Plant Metabolic Flux Analysis pp 155-179

Part of the Methods in Molecular Biology book series (MIMB, volume 1090) | Cite as

Steady-State and Instationary Modeling of Proteinogenic and Free Amino Acid Isotopomers for Flux Quantification

  • Yuting Zheng
  • Ganesh Sriram


Metabolic flux analysis (MFA) is a powerful tool for exploring and quantifying carbon traffic in metabolic networks. Accurate flux quantification requires (1) high-quality isotopomer measurements, usually of biomass components including proteinogenic/free amino acids or central carbon metabolites, and (2) a mathematical model that relates the unknown fluxes to the measured isotopomers. Modeling requires a thorough knowledge of the structure of the underlying metabolic network, often available from many databases, as well as the ability to make reasonable assumptions that will enable simplification of the model. Here we describe a general methodology underlying computer-aided mathematical modeling of a flux–isotopomer relationship and some of the accompanying data-processing steps. One of two modeling strategies will need to be employed, depending on the type of isotope labeling experiment performed. These strategies—steady-state modeling and instationary modeling—have different experimental and computational demands. We discuss the concepts underlying these two types of modeling and demonstrate steady-state modeling in a step-by-step manner. Our methodology should be applicable to most isotope-assisted MFA applications and should serve as a general framework applicable to many realistic metabolic networks with little modification.

Key words

Mathematical modeling Isotope labeling experiment Amino acids Mass spectrometry Steady-state model Instationary model 


  1. 1.
    Stephanopoulos G (1999) Metabolic fluxes and metabolic engineering. Metab Eng 1:1–11PubMedCrossRefGoogle Scholar
  2. 2.
    Wiechert W (2001) 13C metabolic flux analysis. Metab Eng 3:195–206PubMedCrossRefGoogle Scholar
  3. 3.
    Sriram G, Fulton DB, Iyer VV et al (2004) Quantification of compartmented metabolic fluxes in developing soybean embryos by employing biosynthetically directed fractional 13C labeling, two-dimensional [13C, 1H] nuclear magnetic resonance, and comprehensive isotopomer balancing. Plant Physiol 136:3043–3057Google Scholar
  4. 4.
    Sriram G, Fulton DB, Shanks JV (2007) Flux quantification in central carbon metabolism of Catharanthus roseus hairy roots by 13C labeling and comprehensive bondomer balancing. Phytochemistry 68:2243–2257PubMedCrossRefGoogle Scholar
  5. 5.
    Iyer V, Sriram G, Shanks JV (2007) Metabolic flux maps of central carbon metabolism in plant systems. In: Wurtele ES, Nikolau BJ (eds) Concepts in plant metabolomics. Springer, Dordrecht, The Netherlands, pp 125–144CrossRefGoogle Scholar
  6. 6.
    Nargund S, Joffe ME, Tran D, Tugarinov V, Sriram G (2013) Nuclear magnetic resonance methods for metabolic fluxomics. In: Alper HS (ed) Systems metabolic engineering. Humana, New York, NY, pp 335–351CrossRefGoogle Scholar
  7. 7.
    Edwards JS, Palsson BO (2000) Metabolic flux balance analysis and the in silico analysis of Escherichia coli K-12 gene deletions. BMC Bioinformatics 1:1PubMedCrossRefGoogle Scholar
  8. 8.
    Lee JM, Gianchandani EP, Papin JA (2006) Flux balance analysis in the era of metabolomics. Brief Bioinform 7:140–150PubMedCrossRefGoogle Scholar
  9. 9.
    Kauffman KJ, Prakash P, Edwards JS (2003) Advances in flux balance analysis. Curr Opin Biotechnol 14:491–496PubMedCrossRefGoogle Scholar
  10. 10.
    Resendis-Antonio O, Reed JL, Encarnación S, Collado-Vides J, Palsson BØ (2007) Metabolic reconstruction and modeling of nitrogen fixation in Rhizobium etli. PLoS Comput Biol 3:e192CrossRefGoogle Scholar
  11. 11.
    AbuOun M, Suthers PF, Jones GI et al (2009) Genome scale reconstruction of a Salmonella metabolic model: comparison of similarity and differences with a commensal Escherichia coli strain. J Biolog Chem 284:29480–29488CrossRefGoogle Scholar
  12. 12.
    Feist AM, Henry CS, Reed JL et al (2007) A genome-scale metabolic reconstruction for Escherichia coli K-12 MG1655 that accounts for 1260 ORFs and thermodynamic information. Mol Syst Biol 3:121PubMedCrossRefGoogle Scholar
  13. 13.
    Tran LM, Rizk ML, Liao JC (2008) Ensemble modeling of metabolic networks. Biophys J 95:5606–5617PubMedCrossRefGoogle Scholar
  14. 14.
    Wiechert W, Siefke C, de Graaf AA, Marx A (1997) Bidirectional reaction steps in metabolic networks: II. Flux estimation and statistical analysis. Biotechnol Bioeng 55:118–135PubMedCrossRefGoogle Scholar
  15. 15.
    Wiechert W, Möllney M, Isermann N, Wurzel M, De Graaf AA (1999) Bidirectional reaction steps in metabolic networks: III. Explicit solution and analysis of isotopomer labeling systems. Biotechnol Bioeng 66:69–85PubMedCrossRefGoogle Scholar
  16. 16.
    Sriram G, Shanks JV (2004) Improvements in metabolic flux analysis using carbon bond labeling experiments: bondomer balancing and Boolean function mapping. Metab Eng 6:116–132PubMedCrossRefGoogle Scholar
  17. 17.
    van Winden WA, Heijnen JJ, Verheijen PJT (2002) Cumulative bondomers: a new concept in flux analysis from 2D [13C, 1H] COSY NMR data. Biotechnol Bioeng 80:731–745PubMedCrossRefGoogle Scholar
  18. 18.
    Antoniewicz MR, Kelleher JK, Stephanopoulos G (2007) Elementary metabolite units (EMU): a novel framework for modeling isotopic distributions. Metab Eng 9:68–86PubMedCrossRefGoogle Scholar
  19. 19.
    Nöh K, Wiechert W (2006) Experimental design principles for isotopically instationary 13C labeling experiments. Biotechnol Bioeng 94:234–251PubMedCrossRefGoogle Scholar
  20. 20.
    Young JD, Walther JL, Antoniewicz MR, Yoo H, Stephanopoulos G (2008) An elementary metabolite unit (EMU) based method of isotopically nonstationary flux analysis. Biotechnol Bioeng 99:686–699PubMedCrossRefGoogle Scholar
  21. 21.
    Masoudi-Nejad A, Goto S, Endo TR, Kanehisa M (2008) KEGG bioinformatics resource for plant genomics research [Internet]. In: Edwards D (ed) Plant bioinformatics. Humana, New York, NY, pp 437–458Google Scholar
  22. 22.
    Zhang P, Foerster H, Tissier CP et al (2005) MetaCyc and AraCyc. Metabolic pathway databases for plant research. Plant Physiol 138:27–37PubMedCrossRefGoogle Scholar
  23. 23.
    Schwender J, Goffman F, Ohlrogge JB, Shachar-Hill Y (2004) Rubisco without the Calvin cycle improves the carbon efficiency of developing green seeds. Nature 432:779–782PubMedCrossRefGoogle Scholar
  24. 24.
    Yang TH, Heinzle E, Wittmann C (2005) Theoretical aspects of 13C metabolic flux analysis with sole quantification of carbon dioxide labeling. Comput Biol Chem 29:121–133PubMedCrossRefGoogle Scholar
  25. 25.
    Wittmann C, Heinzle E (2001) Modeling and experimental design for metabolic flux analysis of lysine-producing Corynebacteria by mass spectrometry. Metab Eng 3:173–191PubMedCrossRefGoogle Scholar
  26. 26.
    Nargund S, Sriram G (2013) Designer labels for plant metabolism: statistical design of isotope labeling experiments for improved quantification of flux in complex plant metabolic networks. Mol Biosyst 9:99–112PubMedCrossRefGoogle Scholar
  27. 27.
    Weitzel M, Nöh K, Dalman T et al (2012) 13CFLUX2—high-performance software suite for 13C-metabolic flux analysis. Bioinformatics 29:143–145PubMedCrossRefGoogle Scholar
  28. 28.
    Quek L-E, Wittmann C, Nielsen LK, Krömer JO (2009) OpenFLUX: efficient modelling software for 13C-based metabolic flux analysis. Microb Cell Fact 8:25PubMedCrossRefGoogle Scholar
  29. 29.
    Zamboni N, Fischer E, Sauer U (2005) FiatFlux - a software for metabolic flux analysis from 13C-glucose experiments. BMC Bioinformatics 6:209PubMedCrossRefGoogle Scholar
  30. 30.
    Sriram G, Rahib L, He J-S et al (2008) Global metabolic effects of glycerol kinase overexpression in rat hepatoma cells. Mol Genet Metab 93:145–159PubMedCrossRefGoogle Scholar
  31. 31.
    Masakapalli SK, Lay PL, Huddleston JE et al (2010) Subcellular flux analysis of central metabolism in a heterotrophic Arabidopsis thaliana cell suspension using steady-state stable isotope labeling. Plant Physiol 152:602–609PubMedCrossRefGoogle Scholar
  32. 32.
    O’Leary MH (1988) Carbon isotopes in photosynthesis. BioScience 38:328–336CrossRefGoogle Scholar
  33. 33.
    Winden WAV, Wittmann C, Heinzle E, Heijnen JJ (2002) Correcting mass isotopomer distributions for naturally occurring isotopes. Biotechnol Bioeng 80:477–479PubMedCrossRefGoogle Scholar
  34. 34.
    Szyperski T (1998) 13C-NMR, MS and metabolic flux balancing in biotechnology research. Q Rev Biophys 31:41–106PubMedCrossRefGoogle Scholar
  35. 35.
    Isermann N, Wiechert W (2003) Metabolic isotopomer labeling systems. Part II: structural flux identifiability analysis. Math Biosci 183:175–214PubMedCrossRefGoogle Scholar
  36. 36.
    Libourel IGL, Gehan JP, Shachar-Hill Y (2007) Design of substrate label for steady state flux measurements in plant systems using the metabolic network of Brassica napus embryos. Phytochemistry 68:2211–2221PubMedCrossRefGoogle Scholar
  37. 37.
    Crown SB, Antoniewicz MR (2012) Selection of tracers for 13C-metabolic flux analysis using elementary metabolite units (EMU) basis vector methodology. Metab Eng 14:150–161PubMedCrossRefGoogle Scholar
  38. 38.
    Onbaşoğlu E, Özdamar L (2001) Parallel simulated annealing algorithms in global optimization. J Global Optim 19:27–50CrossRefGoogle Scholar
  39. 39.
    Young JD, Shastri AA, Stephanopoulos G, Morgan JA (2011) Mapping photoautotrophic metabolism with isotopically nonstationary 13C flux analysis [Internet]. Metab Eng 13:656–665PubMedCrossRefGoogle Scholar
  40. 40.
    Singh BK (1998) Plant amino acids (Books in soils, plants, & the environment). CRC, USAGoogle Scholar
  41. 41.
    Allen DK, Laclair RW, Ohlrogge JB, Shachar-Hill Y (2012) Isotope labelling of Rubisco subunits provides in vivo information on subcellular biosynthesis and exchange of amino acids between compartments. Plant Cell Environ 35:232–1244CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, New York 2014

Authors and Affiliations

  • Yuting Zheng
    • 1
  • Ganesh Sriram
    • 2
  1. 1.Department of Chemical and Biomolecular EngineeringUniversity of MarylandCollege ParkUSA
  2. 2.A. James Clark School of EngineeringUniversity of MarylandCollege ParkUSA

Personalised recommendations