Fuzzy Continuous Petri Net-Based Approach for Modeling Immune Systems

  • Inho Park
  • Dokyun Na
  • Doheon Lee
  • Kwang H. Lee
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3931)


The immune system has unique defense mechanisms such as innate, humoral and cellular immunity. These mechanisms are closely related to prevent pathogens from spreading in the host and to clear them effectively. To get a comprehensive understanding of the immune system, it is necessary to integrate the knowledge through modeling. Many immune models have been developed based on differential equations and cellular automata. One of the most difficult problem in modeling the immune system is to find or estimate appropriate kinetic parameters. However, it is relatively easy to get qualitative or linguistic knowledge. To incorporate such knowledge, we present a novel approach, fuzzy continuous Petri nets. A fuzzy continuous Petri net has capability of fuzzy inference by adding new types of places and transitions to continuous Petri nets. The new types of places and transitions are called fuzzy places and fuzzy transitions, which act as kinetic parameters and fuzzy inference systems between input places and output places. The approach is applied to model helper T cell differentiation, which is a critical event in determining the direction of the immune response.


Cellular Automaton Fuzzy Rule Fuzzy Inference System Cellular Automaton Linguistic Knowledge 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Janeway, C.A., Travers, P., Walport, M., Shlomchik, M.: Immunology: The Immune System in Health and Disease. Taylor and Francis Inc., London (2001)Google Scholar
  2. 2.
    Aderem, A., Hood, L.: Immunology in the post-genomic era. Nat. Immunol. 2(5), 373–375 (2001)Google Scholar
  3. 3.
    Castiglione, F.: A network of cellular automata for the simulation of the immune system. Int. J. Morden Physics C 10, 677–686 (1999)CrossRefGoogle Scholar
  4. 4.
    Rundell, A., DeCarlo, R., HogenEsch, H., Doerschuk, P.: The humoral immune response to Haemophilis influenzae type b:a mathematical model based on T-zone and germinal center B-cell dynamics. J. Theor. Biol. 228(2) (May 2004)Google Scholar
  5. 5.
    Perelson, A.S.: Modelling viral and immune system dynamics. Nature Rev. Immunol. 2, 28–36 (2002)CrossRefGoogle Scholar
  6. 6.
    Puzone, R., Kohler, B., Seiden, P., Celada, F.: IMMSIM, a flexible model for in machine experiments on immune system responses. Future Generation Computer Systems 18, 961–972 (2002)CrossRefMATHGoogle Scholar
  7. 7.
    Na, D., Park, I., Lee, K.H., Lee, D.: Integration of immune models using petri nets. In: Nicosia, G., Cutello, V., Bentley, P.J., Timmis, J. (eds.) ICARIS 2004. LNCS, vol. 3239, pp. 205–216. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  8. 8.
    Matsuno, H., Doi, A., Nagasaki, M., Miyano, S.: Hybrid Petri net representation of gene regulatroy network. In: Pac. Symp. Biocompute., pp. 341–352 (2000)Google Scholar
  9. 9.
    Peleg, M., Yeh, I., Altman, R.B.: Modelling biological processes using workflow and Petri Net models. Bioinformatics 18(6), 825–837Google Scholar
  10. 10.
    Marino, S., Kirschner, D.E.: The human immune response to Mycobacterium tuberculosis in lung and lymph node. J. Theor. Biol. 227(4) (April 2004)Google Scholar
  11. 11.
    Bocharov, G.A., Romanyukha, A.A.: Mathematical Model of Antiviral Immune Response III. Influenza A Virus Infection. J. Theor. Biol. 167(4) (April 1994)Google Scholar
  12. 12.
    Kleinstein, S.H., Seiden, P.E.: Simulation the immune system. Computing in Science and Engineering 2(4) (July 2000)Google Scholar
  13. 13.
    dos Santos, R.M.Z., Coutinho, S.: Dynamcis of HIV infection: A Cellular Automata Approach. Phys. Rev. Letters 87(16) (October 2001)Google Scholar
  14. 14.
    Peterson, J.L.: Petri net theory and the modeling of systems. Prentice Hall, Englewood Cliff (1981)MATHGoogle Scholar
  15. 15.
    Murata, T.: Petri nets: Properties, analysis and applications. Proc. IEEE 77(4) (April 1989)Google Scholar
  16. 16.
    Alla, H., David, R.: A modeling and analysis tool for discrete event systems: continuous Petri net. Performance Evaluation 33(3) (August 1999)Google Scholar
  17. 17.
    Street, N.E., Mosmann, T.R.: Functional diversity of T lymphocytes due to secrection of different cytokine patterns. FASEB. J. 5, 171–177 (1991)Google Scholar
  18. 18.
    Bergmann, C., Van Hemmen, J.L.: Th1 or Th2: How an Approate T Helper Response can be Made. Bulletin of Mathematical Biology 63, 405–430 (2001)CrossRefMATHGoogle Scholar
  19. 19.
    Chao, D.L., Davenport, M.P., Forrest, S., Perelson, A.S.: A stochastic model of cytotoxic T cell responses. J. Theor. Biol. 228(2) (May 2004)Google Scholar
  20. 20.
    Yates, A., Bergmann, C., Leo Van Hemmen, J., Stark, J., Callard, R.: Cytokine-modulated Regulation of Helper T Cell Populations. J. theor. Biol. 206, 539–560 (2000)CrossRefGoogle Scholar
  21. 21.
    Lee, K.H.: First Course on Fuzzy Theory and Applications. Springer, Heidelberg (2005)MATHGoogle Scholar
  22. 22.
    Fishman, M.A., Perelson, A.S.: Th1/Th2 Differentiation and Crossregulation. Bulletin of Mathematical Biology 61, 403–436 (1999)CrossRefMATHGoogle Scholar
  23. 23.
    Yates, A., Callard, R., Stark, J.: Combining cytokine signalling with T-bet and GATA-3 regulation in Th1 and Th2 differentiation: a model for cellular decision-making. Jour. Theor. Biol. 231, 181–196 (2004)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Inho Park
    • 1
  • Dokyun Na
    • 1
  • Doheon Lee
    • 1
  • Kwang H. Lee
    • 1
  1. 1.Department of BioSystemsKAISTDaejeonRepublic of Korea

Personalised recommendations