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Scanning for relations of neuronal spiking activity and network structure across multifractal network ensembles

Moritz Deger1*, Volker Pernice1, Stefano Cardanobile1 and Stefan Rotter1
  • 1 University of Freiburg, Bernstein Center Freiburg & Faculty of Biology, Germany

Relations between structural features and spiking activity of neuronal networks have recently raised a lot of interest. Current studies typically focus on specific network models and attempt to discover relations between properties of the underlying graph and the signals generated by its neurons [1-4]. Structural parameters often considered in this context are degree distribution, degree correlations, and spectral radius of the adjacency matrix. Parameters typically used to characterize activity dynamics are firing rate, synchrony, spike train regularity, and spike count correlations.

Models of networks generally constrain the statistics of network properties due to their specific construction procedure. Results of the above type can hence be strongly biased by correlations between different features of the specific network model under consideration. Here we employ the multifractal network generator [5] to address network models with a broad distribution of properties and, consequently, generate realizations of networks with much higher variability than usual [4]. This approach can therefore be used to infer and systematically test the validity of structure-dynamics relations in a general context.

We present results based on a large set of simulations of networks comprised of excitatory and inhibitory integrate-and-fire neurons. Biophysical parameters and overall connectivity were arranged such that they would induce an asynchronous irregular activity state in the case of a random network with homogeneous coupling [6]. Firstly, our results indicate that different non-random structures can induce a large variety of activity regimes. Secondly, we find significant correlations between activity parameters and certain structural properties that have so far not received much attention. Thus our data mining approach might eventually lead to the discovery of network characteristics, the functional significance of which was previously unknown.

Acknowledgements

Supported by the German Federal Ministry of Education and Research (BMBF; grant 01GQ0420 BCCN Freiburg, grant 01GQ0830 BFNT Freiburg*Tübingen, grant 01GW0730 Impulse Control), and the German Research Foundation (DFG; CRC 780, subproject C4).

References

1. Riecke, H., Roxin, A., Madruga, S., and Solla, S.A. (2007). Multiple attractors, long chaotic transients, and failure in small-world networks of excitable neurons. Chaos 17:2, 026110. doi: 10.1063/1.2743611
2. Gaiteri, C., and Rubin, J.E. (2011). The interaction of intrinsic dynamics and network topology in determining network burst synchrony. Front. Comput. Neurosci. 5:10. doi: 10.3389/fncom.2011.00010
3. Mäki-Marttunen, T., Aćimović, J., Nykter, M., Kesseli, J., Ruohonen, K., Yli-Harja, O., and Linne, M.-L. (2011). Information diversity in structure and dynamics of simulated neuronal networks. Front. Comput. Neurosci. 5:26. doi: 10.3389/fncom.2011.00026
4. Cardanobile, S., Pernice, V., Deger, M., and Rotter, S. (2012). Inferring general relations between network characteristics from specific network ensembles. Accepted for PLoS ONE. doi: 10.1371/journal.pone.0037911
5. Palla, G., Lovász, L., and Vicsek, T. (2010). Multifractal network generator. P Natl Acad Sci USA 107, 7640-7645. doi: 10.1073/pnas.0912983107
6. Brunel, N. (2000). Dynamics of Sparsely Connected Networks of Excitatory and Inhibitory Spiking Neurons. J. Comput. Neurosci., 8:3, 183-208. doi: 10.1023/A:1008925309027

Keywords: correlations, integrate-and-fire neuron, multifractal network generator, network statistics, network structure, spike train statistics, structure-dynamics-relations, synchrony

Conference: Bernstein Conference 2012, Munich, Germany, 12 Sep - 14 Sep, 2012.

Presentation Type: Poster

Topic: Other

Citation: Deger M, Pernice V, Cardanobile S and Rotter S (2012). Scanning for relations of neuronal spiking activity and network structure across multifractal network ensembles. Front. Comput. Neurosci. Conference Abstract: Bernstein Conference 2012. doi: 10.3389/conf.fncom.2012.55.00261

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Received: 18 Sep 2012; Published Online: 12 Sep 2012.

* Correspondence: Dr. Moritz Deger, University of Freiburg, Bernstein Center Freiburg & Faculty of Biology, Freiburg, Germany, md-web@gmx.org