Information filtering in resonant neurons

Neuronal information transmission is fre- quency specific. In single cells, a band-pass like frequency preference can arise from the subthreshold dynamics of the membrane potential, shaped by properties of the cell's membrane and its ionic channels. In these cases, a cell is termed resonant and its membrane impedance spectrum exhibits a peak at non-vanishing frequencies. Here, we show that this frequency selectivity of neuronal response amplitudes need not translate into a similar frequency selectivity of information transfer. In particular, neurons with resonant but linear subthreshold voltage dynamics (without threshold) do not show a resonance of information transfer at the level of subthreshold voltage; the corresponding coherence has low-pass characteristics. Interestingly, we find that when combined with nonlinearities, subthreshold resonances do shape the frequency dependence of coherence and the peak in the subthreshold impedance translates to a peak in the coherence function. In other words, the nonlinearity inherent to spike generation allows a subthreshold impedance resonance to shape a resonance of voltage-based information transfer. We demonstrate such nonlinearity-mediated band-pass filtering of information at frequencies close to the subthreshold impedance resonance in three different model systems: the resonate-and-fire model, the conductance-based Morris-Lecar model, and linear resonant dynamics combined with a simple static nonlinearity. In the spiking neuron models, the band-pass filtering is most pronounced for low firing rates and a high variability of interspike intervals, similar to the spiking statistics observed in vivo. We show that band-pass filtering is achieved by reducing information transfer over low-frequency components and, consequently, comes along with an overall reduction of information rate. Our work highlights the crucial role of nonlinearities for the frequency dependence of neuronal information transmission.