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The Journal of Neuroscience, January 9, 2008, 28(2):505-518; doi:10.1523/JNEUROSCI.3359-07.2008

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Behavioral/Systems/Cognitive
A Maximum Entropy Model Applied to Spatial and Temporal Correlations from Cortical Networks In Vitro

Aonan Tang,^1 * David Jackson,^4 * Jon Hobbs,¹ Wei Chen,¹ Jodi L. Smith,³ Hema Patel,³ Anita Prieto,² Dumitru Petrusca,⁵ Matthew I. Grivich,⁵ Alexander Sher,⁵ Pawel Hottowy,⁵ Wladyslaw Dabrowski,⁶ Alan M. Litke,⁵ and John M. Beggs¹

Departments of ¹Physics and ²Psychological and Brain Sciences, and ³School of Medicine, Indiana University, Bloomington, Indiana 47405, ⁴Brown University, Providence, Rhode Island 02912, ⁵Institute for Particle Physics, University of California, Santa Cruz, California 95064, and ⁶Faculty of Physics and Applied Computer Science, AGH University of Science and Technology, 30-059, Krakow, Poland

Correspondence should be addressed to John M. Beggs, Indiana University Department of Physics, 727 East Third Street, Bloomington, IN 47405. Email: jmbeggs{at}indiana.edu

Multineuron firing patterns are often observed, yet are predicted to be rare by models that assume independent firing. To explain these correlated network states, two groups recently applied a second-order maximum entropy model that used only observed firing rates and pairwise interactions as parameters (Schneidman et al., 2006; Shlens et al., 2006). Interestingly, with these minimal assumptions they predicted 90–99% of network correlations. If generally applicable, this approach could vastly simplify analyses of complex networks. However, this initial work was done largely on retinal tissue, and its applicability to cortical circuits is mostly unknown. This work also did not address the temporal evolution of correlated states. To investigate these issues, we applied the model to multielectrode data containing spontaneous spikes or local field potentials from cortical slices and cultures. The model worked slightly less well in cortex than in retina, accounting for 88 ± 7% (mean ± SD) of network correlations. In addition, in 8 of 13 preparations, the observed sequences of correlated states were significantly longer than predicted by concatenating states from the model. This suggested that temporal dependencies are a common feature of cortical network activity, and should be considered in future models. We found a significant relationship between strong pairwise temporal correlations and observed sequence length, suggesting that pairwise temporal correlations may allow the model to be extended into the temporal domain. We conclude that although a second-order maximum entropy model successfully predicts correlated states in cortical networks, it should be extended to account for temporal correlations observed between states.

Key words: microelectrode array; culture; slice; human tissue; neuronal avalanche; local field potential

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Received July 24, 2007; revised Nov. 29, 2007; accepted Dec. 3, 2007.

Correspondence should be addressed to John M. Beggs, Indiana University Department of Physics, 727 East Third Street, Bloomington, IN 47405. Email: jmbeggs{at}indiana.edu

This article has been cited by other articles:

				S. Yu, D. Huang, W. Singer, and D. Nikolic A Small World of Neuronal Synchrony Cereb Cortex, April 9, 2008; (2008) bhn047v1. [Abstract] [Full Text] [PDF]

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