Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Article
  • Published:

Optimal dynamical range of excitable networks at criticality

Nature Physics volume 2, pages 348–351 (2006)Cite this article

Abstract

A recurrent idea in the study of complex systems is that optimal information processing is to be found near phase transitions. However, this heuristic hypothesis has few (if any) concrete realizations where a standard and biologically relevant quantity is optimized at criticality. Here we give a clear example of such a phenomenon: a network of excitable elements has its sensitivity and dynamic range maximized at the critical point of a non-equilibrium phase transition. Our results are compatible with the essential role of gap junctions in olfactory glomeruli and retinal ganglionar cell output. Synchronization and global oscillations also emerge from the network dynamics. We propose that the main functional role of electrical coupling is to provide an enhancement of dynamic range, therefore allowing the coding of information spanning several orders of magnitude. The mechanism could provide a microscopic neural basis for psychophysical laws.

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

Access options

Buy this article

  • Purchase on Springer Link
  • Instant access to full article PDF
Buy now

Prices may be subject to local taxes which are calculated during checkout

Figure 1: Network characterization and density of active sites.
Figure 2: Response curves and dynamic range.

Similar content being viewed by others

References

  1. Stevens, S. S. Psychophysics: Introduction to its Perceptual, Neural and Social Prospects (Wiley, New York, 1975).

    Google Scholar 

  2. Wachowiak, M. & Cohen, L. B. Representation of odorants by receptor neuron input to the mouse olfactory bulb. Neuron 32, 723–735 (2001).

    Article  Google Scholar 

  3. Angioy, A. M., Desogus, A., Barbarossa, I. T., Anderson, P. & Hansson, B. S. Extreme sensitivity in an olfactory system. Chem. Senses 28, 279–284 (2003).

    Article  Google Scholar 

  4. Fried, H. U., Fuss, S. H. & Korsching, S. I. Selective imaging of presynaptic activity in the mouse olfactory bulb shows concentration and structure dependence of odor responses in identified glomeruli. Proc. Natl Acad. Sci. USA 99, 3222–3227 (2002).

    Article  ADS  Google Scholar 

  5. Cleland, T. A. & Linster, C. Concentration tuning mediated by spare receptor capacity in olfactory sensory neurons: a theoretical study. Neural Comput. 11, 1673–1690 (1999).

    Article  Google Scholar 

  6. Copelli, M., Roque, A. C., Oliveira, R. F. & Kinouchi, O. Physics of psychophysics: Stevens and Weber-Fechner laws are transfer functions of excitable media. Phys. Rev. E 65, 060901 (2002).

    Article  ADS  Google Scholar 

  7. Copelli, M. & Kinouchi, O. Intensity coding in two-dimensional excitable neural networks. Physica A 349, 431–442 (2005).

    Article  ADS  Google Scholar 

  8. Copelli, M., Oliveira, R. F., Roque, A. C. & Kinouchi, O. Signal compression in the sensory periphery. Neurocomputing 65–66, 691–696 (2005).

    Article  Google Scholar 

  9. Reiser, J. & Matthews, H. Response properties of isolated mouse olfactory receptor cells. J. Physiol. 530, 113–122 (2001).

    Article  Google Scholar 

  10. Tomaru, A. & Kurahashi, T. Mechanisms determining the dynamic range of the bullfrog olfactory receptor cell. J. Neurophysiol. 93, 1880–1888 (2005).

    Article  Google Scholar 

  11. Chater, N. & Brown, G. D. Scale-invariance as a unifying psychological principle. Cognition 69, B17–B24 (1999).

    Article  Google Scholar 

  12. Furtado, L. S. & Copelli, M. Response of electrically coupled spiking neurons: a cellular automaton approach. Phys. Rev. E 73, 011907 (2006).

    Article  ADS  Google Scholar 

  13. Beggs, J. M. & Plenz, D. Neuronal avalanches in neocortical circuits. J. Neurosci. 23, 11167–11177 (2003).

    Article  Google Scholar 

  14. Haldeman, C. & Beggs, J. M. Critical branching captures activity in living neural networks and maximizes the number of metastable states. Phys. Rev. Lett. 94, 058101 (2005).

    Article  ADS  Google Scholar 

  15. Langton, C. G. Computation at the edge of chaos: phase transitions and emergent computation. Physica D 42, 12–37 (1990).

    Article  ADS  MathSciNet  Google Scholar 

  16. Bak, P. How Nature Works: The Science of Self-Organized Criticality (Oxford Univ. Press, New York, 1997).

    MATH  Google Scholar 

  17. Chialvo, D. R. Critical brain networks. Physica A 340, 756–765 (2004).

    Article  ADS  Google Scholar 

  18. Kosaka, T., Deans, M. R., Paul, D. L. & Kosaka, K. Neuronal gap junctions in the mouse main olfactory bulb: morphological analyses on transgenic mice. Neuroscience 134, 757–769 (2005).

    Article  Google Scholar 

  19. Migliore, M., Hines, M. L. & Shepherd, G. M. The role of distal dendritic gap junctions in synchronization of mitral cell axonal output. J. Comput. Neurosci. 18, 151–161 (2005).

    Article  Google Scholar 

  20. Christie, J. M. et al. Connexin36 mediates spike synchrony in olfactory bulb glomeruli. Neuron 46, 761–772 (2005).

    Article  Google Scholar 

  21. Marro, J. & Dickman, R. Nonequilibrium Phase Transitions in Lattice Models (Cambridge Univ. Press, Cambridge, 1999).

    Book  Google Scholar 

  22. Laurent, G. Olfactory network dynamics and the coding of multidimensional signals. Nature Rev. Neurosci. 3, 884–895 (2002).

    Article  Google Scholar 

  23. Lewis, T. J. & Rinzel, J. Topological target patterns and population oscillations in a network with random gap junctional coupling. Neurocomputing 38–40, 763–768 (2001).

    Article  Google Scholar 

  24. Lewis, T. J. & Rinzel, J. Self-organized synchronous oscillations in a network of excitable cells coupled by gap junctions. Network Comput. Neural Syst. 11, 299–320 (2000).

    Article  Google Scholar 

  25. Schubert, T. et al. Connexin36 mediates gap junctional coupling of alpha-ganglion cells in mouse retina. J. Comp. Neurol. 485, 191–201 (2005).

    Article  Google Scholar 

  26. Hidaka, S., Akahori, Y. & Kurosawa, Y. Cellular/molecular dendrodendritic electrical synapses between mammalian retinal ganglion cells. J. Neurosci. 24, 10553–10567 (2005).

    Article  Google Scholar 

  27. Vogt, A., Hormuzdi, S. G. & Monyer, H. Pannexin1 and Pannexin2 expression in the developing and mature rat brain. Brain Res. Mol. Brain Res. 141, 113–120 (2005).

    Article  Google Scholar 

  28. Deans, M. R., Volgyi, B., Goodenough, D. A., Bloomfield, S. A. & Paul, D. L. Connexin36 is essential for transmission of rod-mediated visual signals in the mammalian retina. Neuron 36, 703–712 (2002).

    Article  Google Scholar 

  29. Zhang, C. & Restrepo, D. Expression of connexin 45 in the olfactory system. Brain Res. 929, 37–47 (2002).

    Article  Google Scholar 

  30. Camalet, S., Duke, T., Jülicher, F. & Prost, J. Auditory sensitivity provided by self-tuned critical oscillations of hair cells. Proc. Natl Acad. Sci. USA 97, 3183–3188 (2000).

    Article  ADS  Google Scholar 

  31. Sohl, G., Maxeiner, S. & Willecke, K. Expression and functions of neuronal gap junctions. Nature Rev. Neurosci. 6, 191–200 (2005).

    Article  Google Scholar 

Download references

Acknowledgements

This research is supported by CNPq, FACEPE, CAPES and PRONEX. The authors are grateful for discussions with A. C. Roque, R. F. Oliveira, D. Restrepo, T. Cleland and V. R. Vitorino de Assis and for encouragement from N. Caticha.

Author information

Author notes

  1. Osame Kinouchi and Mauro Copelli: These authors contributed equally to this work

Authors and Affiliations

  1. Departamento de Física e Matemática, Faculdade de Filosofia, Ciências e Letras de Ribeirão Preto, Universidade de São Paulo, Av. dos Bandeirantes 3900, 14040-901 Ribeirão Preto, SP, Brazil

    Osame Kinouchi

  2. Departamento de Física, Laboratório de Física Teórica e Computacional, Universidade Federal de Pernambuco, 50670-901 Recife, PE, Brazil

    Mauro Copelli

Authors
  1. Osame Kinouchi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mauro Copelli
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Osame Kinouchi.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kinouchi, O., Copelli, M. Optimal dynamical range of excitable networks at criticality. Nature Phys 2, 348–351 (2006). https://doi.org/10.1038/nphys289

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nphys289

This article is cited by

Search

Advanced search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing