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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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Top
Abstract
Introduction
Methods
Results
Discussion
References
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This second of three papers, in which we functionally characterize activation gating in Shaker potassium channels, focuses on the properties of a mutant channel (called V2), in which the leucine at position 382 (in the Shaker B sequence) is mutated to valine. The general properties of V2's ionic and gating currents are consistent with changes in late gating transitions, in particular, with V2 disrupting the positively cooperative gating process of the normally activating wild type (WT) channel. An analysis of forward and backward rate constants, analogous to that used for WT in the previous paper, indicates that V2 causes little change in the rates for most of the transitions in the activation path, but causes large changes in the backward rates of the final two transitions. Single channel data indicate that the V2 mutation causes moderate changes in the rates of transitions to states that are not in the activation path, but little change in the rates from these states. V2's data also yield insights into the general properties of the activation gating process that could not be readily obtained from the WT channel, including evidence that intermediate transitions have rapid backward rates, and an estimate of a total charge 2 e0 for the final two transitions. Taken together, these data will help constrain an activation gating model in the third paper of this series, while also providing an explanation for V2's effects.
Key words: ion channel; gating current; single-channel current; patch clamp; kinetic model| |
INTRODUCTION |
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Top
Abstract
Introduction
Methods
Results
Discussion
References
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The S4-S5 region of many voltage-gated channels contains a leucine heptad repeat motif (McCormack et al.,
1989
) that, in the Shaker B amino acid sequence, spans
residues 375-403. A possible role of this motif in the
Shaker channel activation process was suggested by the
work of McCormack et al. (1991) in which the five leucines were individually substituted by other hydrophobic residues. Substitutions of the first two leucines (L1
and L2) by valine were seen to produce positive shifts
of the midpoint voltage of activation of 60 mV or more
and reduce the voltage sensitivity. Substitution of alanine for L1 has a similar effect (Lopez et al., 1991), as
does the substitution of phenylalanine in the L1 position in Domain 1 of the rat brain II sodium channel (Auld et al., 1990).
This paper concerns a mutation in which L2 is substituted by valine, referred to here as the V2 mutation.
Despite the reduced voltage sensitivity of the V2 channel, a comparison of gating currents in noninactivating
wild-type (WT)1 and V2 channels in a previous study
showed no change in the total charge movement per
channel (Schoppa et al., 1992). To interpret these effects, we previously fitted the equilibrium voltage dependence of channel opening and charge movement
to a model similar to:
This model, which invokes the tetrameric structure
of Shaker channels (MacKinnon, 1991; Kavanaugh et
al., 1992; Li et al., 1994), has the channel open after
each of four subunits undergoes one transition (from
S0 to S1) and one additional concerted conformational change. In the context of this model, V2 causes a 70-mV
positive shift in the midpoint voltage for the equilibrium constant k2, but causes a negligible (5-mV) shift in
the midpoint voltage of k1 (Schoppa et al., 1992). The
strongly shifted midpoint voltage of k2 allows the V2
channel to open only at depolarized voltages and confers the weak voltage dependence of k2 on the channel
open probability. Subsequent analysis of other point
mutations of L2 has provided some information about
changes in the local environment of that residue (McCormack et al., 1993; Sigworth, 1994; Holmgren et al.,
1996) and a possible role of this residue in the inactivation process (Ayer and Sigworth, 1997).
While Scheme I provides a useful framework for considering V2's effects on equilibrium properties, it cannot describe Shaker's activation kinetics. The scheme
has the channel undergo only five transitions, which
cannot produce a long enough delay to account for the
channel activation time course (Zagotta et al., 1994a, 1994b; Schoppa and Sigworth, 1998b). Also, the model
has only two different types of transitions, while Shaker
channels have at least three distinct types of transitions
that can be distinguished by their voltage dependences
(Schoppa and Sigworth, 1998a).
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In this paper, we extend the kinetic analysis of the
Shaker channel to the effects of the V2 mutation. This
characterization of V2 serves two purposes. First, it
serves to further delineate the steps in channel activation that are affected by the structural changes caused
by the mutation. Second, it can provide additional information about the channel activation process. Because the V2 mutation leaves the total gating charge
unchanged, we will assume that its effects can be explained by changes in the free energy of conformational states of the protein, leaving unaffected the
charge movements accompanying the transitions. Thus,
we assume that the basic conformational changes that
are involved in channel opening are preserved in V2.
This view is supported by the qualitatively similar effects of four other amino acid substitutions at this position (McCormack et al., 1993; Sigworth, 1994), and by
the similar voltage dependences seen in rate constants
of WT and V2 channels, as will be shown here. From
within this framework, the data obtained from V2 can
provide some insights into the activation gating process
that cannot be directly obtained from WT data. In the
following paper (Schoppa and Sigworth, 1998b), these
data will be used to help constrain a model of the activation process that accounts simultaneously for the
properties of V2 and WT channels.
As in the study of the normally activating WT channel
in the preceding paper, the V2 mutant channel that we
study has its NH2 terminus truncated to remove the fast
inactivation process (Hoshi et al., 1990). It was characterized using patch-clamp measurements of macroscopic ionic and gating currents, and also single channel currents recorded from oocytes expressing the V2
channel. In this paper, we first consider the general effects of the V2 mutation on activation gating, and then
present a detailed analysis of rate constants that parallels
the analysis performed on WT in the previous paper.
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METHODS |
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Top
Abstract
Introduction
Methods
Results
Discussion
References
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V2's macroscopic ionic and gating currents and single channel
currents were measured in inside-out membrane patches from
Xenopus laevis oocytes expressing the V2 channel, which in our
experiments contains a deletion of residues 2-30 to remove N-type
inactivation (Hoshi et al., 1990). The construction of the V2
Shaker 29-4 cDNA and in vitro synthesis of cRNA have been described previously (McCormack et al., 1991; Schoppa et al.,
1992). The current recordings were made as described previously
(Schoppa and Sigworth, 1998a), with some differences in procedures related to possible artifacts as described below.
Ion and Time Effects on V2's Macroscopic Currents
In our previous paper (Schoppa and Sigworth, 1998a), we reported that the substitution of cesium ions for potassium in the bath, done to facilitate the removal of ionic currents, caused small changes in WT's gating currents. A comparison of V2's gating currents recorded in different patches with bath Cs+ or K+ indicated that these currents are kinetically similar, and the Q-V relations that were derived from these two types of measurements are not distinguishable. Gating currents recorded in Cs+ were
thus used more extensively than was the case for WT experiments, and were used in the experiments shown in Figs. 4 C and 8.
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Secondly, it was reported (Schoppa and Sigworth, 1998a) that
WT's macroscopic ionic tail currents displayed a threefold slowing during the first several minutes of a given patch recording.
However, for V2, the time-dependent changes in deactivation
were much smaller: from <45 s after patch excision to 
4 min
later, ionic tail currents showed a nonsignificant slowing of only
15 ± 11% (n = 3). Therefore, in contrast to experiments with
WT channels, V2 tail currents measured immediately after excision were not excluded from the analysis of the deactivation process. None of the other macroscopic gating properties showed
time-dependent effects, as was also observed for WT channels in
the previous study.
Heterogeneity in V2 Single-Channel Behavior
In recordings of single channel currents, one important consideration is the stationarity of the channel behavior, as inhomogeneous kinetics introduce spurious components into the closed and open dwell-time histograms. Here we describe that V2's single channels display two types of nonstationarities and discuss how each was taken into account in our analysis.
The first type of nonstationary behavior corresponds to obvious shifts in the voltage dependence of Po that lasted for tens of minutes. In one single-channel patch recording that lasted 84 min, currents were measured at +7 mV during three different 2-3-min epochs at 10, 35, and 70 min after patch excision. Between the epochs, the mean Po changed from 0.46 ± 0.14 (mean ± SD; n = 151 traces) to 0.20 ± 0.15 (n = 86) and back to 0.50 ± 0.16 (n = 78). The change was well described by a 20-mV shift in the voltage dependence of Po, as well as in many kinetic parameters that were derived from the closed dwell-time histograms, the first latencies, and the ensemble average current taken from the data. A similar reversible switch from high to low Po activity was observed in one other patch recording, with the Po-V relations during the high and low Po periods in this second patch recording being nearly superimposable with the Po-V relations in the first patch recording. Also, in nine additional patch recordings in which Po was relatively stable, the derived Po-V relations clustered around the same two voltage ranges. These results would suggest that the observed changes in Po did not arise from artifacts such as a change in the temperature of the bathing solution; we take this behavior instead as indicative of two gating modes.
To avoid the effects of these shifts in Po, we ignored all low Po-mode activity in the analysis. This approach was justified since
the V2 channel apparently spends much more time in the high than in the low Po mode. Of 11 single-channel patch recordings, two patches displayed both high and low Po-mode activity, seven patches displayed only high Po-mode activity, and only two
patches displayed only low Po-mode activity. In these 11 patches,
high Po-mode activity was displayed during 78% of the total 482 min of recording time. Additionally, an analysis of a variety of
equilibrium and kinetic parameters indicated that V2 macroscopic currents were composed of the summed activity of a large
number of mostly high Po-mode channels. For example, the activation time constant 
a derived from the rising phase of the macroscopic current was similar to the a derived from the ensemble
average of the high Po-mode single channels but not that from
low Po-mode single-channel events.
V2's single channel activity, like WT's (Schoppa and Sigworth,
1998a), also showed a subconductance behavior, in which the channel occasionally shows a reduced current amplitude. This
activity was accounted for by ending the analysis of a given single
channel current trace at the point at which the currents appear
to become smaller.
Evidence that our selection criteria did not significantly bias
the analysis was obtained by considering the properties of the
idealized single channel activity as contained in the event tables
produced by the analysis program. For a channel with one open
state, the form of the macroscopic tail current as a function of
time should match the conditional probability of the channel being open at time t + given that the channel is open at t. In
several patches, this conditional probability was computed within
individual sweeps and averaged across sweeps; the resulting time
course matched well the time course of macroscopic tail currents at the same voltage.
Slow Inactivation
Parameters of double-exponential fits to the slow inactivation phase of V2's currents were very similar to those of WT: at +67 mV, V2's current measured during 4-s pulses decayed with time constants of 76 ± 19 and 1,136 ± 250 ms (n = 3) with the fast component comprising 28 ± 17% of the total amplitude. Fits of exponentials to the ionic currents that are reported include a term reflecting the ~80-ms component of the slow inactivation process.
Characterization of Kinetics and Voltage Dependences
For characterization of the time course of channel activation, a
single-exponential function with time constant and delay 
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(1) |
was fitted to the time course of the current, starting at the time
when the current has reached 50% of its final value Imax. It was
shown in the preceding paper that, in the case of a sequential scheme with unidirectional transitions, provides a remarkably good estimate of the sum of the reciprocals of all of the rate constants, excluding the smallest one. Further, if one transition is
rate limiting, its rate constant is well estimated by 
1; this result
also holds for branched models. In some cases, when this function was fitted to activation time courses, we added a second exponential term with a longer time constant to account for a slow
relaxation that is seen at depolarized voltages.
As before, we assume that rate constants have exponential voltage dependences of the form
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(2) |
where the partial charges q
i and q
i are related to the gating
charge movement zi accompanying a transition from state i 
1 to state i according to
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(3) |
As a simple characterization of the equilibria of voltage-dependent processes, we use fits to a Boltzmann function,
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(4) |
where qB is the effective charge parameter.
Values of quantities are given as mean ± SEM unless otherwise noted.
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RESULTS |
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Top
Abstract
Introduction
Methods
Results
Discussion
References
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General Properties of V2 Channels
Comparison of WT and V2's equilibrium properties.
Fig. 1, A
and B compares the voltage dependence of channel
open probability Po and the single-channel charge
movement q in WT and V2 channels. As described previously (Schoppa et al., 1992), the V2 mutation causes a
large positive shift in the voltage dependence of channel opening, and makes the Po-V curve less steep. In fits of Po-V relations obtained in several patches, values for
the Boltzmann charge parameter ranged from 3 to 4 e0
for WT, but from 1.5 to 2 e0 for V2. For the q-V relation,
V2 causes a large positive shift in the voltage dependence of part of the charge movement, and also apparently reduces the steepness of the q-V relation. A number of possible explanations exist for WT's steep voltage dependence of Po and q (Bezanilla et al., 1994;
Zagotta et al., 1994a); for example, there may be positive cooperativity introduced by a late gating transition
that is very forward biased. V2 might lower the voltage
sensitivity of Po and q, if V2 alters the equilibrium of
such a late gating transition.
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10 mV. This is graphically illustrated in
the plot of the derivative of V2's charge versus voltage
in Fig. 1 C. The derivative plot has two peaks: the largest near 50 mV, which corresponds to the steepest
portion of V2's q-V relation at negative voltages, and a
second peak near +10 mV. These properties would be
consistent with there being two distinct sets of transitions occurring over different voltage ranges. From the
position of the inflection in the q-V relation (Fig. 1 B),
which is near 13 mV, we can divide the charge movement into two parts, qL and qH, associated with the sets
of transitions that occur at low and high voltages, respectively. A value of qH = 2.2 ± 0.3 e0 (n = 6) is estimated for the amount of charge that is associated with
the set of transitions that move at high voltages.
Comparison of WT and V2 channel opening and "on" gating current kinetics.
V2's general effects on gating kinetics are illustrated in the time courses of the macroscopic
ionic current and gating currents in Figs. 2 and 3. In a
comparison of channel opening time courses (Fig. 2),
V2 displays somewhat slower kinetics at both low and high voltages. The difference at lower voltages is reflected in the differences in the values for the activation
time constant a, with V2 displaying a values that are as
much as two to three times slower than WT (Fig. 2 B).
The a values are, however, very similar above +60 mV.
Over the entire voltage range, the delay in the channel
opening time course is roughly similar to WT's (Fig. 2 C).
+67 mV), Shaker's channel
opening time course has a slow component that reflects
the kinetics of an alternate activation path, through the
closed states Ci (Schoppa and Sigworth, 1998a). However, in fits of the sum of two exponentials to the channel
opening time course at V +67 mV, V2 causes no apparent effect on the time constant of the faster component (Fig. 2 B), which we take to be a, reflecting the kinetics of the main activation path. It will be shown more
explicitly below that the difference in the appearance of
the currents at high voltages reflects a higher propensity
for V2 to enter into the slow activation path.
The on gating current time courses of V2 (Fig. 3 A)
are qualitatively similar to WT's. The similar time
courses at many of the voltages are reflected in the similar values for the time constant on of an exponential
fitted to the decay of the on currents (Fig. 3 B). The
similar gating current time courses at voltages above 0 mV, together with the discrepancies in WT and V2
channel opening time courses at the same voltages
(Fig. 2 A), implies that V2 has little effect on early gating transitions, but an effect on late transitions. For a
sequential gating mechanism, decreasing the rate of an
early gating transition would slow both the ionic and
gating current time courses, but a change in a late transition could slow channel opening without affecting
the gating current.
Some moderate differences in the on values are apparent at intermediate voltages, near 40 mV, where
V2's on currents decay nearly twice as rapidly as WT's.
This difference might be an indirect effect of V2's
shifted voltage dependence of channel opening. It has
been reported that WT's on currents at these voltages
include a slow component that reflects the slow kinetics
of channel opening (Bezanilla et al., 1994). Since V2
does not open at these voltages, this component would
not be expected to appear in V2's currents (McCormack et al., 1994). Consistent with this simple interpretation, WT's on currents at 43 mV (Fig. 3 C) can be
fitted by the sum of two exponentials with one component having a time constant ( = 4.2 ± 0.5 ms; n = 4)
that matches WT's activation time constant at this voltage (a = 4.9 ± 0.9 ms; n = 5), and the other component having a time constant ( = 1.2 ± 0.2 ms; n = 4)
that matches the time constant of the single exponential
fitted to V2 gating currents ( = 1.2 ± 0.1 ms; n = 4).
In contrast to the modest effects on the on gating
currents, V2 has a dramatic effect on the decay of the
"off" gating currents. After moderate and large depolarizations, V2's gating currents decay very much more
rapidly than WT's. To explain V2's faster off gating currents, we recognize first that WT's off currents after
large, long depolarizations have a slow decay time
course that reflects the slow return from the open state
but a rapid decay time course after small or short depolarizations that fail to open the channel (Zagotta et al.,
1994; Bezanilla et al., 1994). V2's faster off current after
intermediate depolarizations (e.g., to 33 mV) could,
then, just be due to the fact that V2 does not open at
these voltages (Fig. 1 A). The faster off currents also seen after depolarizations that are large enough to
open V2 channels (V 13 mV) are to be expected
since, as shown below, V2 dramatically speeds the deactivation time course.
Comparison of WT and V2 channel opening kinetics at
equivalent Po.
A final general kinetic effect of the V2
mutation is illustrated in Fig. 2 D, where WT and V2 activation time courses are compared at voltages where Po
is similar for the two channels. The displayed currents
are at 58 mV for WT and 3 mV for V2, where Po is
~0.2 for the two channels. We follow the strategy used
by Zagotta et al. (1994a) by normalizing the amplitude
and the time course of the currents to make comparisons about the sigmoidicity of WT and V2 currents.
a, V2's activation time course is seen to be much more sigmoidal
than WT's. One explanation for the slow rise and relatively small delay of WT currents is that there is positive
cooperativity in the mechanism of activation at these voltages, arising from the presence of forward-biased
late transitions (Zagotta et al., 1994b). The faster rise but
approximately equal delay in V2 activation is consistent
with unchanged early activation steps but a late transition that is less forward biased.
Assignment of Rate Constants from Macroscopic Currents
The preceding sections have outlined the general differences in activation gating for WT and V2 channels. We now consider the rates of individual V2 gating transitions. For this analysis, we use the same general framework that was used to assign rates for WT in the previous paper (Schoppa et al., 1998a), in which the gating process is approximated by a linear sequence of transitions:
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The rates shown are those that were evaluated for
WT in the previous paper. To obtain values for forward
rate constants, we consider mainly macroscopic ionic
and gating currents obtained at depolarized voltages (V 13 mV), where V2's charge movement is mostly complete (Fig. 1 B). Backward rates are mainly evaluated from macroscopic ionic and gating currents measured
at hyperpolarized voltages (V 
93 mV), where little
charge movement occurs.
Estimates of 
1, 
1, and p.
For the WT channel, we
were able to assign values for three rate constants associated with early and intermediate transitions (Schoppa
and Sigworth, 1998a). The forward rate of the first transition 1 was found to be rate limiting for channel activation at voltages near 0 mV, and estimates for 1 were
obtained from the kinetics of channel opening and gating currents. For V2, estimates of 1 could be obtained
with only a more limited analysis. V2's differential effects on the channel opening and on gating currents at
voltages near 0 mV imply that the rate-limiting step to
channel opening is a later transition. We assumed that
the decay of V2's on currents still reflects 1, and estimates for 1(0) = 1,270 s1 (n = 7) and q1 = 0.28 ± 0.02 e0 were obtained (Fig. 4 A) that are similar to those
obtained for WT (1(0) = 1,200 s1, n = 7, and q1 =
0.36 e0). Estimates of the forward rate p of the transition that is rate limiting at large positive voltages for V2
were obtained from the values of the activation time
constant a at very large depolarizations (V +87 mV;
Fig. 4 B). The derived estimates for V2's p(0) = 1,400 ± 100 s1 (n = 5) and qp(0) = 0.19 ± 0.01 e0 are similar to those obtained for WT (p(0) = 2,100 s1 and
qp(0) = 0.17 e0).
1 were obtained from gating currents induced by voltage steps between 93 mV and more hyperpolarized
voltages (Fig. 4 C). We assume that these voltages are
sufficiently negative that the resulting currents reflect
only charge movement in the first gating step (Schoppa
and Sigworth, 1998a). The traces of V2's gating currents at these voltages are virtually superimposable with
WT's, which is consistent with V2 having no significant
effect on 1. Indeed, the estimates of 1(0) = 260 ± 100 s1 (n = 3) and q1 = 0.48 ± 0.05 e0 derived from
these data are similar to those obtained for WT (1(0)
= 190 s1 and q1 = 0.53 e0).
Estimate of N.
For WT, a direct estimate of the forward rate N of the final transition was obtained from a
rapid component in the time course of reactivation observed after very short hyperpolarizations. Fig. 5 A illustrates V2's reactivation time courses at +67 mV after
hyperpolarizations with a fixed amplitude Vh of 93
mV, but of various durations th. In contrast to what was
observed for WT the rising kinetics of V2's reactivation
time course shows little dependence on th (Fig. 5, B and
C). The reactivation time course for the shortest th =
100 µs is reasonably well accounted for by an exponential with the same time constant that is fitted to the reactivation time course for large th values. No fast reactivating current is observed either when Vh is changed to
13 mV (Fig. 5 D), which may be expected to be more
effective in loading channels into closed states that are
near the open state.
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N. An alternative explanation is that V2 accelerates the
backward rate N-1 so that the occupancy in the last
closed state is never high enough for channels reactivating with the kinetics defined by N to be observed. We may nevertheless place a lower bound on the value
of N from fits to the reactivation time courses in Fig. 5.
There the time constant of the rate-limiting step a = 0.33 ms implies that N 3,000 s1 at +67 mV. Using
the estimate of qN obtained for WT, this yields N(0) 1,900 s1. This lower limit is three to four times smaller
than the estimate of N for WT (N(0) = 7,000 s1).
Estimate of N.
The most direct estimate of WT's channel closing rate N was obtained from the time course
of the ionic tail currents, although rather elaborate
measures were required to account for the fact that
WT's channel deactivation time course at most voltages
reflects multiple reopenings of the channel. Estimates
for WT's N were obtained from fits of the sum of two exponentials to the tail currents at extremely hyperpolarized
voltages (between 153 and 203 mV). V2's N, however, could be evaluated using a much simpler strategy.
93 mV.
At all voltages, V2's deactivation is much faster than
WT's. When a single exponential is fitted to these currents, it is seen that the time constants tail are not only
smaller but have a weaker voltage dependence for V2
(Fig. 6 B). Fitting the voltage dependence of tail results in estimates for qtail of 1.1 ± 0.04 e0 (n = 4) and 0.53 ± 0.05 e0 (n = 5) for WT and V2, respectively. On the
other hand, V2's qtail nearly matches the voltage sensitivity of N that was estimated for WT (qN = 0.57 e0).
The similarity between V2's qtail and qN implies that V2
changes the deactivation process from one that reflects
the last two transitions to one that is a simple function
of the channel closing rate N. Consistent with the V2's
tail current time course reflecting a single transition, it
is reasonably well accounted by a single exponential
(Fig. 6 A). The tail values at V 23 mV yielded an estimate for N(0) = 580 ± 100 s1 (n = 5), which is approximately four times larger than the estimate for WT
(N(0) = 150 s1).
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N-1 were obtained by simultaneously considering the fast component in the reactivation time course that corresponds to N, and also the
double-exponential nature of the tail currents. This
analysis could not be performed on V2 since it lacks a
fast component in the reactivation time course and the
tail currents do not show multiple components. The assignment of V2's N-1 will rely on single channel data
described below.
V2's effect on d and d.
While we were unable to assign values for the forward and backward rates of any
other of V2's transitions from macroscopic current
measurements, these data can be used to test whether
V2 causes a change in the rates of these transitions. The
rates of these additional transitions, which make a major contribution to the delay in activation, have been assigned the parameters d and d. As described in the
preceding paper, the parameters reflect the summed
properties of many intermediate transitions.
d and d was
first obtained by comparing WT's and V2's on and off
gating current time courses. While the decay of the on
currents at depolarized voltages reflects the rate-limiting 1, information about the rates of the transitions
that follow 1 resides in the time course of current near
its peak. Fig. 7 A superimposes WT and V2 on currents
that were measured at two depolarized voltages (13
and +27 mV). The time courses match quite well, consistent with V2 having similar forward rates for all of the
rapid intermediate transitions. V2's effect on reverse
rates was evaluated by comparing WT's and V2's off
currents. To remove the contribution of channels residing in the open state to the off current time course,
which would obscure the analysis of the intermediate
transitions, we compared WT's and V2's off gating currents measured after prepulses that preload channels
into intermediate and late closed states but not the
open state. Fig. 7 B compares V2's off currents after a
long depolarization to 33 mV with WT's off currents
measured after a 2-ms depolarization to the same voltage. These prepulses move most (~70-80%) of the
charge but result in few open channels (<15% and
<<1% for WT and V2, respectively). The similar off
current kinetics suggests that V2 has little effect on the
backward rates of virtually all of the gating transitions,
apart from the final transitions.
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d and d was
provided by a comparison of the delay in the macroscopic channel opening time course. At depolarized
voltages, the delay is expected to reflect the forward
rates of all but the rate-limiting step to channel opening (Schoppa and Sigworth, 1998a). The a values for V2 (Fig. 2 C) are very similar to those of WT, tending
however to be slightly longer (by 10-30%). The small
difference in the delay is consistent with V2 having a
small effect on the forward rates of a large number of
transitions. A measure of d was obtained by analyzing
the delay in V2's reactivation time course after hyperpolarizations of different voltages and of different durations th, using a strategy similar to that used for WT in
the previous paper (Schoppa and Sigworth, 1998a).
The resulting relationships between th and the delay a
are nearly identical for WT and V2 (data not shown),
which is consistent with V2 having little effect on d.
V2 also had little effect in an experiment that evaluated the Cole-Moore delay (Cole and Moore, 1960).
This experiment evaluates the effect of different amplitude prepulses on the delay in the channel opening
during a subsequent test pulse. (These data are not
shown here, but see Fig. 18 in Schoppa and Sigworth,
1998b). Since the voltage dependence of the delay reflects the equilibria of the various transitions that contribute to the delay, these results suggest, roughly, that
the ratio of d and d for WT and V2 is similar.
More observations about V2's off gating currents measured
after intermediate amplitude depolarizations.
We report here
results obtained from one additional experiment that
was performed for V2. Off gating currents were measured after prepulses of a fixed amplitude (3 mV)
with variable test voltages between 63 and 113 mV
(Fig. 8 A). Since the prepulse moves most (85%) of
V2's charge but opens few V2 channels (Po = 0.2), the
measured off currents should reflect the backward
rates of both the first and intermediate transitions.
d that determines the voltage sensitivity of the backward rates of intermediate transitions. Single exponentials were fitted to these currents
to estimate a decay time constant off; the off values
were then fitted to an exponential function of voltage,
yielding qd estimates in three patches of 0.44, 0.54,
and 0.61 e0.
Single exponentials failed to fit a rapid component
that is visible at some test voltages, however. The deviation is illustrated in the expanded traces of off current
at 63 mV measured from two patches in Fig. 8 B. We
take the presence of a fast component in the off current to reflect the presence of fast intermediate transitions; in the context of a sequential scheme, a fast component of the gating current must reflect the kinetics
of the first transitions that occur during the relaxation.
In these two patches, no fast component was observed
in the off current at voltages more negative than 63 mV
(data not shown), which might imply that the fast and
slow components have different voltage dependences.
Analysis of Single-Channel Behavior
Additional information about V2's effects on the rates
of the transitions nearest the open state was obtained
from measurements of single channel currents. We begin by describing V2's single channel activity (Fig. 9 A).
At voltages where Po is low (13 and 3 mV), V2 has a
latency to first opening of ~10 ms, and long closures of
a similar duration that separate brief (2-3-ms) bursts of
channel openings are seen. During the bursts, the
channel sometimes closes into short-lived closed states.
With an increase in voltage, the main changes in the
single channel activity are reductions in the time to first
opening and the duration of the long closures (compare the traces at 13 and +7 mV). At the highest voltages (+107 mV), V2's single channels are similar to
WT's (Hoshi et al., 1994; Schoppa and Sigworth,
1998a), opening rapidly at the beginning of the pulse
and remaining open for most of the trace, closing occasionally into short-lived closed states.
|
The closed dwell time histograms that correspond to
these data at voltages between 13 and +27 mV (Fig. 9
B) were well fitted by a mixture of two exponentials.
With increasing voltage there is a marked reduction in
the duration of the long closures, while the relative amplitude of the long closure component and the duration of short closures show less change. The closed
time histograms obtained at the highest voltages (+67
and +107 mV) display the three populations of closures characteristic of WT at the same voltages (Schoppa
and Sigworth, 1998a). At all voltages, V2's open time
histograms (Fig. 9 C) were well fitted by a single exponential, which is consistent with a single open state
(Hoshi et al., 1994).
V2's effects on transitions to Ci, Cf1, and Cf2.
Single channel data from WT channels have been useful for obtaining information about states that are not in the activation path (Hoshi et al., 1994; Schoppa and Sigworth,
1998a). In the previous paper, we suggested that there
are several such states:
|
+47 mV). The shapes of the histograms cannot give direct information about rate constants, since many of
the closures are poorly resolved; however, the fact that
V2's average histogram matches WT's is consistent with
V2 not altering the three rates.
|
+47 mV display a slow component that corresponds to channels entering Ci from closed states in the activation path (Schoppa and Sigworth, 1998a). Compared with the WT latency histogram at +107 mV, V2's histogram has a slow component approximately four times larger in amplitude; the
fitted fast and slow time constants are, however, very
similar. An increased amplitude slow component was
also consistently observed in the macroscopic activation
time course at large depolarizations (V +47 mV),
where, on average, V2's slow component accounted for
26 ± 2% of the time course (n = 28) compared with
WT's 8 ± 1% (n = 21). Since it is not known from
which closed states Shaker channels can enter Ci states,
it is not clear whether the larger slow component for
V2 arises from increased rates for transitions into Ci
states, or simply is an effect of altered occupancies of
states in the activation pathway.
Estimate of N and N-1 from single channels.
V2's single
channel data could also be used to estimate the rates of
the final transitions that are in the activation path. Indeed, one relevant observation has already been presented, which is V2's three- to fourfold shorter channel
open times at depolarized voltages (Fig. 10 B). At these
high voltages, most of the closures that determine the
channel open time reflect closures into states that are
not in the activation path, but it is notable that the magnitude of V2's effect on the open times nearly matches
the fourfold faster channel closing rate into the activation path N that was estimated from macroscopic tail
currents. The rates of channel closure into the states that
are not in the activation path and N would all be expected to reflect the stability of
a)/
a +Ase
0.2. The current traces have normalized amplitudes and have their time
axes scaled to yield the same rising phase kinetics of the current. Patches w312 and v142.
) and V2
(
). The Po values were evaluated from macroscopic ionic currents as described in Fig. 
q/
and 
, respectively). For comparison, the value of 1/
