Graph-Based Decomposition of Biochemical Reaction Networks into Monotone Subsystems

  • Hans-Michael Kaltenbach
  • Simona Constantinescu
  • Justin Feigelman
  • Jörg Stelling
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6833)

Abstract

Large-scale model development for biochemical reaction networks of living cells is currently possible through qualitative model classes such as graphs, Boolean logic, or Petri nets. However, when it is important to understand quantitative dynamic features of a system, uncertainty about the networks often limits large-scale model development. Recent results, especially from monotone systems theory, suggest that structural network constraints can allow consistent system decompositions, and thus modular solutions to the scaling problem. Here, we propose an algorithm for the decomposition of large networks into monotone subsystems, which is a computationally hard problem. In contrast to prior methods, it employs graph mapping and iterative, randomized refinement of modules to approximate a globally optimal decomposition with homogeneous modules and minimal interfaces between them. Application to a medium-scale model for signaling pathways in yeast demonstrates that our algorithm yields efficient and biologically interpretable modularizations; both aspects are critical for extending the scope of (quantitative) cellular network analysis.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Alexander, R.P., Kim, P.M., Emonet, T., Gerstein, M.B.: Understanding modularity in molecular networks requires dynamics. Sci. Signal. 2(81), pe44 (2009)CrossRefGoogle Scholar
  2. 2.
    Banaji, M., Donnell, P., Baigent, S.: P matrix properties, injectivity, and stability in chemical reaction systems. SIAM J. Appl. Math. 67(6), 1523–1547 (2007)CrossRefMATHGoogle Scholar
  3. 3.
    Bowsher, C.G.: Information processing by biochemical networks: a dynamic approach. Journal of The Royal Society Interface 8, 186–200 (2010)CrossRefGoogle Scholar
  4. 4.
    Chen, W.W., Schoeberl, B., Jasper, P.J., Niepel, M., Nielsen, U.B., Lauffenburger, D.A., Sorger, P.K.: Input-output behavior of ErbB signaling pathways as revealed by a mass action model trained against dynamic data. Mol. Syst. Biol. 5, 239 (2009)Google Scholar
  5. 5.
    Craciun, G., Feinberg, M.: Multiple equilibria in complex chemical reaction networks: I. The injectivity property. SIAM J. Appl. Math. 65(5), 1526–1546 (2005)CrossRefMATHGoogle Scholar
  6. 6.
    Craciun, G., Feinberg, M.: Multiple equilibria in complex chemical reaction networks: II. The species-reaction graph. SIAM J. Appl. Math. 66(4), 1321–1338 (2006)CrossRefMATHGoogle Scholar
  7. 7.
    DasGupta, B., Enciso, G.A., Sontag, E., Zhang, Y.: Algorithmic and complexity results for decompositions of biological networks into monotone subsystems. Biosystems 90(1), 161–178 (2007)CrossRefMATHGoogle Scholar
  8. 8.
    Hirsch, M., Smith, H.: Monotone dynamical systems. In: Handbook of Differential Equations: Ordinary Differential Equations, vol. 2, pp. 239–357 (2006)Google Scholar
  9. 9.
    Hüffner, F., Betzler, N., Niedermeier, R.: Optimal edge deletions for signed graph balancing. In: Demetrescu, C. (ed.) WEA 2007. LNCS, vol. 4525, pp. 297–310. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  10. 10.
    Iacono, G., Ramezani, F., Soranzo, N., Altafini, C.: Determining the distance to monotonicity of a biological network: a graph-theoretical approach. IET Systems Biology 4(3), 223–235 (2010)CrossRefGoogle Scholar
  11. 11.
    Johnson, D.B.: Finding all the elementary circuits of a directed graph. SIAM J. Comput. 4(1), 77–84 (1975)CrossRefMATHGoogle Scholar
  12. 12.
    Karlebach, G., Shamir, R.: Modelling and analysis of gene regulatory networks. Nat. Rev. Mol. Cell. Biol. 9(10), 770–780 (2008)CrossRefGoogle Scholar
  13. 13.
    Kholodenko, B.N., Kiyatkin, A., Bruggeman, F.J., Sontag, E.D., Westerhoff, H.V., Hoek, J.B.: Untangling the wires: A strategy to trace functional interactions in signaling and gene networks. Proc. Natl. Acad. Sci. USA 99(20), 12841–12846 (2002)CrossRefGoogle Scholar
  14. 14.
    Li, C., Donizelli, M., Rodriguez, N., Dharuri, H., Endler, L., Chelliah, V., Li, L., He, E., Henry, A., Stefan, M.I., Snoep, J.L., Hucka, M., Le Novère, N., Laibe, C.: BioModels Database: An enhanced, curated and annotated resource for published quantitative kinetic models.. BMC Systems Biology 4, 92 (2010)CrossRefGoogle Scholar
  15. 15.
    Saez-Rodriguez, J., Gayer, S., Ginkel, M., Gilles, E.D.: Automatic decomposition of kinetic models of signaling networks minimizing the retroactivity among modules. Bioinf. 24(16), i213–i219 (2008)CrossRefGoogle Scholar
  16. 16.
    Smith, H.: Monotone dynamical systems: an introduction to the theory of competitive and cooperative systems. Mathematical Surveys and Monographs, vol. 41. American Mathematical Society AMS, Providence (1995)MATHGoogle Scholar
  17. 17.
    Sontag, E.: Monotone and near-monotone biochemical networks. LNCIS, vol. 357, pp. 79–122 (2007)Google Scholar
  18. 18.
    Soranzo, N., Ramezani, F., Iacono, G., Altafini, C.: Graph-theoretical decompositions of large-scale biological networks. Automatica (2010), conditionally acceptedGoogle Scholar
  19. 19.
    Zou, X., Peng, T., Pan, Z.: Modeling specificity in the yeast MAPK signaling networks. J. Theor. Biol. 250(1), 139–155 (2008)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Hans-Michael Kaltenbach
    • 1
  • Simona Constantinescu
    • 2
  • Justin Feigelman
    • 2
  • Jörg Stelling
    • 1
    • 2
  1. 1.Dep. Biosystems Science and EngineeringETH ZurichBaselSwitzerland
  2. 2.Dep. Computer ScienceETH ZurichZurichSwitzerland

Personalised recommendations