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The Journal of Neuroscience, October 15, 2008, 28(42):10734-10745; doi:10.1523/JNEUROSCI.1016-08.2008

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Behavioral/Systems/Cognitive
The Statistics of Repeating Patterns of Cortical Activity Can Be Reproduced by a Model Network of Stochastic Binary Neurons

Alex Roxin,¹ Vincent Hakim,² and Nicolas Brunel^3,4

¹Computational Neuroscience, Department of Information and Communication Technologies, Universitat Pompeu Fabra, 08003 Barcelona, Spain, ²Laboratoire de Physique Statistique, Ecole Normale Supérieure, Centre National de la Recherche Scientifique (CNRS), Unité Mixte de Recherche (UMR) 8550, 75231 Paris, France, and ³Laboratoire de Neurophysique et Physiologie, Université Paris Descartes and ⁴CNRS, UMR 8119, 75006 Paris, France

Correspondence should be addressed to Alex Roxin, Computational Neuroscience, Universitat Pompeu Fabra, Passeig de Circumval·lació, 08003 Barcelona, Spain. Email: alexander.roxin{at}upf.edu

Calcium imaging of the spontaneous activity in cortical slices has revealed repeating spatiotemporal patterns of transitions between so-called down states and up states (Ikegaya et al., 2004). Here we fit a model network of stochastic binary neurons to data from these experiments, and in doing so reproduce the distributions of such patterns. We use two versions of this model: (1) an unconnected network in which neurons are activated as independent Poisson processes; and (2) a network with an interaction matrix, estimated from the data, representing effective interactions between the neurons. The unconnected model (model 1) is sufficient to account for the statistics of repeating patterns in 11 of the 15 datasets studied. Model 2, with interactions between neurons, is required to account for pattern statistics of the remaining four. Three of these four datasets are the ones that contain the largest number of transitions, suggesting that long datasets are in general necessary to render interactions statistically visible. We then study the topology of the matrix of interactions estimated for these four datasets. For three of the four datasets, we find sparse matrices with long-tailed degree distributions and an overrepresentation of certain network motifs. The remaining dataset exhibits a strongly interconnected, spatially localized subgroup of neurons. In all cases, we find that interactions between neurons facilitate the generation of long patterns that do not repeat exactly.

Key words: up and down states; repeating temporal patterns; attractors; stochastic model; calcium imaging; cortex

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Received Oct. 30, 2007; revised July 30, 2008; accepted Aug. 1, 2008.

Correspondence should be addressed to Alex Roxin, Computational Neuroscience, Universitat Pompeu Fabra, Passeig de Circumval·lació, 08003 Barcelona, Spain. Email: alexander.roxin{at}upf.edu

This article has been cited by other articles:

				S. Grun Data-Driven Significance Estimation for Precise Spike Correlation J Neurophysiol, March 1, 2009; 101(3): 1126 - 1140. [Abstract] [Full Text] [PDF]

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