Advertisement

Journal of Mathematical Biology

, Volume 78, Issue 5, pp 1459–1484 | Cite as

Quantitative flux coupling analysis

  • Mojtaba TefaghEmail author
  • Stephen P. Boyd
Article

Abstract

Flux coupling analysis (FCA) aims to describe the functional dependencies among reactions in a metabolic network. Currently studied coupling relations are qualitative in the sense that they identify pairs of reactions for which the activity of one reaction necessitates the activity of the other one, but without giving any numerical bounds relating the possible activity rates. The potential applications of FCA are heavily investigated, however apart from some trivial cases there is no clue of what bottleneck in the metabolic network causes each dependency. In this article, we introduce a quantitative approach to the same flux coupling problem named quantitative flux coupling analysis (QFCA). It generalizes the current concepts as we show that all the qualitative information provided by FCA is readily available in the quantitative flux coupling equations of QFCA, without the need for any additional analysis. Moreover, we design a simple algorithm to efficiently identify these flux coupling equations which scales up to the genome-scale metabolic networks with thousands of reactions and metabolites in an effective way. Furthermore, this framework enables us to quantify the “strength” of the flux coupling relations. We also provide different biologically meaningful interpretations, including one which gives an intuitive certificate of precisely which metabolites in the network enforce each flux coupling relation. Eventually, we conclude by suggesting the probable application of QFCA to the metabolic gap-filling problem, which we only begin to address here and is left for future research to further investigate.

Keywords

Systems biology Metabolic network analysis Flux coupling analysis FCA QFCA Flux coupling equation 

Mathematics Subject Classification

92C42 90C05 49N15 

References

  1. Beard DA, Babson E, Curtis E, Qian H (2004) Thermodynamic constraints for biochemical networks. J Theor Biol 228(3):327–333MathSciNetCrossRefGoogle Scholar
  2. Bonarius HP, Schmid G, Tramper J (1997) Flux analysis of underdetermined metabolic networks: the quest for the missing constraints. Trends Biotechnol 15(8):308–314CrossRefGoogle Scholar
  3. Boyd S, Vandenberghe L (2004) Convex optimization. Cambridge University Press, CambridgeCrossRefzbMATHGoogle Scholar
  4. Brunk E, Sahoo S, Zielinski DC, Altunkaya A, Dräger A, Mih N, Gatto F, Nilsson A, Gonzalez GAP, Aurich MK et al (2018) Recon3D enables a three-dimensional view of gene variation in human metabolism. Nat Biotechnol 36(3):272CrossRefGoogle Scholar
  5. Burgard AP, Nikolaev EV, Schilling CH, Maranas CD (2004) Flux coupling analysis of genome-scale metabolic network reconstructions. Genome Res 14(2):301–312CrossRefGoogle Scholar
  6. Covert MW, Schilling CH, Famili I, Edwards JS, Goryanin II, Selkov E, Palsson BØ (2001) Metabolic modeling of microbial strains in silico. Trends Biochem Sci 26(3):179–186CrossRefGoogle Scholar
  7. David L, Marashi S-A, Larhlimi A, Mieth B, Bockmayr A (2011) FFCA: a feasibility-based method for flux coupling analysis of metabolic networks. BMC Bioinform 12(1):236CrossRefGoogle Scholar
  8. Dreyfuss JM, Zucker JD, Hood HM, Ocasio LR, Sachs MS, Galagan JE (2013) Reconstruction and validation of a genome-scale metabolic model for the filamentous fungus neurospora crassa using farm. PLoS Comput Biol 9(7):e1003126CrossRefGoogle Scholar
  9. Fell DA, Small JR (1986) Fat synthesis in adipose tissue an examination of stoichiometric constraints. Biochem J 238(3):781–786CrossRefGoogle Scholar
  10. Gudmundsson S, Thiele I (2010) Computationally efficient flux variability analysis. BMC Bioinform 11(1):489CrossRefGoogle Scholar
  11. Gunawardena J (2014) Time-scale separation-michaelis and menten’s old idea, still bearing fruit. FEBS J 281(2):473–488CrossRefGoogle Scholar
  12. Haus U-U, Klamt S, Stephen T (2008) Computing knock-out strategies in metabolic networks. J Comput Biol 15(3):259–268MathSciNetCrossRefGoogle Scholar
  13. Herrgård MJ, Swainston N, Dobson P, Dunn WB, Arga KY, Arvas M, Blüthgen N, Borger S, Costenoble R, Heinemann M et al (2008) A consensus yeast metabolic network reconstruction obtained from a community approach to systems biology. Nat Biotechnol 26(10):1155–1160CrossRefGoogle Scholar
  14. Horst R, Pardalos PM (2013) Handbook of global optimization, vol 2. Springer, BerlinzbMATHGoogle Scholar
  15. Larhlimi A, Bockmayr A (2006) A new approach to flux coupling analysis of metabolic networks. In: International symposium on computational life science. Springer, pp 205–215Google Scholar
  16. Larhlimi A, David L, Selbig J, Bockmayr A (2012) F2C2: a fast tool for the computation of flux coupling in genome-scale metabolic networks. BMC Bioinform 13(1):57CrossRefGoogle Scholar
  17. Marashi S-A, Bockmayr A (2011) Flux coupling analysis of metabolic networks is sensitive to missing reactions. Biosystems 103(1):57–66CrossRefGoogle Scholar
  18. Marashi S-A, Tefagh M (2014) A mathematical approach to emergent properties of metabolic networks: partial coupling relations, hyperarcs and flux ratios. J Theor Biol 355:185–193MathSciNetCrossRefzbMATHGoogle Scholar
  19. Notebaart RA, Teusink B, Siezen RJ, Papp B (2008) Co-regulation of metabolic genes is better explained by flux coupling than by network distance. PLoS Comput Biol 4(1):e26CrossRefGoogle Scholar
  20. Orth JD, Palsson BØ (2010) Systematizing the generation of missing metabolic knowledge. Biotechnol Bioeng 107(3):403–412CrossRefGoogle Scholar
  21. Orth J, Fleming R, Palsson B (2010) Reconstruction and use of microbial metabolic networks: the core escherichia coli metabolic model as an educational guide. EcoSal Plus.  https://doi.org/10.1128/ecosalplus.10.2.1
  22. Reed JL, Patel TR, Chen KH, Joyce AR, Applebee MK, Herring CD, Bui OT, Knight EM, Fong SS, Palsson BO (2006) Systems approach to refining genome annotation. Proc Natl Acad Sci 103(46):17480–17484CrossRefGoogle Scholar
  23. Rolfsson O, Palsson BØ, Thiele I (2011) The human metabolic reconstruction Recon 1 directs hypotheses of novel human metabolic functions. BMC Syst Biol 5(1):155CrossRefGoogle Scholar
  24. Satish Kumar V, Dasika MS, Maranas CD (2007) Optimization based automated curation of metabolic reconstructions. BMC Bioinform 8(1):212CrossRefGoogle Scholar
  25. Savinell JM, Palsson BØ (1992) Network analysis of intermediary metabolism using linear optimization. I. development of mathematical formalism. J Theor Biol 154(4):421–454CrossRefGoogle Scholar
  26. Schilling CH, Edwards JS, Palsson BØ (1999a) Toward metabolic phenomics: analysis of genomic data using flux balances. Biotechnol Progress 15(3):288–295CrossRefGoogle Scholar
  27. Schilling CH, Schuster S, Palsson BØ, Heinrich R (1999b) Metabolic pathway analysis: basic concepts and scientific applications in the post-genomic era. Biotechnol Progress 15(3):296–303CrossRefGoogle Scholar
  28. Schuster S, Hilgetag C (1994) On elementary flux modes in biochemical reaction systems at steady state. J Biol Syst 2(02):165–182CrossRefGoogle Scholar
  29. Thiele I, Vlassis N, Fleming RM (2014) fastGapFill: efficient gap filling in metabolic networks. Bioinformatics 30(17):2529–2531CrossRefGoogle Scholar
  30. Varma A, Palsson BØ (1994) Metabolic flux balancing: basic concepts, scientific and practical use. Nat Biotechnol 12:994CrossRefGoogle Scholar
  31. Vlassis N, Pacheco MP, Sauter T (2014) Fast reconstruction of compact context-specific metabolic network models. PLoS Comput Biol 10(1):e1003424CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Information Systems Laboratory, Department of Electrical EngineeringStanford UniversityStanfordUSA

Personalised recommendations