A simple method for simulating biochemical reaction networks | Artificial Life and Robotics Skip to main content
Springer Nature Link
Log in

A simple method for simulating biochemical reaction networks

  • Original Article
  • Published:
Artificial Life and Robotics Aims and scope Submit manuscript

Abstract

We propose a simple method of simulating chemical reaction networks by using a multiset rewriting system: abstract rewriting system on multisets (ARMS). We simulate the oregonator model, a mathematical model of the Belousov-Zhabotinskii reaction, and we obtain the same behavior when the differential equations or the Gillespie method are used. We also compose a 1- and 2-dimensional cellular automata by using ARMS, and confirm that it shows the pattern forming that is observed in the BZ reaction.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
¥17,985 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (Japan)

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

References

  1. Field RJ, Noyes RM (1974) Oscillations in chemical systems. IV. Limit cycle behavior in a model of a real chemical reaction. J Chem Phys 60:1877–1884

    Article  Google Scholar 

  2. Umeki M, Suzuki Y (2007) On the simulation of the oregonator by using abstract rewriting system on multisets. 2nd Coupled Analysis Forum, February 2–3, 2007, Hakata Japan

  3. Nicolis G, Prigogine I (1989) Exploring complexity. An introduction. Freeman, San Francisco

    Google Scholar 

  4. Tyson JJ, Fife PC (1980) Target patterns in a realistic model of the Belousov-Zhabotinskii reaction. J Chem Phys 73:2224–2237

    Article  MathSciNet  Google Scholar 

  5. Gillespie DT (1976) A general method for numerically simulating the stochastic time evolution of coupled chemical reactions. J Comput Phys 22:403–434

    Article  MathSciNet  Google Scholar 

  6. Morton-Firth CJ (1998) Stochastic simulation of cell signalling pathways. PhD Thesis, Cambridge University

  7. Suzuki Y, Tsumoto S, Tanaka H (1996) Analysis of cycles in symbolic chemical system based on abstract rewriting system on multisets. Proceedings of the International Conference on Artificial Life 5 (Alife 5), pp 482–489

  8. Manca V, Bianco L. Biological networks in metabolic P systems. BioSystems, in press

  9. Cazzaniga P, Pescini D, Besozzi D, et al (2006) Tau leaping stochastic simulation method in P systems. Membrane Computing. 7th International Workshop, WMC 2006 LNCS 4361:298–313

  10. Păun G (2000) Computing with membranes. J Comput Syst Sci 61:1

    Article  Google Scholar 

  11. Umeki M, Suzuki Y (2007) On the simulation of the oregonator by using abstract rewriting system on multisets. Proceedings of Workshop on Membrane Computing June 25–28, 2007, Thessaloniki

Download references

Author information

Authors and Affiliations

  1. Nagoya University, Furocho, Chikusa-ku, Nagoya, 464-8603, Japan

    Mai Umeki & Yasuhiro Suzuki

Authors
  1. Mai Umeki
    View author publications

    You can also search for this author inPubMed Google Scholar

  2. Yasuhiro Suzuki
    View author publications

    You can also search for this author inPubMed Google Scholar

Corresponding author

Correspondence to Yasuhiro Suzuki.

Additional information

This work was presented in part at the First European Workshop on Artificial Life and Robotics, Vienna, Austria, July 12–13, 2007

About this article

Cite this article

Umeki, M., Suzuki, Y. A simple method for simulating biochemical reaction networks. Artif Life Robotics 13, 566–569 (2009). https://doi.org/10.1007/s10015-008-0625-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10015-008-0625-2

Key words