A Small World of Neuronal Synchrony

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.

Higher-Order Interactions Characterized in Cortical Activity

“…To study evoked spiking responses in vivo, we used datasets of visually evoked activities recorded from cortical area 17 in two, adult anesthetized cats published previously (Yu et al, 2008). In short, the animals were artificially ventilated and anesthesia was maintained with a mixture of 70% N 2 O and 30% O 2 , supplemented with 0.5-0.6% halothane.…”

“…That is, x ϭ (x 1 , x 2 , x 3 , …, x n ), where x i ϭ 1 if at least one spike generated by unit i and x i ϭ 0 otherwise. We used a ⌬t ϭ 20 ms for ongoing activity in the monkey and a smaller ⌬t ϭ 4 ms for evoked activities in the cat, because of the relatively high firing rates during evoked responses compared with ongoing activity (Yu et al, 2008). The range of ⌬t used here is consistent with previous studies using the Ising model (Schneidman et al, 2006;Yu et al, 2008;Ohiorhenuan et al, 2010), and similar results were obtained by varying ⌬t by at least two folds, i.e., 10 ms for ongoing activity and 8 ms for evoked activity (data not shown).…”

“…Schneidman et al (2006) and Shlens et al (2006) showed that pairwise interactions explain most of the spiking activity in small (Յ10 neurons) retina networks, a finding that was soon extended to include larger systems (Cocco et al, 2009;Shlens et al, 2009;Ganmor et al, 2011a), in vivo cortical networks (Yu et al, 2008;Ohiorhenuan et al, 2010), and correlations among population activities measured in the local field potentials (LFPs) (Tang et al, 2008;Santos et al, 2010). In contrast, a number of more recent studies (Montani et al, 2009;Ohiorhenuan et al, 2010;Santos et al, 2010;Ohiorhenuan and Victor, 2011;Ganmor et al, 2011b) have identified significant higher-order interactions in neuronal spiking and LFP activities, e.g., third-order interactions among closely neighbored (Ͻ300 m) cortical neurons (Ohiorhenuan et al, 2010;Ohiorhenuan and Victor, 2011) and interactions of up to the eighth order among retinal ganglion cells (Ganmor et al, 2011b).…”

Oscillations and synchrony in a cortical neural network

“…The so-called small-world networks have intermediate connectivity properties but exhibit a high degree of clustering as in the regular networks and a small average distance between vertices as in the random networks. Convincing evidences have been presented which support the idea that smallworld networks provide a powerful and versatile tool, leading us towards understanding the structure and function of the human brain (Yu et al 2008;Bassett and Bullmore 2006;Volman et al 2005). Hence, much attention has been devoted to studying the dynamics of small-world neuronal networks (Roxin et al 2004).…”

Reduced brain connectivity and mental flexibility in mild traumatic brain injury

“…To evaluate network topologies for these regions, we chose the graph theoretical measure of node strength. Strength reflects how functionally connected a given region is to other regions in the analyzed network 54, 55…”