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Computational investigations of small-worlds networks in neuronal populations

Antonio G. Zippo1*, Giuliana Gelsomino1, Sara Nencini1, Gian Carlo Caramenti2, Maurizio Valente1 and Gabriele E. Biella1
  • 1 National Research Council, Institute of Molecular Bioimaging and Physiology, Italy
  • 2 National Research Council, Institute of Biomedical Technologies, Italy

The study of the brain as neuronal network allows gaining insights to the analysis of information processing [1]. Network interactions can play a crucial role in this scenario. In fact many studies identify in the modality of neuronal interaction the key of the problem, but limitations in neuronal recordings makes the clear mechanisms elusive [2-4].
In this perspective, we investigated the functional organization of neuronal networks hypothesizing that they work as small-world networks [5]. We developed two different computational approaches: in the first, we asked whether neuronal populations actually express small-world properties during a learning task. To this purpose we developed the Inductive Conceptual Network (ICN), a hierarchical bio-inspired spiking network, able to learn invariant patterns by Variable-order Markov Models implemented in its nodes [6]. We found that the ICN model expressed small-word networks during learning. As control, we exerted the ICN with random binary inputs, where no patterns can be learnt, and we obtained no small-world network functional organization among nodes. Conjecturing that the expression of small-world networks is not only related to learning, in the second part, we built the de facto network assuming that every information process in brain occurs exhibiting functionally a small-world network. In the de facto network the functional dependencies of the small-world networks, were reflected by synchronous spikes. From the analysis of spiking activity, versus the null hypothesis where small-world networks were replaced by random networks, we detected mainly three functional characteristics, observed in biological networks: timing and rate codes, conventional coding strategies [7], and the neuronal avalanches, cascades of bursting activities distributed as a power-law distribution [8]. Interestingly, rate and timing codes are thus allowed to coexist in the same network model yet in nodes at different hierarchical positions.
Our results suggest that small-word functional configurations represent a milestone of brain information processing at the level of neurons. In conclusion, accordingly with other theoretical and experimental works, short path length and sparse connectivity may promote simultaneous performance of information segregation (information retention) and integration (generalization) within neuronal systems.

Acknowledgements

We thank Riccardo Storchi and Jianyi Lin for his helpful suggestions.

References

1. Bassett, D., S. et al. (2010). Efficient Physical Embedding of Topologically Complex Information Processing Networks in Brains and Computer Circuits. PLoS Comput Biol, 6(4): e1000748.
2. Honey, C.,J., Kötter, R., Breakspear, M., Sporns, O. (2007). Network structure of cerebral cortex shapes functional connectivity on multiple time scales. Proc Natl Acad Sci USA 104: 10240-10245.
3. Bullmore, E., Sporns, O. (2009). Complex brain networks: graph theoretical analysis of structural and functional systems. Nature Reviews Neuroscience 10, 186-198.
4. Horwitz, B., (2003). The elusive concept of brain connectivity. Neuroimage 19, 466-470.
5. Bassett, D., Bullmore E. (2006). Small-World Brain Networks, The Neuroscientist, 12(6):512-523.
6. Begleiter, R., El-Yaniv, R., Yona, G. (2004). On Prediction Using Variable Order Markov Models. Journal of Artificial Intelligence Research, 22:385-421.
7. Quiroga RQ, Panzeri S (2009) Extracting information from neuronal populations: information theory and decoding approaches. Nature Rew Neurosci, 10:173-185.
8. Klaus A, Yu S, Plenz D (2011) Statistical Analyses Support Power Law Distributions Found in Neuronal Avalanches. PLoS ONE 6(5): e19779.

Keywords: information abstraction, machine learning, Neural coding, neuronal assemblies, neuronal avalanches, Small-world networks

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

Presentation Type: Poster

Topic: Other

Citation: Zippo AG, Gelsomino G, Nencini S, Caramenti G, Valente M and Biella GE (2012). Computational investigations of small-worlds networks in neuronal populations
. Front. Comput. Neurosci. Conference Abstract: Bernstein Conference 2012. doi: 10.3389/conf.fncom.2012.55.00241

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

* Correspondence: Dr. Antonio G Zippo, National Research Council, Institute of Molecular Bioimaging and Physiology, Segrate, Milano, 20090, Italy, antonio.zippo@gmail.com