Intermediate Conductances during Deactivation of Heteromultimeric Shaker Potassium Channels

The activation of Shaker potassium channels involves many conformational changes. A study by Cole and Moore (1960) showed that 25 independent transitions would be required to explain the activation delay in squid axon potassium currents. Analysis of the time course of Shaker channel opening in response to a voltage step shows that, as a minimum, five to seven sequential transitions must occur during channel activation (Zagotta et al., 1994,a; Schoppa and Sigworth, 1998a). Gating current measurements from Shaker potassium channels (Stühmer et al., 1991; Schoppa et al., 1992; Perozo et al., 1993) and voltage-gated sodium channels (Conti et al., 1984; Vandenberg and Bezanilla, 1991) suggest that the voltage-dependent conformational changes comprise multiple steps and are not identical. The Shaker channel is composed of four identical α subunits (MacKinnon, 1991; Kavanaugh et al., 1992; Li et al., 1994). Some cooperativity between subunits during the activation process seems likely. Evidence for cooperativity in gating and block has been obtained in Shaker wild-type and mutant channels (Tytgat and Hess, 1992; Liman et al., 1992; Heginbotham and MacKinnon, 1992; Schoppa et al., 1992; Ogielska et al., 1995) and is required to model Shaker channel activation gating (Zagotta et al., 1994,b; Bezanilla et al., 1994; Schoppa and Sigworth, 1998b).

Attempts have been made to isolate different steps in the Shaker channel activation time course by manipulating the testing protocols for macroscopic and gating currents (Zagotta et al., 1994,a; Bezanilla et al., 1994; Schoppa and Sigworth, 1998a). In most cases, however, it has been difficult to isolate any of the intermediate steps. Chapman et al. (1997) found activation-dependent subconductance levels in single-channel recordings of the Kv2.1 channel. They concluded that these sublevels represent partially activated channel states in which the pore-forming regions of the various subunits have nonequivalent conformations. Our previous study of the Shaker channel pore mutant T442S has identified two sublevels that are predominantly seen during channel activation and deactivation (Zheng and Sigworth, 1997). The occurrence of these sublevels is kinetically distinct from the subconductance behavior that is occasionally seen in wild-type Shaker channels (Hoshi et al., 1994; Schoppa and Sigworth, 1998a), whose occurrence appears to be unrelated to the activation process. In T442S channels, the larger sublevel is always traversed during channel activation and deactivation. Transitions between the two sublevels and between the larger sublevel and the open level involve identical charge movements, consistent with the idea that each of these transitions arise from equivalent motions occurring in separate subunits. The fact that sublevels of the T442S mutant channel have differing ion selectivities provides a hint that some of the pore structure may be involved in the conformational changes that lead to the channel opening.

The present paper is the second on a series of studies of Shaker channel sublevels. We made use of the tetrameric nature of Shaker channels to study the effect of each subunit on the sublevel behavior. Heteromultimeric channels incorporating various numbers of T442S mutant subunits were obtained by coexpression of the T442S cRNA and its parental cRNA (actually a Shaker-mKv3.1 chimera, which we nevertheless shall refer to as WT).¹ Heteromultimeric channels were also studied by expressing tandem dimer constructs containing cDNAs encoding the two types of subunits. We also included in this study the WT homomultimeric channels. The experiments were designed to answer two questions: first, do sublevels exist in the heteromultimeric and WT channels, and second, if sublevels exist, what is the relationship between sublevels and the final steps in channel activation?

The two subunit types used in this study have been previously described (Zheng and Sigworth, 1997). The “wild-type” subunit (W) is a Shaker B chimera (Lopez et al., 1994) in which the S6 segment is substituted by the S6 sequence of the mKv3.1 (also known as NGK2) potassium channel; the NH₂-terminal inactivation sequence is also removed. The tetrameric WT channel (W₄) has a single-channel conductance approximately fourfold larger than Shaker when expressed in Xenopus oocytes; the gating kinetics seem to be unchanged. The “mutant” subunit (M) carries a pore mutation T442S in the WT background. Both cDNAs were carried by the pBluescript vector (Stratagene Inc., La Jolla, CA).

Heteromultimeric channels were made by coexpressing WT and mutant subunit cRNAs in Xenopus oocytes, and the stoichiometry identified by the conductance and kinetics of the single-channel currents (see results). Heteromultimeric channels were also made by tandem dimer constructs in which two cDNAs were linked together with a sequence encoding a linker peptide 24–64 amino acids in length (J. Zheng, Y. Yan, and F.J. Sigworth, manuscript in preparation). The linker sequence replaces the stop codon of the first protomer. Each construct was verified by restriction mapping. All dimers were carried by the pGEM-A vector (Swanson et al., 1990).

The monomer cDNAs were linearized with EcoO109I and cRNAs were transcribed with the MEGAscript T₃ RNA polymerase kit (Ambion Inc., Austin, TX). The dimer cDNAs were linearized with NotI and cRNAs were transcribed with the MEGAscript T₇ RNA polymerase kit. Sizes of the transcribed cRNAs were verified by gel electrophoresis.

Oocyte preparation and injection protocols were identical to those previously described (Zheng and Sigworth, 1997), except that ND96 solution replaced the OR3 solution in which defolliculated stage V-VI oocytes were stored at 20°C. ND96 contained 96 mM NaCl, 2 mM KCl, 1.8 mM CaCl₂, 1 mM MgCl₂, 50 U/ml penicillin, 50 ng/ml streptomycin, and 5 mM HEPES, adjusted to pH 7.4 with NaOH. 50 nl of cRNA was injected into Xenopus oocytes using a microinjector (Drummond Scientific Co., Broomall, PA). Concentrations of injected cRNAs were measured with a spectrophotometer (Spectronic 1001; Bausch and Lomb, Rochester, NY) and were varied by dilution to control the level of expression.

Single-channel recordings were made from inside-out patches, and in some cases from cell-attached patches. No obvious difference was observed in the kinetics and conductance between data recorded by the two recording methods. Patch pipettes were pulled from 7052 glass (Garner Glass, Claremont, CA) with 1–2.5-μm tip diameters, and were coated with Sylgard (Dow Corning Co., Midland, MI). The pipette solution contained 140 mM K-Aspartate, 1.8 mM CaCl₂, 10 mM HEPES, and the bath solution contained 130 mM K-Aspartate, 10 mM KCl, 1 mM EGTA, 10 mM HEPES, adjusted to pH 7.3 with KOH. The liquid junction potential at the interface of these two solutions was estimated to be 0.8 mV; no correction was applied. For selectivity experiments, Rb⁺ substituted K⁺ in the pipette solution.

Most of the experiments were carried out using an EPC-9 patch clamp amplifier and the Pulse software (HEKA-Electronic, Lambrecht, Germany). Voltage pulses were applied from a holding potential of −100 mV. Current signals were filtered at 2.5 kHz, and data were sampled at 12.5 kHz. Recordings from the W₄ channels were made using an Axopatch 200B amplifier (Axon Instruments, Foster City, CA); the signal was filtered at 10 kHz and sampled at 40 kHz. Leak subtraction was performed using an average of the nearest null traces.

Analysis of the single channel recordings was made using various user-developed programs in the PowerMod environment (HEKA-Electronic) using the Modula-2 language. A digital Gaussian filter was used to further filter the data as required to achieve an appropriate signal-to-noise ratio. Event detection was performed using the threshold-crossing analysis method (Colquhoun and Sigworth, 1995). We used a set of three thresholds to detect transitions among multiple current levels, or two thresholds to determine the total transition time. Amplitude histograms were used for kinetic analysis. A mixture of Gaussian functions was fitted by least squares to the histograms using the Igor data analysis program (WaveMetrics, Lake Oswego, OR).

Statistical quantities are given as mean ± SD.

The distribution of channel types recorded from oocytes coinjected with WT and mutant cRNAs was fitted with a binomial distribution. This was done by the maximum likelihood method, which estimates as P, the probability of incorporating a mutant subunit:

in which q_n is the number of observed channels having n mutant subunits, n = 0–4.

The transition time of single-channel closure was measured as the time between crossing thresholds 90 and 10% of the fully open current level. Maximum-likelihood fitting was applied to individual measurements according to the following theory. Given an instantaneous current transition of unit amplitude at time zero, the time t_i of crossing threshold θ_i is determined by both the filter characteristics (Colquhoun and Sigworth, 1995) and the current noise n_i at that time, such that the following equation holds for the filter step response H(t):

The time spent between the crossings of the two thresholds θ₁ and θ₂ is then given by

where H⁻¹(y) is the inverse function of H(t). In turn, s can be approximated to first order in n₁ and n₂ by

where

Assuming n₁ and n₂ to be independent Gaussian random variables, Eq. 4 suggests that s can be approximated as a Gaussian random variable with mean μ_s = H⁻¹(θ₂) − H⁻¹(θ₁) and variance σ_s² = (k₁σ₁)² + (k₂σ₂)². Thus, the probability density of s can be written:

When a closure traverses one or two sublevels whose lifetimes are exponentially distributed with means τ₁ and τ₂, the total transition time has a probability density function that is a weighted sum of the two exponential functions convolved with f₀,

When only one sublevel is traversed, the amplitude A₂ is zero. On the other hand, if both sublevels are always traversed, the amplitudes are constrained by the relation

with A₁ > 0 in the case that τ₁ > τ₂.

Currents in the homomeric WT and mutant channels differ in three aspects (Zheng and Sigworth, 1997; see Fig. 1, top and bottom). First, the W₄ channel deactivates quickly; at −100 mV the tail current decays to its half-maximum amplitude in 1.5 ms. The M₄ channel has tail currents that decay two to three orders of magnitude more slowly; at −100 mV the half-decay time is ∼600 ms. Second, consistent with the fast deactivation shown in the macroscopic currents, the single channel currents recorded from the W₄ channel have a short mean open time and many brief closures. The M₄ channel has stable openings and a remarkably long mean open time even at very hyperpolarized potentials. Finally, the two channel types differ in their single-channel conductance. The W₄ channel has a mean conductance of 94.7 ± 0.8 pS (n = 12). The M₄ channel has a mean conductance of 28.3 ± 0.9 pS (n = 19), more than three times smaller than the W₄ channel.

We injected various mixtures of WT and mutant cRNAs into Xenopus oocytes. As the Shaker channels are tetramers, if the WT and mutant subunits assemble randomly to form a channel, one should expect three or four heteromultimeric channel types with various stoichiometries. When a large number of single channel recordings was made, we indeed found four populations of single channels besides the two homomultimeric channels (Fig. 1,A). These channel types have single channel conductances of 52.9 ± 4.7 pS (n = 23), 72.3 ± 1.0 pS (n = 18), 78.6 ± 0.9 pS (n = 15), and 88.8 ± 0.9 pS (n = 19). Interestingly, the gating kinetics of these channel populations also showed intermediate phenotypes in such a way that the channels with higher conductance had shorter mean open time and more brief closures (similar to the W₄ channel), and the channels with lower conductance had longer mean open times and were more stable (similar to the M₄ channel). We take the parallel changes in conductance and kinetic properties to reflect various numbers of mutant subunits in the channel tetramer. Accordingly, in Fig. 1 D we give a tentative assignment of subunit stoichiometries to each channel population.

Assuming that the WT and mutant subunits assemble randomly into tetramers, our assignment of stoichiometries can be tested by the way in which the frequencies of channel populations vary as the ratio of WT to mutant cRNA is varied. We coinjected WT and mutant cRNAs at four different ratios (1:1, 1:1.3, 1:2, and 1:4). As shown in Fig. 2, coinjection at the 1:1 ratio yielded channels mainly of the higher conductances. This is expected if the mutant cRNA has reduced competence for translation into functional subunits, as suggested by the low expression level when only the mutant cRNA is injected. When the relative concentration of the mutant cRNA was increased to 1.3, the chance of recording a low conductance channel type was higher, and we recorded the full spectrum of channel populations. Further increase of the ratio of the mutant cRNA to 2 and 4 made the distribution more tilted to the low conductance channel populations. Fitting of a binomial distribution to the data yielded satisfactory results (Fig. 2 B), and confirmed that five channel populations correspond to distinct stoichiometries.²

It should be noted that whatever the cRNA ratio, the probabilities of recording 72.3 and 78.6 pS channels were always similar (Fig. 2 A). This is to be expected if these two channel populations reflect the same subunit stoichiometry (M₂W₂) but differ in some other way, for example having different permutations of subunits. In heteromultimeric cyclic nucleotide–gated channels, it has been found that channels with the same stoichiometry but different relative positions of subunits can be distinguished by a large conductance difference (Liu et al., 1996a).

To further establish the assignment of the channel stoichiometry, tandem dimer constructs were made in which one copy of the WT cDNA was covalently linked with one copy of the mutant cDNA. These constructs were made with both orientations, M–W and W–M. Single channel recordings from oocytes expressing these tandem dimers showed two main channel populations that belong to the putative M₂W₂ channel types (Table I). Of 44 single channels, we recorded 27 belonging to the 72.3-pS population and 14 belonging to the 78.6-pS population. Three channels were seen that belong to the 52.9-pS population. It is known that tandem constructs do not guarantee the stoichiometry of the assembled channels (McCormack et al., 1992; Hurst et al., 1992, 1995; Yang et al., 1997). However, if we make the usual assumption that the majority of the channels have the correct stoichiometry as defined by the tandem linkage (Isacoff et al., 1990; Liman et al., 1992; Heginbotham and MacKinnon, 1992), these results support the assignment of these intermediate conductance populations to M₂W₂ channels.

Tandem W–W and M–M dimer constructs were also made. When these cRNAs were coinjected, the two intermediate conductance channel populations were observed along with the two homomeric channel populations (Table I). Of the intermediate conductances, 78.6-pS channels were observed much more frequently than the 72.3-pS channels. Together with the other results from tandem dimers, this result suggests that the 78.6-pS population represents channels with pairs of like subunits adjacent to each other, while the 72.3-pS channels have like subunits facing each other across the central axis. We shall assume these assignments, which are summarized in Fig. 1 D, for the remainder of this paper.

We have used an amplitude histogram analysis to detect sublevels in the various channel types. Unlike the threshold-crossing method we previously used to estimate dwell times in the M₄ channels (Zheng and Sigworth, 1997), the amplitude histogram method is less sensitive to noise spikes that, if large enough to cross the thresholds, would generate false events. Fig. 3 shows how the two kinds of amplitude histograms were made from single-channel tail currents. Thresholds were used to detect when a channel makes its last transition from the fully open level to the sublevels (the time of crossing the 90% threshold) and from the sublevels to the closed level (the time of crossing the 10% threshold). All the data points in the tail up to the time of crossing the 10% threshold were accumulated in the “tail histogram,” which describes the whole tail current time course (Fig. 3,B). Only those data points that fell between the 90 and 10% thresholds were accumulated to construct the “transition histogram,” which describes dwells in the sublevels (Fig. 3,C). Both histograms were accumulated from many sweeps and were scaled to the units of milliseconds per picoampere so that the value of each bin was proportional to the mean dwell time at that current level. The peaks in the histograms represent stable current levels in single channel recordings, whose position and area give estimates of the mean conductance and the mean lifetime. In the voltage ranges where we used this analysis, the transitions were predominantly unidirectional; the histogram method is expected to overestimate the mean lifetime if multiple dwells in a given state occur during the deactivation time course. In the case shown in Fig. 3, the mean dwell times estimated from the histograms of the open, sub₂, and sub₁ states were 119, 17.7, and 5.4 ms, respectively. Threshold analysis of the same data yielded similar values of the mean dwell times: 80.5, 9.2, and 5.3 ms.

Because of the effect of filtering on the current monitor signal, an instantaneous step transition will appear to have a finite transition rate (Colquhoun and Sigworth, 1995). This will give entries into the above histograms even when a deactivation transition has no dwell in sublevels. We estimated the sensitivity of the amplitude histogram method to this effect by constructing a transition histogram from a step function that had been passed through a Gaussian filter of 1 or 5 kHz bandwidth (Fig. 3,D), similar to the case of the single channel recordings. As shown in Fig. 3,E, the histograms have very low amplitudes, <10 μs per current unit in most of the 10–90% current amplitude range even when the 1-kHz filter is used. Therefore, we expect that the histogram peaks such as in Fig. 3, B and C, mostly reflect dwells in stable current levels rather than the time spent during current transitions.

We have previously shown that in M₄ channels two sublevels can be identified whose conductances are ∼37 and 70% of the fully open current level (Zheng and Sigworth, 1997). Conductances of the sublevels have a linear voltage dependence in the range from −60 to −140 mV. Sublevels are observed during both channel activation and deactivation.

When single channel currents were recorded from the heteromultimeric channels, we found that sublevels also existed. Fig. 4,A shows representative tail currents from each channel type. Dwells in the sublevels could be identified in the tail histograms (Fig. 4,B) for the slowly deactivating channels and are more readily seen in the transition histograms for every channel type (Fig. 4 C). Two sublevels were identified in each channel type. We call the sublevel having a larger conductance sub₂, and the other sub₁, as we did for the M₄ channel sublevels. Similar to those in the M₄ channels, the sublevels are strongly coupled to channel activation. Channel activation usually showed a “staircase” current transition having the closed → sub₁ → sub₂ → open sequence, and the deactivation showed the reverse sequence. Also like the M₄ channel sublevels, the sub₂ sublevels in heteromultimeric channels had longer lifetimes compared with the sub₁ sublevels, as shown by a larger sub₂ peak in most transition histograms. In the case of M₂W₂ channels, an extra sublevel having the smallest conductance was also observed. We call it sub₂′ because its kinetics are most similar to sub₂; it has no counterpart in other channel types, but was seen in both the 72.3- (M₂W_2L) and 78.6-pS (M₂W_2H) channels.

Staircase current transitions were not obvious in W₄ single channel traces, and no sublevel peaks were visible in the tail histogram. But when the transition histogram was constructed, two peaks similar to those in the other channel types were observed. Sublevels could occasionally be seen in the deactivation time course of W₄ channels, such as the one shown in the bottom panel of Fig. 4 A.

With the nearly symmetrical K⁺ solutions used, both the fully open state and the sublevels were found to have linear I-V relationships within the voltage range studied (−60 to −140 mV; narrower voltage ranges were used for the MW₃ and W₄ channels). The current amplitudes at −100 mV are listed in Table II. The slope conductances of the sub₂ sublevels are 54–70% of the fully open level; those of sub₁ are 23–44%. Mean lifetimes of the open level and the sublevels were estimated from histogram fits and are plotted in Fig. 5. It can be seen that both the open times and the dwell times in the sublevels decrease with each additional WT subunit. The mean lifetimes of sub₂ and sub₁ sublevels in the W₄ channels at −100 mV were estimated to be 280 and 70 μs, respectively. The short lifetimes, in addition to the presence of frequent brief closures from the open state, made the sublevels in the W₄ channels not readily observable.

Our previous study of the gating kinetics of the M₄ channel showed that the lifetimes of the open level and sublevels are all voltage dependent. The lifetime of the open level is mainly determined by the voltage-dependent backward transition that becomes slower at more depolarized voltages. The lifetimes of the two sublevels, on the other hand, are determined by both forward and backward transitions. The voltage dependence of these transitions gives rise to a bell-shaped lifetime curve in each sublevel with a peak around −100 mV. In the heteromultimeric and W₄ channels, the lifetimes exhibit very similar voltage dependences (Fig. 5). The main open time is always longer at more depolarized voltages, and the lifetime in each of the sublevels peaks around −100 mV.

Besides the above-stated similarities among sublevels in different channel types, we also tested other gating properties. One feature that is characteristic for the M₄ channel sublevels is the strong coupling between the open level and the sublevels. It was found in the previous study that an activating channel always traverses the sub₂ sublevel before it reaches the final open level. Deactivation also always passes through the sub₂ sublevel. It is harder to carry out the same test in the heteromultimeric and W₄ channels due to the shorter lifetimes of their sublevels. However, we did a less stringent test by asking whether the channel has to traverse at least one sublevel during deactivation.

Evidence for traversal of sublevels comes from the “excess time” measured in the single channel closing time course at −100 mV using two thresholds, 10 and 90% in amplitude. If a channel closes directly from the fully open to the closed level, a finite dwell time will be measured due to the filter rise time. Because the threshold-crossing time is perturbed by the Gaussian background noise, the measured dwell times will have an approximately Gaussian probability density f₀(s) (see Eq. 5). Alternatively, deactivation that traverses sublevels will have the approximate probability density f₁(s) (given by Eq. 6) that is a weighted sum of one or two exponential functions (corresponding to the lifetime of each sublevel) convolved with a Gaussian function. We assumed that a closure could be either a direct transition or one traversing sublevels. Each individual measurement of the transition time was thus fitted with

and the factor, along with the other parameters, was adjusted to generate the best fit to a set of 60–943 measurements. The value of A₀ gave an estimate of how many transitions were direct transitions that avoided traversing sublevels. We chose a test potential of −100 mV because under this condition the sublevels exhibit the longest lifetimes. Fig. 6 shows a histogram of the measured transition times during deactivation for each channel type, and the probability density function that yields the maximum-likelihood fit. It was found that, for the M₄ channel, <10% of the transitions could be described by direct transitions, consistent with the channel always traversing at least one sublevel. Similarly, all the heteromultimeric channels and the W₄ channel had the majority of the measured transitions (>80% in each case) being accounted for by the exponential term(s). Thus, we conclude that all these channel types deactivate through sublevel states.

Our previous study of the mutant channel showed that its activation can take two alternative paths from closed to the final open level. One path is through both sub₁ and sub₂; the other is directly from closed to sub₂. This generates nonzero dwells in sub₂ but a substantial population of zero dwells in sub₁. We tested to see whether the sublevels in the other channel types also show similar correlation. The dwell time in each sublevel was measured during the activation time course at −60 mV by using three thresholds. (This analysis could not be applied to the W₄ channel because of its very brief transition times.) Under these conditions, we indeed observed activation time courses in each channel type that contained substantial dwells in both sub₂ and sub₁ sublevels (Fig. 7), suggesting that the activation of these channels may follow the same pathways as the M₄ channel. However, dwells in the smallest sublevel found in M₂W_2L channels, sub₂′, shows a negative correlation with dwells in the other two sublevels. Of 167 sweeps, there were only 2 for which activation showed nonzero dwells in both the sub₂′ and in the sub₁/sub₂ current ranges. Activation of a single M₂W_2L channel thus seems to show two alternative paths: one proceeds through sub₁ and sub₂ like the mutant channel, while the other path passes only through the sub₂′ state. One example of each alternative is presented in the M₂W_2L panel of Fig. 4 A. Also shown in the figure is the same behavior that was seen in M₂W_2H channels.

In conclusion, the sublevels in all channel types show a similar gating pattern, with the exception of the M₂W₂ channels, which seem to gate through alternative paths. The likely explanation for the similarity is that the sublevels represent the same gating process that is preserved in all the channel types.

It has been previously found that the various conductance levels in the mutant channels have differing ion selectivities (Zheng and Sigworth, 1997). At −100 mV, the amplitude ratio of Rb⁺ to K⁺ current changes from 1.55 in the open state to 0.90 in the sub₂ state, and 0.47 in the sub₁ state. We were interested in testing whether the sublevels in heteromultimeric and W₄ channels also show similar selectivity differences. K⁺ in the pipette was replaced with Rb⁺ in recordings using inside-out patches, and the inward Rb⁺ currents were recorded at −100 mV. As shown in Fig. 8,A, both M₂W_2L and W₄ channels showed sublevels in Rb⁺ currents. We identified two sublevels in M₂W_2L channel currents that were similar to the sub₂ and sub₁ sublevel in K⁺ currents. We could identify only one sublevel in W₄ Rb⁺ currents that resembled the sub₂ sublevel, though it is quite possible that an additional sublevel exists but was indistinguishable from the baseline current. The Rb⁺ ion seems to stabilize the conducting states, as suggested by the 3–10-fold longer lifetimes of both the open and the sublevel states (Fig. 8,A). The longer lifetimes are reflected in the histograms in Fig. 8, B and C, as components with larger areas.

In the M₄ channel, the Rb⁺ current is larger than the K⁺ current in the open level but smaller than the K⁺ current in each sublevel. In contrast, the M₂W_2L and W₄ channels have Rb⁺ currents that are smaller than the K⁺ currents in all current levels (Table II). The Rb⁺ to K⁺ current ratio for the open level was found to be larger than that for each sublevel of the M₂W_2L channels and for sub₂ in the W₄ channels (Fig. 8 D). Thus, in all three channel types, the sublevels tend to exclude the larger Rb⁺ ion.

We have previously reported sublevels in T442S mutant Shaker channels that apparently represent intermediate conformations during voltage-dependent activation (Zheng and Sigworth, 1997). This paper extends the study to heteromultimeric channels containing one to three mutant subunits as well as channels with no mutant subunits. It is found that sublevels with similar kinetic and permeation properties exist in all these channel types, consistent with the idea that the T442S mutation changes the free energies of some conformational states, but does not introduce new states. Each mutant subunit is seen to contribute to the stabilization of the conducting states by approximately the same amount. In addition, the magnitude of this effect is essentially equal in the open level and in each of the two sublevels. Consistent with earlier results on the mutant channel, it is found that sublevels in one heteromultimeric channel type and in the W₄ channel have ion selectivities that differ from that of the fully open level.

Heteromultimeric channels were made by coexpression of the WT and mutant subunits and also by using tandem dimer constructs. To identify the subunit stoichiometry, we made use of the large difference in kinetics and conductance between the two homomultimeric channel types. Several lines of evidence supported our assignment of the stoichiometries. (a) Coexpression gave rise to six channel populations with distinct single channel conductances; the largest conductance was identical to the W₄ channel and the smallest one was identical to the M₄ channel. (b) Parallel to the conductance differences, each channel population showed distinct kinetic properties. Channels with higher conductance had shorter mean open times, fast tail currents, and many brief closures. Changes in the mean lifetimes of the sublevels also followed the same trend. (c) In the coexpression experiments, the distribution of channel populations varied as the ratio of WT to mutant cRNA was changed, such that as more WT cRNA was injected the chance to record a channel with higher conductance was increased. (d) The relative probability of observing two intermediate populations showed no variation with changes in the cRNA ratio, suggesting that these populations represent the same subunit stoichiometry. (e) Expression of tandem dimeric constructs allowed the assignment of the two intermediate populations. Like the result obtained by Liu et al. (1996a) in the case of cyclic nucleotide–gated channels, channels formed by pairs of adjacent WT or mutant subunits were seen to have a higher conductance than those formed by alternating subunit types.

In our previous study (Zheng and Sigworth, 1997), we found that the T442S mutation greatly increases the channel open time while leaving the first latency to opening unchanged. We concluded that the T442S mutation preserves the activation conformational changes but lowers the free energy of the open conformation; by doing so, it also makes short-lived intermediate subconductance states readily visible. If this is the case, one expects that sublevels will persist when the stabilizing effect of the T442S mutation is gradually reduced by replacing each mutant subunit with the WT subunit. Indeed, sublevels are seen with progressively shorter lifetimes, reflecting these states becoming more and more unstable, as the number of mutant subunits was decreased. Despite the differences in lifetimes, sublevels in the various channel types show several common properties. First, the lifetimes in each sublevel show similar voltage dependence, peaking at ∼−100 mV and becoming shorter at more depolarized and hyperpolarized voltages. Second, deactivation in each type of channel nearly always traverses at least one sublevel. Third, it was observed that the sublevels and the open level have differing ion selectivity. The similarities in the gating and permeation properties of these sublevels strongly suggest that they represent the same conformational states preserved among the channel types.

It should be noted that the M₂W₂ channels show an additional sublevel, which we have called sub₂′. Its appearance is negatively correlated with any dwell time in the usual sub₁ and sub₂ states (Fig. 7), and therefore represents an alternative pathway for channel deactivation in this channel type.

Subconductance states have been observed in many channel types (for review see Fox, 1987). Activation-coupled sublevels like the ones studied here have been reported in other members of the voltage-gated potassium channel superfamily, such as the rat muscle calcium-activated K⁺ channel (Ferguson et al., 1993) and the rat Kv2.1 channel. Chapman et al. (1997) have demonstrated activation-coupled sublevels not only in wild-type Kv2.1 but also in two mutant channels that make the sublevels more visible. The W₄ channel used in our study is a chimeric Shaker channel whose S6 segment is transplanted from Kv3.1 (also known as NGK2). The W₄ channel shows gating behavior quite similar to the wild-type Shaker channel, though its conductance is fourfold larger (Lopez at al., 1994). However, the difference in sequence raises the question of whether wild-type Shaker channels would also open through the same sublevels.

The smaller conductance and flickering channel openings make it practically impossible to detect sublevels in Shaker channels. However, the data from related channels could provide some indirect evidence. Previously, we studied a channel with the T442S mutation in the NH₂-terminal-truncated Shaker channel background (which we called SS; Zheng and Sigworth, 1997). This channel showed prolonged channel openings and two activation-coupled sublevels like the M₄ channel in this study. The relationship of Shaker, SS, and the channels we studied here are described in Scheme I.

Channels in the lower row were generated by introducing the T442S mutation; channels at the right hand side were generated by introducing the Kv3.1 S6 region. Activation-coupled sublevels have now been found in SS, M₄, and W₄ channels (indicated by boxes). The fact that the S6 swap and the T442S mutation by themselves did not generate or eliminate the sublevel phenomena thus argues for the existence of sublevels in Shaker channels. In our W₄ channel, the maximal lifetimes of sub₂ and sub₁ are estimated to be 280 and 70 μs, respectively. If the Shaker channel sublevels have the same lifetimes, they will not be easily detected by conventional methods.

It should be noted that sublevels of a different kinetic nature are seen in wild-type Shaker channels (Hoshi et al., 1994; Zheng and Sigworth, 1997). It has been estimated by Schoppa and Sigworth (1998a) that NH₂-terminal-truncated Shaker channels spend 17% of the open time in conductance levels below the main level. These sublevels do not seem to be activation coupled, but rather occur randomly throughout the recording (see Fig. 2,B in Zheng and Sigworth, 1997). A transition to this kind of sublevel would contaminate our measurement of activation-coupled sublevel lifetimes if it were to occur close in time to the final closing transition. Such contamination may explain the slower exponential component that was seen in the W₄ channel deactivation time course (Fig. 6).

The main kinetic effect of the T442S mutation was previously found to be the stabilization of the open conformation (Zheng and Sigworth, 1997). However, depending on the presumed mechanism of subunit interaction, the stabilization effect of each mutant subunit on the lifetimes of the open level and of the sublevels could be quite different. We consider here two extreme possibilities. In the first mechanism, each subunit is assumed to independently undergo voltage-dependent transitions that are equivalent but proceed at different rates in mutant and WT subunits. The scheme of Zagotta et al. (1994 b) is of this form, and has an open state that consists of all four subunits being in the permissive state S₂ (see Scheme II).

According to Scheme II, the lifetime τ_o of the open state is determined by

in which β_m and β_w are rate constants of the mutant and WT subunits, respectively, and n is the number of mutant subunits in the channel. Thus, each subunit has an additive effect on the rate of transition. Our previous study has shown that β_m is two to three orders of magnitude larger than β_w. The prediction of Eq. 8 therefore is that the lifetime of the open state will show a large difference between the M₄ and the M₃W channel, but show much smaller differences as the number of mutant subunits further decreases.

In the second mechanism, the subunits make concerted transitions in the final opening steps; an example is Scheme III, in which the final two transitions are concerted.

Because they are forced to undergo the transitions simultaneously, the subunits have an additive effect on the free energy change of the concerted transitions. Thus, the lifetime of the open state will depend exponentially on the number of mutant subunits,

in which ΔG_m* and ΔG_w* are the free energy contributions to the closing rate constant κ from a single mutant or WT subunit, respectively. The concerted transition mechanism predicts that each subunit affects the lifetime by the same factor.

The observed dependence of the conducting state lifetimes on channel stoichiometry is illustrated in Fig. 9. The lifetime in the open level increases by a factor of ∼2.5 with the addition of each mutant subunit. The sublevel lifetimes change in a parallel manner. That the lifetimes appear to change geometrically with the number of mutant subunits is consistent with the concerted transition mechanism as in Scheme III. The independent transition mechanism as in Scheme II predicts very poorly the dependence of the lifetime on the subunit composition; this is illustrated in the case of the open state lifetimes by the dotted lines in Fig. 9.

The slopes of the fitted lines in Fig. 9 correspond to a subunit difference in the free energy change ΔG_w* − ΔG_m* of ∼0.5 kcal/mol for transitions out of the open level; nearly the same value obtains for transitions from each of the two sublevels. The parallel changes in the stabilities of the three conducting states is illustrated in Fig. 10, which summarizes the kinetic data from our previous study and the present one. It presents hypothetical free energy profiles for the M₄ and W₄ channels, plotted with the gating charge movement as the reaction coordinate. In the energy profiles, the barrier peaks between sub₁ and sub₂ and between sub₂ and the open state are presented as equal in each channel type. The only difference between the W₄ channel and the mutant channel is then that the energy wells are deeper for the mutant channel.

Shaker channel activation involves many voltage-dependent kinetic transitions (Sigworth, 1994). To describe Shaker channel activation, Zagotta et al. (1994,b) proposed a state topology in which each of the four subunits undergoes two conformational transitions. The channel is taken to be open only when all four subunits are in the open state. To explain the sublevel phenomena of the wild-type Kv2.1 channel and two mutants, Chapman et al. (1997) used a scheme with similar topology but proposed that a partially conducting pore may result when one or more subunits are in the “open” conformation. The behavior of the M₄ channel sublevels can also be described by a scheme of this kind (Fig. 11,A), which, like Scheme II, assumes that the final transitions before channel opening arise as transitions in individual subunits. This model is sufficient to explain the following three observations from M₄ channels. First, channel activation can occur without a dwell in sub₁ but always traverses the sub₂ sublevel. In the scheme of Fig. 11,A, the channel may or may not pass through state 11, but must always traverse state 13, in which three subunits are in their open conformation, before entering the open state. Second, the charge movements associated with the sub₁ ↔ sub₂ and the sub₂ ↔ open transitions are essentially equal, consistent with their being identical transitions occurring in separate subunits. Third, the three conducting states have differing selectivities. This is easily explained by having distinct open states (Fig. 11 A, • and ▴) that arise from different conformations of subunits.

In the present study, we find that sublevels in the heteromultimeric and W₄ channels appear to have properties that are similar to those of the M₄ channel. Thus, we conclude that the scheme of Fig. 11 A can describe the sublevel kinetics of heteromultimeric and W₄ channels as well.

We are now confronted with a paradox: as we have seen, the stoichiometry dependence of dwell times is best explained by invoking concerted transitions leading to the conducting states of the channel (Fig. 9 and Scheme III); on the other hand, the sublevel kinetics are well described by an independent-subunit model, as in Fig. 11,A. Another, surprising observation is that for each of the three conducting states the magnitude of energetic stabilization by mutant subunits is nearly the same (Fig. 10). How can these arguments be reconciled? One possible answer is illustrated by the scheme in Fig. 11 B. Again, we assume that there are three open states of the channel having different conductances and selectivities, but in this scheme a final, rapid, forwardly biased transition (indicated by the dotted line) divides nonconducting from conducting states. The dwell times of the channel in the nonconducting states (states 11, 13, and 14) are assumed to be brief compared with the dwell times in the corresponding open states, too brief to be experimentally observed. The forwardly biased equilibria therefore lengthen the observed dwell times (actually the burst durations) in the conducting states by factors equal to the equilibrium constants θ_s1, θ_s2, and θ_o. We assume that θ_o and θ_s2 are larger than unity in the W₄ channel, and that all three equilibrium constants increase as the number of mutant subunits increases.

The equilibrium constant θ_o serves the same role as the parameter θ in the model of Zagotta et al. (1994 b), which suggests a coupling between the final voltage- dependent transition and the opening of the channel. In the model, the lifetime of the open state of the channel is prolonged by the factor θ ≈ 10, and a degree of positive cooperativity is conferred on the activation process. The final transition shown in Fig. 11 B has the same effect of lengthening the dwell time in the open state, but also lengthens the dwell times in the sublevels by the same factor.

It should be kept in mind that the model shown in Fig. 11 B fails to account for many phenomena, and is presented here only as a tentative hypothesis. Most importantly, it does not account for the alternate activation pathway that involves the sub₂′ state. Such a pathway would be expected to arise if an individual subunit's transition rates do depend on the presence of the T442S mutation; as it is, the model assumes kinetic symmetry for simplicity. Also, the underlying scheme of Zagotta et al. (1994,b) is insufficient to account for kinetic phenomena at voltage extremes, and a more complex model is implicated (Schoppa and Sigworth, 1998b). Nevertheless, we prefer to use this simple model for illustrative purposes.

It is commonly accepted that Shaker channels have at least three gates. The first is responsible for the N-type inactivation process, in which the inner mouth of the channel is occluded by a domain formed by the NH₂-terminal region of each subunit (Hoshi et al., 1990). The second is the C-type inactivation gate, whose behavior is sensitive to ion binding and to mutations at the external mouth of the channel and whose closing is accompanied by motions of residues in that region (Hoshi et al., 1991; Lopez-Barneo and Aldrich, 1993; Liu et al., 1996b). When this gate is “closed,” the channel can conduct ions but with greatly altered selectivity (Starkus et al., 1997). A related “P-type” inactivation mechanism has been described that also involves residues near the external mouth (DeBiasi et al., 1993b; Olcese et al., 1997; Yang et al., 1997). Third, there is the main “activation gate” of the channel, which has been mapped by changes in cysteine accessibility to lie at the intracellular end of the S6 helices (Liu et al., 1997). In the structure of the Streptomyces lividans potassium channel (KcsA), the corresponding “inner helices” are seen to form a bundle that has a constriction in this region (Doyle et al., 1998).

Traditionally, the channel gating and selectivity functions have been considered as separate structures in a voltage-gated channel (Hille, 1992). However, the large gating effects of some mutations suggest that the selectivity filter region may also participate in voltage-dependent gating (see, for example, Yool and Schwarz, 1991; Heginbotham et al., 1992; Kirsch et al., 1992; De Biasi et al., 1993a, 1993b; for review see Sigworth, 1994). The activation-coupled subconductance behavior observed by Chapman et al. (1997) and in our previous study suggest that voltage-dependent processes in individual subunits affect ion permeation. The Shaker T442 residue corresponds to T75 in the KcsA channel, which lies at the inner end of the selectivity filter loop. The carbonyl and hydroxyl oxygens of T75 help form the inner ion binding site; it is therefore not surprising that mutations at T442 change the conductance and selectivity of Shaker channels. That mutations at T442 also affect the lifetimes of conducting states suggest that the environment of this residue is influenced by the state of the main activation gate; energetic changes due to the mutation would then be mirrored in changes of the open– closed equilibrium of the activation gate.

The results of the present study lead us reluctantly to suggest the existence of yet another gate in the Shaker channel. (Here we use the term “gate” in the general sense of a region of the channel complex that, through conformational changes, modulates the ion flux.) This “pore gate” would be responsible for switching among the various conductance levels; the most plausible locus for this gate would be at the selectivity filter, where very small atomic motions would have large effects on conductance and selectivity. In the context of Fig. 11 B, we would associate the pore gate with the vertical transitions among the final closed states (states 11, 13, and 14). Its intermediate degrees of opening can be imagined to arise from heteromeric pore conformations, as proposed by Chapman et al. (1997). The allosteric transitions in the scheme are then the transitions of the “main gate” composed of the S6 helix bundle. Voltage-dependent opening of the main gate would be driven by the allosteric equilibrium constants, which increase in the order θ_s1 < θ_s2 < θ_o, reflecting coupling between the conformational changes that drive the pore gate and the energetics of main-gate opening.

This view of two coupled activation gates, one in the selectivity-filter region and the other at the intracellular end of the S6 helices, is only speculative, but it finds some support from three arguments. First, the existence of two activation gates predicts that a class of direct channel closures, due to closing of the main gate, should exist along with the closures through sublevels that are predominantly seen. A class of weakly voltage-dependent, direct closures is in fact observed in mutant channels. These closures (see Figs. 7 and 9 of Zheng and Sigworth, 1997) are kinetically distinct from the highly voltage-dependent transitions through the sublevels. A second argument involves the C-type inactivation process. This process derives its voltage dependence from strong coupling to the activation process (Olcese et al., 1997), but its gate is associated with the selectivity filter and outer pore entrance of the channel. The structural basis of coupling between activation and C-type inactivation would be simply explained if the selectivity filter region also participates in activation-related conformational changes. Third, the T442S mutation has been seen in this study not to produce a new class of subconductance states but instead to stabilize existing states that are probably present even in the wild-type channel. A parsimonious explanation for the simultaneous stabilization of all the conducting states would be an allosteric scheme like that in Fig. 11 B.

We are grateful to Dr. L.Y. Jan (University of California at San Francisco, San Francisco, CA) for the Shaker-NGK2 chimera construct. We also thank Y. Yan for technical assistance with molecular biology and Y. Yang, L. Islas, Q. Jiang, and L. Venkataramanan (all at Yale University) for helpful discussions.

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

M

mutant subunit

W or WT

Shaker-mKv3.1 chimera