Relation between spike correlations and network structure
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1
Albert-Ludwig University Freiburg, Faculty of Biology, Germany
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2
Bernstein Center Freiburg, Germany
Correlations between neural spike trains are a widely studied phenomenon, due to their ubiquity and their influence on neural network dynamics and function. A state of relatively weak correlations and irregular spike trains is often assumed to be a good model for normal activity in cortical networks. 'Balanced' networks of leaky intergrate-and-fire neurons display low average correlations and irregular spike trains. There, the interplay between excitatory and inhibitory populations has been proposed as a key mechanism of correlation reduction. However, the variance of the correlations is typically still large.
We describe pairwise correlations in networks of integrate-and-fire neurons in the framework of point processes [1] considering only linear responses of all neurons. This approximation is applicable under a wide range of conditions, provided that spike activity is sufficiently irregular, and that reset effects are taken into account. The approach yields a simple analytical expression for correlations in the network and the connectivity matrix that encodes the synaptic topology of the network. Differences in correlations can be fully attributed to differences in the connectivity structure between neurons.
As correlations result from multiple direct and indirect synaptic connections [2], the inverse problem -- inference of network structure from correlations -- has no unique solution in general. We find that this fundamental ambiguity can be considerably alleviated, if a priori knowledge about specific features of the network structure, as for example sparse connectivity, is taken into account.
Acknowledgements
We gratefully acknowledge support by the German Research Foundation (CRC 780, subproject C4) and by the German Federal Ministry of Education and Research (BMBF grant 01GQ0420 to BCCN Freiburg).
References
1. Hawkes AG (1971) Point spectra of some mutually exciting point processes. J R Stat Soc Series B Methodol 33: 438–443
2. Pernice V, Staude B, Cardanobile S, Rotter S (2011). How Structure Determines Correlations in Neuronal Networks. PLoS Comput Biol, 7(5): e1002059
Keywords:
correlations,
integrate-and-fire neurons,
network structure,
Neurons,
networks and dynamical systems
Conference:
BC11 : Computational Neuroscience & Neurotechnology Bernstein Conference & Neurex Annual Meeting 2011, Freiburg, Germany, 4 Oct - 6 Oct, 2011.
Presentation Type:
Poster
Topic:
neurons, networks and dynamical systems (please use "neurons, networks and dynamical systems" as keywords)
Citation:
Pernice
V,
Cardanobile
S,
Staude
B and
Rotter
S
(2011). Relation between spike correlations and network structure.
Front. Comput. Neurosci.
Conference Abstract:
BC11 : Computational Neuroscience & Neurotechnology Bernstein Conference & Neurex Annual Meeting 2011.
doi: 10.3389/conf.fncom.2011.53.00065
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Received:
23 Aug 2011;
Published Online:
04 Oct 2011.
*
Correspondence:
Mr. Volker Pernice, Albert-Ludwig University Freiburg, Faculty of Biology, Freiburg, Germany, volker.pernice@lps.ens.fr