Effects of Synaptic Noise and Filtering on the Frequency Response of Spiking Neurons

Noise can have a significant impact on the response dynamics of a nonlinear system. For neurons, the primary source of noise comes from background synaptic input activity. If this is approximated as white noise, the amplitude of the modulation of the firing rate in response to an input current oscillating at frequency $\omega$ decreases as $1/\sqrt{\omega }$ and lags the input by 45° in phase. However, if filtering due to realistic synaptic dynamics is included, the firing rate is modulated by a finite amount even in the limit $\omega \to \infty$ and the phase lag is eliminated. Thus, through its effect on noise inputs, realistic synaptic dynamics can ensure unlagged neuronal responses to high-frequency inputs.