The mean and instantaneous firing rate responses of the fractional model to constant input.

(A) Two levels of hyper-polarizing current followed by the same depolarizing current result in different spiking patterns. (B) The instantaneous firing rate against time for different conditions described in A. (C) The instantaneous firing rates against time for identical hyper-polarizing current (−3 nA) with different durations. (D–F) Comparison of mean and instantaneous firing rates. (D) Top: Applying a hyper-polarizing (pre-stimulus low, dashed lines) current before application of current steps to calculate firing rate responses. Bottom: as in the Top but applying a depolarizing (pre-stimulus high, solid lines) current. (E) The mean firing rates (mean FR) vs injected current show Type I response for both (pre-stimulus low) and (pre-stimulus high) current input paradigms described in D. The dashed and solid lines corresponding to pre-stimulus low and high, respectively, overlap. (F) The instantaneous firing rate to the stimulations described in D calculated from the first inter-spike interval depends on past activities. Dashed lines correspond to pre-stimulus low paradigm, solid lines correspond to pre-stimulus high.