Metabolic flux analysis in systems biology of mammalian cells.

Reaction rates or metabolic fluxes reflect the integrated phenotype of genome, transcriptome and proteome interactions, including regulation at all levels of the cellular hierarchy. Different methods have been developed in the past to analyse intracellular fluxes. However, compartmentation of mammalian cells, varying utilisation of multiple substrates, reversibility of metabolite uptake and production, unbalanced growth behaviour and adaptation of cells to changing environment during cultivation are just some reasons that make metabolic flux analysis (MFA) in mammalian cell culture more challenging compared to microorganisms. In this article MFA using the metabolite balancing methodology and the advantages and disadvantages of (13)C MFA in mammalian cell systems are reviewed. Application examples of MFA in the optimisation of cell culture processes for the production of biopharmaceuticals are presented with a focus on the metabolism of the main industrial workhorse. Another area in which mammalian cell culture plays a key role is in medical and toxicological research. It is shown that MFA can be used to understand pathophysiological mechanisms and can assist in understanding effects of drugs or other compounds on cellular metabolism.

[1]  C. Wittmann,et al.  Metabolic flux analysis using mass spectrometry. , 2002, Advances in biochemical engineering/biotechnology.

[2]  E. Klipp,et al.  Modelling signalling pathways-A yeast approach , 2005 .

[3]  Jens O Krömer,et al.  Towards quantitative metabolomics of mammalian cells: development of a metabolite extraction protocol. , 2010, Analytical biochemistry.

[4]  Elmar Heinzle,et al.  Towards a metabolic and isotopic steady state in CHO batch cultures for reliable isotope‐based metabolic profiling , 2009, Biotechnology journal.

[5]  Niki S. C. Wong,et al.  Engineering mammalian cells in bioprocessing – current achievements and future perspectives , 2010, Biotechnology and applied biochemistry.

[6]  F. Gòdia,et al.  Identification of key patterns in the metabolism of hybridoma cells in culture , 1997 .

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

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

[9]  H. Eagle,et al.  Amino acid metabolism in mammalian cell cultures. , 1959, Science.

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

[11]  F. Gòdia,et al.  Metabolic engineering of animal cells , 2002 .

[12]  Christoph Wittmann,et al.  Fluxome analysis using GC-MS , 2007, Microbial cell factories.

[13]  A. D. de Graaf,et al.  Metabolic flux analysis of CHO cells in perfusion culture by metabolite balancing and 2D [13C, 1H] COSY NMR spectroscopy. , 2010, Metabolic engineering.

[14]  P. Watkins,et al.  The Application of Metabonomics to Predict Drug‐Induced Liver Injury , 2010, Clinical pharmacology and therapeutics.

[15]  A. Illanes,et al.  Analysis of CHO Cells Metabolic Redistribution in a Glutamate‐Based Defined Medium in Continuous Culture , 2001, Biotechnology progress.

[16]  L Xie,et al.  Integrated approaches to the design of media and feeding strategies for fed-batch cultures of animal cells. , 1997, Trends in biotechnology.

[17]  Wei-Shou Hu,et al.  Analysis of cellular metabolism of hybridoma cells at distinct physiological states. , 2003, Journal of bioscience and bioengineering.

[18]  Konstantin Konstantinov,et al.  Towards industrial application of quasi real-time metabolic flux analysis for mammalian cell culture. , 2006, Advances in biochemical engineering/biotechnology.

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

[20]  H. Bonarius,et al.  Flux analysis of underdetermined metabolic networks: the quest for the missing constraints. , 1997 .

[21]  M. Dauner,et al.  Metabolic flux model for an anchorage‐dependent MDCK cell line: Characteristic growth phases and minimum substrate consumption flux distribution , 2008, Biotechnology and bioengineering.

[22]  Wei-Shou Hu,et al.  Large scale gene expression profiling of metabolic shift of mammalian cells in culture. , 2004, Journal of biotechnology.

[23]  S. Srivastava,et al.  Application of metabolic flux analysis to identify the mechanisms of free fatty acid toxicity to human hepatoma cell line , 2008, Biotechnology and bioengineering.

[24]  Elmar Heinzle,et al.  Numerical bias estimation for mass spectrometric mass isotopomer analysis. , 2009, Analytical biochemistry.

[25]  U. Sauer,et al.  Metabolic fluxes in riboflavin-producing Bacillus subtilis , 1997, Nature Biotechnology.

[26]  U. Müller-Vieira,et al.  An integrated approach to improved toxicity prediction for the safety assessment during preclinical drug development using Hep G2 cells. , 2009, Toxicology and applied pharmacology.

[27]  Vicente Bernal,et al.  Metabolic alterations induced by ischemia in primary cultures of astrocytes: merging 13C NMR spectroscopy and metabolic flux analysis , 2010, Journal of neurochemistry.

[28]  F. Gòdia,et al.  Considerations on the lactate consumption by CHO cells in the presence of galactose. , 2006, Journal of biotechnology.

[29]  Alexander Bauer,et al.  Quantification of statin effects on hepatic cholesterol synthesis by transient (13)C-flux analysis. , 2009, Metabolic engineering.

[30]  F. Wurm.  Production of recombinant protein therapeutics in cultivated mammalian cells , 2004, Nature Biotechnology.

[31]  John P. Barford,et al.  Effect of feed rate on growth rate and antibody production in the fed-batch culture of murine hybridoma cells , 2000, Cytotechnology.

[32]  U. Hofmann,et al.  Identification of metabolic fluxes in hepatic cells from transient 13C‐labeling experiments: Part I. Experimental observations , 2008, Biotechnology and bioengineering.

[33]  I. Kola,et al.  Can the pharmaceutical industry reduce attrition rates? , 2004, Nature Reviews Drug Discovery.

[34]  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.

[35]  B. Pfeifer,et al.  Metabolic flux analysis and pharmaceutical production. , 2010, Metabolic engineering.

[36]  Uwe Sauer,et al.  Comparison of quantitative metabolite imaging tools and carbon-13 techniques for fluxomics. , 2009, Methods in molecular biology.

[37]  L. Alberghina,et al.  Systems Biology: Definitions and Perspectives , 2005 .

[38]  J K Kelleher,et al.  Flux estimation using isotopic tracers: common ground for metabolic physiology and metabolic engineering. , 2001, Metabolic engineering.

[39]  Adam L. Meadows,et al.  Estradiol stimulates the biosynthetic pathways of breast cancer cells: detection by metabolic flux analysis. , 2006, Metabolic engineering.

[40]  J. Asenjo,et al.  Viral vectors for the treatment of alcoholism: use of metabolic flux analysis for cell cultivation and vector production. , 2010, Metabolic engineering.

[41]  Hunter N. B. Moseley,et al.  Correcting for the effects of natural abundance in stable isotope resolved metabolomics experiments involving ultra-high resolution mass spectrometry , 2010, BMC Bioinformatics.

[42]  I. Karimi,et al.  Elucidation of metabolism in hybridoma cells grown in fed‐batch culture by genome‐scale modeling , 2009, Biotechnology and bioengineering.

[43]  B. Palsson,et al.  Network analysis of intermediary metabolism using linear optimization. I. Development of mathematical formalism. , 1992, Journal of theoretical biology.

[44]  G. Tannock,et al.  Cell-Based Influenza Vaccines , 2012, Drugs.

[45]  C. Wittmann,et al.  MALDI-TOF MS for quantification of substrates and products in cultivations of Corynebacterium glutamicum. , 2001, Biotechnology and bioengineering.

[46]  U. Reichl,et al.  MDCK and Vero cells for influenza virus vaccine production: a one-to-one comparison up to lab-scale bioreactor cultivation , 2010, Applied Microbiology and Biotechnology.

[47]  Christoph Wittmann,et al.  Flux Design: In silico design of cell factories based on correlation of pathway fluxes to desired properties , 2009, BMC Systems Biology.

[48]  H. Blanch,et al.  Examination of primary metabolic pathways in a murine hybridoma with carbon‐13 nuclear magnetic resonance spectroscopy , 1994, Biotechnology and bioengineering.

[49]  Johannes Tramper,et al.  Metabolic-flux analysis of hybridoma cells under oxidative and reductive stress using mass balances , 2000, Cytotechnology.

[50]  U. Reichl,et al.  Continuous cell lines as a production system for influenza vaccines , 2009, Expert review of vaccines.

[51]  J. Lindon,et al.  Metabonomics: a platform for studying drug toxicity and gene function , 2002, Nature Reviews Drug Discovery.

[52]  E. Heinzle,et al.  Quantitative characterization of metabolism and metabolic shifts during growth of the new human cell line AGE1.HN using time resolved metabolic flux analysis , 2010, Bioprocess and biosystems engineering.

[53]  E. Heinzle,et al.  High throughput, non-invasive and dynamic toxicity screening on adherent cells using respiratory measurements. , 2010, Toxicology in vitro : an international journal published in association with BIBRA.

[54]  U. Sauer,et al.  GC‐MS Analysis of Amino Acids Rapidly Provides Rich Information for Isotopomer Balancing , 2000, Biotechnology progress.

[55]  Christoph Wittmann,et al.  Amplified Expression of Fructose 1,6-Bisphosphatase in Corynebacterium glutamicum Increases In Vivo Flux through the Pentose Phosphate Pathway and Lysine Production on Different Carbon Sources , 2005, Applied and Environmental Microbiology.

[56]  Uwe Sauer,et al.  Metabolic-flux and network analysis in fourteen hemiascomycetous yeasts. , 2005, FEMS yeast research.

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

[58]  T. Omasa,et al.  Enhanced antibody production following intermediate addition based on flux analysis in mammalian cell continuous culture , 2010, Bioprocess and biosystems engineering.

[59]  K. Ülgen,et al.  Reconstruction and flux analysis of coupling between metabolic pathways of astrocytes and neurons: application to cerebral hypoxia , 2007, Theoretical Biology and Medical Modelling.

[60]  M. Fussenegger,et al.  Inducible product gene expression technology tailored to bioprocess engineering. , 2007, Current opinion in biotechnology.

[61]  F Gòdia,et al.  Strategies for fed-batch cultivation of t-PA producing CHO cells: substitution of glucose and glutamine and rational design of culture medium. , 2004, Journal of biotechnology.

[62]  W. Wiechert,et al.  In Vivo Quantification of Parallel and Bidirectional Fluxes in the Anaplerosis of Corynebacterium glutamicum * , 2000, The Journal of Biological Chemistry.

[63]  H. Budman,et al.  Metabolic flux-based modeling of mAb production during batch and fed-batch operations , 2009, Bioprocess and biosystems engineering.

[64]  Christoph Wittmann,et al.  Metabolic flux screening of Saccharomyces cerevisiae single knockout strains on glucose and galactose supports elucidation of gene function. , 2007, Journal of biotechnology.

[65]  Elmar Heinzle,et al.  13C metabolic flux analysis for larger scale cultivation using gas chromatography-combustion-isotope ratio mass spectrometry. , 2010, Metabolic engineering.

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

[67]  H. Blanch,et al.  Using isotopomer path tracing to quantify metabolic fluxes in pathway models containing reversible reactions. , 2001, Biotechnology and bioengineering.

[68]  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.

[69]  E. Heinzle,et al.  Effects of drugs in subtoxic concentrations on the metabolic fluxes in human hepatoma cell line Hep G2. , 2009, Toxicology and applied pharmacology.

[70]  Wolfgang Wiechert,et al.  New tools for mass isotopomer data evaluation in 13C flux analysis: Mass isotope correction, data consistency checking, and precursor relationships , 2004, Biotechnology and bioengineering.

[71]  P F Greenfield,et al.  Cell cycle model to describe animal cell size variation and lag between cell number and biomass dynamics. , 1997, Biotechnology and bioengineering.

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

[73]  Madhukar S. Dasika,et al.  Metabolic flux elucidation for large-scale models using 13C labeled isotopes. , 2007, Metabolic engineering.

[74]  N. Baliga,et al.  The role of predictive modelling in rationally re-engineering biological systems , 2009, Nature Reviews Microbiology.

[75]  U. Sauer,et al.  High-throughput metabolic flux analysis based on gas chromatography-mass spectrometry derived 13C constraints. , 2004, Analytical biochemistry.

[76]  Christoph Wittmann,et al.  Correcting mass isotopomer distributions for naturally occurring isotopes. , 2002, Biotechnology and bioengineering.

[77]  C. Wittmann,et al.  Respirometric 13C flux analysis, Part I: design, construction and validation of a novel multiple reactor system using on-line membrane inlet mass spectrometry. , 2006, Metabolic engineering.

[78]  Daniel I. C. Wang,et al.  Energy metabolism and ATP balance in animal cell cultivation using a stoichiometrically based reaction network , 2000, Biotechnology and bioengineering.

[79]  L. Steinman,et al.  Systems biology and its application to the understanding of neurological diseases , 2009, Annals of neurology.

[80]  J Tramper,et al.  Metabolic flux analysis of hybridoma cells in different culture media using mass balances , 1996, Biotechnology and bioengineering.

[81]  Dong-Yup Lee,et al.  Genome-scale modeling and in silico analysis of mouse cell metabolic network. , 2009, Molecular bioSystems.

[82]  J. P. van Dijken,et al.  Fluxes and enzyme activities in central metabolism of myeloma cells grown in chemostat culture. , 1998, Biotechnology and bioengineering.

[83]  Rui Oliveira,et al.  Combining metabolic flux analysis tools and 13C NMR to estimate intracellular fluxes of cultured astrocytes , 2008, Neurochemistry International.

[84]  H. Qian,et al.  Thermodynamic constraints for biochemical networks. , 2004, Journal of theoretical biology.

[85]  W M Miller,et al.  Effects of dissolved oxygen concentration on hybridoma growth and metabolism in continuous culture , 1987, Journal of cellular physiology.

[86]  Christoph Wittmann,et al.  Metabolic network analysis of lysine producing Corynebacterium glutamicum at a miniaturized scale , 2004, Biotechnology and bioengineering.

[87]  U. Sauer,et al.  Central carbon metabolism of Saccharomyces cerevisiae explored by biosynthetic fractional (13)C labeling of common amino acids. , 2001, European journal of biochemistry.

[88]  Gregory Stephanopoulos,et al.  Evaluation of 13C isotopic tracers for metabolic flux analysis in mammalian cells. , 2009, Journal of biotechnology.

[89]  Christoph Wittmann,et al.  Matrix-assisted laser desorption/ionization time-of-flight mass spectrometry for metabolic flux analyses using isotope-labeled ethanol. , 2007, Rapid communications in mass spectrometry : RCM.

[90]  W Wiechert,et al.  A universal framework for 13C metabolic flux analysis. , 2001, Metabolic engineering.

[91]  Klaus Maier,et al.  Identification of metabolic fluxes in hepatic cells from transient 13C‐labeling experiments: Part II. Flux estimation , 2008, Biotechnology and bioengineering.

[92]  Christoph Wittmann,et al.  In vivo analysis of intracellular amino acid labelings by GC/MS. , 2002, Analytical biochemistry.

[93]  U. Sauer,et al.  Determination of metabolic flux ratios from 13C-experiments and gas chromatography-mass spectrometry data: protocol and principles. , 2007, Methods in molecular biology.

[94]  A. D. de Graaf,et al.  Flux partitioning in the split pathway of lysine synthesis in Corynebacterium glutamicum. Quantification by 13C- and 1H-NMR spectroscopy. , 1993, European journal of biochemistry.

[95]  D K Robinson,et al.  Industrial choices for protein production by large-scale cell culture. , 2001, Current opinion in biotechnology.

[96]  A. Kamen,et al.  Scalable production of influenza virus in HEK-293 cells for efficient vaccine manufacturing. , 2010, Vaccine.

[97]  Monica L. Mo,et al.  Global reconstruction of the human metabolic network based on genomic and bibliomic data , 2007, Proceedings of the National Academy of Sciences.

[98]  Christoph Wittmann,et al.  Analysis of 13C labeling enrichment in microbial culture applying metabolic tracer experiments using gas chromatography-combustion-isotope ratio mass spectrometry. , 2008, Analytical biochemistry.

[99]  G Stephanopoulos,et al.  Metabolic flux analysis of hybridoma continuous culture steady state multiplicity. , 1999, Biotechnology and bioengineering.

[100]  Neelanjana Sengupta,et al.  Metabolic flux analysis of CHO cell metabolism in the late non‐growth phase , 2011, Biotechnology and bioengineering.

[101]  U. Sauer,et al.  Article number: 62 REVIEW Metabolic networks in motion: 13 C-based flux analysis , 2022 .

[102]  M. Perrier,et al.  Metabolic flux analysis of HEK-293 cells in perfusion cultures for the production of adenoviral vectors. , 2005, Metabolic engineering.

[103]  W. Wiechert.  13C metabolic flux analysis. , 2001, Metabolic engineering.

[104]  U. Sauer.  High-throughput phenomics: experimental methods for mapping fluxomes. , 2004, Current opinion in biotechnology.

[105]  J. Kramer,et al.  The application of discovery toxicology and pathology towards the design of safer pharmaceutical lead candidates , 2007, Nature Reviews Drug Discovery.

[106]  F. Wright,et al.  Use of Pharmaco‐Metabonomics for Early Prediction of Acetaminophen‐Induced Hepatotoxicity in Humans , 2010, Clinical pharmacology and therapeutics.

[107]  W Wiechert,et al.  In vivo stationary flux analysis by 13C labeling experiments. , 1996, Advances in biochemical engineering/biotechnology.

[108]  Martin H. Koldijk,et al.  The human cell line PER.C6 provides a new manufacturing system for the production of influenza vaccines. , 2001, Vaccine.

[109]  David C James,et al.  Systems biotechnology of mammalian cell factories. , 2008, Briefings in functional genomics & proteomics.

[110]  G Stephanopoulos,et al.  Metabolism of peptide amino acids by Chinese hamster ovary cells grown in a complex medium. , 1999, Biotechnology and bioengineering.

[111]  J Tramper,et al.  Metabolic-flux analysis of continuously cultured hybridoma cells using (13)CO(2) mass spectrometry in combination with (13)C-lactate nuclear magnetic resonance spectroscopy and metabolite balancing. , 2001, Biotechnology and bioengineering.

[112]  Elmar Heinzle,et al.  Metabolic flux analysis in eukaryotes. , 2010, Current opinion in biotechnology.

[113]  R. Balcarcel,et al.  Metabolic Screening of Mammalian Cell Cultures Using Well‐Plates , 2003, Biotechnology progress.

[114]  L. Quek,et al.  Metabolic flux analysis in mammalian cell culture. , 2010, Metabolic engineering.

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

[116]  J. Russell.  The Energy Spilling Reactions of Bacteria and Other Organisms , 2007, Journal of Molecular Microbiology and Biotechnology.

[117]  J E Bailey,et al.  Estimation of P-to-O ratio in Bacillus subtilis and its influence on maximum riboflavin yield. , 1999, Biotechnology and bioengineering.

[118]  D. Leibfritz,et al.  13C isotopomer analysis of glucose and alanine metabolism reveals cytosolic pyruvate compartmentation as part of energy metabolism in astrocytes , 2001, Glia.

[119]  Jesús Picó,et al.  A procedure for the estimation over time of metabolic fluxes in scenarios where measurements are uncertain and/or insufficient , 2007, BMC Bioinformatics.

[120]  S. Aiba,et al.  Citrate production from n-alkane by Candida lipolytica in reference to carbon fluxes in vivo , 1978, European journal of applied microbiology and biotechnology.

[121]  S. Lloyd,et al.  A critical perspective of the use of (13)C-isotopomer analysis by GCMS and NMR as applied to cardiac metabolism. , 2004, Metabolic engineering.

[122]  Gregory Stephanopoulos,et al.  Metabolic effects on recombinant interferon‐γ glycosylation in continuous culture of Chinese hamster ovary cells , 1999 .

[123]  E. Heinzle,et al.  Mass spectrometry for metabolic flux analysis. , 1999, Biotechnology and bioengineering.

[124]  Bernhard O Palsson,et al.  Isotopomer analysis of myocardial substrate metabolism: A systems biology approach , 2006, Biotechnology and bioengineering.

[125]  Wei-Shou Hu,et al.  Engineering cells for cell culture bioprocessing--physiological fundamentals. , 2006, Advances in biochemical engineering/biotechnology.

[126]  G. Stephanopoulos,et al.  Metabolic flux analysis: a powerful tool for monitoring tissue function. , 1999, Tissue engineering.

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

[128]  H. Miyagawa,et al.  Metabolic flux analysis of the phenylpropanoid pathway in wound-healing potato tuber tissue using stable isotope-labeled tracer and LC-MS spectroscopy. , 2003, Plant & cell physiology.

[129]  B. Palsson,et al.  Network analysis of intermediary metabolism using linear optimization. II. Interpretation of hybridoma cell metabolism. , 1992, Journal of theoretical biology.

[130]  J. Nielsen,et al.  It Is All about MetabolicFluxes , 2003, Journal of bacteriology.

[131]  D. I. Wang,et al.  Material balance studies on animal cell metabolism using a stoichiometrically based reaction network , 2000, Biotechnology and bioengineering.

[132]  G. Stephanopoulos,et al.  Intracellular flux analysis in hybridomas using mass balances and in vitro 13C nmr , 1995, Biotechnology and bioengineering.

[133]  F. Blattner,et al.  In silico design and adaptive evolution of Escherichia coli for production of lactic acid. , 2005, Biotechnology and bioengineering.

[134]  D. Leibfritz,et al.  Regulation of glial metabolism studied by 13C‐NMR , 2003, NMR in biomedicine.

[135]  F. Srienc,et al.  Elementary mode analysis: a useful metabolic pathway analysis tool for characterizing cellular metabolism , 2009, Applied Microbiology and Biotechnology.

[136]  A. Pavlou,et al.  Recombinant protein therapeutics—success rates, market trends and values to 2010 , 2004, Nature Biotechnology.

[137]  Christoph Wittmann,et al.  Genealogy Profiling through Strain Improvement by Using Metabolic Network Analysis: Metabolic Flux Genealogy of Several Generations of Lysine-Producing Corynebacteria , 2002, Applied and Environmental Microbiology.

[138]  V. Sandig,et al.  An avian cell line designed for production of highly attenuated viruses. , 2009, Vaccine.

[139]  A. Gambhir,et al.  Multiple steady states with distinct cellular metabolism in continuous culture of mammalian cells. , 2000, Biotechnology and bioengineering.

[140]  George Stephanopoulos,et al.  Modeling of Isotope Distributions and Intracellular Fluxes in Metabolic Networks Using Atom Mapping Matrices , 1994 .

[141]  Masaru Tomita,et al.  Direct measurement of isotopomer of intracellular metabolites using capillary electrophoresis time-of-flight mass spectrometry for efficient metabolic flux analysis. , 2007, Journal of chromatography. A.

[142]  Wolfgang Wiechert,et al.  The topology of metabolic isotope labeling networks , 2007, BMC Bioinformatics.

[143]  Udo Reichl,et al.  Metabolic effects of influenza virus infection in cultured animal cells: Intra- and extracellular metabolite profiling , 2009, BMC Systems Biology.

[144]  M. Dauner,et al.  Comparison of Metabolic Flux Distributions for MDCK Cell Growth in Glutamine‐ and Pyruvate‐Containing Media , 2008, Biotechnology progress.

[145]  Sangdun Choi,et al.  Introduction To Systems Biology , 2010 .

[146]  Oliver Frick,et al.  Hybrid optimization for 13C metabolic flux analysis using systems parametrized by compactification , 2008, BMC Systems Biology.

[147]  B. Christensen,et al.  Isotopomer analysis using GC-MS. , 1999, Metabolic engineering.

[148]  T. Puck,et al.  GENETICS OF SOMATIC MAMMALIAN CELLS III. LONG-TERM CULTIVATION OF EUPLOID CELLS FROM HUMAN AND ANIMAL SUBJECTS , 1958 .

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

[150]  Christoph Wittmann,et al.  Comparative Metabolic Flux Analysis of Lysine-Producing Corynebacterium glutamicum Cultured on Glucose or Fructose , 2004, Applied and Environmental Microbiology.