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Local cortical circuit model inferred from power-law distributed neuronal avalanches

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Abstract

How cortical neurons process information crucially depends on how their local circuits are organized. Spontaneous synchronous neuronal activity propagating through neocortical slices displays highly diverse, yet repeatable, activity patterns called “neuronal avalanches”. They obey power-law distributions of the event sizes and lifetimes, presumably reflecting the structure of local circuits developed in slice cultures. However, the explicit network structure underlying the power-law statistics remains unclear. Here, we present a neuronal network model of pyramidal and inhibitory neurons that enables stable propagation of avalanche-like spiking activity. We demonstrate a neuronal wiring rule that governs the formation of mutually overlapping cell assemblies during the development of this network. The resultant network comprises a mixture of feedforward chains and recurrent circuits, in which neuronal avalanches are stable if the former structure is predominant. Interestingly, the recurrent synaptic connections formed by this wiring rule limit the number of cell assemblies embeddable in a neuron pool of given size. We investigate how the resultant power laws depend on the details of the cell-assembly formation as well as on the inhibitory feedback. Our model suggests that local cortical circuits may have a more complex topological design than has previously been thought.

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Acknowledgments

The authors express their sincere thanks to T. Hensch and N. Yamamoto for fruitful discussions about the development of the cortical circuits. The present work was partially supported by Grants in Aid for Scientific Research of Priority Areas and Grant-in-Aid for Young Scientists (B) from the Japanese Ministry of Education, Culture, Sports, Science and Technology.

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Correspondence to Tomoki Fukai.

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Competing financial interests: The authors declare that they have no competing financial interests.

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Appendix

Appendix

The average number of synaptic connections

In the proposed model, the number of excitatory connections included in the entire network is approximately given as \(Pms\) under sparseness assumption where we can neglect a small overlap between different chains (\(P,\;s \ll N\)), where P is the total number of synfire chains, m is the number of synaptic projections to each cell, and s is the average size of these chains. The connection probability is therefore given as \(c = \frac{{Pms}}{{N^2 }}\). For a chain of average size s, the product of the probability c and the number of possible neuron pairs \(s^2\) gives the average number of non-purely feedforward (recurrent) connections in this chain, \(\frac{{Pms^3 }}{{N^2 }}\). We note that the ratio of the number of recurrent connections to that of purely feed-forward connections in this chain is \(\frac{{Pms^3 }}{{N^2 }}/ms = P\left( {\frac{s}{N}} \right)^2\). We can similarly obtain the same formula for the average number of synaptic connections between each pair of different chains. This implies that the degree of interferences between synfire chains increases with \(P\).

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Teramae, Jn., Fukai, T. Local cortical circuit model inferred from power-law distributed neuronal avalanches. J Comput Neurosci 22, 301–312 (2007). https://doi.org/10.1007/s10827-006-0014-6

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