STDP-driven networks and the C. elegans neuronal network

We study the dynamics of the structure of a formal neural network wherein the strengths of the synapses are governed by spike-timing-dependent plasticity (STDP). For properly chosen input signals, there exists a steady state with a residual network. We compare the motif profile of such a network with that of a real neural network of C. elegans and identify robust qualitative similarities. In particular, our extensive numerical simulations show that this STDP-driven resulting network is robust under variations of the model parameters.

[1]  H. Markram,et al.  Regulation of Synaptic Efficacy by Coincidence of Postsynaptic APs and EPSPs , 1997, Science.

[2]  M. Newman,et al.  Statistical mechanics of networks. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[3]  S. Shen-Orr,et al.  Superfamilies of Evolved and Designed Networks , 2004, Science.

[4]  Cori Bargmann,et al.  Sensory activity affects sensory axon development in C. elegans. , 1999, Development.

[5]  G. Bi,et al.  Synaptic modification by correlated activity: Hebb's postulate revisited. , 2001, Annual review of neuroscience.

[6]  Axon Pruning: C. elegans Makes the Cut , 2005, Current Biology.

[7]  Jacob G. Foster,et al.  Link and subgraph likelihoods in random undirected networks with fixed and partially fixed degree sequences. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[8]  Jürgen Jost,et al.  Temporal correlation based learning in neuron models , 2005, Theory in Biosciences.

[9]  Seunghwan Kim,et al.  Self-organized criticality and scale-free properties in emergent functional neural networks. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[10]  H. Spencer.  The structure of the nervous system. , 1870 .

[11]  Stefan Bornholdt,et al.  Handbook of Graphs and Networks: From the Genome to the Internet , 2003 .

[12]  Thomas Nowotny,et al.  Spatial representation of temporal information through spike-timing-dependent plasticity. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[13]  Lav R. Varshney,et al.  Structural Properties of the Caenorhabditis elegans Neuronal Network , 2009, PLoS Comput. Biol..

[14]  Albert-László Barabási,et al.  Evolution of Networks: From Biological Nets to the Internet and WWW , 2004 .

[15]  Eckehard Olbrich,et al.  Quantifying structure in networks , 2009, 0912.4450.

[16]  P. Huttenlocher.  Synaptic density in human frontal cortex - developmental changes and effects of aging. , 1979, Brain research.

[18]  Stefan Bornholdt,et al.  Topology of biological networks and reliability of information processing , 2004, Proceedings of the National Academy of Sciences of the United States of America.

[19]  Martin Vingron,et al.  Design and statistical properties of robust functional networks: a model study of biological signal transduction. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[20]  Cornelis J Stam,et al.  Graph theoretical analysis of complex networks in the brain , 2007, Nonlinear biomedical physics.

[21]  Chunguang Li,et al.  Functions of neuronal network motifs. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[22]  Jeff W. Lichtman,et al.  Axon Branch Removal at Developing Synapses by Axosome Shedding , 2004, Neuron.

[23]  G. Cecchi,et al.  Scale-free brain functional networks. , 2003, Physical review letters.

[24]  L. Abbott,et al.  Competitive Hebbian learning through spike-timing-dependent synaptic plasticity , 2000, Nature Neuroscience.

[25]  S. Shen-Orr,et al.  Network motifs: simple building blocks of complex networks. , 2002, Science.

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

[27]  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.

[28]  N. Ay,et al.  Complexity measures from interaction structures. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[29]  Naoki Masuda,et al.  Self-organization of feed-forward structure and entrainment in excitatory neural networks with spike-timing-dependent plasticity. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[30]  Nicolas Brunel,et al.  Fast Global Oscillations in Networks of Integrate-and-Fire Neurons with Low Firing Rates , 1999, Neural Computation.

[31]  R. Traub,et al.  Neuronal Networks of the Hippocampus , 1991 .

[32]  J. Jost,et al.  Evolution of network structure by temporal learning , 2008, 0811.4306.

[33]  Duncan J. Watts,et al.  Collective dynamics of ‘small-world’ networks , 1998, Nature.

[34]  Naoki Masuda,et al.  Formation of feedforward networks and frequency synchrony by spike-timing-dependent plasticity , 2007, Journal of Computational Neuroscience.

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

[36]  D. Johnston,et al.  Regulation of Synaptic Efficacy by Coincidence of Postsynaptic APs and EPSPs , 1997 .