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Biophys J, April 2002, p. 1894-1906, Vol. 82, No. 4
*Department of Physiology, University of Kentucky College of
Medicine, Lexington, Kentucky 40536, and Asbury
College, Department of Physics, Wilmore, Kentucky 40390 USA
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ABSTRACT |
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 TOP
 ABSTRACT
 INTRODUCTION
MATERIALS AND METHODS
RESULTS
DISCUSSION
APPENDIX
REFERENCES
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Recovery from inactivation of T-type Ca channels is slow
and saturates at moderate hyperpolarizing voltage steps compared with
Na channels. To explore this unique kinetic pattern we measured gating
and ionic currents in two closely related isoforms of T-type Ca
channels. Gating current recovers from inactivation much faster than
ionic current, and recovery from inactivation is much more voltage
dependent for gating current than for ionic current. There is a lag in
the onset of gating current recovery at 
80 mV, but no lag is
discernible at 120 mV. The delay in recovery from inactivation of
ionic current is much more evident at all voltages. The time constant
for the decay of off gating current is very similar to the time
constant of deactivation of open channels (ionic tail current), and
both are strongly voltage dependent over a wide voltage range.
Apparently, the development of inactivation has little influence on the
initial deactivation step. These results suggest that movement of
gating charge occurs for inactivated states very quickly. In contrast,
the transitions from inactivated to available states are orders of
magnitude slower, not voltage dependent, and are rate limiting for
ionic recovery. These findings support a deactivation-first path for
T-type Ca channel recovery from inactivation. We have integrated these
concepts into an eight-state kinetic model, which can account for the
major characteristics of T-type Ca channel inactivation.
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INTRODUCTION |
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TOP
ABSTRACT
INTRODUCTION
MATERIALS AND METHODS
RESULTS
DISCUSSION
APPENDIX
REFERENCES
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The combination of a low-voltage activation range
and a relatively slow deactivation rate (Huguenard, 1996
) allows T-type Ca channels to function as a depolarizing current injector in the range
of potentials corresponding to action potential threshold (Kozlov et
al., 1999). With respect to pacemaking, for example, the kinetics of
inactivation and recovery from inactivation of T-type Ca channels
become critical determinants of cellular excitability (Huguenard and
Prince, 1994; Coulter et al.,1989). Thus a quantitative description of
T-type Ca channel kinetics is important for understanding the
contribution of T-type Ca channels to excitability in neurons and
cardiac myocytes. In a continuation of earlier work (Satin and Cribbs,
2000), we now measure gating current in two closely related T-type Ca
channel isoforms (
1G and 1H) to determine how differences in
ionic current recovery from inactivation are related to differences in
certain gating transitions among inactivated states. The main point of
this paper is to elucidate the gating processes underlying recovery
from inactivation by exploring the kinetics and voltage dependence of
gating current and ionic current.
Gating current measurements are essential to achieving a better understanding of the mechanisms underlying channel kinetics. Gating currents represent intramolecular motions of ion channels in response to changes in transmembrane potential. In contrast to ionic currents that only reflect the opening and closing of conducting channels, gating currents manifest transitions between nonconducting channel states. Central to this study, gating current measurements revealed transitions among inactivated states.
Evolutionarily, T-type Ca channels are thought to be intermediate
between high-voltage activated Ca channels and Na channels (reviewed in
Hille, 2001). Not surprisingly, T-type Ca and Na channels have some
qualitatively similar gating kinetics. For example, the inactivation
process itself is voltage independent. The apparent voltage dependence
of macroscopic inactivation can be explained by the voltage dependence
of the activating gating transitions (Aldrich et al., 1983; Chen and
Hess, 1990; Droogmans and Nilius, 1989; Serrano et al. 1999). In
parallel to Na channels, T-type channels appear to follow a
deactivation-first route to recover from inactivation (Kuo and Bean,
1994; Satin and Cribbs, 2000; Kuo and Yang, 2001). The studies of Satin
and Cribbs (2000) and Kuo et al. (2001) used macroscopic ionic current
measurements to infer a deactivation-first pathway for recovery from
inactivation (RFI). We now report our use of gating current
measurements to provide further evidence for a deactivation-first route
for RFI.
To quantitatively define T-type gating characteristics without
contaminating currents, we used cloned channels expressed in heterologous expression systems. The T-type Ca channel family consists
of three genes called 1G (CaV3.1), 1H
(CaV3.2), and 1I
(CaV3.3; nomenclature reviewed by Hille, 2001).
Our initial studies of cloned, heterologously expressed 1G and 1H
ionic currents demonstrated that the 1G and 1H ionic current
characteristics were similar. However, 1G macroscopic inactivation
and RFI kinetics are faster compared with 1H (Klockner et al., 1999;
Satin and Cribbs, 2000).
A central result of our present study is that gating charge movement for transitions between inactivated states are much faster than transitions from inactivated to available states. Furthermore, the transitions from inactivated to available states become rate limiting for ionic current RFI. Consequently, the ionic current RFI rate saturates for modest recovery potentials for this class of Ca channel. The time constants of deactivation and the decay of gating current arising from inactivated gating transitions are similar, and are voltage dependent, over a range where ionic current RFI is already saturated. Taken together, these results support a deactivation-first path for T-type Ca channel RFI. We put these ideas into the framework of a kinetic scheme. Our model captures the major features of our gating and ionic current measurements and quantifies our conceptual understanding of T-type Ca channel gating kinetics.
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MATERIALS AND METHODS |
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TOP
ABSTRACT
INTRODUCTION
MATERIALS AND METHODS
RESULTS
DISCUSSION
APPENDIX
REFERENCES
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Cell culture
1H cDNA (Cribbs et al. 1998) was used to generate a
stably-transfected HEK 293 cell line (Zhang et al. 2000). The 1G
cell line (1G-a; for nomenclature see Monteil et al., 2000b) was
generously provided by Drs. Cribbs and Perez-Reyes (Perez-Reyes et al.
1998). Cells were incubated in DMEM, supplemented with10% fetal bovine serum, 100 U/ml penicillin, 100 mg/ml streptomycin, and 1 mg/mL G-418.
Electrophysiology
Cells were digested with 0.125% trypsin and replated 1-3 days
before recording. Currents were recorded in the whole-cell clamp configuration. Culture media was replaced with the extracellular bath
solution immediately before recording. Recordings were initiated 5 min
after patch break to allow equilibration of the pipette solution with
the cell interior. All recordings from 1G- and 1H-expressing
cells were performed using identical ionic solutions and conditions.
The pipette solution contained (in mM): 110 potassium gluconate, 40 CsCl, 1 MgCl2, 3 EGTA, and 5 Hepes, pH 7.35 with CsOH. The bath consisted of (in mM): 140 NaCl, 2.5 CaCl2, 5 CsCl, 2.5 KCl, 10 TEA-chloride, 1 MgCl2, 5 glucose, and 5 Hepes, pH 7.4 with NaOH.
All experiments were performed at room temperature (20-22°C). Patch
electrodes were 1-2.5 M
using the above pipette solution. Cell
capacitance was <20 pF. The series resistance
(Rs) in the whole-cell configuration
was <5 M before Rs compensation. Rs was compensated >75% with the
circuitry on the Axopatch 200 (Axon Instruments, Foster City, CA).
Currents were low-pass filtered at 10 kHz and sampled at 100 kHz. Leak
and capacity transients were subtracted with either P/6 (ionic current)
or P/8 (ionic and gating current) protocols. Gating current protocols
were performed with both P/8 and P/8 to evaluate whether resolvable
gating charge current moved in the range of potentials used for
subtraction. No difference in gating or ionic current was observed for
P/8 versus P/8 protocols. In addition, execution of the P/8, P/8 either before or after the test step yielded the same result. Therefore, even if a small amount of gating charge moved during our
leak and capacity transient subtraction pulses, we could not detect any
charge movement in the voltage range used for leak/capacity transient
steps. Our electronics limited our resolution of fast gating currents
to transitions slower than ~120 µs.
Stable-transfected HEK 293 cells sporadically failed to express T-type Ca current. These cells were used as controls to monitor endogenous currents. HEK 293 cells showed no detectable endogenous currents in response to the protocols used for this study (Fig. 1).
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Analysis
pClamp 6.04 and 8.02b programs (Axon Instruments) were used for data acquisition and analysis. Nonlinear curve fitting was performed with Origin v.4.1 (Microcal Software, Northampton, MA).
Voltage protocol details are provided in the text and in the figure
legends. Gating currents were assessed by integrating the first 2-6 ms
of the current time course. To assess recovery from inactivation, we
measured current amplitude from single-exponential fits of tail current
following a maximally activating depolarization. A 5-ms step to the
Ca2+ current reversal potential
(Erev; ~+48 mV) coincided roughly with the time to peak of the inward current associated with maximally activating test potentials (>0 mV). The tail was recorded at 100 mV
to amplify the inward current. With this protocol we could resolve
small currents following brief recovery intervals, but the large tail
currents following longer recovery intervals introduced increased error
associated with the voltage drop across the series resistance
(Rs). As a check for
Rs error, we measured decay time constants for tail currents with different amplitudes (associated with
different prepulse intervals) and found that the results deviated
<10% for the same test potentials.
Modeling methods
Simulations were performed in MATLAB 5.3 (Math-Works, Natick, MA), using the built-in matrix exponential (expm) function call. When the voltage step was time dependent, we used the built-in ordinary differential equation (ODE) solvers to solve the kinetic equations. Because of the different time scales involved in the simulation, we used the stiff solver ode23s to numerically integrate the system of ordinary differential equations.
To find optimal model parameters, we used the optimization routines lsqcurvefit and lsqnonlin in the MATLAB Optimization Toolbox. We first fit the parameters using individual protocols. To obtain best-fit parameters, we minimized the least squares error from the following set of protocols: sustained depolarization, activation determined by the current peaks, steady-state inactivation of ionic current and gating charge, on-gating current traces measured during depolarization, recovery from inactivation of ionic current and gating charge, and deactivation of ionic current. The error for each protocol was normalized by the number of data points. By trial and error, we adjusted the weights given to each protocol to reflect the uncertainty in the corresponding data set and the difficulty of obtaining a good fit for that protocol.
There are several parameters in our model (see Fig. 7 below) that are
poorly constrained by the data: k
r',
ki', ki',
ki, and
kI3Io. Our experimentally measured time constants indicate that deactivation governed by
kOC3 is parallel to the first stage in
recovery governed by kIoI3. Thus,
kI3Io is similar to
kC3O because these two conformational
changes appear to be related. To further constrain these parameters, we
invoked microscopic reversibility (MR). We set
ki' = ki;
kI3Io = kC3O;
ki' = ki
and we adjust kr' and
ki' to satisfy MR in the first two boxes.
Refer to Fig. 7 (below) for definition of the rate constants and refer to Tables 1 and
2 for a summary of the
model parameters.
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RESULTS |
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TOP
ABSTRACT
INTRODUCTION
MATERIALS AND METHODS
RESULTS
DISCUSSION
APPENDIX
REFERENCES
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Gating current recovery precedes ionic current recovery from prolonged depolarization
We first measured RFI of ionic and gating current simultaneously
in cells expressing the 1G isoform. Fig.
2 A shows the voltage protocol
we utilized. We first clamped the membrane potential at 0 mV for
10 s. We assumed that the channels were maximally inactivated at
the end of this initial holding voltage
(Vhold); this assumption is supported
by the absence of ionic currents as ascertained by tail current
analysis following prolonged depolarization (data not shown; see also
Kuo and Yang, 2001). We then stepped the cell to hyperpolarized
potentials for variable intervals. Next, to measure recovery of
ON gating charge we stepped the membrane potential to
Erev for 5 ms. Finally, to ascertain
recovery of ionic current we ended the voltage waveform by a step to
100 mV. Fig. 2, B and C, shows representative
currents for the Erev step and the
step back to 100 mV for the 1G isoform. Upon stepping to
Erev (~+48 mV), a brief transient
outward current was evident, which we identified as ON
gating current.
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The transient outward current in Figs. 2 and
3 represents 1G intra-membrane charge
movement at Erev. Fig. 2 C
shows that for a 3-ms recovery interval (for
Vrec = 120 mV) there is almost maximal charge movement but no resolvable ionic current. For recovery intervals less than 6 ms we could not detect ionic current by stepping
back to 100 mV. It is obvious from the data that the time course of
gating charge recovery is faster than that for ionic current. This
experimental result supports the idea that the 1G channel must
deactivate before recovering from inactivation (Satin and Cribbs, 2000;
Kuo and Yang, 2001) rather than recovering directly to the open state.
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In contrast to the dynamics of the voltage-gated Na channel, the
voltage dependence for the time course of 1G channel ionic current
RFI starts to saturate for recovery voltages negative to 80 mV. This
saturation is evident in Fig. 2 where the amplitudes of the ionic tail
currents in C for Vrec = 120 mV are comparable to those in B for
Vrec = 80 mV.
1G channels recover more quickly from inactivation compared with
1H (Satin and Cribbs, 2000). To explore the basis for this observation, we used the same voltage protocol to measure ionic current
and gating charge recovery for the closely related 1H isoform.
Current traces for the 1H isoform are shown in Fig. 3, A
and B. Qualitatively, 1H recovery from inactivation
appears to be similar to that for 1G. (Compare Fig. 3, A
and B, with Fig. 2, B and C).
Thus, as for the 1G isoform, gating charge recovers before
ionic current, and the voltage dependence of recovery of ionic
current starts to saturate at voltages negative to 80 mV.
The RFI kinetics for the two isoforms are directly compared in Fig.
4. The top two panels represent recovery
of ionic current; the lower two panels represent recovery of gating
charge. The symbols represent pooled data whereas the smooth lines are
from simulations based on the eight-state model discussed below (Fig. 7) and detailed in the Appendix. As in the representative data, the
pooled data show that 1) gating charge recovers before ionic current
and 2) ionic current recovery saturates at 100 mV. The delay in
gating charge recovery is strongly voltage dependent. For
Vrec = 80 mV there is a noticeable
lag in the onset of gating current recovery, and for
Vrec of 120 mV the lag is virtually undetectable. The lag in recovery from inactivation is larger for ionic
current (Fig. 4, A and B) than for gating current
(Fig. 4, C and D). Close examination of ionic
recovery intervals less than 100 ms consistently reveals faster
recovery with more hyperpolarized recovery potentials, revealing a
voltage dependence for the delay in recovery from inactivation for
ionic current (Figs 4, A and B).
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The pattern of 1H recovery of gating charge from inactivation is
similar to 1G (compare Fig. 4, C and D). At
hyperpolarizing potentials negative to 120 mV the recovery for
ON gating charge approaches a rapid rate that surpasses the
limit of our resolution. The slower recovery of inactivation of 1H
is apparent for more depolarized recovery potentials. For
Vrec = 80 mV the half-time for on
gating recovery is ~20 ms for 1G (Fig. 4 C), in
contrast to 100-200 ms for 1H (Fig. 4 D). This is
consistent with our prediction that the slower recovery kinetics for
1H is associated with the voltage-dependent deactivation gating
kinetics of this isoform (Satin and Cribbs, 2000).
The delay in recovery from inactivation is related to the voltage dependence of deactivation gating charge movement
In Na channels the delay of recovery from inactivation is related
to deactivation (Groome et al., 1999). To test whether the delay in
ionic current recovery from inactivation for T-type
Ca2+ channels is similarly related to channel
deactivation, we compared gating charge movement from maximally
inactivated channels to ionic current deactivation from the channel
open state. To maximally inactivate channels we prepulsed the cells to
0 mV for 10 s. To study the kinetics of gating charge movement
between inactivated states, we then performed a 10-ms test step back to
various hyperpolarized potentials. Gating current is detectable for
values of Vtest negative to 100 mV
(Fig. 5 A). The transient
inward current that is measured at hyperpolarized potentials represents
inactivated state off gating current
(IQoff). The rate of
IQoff decay is plotted (filled squares) in Fig. 5, C (1G) and D (1H).
Interestingly, the rate of IQoff decay
is similar to the rate of deactivation of ionic current (Fig. 5
B). Deactivation time constants were obtained in the same
cell by measuring tail currents to given test potentials preceded by a
10-ms depolarization prepulse. These deactivation time constants are
also plotted in Fig. 5, C and D (open triangles). The classical interpretation of indistinguishable gating and
deactivation time constants is that the initial step in channel
deactivation is independent of the inactivation process (Patlak, 1991).
Although the kinetics of deactivation and off gating current appear to be similar, both processes are much faster than the delays in RFI that
we measured (Fig. 4). Thus, the time course of off gating current
occurs before ionic recovery can proceed. This experimental result
indicates that the channels must deactivate before they can
significantly recover from inactivation.
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IQoff is not resurgent ionic current
As a test of our hypothesis that what we call OFF
gating current is not a resurgent ionic current, we attempted to block
IQoff with Ni2+.
At 30 mV, Ni2+ blocks ionic current through
1H and 1G with IC50 values of ~10 µM
and ~200 µM, respectively (Lee et al., 1999).
Ni2+ blockade of Ca2+
current is voltage dependent with stronger blockade produced at more
hyperpolarized potentials (Lee et al., 1999).
Ni2+ concentrations >200 µM would thus block
ionic current but would have no effect on
IQoff. Therefore, we tested whether
300-1000 µM Ni2+ selectively altered the
deactivation amplitude and rate of ionic current versus
IQoff in the same cells. For both
1G and 1H, Ni2+ reduced ionic current
amplitude and altered the time course of decay of ionic current.
However, Ni2+ had no effect on
IQoff (Fig.
6 A) or OFF gating
charge (Fig. 6 C). Ni2+ speeded the
ionic current decay time course (Fig. 6 D) similar to that
observed previously (Lee et al., 1999). However,
Ni2+ had no effect on the
IQoff decay rate (Fig. 6
D). Therefore, we conclude that
IQoff is not resurgent ionic current.
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Model simulations predict mechanism for 1G versus 1H isoform
functional differences
Quantitative models of channel gating are useful for
inferring mechanisms of channel function. We have shown that 1G and 1H have indistinguishable voltage dependencies of ionic
current activation and inactivation but distinct recovery from
inactivation profiles. To help interpret these results we developed an
eight-state Markovian model (Fig. 7).
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We constrained the model with ionic and gating current data for the two
T-type Ca channel isoforms. The overall kinetic scheme follows standard
voltage-gated channel models: the vertical C-to-I transitions (which
represent binding and unbinding of the inactivating particle) are
assumed to be voltage independent, whereas the horizontal C-to-C, and
I-to-I transitions (activation/deactivation gating transitions) are
voltage dependent. We modeled the O-to-C transition as a
voltage-dependent rate, because tail deactivation rate data do not
exhibit a voltage-independent region for large hyperpolarizations (cf.
Serrano et al., 1999). In contrast, we modeled the opening step, C to
O, as a voltage-independent transition because the time to peak for
large depolarizations reaches a nearly constant rate over a broad range
of voltages (Chen and Hess, 1990). As for the Na channel, the voltage
dependence of the inactivation time constant of T-type Ca channels is
associated with activation gating transitions (Aldrich et al., 1983).
For large depolarizations, the decay of ionic current saturates at a
voltage-independent rate (ki), which
is associated with the binding of the inactivation gate. Details of the
model are given in the Appendix. The scheme shown in Fig. 7 can
accurately describe many features of the experimental data, including
both ionic current measurements and gating charge measurements obtained
over a voltage range from 190 mV to +50 mV. The model parameters
(Tables 1 and 2) closely fit the data from RFI (Fig. 4, solid lines),
ionic current deactivation time course (Fig. 5, solid lines), and
IQoff time course (Fig. 5, dashed lines) measurements.
Fig. 8 compares the predictions of this
model to data for OFF gating current.
IQoff was elicited by a 10-s
Vhold at 0 mV followed by
hyperpolarized voltage steps ranging from 190 to 130 mV. The smooth
lines are the model predictions superimposed on the experimental data.
Because of the fast gating dynamics involved, we modeled the voltage
step as having a rising phase determined by a fixed electronic time
constant (see Appendix). The model predicts the relative normalization
and the decay of the OFF gating current, although the
rising phase is fit less effectively.
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Fig. 9, A and B,
are simulations of ionic currents obtained using sustained
depolarization for both of the T-type Ca channel isoforms. The smooth
lines superimposed over experimental data are simulations carried out
using the kinetic scheme shown in Fig. 7. As shown by the figure, the
model captures both the time course and the voltage dependence of the
ionic currents. We measured peak inward currents elicited by a
sustained depolarization to obtain the voltage dependence of activation
(Cribbs et al., 2001). Fig. 9, C and D, compare
modeled results (solid line) with experimental data (symbols) for
activation for 1G and 1H, respectively. Fig. 10 shows deactivation of T-type
Ca2+ current elicited by a prepulse to 0 mV for 5 ms, followed by a test potential ranging from 60 to 160 mV. The
solid lines are from simulations based upon the kinetic scheme shown in
Fig. 7, which include both ionic and gating currents. The expanded portion of each curve displays the outward gating current generated during the prepulse to 0 mV. For all protocols tested, the data show
that the model simulations closely resemble the time course and voltage
dependence of 1G and 1H ionic and gating currents.
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DISCUSSION |
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TOP
ABSTRACT
INTRODUCTION
MATERIALS AND METHODS
RESULTS
DISCUSSION
APPENDIX
REFERENCES
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This is the first study to measure gating currents from cloned
1G (CaV3.1) and 1H
(CaV3.2) T-type Ca channels. Our
data show that T-type Ca channel inactivation resembles Na channel inactivation in that deactivation precedes recovery from inactivation; however, there are significant quantitative differences between T-type
Ca and Na channels. For example, inactivation is much slower in T-type
Ca channels.
The similarities of T-type and Na channel kinetics may stem from the
well known topographical homology between Ca and Na channels (Hille,
2001; Catterall, 1998). Unfortunately, unlike the situation for Na
channels the detailed molecular basis of T-type inactivation is not
known. Recent work shows that the IIIS6 transmembrane domain contributes to the rapid inactivation of 1G (Marksteiner et al., 2001), and the amino terminus of the cytosolic carboxy tail also contributes to T-type fast inactivation (Staes et al., 2001). Interestingly the IIIS6 domain also contributes to Na channel fast
inactivation (Yarov-Yarovoy et al., 2001). For simplicity of
discussion, we suggest that the Na channel ball-and-chain conceptual model can be helpful in explaining our results.
We provide evidence that T-type channels recover from inactivation by
first deactivating (present study; Satin and Cribbs, 2000; Kuo and
Yang, 2001). Namely, the time course of recovery of gating charge was
found to be faster than the recovery of ionic current. Again, this
appears to be a conserved feature among different T-type Ca channel
isoforms (1G and 1H, this study) as well as Na channels (Kuo and
Bean, 1994). Although qualitative parallels to Na channel gating
schemes are apparent, the rates of RFI for saturating potentials are
slower for T-type Ca channels than Na channels. Kuo and Bean (1994) for
Na channels reported recovery rates of ~4 ms1
for potentials near 200 mV. In contrast, we find that the recovery rate constant (kr) for T-type channels
is 10,000 fold slower. This slower rate of RFI appears to be associated
with tighter binding of the inactivating gating particle. Because
T-type Ca channels deactivate before recovery from inactivation, the
rate of recovery from inactivation may result from a slow rate of
dissociation of the inactivating gating particle. Accordingly, the rate
of RFI saturates at modest recovery potentials for T-type Ca channels (~90 mV) compared with Na channels (~200 mV).
The strong correspondence between current deactivation and the
decay of OFF gating current
(IQoff) indicate that the
O-C3 and
IO-I3 transitions are
likely to involve very similar conformational changes and that the
kinetics of the conformational change are not strongly affected by the
attachment of the inactivating peptide domain. Physically, this
similarity in the kinetics of IQoff
(which flows during deactivation with the ball attached) and ionic
current deactivation (where the inactivating particle is dissociated) suggest that the binding of the inactivating ball has little effect on
the initial deactivation steps of the channel. Similar correspondence has been noted in Na channels (Kuo and Bean, 1994; Groome et al., 1999). Also, microscopic reversibility (MR) in our gating model is
consistent with the concept that the binding affinity of the ball is
unaffected by the first deactivation step.
Isoform diversity
While the two T-type channel isoforms under study appear to have
very similar binding rates for the inactivation ball, the isoforms appear to differ mainly in their rates of
activation/deactivation gating. Overall, 1H ionic current RFI is
slower than that for 1G. We previously showed that this is a
consequence of the relative proportion of channels recovering with fast
versus slow ionic current recovery time constants rather than
differences in their recovery rates themselves (Satin and Cribbs,
2000). Our present modeling studies quantitatively support our earlier
contention that the explanation for these differences in RFI rests in
slower deactivation gating (I-I) transitions in 1H, compared with
1G, rather than differences in the dissociation rate of the
inactivating ball (the I-C recovery transitions).
Our kinetic scheme shares qualitative features in common with earlier
T-type Ca channel gating models (Chen and Hess, 1990; Droogmans and
Nilius, 1989; Serrano et al., 1999). However, we do not assume that the
gating can occur via four independent gating steps. With our current
knowledge of the structure of the Na and Ca family of
voltage-controlled channels, the assumption of four-fold symmetry
becomes untenable. For example, the number of charges is not conserved
among the S4 -helices in the four different domains of T-type Ca
channels (Perez-Reyes et al., 1998; Cribbs et al., 1998); in parallel,
the homologous domains of the Na channel function unequally during
gating (Cha et al., 1999). The lack of four-fold symmetry leads to
additional rate constants and parameters. Rather than represent a
transition corresponding to the movement of each S4 voltage sensor, we
reduced the number of constants by using only the number of
conformational states necessary to reproduce our experimental data.
In our model, transitions between closed and inactivated states are
voltage independent, as is the open-to-inactivated state transition.
These model transitions are thought to reflect the physical binding and
unbinding of the inactivation ball, which seems to occur largely
outside the electrical field of the membrane. This lack of voltage
dependence is supported by the saturating value for the inactivation
time constant of ionic current following a prolonged depolarization. As
we showed recently (Satin and Cribbs, 2000), this parameter is not
significantly different between 1G and 1H isoforms. Our findings
describing the voltage independence of the inactivation reaction are in
agreement with native T-type ionic current studies (Chen and Hess,
1990) and a previous study of heterologously expressed 1G channels
(Serrano et al., 1999).
The gating scheme shown in Fig. 7 has three loops. We define box
1 as C1-C2-I2-I1, box 2 as C2-C3-I3-I2, and box 3 as C3-O-Io-I3. Our
model satisfies microscopic reversibility (MR) for all three boxes.
Pragmatically, MR is useful because it constrains parameters. MR
imposes a very small, but finite return of channels from
IO to O (constituting a resurgent current; Raman
and Bean, 1997). However, our value for
ki predicts a small-amplitude
resurgent current compared with the amplitude of what we call
IQoff. For the experimental conditions
shown in Fig. 6, the model predicts a resurgent current of 156 pA,
which is ~20% of the measured gating current amplitude of 768 pA.
Therefore, we predict that we cannot experimentally measure resurgent
current because the much larger gating current component is predicted
to mask resurgent current.
Isoform-specific function: correlation with amino acid divergence
The primary amino acid sequences of 1G and 1H are 57%
conserved at the amino acid level (Perez-Reyes et al., 1998; Cribbs et
al., 1998). Most of the divergence is restricted to the large extracellular loops between S5 and S6, the large cytoplasmic loops between homogenous repeats I and II, II and III, and the N- and C-termini. The amino side of the C-terminus is known to be important for fast inactivation (Staes et al., 2001). A sequence of 23 amino acids in this C-terminal region are highly negatively charged and may
serve as binding site for a putative peptide ball. Additional channel
variability arises from alternative splicing (Kunze et al., 2000;
Mittman et al., 1999). 1G is the best studied T-type Ca channel to
date in this regard (Chemin et al., 2001). Fetal cardiac myocytes
express 1G-d (Cribbs et al., 2001; 1G-bc by the nomenclature of
Monteil et al., 2000a), whereas neuronal tissue preferentially
expresses 1G-a or 1Ga-e, depending on the tissue (Dubin et al.,
2000). These splice variants encompass the homologous repeat III-IV, as
well as the II-III cytoplasmic linkers. From our modeling, the major
differences appear to reside in the activation/deactivation gating
transitions. It will therefore be interesting to use our model to
account for phenotypic differences among the 1G splice variants. Future work is needed to determine whether there are specific
amino acid sequences that are not conserved between the two isoforms
(or splice variants) that are critical for these gating transitions.
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APPENDIX |
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TOP
ABSTRACT
INTRODUCTION
MATERIALS AND METHODS
RESULTS
DISCUSSION
APPENDIX
REFERENCES
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All of the rate constants on the top and bottom rows of the
model, except for kC3O = kI3IO, have a voltage dependence
(refer to Fig. 7). In the activation (forward) direction, the rate
constants have the form:
|
= kC1C2,
kC2C3,
kI1I2,
kI2I3. In the deactivation (back)
direction, the rate constants have the form:
|
= kC2C1,
kC3C2,
kI2I1,
kI3I2,
kOC3,
kIOI3, the parameter T
represents the thermal energy associated with room temperature in
electron volts: T = 25.4 mV;
qi, (i = 1, 2, 3)
represents the gating charge (in units of fundamental charge)
associated with the ith box in the model (numbered from left
to right); and V is the membrane potential as determined by
the voltage clamp command.
Assuming that the energy barrier associated with the transition between
states is primarily associated with the membrane potential, the
Boltzmann distribution implies that the ratio of the forward to back
rate constants is given by:
|
represents the fraction of the voltage
dependence associated with the kinetics of the transition in the
forward direction. For Box 3, parameter = 0. For large
depolarizations, the voltage dependence of the rate constants drives
the equilibrium configuration toward the inactivated
IO state. In moving toward this equilibrium
configuration, a certain portion of the channel proteins will pass
through the open state O. Measurements of ionic current give a direct
measure of the population of this open state. For resting (or
hyperpolarized) membrane potentials, the equilibrium configuration is
shifted to the left where an equilibrium is set up between the
I1 and C1 states.
The kinetic scheme shown in Fig. 7 determines the transition matrix
A, which is a function of the rate constants. It is this
transition matrix A(V) that governs the time
evolution of the state vector X:
|
|
|
. In place of their Q column vector, we constructed a gating charge matrix S. The ith row
in the jth column in matrix S represents the
effective amount of gating charge moved across the membrane in going
from conformational state j to conformational state
i. For example:
|
|
|
|
|
Because the dynamics of the gating currents occur on the order of a few
milliseconds, the finite rise time of a voltage step becomes relatively
important for these protocols. As a first step in checking the possible
role of a smoothed voltage step on a measured current trace, we modeled
the voltage step as
![V(t)=&Dgr;V[1−<UP>exp</UP>{<UP>−</UP>k<SUB>elec</SUB> t}(1+k<SUB>elec</SUB> t)],](/content/vol82/issue4/fulltext/1894/img012.gif)
|
V is the voltage step, and
1/kelec is an effective electronic
time constant. At t = 0, both the applied voltage and the time derivative of the voltage are zero.
| |
ACKNOWLEDGMENTS |
|---|
We thank Lindsay Burns for technical support and Dr. Leanne Cribbs
for 1G.
This work was supported by AHA9806307 (D.B.) and National Institutes of Health HL63416 (J.S.).
| |
FOOTNOTES |
|---|
.
Address reprint requests to address for correspondence Dr. Jonathan Satin, Department of Physiology, MS-508, University of Kentucky, College of Medicine Lexington, KY 40536-0298. Tel.: 859-323-5356; Fax: 859-323-1070; E-mail: jsatin1{at}uky.edu.
Submitted August 10, 2001, and accepted for publication January 14, 2002.
| |
REFERENCES |
|---|
|
TOP
ABSTRACT
INTRODUCTION
MATERIALS AND METHODS
RESULTS
DISCUSSION
APPENDIX
REFERENCES
|
|---|
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78:458a1H.
Biophysical Journal
77:3034-30421G, a human brain T calcium channel 1 subunit.
Neurosci. Lett.
274:143-1461G subunit that forms T-type calcium channels.
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275:6090-61001G isoforms of T-type calcium channels with distinct functional properties.
Biophys. J.
78:199a1G T-type calcium channel.
J. Gen. Physiol.
114:185-2011G.
J. Physiol. (Lond.).
530:35-45
), 
), and
). The symbols are pooled experimental data, and the
smooth lines are simulations based on the kinetic scheme shown below in
Fig. 
= 0.77 ms and amplitude = 211 pA. (B)
Ionic tail current from the same cell as A. In contrast
to measurement of IQoff, the prepulse
duration to 0 mV was shortened from 10.8 s to 10 ms to measure
deactivating ionic current. The smooth line is a single-exponential fit
with 
and
) and gating current (
