Advertisement

Stigmergy for Biological Spatial Modeling

  • Megan OlsenEmail author
Chapter
Part of the Understanding Complex Systems book series (UCS)

Abstract

Complex adaptive systems can be characterized as systems that are comprised of groups of agents following simple rules that, collectively, produce emergent, complex behavior. The key to these emergent properties are the interactions—the exchanges of information—between the agents. Many biological systems can be studied using a complex adaptive systems approach, such as colonies of bees or ants. In some of these biological systems, the communication between individual agents is indirect. This type of communication is termed stimergy: a relatively small amount of information being shared through the environment, rather than directly from agent to agent. This information is nonetheless crucial to the self-organizing properties of the system, and is used by the agents to inform decision making, such as when ants follow a trail of pheromones left by other ants. In this chapter we describe computer simulations of two such systems, created and used to conduct experiments on various types of stimergy: collaboration within a predator-prey system, and angiogenesis in cancer growth. The first utilizes a cellular automata model, and the second a multiscale agent-based model. Further, this paper defines various options of communications for these simulations, and examines the use of similar communication paradigms in these two different types of models. Results support that stigmergy can be adapted to a variety of situations. Also, that awareness of the speed of algorithmic decisions can increase its usefulness in biological modeling. These ideas can be adapted to many other modeling situations other than the classic examples of self-organization like bees or ants.

References

  1. 1.
    Abbott, R.: Cancersim: a computer-based simulation of hanahan and weinberg’s hallmarks of cancer. Master’s thesis, University of New Mexico (2002)Google Scholar
  2. 2.
    Allsopp, R.C., Vaziri, H., Patterson, C., Goldstein, S., Younglai, E.V., Futcher, A.B., Greider, C.W., Harley, C.B.: Telomere length predicts replicative capacity of human fibroblasts. Proc. Natl. Acad. Sci. U.S.A. 89(21), 10114–10118 (1992)CrossRefGoogle Scholar
  3. 3.
    Alexander, R.A. Anderson, A.M. Weaver, P.T.: Cummings, and Vito Quaranta. Tumor morphology and phenotypic evolution driven by selective pressure from the microenvironment. Cell 127(5), 905–915 (2006)CrossRefGoogle Scholar
  4. 4.
    Anderson, P.W.: More is different. Science 177(4047) (1972)CrossRefGoogle Scholar
  5. 5.
    Barkai, N., Shilo, B.-Z.: Variability and robustness in biomolecular systems. Mol. Cell 28(5), 755–760 (2007)CrossRefGoogle Scholar
  6. 6.
    Bauer, A.L., Jackson, T.L., Jiang, Y.: A cell-based model exhibiting branching and anastomosis during tumor-induced angiogenesis. Biophys. J. 92(9), 3105–3121 (2007)CrossRefGoogle Scholar
  7. 7.
    Blanchard, D.C., Griebel, G., Blanchard, R.J.: Conditioning and residual emotionality effects of predator stimuli: some reflections on stress and emotion. Prog. Neuro-Psychopharmacol. Biol. Psychiatr. 27, 1177–1185 (2003)CrossRefGoogle Scholar
  8. 8.
    Bonabeau, E., Dorigo, M., Theraulaz, G.: Swarm Intelligence: From Natural to Artificial Systems and. Oxford University Press, Oxford (1999)zbMATHGoogle Scholar
  9. 9.
    Bonabeau, E., Dorigo, M., Theraulaz, G.: Inspiration for optimization from social insect behaviour. Nature 406(6791), 39–42 (2000)CrossRefGoogle Scholar
  10. 10.
    Bo Shim, E., Kwon, Y.-G., Jong Ko, H.: Computational analysis of tumor angiogenesis patterns using a two-dimensional model. Yonsei Med. J. 46(2), 275–283 (2005)CrossRefGoogle Scholar
  11. 11.
    Coffey, D.S.: Self-organization, complexity and chaos: the new biology for medicine. Nat. Med. 4(8), 882–885 (1998). AugustCrossRefGoogle Scholar
  12. 12.
    Couzin, I.: Collective minds. Nature 445, (2007)CrossRefGoogle Scholar
  13. 13.
    Couzin, I.D.: Collective cognition in animal groups. Trends Cognit. Sci. 13, 36–43 (2009)CrossRefGoogle Scholar
  14. 14.
    Couzin, I.D., Krause, J., Franks, N.R., Levin, S.A.: Effective leadership and decision-making in animal groups on the move. Nature 433, 513–516 (2005)CrossRefGoogle Scholar
  15. 15.
    de Carvalho, K.C., Tome, T.: Self-organized patterns of coexistence out of a predator-prey cellular automaton. Int. J. Mod. Phys. C 17, 1647–1662 (2006)MathSciNetCrossRefGoogle Scholar
  16. 16.
    Dewdney, A.K.: Sharks and fish wage an ecological war on the toroidal planet wa-tor. Sci. Am. (1984)Google Scholar
  17. 17.
    Dréau, D., Stanimirov, D., Carmichael, T., Hadzikadic, M.: An agent-based model of solid tumor progression. In: Proceedings of the 1st International Conference on Bioinformatics and Computational Biology, BICoB ’09, pp. 187–198. Springer, Berlin, Heidelberg (2009)CrossRefGoogle Scholar
  18. 18.
    Ekman, P.: Basic Emotions. Wiley, New York (1999)CrossRefGoogle Scholar
  19. 19.
    Farina, F., Dennunzio, A.: A predator-prey cellular automaton with parasitic interactions and environmental effects. Fundam. Inf. 83, 337–353 (2008)MathSciNetzbMATHGoogle Scholar
  20. 20.
    Frank, S.A., Iwasa, Y., Nowak, M.A.: Patterns of cell divisions and the risk of cancer. Genetics 163, 1527–1532 (2003). AprilGoogle Scholar
  21. 21.
    Gardner, M.: The fantastic combinations of john conway’s new solitaire game ’life’. Sci. Am. 223, 120–123 (1970)CrossRefGoogle Scholar
  22. 22.
    Hanahan, D., Weinberg, R.A.: The hallmarks of cancer. Cell 100, 57–70 (2000). JanuaryCrossRefGoogle Scholar
  23. 23.
    Harrington, K., Olsen, M., Siegelmann, H.: Communicated somatic markers benefit both the individual and the species. In: Proceedings of the International Joint Conference on Neural Networks (2011)Google Scholar
  24. 24.
    Harrington, K., Olsen, M., Siegelmann, H.: Computational neuroecology of communicated somatic markers. (2012)Google Scholar
  25. 25.
    Hawick, K.A., Scogings, C.J.: A minimal spatial cellular automata for hierarchical predator-prey simulation of food chains (technical report cstn-040). Technical report, Computer Science, Massey University (2009)Google Scholar
  26. 26.
    Hogeweg, P.: Cellular automata as a paradigm for ecological modeling. Appl. Math. Comput. 27, 81–100 (1988)MathSciNetzbMATHGoogle Scholar
  27. 27.
    Hyung Don Ryoo, T.G., Steller, H.: Apoptotic cells can induce compensatory cell proliferation through the jnk and the wingless signaling pathways. Dev. Cell 7(4), 491–501 (2004)Google Scholar
  28. 28.
    Kitano, H.: Systems biology: a brief overview. Science 295(5560), 1662–1664 (2002)CrossRefGoogle Scholar
  29. 29.
    Lehman, C.L., Tilman, D.: Competition in Spatial Habitats, pp. 185–203. Princeton University Press, Princeton (1997)Google Scholar
  30. 30.
    Lindahl, T., Wood, R.D.: Quality control by dna repair. Science 286(3) (1999)CrossRefGoogle Scholar
  31. 31.
    Lotka, A.J.: Elements of Physical Biology. Williams and Wilkins (1925)Google Scholar
  32. 32.
    Low, A., Lang, P.J., Smith, J.C., Bradley, M.M.: Both predator and prey: emotional arousal in threat and reward. Psychol. Sci. 19, 865–873 (2008)CrossRefGoogle Scholar
  33. 33.
    Mark A.J.C.: Mathematical modelling of angiogenesis. J. Neuro-Oncol. 50, 37–51 (2000).  https://doi.org/10.1023/A:1006446020377CrossRefGoogle Scholar
  34. 34.
    Markus, M., Böhm, D., Schmick, M.: Simulation of vessel morphogenesis using cellular automata. Math. Biosci. 156(1–2), 191–206 (1999)MathSciNetCrossRefGoogle Scholar
  35. 35.
    McDougall, S.R., Anderson, A.R.A., Chaplain, M.A.J.: Mathematical modelling of dynamic adaptive tumour-induced angiogenesis: Clinical implications and therapeutic targeting strategies. J. Theor. Biol. 241(3), 564–589 (2006)MathSciNetCrossRefGoogle Scholar
  36. 36.
    Michor, F., Iwasa, Y., Nowak, M.A.: Dynamics of cancer progression. Nat. Rev. Cancer 4, 197–206 (2004)CrossRefGoogle Scholar
  37. 37.
    Millonas, M.M.: Swarms, phase transitions, and collective intelligence. SFI Stud. Sci. Complex. 17, 417–417 (1994)Google Scholar
  38. 38.
    Olsen, M.M., Siegelmann, H.T.: Multiscale agent-based model of tumor angiogenesis. Proc. Comput. Sci. 18, 1016–1025 (2013)CrossRefGoogle Scholar
  39. 39.
    Olsen, M., Harrington, K., Siegelmann, H.: Conspecific emotional cooperation biases population dynamics: a cellular automata approach. Int. J. Nat. Comput. Res. 1(3), 51–65 (2010)CrossRefGoogle Scholar
  40. 40.
    Olsen, M.M., Siegelmann-Danieli, N., Siegelmann, H.T.: Dynamic computational model suggests that cellular citizenship is fundamental for selective tumor apoptosis. PLoS One 5(5) (2010)CrossRefGoogle Scholar
  41. 41.
    Olsen, M., Harrington, K., Siegelmann, H.: Computational emotions in a population dynamics cellular automata encourage collective behavior. In: International Conference on Complex Systems (2011)Google Scholar
  42. 42.
    Olsen, M.M., Fraczkowski, R.: Co-evolution in predator prey through reinforcement. J Comput Sci. 9, 118–124 (2015).  https://doi.org/10.1016/j.jocs.2015.04.044
  43. 43.
    Owen, M.R., Alarcon, T., Maini, P.K., Byrne, H.M.: Angiogenesis and vascular remodelling in normal and cancerous tissues. J. Math. Biol. 58(4–5), 689–721 (2009)MathSciNetCrossRefGoogle Scholar
  44. 44.
    Park, K.: The internet as a complex system. In: Park, K., Willinger, W. (eds.), The Internet as a Large-Scale Complex System, pp. 1–89. Oxford University Press, Oxford (2005)Google Scholar
  45. 45.
    PawełTopa. Dynamically reorganising vascular networks modelled using cellular automata approach. In: Proceedings of the 8th International Conference on Cellular Automata for Reseach and Industry, ACRI ’08, pp. 494–49. Springer, Berlin (2008)Google Scholar
  46. 46.
    Peirce, S.M., Van Gieson, E.J., Skalak, T.C.: Multicellular simulation predicts microvascular patterning and in silico tissue assembly. FASEB J. 18(6), 731–733 (2004)CrossRefGoogle Scholar
  47. 47.
    Pettet, G.J., Please, C.P., Tindall, M.J., McElwain, D.L.S.: The migration of cells in multicell tumor spheroids. Bull. Math. Bio. 63, 231–257 (2001)CrossRefGoogle Scholar
  48. 48.
    Plotkin, J., Nowak, M.A.: Different effects of apoptosis and dna repair on tumorigenesis. J. Theor. Biol. 214, 453–467 (2002)CrossRefGoogle Scholar
  49. 49.
    Plutchik, R.: The nature of emotions. Am. Sci. 89, 344–350 (2001)CrossRefGoogle Scholar
  50. 50.
    Rolls, E.: What are emotions, Why do We Have Emotions, and What is Their Computational Basis in the Brain?. Oxford University Press, Oxford (2005)CrossRefGoogle Scholar
  51. 51.
    Rohilla Shalizi, C.: Methods and techniques of complex systems science: An overview. In: Micheli-Tzanakou, E., Deisboeck, T.S., Yasha Kresh, J. (eds.), Complex Systems Science in Biomedicine. Topics in Biomedical Engineering International Book Series, pp. 33–114. Springer, Berlin, (2006)Google Scholar
  52. 52.
    Shirinifard, A., Scott Gens, J., Zaitlen.: 3d multi-cell simulation of tumor growth and angiogenesis. PLoS ONE 4(10), e7190 (2009)CrossRefGoogle Scholar
  53. 53.
    Simon, H.: The Organization of Complex Systems. George Braziller (1973)Google Scholar
  54. 54.
    Sirot, E., Touzalin, F.: Coordination and synchronization of vigilance in groups of prey: the role of collective detection and predators’ preference for stragglers. Am. Nat. 173, 47–59 (2009)CrossRefGoogle Scholar
  55. 55.
    Sumpter, D.J.T.: The principles of collective animal behaviour. Phil. Trans. R. Soc. B 361, 5–22 (2006)CrossRefGoogle Scholar
  56. 56.
    Sumpter, D.J.T., Beekman, M.: From nonlinearity to optimality: pheromone trail foraging by ants. Anim. Behav. 66, 273–280 (2003)CrossRefGoogle Scholar
  57. 57.
    Wolkenhauer, O., Auffray, C., Baltrusch, S., Blthgen, N., Byrne, H., Cascante, M., Ciliberto, A., Dale, T., Drasdo, D., Fell, D., Ferrell, J.E., Gallahan, D., Gatenby, R., Gnther, U., Harms, B.D., Herzel, H., Junghanss, C., Kunz, M., van Leeuwen, I., Lenormand, P., Levi, F., Linnebacher, M., Lowengrub, J., Maini, P.K., Malik, A., Rateitschak, K., Sansom, O., Schfer, R., Schrrle, K., Sers, C., Schnell, S., Shibata, D., Tyson, J., Vera, J., White, M., Zhivotovsky, B., Jaster, R.: Systems biologists seek fuller integration of systems biology approaches in new cancer research programs. Cancer Res. 70(1), 12–13 (2010)CrossRefGoogle Scholar
  58. 58.
    Yamada, K.M., Cukierman, E.: Modeling tissue morphogenesis and cancer in 3d. Cell 130 (2007)CrossRefGoogle Scholar
  59. 59.
    Zhang, L., Athale, C.A., Deisboeck, T.S.: Development of a three-dimensional multiscale agent-based tumor model: Simulating gene-protein interaction profiles, cell phenotypes and multicellular patterns in brain cancer. J. Theor. Biol. (2007)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Loyola University MarylandBaltimoreUSA

Personalised recommendations