Frequency-dependent response properties of adapting spiking neurons

The dynamics of a population of integrate and fire (IF) neurons with spike-frequency adaptation (SFA) is studied. Using a population density approach and assuming a slow dynamics for the variable driving SFA, an equation for the emission rate of a finite set of uncoupled neurons is derived. The system dynamics is then analyzed in the neighborhood of its stable fixed points by linearizing the emission rate equation. The information transfer properties are then probed by perturbing the system with a sinusoidal input current: despite the low-pass properties of the dynamical variable associated with SFA, the adapting IF neuron behaves as a band-pass device and a phase-lock condition appears at a frequency related to the characteristic time constants of both neuronal and SFA dynamics. When a finite set of neurons is considered, the power spectral density of the pooled firing rates shows for intermediate ω a rich pattern of resonances. Theoretical predictions are successfully compared to numerical simulations.