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Extended Spatial Evolutionary Games and Induced Bystander Effect

Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 283)

Abstract

The main goal of the study is modelling of radiation induced bystander effect using evolutionary game theory. A payoff table for three different phenotypes (game-theoretic strategies) contains: costs/profits of bystander effect, choice of apoptotic pathway, producing growth factors and resistance against bystander effect. Games are played on a lattice and for that purpose two kinds of spatial evolutionary games are presented and compared. Moreover different polymorphic equilibrium points dependent on model parameters and cells reproductions are discussed.

Keywords

evolutionary games biomathematical modelling carcinogenesis cellular automata polymorphism 

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References

  1. 1.
    Maynard Smith, J., Price, G.R.: The logic of animal conflict. Nature 246(5427), 15–18 (1973)CrossRefGoogle Scholar
  2. 2.
    Maynard Smith, J.: Evolution and the theory of games. Cambridge University Press (1982)Google Scholar
  3. 3.
    Myerson, R.B.: Game theory: analysis of conflict. Harvard University Press (1991)Google Scholar
  4. 4.
    Tomlinson, I.P.M., Bodmer, W.F.: Modelling the consequences of interactions between tumour cells. British J. Cancer 75, 157–160 (1997)CrossRefGoogle Scholar
  5. 5.
    Basanta, D., Deutsch, A.: A game theoretical perspective on the somatic evolution of cancer. In: Bellomo, N., Chaplain, M., Angelis, E. (eds.) Selected Topics in Cancer Modeling: Genesis, Evolution, Immune Competition, and Therapy, pp. 1–16 (2008)Google Scholar
  6. 6.
    Świerniak, A., Krześlak, M.: Application of evolutionary games to modeling carcinogenesis. Mathematical Biosciences and Engineering 10(3), 873–911 (2013)CrossRefMATHMathSciNetGoogle Scholar
  7. 7.
    Hofbauer, J., Shuster, P., Sigmund, K.: Replicator dynamics. J. Theor. Biol. 100, 533–538 (1979)Google Scholar
  8. 8.
    Bach, L.A., Sumpter, D.J.T., Alsner, J., Loeschcke, V.: Spatial evolutionary games of interactions among generic cancer cells. Journal of Theoretical Medicine 5, 47–58 (2003)CrossRefMATHGoogle Scholar
  9. 9.
    Świerniak, A., Krześlak, M.: Game theoretic approach to mathematical modeling of radiation induced bystander effect. In: Proc of the 16 Nat. Conf. on Applications of Mathematics in Biology and Medicine, pp. 99–104 (2010)Google Scholar
  10. 10.
    Krześlak, M., Świerniak, A.: Spatial evolutionary games and radiation induced bystander effect. Archives of Control Sciences 21, 135–150 (2011)MATHGoogle Scholar
  11. 11.
    Wideł, M., Przybyszewski, W., Rzeszowska-Wolny, J.: Radiation-induced bystander effect: The important part of ionizing radiation response. Potential Clinical Implications. Postępy Hig. Med. Dośw. 63, 377–388 (2009) (in Polish)Google Scholar
  12. 12.
    Wideł, M.: Bystander effect induced by UV radiation; why should we be interested? Postępy Hig. Med. Dośw (Online) 66, 828–837 (2012)CrossRefGoogle Scholar
  13. 13.
    Tomlinson, I.P.M.: Game-theory models of interactions between tumour cells. Eur. J. Cancer 33, 1495–1500 (1997)CrossRefGoogle Scholar
  14. 14.
    Herok, R., Konopacka, M., Polańska, J., Świerniak, A., Rogoliński, J., Jaksik, R., Hancock, R., Rzeszowska–Wolny, J.: Bystander effects induced by medium from irradiated cells: similar transcriptome responses in irradiated and bystander K562 cells. Int. J. Radiat. Oncol. Biol. Phys., 244–252 (2010)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Faculty of Automatic Control, Electronics and Computer Science,Department of Automatic ControlSilesian University of TechnologyGliwicePoland

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