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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R. Albert, A.-L. Barabási, Rev. Mod. Phys. 74, 47 (2002)
M.E.J. Newman, SIAM Rev. 45, 167 (2003)
S.N. Dorogovtsev, J.F.F. Mendes, Evolution of Networks: From Biological Nets to the Internet and WWW (Oxford University Press, 2003)
M.E.J. Newman, A.-L. Barabási, D.J. Watts, The Structure and Dynamics of Networks (Princeton University Press, 2006)
S. Boccaletti, V. Latora, Y. Moreno, M. Chavez, D.-U. Hwang, Phys. Rep. 424, 175 (2006)
L.F. Costa, F.A. Rodrigues, G. Travieso, P.R. Villas Boas, Adv. Phys. 56, 167 (2007)
Principles of Neural Science, edited by E.R. Kandel, J.H. Schwartz, T.M. Jessel, 4th edn. (McGraw Hill, New York, 2000)
E. Bullmore, O. Sporns, Nat. Rev. Neurosci. 10, 186 (2009)
O. Sporns, D.R. Chialvo, M. Kaiser, C.C. Hilgetag, Trends Cogn. Sci. 8, 418 (2004)
O. Sporns, G. Tononi, R. Kötter, PLoS Comput. Biol. 1, e42 (2005)
V.M. Eguíluz, D.R. Chialvo, G.A. Cecchi, Marwan Baliki, A. Vania Apkarian, Phys. Rev. Lett. 94, 018102 (2005)
D. Fraiman, P. Balenzuela, J. Foss, D.R. Chialvo, Phys. Rev. E 79, 061922 (2009)
P. Bonifazi, M. Goldin, M.A. Picardo, I. Jorquera, A. Cattani, G. Bianconi, A. Represa, Y. Ben-Ari, R. Cossart, Science 326, 1419 (2009)
L. de Arcangelis, C. Perrone-Capano, H.J. Herrmann, Phys. Rev. Lett. 96, 0281071-4 (2006)
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
A. Levina, J.M. Herrmann, T. Geisel, Natl. Phys. 3, 857 (2007)
L. de Arcangelis, H.J. Herrmann, Proc. Nat. Acad. Sci. 107, 3977 (2010)
C. Sherrington, E.D. Adrian, Nobel Lectures, Physiology or Medicine (Elsevier Publishing Company, Amsterdam, 1965), pp. 1922–1941
J. Kralik, D. Dimitrov, D. Krupa, D. Katz, D. Cohen, Methods 25, 121 (2001)
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)
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)
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)
D. Gervasoni, S.C. Lin, S. Ribeiro, E.S. Soares, J. Pantoja, M.A.L. Nicolelis, J. Neurosci. 24, 11137 (2004)
M.A.L. Nicolelis, M.A. Lebedev, Nat. Rev. Neurosci. 10, 530 (2009)
P. Dayan, L.F. Abbott, Theoretical Neuroscience: Computational and Mathematical Modeling of Neural Systems (MIT Press, 2001)
M.I. Posner, Chronometric explorations of Mind (Oxford University Press, USA), 1986
E. Brenner, J.B.J. Smeets, J. Mot. Behav. 29, 297 (1997)
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)
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)
I.H. Stevenson, J.M. Rebesco, L.E. Miller, K.P. Körding, Curr. Opin. Neurobiol. 18, 582 (2008)
J.W. Pillow, J. Shlens, L. Paninski, A. Sher, A.M. Litke, E.J. Chichilnisky, E.P. Simoncelli, Nature 454, 995 (2008)
E. Schneidman, M.J. Berry, R. Segev, W. Bialek, Nature 440, 1007 (2006)
G. Tkačik, E. Schneidman, M.J. Berry, W. Bialek, arXiv:q-bio.NC/0611072, (2006)
E. Ganmor, R. Segev, E. Schneidman, J. Neurosci. 31, 3044 (2011)
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
W. Quattrociocchi, F. Amblard, E. Galeota, Social Network Analysis and Mining 2, 229 (2012)
V. Kostakos, Physica A 388, 1007 (2009)
R.R. Sokal, F.J. Rohlf, The Principles and Practices of Statistics in Biological Research (W.H. Freeman and Co., New York, 1995)
A. Clauset, C.R. Shalizi, M.E.J. Newman, SIAM Rev. 51, 661 (2009)
A. Klaus, S. Yu, D. Plenz, PloS ONE 6, e19779 (2011)
T.L. Ribeiro, M. Copelli, F. Caixeta, H. Belchior, D.R. Chialvo, M.A.L. Nicolelis, S. Ribeiro, PloS ONE 5, 14129 (2010)
O. Kinouchi, M. Copelli, Nat. Phys. 2, 348 (2006)
W. Shew, H. Yang, T. Petermann, R. Roy, D. Plenz, J. Neurosci. 29,15595 (2009)
S. Ribeiro, M.A.L. Nicolelis, Learn. Memory 11, 686 (2004)
T. Petermann, T.C. Thiagarajana, M.A. Lebedevb, M.A.L. Nicolelis, D.R. Chialvo, D. Plenza, Proc. Natl. Acad. Sci. 106, 15921 (2009)
M.A. Wilson, B.L. McNaughton, Science 265, 676 (1994)
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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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DOI: https://doi.org/10.1140/epjb/e2012-30481-7