/v1/supplement/title
Open Access

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

BMC Neuroscience201213(Suppl 1):P45

DOI: 10.1186/1471-2202-13-S1-P45

Published: 16 July 2012

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).
https://static-content.springer.com/image/art%3A10.1186%2F1471-2202-13-S1-P45/MediaObjects/12868_2012_Article_2582_Fig1_HTML.jpg
Figure 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.

Declarations

Acknowledgements

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

Authors’ Affiliations

(1)
Department of Applied Mathematics, University of Washington
(2)
Program in Neurobiology and Behavior, University of Washington

References

  1. Macke JH, Opper M, Bethge M: Common input explains higher-order correlations and entropy in a simple model of neural population activity. Phys Rev Letters. 2011, 106:Google Scholar
  2. Ostojic S, Brunel N: From spiking neuron models to linear-nonlinear models. PLOS Computational Biology. 2011, 7 (1):
  3. Richardson MJE: Firing rate response of linear and nonlinear integrate and fire neurons to modulated current-based and conductance-based synaptic drive. Phys Rev E. 2007, 76:Google Scholar

Copyright

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

This article is published under license to 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.

Advertisement