Firing frequency of leaky intergrate-and-fire neurons with synaptic current dynamics.
We consider a model of an integrate-and-fire neuron with synaptic current dynamics, in which the synaptic time constant tau' is much smaller than the membrane time constant tau. We calculate analytically the firing frequency of such a neuron for inputs described by a random Gaussian process. We find that the first order correction to the frequency due to tau' is proportional to the square root of the ratio between these time constants radicaltau'/tau. This implies that the correction is important even when the synaptic time constant is small compared with that of the potential. The frequency of a neuron with tau'>0 can be reduced to that of the basic IF neuron (corresponding to tau'=1) using an "effective" threshold which has a linear dependence on radical tau'/tau. Numerical simulations show a very good agreement with the analytical result, and permit an extrapolation of the "effective" threshold to higher orders in radical tau'/tau. The obtained frequency agrees with simulation data for a wide range of parameters.
Brunel
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LPS, Ecole Normale Supérieure, 24 rue Lhomond, Paris Cedex 05, 75231, France.
Sergi
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D000818:Animals; D003198:Computer Simulation; D008564:Membrane Potentials / Q000502:physiology; D008959:Models, Neurological; D009474:Neurons / Q000502:physiology*; D009435:Synaptic Transmission