Percolation in living neural networks.

We study living neural networks by measuring the neurons' response to a global electrical stimulation. Neural connectivity is lowered by reducing the synaptic strength, chemically blocking neurotransmitter receptors. We use a graph-theoretic approach to show that the connectivity undergoes a percolation transition. This occurs as the giant component disintegrates, characterized by a power law with an exponent beta approximately or = 0.65. Beta is independent of the balance between excitatory and inhibitory neurons and indicates that the degree distribution is Gaussian rather than scale free.

[1]  Henry Markram,et al.  Deriving physical connectivity from neuronal morphology , 2003, Biological Cybernetics.

[2]  Albert-László Barabási,et al.  Statistical mechanics of complex networks , 2001, ArXiv.

[3]  Jean-Pierre Eckmann,et al.  Curvature of co-links uncovers hidden thematic layers in the World Wide Web , 2001, Proceedings of the National Academy of Sciences of the United States of America.

[4]  E. Moses,et al.  Transport of Information along Unidimensional Layered Networks of Dissociated Hippocampal Neurons and Implications for Rate Coding , 2006, The Journal of Neuroscience.

[5]  S. Strogatz.  Exploring complex networks , 2001, Nature.

[6]  R. Segev,et al.  Hidden neuronal correlations in cultured networks. , 2004, Physical review letters.

[7]  S. Redner,et al.  Introduction To Percolation Theory , 2018 .

[8]  M. Basta,et al.  An introduction to percolation , 1994 .

[9]  F Harary,et al.  On the Number of Husimi Trees: I. , 1953, Proceedings of the National Academy of Sciences of the United States of America.

[10]  S. Brenner,et al.  The structure of the nervous system of the nematode Caenorhabditis elegans. , 1986, Philosophical transactions of the Royal Society of London. Series B, Biological sciences.

[11]  M. Segal,et al.  Morphological analysis of dendritic spine development in primary cultures of hippocampal neurons , 1995, The Journal of neuroscience : the official journal of the Society for Neuroscience.

[12]  J. M. Oshorn.  Proc. Nat. Acad. Sei , 1978 .

[13]  A. Barabasi,et al.  Percolation in directed scale-free networks. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[14]  Mark E. J. Newman,et al.  The Structure and Function of Complex Networks , 2003, SIAM Rev..

[15]  Jean-Pierre Eckmann,et al.  Entropy of dialogues creates coherent structures in e-mail traffic. , 2004, Proceedings of the National Academy of Sciences of the United States of America.

[16]  H. Robinson,et al.  The mechanisms of generation and propagation of synchronized bursting in developing networks of cortical neurons , 1995, The Journal of neuroscience : the official journal of the Society for Neuroscience.

[17]  S N Davies,et al.  Quinoxalinediones: potent competitive non-NMDA glutamate receptor antagonists. , 1988, Science.

[18]  M. Segal,et al.  Signal propagation along unidimensional neuronal networks. , 2005, Journal of neurophysiology.

[19]  D. Eisenberg,et al.  Detecting protein function and protein-protein interactions from genome sequences. , 1999, Science.

[20]  M. Newman,et al.  Random graphs with arbitrary degree distributions and their applications. , 2000, Physical review. E, Statistical, nonlinear, and soft matter physics.

[21]  Pik-Yin Lai,et al.  Connectivities and synchronous firing in cortical neuronal networks. , 2004, Physical review letters.

[22]  Shimon Marom,et al.  Development, learning and memory in large random networks of cortical neurons: lessons beyond anatomy , 2002, Quarterly Reviews of Biophysics.

[23]  Scott Kirkpatrick,et al.  An introduction to percolation theory , 1971 .

[24]  H. Robinson,et al.  Simultaneous induction of pathway-specific potentiation and depression in networks of cortical neurons. , 1999, Biophysical journal.