¶
¶**
From the * Department of Anesthesiology, Department of Physiology, § Department of Molecular and Medical Pharmacology, and
Brain Research Institute, University of California, Los Angeles, CA 90095-1778; ¶ Centro de Estudios Cientificos de Santiago, and Department of Biology, Faculty of Science, University of Chile, Santiago, 9 Chile; and ** Conicet, Buenos Aires, 1033 Argentina
Prolonged depolarization induces a slow inactivation process in some K+ channels. We have studied
ionic and gating currents during long depolarizations in the mutant Shaker H4-(6-46) K+ channel and in the
nonconducting mutant (Shaker H4-
(6-46)-W434F). These channels lack the amino terminus that confers the fast
(N-type) inactivation (Hoshi, T., W.N. Zagotta, and R.W. Aldrich. 1991. Neuron. 7:547-556). Channels were expressed in oocytes and currents were measured with the cut-open-oocyte and patch-clamp techniques. In both
clones, the curves describing the voltage dependence of the charge movement were shifted toward more negative
potentials when the holding potential was maintained at depolarized potentials. The evidences that this new voltage dependence of the charge movement in the depolarized condition is associated with the process of slow inactivation are the following: (a) the installation of both the slow inactivation of the ionic current and the inactivation of the charge in response to a sustained 1-min depolarization to 0 mV followed the same time course; and (b)
the recovery from inactivation of both ionic and gating currents (induced by repolarizations to
90 mV after a
1-min inactivating pulse at 0 mV) also followed a similar time course. Although prolonged depolarizations induce inactivation of the majority of the channels, a small fraction remains non-slow inactivated. The voltage dependence of this fraction of channels remained unaltered, suggesting that their activation pathway was unmodified by
prolonged depolarization. The data could be fitted to a sequential model for Shaker K+ channels (Bezanilla, F., E. Perozo, and E. Stefani. 1994. Biophys. J. 66:1011-1021), with the addition of a series of parallel nonconducting (inactivated) states that become populated during prolonged depolarization. The data suggest that prolonged depolarization modifies the conformation of the voltage sensor and that this change can be associated with the process
of slow inactivation.
Upon depolarization, the macroscopic conductance increases and then shows a progressive decay. The reduction in conductance with time was referred to as inactivation by Hodgkin and Huxley (1952). Depending on
the nature of the mechanism involved, the time course
of the inactivation process ranges from a few milliseconds (fast inactivation) to several seconds (slow inactivation). To explain the fast inactivation process in Na+
channels from squid giant axon, Armstrong and Bezanilla (1977)
proposed the "ball-and-chain" model. In this
model, a tethered inactivating particle, the ball, is able
to block the ion passage only after channel opening. In
Shaker K+ channels, fast inactivation is mediated by the
first 20 amino acid residues (the ball) that are tethered
in the 60 amino acid residues that lie between the ball
and the first transmembrane domain (Zagotta et al., 1989
,
1990
; Hoshi et al., 1990
). Fast inactivation is induced by
the binding of the amino terminus of the channel protein to the internal mouth of the pore. Because of the
involvement of the amino terminus in this process, fast inactivation is also known as N-type inactivation. During N-type inactivation, the NH2 terminus interacts with
the voltage sensor and slows down the return of the gating charge to its resting position upon repolarization
(Bezanilla et al., 1991
). This slowdown of the charge return prompted by the inactivation process was first observed in Na+ channels and christened "charge immobilization" (Armstrong and Bezanilla, 1977
). Shaker K+
channels with amino acid residues 6-46 deleted (Shaker
H4-
), lacks fast inactivation (Hoshi et al., 1990
) and
charge immobilization (Bezanilla et al., 1991
).
Slow inactivation, on the other hand, is less understood. Ehrenstein and Gilbert (1966) showed that prolonged depolarizations resulted in a slow reduction
of the K+ conductance in squid giant axon. The molecular mechanism of this process can be studied in
Shaker K+ channels lacking fast inactivation (Shaker H4-
)
since they show a relatively voltage insensitive slow decrease in channel open probability as a result of prolonged depolarizations (Hoshi et al., 1991
; Choi et al.,
1991
; Yellen et al., 1994
; Liu et al., 1996
). Since point
mutations in the carboxyl terminus of the channel (S6
transmembrane segment) affect slow inactivation, this
process is commonly denominated C-type inactivation
(Hoshi et al., 1991
; López-Barneo et al., 1993
) and is
produced by a cooperative mechanism (Panyi et al.,
1993
; Ogielska et al., 1995
). However, mutations in regions other than the S6 segment (for example, in the
pore region) can also dramatically alter the inactivation
time course (López-Barneo et al., 1993
; De Biasi et al.,
1993
). These results strongly suggest the presence of
more than one molecular mechanism in determining
the rate of channel inactivation. In those cases in which
pore (P) residues in K+ channels are involved in determining the inactivation kinetics, the process has been
referred to as P-type inactivation (De Biasi et al., 1993
).
The present study, previously presented in abstract
form (Olcese et al., 1994, 1995
), further investigated
the nature of the effect of prolonged depolarization on
the ionic conductance and correlates these effects on
ionic current with effects on gating current in the Shaker
H4-
K+ channel. Prolonged depolarization produced
changes in the voltage dependence of the charge movement similar to the ones described by Bezanilla et al.
(1982)
for the Na+ channel in squid giant axon. Charge
immobilization, as a consequence of long depolarization, has also been reported for the human K+ channel
Kv1.5 (Fedida et al., 1996
).
Molecular Biology and Oocyte Injection
cDNA encoding for Shaker H4 K+ channel (Kamb et al., 1987)
lacking the amino acids 6-46 to remove the fast inactivation (Shaker H4-
) was used for measurements of ionic and gating currents
(Hoshi et al., 1990
). For gating current measurements in the corresponding nonconducting mutant, the mutant Shaker H4-
W434F (Perozo et al., 1993
) was used.
24 h before cRNA injection, Xenopus laevis oocytes (stage V-VI) were treated with collagenase (200 U/ml; GIBCO BRL, Gaithersburg, MD) in a Ca2+-free solution to remove the follicular layer. Oocytes were injected with 50 nl cRNA 1 µg/µl suspended in water using a "nano-injector" (Drummond Scientific Co., Broomall, PA) and maintained at 18°C in modified Barth's solution containing (mM): 100 NaCl, 2 KCl, 1.8 CaCl2, 1 MgCl2, 5 Na-HEPES (pH 7.6), and 50 mg/ml gentamicin.
Gating and Ionic Current Recording
Gating and ionic currents were recorded 1-7 d after injection using
the cut-open oocyte Vaseline gap voltage clamp (COVG) (Stefani
et al., 1994) and conventional cell-attached patch clamp techniques. Methanesulphonic acid (MES)1 was the main anion in the
recording external solutions. In the cut-open oocyte technique,
the external solutions were (mM): 107 Na-MES, 2 Ca-(MES)2, 10 Na-HEPES (isotonic Na-MES), 107 K-MES, 2 Ca-(MES)2, 10 Na-HEPES (isotonic K-MES) or 110 N-methylglucamine-methanesulphonate (NMG-MES), 2 Ca-(MES)2, 10 NMG-HEPES (isotonic
NMG-MES Ca-MES 2). The internal solution contained (mM): 110 K-glutamate, 10 K-HEPES. The oocytes were K+ depleted by internal perfusion of the oocyte with a solution containing (mM): 110 NMG-MES, 10 NMG-HEPES, 10 (NMG)2-EGTA (isotonic NMG-MES). The perfusion (1 ml/h) was attained introducing a 20-50 µm glass pipette connected to a syringe pump in the lower part of
the oocyte. Standard solution for the intracellular recording micropipette was (mM): 2,700 Na-MES, 10 NaCl. Low access resistance to the oocyte interior was obtained by permeabilizing the
oocyte with 0.1% saponin. For the experiments in cell-attached
configuration, after the removal of the vitelline membrane, the
oocytes were K+ depleted in a solution containing (mM): 110 CsMES, 2 MgCl2, 10 Cs-HEPES (isotonic Cs-MES). To speed up
the intracellular K+ replacement by Cs+, the oocyte membrane
was damaged at various places with a thin needle. Patch pipettes
were filled with (mM): 110 Cs-MES, 2 CaCl2, 10 Cs-HEPES (isotonic Cs-MES CaCl2 2). All recording and perfusion solutions
were buffered at pH 7.0 with 10 mM HEPES. All experiments were performed at room temperature of 22-24°C.
In most cases, gating currents were recorded unsubtracted.
Linear components were analogically compensated at positive
potentials (20-40 mV) where the membrane capacity becomes
voltage independent. This is also the case in slow-inactivated channels in which the charge-voltage curve was shifted to more negative potentials. P/4 subtracting protocol (Bezanilla and Armstrong, 1977) from a positive holding potential (20 mV) was used
for some of the experiments describing the time course of charge
inactivation. The filter frequency was 1/5 the sampling frequency.
Modeling
The model-fitting procedure was implemented using the parameter optimization program SCoP (Simulation Resource, Inc., Barren Springs, MI). We used a state kinetic model, expressed as a
system of differential equations, with discrete transitions occurring between states. The transition rates between the horizontal
lines of states (see Fig. 10 A) were exponential functions of the
potential as predicted by the Eyring theory. The vertical transitions are assumed to be voltage independent.
Ionic Current Inactivation
Fig. 1, A and B shows the time course of the current for
Shaker H4 and Shaker H4- for a series of depolarizing
pulses of 50-ms duration. Shaker H4 displays a fast decay
of the ionic current with a time constant of a few milliseconds (Fig. 1 A). In the mutant Shaker H4-
, under
the same experimental conditions and time scale, the
ionic current is maintained during the pulse (Fig. 1 B).
However, in the same deletion-mutant Shaker H4-
,
longer depolarizations make evident a slow inactivation
process with a time constant of several seconds (Fig. 1 C).
Fig. 2 shows a typical experiment to measure the steady
state voltage dependence of the slow inactivation process. The experiments were done in isotonic K-MES. To
reach the steady state for the slow inactivation process,
oocytes were maintained for 1 min at the given holding
potential (HP) before the pulse protocol. Fig. 2 A shows
that the current measured from an HP of 70 mV are
larger than those measured at an HP of
30 mV, indicating that the fraction of inactivated channels increases
as the holding potential becomes more positive. Fig. 2
B illustrates conductance-voltage (G-V) curves obtained
from the amplitude of the tail currents at a constant return potential (
50 mV). Membrane conductance (G)
was calculated from G = I(
50 mV)/(E
EK), where
I(
50 mV) is the peak tail current at
50 mV, E(
50mV) is
the return potential (
50 mV), and EK is the K+ reversal potential (0 mV in isotonic K-MES). At
50 mV return potential, the slow time course of the tail currents
facilitated the peak current determination. Long membrane depolarizations strongly reduce the membrane
conductance without significantly changing the voltage
dependence of channel opening (Fig. 2, B and C). Fig.
2 D shows the steady state slow inactivation curve. The
relative conductance measured as peak tail current at
50 mV for a pulse to
1 mV was plotted as a function
of the holding potential, and the data were fitted to a
Boltzmann equation that gave a half inactivation voltage of
38.5 mV and an effective valence of 7.2. The
holding potential was maintained for 1 min before the
test pulse was applied. The curve represents the reduction in availability of K+ channels to open as a function
of the membrane depolarization and shows that the
steady state inactivation curve is strongly dependent on
the holding potential.
Charge Movement from "Slow Inactivated" Channels
Measurements of charge movement make it possible to
explore the voltage-dependent characteristics of the
different protein conformations that give origin to the
closed states that lead to channel opening. We used
gating current measurements as a tool to investigate
how the activation pathway of the slow inactivated Shaker H4- K channels was altered. Using the cut-open
oocyte voltage clamp and giant macropatch techniques
in K+-depleted oocytes, we measured gating current
uncontaminated by ionic currents. Oocytes expressing
Shaker H4-
were K+ depleted by internal perfusion
with NMG-MES (see MATERIALS AND METHODS). Fig. 3,
A and B show selected gating current traces evoked by
the indicated pulse potentials, from different holding potentials (
90 mV, Fig. 3 A and 0 mV, Fig. 3 B). The
charge moved during the voltage steps, calculated by
integrating the ON gating current, is plotted as a function of the pulse potential (Q-V) in Fig. 3, C and D. Q-V
curves for different holding potentials were constructed
from the charge measured immediately after the voltage steps (ON gating current). These measurements
should minimize some charge recovery that may occur
during repolarizing pulses from depolarized holding
potentials. To obtain a more direct comparison of the
Q-V curves obtained with the different holding potentials, in Fig. 3 D we have plotted the absolute values of
the charge. The total amount of charge that moves in
control conditions (
90 mV HP) and after slow inactivation (0 mV HP) is the same. However, the Q-V curve
generated by the channels in the inactivated state (0 mV HP) was shifted by ~50 mV to the left along the
voltage axis when compared with the Q-V curve obtained from the noninactivated channels (
90 mV HP).
The shift in the Q-V curve indicates that, when the charge
returns from the inactivated state after prolonged depolarization, it sees a different energy landscape than
the charge moving in normally polarized channels from
closed states to the open state. In kinetic terms, this
means that the charge movement from the inactivated
state does not follow the same kinetic pathway as when
the charge moves from the closed to the open state.
Charge Movement after Prolonged Depolarization in the
Nonconducting Shaker H4--W434F
The shift toward more negative potentials of the Q-V
curve, induced by long depolarizations, is also present
in the nonconducting clone Shaker H4--W434F. For
comparison with the conducting clone Shaker H4-
in
the same ionic conditions, oocytes expressing the mutant channel were also K+ depleted, and the internal
medium replaced with 120 mM NMG-MES. Fig. 4, A
and B show representative gating current traces for the
Shaker H4-
-W434F channel. The traces were recorded
during voltage steps to the indicated potentials from
90 (Fig. 4 A) and 0 (Fig. 4 B) mV holding potential.
The Q-V curve of the slow inactivated channels (0 mV
HP) is clearly shifted toward more negative potentials
compared with that obtained from
90 mV HP (Fig. 4
C). The midpoints of the two Q-V curves are ~25
mV apart. Interestingly, in both the conducting and the
nonconducting clones, the voltage dependence of their
charge movements when at hyperpolarized potentials
was very similar (Bezanilla et al., 1991
; compare Figs. 3
D and 4 C) and both have a left-shifted Q-V curve after a
long depolarization. In Shaker H4-
, the left shift of the
Q-V obtained from a holding potential of 0 mV is ~20
mV more negative than in Shaker H4-
-W434F.
Installation of Slow Inactivation
The shift to more negative potentials of the Q-V curve
in slow inactivated channels could be explained as the
conversion of channels from a "permissive" form (available for activation) to a "reluctant" conformation. In
the reluctant (inactivated) conformation, the voltage
sensor moves under a different voltage dependence than the permissive conformation. We propose here
that the gating charge conversion occurring during
long depolarizations is related to the slow inactivation
process. To test this hypothesis, we compared the time
course of the charge conversion with the time course of
the slow inactivation of the current at the same potential. In Fig. 5 A, the membrane potential was held at
90 mV for at least 1 min to fully recover all the channels from inactivation. Inactivating prepulses of different duration to 0 mV were applied before a test pulse
from 0 to
60 mV. It is clear that the gating current at
60 mV is reduced as the prepulse is made longer (Fig. 5 A). To quantify the effect of the prepulse, the integral
of the ON gating current normalized to the maximum
charge (Fig. 5 C,
) was plotted as a function of the
prepulse duration.
As the inactivating prepulse becomes longer, the Q-V
curve progressively shifts to the left, approaching the
position of the Q-V curve obtained after 1 min at 0 mV
HP (steady state) (Fig. 4 C, ). Therefore, the charge
reduction reflects the speed of the shift of the Q-V
curve in depolarizing conditions. There is no charge
reduction, but only a change in its voltage dependence.
To compare the establishment of the charge conversion with the conduction inactivation, we measured the
slow decay of the K+ current due to slow inactivation
during 1-min depolarizing pulse at 0 mV in the conducting clone (Fig. 5 B). At the end of the pulse, the
ionic conductance was reduced by ~85% due to the
slow inactivation. The normalized ionic current decay
was plotted (Fig. 5 C, thick trace) along with the normalized charge in Fig. 5 C. Both processes can be reasonably well fitted simultaneously by the sum of two exponential functions with the same time constants () for
ionic and gating current inactivation of 4.1 and 24 s.
Recovery from Slow Inactivation
The recovery of the charge movement and ionic current were measured after a 1-min preconditioning pulse
to 0 mV that drove most of the channels into a slow inactivated state. Then, repolarizing pulses of different
duration to 90 mV were delivered, allowing different
times of recovery at this potential. The recovery of the
charge and the ionic current as a function of the duration of the
90 mV pulse was measured with a test
pulse from
90 to +20 mV. The recovery of the slow
inactivated charge was measured by integrating the ON
gating current during the test pulse. ON gating current
increased progressively depending on the duration of
the recovery interval (Fig. 6 A). In this case, the charge increase reflects the shift towards the right along the
voltage axis of the Q-V curve. An identical protocol was
used to monitor the recovery of the ionic current (Fig.
6 B). As it was described for the installation of slow inactivation, a tight correlation between the time courses
of charge and ionic current recovery was found. Experimental points describing the recovery of both charge
and ionic current could be well fitted simultaneously to the sum of two exponential functions with the same
time constants. The two
obtained by the fit were 0.01 and 1.1 s (Fig. 6 C), indicating that the recovery from
slow inactivation at
90 mV in Shaker H4-
channel is a
much faster process than the installation at 0 mV.
We measured the recovery of charge movement and
ionic conductance simultaneously in the conducting
clone Shaker H4- to give further support to the hypothesis that the changes in charge movement are correlated to the slow inactivation of the channel. In this case, we took advantage of the low permeability of
Shaker H4-
channels to Cs+ to record at the same time
gating and ionic current of the same order of magnitude. Cs+ currents were recorded in cell attached
patches under symmetrical isotonic Cs-MES in permeabilized oocytes. We confirmed that in external Cs+
slow inactivation is still present (López-Barneo et al.,
1993
). The complete exchange of the internal oocyte
medium with the bath solution (isotonic Cs-MES) was
checked measuring the reversal potential of the ionic
current. Fig. 7 A shows the currents elicited under
these conditions and Fig. 7 B shows the current to voltage (I-V) curve, confirming the symmetry between the
internal and the pipette solutions containing isotonic
Cs-MES with 2 mM CaCl2. Pulsing to the reversal potential for Cs+ (0 mV in our conditions, see I-V curve in
Fig. 7 B), the only outward current elicited is the gating
current (Fig. 8 A) (Noceti et al., 1996
). However, at the
end of the pulse the driving force for the repolarization
to
90 mV favors a large inward Cs+ tail current that is
proportional to the number of channels open at the
end of the depolarizing pulse together with a small
contamination of the OFF gating current (Fig. 8 A). After a 1-min depolarization to 0 mV, we measured the recovery from inactivation after repolarizations of different duration at
90 mV. The current traces in Fig. 8 A
show that both charge movement (transient outward
current) and membrane conductance (tail current) recover as the recovering time to
90 mV increases. The
time course of the recovery for the charge and the
ionic current, plotted in Fig. 8 B, follow a very similar
time course. Both recoveries were fitted simultaneously to the sum of two exponential functions with different
weights (
fast = 0.28 s, and
slow = 6.47 s).
Relative Proportion of the Reluctant and Compliant Components in the Q-V Curves Is a Function of the Holding Potential
We explored the effect of intermediate depolarizations
on the voltage dependence of the charge movement.
Holding potentials ranging between 90 and 0 mV were
applied to evaluate their effects on the charge movement. The holding potential was maintained for at least
1 min before voltage stepping. Fig. 9 A shows Q-V curves obtained in the same oocyte and at different holding
potentials. The gating charge movement was quantified
by fitting two Boltzmann distributions (Q 1 and Q 2).
![]() |
(1) |
where V1 and V2 are the midpoints and z1 and z 2 are the
effective valences for gating charge components Q 1 and
Q 2, respectively. All the Q-V curves could be simultaneously fitted with the same effective valences, z1 and z2,
and with different relative amplitudes for the two components of the Q-V curves: the best fit gave z1 = 2.94, z2 = 4.43. At hyperpolarized holding potentials more
negative than 60 mV, the Q-V curves show a smaller
component that corresponds to the movement of Q 1
(~15-20% of the total charge) with a shallower voltage
dependence (z1 = 2.94) and a second larger component (Q 2) with higher voltage dependence (z 2 = 4.43)
(Stefani et al., 1994
). Raising the HP more positive
than
50 mV (i.e., increasing the population of the
slow inactivated channels), the Q-V curves start shifting
toward the left along the voltage axis. The half activation potential (V1) of Q 1 was ~
70 mV for all holding
potentials showing a very small sensitivity to the HP,
while for Q 2 half activation potential (V2) was less negative for holding potentials more positive than
40 mV
(Fig. 9 B). The changes in the Q-V curves with different holding potentials was mainly due to changes in the relative amplitudes of the components Q 1 and Q 2. Q 1 increased as the HP was made more positive and it
reached almost 100% of the amplitude of the total
charge movement for HP more positive than
30 mV
(Fig. 9 C). At the intermediate holding potentials, between
30 and
50 mV, ~50% of the channels are inactivated (Fig. 2 D), and in this voltage range a clear
separation between Q 1 and Q 2 is observed with ~0.5
relative amplitude. The change in relative amplitudes of Q 1 and Q 2 as the HP is made more positive is most
economically explained on the basis of an increase in
the population of channels that are slow inactivated.
Yellen et al. (1994) and Liu et al. (1996)
have shown
that slow inactivation involves a structural rearrangement of the outer mouth of the Shaker K+ channel.
Changes in the protein structure are likely expected to
modify the position and the mutual interactions of the
charged domains inside a folded protein. We have
shown in this work that long depolarizations modify the
voltage dependence of the gating charge movement
and that this change appears to be related to the process of slow inactivation. From a molecular point of
view, these results can be interpreted as a conformational change of the voltage sensor induced by the slow
inactivation process.
We have shown the correlation between the time
course of the changes in voltage dependence of the
charge movement and the time course of the inactivation during a long depolarization, as well as the recovery of the ionic current and the recovery of the voltage
dependence of the charge after a long depolarization. These data support the hypothesis that slow inactivation involves relatively slow changes in the protein
structure under depolarizing potentials that modify the
"close open" pathway, enhancing the energy barrier
that the protein must overcome to assume a conducting conformation. A consequence of prolonged depolarization is probably the development of new interactions of the voltage sensor within the protein. An evidence of this interaction is easily appreciable considering
the Q-V curves at 0 and
90 HP in Fig. 3 D : a voltage step from 0 to
60 mV is sufficient to move ~90% of
the charge in the noninactivated channel held at
90
HP (Fig. 3 D,
), but if the channel is maintained at 0 mV for a long time (i.e., slow inactivated), the same
voltage step is unable to move charge within the recording period (Fig. 3 D,
). However, in slow inactivated channels it is possible to move the same amount
of total charge, but a voltage step from 0 to ~
120 mV
is required.
Which Type of Inactivation Process Is Associated with the Change in the Voltage Dependence of the Charge Movement?
In the Shaker channel, two types of inactivation have
been distinguished on the basis of their structural determinants. A tethered "ball peptide" formed by the
first 20 amino acids at the NH2-terminal end of the
channel protein is responsible for the so called N-type
inactivation. A second type of inactivation has been
named C-type because of its sensitivity to mutations in
the S6 transmembrane segment (Hoshi et al., 1991).
Recently, C-type inactivation has been used as a synonym of slow inactivation. However, mutations in the
pore region can modulate the rate of the inactivation
process (Labarca and MacKinnon, 1993
; López-Barneo et al., 1993
; De Biasi et al., 1993
). There is no evidence
that C-type inactivation and the one originated by mutations in the pore are the same type of inactivation process from a molecular point of view. The designation
"P-type" inactivation has been properly introduced by
De Biasi et al. (1993)
in describing the effect of a point
mutation in the pore region (V369K) of Kv2.1 channels. This mutation resulted in a fast inactivation of the ionic current having different characteristics from N-
and C-type inactivation.
It has been proposed that the pore mutant Shaker
W434F is a constitutively C-inactivated channel (Yan et
al., 1996). However, we have shown that the W434F mutation has a normal voltage dependence of the charge
movement for
90 mV HP and a left shift on the voltage axis of the Q-V curve after long depolarization at 0 mV. If W434F were a C-inactivated channel, we would
expect the position of its Q-V curve to be left shifted
when the holding potential was
90 mV. Along with
this observation, other Shaker H4-
pore mutants like
D447E and D447N + T449V (Seoh et al., 1996
) have
the same behavior: despite the lack of conduction, in
these mutants the position of the Q-V curves at
90 mV
HP is normal and left shifted when the membrane is
held at 0 mV for prolonged periods of time. This apparent paradox can be easily resolved by assuming that there are two distinct slow inactivation processes: P-
and C-type and that only C-type inactivation is associated with modifications in the voltage sensor conformation that induces shifts in the Q-V curve.
Kinetic Model for the Slow Inactivation
Most of the kinetic and steady state properties shown
here for Shaker H4- and Shaker H4-
-W434F can be reproduced by a simple model (Fig. 10 A) based on the
one presented by Bezanilla et al. (1982)
and that accounts for slow inactivation and Q-V shift for the squid
axon Na+ channels.
The model is based on an eight-states sequential
model (Bezanilla et al., 1994) to which an equal number of inactivated states (I) were added (Fig. 10 A). The
elementary rates connecting the upper and the lower
rows of states,
and
, are voltage independent and
much smaller than the rates connecting the states of
the normal and inactivated modes. Thus, the channel
gates with voltage in two modes: the normal mode (Fig.
10 A, upper row), and the inactivated mode (Fig. 10 A,
lower row). The main assumption of this model is that
the inactivated states are more stabilized as the channel progresses toward the open state. Specifically, this stabilization has been modelled as an interaction with energy W = w/kT that is the same in each of the transitions in the lower row. This interaction energy increases the forward rates between the inactivated states
by a factor equal to exp(W), and the resulting equilibrium constants are represented in the figure as K iexp(W),
where i is the state index. Microscopic reversibility requires that the return rates between the inactivated and
normal states will be multiplied by exp(
iWi), stabilizing the inactivated states in proportion to the proximity
of the open state. It is then easy to see that a positive
holding potential will stabilize the rightmost inactivated state, and that under these conditions a short repolarization will have a leftward shift of the Q-V curve
because the forward rates are increased by a factor
exponentially dependent on the interaction energy.
When the membrane is extremely hyperpolarized, the
channels will be preferentially in the normal mode (
exp[7W] >>
). The relatively small value of the interaction energy (~2.4 kT) could be interpreted in molecular terms as a small and slow conformational change
that affects the energy profile encountered by the voltage sensor. Thus, depolarized potentials maintained for prolonged periods of time make the return of the
voltage sensor to the resting position more unlikely.
For long and strong depolarizations, the relatively
slow population of the inactivated state connected to
the open state produces the slow decay of the ionic current. From the inactivated state connected to the open
state, the transition back to the open state becomes
very unlikely due to the small backward rate constant of
this transition. After the channel has reached the slow
inactivated state, fast repolarizations produce charge
movement that reflects the transition among the inactivated states. The transition I C becomes energetically more probable at hyperpolarized potentials. The
new voltage dependence of the slow inactivated charge
(experimentally corresponding to the left shifted Q-V
curve at depolarized holding potentials) corresponds
to the charge movement related to the transitions among
the inactivated states in the lower line of the proposed
model. For hyperpolarized holding potentials, where no significant slow inactivation is present, the Q-V
curve is generated by the charge moving in the transitions occurring between the closed states.
The kinetic model shown in Fig. 10 A was sufficient
for describing the features of the G(V) curves from different holding potentials (Fig. 10 B) and it predicts the
position of the Q-V curves measured from 90-, 0-, and
41-mV holding potentials. Fig. 10 D shows the time
course of the ionic current after a depolarization step
to 0 mV (thick line) and the prediction of the kinetic
scheme given in Fig. 10 A. The model fails to give an
adequate description of the second slow component of
the recovery from slow inactivation. This is an indication that the inactivation process may occur in more
than one transition. This would add another parallel
line of inactivated states that would make the model
complicated and difficult to test experimentally.
Address correspondence to Dr. Enrico Stefani, Department of Anesthesiology, BH-612 CHS, Box 951778, University of California, Los Angeles, Los Angeles, CA 90095-1778. Fax: 310-825-6649; E-mail: estefani{at}ucla.edu
Received for publication 26 June 1997 and accepted in revised form 25 August 1997.
1 Abbreviations used in this paper: COVG, cut-open oocyte Vaseline gap voltage clamp; G-V, conductance-voltage; HP, holding potential; MES, methanesulphonic acid; NMG-MES, N-methylglucamine-MES.This work was supported by National Institutes of Health grants GM-50550 (E. Stefani) and GM-30376 (F. Bezanilla); Chilean grant FNI 97-739 and grants from CODELCO, CMPC, CGE, Minera Escondida, NOVAGAS, and Business Design Association to R. Latorre. R. Latorre is the recipient of a Catedra Presidencial. L. Toro is an Established Investigator from the American Heart Association (AHA). This work was done during the tenure of an AHA Grant in Aid Greater Los Angeles Affiliate to R. Olcese.
1. | Armstrong, C.M., and F. Bezanilla. 1977. Inactivation of the sodium channel. II. Gating current experiments. J. Gen. Physiol 70: 567-590 [Abstract]. |
2. | Bezanilla, F., R.E Taylor, and J.M. Fernandez. 1982. Distribution and kinetics of membrane dielectric polarization. I. Long-term inactivation of gating currents. J. Gen. Physiol 29: 21-40 . |
3. | Bezanilla, F., E. Perozo, D.M. Papazian, and E. Stefani. 1991. Molecular bases of gating charge immobilization in Shaker potassium channel. Science (Wash. DC). 254: 679-683 [Medline]. |
4. | Bezanilla, F., E. Perozo, and E. Stefani. 1994. The gating of Shaker K+ channels. II. The components of gating currents and a model of channel activation. Biophys. J 66: 1011-1021 [Abstract]. |
5. | Choi, K.L., R.W. Aldrich, and G. Yellen. 1991. Tetraethylammonium blockage distinguishes two inactivation mechanisms in voltage-activated K+ channels. Proc. Natl. Acad. Sci. USA. 88: 5092-5095 [Abstract]. |
6. | De Biasi, M., H.A. Hartmann, J.A. Drewe, M. Taglialatela, A.M. Brown, and G.E Kirsh. 1993. Inactivation determined by a single site in K+ pores. Pflugers Archiv. Eur. J. Physiol. 4224: 335-363 . |
7. | Ehrenstein, G., and D.L. Gilbert. 1966. Slow changes of potassium permeability in the squid giant axon. Biophys. J 6: 553-566 [Medline]. |
8. | Fedida, D., R. Bouchard, and F.S.P. Chen. 1996. Slow gating charge immobilization in the human potassium channel Kv 1.5 and its prevention by 4-aminopyridine. J. Physiol. (Camb.). 494: 377-387 [Abstract]. |
9. | Hodgkin, A.L., and A.F. Huxley. 1952. A quantitative description of membrane current and its application to conduction and excitation in nerve. J. Physiol. (Camb.). 117:500-544. |
10. | Hoshi, T., W.N. Zagotta, and R.W. Aldrich. 1990. Biophysical and molecular mechanisms of Shaker potassium channel inactivation. Science (Wash. DC). 250: 533-538 [Medline]. |
11. | Hoshi, T., W.N. Zagotta, and R.W. Aldrich. 1991. Two types of inactivation in Shaker K+ channels: effects of alterations in the carboxy-terminal region. Neuron. 7: 547-556 [Medline]. |
12. | Kamb, A., L.E. Iverson, and M.A. Tanouye. 1987. Molecular characterization of Shaker, a Drosophila gene that encodes a potassium channel. Cell. 50: 405-413 [Medline]. |
13. | Labarca, P., and R. MacKinnon. 1993. Permeant ions influence the rate of slow inactivation in Shaker channels. Biophys. J. 61: A378 . |
14. | Liu, Y., M.E. Jurman, and G. Yellen. 1996. Dynamic rearrangement of the outer mouth of a K+ channel during gating. Neuron. 16: 859-867 [Medline]. |
15. | López-Barneo, J., T. Hoshi, S.F. Heinemann, and R.W. Aldrich. 1993. Effects of external cations and mutations in the pore region on C-type inactivation of Shaker potassium channels. Receptors Channels. 1: 61-71 [Medline]. |
16. | Noceti, F., P. Baldelli, X. Wei, N. Qin, L. Toro, L. Birnbaumer, and E. Stefani. 1996. Effective gating charges per channel in voltage dependent K+ and Ca2+ channels. J. Gen. Physiol 108: 143-155 [Abstract]. |
17. | Ogielska, E.M., W. Zagotta, T. Hoshi, S.H. Heinemann, J. Haab, and R. Aldrich. 1995. Cooperative subunit interactions in C-type inactivation of K channels. Biophys. J. 69: 2449-2457 [Abstract]. |
18. | Olcese, R., L. Toro, E. Perozo, F. Bezanilla, and E. Stefani. 1994. Prolonged depolarization changes charge movement properties in Shaker-IR W434F K+ channel. Biophys. J. 66: A107 . |
19. | Olcese, R., L. Toro, F. Bezanilla, and E. Stefani. 1995. Correlation between charge movement and ionic current during C-type inactivation in Shaker-IR potassium channels. Biophys. J. 68: A33 . |
20. | Panyi, G., Z. Sheng, L. Tu, and C. Deutsch. 1993. C-type inactivation of voltage gated K channel occurs by a cooperative mechanism. Biophys. J. 69: 896-906 [Abstract]. |
21. | Perozo, E., R. MacKinnon, F. Bezanilla, and E. Stefani. 1993. Gating currents from a non-conducting mutant reveal open-closed conformations in Shaker K+ channels. Neuron. 11: 353-358 [Medline]. |
22. | Seoh, S.-A., D. Starace, D.M. Papazian, E. Stefani, and F. Bezanilla. 1996. D447N and W434F mutations in the pore of Shaker B K+ channels prevent ion conduction but restore conducting states by combined mutation with T449Y. Biophys. J 70: A190 . |
23. | Stefani, E., L. Toro, E. Perozo, and F. Bezanilla. 1994. The gating of Shaker K+ channels. I. Ionic and gating currents. Biophys. J 66: 996-1010 [Abstract]. |
24. | Yan, Y., Y. Yang, and F.J. Sigworth. 1996. How does W434F block Shaker channel current? Biophys. J 70: A190 . |
25. | Yellen, G., D. Sodickson, T.S. Chen, and M.E. Jurman. 1994. An engineered cysteine in the external mouth of a K+ channel allows inactivation to be modulated by metal binding. Biophys. J. 66: 1064-1075 . |
26. | Zagotta, W.N., T. Hoshi, and R.W. Aldrich. 1989. Gating of single Shaker K channels in Drosophila muscle and in Xenopus oocytes injected with Shaker mRNA. Proc. Natl. Acad. Sci. USA. 86:7243- 7247. |
27. | Zagotta, W.N., T. Hoshi, and T. Aldrich. 1990. Restoration of inactivation in mutants of Shaker potassium channels by a peptide derived from ShB. Science (Wash. DC). 250: 568-571 [Medline]. |