Behaviors of Chemical Reactions with Small Number of Molecules

  • Yasuhiro Suzuki
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5777)


Living systems are composed of biochemical reactions and many of them involves a small number of molecules. We investigate the behaviors of chemical reactions of the Lotka-Volterra model with small number of molecules by using Abstract Rewriting System on Multisets, ARMS; ARMS is a stochastic method of simulating chemical reactions and it is based on the reaction rate equation. We confirmed that the magnitude of fluctuations on periodicity of oscillations becomes large, as the number of involved molecules is getting smaller and the dynamical characteristics is changed. We investigate the coarse grained state space of ARMS and show that the mechanism of fluctuations occur in the chemical reactions involved a small number of molecules.


Artificial Chemistries Lotka-Volterra Model Small Number Effects Chemical reactions with a small number of molecules 


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  1. 1.
    Dittrich, P., Ziegler, J., Banzhaf, W.: Artificial chemistries, a review. Artif. Life 7(3), 225–275 (2001)CrossRefGoogle Scholar
  2. 2.
    Gillespie, D.T.: Exact Stochastic Simulation of Coupled Chemical Reactions. J. Phys. Chem. 81(25), 2340–2361 (1977)CrossRefGoogle Scholar
  3. 3.
    Gillespie, D.T.: Approximate accelerated stochastic simulation of chemically reacting systems. J. Chem. Phys. 115(4), 1716–1733 (2001)CrossRefGoogle Scholar
  4. 4.
    Manca, V.: String rewriting and metabolism: a logical perspective, in Computing with Bio-Molecules. Theory and Experiments, pp. 36–60. Springer, Heidelberg (1998)Google Scholar
  5. 5.
    Nicolis, G., Prigogine, I.: Exploring Complexity, An Introduction. Freeman and Company, San Francisco (1989)Google Scholar
  6. 6.
    Hofbauer, J., Sigmund, K.: The Theory of Evolution And Dynamical Systems. Cambridge Univ. Press, Cambridge (1988)zbMATHGoogle Scholar
  7. 7.
    Suzuki, Y., Tsumoto, S., Tanaka, H.: Analysis of Cycles in Symbolic Chemical System based on Abstract Rewriting System on Multisets. In: Artificial Life V, pp. 482–489. MIT Press, Cambridge (1996)Google Scholar
  8. 8.
    Suzuki, Y., Tanaka, H.: Chemical evolution among artificial proto-cells. In: Artificial Life VII, pp. 54–64. MIT Press, Cambridge (2000)Google Scholar
  9. 9.
    Suzuki, Y., Fujiwara, Y., Takabayashi, J., Tanaka, H.: Artificial Life Applications of a Class of P Systems: Abstract Rewriting System on Multisets. In: Calude, C.S., Pun, G., Rozenberg, G., Salomaa, A. (eds.) Multiset Processing. LNCS, vol. 2235, pp. 299–346. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  10. 10.
    Suzuki, Y., Davis, P., Tanaka, H.: Emergence of auto-catalytic structure in stochastic self-reinforcing reaction networks. J. Artif. and Robot. 7, 210–213 (2003)CrossRefGoogle Scholar
  11. 11.
    Suzuki, Y., Tanaka, H.: Modeling P53 signaling network by using multiset processing. In: Applications of Membrane Computing, pp. 203–215. Springer, Tokyo (2006)Google Scholar
  12. 12.
    Suzuki, Y.: An investigation of the Brusselator on the mesoscopic scale. Inter. J. of Parallel, Emergent and Distributed Sys. 22, 91–102 (2007)CrossRefzbMATHGoogle Scholar
  13. 13.
    Umeki, M., Suzuki, Y.: A Simple Membrane Computing Method For Simulating Bio-chemical Reactions 27(3), 529–550 (2008)Google Scholar

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© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Yasuhiro Suzuki
    • 1
  1. 1.Nagoya UniversityFurocho Chikusaku Nagoya city AichiJapan

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