Journal of Computational Neuroscience

, Volume 18, Issue 3, pp 311–321

Dynamics of the Instantaneous Firing Rate in Response to Changes in Input Statistics


DOI: 10.1007/s10827-005-0337-8

Cite this article as:
Fourcaud-Trocmé, N. & Brunel, N. J Comput Neurosci (2005) 18: 311. doi:10.1007/s10827-005-0337-8


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 integrate-and-fire (EIF) model, has a response that decays as 1/f in the large frequency limit and describes very well the response of conductance-based models with a Hodgkin-Huxley 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’ ΔT that controls the sharpness of spike initiation: as 1/ΔT for a step change in mean inputs, and as 1/ΔT2 for a step change in the variance in the inputs.


integrate-and-fire neuron noise dynamical response spiking mechanism 

Copyright information

© Springer Science + Business Media, Inc. 2005

Authors and Affiliations

  1. 1.Department of Mathematics, Center for Neural Basis of CognitionUniversity of PittsburghPittsburghUSA
  2. 2.Laboratory of Neurophysics and PhysiologyUMR8119 CNRS - Université René DescartesParis Cedex 06France

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