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

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Abstract

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.

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Abbreviations

MFA:

Metabolic flux analysis

EFMs:

Elementary flux modes

CHO:

Chinese hamster ovary

Lac:

Lactate

Glc:

Glucose

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Acknowledgments

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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Authors and Affiliations

  1. Department of Mathematics, Optimization and Systems Theory, KTH Royal Institute of Technology, SE-100 44, Stockholm, Sweden

    Hildur Æsa Oddsdóttir & Anders Forsgren

  2. Division of Industrial Biotechnology/Bioprocess Design, KTH Royal Institute of Technology, Albanova Center, SE-106 91, Stockholm, Sweden

    Erika Hagrot & Véronique Chotteau

Authors
  1. Hildur Æsa Oddsdóttir
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  2. Erika Hagrot
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  3. Véronique Chotteau
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  4. Anders Forsgren
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Correspondence to Hildur Æsa Oddsdóttir.

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Oddsdóttir, H.Æ., Hagrot, E., Chotteau, V. et al. On dynamically generating relevant elementary flux modes in a metabolic network using optimization. J. Math. Biol. 71, 903–920 (2015). https://doi.org/10.1007/s00285-014-0844-1

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  • DOI: https://doi.org/10.1007/s00285-014-0844-1

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