From the Department of Molecular Biophysics and Physiology, Rush University School of Medicine, Chicago, Illinois 60612
![]() |
ABSTRACT |
---|
![]() ![]() ![]() ![]() ![]() ![]() ![]() |
---|
In studies of gating currents of rabbit cardiac Ca channels expressed as 1C/
2a or
1C/
2a/
2
subunit combinations in tsA201 cells, we found that long-lasting depolarization shifted the distribution of mobile
charge to very negative potentials. The phenomenon has been termed charge interconversion in native skeletal
muscle (Brum, G., and E. Ríos. 1987. J. Physiol. (Camb.). 387:489-517) and cardiac Ca channels (Shirokov, R., R. Levis, N. Shirokova, and E. Ríos. 1992. J. Gen. Physiol. 99:863-895). Charge 1 (voltage of half-maximal transfer, V1/2
0 mV) gates noninactivated channels, while charge 2 (V1/2
90 mV) is generated in inactivated channels. In
1C/
2a cells, the available charge 1 decreased upon inactivating depolarization with a time constant
8, while
the available charge 2 decreased upon recovery from inactivation (at
200 mV) with
0.3 s. These processes
therefore are much slower than charge movement, which takes <50 ms. This separation between the time scale of
measurable charge movement and that of changes in their availability, which was even wider in the presence of
2
, implies that charges 1 and 2 originate from separate channel modes. Because clear modal separation characterizes slow (C-type) inactivation of Na and K channels, this observation establishes the nature of voltage-dependent inactivation of L-type Ca channels as slow or C-type. The presence of the
2
subunit did not change the V1/2
of charge 2, but sped up the reduction of charge 1 upon inactivation at 40 mV (to
2 s), while slowing the reduction of charge 2 upon recovery (
2 s). The observations were well simulated with a model that describes activation as continuous electrodiffusion (Levitt, D. 1989. Biophys. J. 55:489-498) and inactivation as discrete modal
change. The effects of
2
are reproduced assuming that the subunit lowers the free energy of the inactivated
mode.
![]() |
INTRODUCTION |
---|
![]() ![]() ![]() ![]() ![]() ![]() ![]() |
---|
Voltage-dependent inactivation of Ca channels is an
important mechanism of regulation of Ca2+ entry during repetitive stimulation. Its relatively slow kinetics allow for a long-term, direct control of channel availability by transmembrane electric potential. Although inactivation is thought to be a property of the 1 subunit,
fine tuning of its voltage sensitivity depends on interactions with auxiliary subunits and with other proteins.
In spite of a resemblance between voltage-dependent
inactivation of Ca channels and the so-called slow or C-type
inactivation found in the whole superfamily of voltage-gated channels, the structural underpinnings of this
process have yet to be identified in Ca channels. Slow
inactivation may be characterized by its relatively slow
kinetics (
1 s), dependence on extracellular cations,
and involvement of the extracellular portions of pore forming S5-S6 linkers (Brum et al., 1988
; Hoshi et al.,
1990
; López-Barneo et al., 1993
; Yellen et al., 1994
; Balser
et al., 1996
; Townsend and Horn, 1997
). In addition,
slow inactivation is believed to result in the appearance of
a specific intramembranous charge movement (charge 2;
Brum and Ríos, 1987
) generated by conformational
changes in inactivated channels (Bezanilla et al., 1982
;
Brum and Ríos, 1987
; Shirokov et al., 1992
; Olcese et
al., 1997
). Slow rates of inactivation and recovery are essential for the operational separation of two types of
charge. Charge 2 is well defined and separate from
charge 1 (the charge that moves in noninactivated or
primed channels) because its observable movement proceeds to completion much sooner than inactivation
onset or recovery.
In contrast, fast inactivation of Na channels and N-type
inactivation of Shaker K channels (ball and chain type;
Armstrong and Bezanilla, 1977; Vassilev et al., 1988
; Zagotta et al., 1990
) recovers rapidly at negative potentials,
approximately simultaneously with the inward movement of the intramembranous charge. Because recovery may proceed at rates comparable with that of measurable charge movement, there is no well-defined
mode of charge movement that can be ascribed to this
type of inactivation. The inward charge movement observed at large negative potentials after an inactivating
depolarization occurs in channels as they recover from
inactivation (repriming).
Apparently, a ball and chain-type inactivation is not
present in Ca channels. It has been shown for several
types of Ca channels that the faster component of ionic
current decay is driven by ionic current itself. Because
neither changes in intracellular calcium (Hadley and
Lederer, 1992) nor the ion flow through cardiac channels influence inactivation of gating currents, Shirokov
et al. (1993) concluded that Ca2+-dependent inactivation is a separate process, linked to gating currents only
indirectly, through channel opening.
We have shown previously that decay of Ba2+ current
through L-type Ca channels constituted by 1C and
2a
subunits occurs in two phases. The slow phase (
8 s)
is associated with voltage-dependent inactivation and is
cotemporal with the reduction of available gating charge
upon inactivation at positive voltages (Ferreira et al.,
1997
). We now address in quantitative detail the inactivation of intramembranous charge movement in heterologously expressed
1C channels. Because cardiac Ca channels transiently express at high density in the tsA201 human embryonic kidney cell line, we were able to measure
intramembrane charge movements in these channels
without using pulse protocols for subtraction of control records. This allowed us to study in detail the effects of
conditioning voltage on the movement of voltage sensors, with or without the
2
subunit, and develop a compact biophysical model that describes voltage-dependent
inactivation well. The rate of the slow phase of Ba2+
current decay is three- to fivefold greater in the presence of the
2
subunit (Ferreira et al., 1997
) and is
equal to that in native channels. The biophysical model
described here reproduces in a parsimonious manner
the effects of the
2
subunit.
![]() |
METHODS |
---|
![]() ![]() ![]() ![]() ![]() ![]() ![]() |
---|
Experiments were performed in tsA201 cells grown in DME medium (Sigma Chemical Co., St. Louis, MO) supplemented with
10% FBS (BioWhittaker, Walkersville, MD), 100 U/ml penicillin,
and 0.1 mg/ml streptomycin (Sigma Chemical Co.) in 5% CO2.
Rabbit 1C,
2
a, and rat
2a cDNAs were subcloned in pCR3,
pMT2, and pCMV plasmid vectors, respectively. High purity
(A260/A280
1.90) large-scale plasmid preparations were obtained using standard protocols (QIAGEN Inc., Chatsworth, CA).
Transfections were carried out with 30 µg of each expression
plasmid in two combinations (
1C +
2a and
1C +
2a +
2
a) on
100-mm Petri dishes using a calcium phosphate precipitation
method (Chien et al., 1995
). Electrophysiological recordings
were made within 24-48 h after transfection on round nonclustered cells. No sizable ionic or gating currents were observed in
tsA201 cells in the absence of transfection. After transfection,
the fraction of cells selected and patched that had Ca2+ currents
was ~70%.
Records were obtained by a standard whole-cell patch clamp
procedure using an Axopatch 200A amplifier (Axon Instruments,
Inc., Foster City, CA) and a 16-bit A/D-D/A converter card (HSDAS
16; Analogic Corp., Peabody, MA) on a PC computer. Patch electrodes were pulled from Corning 7052 glass (Warner Instruments, Hamden, CT) and had resistances of 1.0-1.5 M.
The pipette solution contained (mM): 150 CsOH, 110 glutamate, 20 HCl, 10 HEPES, 5 MgATP, and 10 EGTA, pH 7.6. External recording solutions contained 160 TEA-Cl, 10 Tris, and 10 CaCl2, pH 7.2. To record intramembranous charge movement, the bath solution was replaced with one that included 15 µM of GdCl3. All solutions were adjusted to 300-320 mosmol/Kg. All experiments were carried out at room temperature (~20°C).
Whole-cell capacitance was 6-15 pF. The time constant of
membrane charging typically did not exceed 100 µs. Series resistance, calculated from the capacitive transient, was below 10 M.
The single time constant capacitance compensation circuitry of
the Axopatch 200A amplifier was routinely used to offset 95-98%
of the symmetric capacitive transient. Parameters of the compensation circuitry were set with a 10-mV pulse from the holding potential of
90 mV.
For a 200-mV pulse spanning most of the useful voltage range, the residual linear transient corresponded to a transfer of <10 fC/pF of charge, while maximal intramembranous charge transfer from the expressed channels was ~100 fC/pF. With this combination of a relatively fast voltage clamp, high level of expression, and effective linear capacitance compensation, we were able to record asymmetric capacitive transients directly, without acquiring control linear transients for further subtraction.
Gating currents were recorded at 1 kHz bandwidth and sampled at 10 kHz. During prolonged pulses, the sampling rate was switched to between 0.05 and 2 kHz. To let the channels recover from inactivation, sets of conditioning and test pulses were separated by 30 s or longer. Charge transfer was calculated as the time integral of the current transient after subtraction of a steady current, which was determined as a 10-ms average, 40 ms after the beginning of the pulse.
Fig. 1 illustrates a typical experiment. The pulse protocol is
shown at top. A conditioning pulse of 20 s at 40 mV was applied before each test pulse. Conditioning and test pulses were separated by an interval at 20 mV. Current traces were obtained
with different test pulse voltages (V). The charge transferred by
the ON transients (
) and the steady current during the test
pulse (
) are plotted against voltage in Fig. 1 B. The steady current-voltage relationship was linear in the range from
150 to 50 mV, with steepness corresponding to an input resistance of ~5
G
. The steady current at 0 mV was ~
3 pA. The charge transfer-voltage relationship was clearly sigmoidal, saturating at extreme voltages. This demonstrates that the contribution of the
linear capacitance was small, and validates the evaluation of
charge transfer without subtraction of control currents.
|
Data are presented as averages ± SEM. Significance of differences between mean values was evaluated by Student's t test. Voltage distributions and time courses were fitted, respectively, by single Boltzmann and single exponential functions using a nonlinear least-squares routine included in the Sigmaplot software package (SPSS Inc., Chicago, IL).
![]() |
RESULTS |
---|
![]() ![]() ![]() ![]() ![]() ![]() ![]() |
---|
Steady State Distributions of Charge Movement in Primed and Inactivated Channels
To study effects of conditioning depolarization on the
voltage dependence of intramembranous charge movement, we used a double pulse protocol illustrated in
Fig. 2. First, gating currents were recorded in polarized
1/
cells held at
90 mV (Fig. 2 A). The test pulse was
applied from a 50-ms long interpulse at
60 mV. Then
the same protocol was applied again but with a 20-s
long conditioning pulse to 40 mV preceding each interpulse (Fig. 2 B). Current traces are shown on both panels
for a set of test voltages starting at
190 mV in 40-mV
increments. There was little charge movement current
at voltages more negative than
70 mV in polarized
cells, but the conditioning produced a substantial increase of currents at these negative voltages. The
charge transferred during the ON transient for the
same cell is plotted against membrane potential in Fig.
2 C. When the cell was held at
90 mV, and consequently the channels were available for opening, most
of the charge moved during pulses positive to
60 mV
(Fig. 2,
). In inactivated channels, by contrast, about
half of the charge moved in pulses below
60 mV (Fig.
2,
). Curves are fits by a shifted Boltzmann function
![]() |
(1) |
|
where Q0, a negative quantity, is the limit of charge
transfer as V tends to , QMAX is the difference between the maximal positive transfer and Q0, V1/2 is the
voltage of half-maximal transfer, or transition potential, and K is a steepness constant. The measurable
charge movement during the interpulse had ended by
the end of the interpulse. Therefore, the changes in
charge distribution in inactivated channels were long-lived compared with the time scale of the measurable
charge movement.
Addition of the 2
subunit increased the effect of
depolarization on charge transfer. About two thirds of
the charge was mobile below
60 mV in inactivated
1/
/
2
channels (Fig. 3). To compare the effects of
conditioning in
1/
and
1/
/
2
cells, we averaged
charge distributions obtained in different cells, normalized as follows. First, Eq. 1 was fitted to individual Q(V) data, and the fitted shift Q0 was subtracted from Q(V).
Data shifted in this way (referred to as "charge distributions") can be compared without reference to starting
voltage. For averaging, the charge distribution was normalized to the individual QMAX determined in the inactivated cell.1 Averages of normalized distributions are
shown in Fig. 4. The curves are Boltzmann fits with parameters listed in Table I. In polarized cells (Fig. 4,
),
V1/2 was close to 0 mV, but some 12 mV more negative
in
1/
(
8.4 mV) than in
1/
/
2
cells (3.9 mV).
One reason for this small difference is that gating
charge in the primed cells is systematically underestimated at voltages positive to 70 mV (and V1/2 is consequently undervalued), due to the presence of nonspecific outward current. With the
2
subunit present,
maximal charge movement increases approximately
twofold (Bangalore et al., 1996
), which makes the relative error smaller and V1/2 greater.
|
|
|
When charge transfers were measured after the inactivating pulse (Fig. 4, ), V1/2 was shifted by
57 mV in
1/
cells and by
81 mV in
1/
/
2
cells. The difference in shifts was statistically significant (P < 0.05). As
shown in Table I, inactivation induced only minor
changes in steepness and total mobile charge. As was the case for the distribution of charge movement in native cardiomyocytes (Shirokov et al., 1993
), the effect of
inactivation is best described, with either subunit composition, as a simple shift in the transition potential.
The greater shift in the presence of the 2
subunit
could be the result of a greater extent of inactivation
during the conditioning pulse to 40 mV, a slower recovery from inactivation during the interpulse at
60 mV,
or both. To test these possibilities, we studied voltage
distributions of mobile charge after an inactivating pulse, varying the interpulse voltage.
In the extreme case illustrated in Fig. 5, there was no
interpulse. When negative-going test pulses where applied after a 50-ms long step to 40 mV, as shown in Fig.
5 A for an 1/
/
2
cell, charge transfer was nearly
maximal at
100 mV (Fig. 5 C,
). After a 20-s long
conditioning pulse, charge transfer at
100 mV was
only about half-maximal (Fig. 5 C,
). Fig. 5 D plots the corresponding distributions in
1/
/
2
cells. For
comparison, the dashed curves are the best fits in
1/
cells. Addition of the
2
subunit did not change significantly the transition potentials in noninactivated or inactivated channels. The only significant difference was
that charge distribution of inactivated channels was
somewhat steeper in the presence of the
2
subunit.
The experiments in Fig. 5 indicate that the difference
in distributions after conditioning demonstrated in Fig.
4 was mostly due to a faster recovery of
1/
cells during the interpulse at
60 mV. In the absence of an interpulse allowing recovery, the difference induced by
inactivation was about the same with both subunit compositions.
|
When test pulses were applied from an interpulse
level of 150 mV, conditioning again led to a negative
shift of the charge distribution, now manifested as an
increase of gating currents recorded at intermediate
voltages, as shown for an
1/
/
2
cell in Fig. 6, A and
B. As shown in Fig. 6 D, the charge distribution in
primed cells was affected little by the presence of the
2
subunit (Fig. 6,
). In conditioned
1/
/
2
cells,
however, the charge distribution was shifted to more
negative voltages than in
1/
cells, as a consequence
of a slower recovery at
150 mV in the presence of the
2
subunit. Again, the charge movement currents
ended earlier than the interpulse, indicating that even at
150 mV the voltage shift in distribution of mobile
charge induced by inactivation recovers much more
slowly than the measurable return of the mobile charge.
|
These experiments demonstrate that in inactivated
Ca channels all the charge remains mobile, albeit at
voltages more negative than those of activation gating.
The concept of modal conversion applicable to slow inactivation of native Na channels (Bezanilla et al., 1982),
recombinant Shaker K channels (Olcese et al., 1997
), and voltage-dependent inactivation of native Ca channels of skeletal (Brum and Ríos, 1987
) and cardiac
muscle (Shirokov et al., 1992
) is seen to apply to recombinant Ca channels. Gating transitions within the
primed mode of the channel produce charge 1 movements, while transitions within the inactivated mode
produce sterile charge 2.
The present results suggest that the 2
subunit has
little direct effect on charge 1 and charge 2 movements. Apparently, its main effects are on the kinetics
of charge 1-charge 2 interconversion. We confirmed
this impression with the experiments described below.
Kinetics of Inactivation of Charge Movement and Effects of
the 2
Subunit
Time-dependent inactivation of Ba2+ current through
L-type Ca channels has two kinetic phases. In the absence of the 2
subunit, prolonged depolarization reduces gating charge mobile above
60 mV with a time
course parallel to the slower exponential component of
Ba2+ current decay (Ferreira et al., 1997
). The time
constant of this component in
1/
cells is ~8 s at 20 mV, while in
1/
/
2
and in native cells it is ~2 s. In
the experiment illustrated in Fig. 7, we investigated the
effect of the
2
subunit on the onset kinetics of charge
reduction. Charge movement was recorded during OFF transients from depolarizations of different duration (protocol at top). In
1/
cells (Fig. 7 A), the OFF
gating currents were progressively smaller for increasing test pulse durations up to 20 s. In cells with all three
subunits (Fig. 7 B), reduction of the OFF transient saturated after 6 s of depolarization. To average and compare effects in different cells, values of charge moved after the long depolarizations were normalized to the
value obtained from the transient after a 45-ms pulse to
the same voltage. The averages are plotted in Fig. 7, C
and D. Different symbols correspond to different pulse
voltages. Reduction of the mobile charge was about
three times faster in
1/
/
2
cells for all voltages. The time constant of the reduction of gating charge at 40 mV in
1/
/
2
cells was ~1.7 s, similar to that for the
slow phase of Ba2+ current decay in these cells and in
native cardiomyocytes.
|
We studied the effect of 2
on recovery from inactivation applying a double pulse protocol often used with
ionic currents. The experiment is illustrated in Fig. 8.
After conditioning, the membrane was kept at the interpulse voltage for a variable time (Tip), and then a
test pulse to 50 mV was applied to assess charge movement. Reference test currents (Fig. 8, thick traces) were recorded without conditioning. Gating currents elicited by test pulses from
60 mV took much longer to
recover in
1/
/
2
cells (Fig. 8 B) than in
1/
cells
(Fig. 8 A). As shown in Fig. 8, C and D, recovery from
inactivation was substantially delayed by the
2
subunit
at every interpulse voltage tested.
|
In studies of recovery at very negative voltages, it was
simpler to record the charge movement of inactivated
channels (charge 2), which occurs at potentials negative
to 50 mV. For this purpose, a test pulse to
50 mV was
applied from an interpulse at more negative voltages
(Fig. 9). Because inactivation involves a negative shift in
the voltage dependence of charge movement, in the
range negative to
50 mV, recovery is associated with a
reduction in charge transfer. Given the conservation of
total charge (Figs. 4-6), this should be accompanied by
an equivalent increase of charge mobile in noninactivated channels (at potentials positive to
50 mV).
|
Independently of the presence of the 2
subunit,
conditioning caused an approximately twofold increase
of charge transfer between
150 and
50 mV (Fig. 9,
A and B), if recorded 50 ms after conditioning. Very little of this increase remained after 1 s at
150 mV in
1/
cells, but ~50% persisted in
1/
/
2
cells. Fig.
9, C and D, plot the increase of charge mobile between
the interpulse voltage and
50 mV, normalized to the
charge without conditioning, as a function of interpulse duration at
100 (
),
150 (
), and
200 (
)
mV for
1/
and
1/
/
2
cells, respectively. Curves
are single exponential fits. Without the
2
subunit, recovery kinetics were strongly voltage dependent in the
range explored, and fastest at
200 mV (
300 ms).
In contrast, with the
2
subunit recovery was slow (
2 s) and weakly voltage dependent in this range. The
ancillary subunit not only slows the recovery process
but also insulates it from the influence of voltage.
![]() |
DISCUSSION |
---|
![]() ![]() ![]() ![]() ![]() ![]() ![]() |
---|
Modal Interconversion of Intramembrane Charge Movement
during Inactivation of 1C Channels
The main finding of this study is that voltage-dependent inactivation of heterologously expressed cardiac
Ca channels is associated with a large negative shift in
the voltage dependence of their charge movement.
The intramembranous charge movement in inactivated 1/
channels has a transition potential of ~
90 mV,
which is the same as in native L-type Ca channels
(Brum and Ríos, 1987
; Shirokov et al., 1992
). The
charge remains mobile at these voltages until channels
recover from inactivation, a first order process with a
time constant of ~300 ms at
200 mV. Because the
time scale of charge movement in inactivated
1/
channels (
15 ms) is much faster than recovery from
inactivation, the expressed channels exhibit a separate
inactivated mode, and the term charge 2 can be applied to the charge mobile at negative voltages in inactivated channels. With
1/
/
2
channels, the modal
separation is even more clear cut.
We showed previously that the onset of inactivation
of gating currents in 1/
cells is parallel to a slow
phase of Ba2+ current decay (
8 s), and that addition of the
2
subunit increases the slow rate of ionic
current decay, making it similar to that in cardiac cells
(
2 s; Ferreira et al., 1997
). In agreement with these
earlier observations, we now find a time constant of ~2 s
for the reduction of gating currents upon inactivation in cells expressing all three subunits (Fig. 7). Working
with native cells at room temperature, we estimated the
onset
of charge interconversion at
0.6 s (Shirokov et
al., 1993
). This estimate may be at fault because of the
unavoidable contribution of Na channels to the native
gating currents. A discrepancy in the same direction exists for the time course of recovery from inactivation of
gating charge (charge 1) in native cells. We reported a
time constant of 200 ms for this process (Shirokov et
al., 1992
), while in the present measurements with expressed channels containing the
2
subunit
1.5 s
(Fig. 9). Again, and for the same reasons, the present
measurements must be considered more reliable. Interestingly, in native skeletal muscle, recovery of charge 1 is
much slower (
3 s; Brum and Ríos, 1987
). The discrepancy in results in native cells could reflect structural
differences between the two channels. It could also reflect a better determination, given the vast predominance of dihydropyridine receptors over other sources of
intramembranous charge movement in skeletal muscle.
Biophysical Effects of the 2
Subunit
The present results demonstrate that the 2
subunit
promotes inactivation of gating currents in cardiac L-type
Ca channels. We found that the
2
subunit made the
onset of inactivation of intramembrane charge movement three to four times faster, and the recovery from
inactivation about five times slower. On the other
hand, inactivation of gating currents in L-type Ca channels was much slower than activation gating, even in
the presence of the
2
subunit (
2 s). It is therefore
unlikely that the increased rate of inactivation results
from primary changes in activation.
In spite of profound effects of the 2
subunit on inactivation kinetics, the voltage dependence of charge
movement in primed and inactivated channels was not
significantly changed. In agreement with previous findings (Singer et al., 1991
; Welling et al., 1993
; Shistik et
al., 1995
; Bangalore et al., 1996
), we found little effect
of the
2
subunit on voltage dependence of activation of ionic currents on
1/
cells (data not shown). In
contrast, Felix et al. (1997)
reported that the
2
subunit, added to the
1C in the absence of the
subunit,
shifted the activation of ionic currents in tsA201 cells by
~
10 mV. In Xenopus oocytes, coexpression of
2
and
1 subunits increased single channel open probability
(Shistik et al., 1995
), while in HEK 293 cells addition of
2
to
1 and
subunits speeded up activation and deactivation (Bangalore et al., 1996
).
As shown previously (reviewed by Gurnett and Campbell, 1996), the
2
subunit shifts by ~
10 mV the
steady state inactivation curves of recombinant Ca
channels. In light of these observations, our finding that
the charge distributions in inactivated channels are unaffected by the
2
subunit may seem surprising. This
and other aspects, however, may be accounted for with
biophysical models of voltage-dependent inactivation.
Inactivation of gating currents in Ca channels has been represented by a minimal four state diagram (Scheme I). In it, the "horizontal" transitions are fast and voltage dependent, while (voltage-independent) "vertical" transitions are much slower, which qualifies the pairs of states, C, O, and I*, I, as separate modes that account, respectively, for charge 1 and charge 2. The model is "allosteric": inactivation and activation occur at separate sites, as the movement of separate gates that influence each other but move individually.
|
This model already has most of the observed properties, and accommodates the effect of 2
, which could
simply be represented by an equal reduction in the free
energy of states I and I* and a decrease in the energy
barrier between O and I. It is, however, too oversimplified, failing to account for charge movement between and inactivation from closed states.
|
Scheme II represents a generalization of the allosteric model (Marks and Jones, 1992; Kuo and Bean
1994
; Olcese et al., 1997
), in which activation gating is
represented as a multi-step reaction, and inactivation is
likely to occur from closed states.
Scheme II also features charge 1 and charge 2 modes, an aspect used recently by Olcese et al. (1997)
to represent similar observations on gating currents of
Shaker K channels. However, it has many parameters
that cannot be constrained, especially the number of closed states. For this reason, we generalized these
models by incorporating continuum activation gating
(Millhauser et al., 1988
; Lauger, 1988
) in a version of
Levitt (1989)
. This simplified the kinetic scheme, reduced the number of parameters, and gave a more intuitive view of the gating process.
The model equations are presented in detail in the Appendix . Inactivation is described as a voltage-independent reaction, of rate constants kP and kI, between two modes of the channel: P (primed) and I (inactivated). The gating process associated with intramembrane charge movement is represented by a conformational movement along a reaction coordinate x, driven by the electric field (Scheme III). Because there are no free energy barriers, the movement is continuous, akin to diffusion. The generalized reaction coordinate projects to one dimension the set of conformations accessible to the channel. A given value of the coordinate characterizes all conformations that take the same amount of energy from the electric field.
|
The state of the ensemble of channels is described by
two probability density functions, P(x) and I(x). Evolution of these functions is determined by diffusion reaction within the free energy profiles UP(x) and UI(x),
which have chemical and electrical additive components. As stated above, at any given transmembrane voltage the electrical energy term will vary linearly with
x. An additional assumption, primarily made for simplicity, is that the chemical free energy also depends
linearly on x. Therefore, the joint dependence of UP
(or UI) on x and V is represented by ruled surfaces (hyperboloids), as in Fig. 10, where the parameters are
chosen to simulate data in the presence of 2
.
|
To reproduce the tendency to inactivation at positive
and recovery at negative voltages, UP(x) and UI(x) must
cross, so that P is favored at the values of x near 0, which are populated at the resting potential, and the
opposite occurs at x near 1. Because intermodal transitions are assumed to be intrinsically voltage independent, the transfer of charge as a function of x must be the same in the two modes, or, equivalently, UP/
V =
UI/
V. Because voltage cannot directly alter intermodal distribution, the value of x at which P and I are
equally probable (intersection of the planes UP(x,V)
and UI(x,V) in Fig. 10) will be a constant,
, independent of V. The continuum model requires four thermodynamic parameters and three kinetic parameters,
fewer than even the simple state model of Scheme I.
At equilibrium, the distributions satisfy:
![]() |
(2) |
Therefore, in channels held near resting voltages,
P(x,V) is large at x close to 0, while I
(x,V) is very
small. When the voltage is positive, P
(x,V) becomes
small for all x, while I
(x,V) is high at x close to 1. Fig.
11 illustrates the evolution of the system [P(x,t) and
I(x,t)] during a pulse from
100 to 0 mV. The initial
conditions P(x,0) and I(x,0) were calculated as the
equilibrium distributions at
100 mV. The voltage was
changed to 0 mV with exponential time course (
m = 0.2 ms). The system evolved with two widely separated
time scales, one associated with movements along x and
the other with the inactivation transition. The fast process is illustrated in Fig. 11, top. A and B plot P(x,t) and
I(x,t) during the first 5 ms of the voltage step. Both
P(x,t) and I(x,t) redistribute towards x = 1, reaching a
quasi stationary situation, and generating measurable
charge movement associated with diffusion along x
(Fig. 11 C). After the quasi steady state is reached,
probability densities continue to change at a slow rate
determined by the inactivation reaction. Fig. 11, bottom,
illustrates this slow process. The marked complementary changes in total occupancy of modes P and I (Fig.
11 F) are accompanied by additional diffusion along x.
The resulting charge movements are undetectable because of their slow rate, limited by the inactivation reaction. This additional redistribution of charge can be estimated as the difference between steady state charge
transfer, calculated from the equilibrium distributions
(P
and I
), and charge transfer determined by numerical integration of the simulated current, as if it were an
experimental record.
|
Fig. 12 illustrates the comparison. Gating currents
simulated with pulses from 200 mV are shown in Fig. 12
A, left. The areas under ON transients are shown in Fig.
12 B,
. The recordable charge transfer for steps from
200 mV occurs at more positive voltages than the
equilibrium distribution of charge Qeq(V) (Fig. 12,
curve). The vertical difference between the curve and
the symbols corresponds to the additional transfer that
occurs slowly as channels inactivate.
|
Similarly, when pulses are applied from 200 mV,
charge mobile in the fast time domain corresponds to
redistribution of channels in mode I along the x axis,
and the charge transfer (Fig. 12 B, ) occurs at more
negative voltages. Corresponding intramembrane charge
movement currents are shown in Fig. 12 A, right.
The steepness of the Boltzmann fits to the simulated
charge transfer was ~25 mV in both primed and fully
inactivated channels, corresponding to the transfer of
one elementary charge in a single step transition. With
the continuum model, the maximal charge transfer
had to be set to three elementary charges to simulate such shallow distributions. Interestingly, model-independent estimates of maximal unitary gating charge
from gating current noise of Na and K channels provided similar values. 2.4 elementary charges were required assuming that the gating current noise is produced by a number of independent identical particles,
which during activation undergo a single irreversible
transition (Conti and Stühmer, 1989; Sigg et al., 1994
).
The continuum model therefore reconciles estimates
of elementary charge from microscopic and macroscopic gating current measurements, provided that the
macroscopic charge movement is generated by particles with approximately three elementary charges moving independently and with the same half-activation potential. Because 8-12 elementary charges transfer during channel activation, ~4 such independent particles
would be required for channel opening. This would be
the case, for example, if the movement of individual S4
segments occurred independently and over the same
voltage range, and if all four segments had to move to
cause activation.
Charge distributions of squid axon Na, skeletal muscle Ca, and Shaker K channels are less steep after moderate inactivation (Bezanilla et al., 1982; Brum and
Ríos, 1987
; Olcese et al., 1997
). The observation also
applied for moderately inactivated cardiac Ca channels
in the present work (data not shown). Model simulations of this condition are illustrated in Fig. 12 C. The thick curves are simulated charge distributions in primed
and inactivated channels (spline curves through Fig. 12
B,
and
). The dark gray curve simulates with the continuum model the measurable charge transfer upon application of negative-going pulses after a 1-s conditioning at 200 mV. In contrast, the four-state model of
Scheme I2 generated the two-sigmoidal distribution
plotted in thin trace, which is close to a linear combination of the fully primed and fully inactivated distributions. Such sharp separation of sigmoidal components
was never observed experimentally. Even though the two-modal distributions of charge could be isolated experimentally in the presence of
2
, the distribution in
partially inactivated conditions was not a linear combination of the modal distributions. This is well reproduced by the continuum model.
Simulation of the Effect of the 2
Subunit
To model the effects of the 2
subunit on voltage-
dependent inactivation, we had only to assume that the
subunit stabilizes the inactivated mode I. We specifically assumed that it makes the energy difference between I and P more negative at all values of x. Because
of the linearity of UI(x,V), this is equivalent to a decrease in
, the x value of half inactivation. While inactivation of
1/
channels was simulated with
= 0.8,
1/
/
2
, channels required
= 0.55 as sole parameter
change. The simulated charge distributions of primed
and inactivated channels are in Fig. 13. In correspondence with experimental observations (Table I), the transition potentials of simulated charge distributions
in fully primed or fully inactivated channels were not
affected by the change in
. (The reason is simple: the
voltage distribution of mobile charge within modes is
sensitive to the chemical potential gradient, not to an
additive constant.) The model also described well the
observed difference in the steepness of the charge distributions between primed and conditioned
1/
channels. In conditioned
1/
cells, the steepness of charge
distribution measured from an interpulse at 40 mV was
~40 mV, whereas in nonconditioned cells (
150 mV interpulse) it was ~30 mV. In conditions simulating
1/
channels (
= 0.8), the charge distribution of the
inactivated channels was also shallower (33 mV) than
that of noninactivated channels (25 mV). The difference between the steepness of charge distribution in
primed and inactivated
1/
channels is due to the fact
that, because of their fast rate of recovery, the charge
distribution of inactivated
1/
channels cannot be isolated experimentally.
|
The onset kinetics of inactivation in the model were
assessed with the pulse protocol used in the experiment of Fig. 7. The corresponding simulated dependencies of amounts of charge movements on the duration of conditioning depolarization are shown in Fig. 13, C and D. Reduction of charge mobile above 50
mV was more rapid for
= 0.55 (simulating channels
with
2
) than for
= 0.8, giving rates similar to those
obtained experimentally.
Recovery properties of the model were studied with
pulse protocols similar to those illustrated in Fig. 9. Fig.
9, E and F, show dependencies of the amount of charge
mobile below 50 mV on the interpulse duration. As
observed in the experiments with
1/
/
2
(Fig. 9 D),
simulations with
= 0.55 (Fig. 13 F) exhibit a slow recovery rate and are weakly voltage dependent at voltages below
150 mV. In agreement with the observations in
1/
cells (Fig. 9 C), with
= 0.8 recovery is
three to five times faster (Fig. 13 E), approaching the
speed of recordable charge movement. In all, the continuum model reproduces well the effects of
2
, under
the hypothesis that the subunit changes a single parameter of energy distribution.
Modal Separation
With = 0.55, the model behaves similarly to the channels in the presence of
2
, evolving with two well-
defined time scales: a fast one associated with measurable charge movement and a slow one determined by
inactivation. This separation of time scales is a requisite
for a well-defined charge 2, which can be ascribed unequivocally to mode I.
When is close to 1 (simulating the absence of the
2
subunit) the I
P conversion becomes very fast at negative voltages, and the separation between time scales becomes less clear cut. At
200 mV, the most negative potential that is consistently accessible, recovery in simulations of channels lacking
2
has a
= 0.28 s (Fig. 13 E), in
good agreement with the experiment (0.32 s, Fig. 9 C),
and well beyond the time needed to complete the measurable movement of charge (~50 ms). The fastest possible
recovery is achieved from x = 0 (a condition that requires
forbiddingly large negative potentials) and proceeds with
a time constant of ~0.16 s. This is close to but greater than
the time of charge movement, so that modal separation
still prevails in simulations of channels without
2
, even at
experimentally inaccessible negative potentials.
If the rate constant of the I P reaction (see Appendix , Eq. 11) was just an order of magnitude greater
than the value determined for channels without the
2
subunit, modal separation would break down. This
would be reflected in the appearance of a substantial slow component in the charge movement during recovery at intermediate negative voltages, cotemporal with
I
P transitions. Such a component, not observed experimentally in Ca channels, is a distinctive feature of
the gating current in Na channels, the "remobilization"
component observed when channels are reprimed at
130 mV (Armstrong and Bezanilla, 1977
). For the
continuum model to simulate such fast inactivation, it
is necessary that the inactivation processes further stabilize the mobile charged moieties in the trans (open) position. In that case, some values of x close to 0 will
not be populated in the inactivated mode at intermediate negative voltages.
Likewise, Kuo and Bean (1994) were able to simulate
onset and recovery of fast inactivation in Na channels
with the model illustrated by Scheme II. Therefore, both
modal interconversion, documented in the present work,
and the so-called charge immobilization phenomena that
accompany fast inactivation can be reproduced with general allosteric models of the types represented by
Schemes II and III.
The preceding considerations are relevant to whether voltage-dependent inactivation in L-type Ca channels is slow (C-type) or fast (N-type). Inactivation appears to be slow because it exhibits clear modal separation.
On the other hand, there is an important distinction
between voltage-dependent inactivation of Ca channels
and slow inactivation of Na and K channels. Whereas in
these channels recovery from slow inactivation takes
many seconds, in L-type Ca channels recovery would be
fast, were it not for the stabilizing effect of the 2
subunit on the voltage-inactivated states. Structure-function studies are required for establishing the mechanism of this stabilization.
![]() |
FOOTNOTES |
---|
Address correspondence to Roman Shirokov, Department of Molecular Biophysics and Physiology, Rush University School of Medicine, 1750 W. Harrison Street, Suite 1279JS, Chicago, IL 60612. Fax: 312-942-8711; E-mail: rshiroko{at}rush.edu
Received for publication 8 January 1998 and accepted in revised form 23 March 1998.
Dr. Ferreira's permanent address is Depto. Biofisica, Facultad de Medicina, Montevideo, Uruguay CP 11800. Dr. Shirokov's permanent address is A.A. Bogomoletz Institute of Physiology, Kiev, Ukraine 252024.We thank Drs. Duanpin Chen (Rush University) for discussions and help with th e continuum model, and Werner Melzer (University of Ulm, Ulm, Germany ) for many comments on the manuscript.
This work was supported by a Scientist Development Grant from the America n Heart Association (to R. Shirokov) and by National Institutes of Health grant AR-43113 (to E. Ríos) .
![]() |
![]() |
APPENDIX |
---|
The continuum model of inactivation, represented in Scheme III, comprises the following set of equations. The energies of modes P and I, in dimensionless expressions are:
![]() |
(3) |
where q = Q/e is the total charge transfer (in number
of electrons), v is dimensionless voltage, equal to Ve/
kBT, vP and vI are the transition potentials of the corresponding modes, IP is the energy difference between
UI and UP at x = 1, and A, B, C, and ng are constants
(Levitt, 1989
).
To emphasize that at x =
1
B the energy difference UIP changes its sign, Eq. 3 can be rewritten as
![]() |
(4) |
The steady state probability densities are defined as follows:
![]() |
(5) |
The steady state charge distribution Qeq(V) is calculated numerically from
![]() |
(6) |
Transitions between the two modes are described by the following set of differential equations:
![]() |
(7) |
where DP and DI are generalized diffusion coefficients. The fluxes satisfy reflective boundary conditions:
![]() |
(8) |
The rate constants of the interconversion are defined by the energy profiles. For a symmetrical barrier, the rates are
![]() |
(9) |
Eqs. 7 and 8 were solved using a fully implicit finite
differencing scheme with a band diagonal system of linear equations. The band diagonal system was solved by
the bandec and banbks routines of Press et al. (1992)
(The computer program for simulation [DOS and
X-Win versions] can be obtained by e-mail request to
rshiroko{at}rush.edu). The x grade was 50. The time
steps were automatically adjustable depending on accuracy of solution. The accuracy of the solution was determined as deviation of the total probability from 1 and it
was set at 3%. For simulations we used: q = 3, vP = 0, vI = 4 (equivalent to
100 mV at room temperature),
DP = 100 s
1, DI = 50 s
1, k0 = 0.05 s
1, and
= 0.8 for
1/
channels or
= 0.55 for
1/
/
2
channels.
The transfer of mobile charge (from an all-in starting distribution) is calculated by
![]() |
(10) |
consistent with the definition of the potentials (Eq. 3). The charge movement current is ig(t) = dQ/dt.
From Eqs. 4 and 9, the time constant of the I P
transition (
IP) is limited by
![]() |
(11) |
or ln(IP k0)
6 (
x) for the parameters used. Because the difference between vP and vI is substantial,
the time constant
IP is small compared with k0, when
is close to 1 and at x is close to 0.
![]() |
REFERENCES |
---|
![]() ![]() ![]() ![]() ![]() ![]() ![]() |
---|
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. |
Bangalore, R.,
G. Mehrke,
K. Gingrich,
F. Hofmann, and
R.S. Kass.
1996.
Influence of L-type Ca channel ![]() ![]() |
3. | Balser, J.R., H.B. Nuss, D. Romashko, E. Marban, and G.T. Tomaselli. 1996. Functional consequences of lidocaine binding to slow-inactivated sodium channels. J. Gen. Physiol. 107: 643-658 [Abstract]. |
4. | Bezanilla, F., R.E. Taylor, and J. Fernandez. 1982. Distribution and kinetics of membrane dielectric polarization. I. Long-term inactivation of gating currents. J. Gen. Physiol 79: 21-40 [Abstract]. |
5. | Brum, G., and E. Ríos. 1987. Intramembrane charge movement in frog skeletal fibers. Properties of charge 2. J. Physiol. (Camb.). 387: 489-517 [Abstract]. |
6. | Brum, G., R. Fitts, G. Pizarro, and E. Ríos. 1988. Voltage sensors of the frog skeletal muscle membrane require calcium to function in excitation-contraction coupling. J. Physiol. (Camb.). 398: 475-505 [Abstract]. |
7. |
Chien, A.,
X. Zhao,
R. Shirokov,
T. Puri,
C.F. Chang,
D. Sun,
E. Ríos, and
M. Hosey.
1995.
Roles of membrane-localized ![]() |
8. | Conti, F., and W. Stühmer. 1989. Quantal charge redistributions accompanying the structural transitions of sodium channels. Eur. Biophys. J. 17: 53-59 [Medline]. |
9. |
Felix, R.,
C. Gurnett,
M. De Waard, and
K. Campbell.
1997.
Dissection of functional domaines of the voltage-dependent Ca2+ channel ![]() ![]() |
10. |
Ferreira, G.,
J. Yi,
E. Ríos, and
R. Shirokov.
1997.
Ion-dependent inactivation of barium current through L-type Ca channels.
J. Gen.
Physiol.
109:
449-461
|
11. |
Gurnett, C., and
K. Campbell.
1996.
Transmembrane auxiliary subunits of voltage-dependent ion channels.
J. Biol. Chem.
271:
27975-27978
|
12. | Hadley, R.W., and W.J. Lederer. 1991. Ca2+ and voltage inactivate Ca2+ channels in guinea-pig ventricular myocytes through independent mechanisms. J. Physiol. (Camb.). 444: 257-268 [Abstract]. |
13. | Hoshi, T., W.N. Zagotta, and R.W. Aldrich. 1990. Biophysical and molecular mechanisms of Shaker potassium channel inactivation. Science. 250: 533-538 [Medline]. |
14. | Kuo, C.-C., and B.P. Bean. 1994. Na+ channels must deactivate to recover from inactivation. Neuron. 12: 819-829 [Medline]. |
15. | Lauger, P.. 1988. Internal motions in proteins and gating kinetics of ionic channels. Biophys. J. 53: 877-884 [Abstract]. |
16. | Levitt, D.. 1989. Continuum model of voltage-dependent gating. Macroscopic conductance, gating current, and single-channel behavior. Biophys. J 55: 489-498 [Abstract]. |
17. | López-Barneo, J., T. Hoshi, S.H. 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]. |
18. | Marks, T., and S.W. Jones. 1992. Calcium currents in the A7r5 smooth muscle-derived cell line. An allosteric model for Ca channel activation and dihydropyridine agonist action. J. Gen. Physiol. 99: 367-390 [Abstract]. |
19. | Millhauser, G.L., E.E. Salpeter, and R.E. Oswald. 1988. Diffusion models of ion-channel gating and the origin of power low distributions from single-channel recording. Proc. Natl. Acad. Sci. USA. 85: 1503-1507 [Abstract]. |
20. |
Olcese, R.,
R. Latorre,
L. Toro,
F. Bezanilla, and
E. Stefani.
1997.
Correlation between charge movement and ionic current during
slow inactivation in Shaker K+ channels.
J. Gen. Physiol.
110:
579-589
|
21. | Press, W.H., B.P. Flannery, S.A. Teukolsky, and W.T. Vetterling. 1988-1992. Numerical recipes in C: the art of scientific computing. Cambridge University Press. 50-54. |
22. |
Shistik, E.,
T. Ivanina,
T. Puri,
M. Hosey, and
N. Dascal.
1995.
Ca2+
current enhancement by ![]() ![]() ![]() ![]() |
23. | Sigg, D., E. Stefani, and F. Bezanilla. 1994. Gating current noise produced by elementary transitions in Shaker potassium channels. Science. 264: 578-582 [Medline]. |
24. | Singer, D., M. Biel, I. Lotan, V. Flockerzi, F. Hofmann, and N. Dascal. 1991. The roles of the subunits in the function of the Ca channel. Science. 253: 1553-1557 [Medline]. |
25. | Shirokov, R., R. Levis, N. Shirokova, and E. Ríos. 1992. Two classes of gating current from L-type Ca channels in guinea pig ventricular myocytes. J. Gen. Physiol. 99: 863-895 [Abstract]. |
26. | Shirokov, R., R. Levis, N. Shirokova, and E. Ríos. 1993. Ca2+-dependent inactivation of cardiac L-type Ca channels does not affect their voltage sensor. J. Gen. Physiol. 102: 1005-1030 [Abstract]. |
27. |
Townsend, C., and
R. Horn.
1997.
Effect of alkali metal cations on
slow inactivation of cardiac Na+ channels.
J. Gen. Physiol.
110:
23-33
|
28. | Vassilev, P.M., T. Scheuer, and W.A. Catterall. 1988. Identification of an intracellular peptide segment involved in sodium channel inactivation. Science. 241: 1658-1661 [Medline]. |
29. |
Welling, A.,
E. Bosse,
A. Cavalié,
R. Bottlender,
A. Ludwig,
W. Nastainczyk,
V. Flockerzi, and
F. Hofmann.
1993.
Stable coexpression of Ca channel ![]() ![]() ![]() ![]() |
30. | Yellen, G., D. Sodickson, T.-Y. Chen, and M.E. Yurman. 1994. An engineered cysteine in the external mouth of a K channel allows inactivation to be modulated by metal binding. Biophys. J. 66: 1068-1075 [Abstract]. |
31. | Zagotta, W.N., T. Hoshi, and R.W. Aldrich. 1990. Restoration of inactivation in mutants of Shaker potassium channels by peptide derived from ShB. Science. 250: 568-571 [Medline]. |