Rate dynamics in integrate-and-fire neurons: two regimes and multiple time scales

Arguing from first principles, it is shown that firing rates in integrate-and-fire neurons can be written as a product of two terms, one governed chiefly by the membrane voltage, the other by the synaptic current. The analysis also reveals that in the so-called regular firing regime, rate encoding follows the mean synaptic current, whereas the distribution of membrane voltage affects the degree of phase synchrony induced by input transients. In the randomly firing or "balanced" regime, both the variance and the mean of the current and voltage distributions contribute, and rate encoding is governed by five distinct time constants.