Phase-response approach to firing-rate selectivity in neurons with subthreshold oscillations

Subthreshold oscillations provide neurons with a filtering mechanism that allows their membrane potential to respond selectively to oscillatory currents depending on their frequency. On the other hand, the phase of such oscillations is known to affect the precise timing at which action potentials can be elicited by input spikes. Here we study the combined effect of these two properties by examining the response of a model neuron to periodic spike trains of defined frequency, in the presence of subthreshold oscillatory activity. Numerical results show a marked resonance with the input firing rate, irrespective of the initial relative phase between the input spike train and the intrinsic subthreshold oscillation. This behavior can be understood in terms of a delayed phase transition curve, from which an iterative map can be built that describes the evolution of the phase response to the periodic succession of input spike perturbations. Depending on the input period, the map exhibits stationary, periodic, or chaotic dynamics that predict in a quantitative way the response of the neuron to the spike train. Propagation of the spike train through a chain of neurons is also examined, and the resonant behavior is seen to be enhanced upon propagation.