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Sparsely-synchronized brain rhythm in a small-world neural network

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Abstract

Sparsely-synchronized cortical rhythms, associated with diverse cognitive functions, have been observed in electric recordings of brain activity. At the population level, cortical rhythms exhibit small-amplitude fast oscillations while at the cellular level, individual neurons show stochastic firings sparsely at a much lower rate than the population rate. We study the effect of network architecture on sparse synchronization in an inhibitory population of subthreshold Morris-Lecar neurons (which cannot fire spontaneously without noise). Previously, sparse synchronization was found to occur for cases of both global coupling (i.e., regular all-to-all coupling) and random coupling. However, a real neural network is known to be non-regular and non-random. Here, we consider sparse Watts-Strogatz small-world networks which interpolate between a regular lattice and a random graph via rewiring. We start from a regular lattice with only short-range connections and then investigate the emergence of sparse synchronization by increasing the rewiring probability p for the short-range connections. For p = 0, the average synaptic path length between pairs of neurons becomes long; hence, only an unsynchronized population state exists because the global efficiency of information transfer is low. However, as p is increased, long-range connections begin to appear, and global effective communication between distant neurons may be available via shorter synaptic paths. Consequently, as p passes a threshold p th (}~ 0.044), sparsely-synchronized population rhythms emerge. However, with increasing p, longer axon wirings become expensive because of their material and energy costs. At an optimal value p* DE (}~ 0.24) of the rewiring probability, the ratio of the synchrony degree to the wiring cost is found to become maximal. In this way, an optimal sparse synchronization is found to occur at a minimal wiring cost in an economic small-world network through trade-off between synchrony and wiring cost.

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Authors and Affiliations

  1. Research Division, LABASIS Corporation, Chunchon, 200-702, Korea

    Sang-Yoon Kim

  2. Department of Science Education, Daegu National University of Education, Daegu, 705-115, Korea

    Woochang Lim

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  1. Sang-Yoon Kim
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Correspondence to Woochang Lim.

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Kim, SY., Lim, W. Sparsely-synchronized brain rhythm in a small-world neural network. Journal of the Korean Physical Society 63, 104–113 (2013). https://doi.org/10.3938/jkps.63.104

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