The Spike-Triggered Average of the Integrate-and-Fire Cell Driven by Gaussian White Noise

Authors:
Liam Paninski
Affiliations:
Department of Statistics, New York University, New York, NY 10027, U.S.A. liam@stat.columbia.edu
Venue:
Neural Computation
Year:
2006

Citing 10
Cited 3

Noise adaptation in integrate-and-fire neurons

Neural Computation
Analysis of integrate-and-fire neurons: synchronization of synaptic input and spike output

Neural Computation
Spikes: exploring the neural code

Spikes: exploring the neural code
Fast global oscillations in networks of integrate-and-fire neurons with low firing rates

Neural Computation
Numerical Recipes in C: The Art of Scientific Computing

Numerical Recipes in C: The Art of Scientific Computing
Spiking Neuron Models: An Introduction

Spiking Neuron Models: An Introduction
What causes a Neuron to spike?

Neural Computation
Firing rate of the noisy quadratic integrate-and-fire neuron

Neural Computation
Maximum Likelihood Estimation of a Stochastic Integrate-and-Fire Neural Encoding Model

Neural Computation
Dependence of the spike-triggered average voltage on membrane response properties

Neurocomputing

Stimulus-dependent correlations in threshold-crossing spiking neurons

Neural Computation
Feature selection in simple neurons: How coding depends on spiking dynamics

Neural Computation
Efficient computation of the maximum a posteriori path and parameter estimation in integrate-and-fire and more general state-space models

Journal of Computational Neuroscience

Quantified Score

Hi-index	0.00

Visualization

Abstract

We compute the exact spike-triggered average (STA) of the voltage for the nonleaky integrate-and-fire (IF) cell in continuous time, driven by gaussian white noise. The computation is based on techniques from the theory of renewal processes and continuous-time hidden Markov processes (e.g., the backward and forward Fokker-Planck partial differential equations associated with first-passage time densities). From the STA voltage, it is straightforward to derive the STA input current. The theory also gives an explicit asymptotic approximation for the STA of the leaky IF cell, valid in the low-noise regime σ → 0. We consider both the STA and the conditional average voltage given an observed spike “doublet” event, that is, two spikes separated by some fixed period of silence. In each case, we find that the STA as a function of time-preceding-spike, τ, has a square root singularity as τ approaches zero from below and scales linearly with the scale of injected noise current. We close by briefly examining the discrete-time case, where similar phenomena are observed.