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A small world of neuronal synchrony.

Yu S, Huang D, Singer W, Nikolic D - Cereb. Cortex (2008)

Bottom Line: Neurons differed considerably with respect to the number and strength of interactions, suggesting the existence of "hubs" in the network.Notably, there was no evidence for scale-free properties.These results suggest that cortical networks are optimized for the coexistence of local and global computations: feature detection and feature integration or binding.

View Article: PubMed Central - PubMed

Affiliation: Department of Neurophysiology, Max-Planck Institute for Brain Research, D-60528 Frankfurt am Main, Germany.

ABSTRACT
A small-world network has been suggested to be an efficient solution for achieving both modular and global processing-a property highly desirable for brain computations. Here, we investigated functional networks of cortical neurons using correlation analysis to identify functional connectivity. To reconstruct the interaction network, we applied the Ising model based on the principle of maximum entropy. This allowed us to assess the interactions by measuring pairwise correlations and to assess the strength of coupling from the degree of synchrony. Visual responses were recorded in visual cortex of anesthetized cats, simultaneously from up to 24 neurons. First, pairwise correlations captured most of the patterns in the population's activity and, therefore, provided a reliable basis for the reconstruction of the interaction networks. Second, and most importantly, the resulting networks had small-world properties; the average path lengths were as short as in simulated random networks, but the clustering coefficients were larger. Neurons differed considerably with respect to the number and strength of interactions, suggesting the existence of "hubs" in the network. Notably, there was no evidence for scale-free properties. These results suggest that cortical networks are optimized for the coexistence of local and global computations: feature detection and feature integration or binding.

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Correlations in neuronal activity and model approximation of the firing patterns. (A) Distribution of correlation coefficients between neuronal pairs computed from their original spiking activity (blue) and from trial-shuffled activity (50 repetitions of shuffling; gray). Error bars represent the SD. Neuronal pairs (pair index) are sorted by the magnitude of the correlation coefficient obtained for the actual (nonshuffled) data. (B) For an example of a 10-neuron group, the observed frequency of individual firing patterns is plotted against the frequency predicted by the Ising model (2nd-order correlation; red dots) and the predictions from the independent model (no correlation; light-blue dots). The solid line indicates equality.
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fig1: Correlations in neuronal activity and model approximation of the firing patterns. (A) Distribution of correlation coefficients between neuronal pairs computed from their original spiking activity (blue) and from trial-shuffled activity (50 repetitions of shuffling; gray). Error bars represent the SD. Neuronal pairs (pair index) are sorted by the magnitude of the correlation coefficient obtained for the actual (nonshuffled) data. (B) For an example of a 10-neuron group, the observed frequency of individual firing patterns is plotted against the frequency predicted by the Ising model (2nd-order correlation; red dots) and the predictions from the independent model (no correlation; light-blue dots). The solid line indicates equality.

Mentions: Spike trains were binned in windows of 2 ms and digitized, yielding time series of zeros and ones. We computed Pearson’s correlation coefficients for pairs of such binary series (i.e., phi-coefficient; 2nd-order correlation), which corresponded to the height of the central peak (zero-shift) in an appropriately normalized cross-correlation histogram. These coefficients were larger than zero and got strongly reduced by shuffling the trials in which the identical stimuli were presented (Fig. 1A). If the observed correlations were due to neuronal responses being tightly time locked to the stimuli, the strength of the correlations would have stayed unchanged after the trial shuffling. The finding that the correlations largely disappeared after the shuffling procedure indicates that those correlations originated mostly from the synchronization generated internally and not from the temporal dynamics of the stimulus.


A small world of neuronal synchrony.

Yu S, Huang D, Singer W, Nikolic D - Cereb. Cortex (2008)

Correlations in neuronal activity and model approximation of the firing patterns. (A) Distribution of correlation coefficients between neuronal pairs computed from their original spiking activity (blue) and from trial-shuffled activity (50 repetitions of shuffling; gray). Error bars represent the SD. Neuronal pairs (pair index) are sorted by the magnitude of the correlation coefficient obtained for the actual (nonshuffled) data. (B) For an example of a 10-neuron group, the observed frequency of individual firing patterns is plotted against the frequency predicted by the Ising model (2nd-order correlation; red dots) and the predictions from the independent model (no correlation; light-blue dots). The solid line indicates equality.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC2583154&req=5

fig1: Correlations in neuronal activity and model approximation of the firing patterns. (A) Distribution of correlation coefficients between neuronal pairs computed from their original spiking activity (blue) and from trial-shuffled activity (50 repetitions of shuffling; gray). Error bars represent the SD. Neuronal pairs (pair index) are sorted by the magnitude of the correlation coefficient obtained for the actual (nonshuffled) data. (B) For an example of a 10-neuron group, the observed frequency of individual firing patterns is plotted against the frequency predicted by the Ising model (2nd-order correlation; red dots) and the predictions from the independent model (no correlation; light-blue dots). The solid line indicates equality.
Mentions: Spike trains were binned in windows of 2 ms and digitized, yielding time series of zeros and ones. We computed Pearson’s correlation coefficients for pairs of such binary series (i.e., phi-coefficient; 2nd-order correlation), which corresponded to the height of the central peak (zero-shift) in an appropriately normalized cross-correlation histogram. These coefficients were larger than zero and got strongly reduced by shuffling the trials in which the identical stimuli were presented (Fig. 1A). If the observed correlations were due to neuronal responses being tightly time locked to the stimuli, the strength of the correlations would have stayed unchanged after the trial shuffling. The finding that the correlations largely disappeared after the shuffling procedure indicates that those correlations originated mostly from the synchronization generated internally and not from the temporal dynamics of the stimulus.

Bottom Line: Neurons differed considerably with respect to the number and strength of interactions, suggesting the existence of "hubs" in the network.Notably, there was no evidence for scale-free properties.These results suggest that cortical networks are optimized for the coexistence of local and global computations: feature detection and feature integration or binding.

View Article: PubMed Central - PubMed

Affiliation: Department of Neurophysiology, Max-Planck Institute for Brain Research, D-60528 Frankfurt am Main, Germany.

ABSTRACT
A small-world network has been suggested to be an efficient solution for achieving both modular and global processing-a property highly desirable for brain computations. Here, we investigated functional networks of cortical neurons using correlation analysis to identify functional connectivity. To reconstruct the interaction network, we applied the Ising model based on the principle of maximum entropy. This allowed us to assess the interactions by measuring pairwise correlations and to assess the strength of coupling from the degree of synchrony. Visual responses were recorded in visual cortex of anesthetized cats, simultaneously from up to 24 neurons. First, pairwise correlations captured most of the patterns in the population's activity and, therefore, provided a reliable basis for the reconstruction of the interaction networks. Second, and most importantly, the resulting networks had small-world properties; the average path lengths were as short as in simulated random networks, but the clustering coefficients were larger. Neurons differed considerably with respect to the number and strength of interactions, suggesting the existence of "hubs" in the network. Notably, there was no evidence for scale-free properties. These results suggest that cortical networks are optimized for the coexistence of local and global computations: feature detection and feature integration or binding.

Show MeSH