Local cortical circuit model inferred from powerl

Authors: Junnosuke Teramae Tomoki Fukai

Publish Date: 2007/01/17

Volume: 22, Issue: 3, Pages: 301-312

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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 powerlaw 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 powerlaw statistics remains unclear Here we present a neuronal network model of pyramidal and inhibitory neurons that enables stable propagation of avalanchelike 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 cellassembly 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 thoughtThe 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 GrantinAid for Young Scientists B from the Japanese Ministry of Education Culture Sports Science and TechnologyIn 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 Ps 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 = fracPmsN2 For a chain of average size s the product of the probability c and the number of possible neuron pairs s2 gives the average number of nonpurely feedforward recurrent connections in this chain fracPms3 N2 We note that the ratio of the number of recurrent connections to that of purely feedforward connections in this chain is fracPms3 N2 /ms = Pleft fracsN right2 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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