Abstract
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.
Keywords
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Dittrich, P., Ziegler, J., Banzhaf, W.: Artificial chemistries, a review. Artif. Life 7(3), 225–275 (2001)
Gillespie, D.T.: Exact Stochastic Simulation of Coupled Chemical Reactions. J. Phys. Chem. 81(25), 2340–2361 (1977)
Gillespie, D.T.: Approximate accelerated stochastic simulation of chemically reacting systems. J. Chem. Phys. 115(4), 1716–1733 (2001)
Manca, V.: String rewriting and metabolism: a logical perspective, in Computing with Bio-Molecules. Theory and Experiments, pp. 36–60. Springer, Heidelberg (1998)
Nicolis, G., Prigogine, I.: Exploring Complexity, An Introduction. Freeman and Company, San Francisco (1989)
Hofbauer, J., Sigmund, K.: The Theory of Evolution And Dynamical Systems. Cambridge Univ. Press, Cambridge (1988)
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)
Suzuki, Y., Tanaka, H.: Chemical evolution among artificial proto-cells. In: Artificial Life VII, pp. 54–64. MIT Press, Cambridge (2000)
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)
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)
Suzuki, Y., Tanaka, H.: Modeling P53 signaling network by using multiset processing. In: Applications of Membrane Computing, pp. 203–215. Springer, Tokyo (2006)
Suzuki, Y.: An investigation of the Brusselator on the mesoscopic scale. Inter. J. of Parallel, Emergent and Distributed Sys. 22, 91–102 (2007)
Umeki, M., Suzuki, Y.: A Simple Membrane Computing Method For Simulating Bio-chemical Reactions 27(3), 529–550 (2008)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Suzuki, Y. (2011). Behaviors of Chemical Reactions with Small Number of Molecules. In: Kampis, G., Karsai, I., Szathmáry, E. (eds) Advances in Artificial Life. Darwin Meets von Neumann. ECAL 2009. Lecture Notes in Computer Science(), vol 5777. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21283-3_49
Download citation
DOI: https://doi.org/10.1007/978-3-642-21283-3_49
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-21282-6
Online ISBN: 978-3-642-21283-3
eBook Packages: Computer ScienceComputer Science (R0)