Dynamics of Content-Based Networks

  • Duygu Balcan
  • Ayşe Erzan
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3993)


Content-based networks are introduced and their topological properties are outlined. A content-based model with Random Boolean dynamics, designed to mimic the gene regulation network, exhibits an increase in the number and complexity of attractors for increasing number of nodes. However, contrary to expectations based on Mean Field calculations for random scale-free networks, the attractors are not chaotic, even for average connectivities in excess of 2. Thus, the present model offers a promising tool for understanding complex biological networks.


Boolean Function Length Distribution Gene Regulation Network Linear Code String Length 


  1. 1.
    Bollobas, B.: Modern Graph Theory. Springer, New York (1998)MATHGoogle Scholar
  2. 2.
    Pastor-Satorras, R., Vespignani, A.: Evolution and Structure of the Internet: A Statistical Physics Approach. Cambridge University Press, London (2004)CrossRefGoogle Scholar
  3. 3.
    Dorogovstsev, S.N., Mendes, J.F.F.: Evolution of Networks. Adv. Phys. 51, 1079–1187 (2002)CrossRefGoogle Scholar
  4. 4.
    Albert, R., Barabási, A.-L.: Statistical Mechanics of Complex Networks. Rev. Mod. Phys. 74, 47–97 (2002)CrossRefMATHGoogle Scholar
  5. 5.
    Sole, R.V., Pastor-Satorras, R.: Complex Networks in Genomics and Proteomics. In: Bornholdt, S., Schuster, H.G. (eds.) Handbook of Graphs and Networks. Wiley-VCH Verlag, Berlin (2002)Google Scholar
  6. 6.
    Barabási, A.-L., Oltvai, Z.N.: Network Biology: Understanding the Cell’s Functional Organization. Nat. Rev. Genet. 5, 101–113 (2004)CrossRefGoogle Scholar
  7. 7.
    Balcan, D., Erzan, A.: Random model for RNA interference yields scale free network. Eur. Phys. J. B 38, 253–260 (2004)CrossRefGoogle Scholar
  8. 8.
    Mungan, M., Kabakçıoğlu, A., Balcan, D., Erzan, A.: Analytical solution of a stochastic content-based network model. J. Phys A: Math Gen. 38, 9599–9620 (2005)MATHCrossRefGoogle Scholar
  9. 9.
    Reil, T.: Dynamics of gene expression in an artificial genome - implications for biological and artificial ontogeny. In: Floreano, D., Mondada, F. (eds.) ECAL 1999. LNCS, vol. 1674, pp. 457–466. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  10. 10.
    Alberts, B., et al.: Molecular Biology of the Cell, ch. 9. Garland Science, N.Y (2002)Google Scholar
  11. 11.
    Kabakçıoğlu, A., Mungan, M., Balcan, D., Erzan, A.: in preparationGoogle Scholar
  12. 12.
    Kauffman, S.A.: Metabolic stability and epigenesis in randomly connected nets. J. Theor. Biol. 22, 437–467 (1969)CrossRefMathSciNetGoogle Scholar
  13. 13.
    Kauffman, S.A.: The Origins of Order: Self-organization and Selection in Evolution. Oxford University Press, N.Y (1993)Google Scholar
  14. 14.
    Cohen, R., Erez, K., Ben-Avraham, D., Havlin, S.: Resilience of the Internet to Random Breakdowns. Phys. Rev. Lett. 85, 4625–4628 (2000)Google Scholar
  15. 15.
    Carlson, J.M., Doyle, J.: Highly Optimised Tolerance: A mechanism for power laws in designed systems. Phys. Rev. E 60, 1412–1427 (1999)CrossRefGoogle Scholar
  16. 16.
    Aldana, M.: Boolean dynamics of networks with scale-free topology. Physica D 185, 45–66 (2003)MATHCrossRefMathSciNetGoogle Scholar
  17. 17.
    Derrida, B., Eckmann, J.-P., Erzan, A.: Renormalisation groups with periodic and aperiodic orbits. J. Phys. A: Math. Gen. 16, 893–906 (1983)CrossRefMathSciNetGoogle Scholar
  18. 18.
    Lee, T.I., et al.: Transcriptional Regulatory Networks in Saccharomyces cerevisiae. Science 298, 799–804 (2002)CrossRefGoogle Scholar
  19. 19.
    Harbison, C.T., et al.: Transcriptional regulatory code of a eukaryotic genome. Nature 431, 99–104 (2004)CrossRefGoogle Scholar
  20. 20.
    Oikonomou, T., Provata, A.: Non-extensive trends in the size distribution of Coding and Non-coding DNA sequences in the Human Genome. Eur. Phys. J. B (in press); The length distributions for the coding (non-coding) regions of the human genome are found to display different power law tails, here interpreted as indicative of short (long) range correlations, depending on the exponents. Note, however, that some of the so called intergenic non-coding regions actually code the highly conserved binding sites for the transcription factors.See Refs. [10,19]Google Scholar
  21. 21.
    Zivković, J., Tadić, B., Wick, N., Thurner, S.: Statistical Indicators of Collective Behaviour and Functional Clusters in Gene Networks of Yeast. Eur. Phys. J. B (in press)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Duygu Balcan
    • 1
  • Ayşe Erzan
    • 1
    • 2
  1. 1.Department of Physics, Faculty of Sciences and LettersIstanbul Technical UniversityMaslakTurkey
  2. 2.Gürsey InstituteIstanbulTurkey

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