Skip to main content

Simulating Neurons in Reaction-Diffusion Chemistry

  • Conference paper

Part of the Lecture Notes in Computer Science book series (LNTCS,volume 7223)

Abstract

Diffusive Computation is a method of using diffusing particles as a representation of data. The work presented attempts to show that through simulating spiking neurons, diffusive computation has at least the same computational power as spiking neural networks. We demonstrate (by simulation) that wavefronts in a Reaction-Diffusion system have a cumulative effect on concentration of reaction components when they arrive at the same point in the reactor, and that a catalyst-free region acts as a threshold on the initiation of an outgoing wave. Spiking neuron models can be mapped onto this system, and therefore RD systems can be used for computation using the same models as are applied to spiking neurons.

Keywords

  • Spike Train
  • Synaptic Cleft
  • Multiple Wave
  • Chemical Synapse
  • Delay Loop

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   54.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   69.99
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Adamatzky, A., Bull, L., De Lacy Costello, B., Holley, J., Jahan, I.: Computational Modalities of Belousov-Zhabotinsky Encapsulated Vesicles. ArXiv e-prints (September 2010)

    Google Scholar 

  2. Adamatzky, A.: Collision-based computing in Belousov-Zhabotinsky medium. Chaos, Solitons & Fractals 21(5), 1259–1264 (2004)

    CrossRef  MATH  Google Scholar 

  3. Adamatzky, A., De Lacy Costello, B.: Binary collisions between wave-fragments in a sub-excitable Belousov-Zhabotinsky medium. Chaos, Solitons & Fractals 34(2), 307–315 (2007)

    CrossRef  MathSciNet  MATH  Google Scholar 

  4. Austin, J., Stonham, T.: Distributed associative memory for use in scene analysis. Image and Vision Computing 5(4), 251–260 (1987)

    CrossRef  Google Scholar 

  5. Belousov, B.P.: A periodic reaction and its mechanism. Med. Publ., Moscow (1959)

    Google Scholar 

  6. Conrad, M., Zauner, K.: Molecular Computing Conformation-Based Computing: A Rationale and a Recipe, pp. 1–31. MIT Press (2003)

    Google Scholar 

  7. Gorecki, J., Gorecka, J., Igarashi, Y.: Information processing with structured excitable medium. Natural Computing 8, 473–492 (2009)

    CrossRef  MathSciNet  MATH  Google Scholar 

  8. Gorecki, J., Yoshikawa, K., Igarashi, Y.: On chemical reactors that can count. The Journal of Physical Chemistry A 107(10), 1664–1669 (2003)

    CrossRef  Google Scholar 

  9. Janz, R.D., Vanecek, D.J., Field, R.J.: Composite double oscillation in a modified version of the oregonator model of the Belousov-Zhabotinsky reaction. The Journal of Chemical Physics 73(7), 3132–3138 (1980)

    CrossRef  MathSciNet  Google Scholar 

  10. Kuhnert, L., Agladze, K.I., Krinsky, V.I.: Image processing using light-sensitive chemical waves. Nature 337(6204), 244–247 (1989)

    CrossRef  Google Scholar 

  11. Motoike, I., Yoshikawa, K.: Information operations with an excitable field. Phys. Rev. E 59, 5354–5360 (1999)

    CrossRef  Google Scholar 

  12. Rovinsky, A.B.: Spiral waves in a model of the ferroin catalyzed Belousov-Zhabotinsky reaction. The Journal of Physical Chemistry 90(2), 217–219 (1986)

    CrossRef  Google Scholar 

  13. Rovinsky, A.B., Zhabotinsky, A.M.: Mechanism and mathematical model of the oscillating bromate-ferroin-bromomalonic acid reaction. The Journal of Physical Chemistry 88(25), 6081–6084 (1984)

    CrossRef  Google Scholar 

  14. Tóth, Á., Showalter, K.: Logic gates in excitable media. J. Chem Phys. 103(6), 2058–2066 (1995)

    CrossRef  Google Scholar 

  15. Turing, A.M.: The chemical basis of morphogenesis. Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences 237(641), 37–72 (1952)

    CrossRef  Google Scholar 

  16. Maass, W.: Networks of spiking neurons: The third generation of neural network models. Neural Networks 10(9), 1659–1671 (1997)

    CrossRef  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 2012 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Stovold, J., O’Keefe, S. (2012). Simulating Neurons in Reaction-Diffusion Chemistry. In: Lones, M.A., Smith, S.L., Teichmann, S., Naef, F., Walker, J.A., Trefzer, M.A. (eds) Information Processign in Cells and Tissues. IPCAT 2012. Lecture Notes in Computer Science, vol 7223. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28792-3_19

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-28792-3_19

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-28791-6

  • Online ISBN: 978-3-642-28792-3

  • eBook Packages: Computer ScienceComputer Science (R0)