A Reduction of Logical Regulatory Graphs Preserving Essential Dynamical Properties

  • Aurélien Naldi
  • Elisabeth Remy
  • Denis Thieffry
  • Claudine Chaouiya
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5688)

Abstract

To cope with the increasing complexity of regulatory networks, we define a reduction method for multi-valued logical models.

Starting with a detailed model, this method enables the computation of a reduced model by iteratively “hiding” regulatory components. To keep a consistent behaviour, the logical rules associated with the targets of each hidden node are actualised to account for the (indirect) effects of its regulators.

The construction of reduced models ensures the preservation of a number of dynamical properties of the original model. In particular, stable states and more complex attractors are conserved. More generally, we focus on the relationship between the attractor configuration of the original model and that of the reduced model, along with the issue of attractor reachability.

The power of the reduction method is illustrated by its application to a multi-valued model of the segment-polarity network Controlling segmentation in the fly Drosophila melanogaster.

Keywords

Regulatory networks logical modelling model reduction decision diagrams regulatory circuits stable states complex attractors Drosophila development segmentation 

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References

  1. 1.
    Saez-Rodriguez, J., Simeoni, L., Lindquist, J., Hemenway, R., Bommhardt, U., Arndt, B., Haus, U., Weismantel, R., Gilles, E., Klamt, S., Schraven, B.: A logical model provides insights into t cell receptor signaling. PLoS Comput. Biol. 3(8), e163 (2007)Google Scholar
  2. 2.
    Franke, R., Müller, M., Wundrack, N., Gilles, E.D., Klamt, S., Kähne, T., Naumann, M.: Host-pathogen systems biology: logical modelling of hepatocyte growth factor and helicobacter pylori induced c-met signal transduction. BMC Syst. Biol. 2, 4 (2008)Google Scholar
  3. 3.
    Chaouiya, C., Remy, E., Mossé, B., Thieffry, D.: Qualitative analysis of regulatory graphs: a computational tool based on a discrete formal framework. LNCIS, vol. 294, pp. 119–126 (2003)Google Scholar
  4. 4.
    Naldi, A., Berenguier, D., Fauré, A., Lopez, F., Thieffry, D., Chaouiya, C.: Logical modelling of regulatory networks with GINsim 2.3. BioSystems (in press)Google Scholar
  5. 5.
    Thomas, R.: Regulatory networks seen as asynchronous automata: A logical description. J. Theor. Biol. 153, 1–23 (1991)CrossRefGoogle Scholar
  6. 6.
    Thomas, R., Thieffry, D., Kaufman, M.: Dynamical behaviour of biological regulatory networks–i. biological role of feedback loops and practical use of the concept of the loop-characteristic state. Bull. Math. Biol. 57(2), 247–276 (1995)PubMedGoogle Scholar
  7. 7.
    Bryant, R.E.: Graph-based algorithms for boolean function manipulation. IEEE Trans. Comput. 35, 677–691 (1986)CrossRefGoogle Scholar
  8. 8.
    Kam, T., Villa, T., Brayton, R.K., Sangiovanni-Vincentelli, A.L.: Multi-valued decision diagrams: Theory and applications. Int. J. Multi. Logic 4, 9–12 (1998)Google Scholar
  9. 9.
    Naldi, A., Thieffry, D., Chaouiya, C.: Decision diagrams for the representation and analysis of logical models of genetic networks. In: Calder, M., Gilmore, S. (eds.) CMSB 2007. LNCS (LNBI), vol. 4695, pp. 233–247. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  10. 10.
    Meinhardt, H.: Hierarchical inductions of cell states: a model for segmentation in drosophila. J. Cell Sci. Suppl. 4, 357–381 (1986)CrossRefPubMedGoogle Scholar
  11. 11.
    von Dassow, G., Meir, E., Munro, E.M., Odell, G.M.: The segment polarity network is a robust developmental module. Nature 406(6792), 188–192 (2000)CrossRefGoogle Scholar
  12. 12.
    Ingolia, N.T.: Topology and robustness in the drosophila segment polarity network. PLoS Biol. 2(6), e123 (2004)CrossRefGoogle Scholar
  13. 13.
    Albert, R., Othmer, H.G.: The topology of the regulatory interactions predicts the expression pattern of the segment polarity genes in drosophila melanogaster. J. Theor. Biol. 223(1), 1–18 (2003)CrossRefPubMedGoogle Scholar
  14. 14.
    Chaves, M., Albert, R., Sontag, E.D.: Robustness and fragility of boolean models for genetic regulatory networks. J. Theor. Biol. 235(3), 431–449 (2005)CrossRefPubMedGoogle Scholar
  15. 15.
    Sánchez, L., Chaouiya, C., Thieffry, D.: Segmenting the fly embryo: logical analysis of the role of the segment polarity cross-regulatory module. Int. J. Dev. Biol. 52(8), 1059–1075 (2008)PubMedGoogle Scholar
  16. 16.
    González, A., Chaouiya, C., Thieffry, D.: Logical modelling of the role of the hh pathway in the patterning of the drosophila wing disc. Bioinformatics 24(16), i234–i240 (2008)CrossRefGoogle Scholar
  17. 17.
    Sánchez, L., Thieffry, D.: Segmenting the fly embryo: a logical analysis of the pair-rule cross-regulatory module. J. Theor. Biol. 224(4), 517–537 (2003)CrossRefPubMedGoogle Scholar
  18. 18.
    Fauré, A., Naldi, A., Chaouiya, C., Thieffry, D.: Dynamical analysis of a generic boolean model for the control of the mammalian cell cycle. Bioinformatics 22(14), e124–e131 (2006)CrossRefGoogle Scholar
  19. 19.
    Remy, E., Ruet, P.: From minimal signed circuits to the dynamics of boolean regulatory networks. Bioinformatics 24(16), i220–i226 (2008)CrossRefGoogle Scholar
  20. 20.
    Garg, A., Di Cara, A., Xenarios, I., Mendoza, L., De Micheli, G.: Synchronous versus asynchronous modeling of gene regulatory networks. Bioinformatics 24(17), 1917–1925 (2008)CrossRefPubMedPubMedCentralGoogle Scholar
  21. 21.
    Monteiro, P.T., Ropers, D., Mateescu, R., Freitas, A.T., de Jong, H.: Temporal logic patterns for querying dynamic models of cellular interaction networks. Bioinformatics 24(16), i227–i233 (2008)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Aurélien Naldi
    • 1
  • Elisabeth Remy
    • 2
  • Denis Thieffry
    • 1
    • 3
  • Claudine Chaouiya
    • 1
    • 4
  1. 1.TAGC Inserm U928Université de la MéditerranéeMarseilleFrance
  2. 2.IML UMR 6206MarseilleFrance
  3. 3.CONTRAINTESINRIA Paris RocquencourtFrance
  4. 4.IGCInstituto Gulbenkian de CiênciaOeirasPortugal

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