Table of Contents
Journal of Complex Systems
Volume 2013, Article ID 675818, 7 pages
http://dx.doi.org/10.1155/2013/675818
Research Article

A Small Morris-Lecar Neuron Network Gets Close to Critical Only in the Small-World Regimen

1Laboratorio de Dinámica Estocástica, Centro de Física, Instituto Venezolano de Investigaciones Científicas, Caracas 1020-A, Venezuela
2Instituto de Física de Líquidos y Sistemas Biológicos, CCT-CONICET La Plata, UNLP, 789 Calle 59, 1900 La Plata, Argentina

Received 29 March 2013; Revised 11 September 2013; Accepted 16 September 2013

Academic Editor: Julián Candia

Copyright © 2013 Juan Luis Cabrera et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. J. M. Beggs and D. Plenz, “Neuronal avalanches in neocortical circuits,” Journal of Neuroscience, vol. 23, no. 35, pp. 11167–11177, 2003. View at Google Scholar · View at Scopus
  2. J. M. Beggs and D. Plenz, “Neuronal avalanches are diverse and precise activity patterns that are stable for many hours in cortical slice cultures,” Journal of Neuroscience, vol. 24, no. 22, pp. 5216–5229, 2004. View at Publisher · View at Google Scholar · View at Scopus
  3. C. V. Stewart and D. Plenz, “Inverted-U profile of dopamine-NMDA-mediated spontaneous avalanche recurrence in superficial layers of rat prefrontal cortex,” Journal of Neuroscience, vol. 26, no. 31, pp. 8148–8159, 2006. View at Publisher · View at Google Scholar · View at Scopus
  4. E. D. Gireesh and D. Plenz, “Neuronal avalanches organize as nested theta- and beta/gamma-oscillations during development of cortical layer 2/3,” Proceedings of the National Academy of Sciences of the United States of America, vol. 105, no. 21, pp. 7576–7581, 2008. View at Publisher · View at Google Scholar
  5. G. Hahn, T. Petermann, M. N. Havenith et al., “Neuronal avalanches in spontaneous activity in vivo,” Journal of Neurophysiology, vol. 104, no. 6, pp. 3312–3322, 2010. View at Publisher · View at Google Scholar · View at Scopus
  6. A. Mazzoni, F. D. Broccard, E. Garcia-Perez, P. Bonifazi, M. E. Ruaro, and V. Torre, “On the dynamics of the spontaneous activity in neuronal networks,” PLoS ONE, vol. 2, no. 5, article e439, 2007. View at Publisher · View at Google Scholar · View at Scopus
  7. V. Pasquale, P. Massobrio, L. L. Bologna, M. Chiappalone, and S. Martinoia, “Self-organization and neuronal avalanches in networks of dissociated cortical neurons,” Neuroscience, vol. 153, no. 4, pp. 1354–1369, 2008. View at Publisher · View at Google Scholar · View at Scopus
  8. T. L. Ribeiro, M. Copelli, F. Caixeta et al., “Spike avalanches exhibit universal dynamics across the sleep-wake cycle,” PLoS ONE, vol. 5, no. 11, Article ID e14129, 2010. View at Publisher · View at Google Scholar · View at Scopus
  9. G. L. Pellegrini, L. de Arcangelis, H. J. Herrmann, and C. Perrone-Capano, “Activity-dependent neural network model on scale-free networks,” Physical Review E, vol. 76, no. 1, part 2, Article ID 016107, 2007. View at Google Scholar
  10. L. de Arcangelis, C. Perrone-Capano, and H. J. Herrmann, “Self-organized criticality model for brain plasticity,” Physical Review Letters, vol. 96, no. 2, Article ID 028107, 2006. View at Google Scholar
  11. A. Levina, J. M. Herrmann, and T. Geisel, “Dynamical synapses causing self-organized criticality in neural networks,” Nature Physics, vol. 3, no. 12, pp. 857–860, 2007. View at Publisher · View at Google Scholar · View at Scopus
  12. J.-N. Teramae and T. Fukai, “Local cortical circuit model inferred from power-law distributed neuronal avalanches,” Journal of Computational Neuroscience, vol. 22, no. 3, pp. 301–312, 2007. View at Publisher · View at Google Scholar · View at Scopus
  13. L. F. Abbott and R. Rohrkemper, “A simple growth model constructs critical avalanche networks,” Progress in Brain Research, vol. 165, pp. 13–19, 2007. View at Publisher · View at Google Scholar · View at Scopus
  14. C. Morris and H. Lecar, “Voltage oscillations in the barnacle giant muscle fiber,” Biophysical Journal, vol. 35, no. 1, pp. 193–213, 1981. View at Google Scholar
  15. J. Rinzel and G. B. Ermentrout, “Analysis of neural excitability and oscillations,” in Methods in Neural Modeling: From Synapses to Networks, C. Koch and I. Segev, Eds., pp. 135–169, MIT Press, Cambridge, Mass, USA, 1989. View at Google Scholar
  16. A. L. Hodgkin and A. F. Huxley, “A quantitative description of membrane current and its application to conduction and excitation in nerve,” The Journal of physiology, vol. 117, no. 4, pp. 500–544, 1952. View at Google Scholar · View at Scopus
  17. D. J. Watts and S. H. Strogatz, “Collective dynamics of 'small-world9 networks,” Nature, vol. 393, no. 6684, pp. 440–442, 1998. View at Google Scholar · View at Scopus
  18. M. Newman, A. L. Barabasi, and D. J. Watts, The Structure and Dynamics of Networks, Princeton University Press, 2006.
  19. A. Roxin, H. Riecke, and S. A. Solla, “Self-sustained activity in a small-world network of excitable neurons,” Physical Review Letters, vol. 92, no. 19, article 198101, 4 pages, 2004. View at Publisher · View at Google Scholar · View at Scopus
  20. V. Latora and M. Marchiori, “Efficient behavior of small-world networks,” Physical Review Letters, vol. 87, no. 19, Article ID 198701, 2001. View at Google Scholar · View at Scopus
  21. V. Latora and M. Marchiori, “Economic small-world behavior in weighted networks,” European Physical Journal B, vol. 32, no. 2, pp. 249–263, 2003. View at Publisher · View at Google Scholar · View at Scopus
  22. J. X. de Carvalho and C. P. C. Prado, “Self-organized criticality in the olami-feder-christensen model,” Physical Review Letters, vol. 84, no. 17, pp. 4006–4009, 2000. View at Publisher · View at Google Scholar
  23. D. S. Bassett and E. Bullmore, “Small-world brain networks,” Neuroscientist, vol. 12, no. 6, pp. 512–523, 2006. View at Publisher · View at Google Scholar · View at Scopus
  24. C. C. Hilgetag, G. A. P. C. Burns, M. A. O'Neill, J. W. Scannell, and M. P. Young, “Anatomical connectivity defines the organization of clusters of cortical areas in the macaque monkey and the cat,” Philosophical Transactions of the Royal Society B, vol. 355, no. 1393, pp. 91–110, 2000. View at Google Scholar
  25. R. K. Kötter and F. T. Sommer, “Global relationship between anatomical connectivity and activity propagation in the cerebral cortex,” Philosophical Transactions of the Royal Society B, vol. 355, no. 1393, pp. 127–134, 2000. View at Google Scholar
  26. K. Stephan, C. C. Hilgetag, G. A. P. C. Burns, M. A. O'Neill, M. P. Young, and R. K. Kötter, “Computational analysis of functional connectivity between areas of primate cerebral cortex,” Philosophical Transactions of the Royal Society B, vol. 355, no. 1393, pp. 111–126, 2000. View at Google Scholar
  27. S. Yu, D. Huang, W. Singer, and D. Nikolic, “A small world of neuronal synchrony,” Cereb Cortex, vol. 18, pp. 2891–2901, 2008. View at Google Scholar
  28. C. J. Stam, “Functional connectivity patterns of human magnetoencephalographic recordings: a 'small-world' network?” Neuroscience Letters, vol. 355, no. 1-2, pp. 25–28, 2004. View at Publisher · View at Google Scholar · View at Scopus
  29. S. Micheloyannis, E. Pachou, C. J. Stam, M. Vourkas, S. Erimaki, and V. Tsirka, “Using graph theoretical analysis of multi channel EEG to evaluate the neural efficiency hypothesis,” Neuroscience Letters, vol. 402, no. 3, pp. 273–277, 2006. View at Publisher · View at Google Scholar · View at Scopus
  30. R. Salvador, J. Suckling, M. R. Coleman, J. D. Pickard, D. Menon, and E. Bullmore, “Neurophysiological architecture of functional magnetic resonance images of human brain,” Cerebral Cortex, vol. 15, no. 9, pp. 1332–2342, 2005. View at Publisher · View at Google Scholar · View at Scopus
  31. P. Hagmann, L. Cammoun, X. Gigandet et al., “Mapping the structural core of human cerebral cortex,” PLoS Biology, vol. 6, no. 7, p. e159, 2008. View at Publisher · View at Google Scholar · View at Scopus
  32. S. Pajevic and D. Plenz, “The organization of strong links in complex networks,” Nature Physics, vol. 8, pp. 429–436, 2012. View at Publisher · View at Google Scholar
  33. J. G. Restrepo, E. Ott, and B. R. Hunt, “Weighted percolation on directed networks,” Physical Review Letters, vol. 100, no. 5, Article ID 058701, 4 pages, 2008. View at Publisher · View at Google Scholar
  34. D. B. Larremore, W. L. Shew, and J. G. Restrepo, “Predicting criticality and dynamic range in complex networks: effects of topology,” Physical Review Letters, vol. 106, no. 5, Article ID 058101, 4 pages, 2011. View at Publisher · View at Google Scholar
  35. M. G. Kitzbichler, M. L. Smith, S. R. Christensen, and E. Bullmore, “Broadband criticality of human brain network synchronization,” PLOS Computational Biology, vol. 5, no. 3, Article ID e1000314, 2009. View at Publisher · View at Google Scholar