Journal of Mathematical Biology

, Volume 71, Issue 4, pp 903–920 | Cite as

On dynamically generating relevant elementary flux modes in a metabolic network using optimization

  • Hildur Æsa OddsdóttirEmail author
  • Erika Hagrot
  • Véronique Chotteau
  • Anders Forsgren


Elementary flux modes (EFMs) are pathways through a metabolic reaction network that connect external substrates to products. Using EFMs, a metabolic network can be transformed into its macroscopic counterpart, in which the internal metabolites have been eliminated and only external metabolites remain. In EFMs-based metabolic flux analysis (MFA) experimentally determined external fluxes are used to estimate the flux of each EFM. It is in general prohibitive to enumerate all EFMs for complex networks, since the number of EFMs increases rapidly with network complexity. In this work we present an optimization-based method that dynamically generates a subset of EFMs and solves the EFMs-based MFA problem simultaneously. The obtained subset contains EFMs that contribute to the optimal solution of the EFMs-based MFA problem. The usefulness of our method was examined in a case-study using data from a Chinese hamster ovary cell culture and two networks of varied complexity. It was demonstrated that the EFMs-based MFA problem could be solved at a low computational cost, even for the more complex network. Additionally, only a fraction of the total number of EFMs was needed to compute the optimal solution.


Metabolic network Optimization Algorithm Elementary flux mode Metabolic flux analysis Chinese hamster ovary cell 



Metabolic flux analysis


Elementary flux modes


Chinese hamster ovary





Mathematics Subject Classfication

90C20 90C35 90C90 92C42 



The work of the authors from the Department of Mathematics was supported by the Swedish Research Council. The work of the authors from the Division of Industrial Biotechnology was supported by KTH and the Swedish Governmental Agency for Innovation Systems (VINNOVA). The CHO cell line was kindly provided by Selexis (Switzerland). Culture media were kindly provided by Irvine Scientific (CA, USA). Finally, we thank the editor and the two anonymous referees for their valuable comments and suggestions.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Hildur Æsa Oddsdóttir
    • 1
    Email author
  • Erika Hagrot
    • 2
  • Véronique Chotteau
    • 2
  • Anders Forsgren
    • 1
  1. 1.Department of Mathematics, Optimization and Systems TheoryKTH Royal Institute of TechnologyStockholmSweden
  2. 2.Division of Industrial Biotechnology/Bioprocess DesignKTH Royal Institute of TechnologyStockholmSweden

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