Firing-rate resonance in a generalized integrate-and-fire neuron with subthreshold resonance

Neurons that exhibit a peak at finite frequency in their membrane potential response to oscillatory inputs are widespread in the nervous system. However, the influence of this subthreshold resonance on spiking properties has not yet been thoroughly analyzed. To this end, generalized integrate-and-fire models are introduced that reproduce at the linear level the subthreshold behavior of any given conductance-based model. A detailed analysis is presented of the simplest resonant model of this kind that has two variables: the membrane potential and a supplementary voltage-gated resonant variable. The firing-rate modulation created by a noisy weak oscillatory drive, mimicking an in vivo environment, is computed numerically and analytically when the dynamics of the resonant variable is slow compared to that of the membrane potential. The results show that the firing-rate modulation is shaped by the subthreshold resonance. For weak noise, the firing-rate modulation has a minimum near the preferred subthreshold frequency. For higher noise, such as that prevailing in vivo, the firing-rate modulation peaks near the preferred subthreshold frequency.