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Statistical characterization of an ensemble of functional neural networks

Abstract

This work uses a complex network approach to analyze temporal sequences of electrophysiological signals of brain activity from freely behaving rats. A network node represents a neuron and a network link is included between a pair of nodes whenever their firing rates are correlated. The framework of time varying graph (TVG) is used to deal with a very large number (>30 000) of time dependent networks, which are set up by taking into account correlations between neuron firing rates in a moving time lag window of suitable width. Statistical distributions for the following network measures are obtained: size of the largest connected cluster, number of edges, average node degree, and average minimal path. We find that the number of networks with highly correlated activity in distinct brain areas has a fat-tailed distribution, irrespective of the behavioral state of the animal. This contrasts with short-tailed distributions for surrogates obtained by shuffling the original data, and reflects the fact that neurons in the neocortex and hippocampus often act in precise temporal coordination. Our results also suggest that functional neuronal networks at the millimeter scale undergo statistically nontrivial rearrangements over time, thus delimitating an empirical constraint for models of brain activity.

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References

  1. 1.

    R. Albert, A.-L. Barabási, Rev. Mod. Phys. 74, 47 (2002)

    ADS  MATH  Article  Google Scholar 

  2. 2.

    M.E.J. Newman, SIAM Rev. 45, 167 (2003)

    MathSciNet  ADS  MATH  Article  Google Scholar 

  3. 3.

    S.N. Dorogovtsev, J.F.F. Mendes, Evolution of Networks: From Biological Nets to the Internet and WWW (Oxford University Press, 2003)

  4. 4.

    M.E.J. Newman, A.-L. Barabási, D.J. Watts, The Structure and Dynamics of Networks (Princeton University Press, 2006)

  5. 5.

    S. Boccaletti, V. Latora, Y. Moreno, M. Chavez, D.-U. Hwang, Phys. Rep. 424, 175 (2006)

    MathSciNet  ADS  Article  Google Scholar 

  6. 6.

    L.F. Costa, F.A. Rodrigues, G. Travieso, P.R. Villas Boas, Adv. Phys. 56, 167 (2007)

    ADS  Article  Google Scholar 

  7. 7.

    Principles of Neural Science, edited by E.R. Kandel, J.H. Schwartz, T.M. Jessel, 4th edn. (McGraw Hill, New York, 2000)

  8. 8.

    E. Bullmore, O. Sporns, Nat. Rev. Neurosci. 10, 186 (2009)

    Article  Google Scholar 

  9. 9.

    O. Sporns, D.R. Chialvo, M. Kaiser, C.C. Hilgetag, Trends Cogn. Sci. 8, 418 (2004)

    Article  Google Scholar 

  10. 10.

    O. Sporns, G. Tononi, R. Kötter, PLoS Comput. Biol. 1, e42 (2005)

    ADS  Article  Google Scholar 

  11. 11.

    V.M. Eguíluz, D.R. Chialvo, G.A. Cecchi, Marwan Baliki, A. Vania Apkarian, Phys. Rev. Lett. 94, 018102 (2005)

    ADS  Article  Google Scholar 

  12. 12.

    D. Fraiman, P. Balenzuela, J. Foss, D.R. Chialvo, Phys. Rev. E 79, 061922 (2009)

    ADS  Article  Google Scholar 

  13. 13.

    P. Bonifazi, M. Goldin, M.A. Picardo, I. Jorquera, A. Cattani, G. Bianconi, A. Represa, Y. Ben-Ari, R. Cossart, Science 326, 1419 (2009)

    ADS  Article  Google Scholar 

  14. 14.

    L. de Arcangelis, C. Perrone-Capano, H.J. Herrmann, Phys. Rev. Lett. 96, 0281071-4 (2006)

    Google Scholar 

  15. 15.

    A. Levina, J.M. Herrmann, T. Geisel, in Advances in Neural Information Processing Systems, edited by Y. Weiss, B. Schölkopf, J. Platt (MIT Press, Cambridge, MA, 2006), Vol. 18, pp. 771–778

  16. 16.

    A. Levina, J.M. Herrmann, T. Geisel, Natl. Phys. 3, 857 (2007)

    Article  Google Scholar 

  17. 17.

    L. de Arcangelis, H.J. Herrmann, Proc. Nat. Acad. Sci. 107, 3977 (2010)

    ADS  Article  Google Scholar 

  18. 18.

    C. Sherrington, E.D. Adrian, Nobel Lectures, Physiology or Medicine (Elsevier Publishing Company, Amsterdam, 1965), pp. 1922–1941

  19. 19.

    J. Kralik, D. Dimitrov, D. Krupa, D. Katz, D. Cohen, Methods 25, 121 (2001)

    Article  Google Scholar 

  20. 20.

    S. Ribeiro, D. Gervasoni, E.S. Soares, Y. Zhou, S.C. Lin, P. Pantoja, M. Lavine, M.A.L. Nicolelis, PLoS Biol. 2, 126 (2004)

    Article  Google Scholar 

  21. 21.

    S. Ribeiro, X. Shi, M. Engelhard, Y. Zhou, H. Zhang, D. Gervasoni, S.C. Lin, K. Wada, N.A. Lemos, M.A.L. Nicolelis, Front. Neurosci. 1, 43 (2007)

    Article  Google Scholar 

  22. 22.

    M.A.L. Nicolelis, D. Dimitrov, J.M. Carmena, R. Crist, G. Lehew, J.D. Kralik, Steven P. Wise, Proc. Natl. Acad. Sci. USA 100, 11041 (2003)

    ADS  Article  Google Scholar 

  23. 23.

    D. Gervasoni, S.C. Lin, S. Ribeiro, E.S. Soares, J. Pantoja, M.A.L. Nicolelis, J. Neurosci. 24, 11137 (2004)

    Article  Google Scholar 

  24. 24.

    M.A.L. Nicolelis, M.A. Lebedev, Nat. Rev. Neurosci. 10, 530 (2009)

    Article  Google Scholar 

  25. 25.

    P. Dayan, L.F. Abbott, Theoretical Neuroscience: Computational and Mathematical Modeling of Neural Systems (MIT Press, 2001)

  26. 26.

    M.I. Posner, Chronometric explorations of Mind (Oxford University Press, USA), 1986

  27. 27.

    E. Brenner, J.B.J. Smeets, J. Mot. Behav. 29, 297 (1997)

    Article  Google Scholar 

  28. 28.

    N.A.P. Vasconcelos, J. Pantoja, H. Belchior, F.V. Caixeta, J. Faber, M.A.M. Freire, V.R. Cota, E.A. de Macedo, D.A. Laplagne, H.H. Gomes, S. Ribeiro, Proc. Natl. Acad. Sci. USA 108, 15408 (2011)

    ADS  Article  Google Scholar 

  29. 29.

    N.A.P. Vasconcelos, W.Blanco, J. Faber, H.M. Gomes, T.M. Barros, S. Ribeiro, in The Relevance of the Time Domain to Neural Network Models, edited by A.R. Rao, G.A. Cecchi (Springer Series in Cognitive and Neural Systems, Springer, 2011)

  30. 30.

    I.H. Stevenson, J.M. Rebesco, L.E. Miller, K.P. Körding, Curr. Opin. Neurobiol. 18, 582 (2008)

    Article  Google Scholar 

  31. 31.

    J.W. Pillow, J. Shlens, L. Paninski, A. Sher, A.M. Litke, E.J. Chichilnisky, E.P. Simoncelli, Nature 454, 995 (2008)

    ADS  Article  Google Scholar 

  32. 32.

    E. Schneidman, M.J. Berry, R. Segev, W. Bialek, Nature 440, 1007 (2006)

    ADS  Article  Google Scholar 

  33. 33.

    G. Tkačik, E. Schneidman, M.J. Berry, W. Bialek, arXiv:q-bio.NC/0611072, (2006)

  34. 34.

    E. Ganmor, R. Segev, E. Schneidman, J. Neurosci. 31, 3044 (2011)

    Article  Google Scholar 

  35. 35.

    N. Santoro, W. Quattrociocchi, P. Flocchini, A. Casteigts, F. Amblard, in 3rd AISB Social Networks and Multiagent Systems Symposium (SNAMAS), 2011, edited by AISB (York, UK), pp. 32–38

  36. 36.

    W. Quattrociocchi, F. Amblard, E. Galeota, Social Network Analysis and Mining 2, 229 (2012)

    Article  Google Scholar 

  37. 37.

    V. Kostakos, Physica A 388, 1007 (2009)

    MathSciNet  ADS  Article  Google Scholar 

  38. 38.

    R.R. Sokal, F.J. Rohlf, The Principles and Practices of Statistics in Biological Research (W.H. Freeman and Co., New York, 1995)

  39. 39.

    A. Clauset, C.R. Shalizi, M.E.J. Newman, SIAM Rev. 51, 661 (2009)

    MathSciNet  ADS  MATH  Article  Google Scholar 

  40. 40.

    A. Klaus, S. Yu, D. Plenz, PloS ONE 6, e19779 (2011)

    ADS  Article  Google Scholar 

  41. 41.

    T.L. Ribeiro, M. Copelli, F. Caixeta, H. Belchior, D.R. Chialvo, M.A.L. Nicolelis, S. Ribeiro, PloS ONE 5, 14129 (2010)

    ADS  Article  Google Scholar 

  42. 42.

    O. Kinouchi, M. Copelli, Nat. Phys. 2, 348 (2006)

    Article  Google Scholar 

  43. 43.

    W. Shew, H. Yang, T. Petermann, R. Roy, D. Plenz, J. Neurosci. 29,15595 (2009)

    Article  Google Scholar 

  44. 44.

    S. Ribeiro, M.A.L. Nicolelis, Learn. Memory 11, 686 (2004)

    Article  Google Scholar 

  45. 45.

    T. Petermann, T.C. Thiagarajana, M.A. Lebedevb, M.A.L. Nicolelis, D.R. Chialvo, D. Plenza, Proc. Natl. Acad. Sci. 106, 15921 (2009)

    ADS  Article  Google Scholar 

  46. 46.

    M.A. Wilson, B.L. McNaughton, Science 265, 676 (1994)

    ADS  Article  Google Scholar 

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Correspondence to R. F. S. Andrade.

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Silva, B.B.M., Miranda, J.G.V., Corso, G. et al. Statistical characterization of an ensemble of functional neural networks. Eur. Phys. J. B 85, 358 (2012). https://doi.org/10.1140/epjb/e2012-30481-7

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Keywords

  • Statistical and Nonlinear Physics