Dynamics of the Instantaneous Firing Rate in Response to Changes in Input Statistics
 Nicolas FourcaudTrocmé,
 Nicolas Brunel
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We review and extend recent results on the instantaneous firing rate dynamics of simplified models of spiking neurons in response to noisy current inputs. It has been shown recently that the response of the instantaneous firing rate to small amplitude oscillations in the mean inputs depends in the large frequency limit f on the spike initiation dynamics. A particular simplified model, the exponential integrateandfire (EIF) model, has a response that decays as 1/f in the large frequency limit and describes very well the response of conductancebased models with a HodgkinHuxley type fast sodium current. Here, we show that the response of the EIF instantaneous firing rate also decays as 1/f in the case of an oscillation in the variance of the inputs for both white and colored noise. We then compute the initial transient response of the firing rate of the EIF model to a step change in its mean inputs and/or in the variance of its inputs. We show that in both cases the response speed is proportional to the neuron stationary firing rate and inversely proportional to a ‘spike slope factor’ Δ_{ T } that controls the sharpness of spike initiation: as 1/Δ_{ T } for a step change in mean inputs, and as 1/Δ_{ T } ^{2} for a step change in the variance in the inputs.
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 Title
 Dynamics of the Instantaneous Firing Rate in Response to Changes in Input Statistics
 Journal

Journal of Computational Neuroscience
Volume 18, Issue 3 , pp 311321
 Cover Date
 20050601
 DOI
 10.1007/s1082700503378
 Print ISSN
 09295313
 Online ISSN
 15736873
 Publisher
 Kluwer Academic Publishers
 Additional Links
 Topics
 Keywords

 integrateandfire neuron
 noise
 dynamical response
 spiking mechanism
 Industry Sectors
 Authors

 Nicolas FourcaudTrocmé ^{(1)}
 Nicolas Brunel ^{(2)}
 Author Affiliations

 1. Department of Mathematics, Center for Neural Basis of Cognition, University of Pittsburgh, Pittsburgh, PA, 15213, USA
 2. Laboratory of Neurophysics and Physiology, UMR8119 CNRS  Université René Descartes, 45 Rue des Saints Pères, 75270, Paris Cedex 06, France