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This article is part of the supplement: Twenty First Annual Computational Neuroscience Meeting: CNS*2012

Open Access Poster presentation

A simple mechanism for higher-order correlations in integrate-and-fire neurons

David A Leen1* and Eric Shea-Brown12

Author Affiliations

1 Department of Applied Mathematics, University of Washington, Seattle, WA 98195, USA

2 Program in Neurobiology and Behavior, University of Washington, Seattle, WA, 98195, USA

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BMC Neuroscience 2012, 13(Suppl 1):P45  doi:10.1186/1471-2202-13-S1-P45

The electronic version of this article is the complete one and can be found online at: http://www.biomedcentral.com/1471-2202/13/S1/P45


Published:16 July 2012

© 2012 Leen and Shea-Brown; licensee BioMed Central Ltd.

This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Poster presentation

Recent work [1] shows that common input gives rise to higher-order correlations in the Dichotomized Gaussian neuron model. Here we study a homogeneous population of integrate-and-fire neurons receiving correlated input. Each neuron receives an independent white noise input and all neurons receive a common Gaussian input. To quantify the contributions of higher-order correlations we use a maximum entropy model. The model with interactions up to second order (i.e. pairwise correlations) is known as the Ising model. The Kullbach-Leibler divergence between the Ising model and the model with interactions of all orders allows us to quantitatively describe the presence of higher-order correlations.

We observe from numerical simulations that for low firing rates, the Kullbach-Leibler divergence grows with increasing correlation i.e. strength of the common input (Figure 1A). For population size N=100, the Ising model predicts a vastly different distribution of spike outputs (Figures 1B,C).

thumbnailFigure 1. A, KL-divergence grows with increasing correlation between the neurons. B, Distribution of spike outputs from numerical simulation of LIF neurons. C, Predicted distribution of spike outputs from Ising model.

For a leaky IF or exponential IF neuron receiving an input signal identical in all trials, and a background noise independent from trial to trial, it is possible to explicitly calculate the linear response function [2,3]. We use this linear filter to compute instantaneous firing probabilities for the N cells in our setup. This gives us a theoretical basis for our central finding that strong higher-order correlations arise naturally in integrate and fire cells receiving common inputs.

Acknowledgements

This work was funded in part by the Burroughs Wellcome Fund Scientific Interfaces Program.

References

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  2. Ostojic S, Brunel N: From spiking neuron models to linear-nonlinear models.

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  3. Richardson MJE: Firing rate response of linear and nonlinear integrate and fire neurons to modulated current-based and conductance-based synaptic drive.

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