Voltage Sensitivity and Gating Charge in Shaker and Shab Family Potassium Channels

Voltage-gated ion channels are remarkably sensitive to membrane potential changes. Large charge movements in the channel protein couple changes in membrane potential to the channel opening process. In the skeletal muscle sodium channel and the Shaker potassium channel, the size of this “gating charge” movement is seen to be equivalent to the displacement of 12–14 elementary charges entirely across the membrane (Hirschberg et al. 1995; Schoppa et al. 1992; Aggarwal and MacKinnon 1996; Noceti et al. 1996). The large charge movement makes sense for the sodium channel, where the resulting high sensitivity helps to establish a firing threshold for excitable cells. For transient potassium channels such as Shaker, the high sensitivity is important to allow channel activation during threshold depolarization, enabling these channels to control repetitive firing rates in neurons (Neher 1971; Connor and Stevens 1971a,Connor and Stevens 1971b). On the other hand, high voltage sensitivity in delayed-rectifier potassium channels is arguably less important: these channels need only be activated by the large excursions of action potentials, and indeed the presence of large charge movements can be detrimental. As pointed out by Hodgkin 1975, gating charge movements serve as a capacitive “load” on the action potential, increasing metabolic requirements and decreasing the velocity of action potential propagation in excitable cells.

The various voltage-gated potassium channels contain four α subunits; many of these subunits show differences in their S4 regions that are suggestive of differing amounts of gating charge. The S4 region is thought to be the primary voltage-sensing region (Stühmer et al. 1989; Aggarwal and MacKinnon 1996; Seoh et al. 1996); in the Shaker family it has seven positively charged residues and in the other potassium channel families it has between four and six. Some mutations in Shaker that reduce the number of basic residues reduce the apparent voltage sensitivity, but other mutations leave the voltage sensitivity apparently unchanged (Smith-Maxwell et al. 1998). It should be pointed out that in members of Shaker and other related families, the acidic residues in S2 and S3 are conserved; one of these, the second glutamate in S2, has also been implicated in the voltage-sensing function (Seoh et al. 1996).

Because of uncertainties in past measurements of charge movement based on voltage sensitivity, and to complement the studies in which the magnitude of gating charge has been changed through mutations, we report here measurements of the gating charge in four “native” voltage-gated potassium channel types using improved methods.

Gating charge movement is most directly measured by integrating the gating currents that are recorded from membranes having a high density of channels, under conditions in which no ionic current flows through the channels. To then evaluate the charge movement in a single channel, the number of channels contributing to the gating current must be estimated; this has been done for Shaker channels using either fluctuation analysis (Schoppa et al. 1992; Seoh et al. 1996; Noceti et al. 1996) or radioligand binding (Aggarwal and MacKinnon 1996). The results of the two methods agree well, yielding values of the single-channel charge of 12–14 e_o. An alternative approach is called the “limiting-slope” method, and is analogous to the determination of the Hill coefficient of a binding reaction. It involves measuring the dependence of the channel open probability, P, on membrane potential V. Given a channel that opens with depolarization and has a single open state, then asymptotically, as V → −∞ (and P → 0), the apparent charge,

approaches the total charge movement q_T (Almers 1978). The limiting-slope method has been applied to Shaker and some mutants (Noceti et al. 1996; Seoh et al. 1996) and its results are in good agreement with the direct charge measurements outlined above.

The limiting-slope method has the advantage that it measures charge that is actually involved in opening the channel. Its asymptotic nature, on the other hand, poses a problem: how can one be sure that q_s is evaluated at sufficiently negative V? Two recent advances now allow this problem to be addressed in a rigorous fashion. The first is the development by Hirschberg et al. 1995 of a method for measuring very small P values at the very negative membrane potentials where one hopes that the asymptotic limit is reached. The method involves measuring single-channel events in membrane patches having large numbers of channels N. For channels having brief open times, the aggregate open probability NP can be measured in such patches down to values of 10⁻⁴ or less; with N on the order of 10³, P can be reliably estimated down to values of 10⁻⁷ or less.

The second advance is the theory of Sigg and Bezanilla 1997, which shows that an ordinary gating current measurement can be used as an independent test of the extrapolation of q_s values to estimate q_T. Let Q̂Vbe the macroscopic gating charge that is obtained by integrating the gating current, normalized such that Q̂−∞=0andQ̂ +∞=1. Then, in the case of a channel that is found in its single open state at large depolarizations, the apparent charge q_s is related to Q̂by:

Thus, given experimentally determined values of q_s and Q̂, a one-parameter curve fit can be used to estimate the value of q_T.

In this paper, we incorporate these advances to the limiting-slope method and apply it to the determination of charge movements in homomeric channels encoded by the Drosophila potassium channel genes Shaker and Shab, and from the rat homologues Kv1.1 and Kv2.1. A comparison of these channel types is interesting in view of their differing amino acid sequences (Fig. 1). Shaker and Kv1.1 both have seven basic residues in the S4 region, while Shab and Kv2.1 have five.

Shaker H4 with N-type inactivation removed and the W434F mutant were subcloned into the vector pGEM, linearized with Not I and transcribed with T7 RNA polymerase. The final cRNA concentration was 1 μg/μl. Kv1.1 was subcloned into pGEMHE, linearized with PstI and transcribed using T7 polymerase. Shab was subcloned in a modified version of Bluescript for oocyte experiments. Linearization of cDNA was carried out with NotI and transcription with T3 polymerase.

The rat clone Kv2.1-Δ7 (DRK1-Δ7), derived from DRK1 (Frech et al. 1989) was provided by Drs. R. MacKinnon (The Rockefeller University, New York, NY) and S. Aggarwal (Harvard Medical School, Cambridge, MA). This construct has seven point mutations in the putative pore mouth that permit very high affinity binding (K_d ≈ 15 pM) of the channel blocker Agitoxin-1 (Gross et al. 1994). Kv2.1-Δ7 in Bluescript was linearized with NotI, transcribed with T7 RNA polymerase and resuspended in water to a final concentration of 0.3–0.5 μg/μl.

Xenopus laevis oocytes were harvested under anesthesia and defolliculated by incubation in Ca⁺²-free OR2 solution supplemented with 2 mg/ml collagenase 1A for 1 h. Oocytes were incubated at 20°C in a solution containing (mM): 96 NaCl, 2 KCl, 1.8 CaCl₂, 1 MgCl₂, 5 HEPES, and injected 1 or 2 d after harvesting with 50 nl of cRNA solution with a Nanostepper (Drummond Scientific Co.) using pipettes of 20-μm opening diameter. Oocytes were used for experiments 1–7 d after injection.

In some cases, oocytes expressing Kv2.1-Δ7 were incubated in the presence of Agitoxin-1 at a concentration of 1–3 μM for the period of channel expression. This resulted in an increase in expression of two- to threefold.

The Shab channel was expressed in Sf9 cells for the recording of gating currents in whole cells. The Bac-to-Bac™ recombinant baculovirus system (GIBCO BRL) was used. After transfer of the Shab gene to a bacmid vector, Sf9 cells at 70% confluence were transfected with lipofectin in Sf900 medium (GIBCO BRL). The culture medium containing the Shab baculovirus was collected after 48 h of culture and stored at 4°C. After infection, expression of channels in cells was assessed by electrophysiological recording. Sf9 cells were maintained in an incubator at 26°C in 1% CO₂.

Patch-clamp recordings were obtained using standard techniques. All recordings reported here were made in the cell-attached configuration, for maximum patch stability. Oocytes were bathed in a depolarizing solution that effectively zeroed the membrane potential as checked with a two-microelectrode voltage clamp. The bath solution contained (mM): 120 K-aspartate, 20 KCl, 1.8 CaCl₂, 10 HEPES, adjusted to pH 7.4. Unless otherwise stated in the figure legends, pipettes were filled with a solution of the following composition (mM): 40 K-aspartate, 20 KCl, 1.8 CaCl₂, 60 N-methyl-d-glucamine (NMDG)¹-aspartate, 10 HEPES, pH 7.4. Gating currents of Kv2.1-Δ7 were recorded using a similar solution that contained 120 mM NMDG-aspartate and no K⁺, and included 1 μM Agitoxin-1. The same solution was used for Shaker gating currents without the Agitoxin-1. For gating currents, 20 sweeps were averaged at every voltage. A P/5 subtraction protocol was used to subtract linear capacity and leak currents, using a leak-holding potential of −120 mV.

Pipettes were pulled from soft borosilicate glass capillaries (Kimax-51) and had resistance in the range 1.5–3 MΩ. Currents were recorded with an EPC-9 amplifier running the Pulse software (HEKA Elektronik) on a Macintosh computer. In macroscopic current recordings, the linear current components were subtracted by the use of a P/5 protocol and were filtered at 2.5 kHz (−3 dB) with a Bessel filter and sampled at 15 kHz. Single-channel recordings were obtained in the same patches as macroscopic currents, with the same filter cut-off frequency and a sample frequency of 10 kHz. Null-trace averages were used to subtract the linear capacitive and leak currents. All recordings were obtained at room temperature (22°C).

Whole-cell gating currents in Sf9 cells were recorded using the following solutions (mM): Pipette: 150 NMDG-HCl, 10 MOPS, 5 EGTA, 1 MgCl₂, pH 7.2; Bath: 150 NMDG-HCl, 10 MOPS, 10 CaCl₂, 1 MgCl₂, pH 6.7. Recording electrodes had a resistance of 0.5–1 MΩ and were coated with Sylgard^® to reduce capacitance. No series resistance compensation was used. The capacitance of the Sf9 cells used for gating current recordings ranged from 20 to 42 pF. The settling time of capacity transients was ∼100 μs. The subtraction protocol was similar to that used for Kv2.1.

For macroscopic currents, the voltage dependence of the open probability was estimated from tail current measurements; the size of the tail current is proportional to the channel open probability at the end of the preceding depolarization. We averaged the first millisecond of tail current at −100 mV in the case of Kv2.1 channels. For Shaker and Shab, the first 300 μs of tail currents at −90 mV were averaged and for Kv1.1, 400 μs was averaged. The values obtained were in very close agreement to the more traditional method of measuring P from the steady state currents and normalizing by the instantaneous current–voltage curve. Contamination of the ionic tail currents by gating currents was taken to be negligible because OFF gating current amplitudes were <0.5% of the maximal tail current amplitude.

Estimation of the number of channels in a patch of membrane was done by nonstationary noise analysis (Sigworth 1980; Heinemann and Conti 1992). The mean and variance were calculated from 50–60 current traces elicited by depolarizing steps to the indicated membrane potential filtered at 5 kHz. Pulses were delivered at 0.5-s intervals. The variance estimation made use of groups of four sweeps, to reduce the influence of drifting baselines and channel rundown. The data were displayed in the form of mean-variance relationships and fitted to the equation:

where σ² is the variance, I is the mean current, i is the single channel current, and n is the number of channels. The maximal open probability was then obtained as P_max = I_max/Ni.

The analysis of the single channel traces to obtain the time-dependent NP values was carried out as follows. The current traces were leak subtracted using a template of averaged null sweeps (sweeps that contain no channel openings), digitally filtered with a Gaussian filter to 1.5 kHz and analyzed with the 50% threshold crossing method (Colquhoun and Sigworth 1995) with multiple thresholds to allow detection of overlapping channel currents. This produced an idealized record of open and closed events. The idealizations of 100–1,000 sweeps were then averaged, with null traces included. The steady state average value, typically computed from the last 150 ms of the averaged idealization, was taken as the final value for NP. Open and closed dwell time histograms were obtained using a single threshold from sweeps with no overlapping openings and constructed according to the log-binning technique (Sigworth and Sine 1987) and probability density functions were fitted by the method of maximum likelihood.

The apparent charge q_s was estimated from experimental data by discretizing in the following way. Given open probabilities P₁ and P₂ obtained at adjacent voltages V₁ and V₂, and letting V′ = (V₁ + V₂)/2, we computed q_s as:

The equilibrium voltage dependence of state occupancies was computed according to :

where P_n is the probability of occupancy of state n, K_jis the equilibrium constant for transition from state j − 1 to state j, and the M states are linearly connected.

Statistical quantities are given as mean ± SEM

To extend the previous studies of Shab channel currents (Tsunoda and Salkoff 1995), we first compare Shab channel properties with those of the other channel types. For this study, we have used a Shaker construct having a deletion at the NH₂ terminus to remove fast inactivation, to simplify the determination of steady state open probability. For Kv2.1, we have used a mutant, DRK1-Δ7, that was engineered to bind the pore blocker Agitoxin-1 with high affinity (Aggarwal and MacKinnon 1996; Gross et al. 1994), making possible the measurement of gating currents. Macroscopic currents were obtained in cell-attached patch recordings from mRNA-injected oocytes or in whole-cell recordings from recombinant baculovirus-infected Sf9 cells in the case of Shab channels. Representative current traces are shown in Fig. 2 A. The channel open probabilities P for each channel type approach limiting values between 0.7 and 0.9 for large depolarizations. The voltage-dependence of P for Shaker and Kv1.1 (Fig. 2 B) can be described well by the fourth power of a Boltzmann function, as would be predicted by a simple model incorporating four independently acting voltage sensors (Zagotta et al. 1994). The gating charges estimated from these fits are 11.5 and 7.7 e_o for Shaker and Kv1.1, respectively; it should be emphasized, however, that such gating-charge estimates are strongly dependent on the particular model used. The corresponding fit to the P–V relationship for Shab channels yields an apparent charge of 6.3 e_o, while for Kv2.1 it yields 10.1 e_o (Fig. 2 C).

Activation time constants τ were estimated from exponential fits to the second half of the activation time course of macroscopic currents (Schoppa and Sigworth 1998a). From these fits an estimate of the delay in activation δ was also obtained. Shaker channels show a small activation time constant that is rather weakly voltage dependent with an effective charge of 0.51 e_o; the delay is roughly equal to the time constant and has similar voltage dependence (Fig. 2D and Fig. E) over the positive voltage range. The kinetic features of Kv1.1 channels are nearly identical to those of Shaker, having almost identical activation time constants and delay values, with the main difference being a slightly steeper activation curve.

Like Shaker, Shab channels activate and deactivate quickly, with time constants similar to those of Shaker. Shab channels activate, however, with a smaller delay that is more steeply voltage dependent (Fig. 2 E); this means that at positive voltages these channels show less sigmoidicity in their activation time course than Shaker (Zagotta et al. 1994; Smith-Maxwell et al. 1998). This behavior can be explained if the rate-limiting step for activation (which determines τ; Schoppa and Sigworth 1998a) is less voltage dependent than other steps that determine the delay. The same general phenomenon is seen in Kv2.1, although here the much slower activation is reflected by τ and δ having values that are larger by an order of magnitude.

The time course of charge movement of Shaker, Kv2.1, and Shab channels was directly measured in the form of gating currents. Shaker gating currents were obtained from cell-attached patches in oocytes expressing the nonconducting mutant W434F (Perozo et al. 1993) using the same solutions as those used to record macroscopic ionic currents. The voltage dependence of the charge obtained from integration of ON gating currents is similar to that previously reported, as is the decay time constant of ON currents (Fig. 3B and Fig. C).

Kv2.1 gating currents were also measured in cell-attached patches in oocytes, using Agitoxin-1 to block the ionic currents. The general characteristics are similar to those previously reported (Taglialatela and Stefani 1993) from the cut-open oocyte recording technique. ON gating current decays are approximately five times slower than Shaker's (at 0 mV), but show a steeper voltage dependence of the time constant. Taglialatela and Stefani 1993 observed gating current decay time constants that were very close to the ionic current time constants; however, under our recording conditions and with the mutant channel that we are using, the gating current time constants are severalfold shorter than the ionic current time constants. Thus, we observe a gating current time constant that is similar to the delay of ionic currents but is shorter than the activation time constant. This can be explained if the gating current comes predominantly from early voltage-dependent transitions that give rise to the ionic current delay, and the rate-limiting step comes later in the activation process.

The Kv2.1 charge movement curve lies to the left of the P(V) curve in the voltage axis, as is expected for a channel that has multiple closed states before the open state. The voltage dependence of charge can be fitted to a Boltzmann function with a charge of 2 e_o (Fig. 3 B).

Shab gating currents were recorded in the whole-cell configuration from baculovirus-infected Sf9 insect cells, with ionic currents eliminated through the use of impermeant N-methyl glucamine (NMG) cations. Fig. 3B and Fig. C, compares the voltage dependence of ON charge and the voltage dependence of the time constant of ON currents in these channels. Shab ON gating currents are less voltage dependent than those of Shaker or Kv2.1, and their kinetics are intermediate. Shab OFF gating currents are, however, very different in having a much faster time course than the others. The slow OFF time course in Shaker channels arises from slow initial closing transitions (Zagotta et al. 1994; Schoppa and Sigworth 1998a); in Shab, these transitions presumably proceed much more quickly.

With the high expression obtained with Shaker in oocytes, it was possible to record from patches containing hundreds or thousands of channels. The number N of channels in a patch was estimated by nonstationary fluctuation analysis, using depolarizations to +70 mV. Subsequent recordings using small depolarizing pulses allowed NP to be estimated from the statistics of single-channel events in the same patch. Recordings from a representative patch containing 2,250 channels are shown in Fig. 4 A. The channel openings observed during the small depolarizations were identified as Shaker channels based on their conductance and kinetics.

To obtain the steady state open probability from pulsed data sweeps, we first performed an idealization of the single channel events for each sweep, and then averaged these idealized records. This ensemble average (Fig. 4 B) represents the product NP of the open probability and the number of channels that contribute to the record. No inactivation is visible in these time courses, and because of the high external K⁺ concentration the degree of slow “C-type” inactivation on these channels is expected to be very small (Lopez-Barneo et al. 1993), reducing P by at most 2% at −60 mV (Yang et al. 1996).

At the most negative voltages (−70 to −55 mV), the value of NP changed by about a factor of 10 for each 5-mV change in the depolarization. No openings were detected during the total 450 s of recording at the holding potential of −80 mV. At −80 mV, the mean burst duration is expected to be ∼1.5 ms so that, were a single opening to occur, it would correspond to NP ≈ 3.3 × 10⁻⁶. The fact that no events were observed at −80 mV in this patch or in two others having similar numbers of channels implies that at −80 mV P is smaller than ∼10⁻⁹.

Fig. 4 C shows the result of combining the single channel data with macroscopic activation measurements and the value of n obtained from nonstationary noise analysis. The smallest open probability measured in these patches was ∼10⁻⁷, and the maximum was 0.79. At values of P between 10⁻⁷ and 10⁻⁴ the P(V) relation is very nearly exponential and can be well fitted to the relationship

The charge estimate q_l from this linear fit to the log-transformed P values represents a local average of q_s as defined in ; for these channels it had the value 12.7 ± 0.3 e_o (n = 3).

We performed two tests to determine whether these experiments can provide estimates of the apparent charge that approach the true asymptotic value. First, we computed q_s from at each voltage and compared its behavior with that of two simple models in which P is given by a Boltzmann function or by the fourth power of a Boltzmann function. The comparison is done by plotting the logarithmic slope variable q_s as a function of P, with V being the independent variable (Zagotta et al. 1994; Fig. 4 D). Quite good correspondence is seen with the latter model given a total charge of 13 e_o; were this model correct, our estimated slope q_l would be within 4% of the true limiting slope.

In the second test, q_s(V) is compared with the function, which from should yield identical values. Fig. 4 E makes this comparison for the case q_T = 13 e_o, where it is seen that the voltage dependences are very similar. Most importantly, the charge movement shows very little change below V = ∼70 mV, implying that q_s will remain essentially constant below this membrane potential. On the basis of this fit, we extrapolate the q_s values to obtain an estimate of 13.0 e_o for the total charge q_T.

Rat Kv1.1 (previously called RCK1) is a potassium channel that does not have fast inactivation. Its general gating characteristics are very similar to those of inactivation-removed Shaker and the amino acid sequence in the S4 region is identical (Koren et al. 1990; Fig. 1). Not surprisingly, our limiting-slope estimates of gating charge in Kv1.1 are almost exactly the same as those from Shaker channels. Single-channel estimates of NP show 10-fold changes for 5-mV changes in membrane potential (Fig. 5A and Fig. B). The apparent gating charge q_l computed for values of P between 10⁻⁶ and 10⁻⁴ using , was 11.5 ± 1.3 e_o (n = 3). The smallest open probability attained in this measurement was two orders of magnitude higher than in Shaker, due to a lower density of channels in patches. Nevertheless, estimates of q_s extrapolate well to a value of q_T = 13.0 e_o (Fig. 5 C).

Because of the low channel density, we were unable to record gating currents from patches containing Kv1.1 channels; therefore, we were unable to provide an independent check on the approach to the limiting charge movement. We conclude that q_T is at least 11.5 e_o and is probably near 13 e_o, as is the case with Shaker.

Although no inactivation is apparent in the reconstructed time courses of Fig. 5 B, it is conceivable that slow inactivation or rundown could introduce errors into our estimates for P. We therefore compared the N values obtained from noise analysis before and immediately after delivering the 600 depolarizing pulses to −60 and −50 mV for single-channel analysis of one patch; the values of N were 14 and 12, respectively. If the reduction in the number of channels is caused by inactivation, this indicates that there was at most 14% long-term inactivation. In our experiments, this small amount of inactivation at negative voltages would, if anything, have led to an underestimation of the limiting slope.

Previous estimates of the gating charge of the rat Kv2.1 channel (Taglialatela and Stefani 1993) and the human homologue, hKv2.1 (Benndorf et al. 1994) were in the range 6–7 e_o. These were obtained from model-dependent fitting, a methodology which often underestimates the gating charge. As with Shaker, we were able to record from patches containing hundreds of Kv2.1 channels in which we could measure macroscopic currents at depolarizing voltages and resolve single-channel openings at hyperpolarized voltages. Fig. 6 shows recordings from a patch containing ∼1,650 Kv2.1 channels.

At the most negative voltages (−45 to −65 mV), the value of NP decreased by a factor of ∼10 per 5-mV decrease in depolarization (Fig. 6 B). No openings that could be assigned to Kv2.1 channels were detected at the holding potential of −80 mV in two experiments where the total time of recording at −80 mV was 118 and 180 s and the number of channels N was 967 and 1,250, respectively. The channel burst duration, extrapolated to −80 mV, is ∼10 ms. Were a single burst of openings to occur in one of these records, this would correspond to the open probability P ≈ 4 × 10⁻⁸. Therefore, we take the value of P at −80 mV to be less than ∼4 × 10⁻⁸.

The result of combining the single channel data with the values of N and P_max is shown in Fig. 6 C. The minimum measured value of the absolute open probability in this patch is ∼10⁻⁷ and the maximum, from noise analysis at 70 mV, was 0.71. At values of P between 10⁻⁷ and 10⁻⁴ exponential fits of the P(V) relation yield an apparent charge q_s of 12.1 ± 0.5 e_o. A fourth power Boltzmann function with 12 or 13 e_o total charge (continuous curves) superimposes fairly well on the data (Fig. 6 C) when q_s is plotted as a function of P.

The same charge estimate results in comparing q_s with the macroscopic charge movement. The quantity superimposes well on the q_s data (Fig. 6 D) with the fitted value q_T = 12.5 e_o. Thus, this channel behaves as expected from and the charge movement in the voltage range below that accessible to our q_s measurements is seen to be small. Our best estimate of the total charge for Kv2.1 is therefore 12.5 e_o.

It is unlikely that this estimate of total charge is in error due to inactivation or missed channel events. Inactivation in the Kv2.1 channels was measured with 500-ms prepulses (Fig. 7 A) and was found to be negligible at potentials below −50 mV (Fig. 7 B). Single-channel events at negative voltages show a single open-time component with a mean duration of 8 ms (Fig. 7 C), consistent with the presence of only one open state of the channel. The duration of bursts of openings, ∼15 ms (Fig. 7 D), is essentially voltage independent, always much greater than the detection dead-time of 120 μs; thus, a very small and voltage-independent fraction of events is expected to be missed in the evaluation of NP.

In Xenopus oocytes, the expression of Shab channels was low, producing maximal whole-cell currents of ∼10 μA at +40 mV. To obtain higher channel densities and to allow the possibility of whole-cell recording of Shab gating currents, we established a baculovirus expression system using Sf9 insect cells. The currents obtained in cell-attached patches from Sf9 cells infected with the Shab baculovirus have very similar characteristics to those recorded in patches in oocytes. No voltage-dependent currents were observed in whole-cell recordings from five uninfected Sf9 cells.

Interestingly, single Shab channels in single-channel patches and in recordings from multiple channel patches show a tendency to open to subconductance states. These events arise from Shab channels since direct transitions are observed between the subconductance and the fully open states. Fig. 8 A shows representative current recordings at −70 mV. Indicated are the fully open state and the substate level at 40% of the full open current level. It is evident that the channel can dwell only in the substate or make transitions to the open state with or without having to traverse the substate level.

Subconductance openings are more prominent at negative voltages. At −90 mV, less than one percent of the time is spent in the subconductance level, but 98% of the observed events are subconductance openings. This is illustrated in Fig. 8 B, where all-points histograms of current recordings from multichannel patches at the indicated potentials are shown. The intermediate Gaussian component fitted to the histogram corresponds to the substate and its integral is proportional to the probability of occupancy of the substate. At potentials more negative than −70 mV, the probability of the substate P_s is greater than the probability of the fully open state, P. These probabilities are plotted in Fig. 8 C; it is seen that while P increases monotonically, P_s increases and then decreases with depolarization. This characteristic of P_s, along with its smaller voltage dependence (the apparent charge is only 2.2 e₀ between −90 and −70 mV) is consistent with the sublevel representing an intermediate state in the activation pathway.

The voltage dependence of occupancies of the substate and the fully open state can be described by specific schemes. The steady state occupancy curves in Fig. 8 C were computed from the model shown in that figure in which sequential transitions bring the channel to a substate (S), and then the fully open state. In the model, a parallel pathway also allows direct openings without passing through the substate; this provision is necessary because the substate is traversed in only ∼6% of full openings of the channel. The model yields a limiting slope corresponding to a total charge of 7.2 e_o for the open state and 5 e_o for the substate.

Kinetic analysis of the substate was carried out to characterize the transitions near the open and subconductance states at negative potentials. The rate constants for transitions away from the substate were obtained from the dwell-time distribution in the substate and the fraction of transitions occurring in each particular path. For example, at negative voltages, dwells in the substate were seen to be terminated by transitions to the open state, to a closed state, or transitions to a closed state followed, after a delay of ∼50 ms, by channel opening. The rate constants k_ij were obtained:

where τ_i is the mean dwell time in state i and f_ij is the fraction of all transitions leaving state i that end in state j (Zheng and Sigworth, 1997). Dwell-time distributions in the fully open state were used to obtain rates for transitions to the closed state in the activation pathway identified as C_n, and to the substate, using the same method. Values of the rate constants for transitions near the open state obtained in this way are shown in Fig. 8 D, which is presented as an example of a scheme that can account for the kinetic phenomena we observe. In conclusion, both the steady state and kinetic behaviors are consistent with the subconductance level being associated with a state that is a kinetic intermediate and that is reached with less than the full charge movement.

For the estimation of total charge movement, we ignore dwells at the sublevel because these reflect an intermediate state. Instead, we make use of only the probability P of the fully open state, which is the predominant state at large depolarizations. Sublevel dwells will not affect the estimation of N by noise analysis because they are brief and very rare at the test voltage of +60 mV.

Even ignoring the sublevels, activation of Shab channels is not as voltage dependent as that of Kv2.1. At a holding potential of −90 mV it is possible to observe channel openings, and NP for the fully open state is seen to change only 10-fold for 10-mV depolarizations (Fig. 9A and Fig. B); this is about half the sensitivity seen for the other channel types. In constructing idealized traces, we took care not to confuse overlapping sublevel currents with open-state events; such overlapping events were very rare except at relatively depolarized voltages such as −70 mV. The resulting apparent charge estimate, based on P values between 10⁻⁵ and 10⁻³ was q_l = 7.1 ± 0.3 e_o (n = 2; Fig. 9 C). Plotting q_s against P, the asymptotic value appears to be 7.5 e_o (Fig. 9 D). Similarly, low apparent charge values were seen in recordings from Shab channels in oocytes, where q_l = 7.5 ± 0.3 e_o (n = 3) when evaluated over the range of P values from 10⁻⁶ to 10⁻⁴. Whole-cell recordings of gating currents in Sf9 cells allow the comparison of macroscopic charge movements with the voltage dependence of q_s. The quantity superimposes fairly well on q_s values with q_T = 7.5 e_o (Fig. 9 E) and demonstrates that very little charge movement occurs at voltages negative to −90 mV. We therefore take 7.5 e₀ to be the estimate for the total charge in this channel.

Sigg and Bezanilla 1997 point out that limiting-slope estimates of charge can be in error when there are multiple open states of a channel. For example, our estimate for Shab charge could be in error if there were an additional open state O′, having indistinguishable conductance, connected to the main open state O through a voltage-dependent transition. For example, Scheme I could account for the “missing” 5 e_o of charge. To be consistent with the relatively shallow activation curve (Fig. 8 C), the transition from O to O′ would necessarily occur in the voltage range of −40 mV and above. This additional transition will give rise to a large gating-charge movement that occurs at depolarized potentials.

A comparison of the voltage dependence of q_s with that predicted from Q(V) indeed shows a small discrepancy of this sort: a minor component of the gating charge Q(V) moves at potentials above −40 mV, where the q_s curve is essentially flat. This component is, however, much smaller than that expected from Scheme I and therefore is unlikely to arise from an additional open state. The discrepancy between q_s and Q(V) is in fact similar to the discrepancies seen in Shaker and Kv2.1 channels (Fig. 4 E and 6 D). Because the discrepancy occurs in the voltage range of channel opening, we believe that it arises from an interaction of permeant ions with the open channel. Effects of permeating ions on activation gating have been studied in sodium channels (Townsend et al. 1997) and potassium channels (Swenson and Armstrong 1981; Demo and Yellen 1992; Chen et al. 1997) and effects on Shaker channels have been noted (Stefani et al. 1994; Schoppa and Sigworth 1998a). In most cases, the presence of permeant ions is seen to result in the stabilization of the open state; meanwhile, blocking the ionic current with a toxin or pore mutation has an effect similar to the removal of extracellular ions.

We expect that, in the presence of permeant ions, the equilibrium of the final opening transition is shifted toward the open state, tending to increase the cooperativity of channel opening and resulting in a steeper voltage dependence of q_s. In our gating-current experiments, permeant ions were either absent or prevented from entering the pore, so the cooperative effect would be absent, yielding the shallower Q(V) curves that are observed. We conclude that there is no evidence for a large, additional charge movement that occurs while the channel is open.

As a further check for the possible existence of multiple open states, we examined the single-channel kinetics of Shab channels. Fig. 10 A shows recordings from a patch containing a single Shab channel. Over the range of voltages from −30 to +40 mV, the open time distribution showed a single exponential component (Fig. 10 B). Data from multichannel patches also show no evidence for a second open-time component at voltages down to −80 mV. The mean burst duration at −60 mV is 3.7 ± 0.1 ms (n = 3) and has a very weak voltage dependence corresponding to a partial charge of 0.1 e_o. The single-exponential open-time distributions support the idea that Shab has only one fully open state. Thus again, we find no reason to expect multiple open states, and find the simplest conclusion to be that Shab channels have a reduced gating charge of ∼7.5 e₀.

Ideally, this estimate of gating charge should be confirmed with an independent measure in which the total integrated gating current is normalized by the number of channels. Unfortunately, the relatively low expression level of Shab channels has precluded this sort of measurement, which requires either the ability to measure gating currents in a patch membrane or the ability to measure radioligand binding to a single cell.

The Shab single-channel closed-time distributions were well described by three exponential components (Fig. 10 B). The fastest closures are most frequent at the largest depolarization of +40 mV. The dwell time in this closed state is essentially voltage independent (Fig. 10 C, ▵). This closed state may be the result of block by intracellular components or it could be a conformational state that is entered after the channel has opened, as is the case in Shaker channels (Hoshi et al. 1994). We favor the latter interpretation since the rapid closures are also observed in inside-out patch recordings where the only solutes bathing the internal membrane surface are K⁺, aspartate, HEPES, and EGTA.

Transitions to this fast closed state from the open state accounts for the fact that P does not approach unity at large depolarizations. The value of P_max is 0.72, as obtained from noise analysis of macroscopic currents at +50 to +70 mV. From the single-channel recordings, we calculate an open probability of 0.68 at +60 mV, very close to the estimate from noise analysis.

Shab channels inactivate on a time scale of seconds and with a half-inactivation voltage of −30 mV (Tsunoda and Salkoff 1995). To test for possible inactivation effects in our experiments, we measured the inactivation induced by 500-ms prepulses (Fig. 10 D). The reduction in current due to inactivation during depolarization to −60 mV or below is seen to be at most 5%, which would have a negligible influence in our estimates of the voltage dependence of P.

In the experiments described in this report, we have estimated the effective gating charge of four members of the voltage-gated K⁺ channel superfamily. We find that Shaker and Kv1.1 have an effective gating charge of ∼13 e_o, as does the Kv2.1 channel. Shab channels, on the other hand, have an effective gating charge of only 7.5 e_o. The estimates of gating charge are based on measurements of the channel open probability P at negative membrane potentials where P is very small. The voltage dependence of P provides a lower-bound estimate on the total charge movement (Almers 1978); in all channel types except Kv1.1, the reliability of the gating-charge estimate was confirmed by comparison of the voltage dependence of gating current according to the theory of Sigg and Bezanilla 1997. We have also determined that the probability of any voltage-independent openings is very small in these channels and that the charge movement is tightly coupled to channel opening in Shaker and Kv2.1.

In measuring the open probability, we are confronted with several possible sources of error. First, an artifactually large voltage dependence of P would result if the probability of missing brief channel openings increased substantially as the membrane potential was made more negative. We find, however, that the channel burst durations are weakly dependent on voltage in the range of potentials examined for each of the four channel types so that most bursts of openings are sufficiently long to be detected (Table). The measurements in Shaker and Shab channels were the most susceptible to this effect, since the mean burst duration becomes <4 ms at −70 mV. This is nevertheless considerably longer than the minimum detectable event duration, 120 μs at our analysis bandwidth of 1.5 kHz, so that the error is negligible.

A second source of error would arise from voltage-dependent inactivation of channels, resulting in an artifactually reduced apparent voltage dependence. The known properties of Shaker channels, and tests for inactivation in Kv1.1, Kv2.1, and Shab channels, however, showed that inactivation effects were negligible under the conditions of our measurements.

Finally, our estimates of P to very low values make use of the assumption of a homogeneous population of channels; if a fraction of channels has a shifted voltage dependence, then the estimated voltage dependence of P would be distorted. Heterogeneity in the voltage dependence of single, mutant Shaker channels has been observed (Schoppa and Sigworth 1998b), but this is of a form (a positive shift of a minority of the channels) that would have little influence on our estimates; such heterogeneity was not seen in the wild-type truncated Shaker channels studied here (Schoppa and Sigworth 1998a). We encountered no evidence for such heterogeneity in the single-channel behavior of the other channel types; if it were present, it would reduce the apparent voltage dependence of P at intermediate voltages, but leave the asymptotic voltage dependence unaffected. We take the relatively good agreement between the voltage dependence of q_s and Q̂as evidence that errors from heterogeneity are small.

Logothetis et al. 1993 observed that Shab channels have a low voltage sensitivity, only ∼60% of that seen in Kv1.1 channels. They ascribed this difference to the differences in the S4 regions, where Shab has only five basic residues as compared with seven in the Shaker family channels. They also found a similar reduction in voltage sensitivity in Kv1.1 when the first (R1) and last (K7) basic residues were replaced with the neutral residues found in Shab, consistent with the idea that these two residues contribute to the gating charge in Kv1.1.

Our experiments, which provide limiting-slope estimates of charge to much lower open probabilities and which distinguish between the main conductance level and a subconductance state in Shab, nevertheless confirm the view that Shab's total charge movement is much smaller, only 7.5 e_o, compared with 13 e_o in Kv1.1.

Other evidence from mutation studies is equivocal about the role of residues R1 and K7 in the voltage sensor. Early studies showed moderate effects on the voltage dependence of gating from the neutralization of these residues in Shaker (Papazian et al. 1991), but large effects from their neutralization in Kv1.1 (Liman et al. 1991; Logothetis et al. 1992). More rigorous Shaker mutation studies involving the direct measurement of gating charge show a large decrease in charge when R1 is neutralized, but no effect from the neutralization of K7 (Aggarwal and MacKinnon 1996; Seoh et al. 1996). Studies in which cysteines were placed at or near the R1 position of Shaker show that this residue undergoes a moderate, voltage-dependent change in accessibility to externally applied reagents PCMBS (Yusaf et al. 1996) and [2-(trimethylammonium)ethyl]methanethiosulfonate (MTSET; Larsson et al. 1996), leading Baker et al. 1998 to assign it an effective electrical distance change δ = 0.5. Meanwhile, near K7, no voltage-dependent accessibility change is seen (Larsson et al. 1996). From these studies, one concludes that, in Shaker, R1 seems to contribute to the gating charge movement, while K7 does not.

In view of these results, the large charge movement in Kv2.1 channels, indistinguishable from that in Shaker channels, comes as a surprise. Like Shab, Kv2.1 has only five basic residues in S4, and serves as a counterexample to the requirement of R1 for full charge movement. Instead, this result is consistent with the idea originally proposed by Larsson et al. 1996 that only the central five S4 residues participate in the gating charge movement.

Previous estimates of the gating charge of Kv2.1 are much smaller than ours, in the range of 4–6 e_o. They were obtained from the steepness of channel activation over the range of open probabilities from 0.005 to 0.1 (Taglialatela and Stefani 1993) or from the fit of macroscopic and other kinetic data to a particular sequential gating scheme (Benndorf et al. 1994). The relatively small charge values can be understood from the limited range of P values that were measured by these authors; only at negative potentials where P is smaller than ∼10⁻⁵ is an asymptotic steepness corresponding to 13 e_o approached (Fig. 6 C). It should be kept in mind that our experiments made use of a channel with mutations in the outer pore region, but it seems to us very unlikely that these mutations could underlie an increased voltage sensitivity of the channels.

Why is the behavior of Shab so different from its mammalian homologue Kv2.1? In these channels, the sequences of S2, S3, and S4 are very well conserved, with identical charged residues. Since the gating charge movement arises from charges within the protein (Sigworth 1994), it seems inescapable that it is the degree of movement of charged groups in the membrane field, rather than the total charge, that is reduced in Shab compared with Kv2.1. It is not difficult to imagine how the degree of movement could be decreased. Charge movement in voltage-gated channels occurs in multiple steps; in Shaker channels, at least two, and probably three or more, sequential, charge-moving conformational changes occur in each subunit (Zagotta et al. 1994; Bezanilla et al. 1994; Schoppa and Sigworth 1998c). Perhaps in Shab channels one of these steps does not occur, limiting the total charge movement to ∼60% of that of Shaker.

Ligand-gated ion channels show a finite open probability even in the absence of agonists. The mouse muscle acetylcholine receptor channel has a spontaneous open probability of ∼5 × 10⁻⁶ (Jackson 1988), while cyclic nucleotide–gated channels have spontaneous open probabilities on the order of 10⁻⁵ to 10⁻³ (Ruiz and Karpen 1997; Tibbs et al. 1997). The activation of these channels is well described by allosteric models in which the open state is stabilized by the binding of ligands. In the present study, we find that the voltage-insensitive open probability of Shaker channels is very much smaller, <10⁻⁹; this suggests an obligatory coupling of charge movement to channel opening rather than a traditional allosteric mechanism. At the most negative potentials studied here, the steepness of the open probability curve does not decrease, and the effective charge computed from that steepness agrees well with other estimates of the total gating charge per channel. Taken together, these results imply that essentially all of the charge movement is obligatorily coupled to channel opening; that is, Shaker channels cannot open unless all of the charge movement has occurred in each subunit. The only exception to this obligatory coupling is a small, weakly voltage-dependent charge movement in Shaker channels that has been recently described by Stefani and Bezanilla 1996.

The same strict coupling between charge movement and channel opening is seen in Kv2.1 channels, where we have estimated the voltage-insensitive open probability to be <4 × 10⁻⁸, and in sodium channels, where the open probability has been measured down to 10⁻⁷ (Hirschberg et al. 1995). The situation is, however, different in Shab channels, where even at −90 mV the probability of occurrence of a subconductance state was the relatively large value of 8 × 10⁻³. This subconductance state appears to represent an intermediate step in channel activation, becoming predominant only at negative potentials. Subconductance states representing kinetic intermediates in channel activation have been observed in Kv2.1 and Shaker channels (Chapman et al. 1997; Zheng and Sigworth 1998), but isolated openings to these levels were not detected in our measurements because either their lifetimes were too short or their equilibrium occupancies were even lower than that of the main conductance state, under the conditions we used.

As might be expected for the reduced voltage sensitivity requirement of delayed-rectifier potassium channels, Shab channels have a much lower voltage dependence of channel activation. They also have less gating charge movement than the A-type Shaker channel and its homologue, Kv1.1, which also produces transient currents when coexpressed with beta subunits (Rettig et al. 1994). It is surprising that the homologous mammalian delayed rectifier Kv2.1 does not have a similarly reduced charge movement. It will be interesting to see what is the molecular origin of this difference.

We thank Dr. R. MacKinnon for providing the Kv2.1 construct and Agitoxin, and Dr. D. Logothetis (Mount Sinai Medical Center, New York, NY) for Kv1.1 and Shab DNA. We also thank Y.-Y. Yan for expert technical assistance and Y. Yang, J. Zheng, Q.-X. Jiang, T. Rosenbaum, and S. Basavappa for helpful comments.

This work was supported by National Institute of Health grant NS 21501.