Exploring the Cellular Objective in Flux Balance Constraint-Based Models

  • Rafael S. Costa
  • Son Nguyen
  • Andras Hartmann
  • Susana Vinga
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8859)


Genome-scale reconstructions are usually stoichiometric and analyzed under steady-state assumptions using constraint-based modelling with flux balance analysis (FBA). FBA requires not only the stoichiometry of the network, but also an appropriate cellular objective function and possible additional physico-chemical constraints to predict the set of resulting flux distributions of an organism.

To compute the metabolic flux distributions in microbes, the most common objective is to consider the maximization of the growth rate or yield. However, other objectives may be more accurate in predicting phenotypes. Since in general objective function selection is highly dependent on the growth conditions, the quality of the constraints and the dataset, further investigation is required for better understanding the universality of the objective function. In this work, we explore the validity of different classes of optimality criteria and the effect of single (or combinations of) standard constraints in order to improve the predictive power of intracellular flux distribution. These were evaluated to compare predicted fluxes to published experimental 13C-labelling fluxomic datasets using two metabolic systems with different conditions and comparison datasets.

It can be observed that by using different conditions and metabolic systems, the fidelity patterns of FBA can differ considerably. However, despite of the observed variations, several conclusions could be drawn. First, the maximization of biomass yield achieves one of the best objective function under all conditions studied. For the batch growth condition the most consistent optimality criteria appears to be described by maximization of the biomass yield per flux or by the objective of maximization ATP yield per flux unit. Moreover, under N-limited continuous cultures the criteria minimization of the flux distribution across the network or by the maximization of the biomass yield was determined as the most significant. Secondly, the predictions obtained by flux balance analysis using additional combined standard constraints are not necessarily better than those obtained using only one single constraint.


metabolic networks constraint-based models flux balance analysis objective functions constraints flux distributions prediction 


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  1. 1.
    Becker, S.A., Feist, A.M., Mo, M.L., Hannum, G., Palsson, B.O., Herrgard, M.J.: Quantitative prediction of cellular metabolism with constraint-based models: the COBRA Toolbox. Nature Protocols 2, 727–738 (2007)CrossRefGoogle Scholar
  2. 2.
    Bordbar, A., Monk, J.M., King, Z.A., Palsson, B.O.: Constraint-based models predict metabolic and associated cellular functions. Nature Reviews Genetics 15(2), 107–120 (2014)CrossRefGoogle Scholar
  3. 3.
    Bonarius, H.P., Hatzimanikatis, V., Meesters, K.P., De Gooijer, C.D., Schmid, G., Tramper, J.: Metabolic flux analysis of hybridoma cells in different culture media using mass balances. Biotechnology and Bioengineering 50, 299–318 (1996)CrossRefGoogle Scholar
  4. 4.
    Bornstein, B.J., Keating, S.M., Jouraku, A., Hucka, M.: LibSBML: an API library for SBML. Bioinformatics 24, 880–881 (2008)CrossRefGoogle Scholar
  5. 5.
    Burgard, A.P., Maranas, C.D.: Optimization-based framework for inferring and testing hypothesized metabolic objective functions. Biotechnology and Bioengineering 82, 670–677 (2003)CrossRefGoogle Scholar
  6. 6.
    Costa, R.S., Machado, D., Rocha, I., Ferreira, E.C.: Critical perspective on the consequences of the limited availability of kinetic data in metabolic dynamic modelling. IET Systems Biology 5(3), 157–163 (2011)CrossRefGoogle Scholar
  7. 7.
    Emmerling, M., Dauner, M., Ponti, A., Fiaux, J., Hochuli, M., Szyperski, T., et al.: Metabolic flux responses to pyruvate kinase knockout in Escherichia coli. Journal of Bacteriology 184, 152–164 (2002)CrossRefGoogle Scholar
  8. 8.
    Feist, A.M., Herrgard, M.J., Thiele, I., Reed, J.L., Palsson, B.O.: Reconstruction of biochemical networks in microorganisms. Nature Reviews Microbiology 7, 129–143 (2009)CrossRefGoogle Scholar
  9. 9.
    Feist, A.M., Palsson, B.O.: The biomass objective function. Current Opinion in Microbiology 13, 344–349 (2010)CrossRefGoogle Scholar
  10. 10.
    Feist, A.M., Henry, C.S., Reed, J.L., Krummenacker, M., Joyce, A.R., Karp, P.D., et al.: A genome-scale metabolic reconstruction for Escherichia coli K-12 MG1655 that accounts for 1260 ORFs and thermodynamic information. Molecular Systems Biology 3, 121 (2007)CrossRefGoogle Scholar
  11. 11.
    Gianchandani, E.P., Oberhardt, M.A., Burgard, A.P., Maranas, D.C., Papin, J.A.: Predicting biologicsl system objectives de novo from internal state measurements. BMC Bioinformatics 9, 43–55 (2008)CrossRefGoogle Scholar
  12. 12.
    Harcombe, W.R., Delaney, N.F., Leiby, N., Klitgord, N., Marx, C.J.: The Ability of Flux Balance Analysis to Predict Evolution of Central Metabolism Scales with the Initial Distance to the Optimum. Plos Computational Biology 9 (2013)Google Scholar
  13. 13.
    Holm, A.K., Blank, L.M., Oldiges, M., Schmid, A., Solem, C., Jensen, P.R., et al.: Metabolic and Transcriptional Response to Cofactor Perturbations in Escherichia coli. Journal of Biological Chemistry 285, 17498–17506 (2010)CrossRefGoogle Scholar
  14. 14.
    Ibarra, R.U., Edwards, J.S., Palsson, B.O.: Escherichia coli K-12 undergoes adaptive evolution to achieve in silico predicted optimal growth. Nature 420, 186–189 (2002)CrossRefGoogle Scholar
  15. 15.
    Ishii, N., Nakahigashi, K., Baba, T., Robert, M., Soga, T., Kanai, A., et al.: Multiple high-throughput analyses monitor the response of E-coli to perturbations. Science 316, 593–597 (2007)CrossRefGoogle Scholar
  16. 16.
    Kauffman, K.J., Prakash, P., Edwards, J.S.: Advances in flux balance analysis. Current Opinion in Biotechnology 14, 491–496 (2003)CrossRefGoogle Scholar
  17. 17.
    Knorr, A.L., Jain, R., Srivastava, R.: Bayesian-based selection of metabolic objective functions. Bioinformatics 23, 351–357 (2007)CrossRefGoogle Scholar
  18. 18.
    Lewis, N.E., Nagarajan, H., Palsson, B.O.: Constraining the metabolic genotype-phenotype relationship using a phylogeny of in silico methods. Nature Reviews Microbiology 10, 291–305 (2012)Google Scholar
  19. 19.
    Lewis, N.E., Hixson, K.K., Conrad, T.M., Lerman, J.A., Charusanti, P., Polpitiya, A.D., Palsson, B.O., et al.: Omic data from evolved E. coli are consistent with computed optimal growth from genome scale models. Molecular Systems Biology 6(1) (2010)Google Scholar
  20. 20.
    Machado, D., Costa, R.S., Ferreira, E.C., Rocha, I., Tidor, B.: Exploring the gap between dynamic and constraint-based models of metabolism. Metabolic Engineering 14(2), 112–119 (2012)CrossRefGoogle Scholar
  21. 21.
    Makhorin, A.: GLPK (GNU linear programming kit) (2008)Google Scholar
  22. 22.
    Marler, R.T., Arora, J.S.: Survey of multi-objective optimization methods for engineering. Structural and Multidisciplinary Optimization 26, 369–395 (2004)MathSciNetCrossRefzbMATHGoogle Scholar
  23. 23.
    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
  24. 24.
    Molenaar, D., Van Berlo, R., Ve Ridder, D., Teusink, B.: Shifts in growth strategies reflect tradeoffs in cellular economics. Molecular Systems Biology 5 (2009)Google Scholar
  25. 25.
    Oberhardt, M.A., Palsson, B.O., Papin, J.A.: Applications of genome-scale metabolic reconstructions. Molecular Systems Biology 5, 320 (2009)CrossRefGoogle Scholar
  26. 26.
    Orth, J.D., Thiele, I., Palsson, B.O.: What is flux balance analysis? Nature Biotechnology 28, 245–248 (2010)CrossRefGoogle Scholar
  27. 27.
    Orth, J.D., Fleming, R.M.T., Palsson, B.O.: Reconstruction and use of microbial metabolic networks: the core Escherichia coli metabolic model as an Educational Guide. In: Escherichia Coli and Salmonella: Cellular and Molecular Biology, ASM Press (2010)Google Scholar
  28. 28.
    Ow, D.S.W., Lee, D.Y., Yap, M., Oh, S.K.W.: Identification of cellular objective for elucidating the physiological state of plasmid-bearing E. coli using genome-scale in silico analysis. AIChE 25, 61–67 (2009)Google Scholar
  29. 29.
    Perrenoud, A., Sauer, U.: Impact of global transcriptional regulation by ArcA, ArcB, Cra, Crp, Cya, Fnr, and Mlc o glucose catabolism in Escherichia coli. J. Bacteriol. 187, 3171–3179 (2005)CrossRefGoogle Scholar
  30. 30.
    Price, N.D., Reed, J.L., Palsson, B.O.: Genome-scale models of microbial cells: evaluating the consequences of constraints. Nature Reviews Microbiology 2, 886–897 (2004)CrossRefGoogle Scholar
  31. 31.
    Price, N.D., Papin, J.A., Schilling, C.H., Palsson, B.O.: Genome-scale microbial in silico models: the constraints-based approach. Trends in Biotechnology 21, 162–169 (2003)CrossRefGoogle Scholar
  32. 32.
    Ramakrishna, R., Edwards, J.S., McCulloch, A., Palsson, B.O.: Flux-balance analysis of mitochondrial energy metabolism: consequences of systemic stoichiometric constraints. American Journal of Physiology-Regulatory, Integrative and Comparative Physiology 280(3), R695–R704 (2001)Google Scholar
  33. 33.
    Schuetz, R., Kuepfer, L., Sauer, U.: Systematic evaluation of objective functions for predicting intracellular fluxes in Escherichia coli. Molecular Systems Biology 3, 119 (2007)CrossRefGoogle Scholar
  34. 34.
    Schuetz, R., Zamboni, N., Zampieri, M., Heinemann, M., Sauer, U.: Multidimensional Optimality of Microbial Metabolism. Science 336, 601–604 (2012)CrossRefGoogle Scholar
  35. 35.
    Varma, A., Palsson, B.O.: Stoichiometric Flux Balance Models Quantitatively Predict Growth and Metabolic By-Product Secretion in Wild-Type Escherichia-Coli W3110. Applied and Environmental Microbiology 60, 3724–3731 (1994)Google Scholar
  36. 36.
    Van Gulik, W.M., Heijnen, J.J.: A Metabolic Network Stoichiometry Analysis of Microbial-Growth and Product Formation. Biotechnology and Bioengineering 48, 681–698 (1995)CrossRefGoogle Scholar
  37. 37.
    Zhao, J., Shimizu, K.: Metabolic flux analysis of Escherichia coli K12 grown on C 13-labeled acetate and glucose using GG-MS and powerful flux calculation method. Journal of Biotechnology 101, 101–117 (2003)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Rafael S. Costa
    • 1
    • 2
  • Son Nguyen
    • 3
  • Andras Hartmann
    • 1
    • 2
  • Susana Vinga
    • 2
  1. 1.Instituto de Engenharia de Sistemas e ComputadoresInvestigacão e Desenvolvimento (INESC-ID)LisboaPortugal
  2. 2.Center for Intelligent Systems, LAETA, IDMEC, Instituto Superior TécnicoUniversidade de LisboaLisboaPortugal
  3. 3.Instituto Superior TécnicoUniversidade de LisboaLisboaPortugal

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