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  • Open Access

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

BMC Neuroscience201213 (Suppl 1) :P45

  • Published:


  • Firing Rate
  • Ising Model
  • Neuron Model
  • Pairwise Correlation
  • Linear Filter

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).
Figure 1
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.



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

Authors’ Affiliations

Department of Applied Mathematics, University of Washington, Seattle, WA 98195, USA
Program in Neurobiology and Behavior, University of Washington, Seattle, WA 98195, USA


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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. Phys Rev E. 2007, 76:Google Scholar