Firing frequency of leaky integrate-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 τ' is much smaller than the membrane time constant τ. 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 τ' is proportional to the square root of the ratio between these time constants, √τ'/τ. 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 τ' > 0 can be reduced to that of the basic IF neuron (corresponding to τ' = 0) using an 'effective' threshold which has a linear dependence on √τ'/τ. Numerical simulations show a very good agreement with the analytical result, and permit an extrapolation of the 'effective' threshold to higher orders in √τ'/τ. The obtained frequency agrees with simulation data for a wide range of parameters.