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ABSTRACT |
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 Top ABSTRACT introductionmethodsresultsdiscussionreferences |
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0.5 kcal/mol. Consistent with previous results in the mutant channel, sublevels in channels with two or no mutant subunits also showed ion selectivities that differ from that of the fully open level, having relatively higher K+ than Rb+ conductances. A model is presented in which Shaker channels have two coupled activation gates, one associated with the selectivity filter and a second associated with the S6 helix bundle.
Key Words: ion channel gating • selectivity • subconductance • cooperativity • subunit stoichiometry
Abbreviations: M, mutant subunit; W or WT, Shaker-mKv3.1 chimera
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introduction |
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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., 1994a; 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 
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., 1994b; 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., 1994a; 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?
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). 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 Recording
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.
Data Analysis
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.
Binomial Fitting
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:
 | (1) |
in which qn is the number of observed channels having n mutant subunits, n = 0–4.
Distribution of Transition Times
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 ti of crossing threshold 
i is determined by both the filter characteristics (Colquhoun and Sigworth, 1995) and the current noise ni at that time, such that the following equation holds for the filter step response H(t):
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The time spent between the crossings of the two thresholds 1 and 2 is then given by
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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
 | (4) |
where
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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 µs = H–1(2) – H–1(1) and variance 
s2 = (k11)2 + (k22)2. Thus, the probability density of s can be written:
 | (5) |
When a closure traverses one or two sublevels whose lifetimes are exponentially distributed with means 
1 and 2, the total transition time has a probability density function that is a weighted sum of the two exponential functions convolved with f0,
 | (6) |
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
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with A1 > 0 in the case that 1 > 2.
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results |
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; 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.
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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
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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.
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Characterization of Sublevels
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.
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). 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.
Sublevels Exist in Heteromultimeric and W4 Channels
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- (M2W2L) and 78.6-pS (M2W2H) channels.
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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.
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Sublevels in the Various Channel Types Show Similar Kinetic Behaviors
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
 | (7) |
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.
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Sublevels Have Differing Ion Selectivities
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 M2W2L and W4 channels showed sublevels in Rb+ currents. We identified two sublevels in M2W2L 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.
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discussion |
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). 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.
Stoichiometries of Heteromultimeric Channels
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.
Sublevels in Heteromultimeric Channels and W4 Channels
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.
Do Activation-coupled Sublevels Exist in Shaker Channels?
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).
Subunit Effects on Dwell Times Suggest Concerted Steps
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. (1994b) 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 o of the open state is determined by
 | (8) |
in which βm and βw 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 βm is two to three orders of magnitude larger than βw. 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,
 | (9) |
in which 
Gm* and Gw* are the free energy contributions to the closing rate constant 
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 SII 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.
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Gw* – Gm* 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.
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). To describe Shaker channel activation, Zagotta et al. (1994b) 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.
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Subunit Transitions or Concerted Transitions?
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 s1, s2, and o. We assume that o and 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 o serves the same role as the parameter in the model of Zagotta et al. (1994b), 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 
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. (1994b) 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.
Multiple Activation Gates in the Shaker Channel
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 s1 < s2 < 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.
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ACKNOWLEDGMENTS |
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This work was supported by National Institutes of Health grant NS-21501.
Submitted: 12 February 1998
Accepted: 29 July 1998
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and •, respectively, corresponding to the channel phenotypes. M, mutant subunit; W, WT subunit.
). Solid lines are fits to the lifetimes at –100 mV of an exponential function in which n is the number of mutant subunits as expected from Eq. 
