Multiple time scales in a model of a membrane patch. a, Fraction of inactivated channels after a depolarizing voltage applied for various durations, plotted as a function of time from end of depolarization. Model parameters: β = 1 Hz; α0 = 0.8 Hz. b, Characteristic time scale for recovery, defined by the decrease of inactivated fraction to a given threshold, plotted as a function of stimulation duration. These times obey a power-law scaling relationship with a power of ∼1. This scaling is weakly dependent on the choice of threshold for recovery (0.5 for top lines, crosses, and circles and 0.6 for bottom line). The same scaling is observed under cumulative inactivation; the dashed line with crosses shows the results for a periodic pulse train stimulus (25 Hz).