Behaviors of Chemical Reactions with Small Number of Molecules
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.
KeywordsArtificial Chemistries Lotka-Volterra Model Small Number Effects Chemical reactions with a small number of molecules
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- 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.Nicolis, G., Prigogine, I.: Exploring Complexity, An Introduction. Freeman and Company, San Francisco (1989)Google Scholar
- 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.Suzuki, Y., Tanaka, H.: Chemical evolution among artificial proto-cells. In: Artificial Life VII, pp. 54–64. MIT Press, Cambridge (2000)Google Scholar
- 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
- 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
- 13.Umeki, M., Suzuki, Y.: A Simple Membrane Computing Method For Simulating Bio-chemical Reactions 27(3), 529–550 (2008)Google Scholar