulses , 2004, Biotechnology and bioengineering.

[154]  A. Burgard,et al.  Optknock: A bilevel programming framework for identifying gene knockout strategies for microbial strain optimization , 2003, Biotechnology and bioengineering.

[155]  G. Church,et al.  Analysis of optimality in natural and perturbed metabolic networks , 2002 .

[156]  C. Cooney,et al.  A Novel Fermentation: The Production of R(–)–1,2–Propanediol and Acetol by Clostridium thermosaccharolyticum , 1986, Bio/Technology.

[157]  Erwin P. Gianchandani,et al.  Dynamic Analysis of Integrated Signaling, Metabolic, and Regulatory Networks , 2008, PLoS Comput. Biol..

[158]  Vassily Hatzimanikatis,et al.  Inverse metabolic engineering: a strategy for directed genetic engineering of useful phenotypes. , 2002, Biotechnology and bioengineering.

[159]  B. Palsson,et al.  An expanded genome-scale model of Escherichia coli K-12 (iJR904 GSM/GPR) , 2003, Genome Biology.

[160]  Barbara M. Bakker,et al.  Can yeast glycolysis be understood in terms of in vitro kinetics of the constituent enzymes? Testing biochemistry. , 2000, European journal of biochemistry.

[161]  D Weuster-Botz,et al.  Automated sampling device for monitoring intracellular metabolite dynamics. , 1999, Analytical biochemistry.

[162]  Nicola Zamboni,et al.  FiatFlux – a software for metabolic flux analysis from 13C-glucose experiments , 2005, BMC Bioinformatics.

[163]  Christoph Wittmann,et al.  Metabolic pathway analysis for rational design of L-methionine production by Escherichia coli and Corynebacterium glutamicum. , 2006, Metabolic engineering.

[164]  W. Wiechert,et al.  Bidirectional reaction steps in metabolic networks: III. Explicit solution and analysis of isotopomer labeling systems. , 1999, Biotechnology and bioengineering.

[165]  A. Narang,et al.  New patterns of mixed-substrate utilization during batch growth of Escherichia coli K12. , 1997, Biotechnology and bioengineering.

[166]  D. Fraenkel,et al.  The effect of increased phosphoglucose isomerase on glucose metabolism in Saccharomyces cerevisiae. , 1994, The Journal of biological chemistry.

[167]  G. Stephanopoulos,et al.  Elementary metabolite units (EMU): a novel framework for modeling isotopic distributions. , 2007, Metabolic engineering.

[168]  BMC Bioinformatics , 2005 .

[169]  J. Keasling,et al.  Mathematical Model of the lac Operon: Inducer Exclusion, Catabolite Repression, and Diauxic Growth on Glucose and Lactose , 1997, Biotechnology progress.

[170]  日本自動制御協会,et al.  システムと制御 = Systems and control , 1971 .

[171]  J. Heijnen,et al.  Application of metabolic flux analysis for the identification of metabolic bottlenecks in the biosynthesis of penicillin-G. , 2000, Biotechnology and bioengineering.

[172]  G. T. Tsao,et al.  Cybernetic modeling of microbial growth on multiple substrates , 1984, Biotechnology and bioengineering.