From the Department of Cellular and Molecular Physiology, Yale University School of Medicine, New Haven, Connecticut 06520
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ABSTRACT |
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The conformational changes associated with activation gating in Shaker potassium channels are functionally characterized in patch-clamp recordings made from Xenopus laevis oocytes expressing Shaker channels with fast inactivation removed. Estimates of the forward and backward rates for transitions are obtained by fitting exponentials to macroscopic ionic and gating current relaxations at voltage extremes, where we assume that transitions are unidirectional. The assignment of different rates is facilitated by using voltage protocols that incorporate prepulses to preload channels into different distributions of states, yielding test currents that reflect different subsets of transitions. These data yield direct estimates of the rate constants and partial charges associated with three forward and three backward transitions, as well as estimates of the partial charges associated with other transitions. The partial charges correspond to an average charge movement of 0.5 e0 during each transition in the activation process. This value implies that activation gating involves a large number of transitions to account for the total gating charge displacement of 13 e0. The characterization of the gating transitions here forms the basis for constraining a detailed gating model to be described in a subsequent paper of this series.
Key words: ion channel; gating current; single-channel current; patch clamp; kinetic model ![]() |
INTRODUCTION |
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Voltage-gated sodium, calcium, and potassium channels underlie the electrical properties of excitable cells.
Insights into the structural changes involved in the voltage-dependent opening of these channels first came
from functional studies performed in the squid axon
(Hodgkin and Huxley, 1952a, 1952b
). The steep voltage sensitivity of the observed potassium and sodium
conductances suggested that the channel opening process involves the displacement of a large amount of
charge across the cell membrane. The long delay in the
time courses of activation implied that channel opening involves multiple kinetic steps. The structural origins of these functional properties are now becoming
clear. The alpha subunits of voltage-gated sodium and
calcium channels are each encoded by a single long
transcript with four homologous regions (Noda et al.,
1984
; Tanabe et al., 1987
), while voltage-gated potassium channels are encoded by a transcript that is approximately one-fourth as long (Tempel et al., 1987
;
Kamb et al., 1988
), with a channel complex formed by
four subunits (MacKinnon, 1991
; Kavanaugh et al.,
1992
; Li et al., 1994
). A requirement for separate activation of each of these units helps to explain the delay in
channel activation. Each of the protomers or subunits
of these channels contains a putative transmembrane
segment S4 that has a number of conserved basic residues and is a candidate for the charged region of the channel that moves in response to voltage, leading to
channel activation (Guy and Seetharamulu, 1986
;
Noda et al., 1986
). Mutations in the S4 region yield
large effects on the voltage dependence of activation
(Stühmer et al., 1989
; Liman et al., 1991
; Lopez et al.,
1991
; McCormack et al., 1991
; Papazian et al., 1991
;
Logothetis et al., 1992
; summarized in Sigworth, 1994
).
Also, it has been shown recently that membrane potential changes cause changes in accessibility of S4 residues (Yang and Horn, 1995
; Yang et al., 1996
; Mannuzzu et al., 1996
; Larsson et al., 1996
), and that S4 charge changes cause changes in total gating charge
movement (Aggarwal and MacKinnon, 1996
; Seoh et
al., 1996
).
Insights into the mechanics of activation gating have
also come from extensions of the functional studies
that were first performed by Hodgkin and Huxley
(1952a, 1952b
). In voltage-clamp measurements of
macroscopic and single-channel ionic currents, various
voltage protocols have been used to emphasize particular steps in the activation process (Cole and Moore,
1960
). The voltage-dependent transitions among
closed states have also been characterized from the
time courses of gating currents, which are the direct
electrical manifestation of the charge displacements associated with conformational changes (Armstrong and
Bezanilla, 1973
; Schneider and Chandler, 1973
; Keynes
and Rojas, 1974
). Additionally, the fluctuations in the
gating currents can provide information about the size of the charge displacements in single gating transitions
(Conti and Stühmer, 1989; Crouzy and Sigworth, 1993
;
Sigg et al., 1994b
). Ultimately, the understanding of
voltage gating in ion channels will require combining
this detailed functional information with experiments
that give more direct structural information.
Examples of the value of detailed functional studies
are seen in the recent work on the Shaker potassium
channel (Bezanilla et al., 1991; Stühmer et al., 1991
;
Schoppa et al., 1992
; Bezanilla et al., 1994
; Hoshi et al.,
1994
; McCormack et al., 1994
; Perozo et al., 1994
; Stefani et al., 1994
; Zagotta et al., 1994
a, 1994b). Shaker
channels have been a favorite in the study of activation gating for a variety of reasons. They can be made noninactivating through a NH2-terminal truncation (Hoshi
et al., 1990
) and they express well in Xenopus oocytes,
allowing the measurement of gating currents as well as
ionic currents. Also, because they are tetramers, the
presumed fourfold functional symmetry of Shaker channels can be exploited in developing simpler kinetic
models. The major results from the recent studies on
these channels may be summarized as follows.
(a) The total gating charge per channel is ~13 e0.
This value was obtained from calibrated measurements
of gating currents (Schoppa et al., 1992; Aggarwal and
MacKinnon, 1996
; Seoh et al., 1996
), and corroborated
by measurements of limiting voltage sensitivity (Zagotta
et al., 1994
a; Seoh et al., 1996
).
(b) Between the resting and the open state, the channel undergoes a minimum of five kinetic transitions, as
estimated from the time course of channel opening in
response to a voltage step (Zagotta et al., 1994a).
(c) The time course of the "on" gating current induced by a step depolarization has a rising or plateau
phase (Bezanilla et al., 1994), implying that the first kinetic steps in channel activation are slower or less voltage dependent than subsequent steps.
(d) After large depolarizations, the time course of
the "off" gating current induced by a voltage step back
to the holding potential has a rising phase (Bezanilla et
al., 1991) and also decay kinetics that match the time
course of channel deactivation (Zagotta et al., 1994
a).
Thus, the first kinetic steps in channel deactivation are
slower than subsequent steps.
(e) At intermediate voltages, the gating currents display a fast component that is followed by a slow exponential component that is correlated with channel
opening (Bezanilla et al., 1994). Also, at these voltages,
the ionic currents have a relatively short delay, followed
by a very slow rise to the peak current (Zagotta et al.,
1994
a). These phenomena imply that channel opening at these voltages is much slower than the rate that the
channel traverses through early closed states.
(f) Shaker's voltage dependence of charge movement
(Q-V) relation is shallow at hyperpolarized voltages but
is steeper over the voltage range where channels open
(Stefani et al., 1994; Bezanilla et al., 1994
).
(g) Components of charge in the Q-V relation have
been shown to be differentially affected by some mutations in the S4 region (Schoppa et al., 1992; Perozo et
al., 1994
) and also by drug binding (McCormack et al.,
1994
). The differential effects suggest the existence of
different types of voltage-dependent conformational changes.
(h) Measurements of gating current fluctuations suggest that elementary charge movements are roughly 2 e0 in size (Sigg et al., 1994b; Sigworth, 1994
).
(i) The distribution of channel open times is well described by a single exponential function (Hoshi et al.,
1994), which is consistent with Shaker channels having a
single open state. The single channel data also suggest
the presence of closed states that are not in the main
activation path (Hoshi et al., 1994
).
Several kinetic models have been proposed that take
into account subsets of these functional properties for
Shaker channels (Schoppa et al., 1992; Tytgat and Hess,
1992
; Bezanilla et al., 1994
; McCormack et al., 1994
;
Zagotta et al., 1994
b). Interestingly, however, these
models have little in common with each other, with different models explaining the same functional data
through very different mechanisms. For example, the
steep voltage dependence of charge movement and
channel opening is explained in the model proposed
by Bezanilla et al. (1994)
by a transition with a large valence, while the model of Zagotta et al. (1994
b)
achieves this through smaller charge movements but
with a slow channel closing rate. The discrepancies between the models point to the need of further analysis
of the activation properties of Shaker channels.
In this paper and the two papers that follow
(Schoppa and Sigworth, 1998a, 1998b
), we present further functional studies on activation gating in Shaker
potassium channels. Our general strategy is to perform
a systematic study of the different gating steps in
Shaker's activation process. This first paper will focus on measurements of macroscopic ionic and gating currents measured at extreme depolarizations and hyperpolarizations, which yield estimates of forward and
backward rates. Some of the described experiments are
similar to those that have been reported previously, but
new insights into the activation gating process are
gained by analyzing the data in new ways, and also by
extending the voltage range of the current measurements. The channel studied, which has its NH2 terminus truncated to remove fast inactivation, will be referred to as wild type (WT)1 to distinguish it from a mutant channel (V2) that will be the focus of the second
paper. The third paper will use results from both WT
and V2 channels to develop a new kinetic model for
Shaker channel activation.
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METHODS |
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Channel Expression
The construction of noninactivating WT Shaker 29-4 cDNAs and
in vitro synthesis of cRNA have been described previously (Iverson et al., 1990; Schoppa et al., 1992). Channels were expressed
in Xenopus laevis oocytes injected with ~3 ng cRNA for recordings of macroscopic ionic and gating currents, and 50-100-fold less cRNA for single channel recordings. Current measurements
were made 4-21 d after injection with the patch-clamp technique
(Hamill et al., 1981
) using an EPC-9 patch clamp amplifier
(HEKA Electronic, Lambrecht, Germany).
Measurements of Macroscopic Ionic and Gating Currents
Macroscopic ionic and gating currents were recorded in inside-out membrane patches using conventional oocyte macropatch
techniques (Stühmer et al., 1991). Patch recordings used pipettes pulled from Kimax capillary tubes with tip diameters ranging from 3 to 10 µm (0.5-3.0 M
resistance). Voltage pulses were
applied from a holding potential of
93 mV. Current signals
were filtered (unless otherwise indicated) at 10 and 5 kHz (Bessel
characteristic) for recordings of ionic and gating currents, respectively. Data were sampled at five to seven times the filtering
frequency. For subtraction of linear leak and capacitive currents
in recordings of macroscopic ionic currents, alternating positive
and negative pulses of 20-mV amplitude from a
133-mV leak
holding potential were applied, and the resulting current was
scaled appropriately. For gating currents, a scaled current response induced by only a negative going voltage pulse from
133
to
153 was subtracted. This modification reduced the artifact in
leak subtraction from charge movement at voltages positive to
133 mV (Stühmer et al., 1991
). To increase the signal-to-noise
ratio, 10-100 sweeps were averaged before the data were stored.
The pulse frequency was set to be high (1-5 Hz) to allow rapid
measurement of many sweeps, but we determined that the frequencies used did not induce rundown of the ionic or gating currents, arising from slow inactivation. Displayed gating current
traces were sometimes additionally filtered with a Gaussian digital filter to 2.5-3.5 kHz.
Most of the ionic current measurements were made with pipettes filled with 140 mM N-methyl-D-glucamine (NMDG) aspartate (Asp), 1.8 mM CaCl2, and 10 mM HEPES, and the bath solution contained 139 mM KAsp, 1 mM KCl, 1 mM EGTA, and 10 mM HEPES. Most of the gating current measurements were
made with the same solutions, except with 2 µM charybdotoxin
(CTx) added to the pipette solution to block ionic currents (Lucchesi et al., 1989). CTx did not appear to alter the properties of
the charge movement, as the currents recorded in the presence
of CTx were similar to those recorded in the absence of CTx but
with NMDG+ replacing K+ in the bath to remove the ionic current. Membrane potential values were corrected for a liquid junction potential at the interface of the NMDG+ pipette and K+ bath
solutions, which we estimated to be
13 mV (Neher, 1992
). All
experiments were done at room temperature. The bath chamber was not perfused in these experiments.
Voltage steps to very positive and negative voltages were kept
short (5 ms at V > +100 mV and V <
120 mV) to reduce
contamination of the recorded ionic currents by endogenous oocyte currents. Corresponding gating current recordings made in
the presence of CTx showed little background current, suggesting that contamination of our ionic currents by endogenous currents is likely to be negligible.
The large pipette sizes used in recordings of gating currents encouraged the formation of membrane vesicles or partial vesicles when the patch was pulled off the oocyte. Gating current recordings were rejected if the measured on current did not show an instantaneous component of the rising phase: specifically, a component with amplitude at least 50% of the peak on current was expected to rise with the same time course as the measured step response of the recording system (see below). Further, recordings with very large ionic currents (>2.5 nA) were rejected to avoid errors due to series resistance.
To allow the interpretation of the rapid gating events reflected
in the recordings of ionic tail currents and reactivation time
courses, the step response of the recording system, including the
filter, was determined by injecting a step of current into the
patch clamp head stage using the test facility of the EPC-9 and
measuring the current response. At the low gains at which the
macroscopic ionic and gating currents were measured (500 M feedback resistor), the response time, defined as the time required for the current to reach 50% of its peak in response to a
step current input, was found to be 40 and 25 µs at the 10 and 15 kHz filtering bandwidths used for most ionic current measurements, respectively. Other delays in the stimulus and recording
system were expected to be negligible: the stimulus filter risetime
was set at 2 µs for measurements of tail currents and reactivation time courses, while the patch membrane charging time constant was expected to be below 1 µs. To account for the total delays, the recorded current traces were offset in time by three sample intervals. In the measured time course of the step response of the
recording system, it was also determined that an additional approximately three sample intervals were required for the step response to settle to near its final level. Thus, an additional three
sample intervals were always ignored in the fitting of exponentials to the tail current and reactivation time courses.
The time courses of the macroscopic ionic and gating currents were fitted to the sums of exponentials by least squares within the Igor data analysis program (WaveMetrics, Lake Oswego, OR). The derived parameter estimates were consistently independent of the initial guesses supplied.
In the text, errors in all measured quantities are given as the mean ± SEM.
Measurement of Single-Channel Ionic Currents
Single-channel recordings were made in inside-out patches in response to step depolarizations from a 93-mV holding potential. Patch pipettes were pulled from 7052 glass (Garner Glass, Claremont, CA) with 1-2-µm tip diameters (4-10 M
resistance). The
recording solutions were identical to those used in the measurements of macroscopic ionic currents. Filtering and sampling frequencies were variable, appropriate for the amplitude of the single-channel activity at a given voltage. Leak subtraction was performed by subtracting an average of 8-20 of the nearest null
traces. To allow the measurement of a large number of single
channel sweeps, the pulse frequency was set to be high (1-5 Hz);
however, there was no indication of slow inactivation, which
would have caused a time-dependent increase in the number of
null traces. The displayed single channel data are filtered at the
frequencies used for the event detection, as described below.
The single-channel activity apparently arose from Shaker channels since (a) no such single channel activity was observed in patches in which CTx was included in the pipette, and (b) the ensemble averages of WT's single-channel current traces were kinetically identical to the macroscopic currents in patches from oocytes injected with 50-100-fold more cRNA. Infrequently, a patch would display other single-channel activity, but this activity was easily distinguishable from Shaker's in its voltage-dependence, kinetics, and conductance properties.
The analysis of the equilibrium single-channel closed and
open times was performed with the TAC single-channel analysis
program, which is based on THAC (Sigworth, 1983). Data were
filtered with a digital Gaussian filter to achieve an appropriate
signal-to-noise ratio, and event detection was performed using
the standard half-amplitude threshold analysis (Colquhoun and
Sigworth, 1995
). Complicating the analysis of the single-channel
events was the presence of apparent subconductance activity
(Hoshi et al., 1994
). The event detection for a given trace was
stopped at the time point at which the channel first exhibited
such behavior. Ignoring these data was unlikely to introduce a
significant error in our results since subconductance activity was
relatively infrequent: in one patch recording of 613 consecutive
traces of single channel activity at +27 mV, the open channel
spent only 14% of the total 16.6 s of recorded open time at a subconductance level. Here a subconductance level was defined to
be an amplitude level smaller than 75% of the most common amplitude level.
For the construction of closed- and open-time histograms, the
deadtime (Td) for a given analysis filtering frequency fc was taken
to be Td = 0.179/fc and short-event durations were adjusted appropriately for Gaussian filtering as described (Colquhoun and Sigworth, 1995). Closed and open times were binned logarithmically and the square root of the number of events was plotted
(Sigworth and Sine, 1987
). The minimum-duration bin for each
histogram was set to be the deadtime corresponding to the analysis filtering frequency used for the event detection. The event
histograms were fitted to a mixture of exponential components
with the amplitudes and time constants adjusted using the binned
maximum likelihood method (Sigworth and Sine, 1987
). The
number of exponential components fitted to the histograms was
determined by the likelihood ratio test for nested models (Horn
and Lange, 1983
), which can be applied to the problem of comparing fits with different numbers of exponentials (McManus
and Magleby, 1988
).
Accounting for Three Artifacts
In the following section, we describe how we accounted for three additional potential artifacts that could affect our interpretation of the data.
Effects of different recording solutions. While most of the recordings were made with the bath and pipette solutions indicated above, different solutions were sometimes used to facilitate certain types of the measurements. For these instances, it was important to show that changing the recording solution had no effect on activation gating.
First, to allow the measurement of large inward ionic tail currents at very hyperpolarized voltages (see Fig. 7 A), measurements were routinely performed while replacing 14.3 mM of the NMDG+ in the pipette with an equimolar amount of K+. High concentrations of external K+ have been shown to alter the ionic tail currents for Shaker channels (Stefani et al., 1994
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Nonstationarities in channel behavior.
Sigg et al. (1994a) have reported that the decay of Shaker's ionic tail currents recorded in
excised membrane patches slows by a factor of ~3 during the
first several minutes after patch excision. We observed a similar
time-dependent slowing in WT's tail currents. In eight patches,
tail currents at
93 mV recorded at least 6 min after patch excision had decay time constants that were 2.9 ± 1.1-fold longer
than tail currents recorded less than 1 min after patch excision.
Time-dependent changes were also observed in the decay of
WT's off gating currents after large depolarizations, which also
reflect the kinetics of channel deactivation (Bezanilla et al., 1994
;
Zagotta et al., 1994
a). For the analysis of the macroscopic ionic
tail currents and off gating currents, we therefore limited the
analysis of tail currents to those measured at least 6 min after
patch excision, when most of the time-dependent effects were apparently over. In seven patch recordings, in which tail currents
were measured at different times up to 11 min or more after
patch excision, the time-dependent slowing effect occurred with
a time course that was approximated by a single exponential with
= 6.2 ± 1.5 min.
Slow inactivation.
A final potential problem for the interpretation of the macroscopic current time courses was slow-inactivation gating (Hoshi et al., 1991; Lopez-Barneo et al., 1993
). In recordings made with 4-8-s voltage pulses to between
53 and +67
mV, macroscopic ionic currents decayed with voltage-independent kinetics that were fitted by the sum of two exponentials with
time constants (at
13 mV) of 70 ± 13 and 870 ± 76 ms (n = 7);
the 70-ms component comprised 26 ± 19% of the total amplitude. The slow inactivation time course was much slower than
most, but not all, phenomena associated with activation gating.
Thus, in the fits of exponentials to the channel opening time
courses that are reported, an additional exponential component
was always added that reflected the 70-ms component of the slow
inactivation process.
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RESULTS |
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The goal of this study is to identify kinetic transitions in
activation gating and assign rate constants for the WT
channel. Experiments were designed to isolate, as
much as possible, the rates of individual steps in the activation process. In the first studies that we describe, we
make use of data obtained at voltage extremes to study
kinetic constants. We consider forward rates, assigning
values and voltage dependences to the first forward rate 1, the limiting rate at large positive potentials
p,
and the final opening rate
N. An estimate for the voltage dependence q
d of intermediate steps is also obtained. Similarly, the first and the last two backward
rates
1,
N, and
N-1 are determined, along with an estimate of the "average" rate of intermediate steps
d. In
the second group of studies, we characterize the transitions to several channel-closed states that are distinct
from those traversed in the depolarization-induced activation process.
General Framework
We assume a discrete, homogenous Markov model for activation gating. Thus, activation is taken to involve transitions between discrete closed and open states separated by large energy barriers. For a sequential gating scheme, this framework can be depicted as
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The forward and backward rates i and
i are taken to
be exponential functions of the membrane potential V,
scaled by the partial charges q
i and q
i,
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(1) |
(Terms with higher powers of V in the exponent are
not included because any charge movement with the
expected properties, if present, is very small; see Sigworth, 1994.) The gating charge movement accompanying a transition from state i
1 to state i is then given
from the partial charges as
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(2) |
Within this framework, we estimate the forward and
backward rate constants i and
i for various gating
transitions. Many of the current measurements were
made at voltages where we could presume that either
forward or backward rates predominate. Following Zagotta et al. (1994
a), we define three voltage ranges. Forward rates are presumed to predominate in the depolarized voltage range, where WT's equilibrium Po and
charge movement Q saturate. In WT's Po
V and Q-V
relations in Fig. 1, this appears to occur above
20 mV.
(Although small changes in channel Po continue at
higher voltages, this property reflects the voltage dependence of a transition to a state that is not in the activation path and which carries only ~0.3 e0 of charge;
Zagotta et al., 1994
a.) Backward rates are presumed to
predominate at all voltages where most channels reside
amongst the earliest closed states at equilibrium. These hyperpolarized voltages were taken to be V
90 mV
because only 8% of WT's charge movement occurs negative to
90 mV. A third voltage range, activation voltages, between
90 and
20 mV, is the range in which
WT's channel Po and charge movement are undergoing most of their changes.
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Given the special condition that all of the backward
rates in Scheme I are negligible, information about the
forward rate constants in any sequential scheme can be
obtained from a simple analysis of the time course of
the open probability. At depolarized voltages, where we
assume i
0 for all i, the mean latency to arrive at the
open state ON is given by
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(3) |
Now suppose that one of the rates, j, is much smaller
than the others. Then the time course of channel activation can be approximated by the exponential function
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(4) |
with time constant =
j
1 and with a time delay equal
to the latency due to the other steps,
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(5) |
The approximate time course given by Eq. 4 has a
mean latency that is equal to tl; however, the time
course is correct only as the limiting rate j becomes
much smaller than the other rates. Useful estimates of
the limiting rate and of
can nevertheless be obtained
from fits of Eq. 4 when the limiting rate differs little
from the other rates. This is illustrated in Fig. 2, where fits were made to the "upper half" of the time course,
starting at the time when Po is equal to half of the final
value. In Fig. 2 A, an "n4" scheme where the next slowest rate is only twice that of the slowest one, the limiting
rate is estimated with 11% error, while
is estimated
within 1%. Fig. 2 B demonstrates the worst case, in
which no rate constant is smaller than the others. Here,
the limiting rate is underestimated by a factor of two,
while the error in
is only 20%. Similar deviations between the measurements and theory are obtained from
sequential schemes with more transitions. For an "n8"
scheme, the deviations in the measured and predicted
1 and
are only 13 and 1%, respectively; for eight
equivalent rates, the deviations in
1 and
are 61 and
13%. These results suggest that fits of Eq. 4 to activation time courses for sequential models can yield reasonable first-pass estimates of the rate-limiting rate constant, though this rate will tend to be underestimated
in cases where several rates are comparable in magnitude. Information about the other transitions is also obtained with surprisingly good accuracy from the delay
value.
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The approximation of Eq. 4 can also be used to obtain a simple characterization of dwell times during activation in branched models. Consider a model like
that of Zagotta et al. (1994b) in which four independent subunits each undergo two steps,
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When this scheme is expanded, it is seen that there are many distinct paths (14 in all) leading from closed state C0 to the open
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The mean latency tl can be computed as a weighted average of the time spent in each path, with the weights being the probabilities of the paths. The time spent in each path is the sum of the dwell times in each state of the path.
Fig. 2 C shows an example of fits to the time course
for this scheme in the case where a1 = 1 and a2 = 4, yielding tl = 2.369 time units. The simple theory predicts to be equal to the reciprocal of the slowest rate,
and the delay parameter to be given by
= tl
. A single-exponential fit (dotted curve) yields a value for
1
that differs by 11% from the slowest rate, and a value of
that differs only 1% from the theoretical value. Fig. 2
D demonstrates the most difficult case, in which a1 = a2. As in the corresponding case of a sequential scheme
(Fig. 2 B), the error in the time constant is moderate,
~30%, but the error in
is small, <1%. Thus, the parameters of a fitted single-exponential function give surprisingly good estimates for the aggregate dwell
times in branched models as well as in linear models.
Estimates of Forward Rates
Estimates of 1.
The forward rate constant
1 for the
first transition was evaluated from the time courses of
ionic currents and gating currents at depolarizing voltages, as illustrated in Fig. 3. Fits of the single-exponential function (Eq. 4) to the ionic current from the 50%
amplitude level to its final value yielded the "activation time constant"
a and the activation delay
a (Fig. 3 A).
From the exponential decay of gating currents at depolarized voltages, the time constant
on was determined
(Fig. 3 B).
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Estimate of p.
If one or more transitions have forward rates with smaller voltage dependences than
1,
one of these should be rate limiting at sufficiently high
voltages, and should be reflected in the voltage dependence of
a at very large positive voltages. Thus, we obtained current recordings at voltages up to +147 mV
(Fig. 4 A). The analysis of the channel opening time
course at high depolarized voltages is complicated by
the fact that the rising phase of the current is usually
not well fitted by a single exponential. After a rapid
rise, a slow "creep" up to the final value is observed at
these voltages. In a more complete discussion of this
phenomenon below, we will show that this slow component reflects an alternate activation path that a small
fraction of the channels enter before opening. Here, to
estimate the kinetics of the main activation path, the
currents were fitted to the sum of two exponentials,
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(6) |
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Estimate of N.
Macroscopic ionic currents were measured with one additional voltage protocol to attempt
to estimate the forward rate
N of the very last step in
the activation path (Fig. 5). A sequence of three voltage
pulses was applied (Fig. 5 A): an initial depolarization to +47 mV to open most of the channels, a second
pulse to a hyperpolarized voltage Vh (
153 mV in this
case) of duration th to close a fraction of the channels,
and a third pulse to +47 mV to reopen the channels that closed during the second pulse. In principle, for
small enough th, channels should not have time to close
to states beyond the first closed state, and the kinetics
of channel reactivation should reflect the forward rate
of the last transition in the activation path. This time
course will be distinctly faster if the forward rate of the
last transition is faster than that of the earlier gating
steps. Zagotta et al. (1994
a) measured currents using a similar voltage protocol with th as small as 1 ms, but we
employed second-pulse hyperpolarizations that were
much shorter, as short as 70 µs. In our experiments,
briefer hyperpolarizing pulses make the reactivating
currents much faster (Fig. 5, A and B). Compared with
the 400-µs activation time constant
a taken from the reactivation time course after a relatively long th = 1 ms
hyperpolarization, single exponential fits of the reactivation time courses for shorter th yielded
a values of
300, 170, and 110 µs for th = 300, 150, and 70 µs, respectively.
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(7) |
Estimate of qd.
The long delay in Shaker's channel
opening time course (Zagotta et al., 1994
a) is expected
to reflect the forward rates of a large number of transitions. While we were unable to determine directly the
forward rates of most of the transitions that come between the very first and last transitions, information
about the partial charges q
d associated with the forward rates of these intermediate transitions is available
from the voltage dependence of the delay
a in the
channel opening time course (Fig. 4 B). The
a value
represents the sum of contributions from multiple
steps; its voltage dependence is not well fitted by a single exponential across the wide voltage range, which is
consistent with transitions with forward rates with different voltage dependences predominating at different
voltages. Nevertheless, to approximate the partial
charges of a large number of these transitions here, the
a values between
13 and +147 mV were fitted to a
single exponential (not shown), which yielded a charge
estimate of 0.25 e0 for q
d.
Estimates of Backward Rates
Estimates of the voltage dependences of the backward rates of three transitions were obtained from the kinetics of macroscopic ionic and gating currents at hyperpolarized voltages.
Estimate of 1.
The small fraction (<8%) of the total
charge movement that occurs at voltages negative to
90 mV (Fig. 1) is consistent with the idea that at these
voltages channels reside among the earliest closed
states at equilibrium. If it is assumed that at
93 mV, most channels reside in either the first or second closed
states, the off gating currents measured with voltage
pulses from
93 mV to more hyperpolarized voltages
will decay with a time course given by the backward rate
1 of the first transition. Consistent with the expected
two-state behavior, the measured currents (Fig. 6 A)
rise instantaneously and have a single exponential decay that becomes faster at more hyperpolarized voltages. The time constants of the single exponentials fitted to these gating currents (Fig. 6 B) in three patches
yielded an estimate for a backward rate of the earliest
gating step
1(0) = 190 ± 60 s
1 and q
1 =
0.53 ± 0.03 e0. Numerous reports of Shaker's gating currents
exist in the literature (Bezanilla et al., 1991
, 1994
;
McCormack et al., 1994
; Zagotta et al., 1994
a), but
none of these include gating currents measured with
voltage steps between different hyperpolarized voltages, which are required to estimate
1.
Estimate of d(
93).
It has been previously shown that
Shaker's off gating currents after large depolarizations
have a rising phase and decay kinetics dominated by
the slow kinetics of channel closing from the open state
(Bezanilla et al., 1991
; Zagotta et al., 1994
a). However, the off current kinetics after short depolarizations that
fail to open channels are much more rapid, presumably reflecting the relatively rapid backward kinetics of
the transitions that come before the last transition
(Zagotta et al., 1994
a). We use this rapid off current
time course here to obtain an approximate estimate
d
for the backward rate of intermediate transitions. Fig. 6
C illustrates the off current measured after a short 2-ms
depolarization to
33 mV. From the time integral of
the gating current at this voltage, we estimate that 80%
of the total gating charge movement occurs by the end
of the 2-ms depolarization, indicating that most channels reside in relatively late activation states; however, from the channel opening time course, we estimate
that only 15% of the channels are open. Exponential
fits of the off currents after the 2-ms depolarization to
33 mV in two patches yielded time constants of 0.82 and 0.62 ms.
Estimate of N.
Zagotta et al. (1994
a) made estimates
of the channel closing rate
N from macroscopic ionic
tail currents measured between
60 and
140 mV. For
our estimates of
N, we chose to use tail currents measured at even more negative voltages. While the position of the Q-V relation on the voltage axis would suggest that most of the forward rates are negligible in the
hyperpolarizing voltage range (
93 mV), it has been
shown above that the forward rate of the last transition
N is considerably faster than the forward rates of the
preceding transitions, and could have values at voltages near
93 mV that are comparable to backward rates.
Indeed, according to our fits,
N(
93) = 3,600 s
1 is
greater than
1(
93) = 1,300 s
1. Considering a partial
scheme consisting of the last three states of Scheme I,
|
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(8) |
Estimate of N-1.
If WT's channel deactivation time
course is determined at most voltages by the channel
closing rate and by reopenings from the last closed
state CN-1, this time course provides one way to estimate
the backward rate
N-1 from the pentultimate state. A
second measure of
N-1 is provided by the reactivation
time courses (Fig. 5 A). The amplitude of the fast reactivation component should reflect the occupancy in CN-1
during the preceding hyperpolarization. The voltage
dependences of the rates of the transitions out of CN-1,
including
N-1, will determine the way in which this amplitude varies with the duration th and amplitude Vh of
the preceding hyperpolarization.
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(9) |
Estimate of qd.
A measure of the partial charge q
d associated with the backward rates of intermediate transitions was obtained from measurements of macroscopic
ionic currents, using a strategy that is analogous to that
used above to estimate q
d. In that case, the voltage dependence of the delay in channel activation gave a
rough estimate of the voltage dependence of the underlying rate constants of intermediate transitions.
Here we measure the activation delay as initial state occupancies are varied using repolarizing pulses of duration th and amplitude Vh that follow an initial depolarization that loads the channels into the open state. Let the
initial occupancy of state i be pi, and let
i be the forward rate from state i to state i + 1. Then Eq. 5 can be
generalized to give the delay with arbitrary occupancies,
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(10) |
|
Transitions to States that Are Not in the Activation Path
Up to this point, we have characterized the transitions
that the Shaker channel undergoes in the depolarization-induced activation process. However, Hoshi et al.
(1994) have shown from Shaker's single channel data
that there are at least two additional closed states,
called Cf and Ci, into which the channel enters only after it has opened. The state Cf corresponds to a predominant, fast 200-300-µs component in their single
channel closed dwell-time histograms at depolarized
voltages, and the other closed state Ci accounts for a
voltage-independent, 1-2-ms component in the closed
time histograms at depolarized voltages. In the following, we use a combination of single channel and macroscopic current measurements to further characterize
the transitions to these additional states.
We begin by outlining the general properties observed
in our single channel measurements at depolarized
voltages. As was observed by Hoshi et al. (1994), we find
that the channel opens quickly after the beginning of a
voltage pulse (Fig. 10 A) and remains open for most of
the trace, occasionally closing briefly into short-lived
closed states. Infrequently, the channel displays longer
closures (see the third trace at +67 mV). The closed
time histograms constructed from our single channel
activity are always fitted by a mixture of three exponentials (Fig. 10 B), including one large-amplitude component with a very fast (
1 = 40-100 µs) time constant, a
second component with an intermediate amplitude and
duration (
2 = 200-500 µs), and a third component
with a 1-3-ms time constant (
3) and a very small amplitude (comprising ~1% of the closures). Our fit of two
exponentials to closures with durations of <500 µs differs from the single exponential fitted to these closures
by Hoshi et al. (1994)
. It is difficult to interpret the voltage dependences of the two faster closed time components (Fig. 10 D), since the rapid closures are near the
limit of time resolution and, additionally, the two rapid
closed-time components are not well resolved from each
other. The third, slowest component has a voltage-independent duration and corresponds to the Ci closures observed by Hoshi et al. (1994)
.
|
As shown previously (Hoshi et al., 1994), the open
times (Fig. 10 C) are well fitted by a single exponential
with time constants near 3 ms, consistent with the presence of a single open state. The measured open times
display little voltage dependence (Fig. 10 E). No effort
was made to correct the open times for missed fast closures because the missed event correction would rely
on the amplitude and time constant estimates for the
fastest closures, which are quite unreliable.
Characterization of the Transitions to Ci
The first new property that we assign to Ci is that it is a state that can be entered from not only the open state but also from closed states in the activation path. This property for Ci is required by the fact that Ci contributes to occasionally observed long first latencies to channel opening at depolarized voltages.
An instance in which the channel enters into a long-lived closed state before it opens is evident in the second
trace at +67 mV in Fig. 10 A. Entries into long-lived
closed states before first opening are also apparent in
the shape of the cumulative first latency histogram
(Fig. 11 A), which displays a gradual rise superimposed on the dominant faster component. The same slow
component was also usually observed in the time course
of macroscopic ionic currents at high depolarized voltages (V +67 mV; Fig. 4 A). While a single-exponential
fit may account for the time course for even a complex
gating scheme depending on the way that the fitting is
performed, the observed deviation from a single-exponential time course in the final approach of the current
in our fits is good evidence that individual channels are
traversing different rate-limiting steps to opening. The
observed two components in our time courses apparently are not, however, due to differences in the initial
conditions for different channels, because the size of
the slow component in the macroscopic current does
not change with a very hyperpolarizing prepulse to
143 mV (in three patches; data not shown); this
prepulse is expected to preload virtually all channels
into the very first closed state. The slow component is
also probably not due to modal gating, as it was found
in one single channel patch recording that there was
no apparent pulse-pulse correlation in the appearance
of long first latency. Instead, we take the presence of
two components in the final approach of the ionic current to imply that there are two pathways to channel
opening; that is, a fraction of channels pass through
closed states in a slow path that is distinct from the main activation path.
|
In fits of two single-channel first latency histograms at
V +67 mV to the sum of two exponentials (Eq. 6),
the fitted slow exponential had time constant
s values
of 1.6 and 1.8 ms (Fig. 11, A and B), similar to the 1.9 ± 0.5-ms mean duration of the
3 component in the
closed dwell-time histograms at the same voltages (n = 3; Fig. 10 D). Fits of 21 macroscopic ionic current time
courses to Eq. 6 yielded
s = 1.5 ± 2 ms, also similar to
3. (The time course of the slow component in the macroscopic ionic current can be compared with
3 because backward rates at high voltages are negligible,
making the ionic current have essentially the same time
course as the cumulative first latency histogram; Hoshi et al., 1994
.) We take the similarity in the latency time
constant and
3 to imply that the long latencies to
opening reflect sojourns in the same family of states as
the Ci closures that follow the first opening, except
these sojourns in Ci are made from closed states in the
activation path. The experiments of Hoshi et al. (1994)
were not able to discriminate transitions into Ci before opening because their single channel measurements
were not made at sufficiently high voltages; at lower
voltages, the kinetics of the transitions through this secondary activation path are not substantially slower than
the kinetics of the main activation path.
The slow component accounts for on average ~10% of the total current relaxation (Fig. 11 C), implying that an opening channel has a 10% chance of entering one of a family of Ci states from closed states in the activation path before opening. For example, in the following scheme,
|
the opening channel might move from the resting state C0 into CN-1, and then into CiN-1 and CiN, before reaching the open state ON. From which particular set of closed states the channel can enter the Ci states remains unclear. Scheme IV does not include transitions between CiN and Cf, because we prefer a simple model for these states.
If it is assumed that most of the Ci closures observed
at equilibrium at depolarized voltages correspond to
sojourns in the state CiN, which is entered directly from
the open state, we can use the closed and open dwell-time histograms to assign estimates for the rates c and d
of this transition. The values of the time constants fitted to the Ci closures at different voltages give an estimate for the rate d from CiN to the open state (d(0) = 300 s1 and qd = 0.07 e0; Fig. 11 D). The open times
and amplitude of the Ci closed time component (Fig.
10 F) give estimates for the rate c from the open state
into CiN (c(0) = 5 s
1 and qc = 0.09 e0). This estimate
for c is an upper limit, if some of the Ci closures observed under equilibrium conditions reflect sojourns in
states entered from closed states in the activation path.
Evidence for Cf1 and Cf2
We next evaluate the transitions that correspond to the
two rapid components of the closed-time histograms in
Fig. 10 B. Since Hoshi et al. (1994) have shown that
many of the rapid closures at depolarized voltages are
to states that are not in the activation path, our starting
hypothesis will be that the two rapid components correspond to two different such states: Cf1 and Cf2. The alternate possibility is that one of the components corresponds to closures in the activation path (e.g., to the
last closed state CN-1). We can address this second possibility by comparing the measured channel open times
and the reciprocal of our estimated channel closing
rate
N (Fig. 10 E). At the most depolarized voltage
where currents were measured (+147 mV), the measured channel open time (3 ms) is 60 times shorter
than the expected value of 1/
N = 180 ms at that voltage. (Were we to correct the open time for missed brief
closures, the discrepancy with 1/
N would be even
larger.) This large difference implies that virtually all of
the measured closures at this voltage reflect closures to
states that are not in the activation path. Since the two
rapid components of the closed time histograms at
+147 mV comprise 73 and 25% of the total measured
closures, both very much larger than the ~2% component expected for closures to CN-1, we take both components to reflect closures to states Cf1 and Cf2 not in the
activation path.
While there are a number of different ways to model these two states, we suggest that Cf1 and Cf2 are states into which the open channel closes directly:
|
We cannot easily rule out alternative models (e.g., having channels in ON close first into Cf2 and then into Cf1), but we choose Scheme V because of its simplicity.
Since the rapid closures in the single channel recordings are not well resolved, the parameter values derived from exponential fits to the histograms do not yield quantitatively reliable estimates of the rates associated with the transitions to Cf1 and Cf2. We nevertheless obtain rough estimates of these rates by using various strategies.
Estimating Rates for the Transition to Cf1
If the transition to either Cf1 or Cf2 carries any amount
of charge, the rates for this transition can be estimated
from the relaxation of macroscopic ionic currents that
are elicited by a double pulse protocol. To achieve test
currents that predominately reflect the transition to Cf1
or Cf2, prepulses are required that are large enough
that virtually no channels reside in states in the activation path at the end of the prepulse. A comparison of the measured channel open times and the reciprocal of
the closing rate N in Fig. 10 E indicates that at voltages
+7 mV, open times are approximately the same or
shorter than 1/
N; this would imply that much of the
test current relaxation after prepulses above +7 mV reflects transitions to states outside the activation path.
Fig. 12 A illustrates an experiment in which we apply
voltage steps from +7 to +127 mV, and also from +47
to +147 mV. These voltage jumps elicited small current
relaxations with activation time constants of r = 230 and 180 µs. The time course of the current relaxation
at +147 mV (
r = 180 µs) is threefold slower than the
fast reactivation time constant that corresponds to the last transition in the activation path (Fig. 5 D); this indicates that the observed current must reflect a transition
that is distinct from the last activation transition. The
observed relaxation also cannot reflect the transition to
CiN. Given the estimates for c and d assigned above, the
transition to CiN would contribute to a change in open
probability
Po << 1% during these voltage jumps, but
the amplitudes of the relaxations correspond to
Po
6% (see legend to Fig. 12). Thus, these relaxations almost certainly reflect transitions to Cf1 or Cf2, and we assign them to Cf1. Since these currents are recorded at
depolarized voltages, we assume that the current time
course mostly reflects the rate f1 from Cf1 to the open
state, yielding estimates of f1(0) = 1,600 s
1 and qf1 = 0.2 e0 (Fig. 12 B).
The value of the rate constant e1 for the entry into Cf1
can be determined using the amplitude of the current
relaxation in the voltage jump experiment in Fig. 12 A.
The 10% change in relative Po induced by the voltage
jump from +7 to +127 mV, together with the value for
f1 derived above, gives e1 = 190 s1 at +7 mV (assuming
that the transition to Cf1 is saturated at +127 mV). We
assume that this transition is voltage independent.
The current relaxations in Fig. 12 A verify one feature of data presented earlier in this paper. In the voltage dependence of channel opening for Shaker (Fig. 1),
Po rises steeply to ~80% of its maximal value, but displays a slow upward drift at higher voltages. The presence of the gradual rise, however, has been reported to
be dependent on the method by which Po is measured (Zagotta et al., 1994a). The 12% change in relative Po
that we estimate to occur between +7 and +67 mV using the tail-current method for estimating relative Po
(described in the legend of Fig. 1) is, notably, similar to
the 10% change in relative Po induced by the voltage
jump from +7 to +127 mV. In our modeling paper
(Schoppa and Sigworth, 1998b
), we will use the shape of the Po-V relation at depolarized voltages to help constrain
the total charge associated with the transition to Cf1.
Estimating Rates of the Transition to Cf2
The relaxations of the macroscopic currents in Fig. 12
A that correspond to Cf1 O have similar time-constant values as the intermediate duration
2 component
of the single-channel closed dwell-time histograms at
similar voltages (Fig. 10 D); at V > +100 mV,
2 is between 200 and 300 µs. If the transition from Cf1 corresponds roughly to the intermediate duration closures
in the dwell-time histograms, the transition from Cf2
must correspond to the very rapid 40-100 µs closures.
These closures are poorly resolved, but the short apparent time constant implies that the rate f2 from Cf2 to the
open state is very rapid (near 104 s
1). Information
about this transition can also be obtained from estimates of absolute Po, which can be derived from the
mean open and closed times in the single channel measurements (Fig. 12 C). From measurements obtained at
voltages as large as +147 mV, the derived absolute Po
values apparently saturate near 0.9. The fact that Po at
very high voltages saturates at a value less than unity implies that the transition to Cf2 is nearly voltage independent (giving qe2 + qf2
0.0). A saturating value of Po =
0.9 implies a ratio of the two rates e2/f2 near 0.1, giving
e2
103 s
1.
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DISCUSSION |
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In this and the following two papers (Schoppa and Sigworth, 1998a, 1998b
), we characterize activation gating
for the normally activating Shaker channel (WT) and a
mutant version of the channel to arrive at a relatively
well-constrained activation gating model. In this first
paper, we have undertaken a detailed analysis of the kinetics of WT's macroscopic ionic and gating currents
and single channel currents in an effort to obtain estimates of several rate constants. Previous efforts at characterizing Shaker's activation gating process exploited
experimental strategies that were similar to ours in order to isolate particular activation gating transitions (Hoshi et al., 1994
; Zagotta et al., 1994
a; Bezanilla et
al., 1994
a). However, we have gained new insights by
analyzing the current time courses in novel ways and by
extending the voltage range of the current measurements.
Estimates of Forward and Backward Rates for Transitions in the Activation Path
We have assumed that activation gating is described by a Markov process with transitions between discrete states separated by large energy barriers. Fits of exponentials to selected ionic and gating current time courses at extreme voltages yielded estimates of the rate constants depicted here.
|
For the forward rates, we have obtained estimates of
the first forward rate 1, the limiting rate at large positive potentials
p, the final opening rate
N, and an estimate of the partial charge q
d that determines the voltage dependence of forward rates of intermediate steps.
For backward rates, we have obtained estimates of the
first and last two backward rates (
1,
N-1, and
N), and
an estimate of the backward rates of intermediate steps
d. The values obtained are given in Table I. We have
also extended on the work of Hoshi et al. (1994)
by
characterizing the transitions to several closed states
that are not normally traversed before the channel
opens. Hoshi et al. (1994)
showed that there were at
least two such states Ci and Cf; from an analysis of single
channel data, we have shown that there are at least four
such states. These results are summarized by Scheme V
above and the list of rate estimates in Table II.
|
|
It should be emphasized that the parameters qd, q
d,
and
d(0) that we ascribe to intermediate transitions
should be taken as quite rough approximations; these
are shown in Scheme VI with parentheses. The charge
parameters q
d and q
d were derived from the delay in
the channel opening time course, which reflects the
composite properties of many transitions. These parameters are also somewhat difficult to interpret because transitions with the fastest forward rates contribute little to the delay. Thus, these charge parameters
are not likely to reflect the partial charges associated
with the most rapid transitions. However, the number
of rates with partial charges similar to q
d and q
d is
likely to be quite large. Zagotta et al. (1994
b) estimated that a minimum of five transitions are required to account for the delay in the ionic current time course;
our own analysis gives a minimum estimate of seven
transitions (Schoppa et al., 1998b), implying that at
least six transitions contribute significantly to the delay.
Assumptions Used in the Derivation of Rate Constants
The accuracy of these rate estimates has relied on a
number of assumptions, besides the assumption of a
Markov process. The first of these is that our current
measurements were made at sufficiently positive and
negative voltages to yield unidirectional transitions, so
that our current measurements reflect only a single microscopic rate constant. All but one of the forward rates
were estimated from currents measured at V +67
mV, which is 80 mV higher than where the Q-V relation
saturates, and all backward rates were estimated from
currents measured at V
93 mV, where <8% of the charge movement occurs. While we cannot be certain
that transitions are unidirectional at these voltages, our
current measurements were made at more extreme
voltages than those that have been published previously. Thus, for example, in the estimate of the channel closing rate
N, our estimates are likely to be more
reliable than those that have been reported previously.
The forward rate 1 of the first transition was estimated from current measurements made at voltages
between
13 and +67 mV. The reason for concern
about voltage ranges for this estimate is the following.
Whereas the equilibrium Po-V and Q-V relations appear
to saturate near 0 mV (Fig. 1), previous models for
Shaker's gating (Bezanilla et al., 1994
; Zagotta et al.,
1994
b) have included at least one transition that has a
relatively large backward rate at this voltage; the channel nevertheless opens due to the driving action of a
later forward-biased transition. Thus, for example, nonnegligible backward rates at voltages near 0 mV will
yield an estimate for
1 from the final approach of the
ionic current that is smaller than its actual value.
A second assumption that we have made for simplicity is that activation gating follows a linear sequence of
transitions as in Scheme VI. Many of the models that
have been used to describe the activation gating process for Shaker channels, however, are branched models
that reflect the tetrameric structure of the channels (McCormick et al., 1994; Zagotta et al., 1994b); we also
will propose branched models in a subsequent paper.
The estimates for rate constants given here are likely to
be valid for such branched models. Many of our rate estimates rely on fits of exponentials to macroscopic
ionic current time courses yielding a time constant
a
and a delay parameter
a. As we have shown in the simulations of branched models in Fig. 2, C and D, the
rates of rate-limiting steps are estimated without large
errors by this approach.
In this paper, we have considered evidence that activation gating for Shaker deviates from a sequential
model in that there are three closed states (CiN, Cf1,
and Cf2) that the channel enters after the channel
opens, and at least one additional closed state Ci that
the channel can enter from closed states in the activation path. The transitions to the three states CiN, Cf1,
and Cf2 are problematic to our analysis because these
transitions could affect the macroscopic tail current
and reactivation time courses that yielded our estimates
of N,
N, and
N-1. For example, channels undergoing
slightly voltage-dependent transitions from the open state to CiN or Cf1 could contribute to additional decay
components in the tail current (Zagotta et al., 1994
a).
However, these components are expected to be small
due to the transitions' small voltage dependences; also,
at hyperpolarized voltages (
193 mV), the rates of the
transitions from the open state to CiN and Cf1 (c = 3 s
1
and e1 = 103 s
1) are much smaller than the rate of
channel closing into the activation path (
N(
193) = 11,400 s
1). The additional states Ci entered from
closed states in the activation path make a small contribution to the channel activation time course at high
voltages, and thus could affect our estimate of the high
voltage rate-limiting step
p; however, we explicitly account for these transitions by fitting the ionic currents
to the sum of two exponentials.
The best evidence that the simplified analysis of the
Shaker's gating process in this paper is reasonable
comes from comparing the first-pass estimates of various rates obtained here (in Tables I and II) with the results of the modeling in the third paper in this series
(Schoppa and Sigworth, 1998b). There, we consider a
number of different branched models that are similar
to Scheme II. We derive starting rate estimates for the
transitions in the models from each of the rate estimates obtained here; the rate values that then yield the
best fits of the data are quite similar to these starting estimates, being at most a factor of 2-3 different.
Activation Gating Involves Many Transitions with Small Valences
The characterization of the different activation gating
transitions performed in this paper leads to a few general results about the activation gating process. The
first is a rough estimate of the average amount of
charge associated with each of the transitions. We use
here the estimated partial charges (qd and q
d) for the
forward and backward rates, which were derived from
the delay in the channel opening time courses. The derived q
d and q
d estimates (0.25 and
0.24 e0) yield a
single transition charge estimate (q
d
q
d) of 0.5 e0.
This estimate of the average amount of charge associated with each transition, in turn, leads to an estimate
of the number of gating transitions n. If an activating
Shaker channel moves a total charge of 13 e0 (Schoppa
et al., 1992
; Aggarwal and MacKinnon, 1996
; Seoh et al., 1996
), our estimate of 0.5 e0 for the transition
charge implies that an opening channel undergoes n
26 gating transitions.
The value of 0.5 e0 for the transition charge may be
too small since, as described above, the delay does not
provide a good measure of the transitions with the
most rapid rates. Indeed, fluctuation analysis of gating
currents at depolarized voltages (Sigg et al., 1994b;
1996
) suggests that there are some transitions that have
valences near 2. These considerations also imply that the estimate of 26 transitions may be somewhat too large.
Activation Gating Involves at least Three Different Types of Gating Transitions
A second insight that we obtain here is an estimate of
the number of different types of gating transitions. This
is derived from the partial charges that define the voltage dependences of the different rates. The list in Table I includes q1 = 0.36 e0, q
N = 0.18 e0, q
1 =
0.53
e0, q
N-1 =
0.30 e0, and q
N =
0.57 e0. From these estimates, two types of transitions can be distinguished by
having different partial charges for their forward rates.
These correspond to the very first and very last transitions, with charges q
1 and q
N. A third transition has a
partial charge for its backward rate (q
N-1 =
0.30 e0)
that is different from that for the backward rate of either the first or last transition (q
1 =
0.53 e0 and q
N =
0.57 e0). These considerations will be important in
the discrimination between different models in the
third paper in this series (Schoppa and Sigworth, 1998b
).
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FOOTNOTES |
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Address correspondence to Fred J. Sigworth, Department of Cellular and Molecular Physiology, Yale University School of Medicine, 333 Cedar Street, New Haven, CT 06520. Fax: 203-785-4951; E-mail: fred.sigworth{at}yale.edu
Received for publication 3 June 1997 and accepted in revised form 24 November 1997.
Dr. Schoppa's present address is Vollum Institute, Oregon Health Sciences University L-474, Portland, OR 97201-3098.We thank L. Lin for oocyte preparation; E. Moczydlowski and R. MacKinnon for CTx; and R.K. Ayer, W.K. Chandler, K. McCormack, Y. Yang, and W.N. Zagotta for helpful discussions.
This study was supported by National Institutes of Health grant NS-21501 to F.J. Sigworth.
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