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The Journal of Neuroscience, December 17, 2003, 23(37):11628-11640
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Behavioral/Systems/Cognitive
How Spike Generation Mechanisms Determine the Neuronal Response to Fluctuating Inputs
Nicolas Fourcaud-Trocmé,
David Hansel,
Carl van Vreeswijk, and
Nicolas Brunel
Centre National de la Recherche Scientifique Unité Mixte de Recherche 8119, Neurophysique et Physiologie du Système Moteur, Unité de Formation et de Recherche Biomédicale, Université Paris 5 René Descartes, 75270 Paris Cedex 06, France
This study examines the ability of neurons to track temporally varying inputs, namely by investigating how the instantaneous firing rate of a neuron is modulated by a noisy input with a small sinusoidal component with frequency (f). Using numerical simulations of conductance-based neurons and analytical calculations of one-variable nonlinear integrate-and-fire neurons, we characterized the dependence of this modulation on f. For sufficiently high noise, the neuron acts as a low-pass filter. The modulation amplitude is approximately constant for frequencies up to a cutoff frequency, fc, after which it decays. The cutoff frequency increases almost linearly with the firing rate. For higher frequencies, the modulation amplitude decays as C/f , where the power depends on the spike initiation mechanism. For conductance-based models, = 1, and the prefactor C depends solely on the average firing rate and a spike "slope factor," which determines the sharpness of the spike initiation. These results are attributable to the fact that near threshold, the sodium activation variable can be approximated by an exponential function. Using this feature, we propose a simplified one-variable model, the "exponential integrate-and-fire neuron," as an approximation of a conductance-based model. We show that this model reproduces the dynamics of a simple conductance-based model extremely well. Our study shows how an intrinsic neuronal property (the characteristics of fast sodium channels) determines the speed with which neurons can track changes in input.
Key words: populations of spiking neurons; noise; dynamics; sodium channel; integrate-and-fire model; conductance-based model
Received July 28, 2003;
revised October 15, 2003;
accepted October 15, 2003.
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