Analysis of a Growth Model for Idiotypic Networks

  • Emma Hart
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4163)


This paper presents an analysis of the global physical properties of an idiotypic network, using a growth model with complete dynamics. Detailed studies of the properties of idiotypic networks are valuable as one the one hand they offer a potential explanation for immunological memory, and on the other have been used by engineers in application of AIS to a range of diverse applications. The properties of both homogeneous and heterogeneous networks resulting from the model in an integer-valued shape-space are analysed and compared. In addition, the results are contrasted to those obtained using other generic growth models found in the literature which have been proposed to explain the structure and growth of biological networks, and also make a useful addition to previous published results obtained in alternative shape-spaces. We find a number of both similarities and differences with other growth models that are worthy of further study.


Growth Model Degree Distribution Biological Network Heterogeneous Network Preferential Attachment 


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  1. 1.
    Barabasi, L., Albert, R.: Emergence of scaling in random networks. Science 286, 509–512 (1999)CrossRefMathSciNetGoogle Scholar
  2. 2.
    Bersini, H.: Self-assertion vs self-recogntion: A tribute to francisco varela. In: Proceedings of ICARIS 2002 (2002)Google Scholar
  3. 3.
    Bersini, H.: Revisiting Idiotypic Immune Networks. In: Banzhaf, W., Ziegler, J., Christaller, T., Dittrich, P., Kim, J.T. (eds.) ECAL 2003. LNCS, vol. 2801, pp. 164–174. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  4. 4.
    Bersini, H., Lenaerts, T., Santos, F.: Growing biological networks: beyond the gene duplication model. Journal of Theoretical Biology (2006)Google Scholar
  5. 5.
    Brede, M., Behn, U.: The architecture of idiotypic networks: Percolation and scaling behaviour. Physical Review E 64(1) (2001)Google Scholar
  6. 6.
    Brede, M., Behn, U.: Patterns in randomly evolving networks: Idiotypic networks. Physical. Review E (2003)Google Scholar
  7. 7.
    Carneiro, J., Coutinho, A., Stewart, J.: A Model of the Immune Network with B-T Cell Cooperation. ii - the Simulation of Ontogenesis. Journal of Theoretical Biology 182, 531–547 (1996)CrossRefGoogle Scholar
  8. 8.
    Farmer, J.D., Packard, N., Perelson, A.: The immune system, adaptation and machine learning. Physica D 22, 187–204 (1986)CrossRefMathSciNetGoogle Scholar
  9. 9.
    Hart, E.: Not all balls are round: An investigation of alternative recognition-region shapes. In: Jacob, C., Pilat, M.L., Bentley, P.J., Timmis, J.I. (eds.) ICARIS 2005. LNCS, vol. 3627, pp. 29–42. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  10. 10.
    Hart, E., Ross, P.: The impact of the shape of antibody recognition regions on the emergence of idiotypic networks. International Journal of Unconventional Computing (2005)Google Scholar
  11. 11.
    Jeong, H., Mason, S., Barabsi, A., Oltavi, Z.: Lethality and centrality in protein networks. Nature 411, 41–42 (2001)CrossRefGoogle Scholar
  12. 12.
    Jerne, N.K.: Towards a network theory of the immune system. Annals of Immunology (Institute Pasteur) (1974)Google Scholar
  13. 13.
    Lenaerts, T., Bersini, H., Santos, F.: How scale-free type-based networks emerge from instance-based dynamics. In: Proceedings of 10th ALife Conference (2006)Google Scholar
  14. 14.
    Neal, M.: Meta-stable memory in an artificial immune network. In: Timmis, J., Bentley, P.J., Hart, E. (eds.) ICARIS 2003. LNCS, vol. 2787, pp. 168–180. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  15. 15.
    Newman, M.E.J.: The structure and function of complex networks. Society for Industrial and Applied Mathematics Review 45(2), 167–256 (2003)MATHGoogle Scholar
  16. 16.
    Takumi, K., De Boer, R.: Self assertion modeled as a network repertoire of multi-determinant antibodies. Journal of Theoretical Biology 183, 55–66 (1996)CrossRefGoogle Scholar
  17. 17.
    Varela, F., Coutinho, A.: Second generation immune network. Immunology Today 12(5), 159–166 (1991)Google Scholar
  18. 18.
    Vasquez, F., Flamimi, A., Maritan, A., Vespignani, A.: Modelling interaction of protein interaction networks. Complexs 1, 38–44 (2003)CrossRefGoogle Scholar
  19. 19.
    Watanabe, Y., Ishiguro, A., Shiraio, Y., Uchikawa, Y.: Emergent construction of a behaviour arbitration mechanism based on the immune system. Advanced Robotics 12(3), 227–242 (1998)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Emma Hart
    • 1
  1. 1.School of ComputingNapier University 

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