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Abstract |
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Cooperativity among the four subunits helps give rise to the remarkable voltage sensitivity of Shaker potassium channels, whose open probability changes tenfold for a 5-mV change in membrane potential. The cooperativity in these channels is thought to arise from a concerted structural transition as the final step in opening the channel. Recordings of single-channel ionic currents from certain other channel types, as well as our previous recordings from T442S mutant Shaker channels, however, display intermediate conductance levels in addition to the fully open and closed states. These sublevels might represent stepwise, rather than concerted, transitions in the final steps of channel activation. Here, we report a similar fine structure in the closing transitions of Shaker channels lacking the mutation. Describing the deactivation time course with hidden Markov models, we find that two subconductance levels are rapidly traversed during most closing transitions of chimeric, high conductance Shaker channels. The lifetimes of these levels are voltage-dependent, with maximal values of 52 and 22 µs at -100 mV, and the voltage dependences of transitions among these states suggest that they arise from equivalent conformational changes occurring in individual subunits. At least one subconductance level is found to be traversed in normal conductance Shaker channels. We speculate that voltage-dependent conformational changes in the subunits give rise to changes in a "pore gate" associated with the selectivity filter region of the channel, producing the subconductance states. As a control for the hidden Markov analysis, we applied the same procedures to recordings of the recovery from N-type inactivation in Shaker channels. These transitions are found to be instantaneous in comparison.
Key Words: likelihood, patch clamp, subconductance, cooperativity, HMM
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INTRODUCTION |
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Shaker potassium channels are formed by four identical subunits surrounding a central ion-conducting pore (
Work on Kv2.1 channels (
Our previous study of channels having various numbers of mutant subunits (
Here, we report that sublevels are clearly identified to occur during deactivation of the "intact-pore" channels. Although their dwell times are 200-fold shorter, these sublevels have similar properties to those observed in the T442S "mutant-pore" channels: most deactivation transitions traverse the sublevels, and the mean lifetime of each sublevel has similar voltage dependence. These results, together with our previous studies of T442S mutant channel sublevels, are consistent with the hypothesis that the final gating steps of Shaker channels involve movements in the ion-selectivity filter region as well as movements of the "main gate" that is formed by the S6 helices.
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MATERIALS AND METHODS |
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cDNA Constructs and Oocyte Expression
Three constructs were used in this study. The channel denoted SN is a Shaker B chimera (provided by Dr. L.Y. Jan, University of California at San Francisco, San Francisco, CA) in which the S6 sequence was substituted with the corresponding sequence from the mKv3.1 (also known as NGK2) channel, and in which the NH2-terminal inactivation sequence was removed (
). N-type inactivation was reinstalled in SN
by subcloning the core sequence of SN
(between the T1 domain and the end of the COOH terminus) into Shaker 29-4 using the restriction sites SnaBI and BsgI. This "full-length" construct was denoted SN. The usual Shaker construct, denoted Sh
, is Shaker H4 having the
6-46 NH2-terminal deletion to remove inactivation. The amino acid sequence of Shaker H4 (
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Oocytes were obtained from Xenopus laevis following the protocol previously described (
Low Noise Single-channel Recording
Single-channel recordings were made in inside-out patches at room temperature. Patch pipettes were pulled from 7052 glass (Garner Glass) or from quartz capillaries (Sutter Instrument Company) using a laser-based pipette puller (model P2000; Sutter Instrument Co.); the pipette tip diameters were 0.51.5 µm. Pipettes were heavily coated with Sylgard (Dow Corning Co.). In our hands, quartz pipettes ( 5 x 10-30 and 10-29 A2/Hz, respectively. The pipette solution contained 140 mM potassium aspartate, 1.8 mM CaCl2, 10 mM HEPES, and the bath solution contained 130 mM potassium aspartate, 10 mM KCl, 1 mM EGTA, 10 mM HEPES; each was 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.
Recordings were made using an Axopatch 200B amplifier (Axon Instruments). To avoid magnetic interference, an LCD monitor was used as the computer display. The Pulse software (HEKA Electronic) was used for data collection. Voltage pulses were applied from a holding potential of -100 mV. Current signals were filtered at 30 kHz with a Bessel filter and sampled at 200 kHz. For each pulse protocol, 3,000 sweeps were collected at a rate of 3 sweeps/s; of these sweeps >20% were blank and were later used for leak and capacitive current subtraction. Open probability was routinely checked to ensure that the channel retained normal gating properties during the long recording time.
Step Response and Inverse Filter
The step response of the recording system was measured by providing a triangular waveform voltage through a metal wire that was placed close to the pipette holder (
with the corner frequency fx = 0.4 times the sampling frequency and the steepness parameter f=
. The relatively short rise time of this type of filter results in more efficient HMM calculations, even though the filter shows an overshoot
10% in amplitude. In our use, the final effective filter bandwidth was 80 kHz. The effect of applying the inverse filter to a recorded trace is shown in Fig 1 A; the power spectrum of the background noise after inverse filtering is shown in Fig 1 B.
HMM analysis is sensitive to baseline drifts during experiments. To subtract any baseline shift as well as the transient currents caused by voltage steps in the pulse protocols, >100 nearby blank sweeps were averaged and used to subtract each sweep. The subtracted data were then inverse-filtered to produce the data set for HMM analysis.
HMM Analysis
In this study, we focused on the vicinity of the last closing transition, which was identified in each recorded sweep as follows. A digital Gaussian filter was used to filter the data to 10 kHz bandwidth. Two thresholds, 90% and 10% of the full single-channel amplitude, were used to locate the time points when a channel makes its last transition leaving the open level and when it arrives at the closed level, respectively. 520 additional sample points (25100 µs) were added at each end of the selected segments to include enough data points that represent the open and closed current levels.
The HMM analysis took three inputs: (1) inverse-filtered raw data; (2) a kinetic model containing information of the number of states and their current levels, the connectivity of those states, transition rates, as well as the auto-regressive coefficients that describe the background noise; and (3) an events list that contains pointers to the data selections, obtained as described above. The HMM model was refined iteratively using the Baum-Welch algorithm (
The HMM analysis code has been integrated into the TAC single-channel analysis software (Bruxton Corp.); it was run on two Macintosh G3 computers with 233300 MHz clock speed and 256 MB of memory. We used the modified version TAC X4.0.5 run with the "continuous-time" option, which invokes the H-noise algorithm (
The starting value of the current in the fully open level was assigned as that measured from an all-points histogram; those of the sublevels were assigned using the relative conductances of the sublevels in the T442S mutant channels. The initial probability of the open state was assigned to be unity. Usually 300 iterations were conducted for each fitting process. The speed of the fitting process was tested with a data set containing 600 data segments with an average length of 120 points. Using a model with three states and four free parameters as well as four AR coefficients, it took a G3 computer 21 s to perform each iteration. With the actual data sets, a few hours were required to run 300 iterations for a simple model and overnight to run a complex model.
Likelihood Interval Estimation
Errors associated with the estimation of the transition rates were evaluated as likelihood intervals. This was done by mapping the likelihood surface curvature near the apex in each dimension represented by a free parameter (
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RESULTS |
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Deactivation of SN Channels Is Not Instantaneous
Activation-associated sublevels have been observed previously in Shaker channels with the pore mutation T442S (. Fig 2 A shows a single-channel trace recorded from a SN
channel expressed in Xenopus oocytes. At a low bandwidth (Fig 2 A, 5 kHz), the deactivation appears to be instantaneous; however, at a higher bandwidth, the time course of the deactivation transitions sometimes appears to progress through intermediate steps. Examples of the last closing transition (as marked by a box in Fig 2 A), are shown in Fig 2 B at 15 kHz bandwidth.
Due to the effect of filtering, an instantaneous step transition will appear to have a finite transition time. At 15 kHz, the rise time (1090% amplitude) of a direct transition from the open level to the closed level is expected to be 0.34/fc = 23 µs, in which fc is the filtering frequency ( current trace. The apparently slower closing rate of SN
channels observed in most traces is consistent with the possibility that deactivation transitions of SN
traverse intermediate conductance levels. The lifetimes of these sublevels are expected to be brief, in the range of tens to hundreds of microseconds (
HMM Analysis Reveals Multiple Sublevels in SN Channels
In this study, we wanted to determine the number of sublevels during deactivation and the mean lifetime of each sublevel at various voltages. The HMM method turned out to be a natural choice for this task. Unlike threshold analysis that relies on detection of current crossing of a certain level to determine current transitions, HMM analysis finds the model parameters that maximize the probability of observing the entire data set given the model (
The first question we tried to answer using HMM was whether SN channels traverse sublevels during deactivation. We started with linear models with increasing numbers of conducting states (Fig 3, Models IIV). The existence of an additional state would be implied by a large increase in the likelihood value, relative to the increase in number of free parameters, when a new state is added. An increase of about two log-likelihood units is expected on theoretical grounds (
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These lifetime estimates are briefer than the dwell-time estimates of 70 and 280 µs that we previously obtained using an amplitude histogram approach on the deactivation time course of SN channels (
Are there more than two sublevels in SN channels? As shown in Table 1, the model having a third sublevel (Model IV) indeed further increased the likelihood value by 43 log units per free parameter over Model III. However, it is noticed that the current level of the additional state S3 in Model IV is larger than that of the open state (though only by 10%) and the transitions into and out of this state are unidirectional and very rapid. Thus the model describes a brief increase in channel current just preceding the closing transitions. The single-channel recordings of SN
channels, similar to those of wild-type Shaker channels, contained many brief closures (flickers). One explanation for the increased likelihood from Model IV is that some of the deactivation transitions we selected may start from a flickering state and then proceed through the open state. However, because the rate constants and current levels of the other states in Model IV are indistinguishable from the values for Model III, we take Model III to be a good approximate description of the channel behavior, having two main sublevels.
The next question we asked was whether the two sublevels, denoted S2 and S1, are always traversed during channel deactivation. A model having S2 outside of the deactivation pathway (Model III') clearly did not work, as indicated by its much lower likelihood value compared with Model III. We also constructed models in which direct transitions to closed states were allowed from the open state and from the higher conductance sublevel S2 (Models VVII). In models containing loops, no constraint for detailed balance was applied. Nevertheless, with these models, we found at most only moderate increases in the likelihood value. As shown in Table 1, a direct OC transition gave Model V an increase in likelihood by 25 log units per free parameter over Model II; similar direct transitions from O and S2 to C reduced the likelihood value of Model VII by
11 log units per free parameter compared with Model III (the reduction probably reflects a convergence error; see below). In both cases, the O
C rate was smaller than the corresponding O
S rate, suggesting that the O
C transition rarely occurs. The S2
C transition also moderately increased the likelihood value of Model VI over Model III, by only 6 log units per free parameter. We conclude that these direct-closing pathways are not ruled out, but their inclusion results in little increase in the likelihood values. The simplest description of our data is that most or all closing transitions occur through both sublevels.
To test whether there are other sublevels that are not in the S2-S1 pathway, models were considered with a branching path containing another set of sublevels, denoted T2 and T1 (Models VIIIXI). A branching path clearly increased the likelihood values. For example, the likelihood of Model VIII was 54 log units per free parameter higher than that of Model II. Compared with the S states, the T states (especially T1) had much longer mean lifetimes. On the other hand, fewer than 10% of the deactivation transitions took the T pathway, so that the states T2 and T1 are rarely visited. Evidence for an alternative sublevel state like T1 has been presented previously in the study of heteromultimeric channels containing pore mutant subunits (
The above results are summarized in Fig 4, in which the log-likelihood value is plotted against the number of free parameters in each model. It is clearly seen that the inclusion of one and two sublevels (going from Model I to Models II and III) gave the most dramatic increases in likelihood. Adding T2 and T1 gave further increases, but their contributions were much smaller (Models IX and XI). In theory, a model with more free parameters should always give a higher likelihood value (
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SN Channel Sublevels Show Voltage-dependent Lifetimes
Deactivation transitions in the voltage range from -80 to -140 mV were analyzed with Model III. At each voltage, S2 and S1 were seen to have distinct current levels with linear I-V relationships like that of the open state (Fig 5 A). The relative conductances of S2 and S1 are estimated to be 81 and 13% of the open level, respectively. It was found that the mean lifetime of each sublevel was voltage-dependent (Fig 5 B), following similar bell-shaped curves. The longest lifetimes for S2 and S1 were found to occur near -100 mV, with the estimated values to be 52 and 22 µs, respectively. The estimated transition rates at -120 mV and the partial charges, estimated by exponential fitting of the transition rates as functions of voltage (Fig 5 C), are given in Fig 5 D. At -120 mV, SN channels deactivate quickly; accordingly, the backward transitions showed higher rates than the forward transitions. All the transition rates were voltage-dependent. The amount of charge movement in the S2
S1 and S1
C transitions, 1.0 e0 and 1.2 e0, respectively, is smaller than, but comparable to, our earlier estimates from the T442S mutant channel sublevels, which were 1.6 e0 and 1.7 e0, respectively (
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It is interesting to compare the size of these estimated charge movements with those of the elementary charge movements of the Shaker channel voltage sensors.
The estimated forward transition rate S1S2 is much higher than the other two forward rates and is comparable to the backward transition S2
S1. The result would predict fast flickering between the two sublevels. Simulations using the model shown in Fig 5 D indeed generated flickerings between S1 and S2 (Fig 5 E). Such flickering behavior was not obvious in the T442S mutant channels (
Errors associated with the estimation of each Model III transition rate were evaluated by fitting the same data while fixing the rate in question to a certain percent away from its optimal value (Fig 6). From this analysis, we obtained the two-unit likelihood interval for each rate, which is given in Fig 5 D. (Two likelihood units are comparable to two standard deviations, with the two measures of error being identical in the case of the normal distribution; C0 transition, which had the very slow rate of 210 s-1 (representing a rare transition) and a 130% confidence interval. It should be noted that the data set at -120 mV was our smallest, containing only 622 deactivation time courses. The data sets at other voltages contained 1,2861,700 deactivation time courses. It is expected that the errors associated with the estimates at those voltages should be smaller.
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Does Deactivation of "Wild-type" Shaker Channels Also Traverse Sublevels?
The SN channel is a Shaker B chimera having the S6 segment sequence from mKv3.1 (
channels is very similar to "wild-type" Sh
channels (
channels.
A set of 716 deactivation transitions recorded from a Sh channel at -100 mV was analyzed with the HMM method. Examples of Sh
channel deactivations are shown in Fig 7 (A and B). When Model II (Fig 3) was used, the sublevel was assigned an amplitude of -2.4 pA and a mean lifetime of 56 µs. Compared with Model I having no sublevel, the likelihood of Model II was 192 log units greater (Fig 7 C). The transition rates are listed in Table 2. The relative amplitude of the detected sublevel was similar to that of the S2 sublevel in SN
channels.
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The possibility that Sh channels also have a second sublevel was tested using Model III. However, although this and other more complex models yielded higher log-likelihood values than Model II (Fig 7 C), in each case one or more of the estimated rates exceeded 100,000 s-1. We take rate constant values of this magnitude, greater than half the sampling rate, to be artifactual; in our experience with simulations, they typically arise from attempts of the HMM algorithm to fit features of the noise. Therefore, we take the only reliable result of this analysis to be the conclusion that Model II is much superior to Model I, and that the Sh
channel passes through at least one sublevel during deactivation. The lifetime of the detected subconductance state is
50 µs at -100 mV, and its relative conductance is
60% of the full channel conductance level. These characteristics are essentially the same as the main sublevel S2 of the SN
channel.
The poor performance of Model III means only that we cannot tell whether there is more than one sublevel in Sh channels. It is quite possible that a second sublevel corresponding to S1, having a smaller conductance and a shorter lifetime, does in fact exist. That such a sublevel is not detected may probably result from the lower signal-to-noise ratio of the Sh
current recordings.
An Internal Control: N-type Inactivation Transitions
Several possible control experiments can be envisioned that would allow the reliability and sensitivity of the HMM method to be tested. One test would be to conduct a parallel analysis on simulated data to see if HMM analysis would come up with the same parameters that have been used to generate the data. This was the major test used by channels, yielding the SN channel type, and to analyze N-type inactivation recovery transitions in the same way as we did with deactivation transitions. This approach has several advantages. First, the two kinds of transitions are recorded from the same channel under identical conditions. This avoids any variation in experimental conditions and data processing. Second, N-type inactivation is a well understood process in voltage-dependent potassium channels, achieved by an NH2-terminal domain that physically blocks ion permeation (
channels.
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Single-channel currents were recorded from SN channels (Fig 8, B1 and B2). A total of 765 channel events during tail currents at -120 mV were selected, based on the criteria that the current recovered to the fully open level and stayed at that level for a time long enough to allow reliable estimation of the current amplitude. Segments of the current rising phase and decaying phase were selected and analyzed independently using HMMs. It was found that models with one or two sublevels provided dramatically improved fits to the deactivation transitions over Model 1 that had only open and closed states. The log-likelihood values increased by 673 and 395 units in going from Model 1 to 2 and 3 (Fig 8 C). The two sublevels detected by Model 3 had conductance values and mean lifetimes similar to those found in SN channel deactivations (the mean lifetimes are plotted in Fig 5 for comparison), confirming that the deactivation process was not affected by restoring the N-type inactivation.
On the other hand, having additional sublevels did not fit the inactivation-recovery transition any better than Model 1. The small increases in log-likelihood values, 6 and 22 for Models 2 and 3, respectively, are well within the range expected from the addition of one or four free parameters. In the case of Model 2, the estimated lifetime of the sublevel was 12 µs and its estimated amplitude was 2% of the open current, making it essentially indistinguishable from the closed level. Increasing the number of AR coefficients in the noise model from four to five and six further reduced the estimated lifetime and conductance of this state, suggesting that this state reflects only an imperfection in modeling the noise. As a further test, we fixed the conductance of the sublevel to values close to those of the ones found in the deactivation transitions of the same channels (Fig 8 C, Models 2' and 2''). This dramatically reduced the likelihood value generated from fitting the inactivation-recovery transitions but had little effect on those generated from fitting the deactivation transitions. We thus conclude that the inactivation-recovery transition is direct while the deactivation transition clearly passes through sublevels.
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DISCUSSION |
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The present paper is the third in a series of studies of the activation-coupled sublevels in Shaker potassium channels (
HMM Analysis of Single-channel Currents
The behavior of many ion channels can be well described by finite-state Markov models, suggesting that the gating transitions occur between well-defined states (
The theory of hidden Markov models, which has been very successfully applied in speech recognition, was first introduced to single-channel analysis 10 yr ago (
In early applications of HMM analysis, the background noise in successive data samples was assumed to be uncorrelated (the white noise case). The high resolution measurement of current with the patch clamp, however, inevitably yields colored noise, due to noise currents induced in the capacitance at the preamplifier input as well as noise from relaxation processes (
Our application of the continuous-time HMM analysis has allowed us to deduce the properties of sublevels with mean lifetimes in the range of tens of microseconds. The existence of such sublevels has been suggested by our previous experiments on channels with mutant subunits that dramatically prolong the sublevel durations (
Sublevels Are Associated with Subunit Gating Transitions
It has been found that gating transitions of Shaker channels are coupled to charge movements totaling 13 e0 (
1.0 e0. A comparable voltage dependence (1.6 e0) was seen in channels containing the T442S mutation (
Activation-coupled subconductance levels have been observed in various members of the voltage-gated potassium channel superfamily. The large conductance Ca2+-activated potassium channel appears to close through a brief sublevel 510% in amplitude (
Fine Structure in the Final Concerted Step of Channel Opening
Detailed studies of Shaker channel activation (
In the T442S mutant of the SN channel (
and the T442S variant (see Fig 9B and Fig C) shows that the voltage dependences are similar, but the mean lifetimes differ by a factor of
200. SN
and wild-type Shaker channels pass through these sublevels very quickly; if our estimates for the rate constants of SN
are extrapolated to -45 mV (the approximate half-activation voltage) Model III becomes
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where rates are given in seconds-1 at -45 mV and question marks denote rate constants that were not determined in the present study. The strongly forward-biased transition S1S2 can explain much of the forwardly directed equilibrium that has been ascribed previously to the final concerted steps in channel opening. However, the S1
S2 transition is only one of three transitions that we now see to occur in rapid succession before channel opening; all of these occur on a much shorter time scale than the macroscopic activation time constant of
8 ms at this potential.
We conclude that the concerted transitions postulated in previous kinetic studies of Shaker channels actually contain a fine structure, in which voltage-dependent transitions in individual subunits give rise to a stairstep increase in channel conductance. However, these transitions are highly cooperative, such that they occur in very rapid succession toward the fully-open channel configuration.
Gating Role of the Outer Pore
The residue T442 corresponds to T75 at the interior end of the pore helix of the KcsA channel (
The main activation gate of the Shaker channel has been mapped to residues at the intracellular end of the S6 transmembrane domain (
What is the relationship between the pore gate and the main S6 gate in a Shaker channel? During the deactivation process, the channel rapidly moves from the open state through one or more sublevels; we take these transitions to be the action of the pore gate, with each step representing a conformational change in the outer pore region reflecting a deactivation transition in an individual subunit. The channel then becomes closed (i.e., its current becomes unmeasurably small) either from further closing of the pore gate or from the eventual closing of the main gate. There are many kinetically distinguishable closed states of the channel; judging from the effects of intracellular blockers and the inactivation particle on channel-gating behavior, we expect that most of the closed states will correspond to the main gate being closed. It is quite possible that some closed statesmainly ones closest to open statesmay represent states in which the main gate is open but the pore gate, although not being maximally closed, provides a sufficient barrier to ion passage that the ionic current is too small to observe.
Our speculative picture is one in which the main gate is typically the first to open during activation and the last to close during deactivation. In the T442S mutant channels (
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Footnotes |
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J. Zheng's current address is Department of Physiology and Biophysics, Howard Hughes Medical Institute, University of Washington, Seattle, WA 98195-7290
Address correspondence to F.J. Sigworth, Yale University School of Medicine, Department of Cellular and Molecular Physiology, 333 Cedar Street, New Haven, CT 06520. Fax: (203) 785-4951; E-mail: fred.sigworth{at}yale.edu
* Abbreviations used in this paper: AR, auto-regressive; HMM, hidden Markov model.
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Acknowledgements |
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We are grateful to Dr. Lily Y. Jan for the Shaker-NGK2 chimera construct, Dan Brown and Lin Ci Brown (Bruxton Corp., Seattle, WA) for their help with the application of the TAC program; and Dr. Richard Ayer and the Sutter Instrument Co. for the loan of a laser-based pipette puller. We also thank Yangyang Yan for technical assistance and Youshan Yang, Leon Islas, Qiuxing Jiang, and Kathryn Klemic (all from Yale University) for helpful discussions. J. Zheng is grateful to William N. Zagotta (University of Washington, Seattle, WA) for insights and support during the later phase of this study.
This work was supported by National Institutes of Health grant NS-21501.
Submitted: 26 March 2001
Revised: 3 August 2001
Accepted: 4 September 2001
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References |
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---|
Armstrong, C.M. 1971. Interaction of tetraethylammonium ion derivatives with the potassium channels of giant axons. J. Gen. Physiol 58:413-437[Medline].
Baum, L.E., Petrie, T., Soules, G., and Weiss, N. 1970. A maximization technique occurring in the statistical analysis of probabilistic functions of Markov chanins. Ann. Math. Statist. 41:164-171.
Becchetti, A., Gamel, K., and Torre, V. 1999. Cyclic nucleotidegated channels. Pore topology studied through the accessibility of reporter cysteines. J. Gen. Physiol 114:377-392[Abstract/Full Text].
Benndorf, K. 1995. Low-noise recording. In Sakmann B., Neher E., eds. Single-channel Recording. New York, Plenum Press, 129-145.
Bezanilla, F. 2000. The voltage sensor in voltage-dependent ion channels. Physiol. Rev 80:555-592[Abstract/Full Text].
Bezanilla, F., Perozo, E., and Stefani, E. 1994. Gating of Shaker K+ channels: II. The components of gating currents and a model of channel activation. Biophys. J 66:1011-1021[Abstract].
Chapman, M.L., VanDonGen, H.M., and VanDonGen, A.M. 1997. Activation-dependent subconductance levels in the drk1 K channel suggest a subunit basis for ion permeation and gating. Biophys. J 72:708-719[Abstract].
Chung, S.H., Moore, J.B., Xia, L.G., Premkumar, L.S., and Gage, P.W. 1990. Characterization of single channel currents using digital signal processing techniques based on hidden Markov models. Philos. Trans. R. Soc. Lond. B Biol. Sci 329:265-285[Medline].
Chung, S.H., Krishnamurthy, V., and Moore, J.B. 1991. Adaptive processing techniques based on hidden Markov models for characterizing very small channel currents buried in noise and deterministic interferences. Philos. Trans. R. Soc. Lond. B Biol. Sci 334:357-384[Medline].
Colquhoun, D., and Sigworth, F.J. 1995. Fitting and statistical analysis of single-channel records. In Sakmann B., Neher E., eds. Single-channel Recording. New York, Plenum Press, 95-127.
Del Camino, D., Webster, S.M., and Yellen, G. 2001. An intracellular gate for metal cations in Shaker K+ channels. Biophys. J 80:16A. (Abstr.
De Biasi, M., Drewe, J.A., Kirsch, G.E., and Brown, A.M. 1993. Histidine substitution identifies a surface position and confers Cs+ selectivity on a K+ pore. Biophys. J 65:1235-1242[Abstract].
Doyle, D.A., Morais Cabral, J., Pfuetzner, R.A., Kuo, A., Gulbis, J.M., Cohen, S.L., Chait, B.T., and MacKinnon, R. 1998. The structure of the potassium channel: molecular basis of K+ conduction and selectivity. Science 280:69-77[Abstract/Full Text].
Ferguson, W.B., McManus, O.B., and Magleby, K.L. 1993. Opening and closing transitions for BK channels often occur in two steps via sojourns through a brief lifetime subconductance state. Biophys. J 65:702-714[Abstract].
Flynn, G.E., and Zagotta, W.N. 2001. Conformational changes in S6 coupled to the opening of cyclic nucleotide-gated channels. Neuron 30:689-698[Medline].
Fox, J.A. 1987. Ion channel subconductance states. J. Membr Biol 97:1-8[Medline].
Fredkin, D.R., and Rice, J.A. 1992. Maximum likelihood estimation and identification directly from single-channel recordings. Proc. R. Soc. Lond. B Biol. Sci 249:125-132[Medline].
Heginbotham, L., Abramson, T., and MacKinnon, R. 1992. A functional connection between the pores of distantly related ion channels as revealed by mutant K+ channels. Science 258:1152-1155[Medline].
Holmgren, M., Smith, P.L., and Yellen, G. 1997. Trapping of organic blockers by closing of voltage-dependent K+ channels: evidence for a trap door mechanism of activation gating. J. Gen. Physiol 109:527-535[Abstract/Full Text].
Holmgren, M., Shin, K.S., and Yellen, G. 1998. The activation gate of a voltage-gated K+ channel can be trapped in the open state by an intersubunit metal bridge. Neuron 21:617-621[Medline].
Horn, R. 1987. Statistical methods for model discrimination. Applications to gating kinetics and permeation of the acetylcholine receptor channel. Biophys. J 51:255-263[Abstract].
Hoshi, T., Zagotta, W.N., and Aldrich, R.W. 1990. Biophysical and molecular mechanisms of Shaker potassium channel inactivation. Science 250:533-538[Medline].
Kamb, A., Tseng-Crank, J., and Tanouye, M.A. 1988. Multiple products of the Drosophila Shaker gene may contribute to potassium channel diversity. Neuron 1:421-430[Medline].
Kirsch, G.E., Drewe, J.A., Hartmann, H.A., Taglialatela, M., de Biasi, M., Brown, A.M., and Joho, R.H. 1992. Differences between the deep pores of K+ channels determined by an interacting pair of nonpolar amino acids. Neuron 8:499-505[Medline].
Levis, R.A., and Rae, J.L. 1993. The use of quartz patch pipettes for low noise single channel recording. Biophys. J 65:1666-1677[Abstract].
Liu, J., and Siegelbaum, S.A. 2000. Change of pore helix conformational state upon opening of cyclic nucleotide-gated channels. Neuron 28:899-909[Medline].
Liu, Y., Holmgren, M., Jurman, M.E., and Yellen, G. 1997. Gated access to the pore of a voltage-dependent K+ channel. Neuron 19:175-184[Medline].
Lopez, G.A., Jan, Y.N., and Jan, L.Y. 1994. Evidence that the S6 segment of the Shaker voltage-gated K+ channel comprises part of the pore. Nature 367:179-182[Medline].
Lu, T., Ting, A.Y., Mainland, J., Jan, L.Y., Schultz, P.G., and Yang, J. 2001. Probing ion permeation and gating in a K+ channel with backbone mutations in the selectivity filter. Nat. Neurosci 4:239-246[Medline].
MacKinnon, R. 1991. Determination of the subunit stoichiometry of a voltage-activated potassium channel. Nature 350:232-235[Medline].
Michalek, S., Wagner, M., and Timmer, J. 2000. A new approximate likelihood estimator for ARMA-filtered hidden Markov models. IEEE Trans. Sig. Proc. 48:1537-1547.
Perozo, E., Cortes, D.M., and Cuello, L.G. 1999. Structural rearrangements underlying K+ channel activation gating. Science 285:73-78[Abstract/Full Text].
Qin, F., Auerbach, A., and Sachs, F. 2000. Hidden Markov modeling for single channel kinetics with filtering and correlated noise. Biophys. J 79:1928-1944[Abstract/Full Text].
Rosenmund, C., Stern-Bach, Y., and Stevens, C.F. 1998. The tetrameric structure of a glutamate receptor channel. Science 280:1596-1599[Abstract/Full Text].
Ruiz, M.L., and Karpen, J.W. 1997. Single cyclic nucleotide-gated channels locked in different ligand- bound states. Nature 389:389-392[Medline].
Schneggenburger, R., and Ascher, P. 1997. Coupling of permeation and gating in an NMDA-channel pore mutant. Neuron 18:167-177[Medline].
Schoppa, N.E., and Sigworth, F.J. 1998a. Activation of Shaker potassium channels. I. Characterization of voltage-dependent transitions. J. Gen. Physiol 111:271-294[Abstract/Full Text].
Schoppa, N.E., and Sigworth, F.J. 1998b. Activation of Shaker potassium channels. III. An activation gating model for wild-type and V2 mutant channels. J. Gen. Physiol 111:313-342[Abstract/Full Text].
Schwarz, T.L., Tempel, B.L., Papazian, D.M., Jan, Y.N., and Jan, L.Y. 1988. Multiple potassium-channel components are produced by alternative splicing at the Shaker locus in Drosophila. Nature 331:137-142[Medline].
Sigworth, F.J. 1995. Electronic design of the patch clamp. In Sakmann B., Neher E., eds. Single-channel Recording. New York, Plenum Press, 95-127.
Sokolova, O., Kolmakova-Partensky, L., and Grigorieff, N. 2001. Three-dimensional structure of a voltage-gated potassium channel at 2.5 nm resolution. Structure 9:215-220[Medline].
Sun, Z.P., Akabas, M.H., Goulding, E.H., Karlin, A., and Siegelbaum, S.A. 1996. Exposure of residues in the cyclic nucleotide-gated channel pore: P region structure and function in gating. Neuron 16:141-149[Medline].
Sunderman, E.R., and Zagotta, W.N. 1999a. Mechanism of allosteric modulation of rod cyclic nucleotide-gated channels. J. Gen. Physiol 113:601-620[Abstract/Full Text].
Sunderman, E.R., and Zagotta, W.N. 1999b. Sequence of events underlying the allosteric transition of rod cyclic nucleotide-gated channels. J. Gen. Physiol 113:621-640[Abstract/Full Text].
Taylor, W.R., and Baylor, D.A. 1995. Conductance and kinetics of single cGMP-activated channels in salamander rod outer segments. J. Physiol. 483:567-582[Abstract].
Venkataramanan, L., Kuc, R., and Sigworth, F.J. 1998a. Identification of hidden Markov models for ion channel currents--part II: state-dependent excess moise. IEEE Trans. Sig. Proc. 46:1916-1929.
Venkataramanan, L., Walsh, J.L., Kuc, R., and Sigworth, F.J. 1998b. Identification of hidden Markov models for ion channel currentspart I: colored background noise. IEEE Trans. Sig. Proc. 46:1901-1915.
Venkataramanan, L., Kuc, R., and Sigworth, F.J. 2000. Identification of hidden Markov models for ion channel currentspart III: bandlimited, sampled data. IEEE Trans. Sig. Proc. 48:376-385.
Yellen, G. 1998. The moving parts of voltage-gated ion channels. Q. Rev. Biophys. 31:239-295[Medline].
Yellen, G., Jurman, M.E., Abramson, T., and MacKinnon, R. 1991. Mutations affecting internal TEA blockade identify the probable pore- forming region of a K+ channel. Science 251:939-942[Medline].
Yool, A.J., and Schwarz, T.L. 1991. Alteration of ionic selectivity of a K+ channel by mutation of the H5 region. Nature 349:700-704[Medline].
Yool, A.J., and Schwarz, T.L. 1995. Interactions of the H5 pore region and hydroxylamine with N-type inactivation in the Shaker K+ channel. Biophys. J 68:448-458[Abstract].
Zagotta, W.N., Hoshi, T., and Aldrich, R.W. 1990. Restoration of inactivation in mutants of Shaker potassium channels by a peptide derived from ShB. Science 250:568-571[Medline].
Zagotta, W.N., Hoshi, T., and Aldrich, R.W. 1994. Shaker potassium channel gating. III: Evaluation of kinetic models for activation. J. Gen. Physiol 103:321-362[Abstract].
Zheng, J., and Sigworth, F.J. 1997. Selectivity changes during activation of mutant Shaker potassium channels. J. Gen. Physiol 110:101-117[Abstract/Full Text].
Zheng, J., and Sigworth, F.J. 1998. Intermediate conductances during deactivation of heteromultimeric Shaker potassium channels. J. Gen. Physiol 112:457-474[Abstract/Full Text].
Zhou, M, Morais-Cabral, J.H., Mann, S., and MacKinnon, R. 2001. Potassium channel receptor site for the inactivation gate and quaternary amine inhibitors. Nature. 411:657-661[Medline].
Zimmerman, A.L., and Baylor, D.A. 1986. Cyclic GMP-sensitive conductance of retinal rods consists of aqueous pores. Nature 321:70-72[Medline].