Equivalence of Metabolite Fragments and Flow Analysis of Isotopomer Distributions for Flux Estimation

  • Ari Rantanen
  • Hannu Maaheimo
  • Esa Pitkänen
  • Juho Rousu
  • Esko Ukkonen
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4220)


The most accurate estimates of the activity of metabolic pathways are obtained by conducting isotopomer tracer experiments. The success of this method, however, is intimately dependent on the quality and amount of data on isotopomer distributions of intermediate metabolites. In this paper we present a novel method for discovering sets of metabolite fragments that always have identical isotopomer distributions, regardless of the velocities of the reactions in the metabolic network. We outline several applications of this equivalence concept, including improved propagation of measurements, experiment planning and consistency checking of metabolic network. Our computational experiments in measurement propagation indicate that the improvement via the use of this technique may be substantial.


Metabolic Network Measured Metabolite Metabolite Pool Junction Fragment Isotopomer Distribution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Appel, A.: Modern Compiler Implementation in Java. Cambridge University Press, Cambridge (1998)Google Scholar
  2. 2.
    Arita, M.: In silico atomic tracing of substrate-product relationships in escherichia coli intermediary metabolism. Genome Research 13, 2455–2466 (2003)CrossRefGoogle Scholar
  3. 3.
    Boros, L., Serkova, N., Cascante, M., Lee, W.-N.: Use of metabolic pathway flux information in targeted cancer drug design. Drug Discovery Today: Therapeutic Strategies 1(4), 435–443 (2004)CrossRefGoogle Scholar
  4. 4.
    Christensen, B., Nielsen, J.: Isotopomer analysis using GC-MS. Metabolic Engineering 16, E8–E16 (1999)Google Scholar
  5. 5.
    Eisenreich, W., Slaghuis, J., Laupitz, R., Bussemer, J., Stritzker, J., Schwarz, C., Schwarz, R., Dankekar, T., Goebel, W., Bacher, A.: 13 c isotopologue perturbation studies of listeria monocytogenes carbon metabolism and its modulation by the virulence regulator PRFA. In: Proceedings of the National Academy of Sciences of the United States of America (PNAS), vol. 103, pp. 2040–2045 (2006)Google Scholar
  6. 6.
    Fisher, E., Zamboni, N., Sauer, U.: High-throughput metabolic flux analysis based on gas chromatography-mass spectrometry derived 13 C constraints. Analytical Biochemistry 325, 308–316 (2004)CrossRefGoogle Scholar
  7. 7.
    Ghosh, S., Zhu, T., Grossmann, I.E., Ataai, M.M., Domach, M.M.: Closing the loop between feasible flux scenario identification for construct evaluation and resolution of realized fluxes via NMR. Journal of Bacteriology 183, 1441–1451 (2001)CrossRefGoogle Scholar
  8. 8.
    Harel, D.: A linear algorithm for finding dominators in flow graphs and related problems. In: Proceedings of the 17th annual ACM symposium on Theory of computing, pp. 185–194 (1985)Google Scholar
  9. 9.
    Isermann, N., Wiechert, W.: Metabolic isotopomer labeling systems. part ii: structural identifibiality analysis. Mathematical Biosciences 183, 175–214 (2003)MATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Kelleher, J.: Flux estimation using isotopic tracers: Common ground for metabolic physiology and metabolic engineering. Metabolic engineering 3, 100–110 (2001)CrossRefGoogle Scholar
  11. 11.
    Klamt, S., Schuster, S.: Calculating as many fluxes as possible in underdetermined metabolic networks. Molecular Biology Reports 29, 243 (2002)CrossRefGoogle Scholar
  12. 12.
    Lengauer, T., Tarjan, R.: A fast algorithm for finding dominators in a flowgraph. ACM Transactions on Programming Languages and Systems 1, 121–141 (1979)MATHCrossRefGoogle Scholar
  13. 13.
    Marx, A., de Graaf, A., Wiechert, W., Eggeling, L., Sahm, H.: Determination of the fluxes in the central metabolism of corynebacterium glutamicum by nuclear magnetic resonance spectroscopy combined with metabolite balancing. Biotechnology and Bioengineering 49, 111–129 (1996)CrossRefGoogle Scholar
  14. 14.
    Möllney, M., Wiechert, W., Kownatzki, D., de Graaf, A.: Bidirectional reaction steps in metabolic networks IV: Optimal design of isotopomer labeling systems. Biotechnology and Bioengineering 66, 86–103 (1999)CrossRefGoogle Scholar
  15. 15.
    Nielsen, J.: It is all about metabolic fluxes. Journal of Bacteriology 185 (2003)Google Scholar
  16. 16.
    Rantanen, A., Mielikäinen, T., Rousu, J., Maaheimo, H., Ukkonen, E.: Planning optimal measurements of isotopomer distributions for estimation of metabolic fluxes. Bioinformatics, Advance Access, February 27 (2006) (in print)Google Scholar
  17. 17.
    Rousu, J., Rantanen, A., Maaheimo, H., Pitkänen, E., Saarela, K., Ukkonen, E.: A method for estimating metabolic fluxes from incomplete isotopomer information. In: Priami, C. (ed.) CMSB 2003. LNCS, vol. 2602, pp. 88–103. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  18. 18.
    Schmidt, K., Carlsen, M., Nielsen, J., Viladsen, J.: Modeling isotopomer distributions in biochemical networks using isotopomer mapping matrices. Biotechnology and Bioengineering 55, 831–840 (1997)CrossRefGoogle Scholar
  19. 19.
    Schwarz, H.: Numerical Analysis: A Comprehensive Introduction. John Wiley & Sons, Chichester (1989)MATHGoogle Scholar
  20. 20.
    Selivanov, V., Puigjaner, J., Sillero, A., Centelles, J., Ramos-Montoya, A., Lee, P., Cascante, M.: An optimized algorithm for flux estimation from isotopomer distribution in glucose metabolites. Bioinformatics 20, 3387–3397 (2004)CrossRefGoogle Scholar
  21. 21.
    Sola, A., Maaheimo, H., Ylönen, K., Ferrer, P., Szyperski, T.: Amino acid biosynthesis and metabolic flux profiling of pichia pastoris. FEBS Journal 271, 2462–2470 (2004)Google Scholar
  22. 22.
    Stephanopoulos, G., Aristidou, A., Nielsen, J.: Metabolic engineering: Principles and Methodologies. Academic Press, London (1998)Google Scholar
  23. 23.
    Szyperski, T.: Biosynthetically directed fractional 13 C-labelling of proteinogenic amino acids. European Journal of Biochemistry 232, 433–448 (1995)CrossRefGoogle Scholar
  24. 24.
    Szyperski, T., Glaser, R., Hochuli, M., Fiaux, J., Sauer, U., Bailey, J., Wütrich, K.: Bioreaction network topology and metabolic flux ratio analysis by biosynthetic fractional 13 C labeling and two-dimensional NMR spectrometry. Metabolic Engineering 1, 189–197 (1999)CrossRefGoogle Scholar
  25. 25.
    Vallino, J.J., Stephanopoulos, G.: Metabolic flux distribution in corynebacterium glutamicum during growth and lysine overproduction. Biotechnology and Bioengineering 41, 633–646 (1993)CrossRefGoogle Scholar
  26. 26.
    van Winden, W., Heijnen, J., Verheijen, P., Grievink, J.: A priori analysis of metabolic flux identifiability from (13)c-labeling data. Biotechnology and Bioengineering 74, 505–516 (2001)CrossRefGoogle Scholar
  27. 27.
    Varma, A., Palsson, B.O.: Metabolic flux balancing: basic concepts, scientific and practical use. Nature Biotechnology 12, 994–998 (1994)CrossRefGoogle Scholar
  28. 28.
    Wiechert, W.: Modeling and simulation: tools for metabolic engineering. Journal of Biotechnology 94, 37–63 (2002)CrossRefGoogle Scholar
  29. 29.
    Wiechert, W., Möllney, M., Petersen, S., de Graaf, A.: A universal framework for 13 C metabolic flux analysis. Metabolic Engineering 3, 265–283 (2001)CrossRefGoogle Scholar
  30. 30.
    Wiechert, W., Wurzel, M.: Metabolic isotopomer labeling systems part i: global dynamic behavior. Mathematical Biosciences 169, 173–205 (2001)MATHCrossRefMathSciNetGoogle Scholar
  31. 31.
    Wittmann, C., Heinzle, E.: Mass spectrometry for metabolic flux analysis. Biotechnology and Bioenginering 62, 739–750 (1999)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Ari Rantanen
    • 1
  • Hannu Maaheimo
    • 2
  • Esa Pitkänen
    • 1
  • Juho Rousu
    • 1
  • Esko Ukkonen
    • 1
  1. 1.Dept. of Computer Science and HIIT Basic Research UnitUniversity of HelsinkiFinland
  2. 2.VTT Technical Research Centre of Finland 

Personalised recommendations