Flux Measurement Selection in Metabolic Networks

  • Wout Megchelenbrink
  • Martijn Huynen
  • Elena Marchiori
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7036)


Genome-scale metabolic networks can be reconstructed using a constraint-based modeling approach. The stoichiometry of the network and the physiochemical laws still enable organisms to achieve certain objectives -such as biomass composition- through many various pathways. This means that the system is underdetermined and many alternative solutions exist. A known method used to reduce the number of alternative pathways is Flux Balance Analysis (FBA), which tries to optimize a given biological objective function. FBA does not always find a correct solution and for many networks the biological objective function is simply unknown. This leaves researchers no other choice than to measure certain fluxes. In this article we propose a method that combines a sampling approach with a greedy algorithm for finding a subset of k fluxes that, if measured, are expected to reduce as much as possible the solution space towards the ‘true’ flux distribution. The parameter k is given by the user. Application of the proposed method to a toy example and two real-life metabolic networks indicate its effectiveness. The method achieves significantly more reduction of the solution space than when k fluxes are selected either at random or by a faster simple heuristic procedure. It can be used for guiding the biologists to perform experimental analysis of metabolic networks.


Solution Space Metabolic Network Search Tree Flux Balance Analysis Convex Polytope 
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.


  1. 1.
    Almaas, E., Kovács, B., Vicsek, T., Oltvai, Z.N., Barabási, A.-L.: Global organization of metabolic fluxes in the bacterium escherichia coli. Nature 427(6977), 839–843 (2004)CrossRefGoogle Scholar
  2. 2.
    Beeler, B., Enge, A., Fukuda, K., Lthi, H.-J.: Exact volume computation for polytopes: a practical study. In: 12th European Workshop on Computational Geometry, Muenster, Germany (1996)Google Scholar
  3. 3.
    Braunstein, A., Mulet, R., Pagnani, A.: Estimating the size of the solution space of metabolic networks. BMC Bioinformatics 9(1), 240 (2008)CrossRefGoogle Scholar
  4. 4.
    Burgard, A.P., Nikolaev, E.V., Schilling, C.H., Maranas, C.D.: Flux coupling analysis of genome-scale metabolic network reconstructions. Genome Research 14(2), 301–312 (2004)CrossRefGoogle Scholar
  5. 5.
    Chaloner, K., Verdinelli, I.: Bayesian experimental design: A review. Statistical Science 10(3), 273–304 (1995)zbMATHCrossRefGoogle Scholar
  6. 6.
    David, L., Marashi, S.-A., Larhlimi, A., Mieth, B., Bockmayr, A.: FFCA: a feasibility-based method for flux coupling analysis of metabolic networks. BMC Bioinformatics 12(1), 236 (2011)CrossRefGoogle Scholar
  7. 7.
    Gudmundsson, S., Thiele, I.: Computationally efficient flux variability analysis. BMC Bioinformatics 11, 489 (2010)CrossRefGoogle Scholar
  8. 8.
    Jamshidi, N., Edwards, J.S., Fahland, T., Church, G.M., Palsson, B.O.: Dynamic simulation of the human red blood cell metabolic network. Bioinformatics 17(3), 286–287 (2001)CrossRefGoogle Scholar
  9. 9.
    Kauffman, K.J., Prakash, P., Edwards, J.S.: Advances in flux balance analysis. Current Opinion in Biotechnology 14(5), 491–496 (2003)CrossRefGoogle Scholar
  10. 10.
    Kaufman, D.E., Smith, R.L.: Direction choice for accelerated convergence in hit-and-run sampling. Operations Research 46(1), 84–95 (1998)zbMATHCrossRefGoogle Scholar
  11. 11.
    Mahadevan, R., Schilling, C.H.: The effects of alternate optimal solutions in constraint-based genome-scale metabolic models. Metabolic Engineering 5(4), 264–276 (2003)CrossRefGoogle Scholar
  12. 12.
    Orth, J.D., Thiele, I., Palsson, B.O.: What is flux balance analysis? Nature Biotechnology 28(3), 245–248 (2010)CrossRefGoogle Scholar
  13. 13.
    Palsson, B.O.: Systems Biology: Properties of Reconstructed Networks, 1st edn. Cambridge University Press (2006)Google Scholar
  14. 14.
    Price, N.D., Reed, J.L., Palsson, B.O.: Genome-scale models of microbial cells: evaluating the consequences of constraints. Nature Reviews Microbiology 2(11), 886–897 (2004)CrossRefGoogle Scholar
  15. 15.
    Price, N.D., Schellenberger, J., Palsson, B.O.: Uniform sampling of Steady-State flux spaces: Means to design experiments and to interpret enzymopathies. Biophysical Journal 87(4), 2172–2186 (2004)CrossRefGoogle Scholar
  16. 16.
    Sauer, U.: Metabolic networks in motion: 13C-based flux analysis. Molecular Systems Biology 2, 62 (2006)CrossRefGoogle Scholar
  17. 17.
    Savinell, J.M., Palsson, B.O.: Optimal selection of metabolic fluxes for in vivo measurement. I. Development of mathematical methods. Journal of Theoretical Biology 155(2), 201–214 (1992)CrossRefGoogle Scholar
  18. 18.
    Savinell, J.M., Palsson, B.O.: Optimal selection of metabolic fluxes for in vivo measurement. II. Application to escherichia coli and hybridoma cell metabolism. Journal of Theoretical Biology 155(2), 215–242 (1992)CrossRefGoogle Scholar
  19. 19.
    Schellenberger, J., Lewis, N.E., Palsson, B.O.: Elimination of thermodynamically infeasible loops in steady-state metabolic models. Biophysical Journal 100(3), 544–553 (2011)CrossRefGoogle Scholar
  20. 20.
    Schellenberger, J., Palsson, B.O.: Use of randomized sampling for analysis of metabolic networks. The Journal of Biological Chemistry 284(9), 5457–5461 (2009)CrossRefGoogle Scholar
  21. 21.
    Schellenberger, J., et al.: Quantitative prediction of cellular metabolism with constraint-basded models: the cobra toolbox v2.0. Nature Protocols 6(9), 1290–1307 (2011)CrossRefGoogle Scholar
  22. 22.
    Segré, D., Vitkup, D., Church, G.M.: Analysis of optimality in natural and perturbed metabolic networks. Proceedings of the National Academy of Sciences of the United States of America 99(23), 15112–15117 (2002)CrossRefGoogle Scholar
  23. 23.
    Smallbone, K., Simeonidis, E.: Flux balance analysis: a geometric perspective. Journal of Theoretical Biology 258(2), 311–315 (2009)CrossRefGoogle Scholar
  24. 24.
    Varma, A., Palsson, B.O.: Metabolic flux balancing: Basic concepts, scientific and practical use. Nature Biotechnology 12, 994 (1994)CrossRefGoogle Scholar
  25. 25.
    Wiback, S.J., Famili, I., Harvey, J., Greenberg, H.J., Palsson, B.O.: Monte carlo sampling can be used to determine the size and shape of the steady-state flux space. Journal of Theoretical Biology 228(4), 437–447 (2004)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Wout Megchelenbrink
    • 1
  • Martijn Huynen
    • 1
  • Elena Marchiori
    • 1
  1. 1.Radboud UniversityNijmegenThe Netherlands

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