Labro AJ , Priest MF , Lacroix JJ , Snyders DJ , Bezanilla F .

F31 NS081954 NINDS NIH HHS , R37 GM030376 NIGMS NIH HHS , R01 GM030376 NIGMS NIH HHS , NIH-NS081954 NINDS NIH HHS , NIH-GM030376 NIGMS NIH HHS

	Figure 1. Kv3.1b gating current recordings monitor the VSD movement.(a) Gating currents (Ig) of WT Kv3.1b after depletion of K+ and subsequent application of external TEA to block the remaining ionic current. Ig recordings were obtained using the activation pulse protocol shown on top. The holding potential was −120 mV and cells were depolarized in 5-mV increments from −120 mV to +80 mV. Background leak and capacitive currents were subtracted using a –P/4 protocol. Inset shows a scaled-up view of the Igoff currents obtained by stepping to −90 mV. (b) Pulse protocol to analyse the deactivating Igdeac currents. (c) Voltage dependence of activating charge movement (QV curve, open triangles), which was obtained by integrating the Igoff currents from pulse protocols shown in a (data are shown as average±s.e.m., n=6). For comparison, the ionic GV curve from Supplementary Fig. 1 is displayed (grey circles). (d) Voltage dependence of the average time constants±s.e.m. of Igac (τIgac, open triangles, n=6) and Igdeac (τIgdeac, black circles, n=6). τIgac kinetics were obtained from fitting the Igac current decays (from pulse protocols shown in a) with a single exponential function. τIgdeac kinetics were obtained by approximating the Igdeac current decays (from pulse protocols shown in b) with a double exponential function and represented values are the weighted time constants. As comparison the ionic τIiac and τIideac kinetics (Supplementary Fig. 1) are displayed in grey circles and triangles, respectively.
	Figure 2. Igdeac kinetics of Kv3.1b as a function of activating pulse duration.(a) Igdeac currents upon very short depolarizations to +40 mV elicited using the pulse protocol shown on top. (b) Superposition of Igdeac recordings from a at −60-mV repolarization following a 0.3-ms (grey, with a scaled version shown in red), a 0.5-ms (blue) and a 1-ms (black) long activating pulse to +40 mV. Note the gradual deceleration in Igdeac with increasing pulse duration. (c) Igdeac currents on different pulse durations at +40 mV (2 ms to 5 s in duration). The protocols were applied in a random order to exclude non-specific or depletion artifacts that might affect the kinetics over time, such as depletion of PIP2 levels57. (d) Left, superposition of Igdeac at −60 mV following 2-, 5- and 10-ms-long activating pulses. Right, superposition of Igdeac at −60 mV following 50-ms (black), 0.2-s (red) and 5-s (blue) long activating pulses. Prolonging the pulse from 2 to 10 ms slowed down Igdeac decay further whereas longer pulses had no additional effect. (e) Voltage dependence of the weighted τIgdeac time constants as a function of activating pulse duration. Data is shown as mean±s.e.m. (n=5). Note the gradual slowing in τIgdeac when depolarization times became longer. (f) Top panel shows the mean±s.e.m. of the weighted τIgdeac time constant at −60 mV as a function of depolarization time (n=5). This plot shows that there are two slowing processes, and fitting this relation with a double exponential function indicated that the deceleration in τIgdeac developed with a fast time constant (τf) of 1.8±0.7 ms and a slower component (τs) of 6.3±0.6 ms (n=5). The bottom panel displays a superposition of the same Igdeac kinetics and a scaled ionic current activation (the first spike in ionic current trace is the remaining capacitive transient). Note that the second slowing process (τs) matched the time course of channel opening.
	Figure 3. Iideac kinetics of Kv3.1b as a function of activating pulse duration.(a) Ionic current deactivation (Iideac) of Kv3.1b elicited using the pulse protocols shown on top. From left to right the activating pulse at +40 mV was increased from 5 to 50 ms, and to 100 ms. (b) Left panel shows a superposition of Iideac at −10 mV following a 5-ms (black), a 50-ms (red) and a 100-ms (blue) long activating pulse. Right panel displays a superposition of the same Iideac currents after rescaling them. Note the slowing in Iideac decay time (τIideac) when the duration of the activating pulse was increased. (c) Voltage dependence of the weighted τIideac as a function of activating pulse duration at +40 mV, shown as mean±s.e.m. (n=5). When the duration time was increased from 2 ms (white) up to 50 ms (green) there was a gradual deceleration in τIideac. Note that depolarizations longer than 50 ms in duration did not cause any further significant changes in τIideac. (d) Weighted τIideac at −60 mV as a function of depolarization time. This plot shows, in contrast to Igdeac kinetics, that the Iideac kinetics displayed only a single slowing process, which developed with a time constant of 6.6±1.7 ms (n=5, data represented as mean±s.e.m.).
	Figure 4. Kv3.1b relaxes from a pre-active state in the presence of 4-AP.(a) Igdeac currents of Kv3.1b in the presence of 1 mM 4-aminopyridine (4-AP) with different activating pulse durations at +40 mV. (b) Top panel, superposition of Igdeac at −60 mV on a 1-ms (black), 5-ms (blue) and 10-ms (red) long depolarization to +40 mV. Bottom panel, superposition of the same Igdeac currents after normalization. Note the gradual deceleration in Igdeac decay as the activating pulses are prolonged. (c) Igdeac kinetics (τIgdeac) as a function of depolarization time in the presence of 1 mM 4-AP, displayed as mean±s.e.m. (n=5). Even in the presence of 1 mM 4-AP there was a noticeable deceleration in τIgdeac that developed relatively quickly. For example, compare τIideac on a 0.3-ms (pink) and a 3-ms (green) activating pulse at+40 mV. (d) Weighted τIgdeac at −60 mV as a function of the activating pulse duration in both the absence (grey) and presence of 1 mM 4-AP (red), shown as mean±s.e.m. (n=5). τIgdeac was slowed down in presence of 4-AP, a deceleration that developed over a similar time window as the fast slowing process (τf) in control conditions.
	Figure 5. Kv3.1b displays a hooked ionic tail current on short activating pulses.(a) Kv3.1b deactivating ionic currents on a 1-ms activating pulse to +40 mV. A resurgent K+ (hooked tail) current was observed on the subsequent repolarization to potentials below the threshold for channel opening, which localizes around −10 mV (Supplementary Fig. 1c). (b) Kv3.1b deactivating ionic currents on a 2-ms (left panels) or a 5-ms (right panels) activating pulse to +40 mV. When the activating pulse was prolonged (for example, 5 ms), the resurgent K+ current disappeared gradually. See also Supplementary Fig. 3. (c) Deactivating ionic currents (Iideac) of the Shaker channel using similar pulse protocols. Since the τIiac kinetics of Shaker are slightly faster than those of Kv3.1b, even shorter activating pulses were applied. However, in contrast to Kv3.1b, the Shaker channel never displayed a hooked tail current even on activating pulses as short as 0.5 ms (left panels) or 1 ms (recordings on the right). (d) Normalized amplitude of the resurgent K+ current in Kv3.1b on a repolarization to −10 mV as a function of activating pulse duration. On very short activating pulses (for example, 0.5 ms), the amplitude of the hooked tail amounted to ∼23% of the total tail current amplitude. When the duration of the activating pulse was prolonged, the amplitude of the resurgent K+ current decreased exponentially with a time constant of 1.7±0.8 ms (grey line, n=5, data represented as mean±s.e.m.).
	Figure 6. A chimeric Shaker channel with Kv3.1b's S3–S4 linker generates a resurgent K+ current.(a) On top, a cartoon of the topology of a Kv α-subunit composed of six transmembrane segments (S1–S6) with the VSD's S3–S4 linker highlighted in grey. Below a sequence alignment of the S3–S4 linker of Shaker and the different Kv3 family members. (b) Representative ionic Iiac current recordings of the Shaker_S3S4_Kv3.1 chimera elicited with the pulse protocol shown on top. See also Supplementary Fig. 4. (c) Weighted time constants±s.e.m. of channel gate opening (τIiac, n=9) and closing (τIideac) for the Shaker_S3S4_Kv3.1 chimera (black circles, n=4). The time constants for Kv3.1b (grey) and Shaker (open) are taken from Fig. 1d and redisplayed as comparison. (d) Iideac currents of the Shaker_S3S4_Kv3.1 chimera elicited at 0 mV (left recording) and −10 mV (right recording) on a 1-ms activating pulse to +40 mV, respectively. On such brief activating pulses, the Shaker_S3S4_Kv3.1 chimera displayed a resurgent K+ (hooked tail) current. (e) Iideac at −10 mV elicited on a 5-ms activating pulse to +40 mV. Note the absence of a resurgent K+ current. (f) Normalized amplitude of the resurgent K+ current on a repolarization to −10 mV as a function of activating pulse duration. The amplitude of the resurgent K+ current was maximally about 25% of the total tail current amplitude, and decreased in amplitude when the activating pulse was prolonged (the loss of a resurgent K+ current developed with a time constant of 1.2±0.4 ms, n=5, data shown as mean±s.e.m.).
	Figure 7. A Markov model recapitulates a resurgent K+ current based on a deceleration of VSD return.(a) A simplified state model of the VSD and pore, modified from ref. 34. For clarity, we have excluded the open stabilized state that is linked to channel gate opening. The proposed pathway followed by the Shaker channel is highlighted in blue, while that followed by the Kv3.1b channel is in red. (b) Four-state Markov model of the voltage-sensing domain of Kv3.1b with three non-conducting and one conducting state (channel gate status is represented below between parentheses). The rate constants and valences of the different state transitions are represented in Supplementary Table 1. (c) The four-state Markov model depicted in b could recapitulate Kv3.1b ionic current activations well using parameters based on experimental data (see Methods and Supplementary Table 1). (d) Under simulation of activation pulse protocols that produce resurgent K+ currents experimentally, resurgent K+ ionic currents were also generated by this four-state model (black trace, 0.8 ms). As in experimental results, extending the duration of the depolarizing pulse dramatically reduced the resurgent K+ current (pink trace, 1.5 ms; green trace, 5 ms). (e) A threefold acceleration of the rate of return from the relaxed state (βl) with respect to the reference trace (black) reduced this resurgent K+ current (red trace), while slowing the rate of return enhanced it (blue trace), suggesting that this is a critical parameter by which the resurgent K+ current in Kv3.1b is generated in this model. For exact rate constants, please see Supplementary Table 1.

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