Advertisement

Randomization and Feedback Properties of Directed Graphs Inspired by Gene Networks

  • M. Cosentino Lagomarsino
  • P. Jona
  • B. Bassetti
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4210)

Abstract

Having in mind the large-scale analysis of gene regulatory networks, we review a graph decimation algorithm, called “leaf-removal”, which can be used to evaluate the feedback in a random graph ensemble. In doing this, we consider the possibility of analyzing networks where the diagonal of the adjacency matrix is structured, that is, has a fixed number of nonzero entries. We test these ideas on a network model with fixed degree, using both numerical and analytical calculations. Our results are the following. First, the leaf-removal behavior for large system size enables to distinguish between different regimes of feedback. We show their relations and the connection with the onset of complexity in the graph. Second, the influence of the diagonal structure on this behavior can be relevant.

Keywords

Adjacency Matrix Random Graph Gene Regulatory Network Oriented Graph Simple Cycle 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Uetz, P., Finley Jr., R.: From protein networks to biological systems. FEBS Lett. 579(8), 1821–1827 (2005)CrossRefGoogle Scholar
  2. 2.
    Babu, M., Luscombe, N., Aravind, L., Gerstein, M., Teichmann, S.: Structure and evolution of transcriptional regulatory networks. Curr. Opin. Struct. Biol. 14(3), 283–291 (2004)CrossRefGoogle Scholar
  3. 3.
    Davidson, E., Rast, J., Oliveri, P., Ransick, A., Calestani, C., Yuh, C., Minokawa, T., Amore, G., Hinman, V., Arenas-Mena, C., Otim, O., Brown, C., Livi, C., Lee, P., Revilla, R., Rust, A., Pan, Z., Schilstra, M., Clarke, P., Arnone, M., Rowen, L., Cameron, R., McClay, D., Hood, L., Bolouri, H.: A genomic regulatory network for development. Science 295(5560), 1669–1678 (2002)CrossRefGoogle Scholar
  4. 4.
    Price, N., Reed, J., Palsson, B.: Genome-scale models of microbial cells: evaluating the consequences of constraints. Nat. Rev. Microbiol. 2(11), 886–897 (2004)CrossRefGoogle Scholar
  5. 5.
    Yook, S., Oltvai, Z., Barabasi, A.: Functional and topological characterization of protein interaction networks. Proteomics 4(4), 928–942 (2004)CrossRefGoogle Scholar
  6. 6.
    Hurst, L., Pal, C., Lercher, M.: The evolutionary dynamics of eukaryotic gene order. Nat. Rev. Genet. 5(4), 299–310 (2004)CrossRefGoogle Scholar
  7. 7.
    Kepes, F.: Periodic epi-organization of the yeast genome revealed by the distribution of promoter sites. J. Mol. Biol. 329(5), 859–865 (2003)CrossRefGoogle Scholar
  8. 8.
    Teichmann, S., Babu, M.: Gene regulatory network growth by duplication. Nat. Genet. 36(5), 492–496 (2004)CrossRefGoogle Scholar
  9. 9.
    Hahn, M., Conant, G., Wagner, A.: Molecular evolution in large genetic networks: does connectivity equal constraint? J. Mol. Evol. 58(2), 203–211 (2004)CrossRefGoogle Scholar
  10. 10.
    Luscombe, N., Babu, M., Yu, H., Snyder, M., Teichmann, S., Gerstein, M.: Genomic analysis of regulatory network dynamics reveals large topological changes. Nature 431(7006), 308–312 (2004)CrossRefGoogle Scholar
  11. 11.
    Milo, R., Itzkovitz, S., Kashtan, N., Levitt, R., Shen-Orr, S., Ayzenshtat, I., Sheffer, M., Alon, U.: Superfamilies of evolved and designed networks. Science 303(5663), 1538–1542 (2004)CrossRefGoogle Scholar
  12. 12.
    Thomas, R.: Boolean formalization of genetic control circuits. J. Theor. Biol. 42(3), 563–585 (1973)CrossRefGoogle Scholar
  13. 13.
    Lagomarsino, M., Jona, P., Bassetti, B.: Logic backbone of a transcription network. Phys. Rev. Lett. 95(15), 158701 (2005)CrossRefGoogle Scholar
  14. 14.
    Correale, L., Leone, M., Pagnani, A., Weigt, M., Zecchina, R.: Core Percolation and Onset of Complexity in Boolean Networks. Phys. Rev. Lett. 96, 18101 (2006)CrossRefGoogle Scholar
  15. 15.
    Bauer, M., Golinelli, O.: Core percolation in random graphs: a critical phenomena analysis. Eur. Phys. J. B 24, 339–352 (2001)CrossRefGoogle Scholar
  16. 16.
    Mezard, M., Ricci-Tersenghi, F., Zecchina, R.: Alternative solutions to diluted p-spin models and XORSAT problems. J. Stat. Phys. 505 (2003)Google Scholar
  17. 17.
    Levitskaya, A.A.: Systems of Random Equations over Finite Algebraic Structures. Cybernetics and System Analysis 41(1), 67 (2005)MATHCrossRefMathSciNetGoogle Scholar
  18. 18.
    Itzkovitz, S., Milo, R., Kashtan, N., Ziv, G., Alon, U.: Subgraphs in random networks. Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 68(2 Pt 2), 26127 (2003)MathSciNetCrossRefGoogle Scholar
  19. 19.
    Mezard, M., Parisi, G., Zecchina, R.: Analytic and algorithmic solution of random satisfiability problems. Science 297(5582), 812–815 (2002)CrossRefGoogle Scholar
  20. 20.
    Kolchin, V.F.: Random Graphs. Cambridge University Press, New York (1998)CrossRefGoogle Scholar
  21. 21.
    Shen-Orr, S., Milo, R., Mangan, S., Alon, U.: Network motifs in the transcriptional regulation network of Escherichia coli. Nat. Genet. 31(1), 64–68 (2002)CrossRefGoogle Scholar
  22. 22.
    Weigt, M.: Dynamics of heuristic optimization algorithms on random graphs. Eur. Phys. J. B. 28, 369 (2002)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • M. Cosentino Lagomarsino
    • 1
    • 2
  • P. Jona
    • 3
  • B. Bassetti
    • 2
    • 4
  1. 1.UMR 168 / Institut CurieParisFrance
  2. 2.Dip. FisicaUniversità degli Studi di MilanoMilanoItaly
  3. 3.Dip. FisicaPolitecnico di MilanoMilanoItaly
  4. 4.I.N.F.N. MilanoItaly

Personalised recommendations