Predicted state occupancies and peak current decrement during trains of different frequencies. (A) Schematic of pulse train design and time points used for calculation of occupancies. Trains of twenty 5-ms depolarizations to 0 mV were evoked from a holding potential of −80 mV (e.g., Fig. 8), with interpulse intervals of 10 ms (66.7 Hz), 95 ms (10 Hz), 245 ms (4 Hz), or 995 ms (1 Hz). Red arrows mark time points immediately before depolarizations to 0 mV, at which occupancies prestimulus were determined. The fraction of noninactivated channels at this point defines the effective peak current activated during the subsequent depolarization. Green arrows mark the time point immediately after termination of the depolarizing pulse. The fraction of channels in slow- and fast-recovering inactivated states defines the fraction of fast- and slow-recover components that one would predict during recovery intervals begun at these time points. To determine fractional occupancies, the following assumptions and calculations were made. First, beginning from a holding potential of −80 mV and from the steady-state inactivation curve of Fig. 1 E, the fraction of available channels is 0.95, with 0.025 each in slow and fast inactivated states. Second, we assume that whatever the fraction of channels activated by a depolarization, half will inactivate into fast recovery pathways and half into slow recovery pathways. Third, the fraction of channels that inactivated into each path during the 5-ms depolarization are incremented by the fraction of channels that remained in fast and slow recovery paths before the depolarization. These sums then define the fractions of channels in fast and slow recovery paths, if recovery was then allowed to proceed. Fourth, for each recovery interval (whether 10, 95, 245, or 995 ms), the time constants for fast and slow recovery from Fig. 3 C at −80 mV were used to calculate the fraction of fast or slow inactivated channels that would be expected to recover from inactivation during that interval. This then allows determination of the fractional occupancies before each subsequent depolarization. (B) The decrement in peak Nav current based on determination of fractional availability before each 5-ms depolarization was determined and plotted as a function of number of the pulse in a train for each of the indicated frequencies based on inactivation time constants from Fig. 3. Compare with measured decrements in depolarization-evoked Nav currents during trains in Fig. 8. (C) Replot of the values in B as a function of time. (D) The calculated state occupancies for channels available for activation (immediately before each 5-ms depolarization), channels in fast recovery inactvated states, and channels in slow recovery inactivated states are plotted for, from top to bottom, trains of 1, 4, 10, and 66.7 Hz. Note that for train frequencies or 1, 4, and 10 Hz, essentially all channels that inactivate into fast recovery inactivated states recover from inactivation between each depolarization, while at 66.7 Hz, there is an initial increase in the fraction of channels in fast recovery states for early pulses, which then decreases as occupancy of channels in slow recovery states increases. (E) State occupancies for channels in fast recovery pathways and slow recovery pathways immediately following the 5-ms depolarization are plotted for, from top to bottom, trains at 1, 4, 10, and 66.7 Hz, respectively. In all cases, time constants were taken from Fig. 3 C (τ_f = 16 ms; τ_s = 388 ms) and used for all trains. (F) As in E, but values for τ_f and τ_s were assumed to vary with train frequency as in Fig. 8 G, for which τ_f becomes slower as train frequency is increased. For train frequencies of 1, 4, and 10 Hz, the recovery intervals are sufficiently long that fractional occupancies are similar for the small differences in time constants used. At 66.7 Hz, changes in the fast recovery time constant result in substantial changes in fractional recovery during the 10-ms recovery interval, thereby slowing the decrease in occupancy of channels in fast recovery states. (G) Changes in the fraction of fast recovery following a 10-pulse train at various frequencies are plotted, showing the data plotted from Fig. 8 F, along with the calculated occupancy of fast recovery states from E, and also the occupancies from F. Although peak current amplitudes during a train at 10 Hz fall to levels <0.05, depending on apparent time constants of fast inactivation, fractional occupancy of channels in fast recovery states can still be as much as 0.2, generally consistent with experimental observations (Fig. 7 E and Fig. 8 G).