State-Dependent Inactivation of the α1g T-Type Calcium Channel

Voltage-dependent Ca²⁺ channels provide a pathway for rapid influx of Ca²⁺ into cells, which plays a crucial role in both electrical and metabolic signaling. Electrophysiological studies have identified two primary channel types, high voltage-activated (HVA)¹ and low voltage-activated (LVA, or T-type) channels (Bean 1989). Beginning in 1987, the cloning of several HVA channels allowed detailed study of their properties (Catterall 1996), but the molecular basis of T-channels proved more elusive. The recent cloning of α1G, which exhibits the key functional properties of T-channels when expressed in Xenopus oocytes (Perez-Reyes et al. 1998), was an important step toward understanding the biology of T-channels.

T-Channels have been distinguished from HVA channels by a set of biophysical properties, including a more negative voltage range for both activation and inactivation, rapid and nearly complete inactivation, and relatively slow channel closing upon repolarization (deactivation) (Carbone and Lux 1984; Armstrong and Matteson 1985; Fox et al. 1987). T-channels also have a lower single channel conductance in isotonic Ba²⁺, and differ from most HVA channels in selectivity among divalent cations for permeation and block (Bean 1985; Nilius et al. 1985; Nowycky et al. 1985; Narahashi et al. 1987). The kinetic properties of T-channels suggest a key role in regulating electrical activity in the critical voltage region near threshold. For example, T-channels are involved in generation of bursts of action potentials in thalamic neurons (Huguenard 1996).

Significant heterogeneity has been observed in the kinetics of T-channel gating, particularly inactivation rates and the voltage dependence of steady state inactivation (Huguenard 1996). This may be partially explained by use of different experimental conditions, notably the nonphysiological ionic conditions often required to isolate T-current from currents through other ion channels. However, T-currents can genuinely differ in kinetics and pharmacology among cell types (Chen and Hess 1990; Huguenard and Prince 1992; Todorovic and Lingle 1998). This may reflect the emerging molecular diversity among T-channels, with three clones (α1G, α1H, and α1I) known to date (Perez-Reyes et al. 1998; Cribbs et al. 1998; Lee et al. 1999).

Cloned T-channels have putative S4 transmembrane regions, suggesting that the mechanism of voltage-dependent activation is essentially the same as in other members of the extended family of K⁺, Na⁺, and Ca²⁺ channels. However, little is known about the mechanism of inactivation in T-channels, or its relationship to the various fast and slow voltage-dependent inactivation processes known for other channels. T-channel inactivation has been described either by models based on Hodgkin and Huxley 1952b that assume intrinsically voltage-dependent inactivation (Wang et al. 1991; Huguenard and McCormick 1992), or by state-dependent inactivation (Chen and Hess 1990).

The goal of this study was to characterize the gating of T-channels using whole-cell recording from HEK 293 cells stably expressing the α1G clone, with emphasis on the kinetics of inactivation. In this system, it was possible to characterize T-currents over a wide voltage range, under nearly normal ionic conditions (notably, 2 mM Ca²⁺ as the charge carrier). We found that α1G channels inactivate primarily from the open state, although inactivation at hyperpolarized voltages involves “partially activated” closed states, and the main pathway for recovery from inactivation bypasses the open state. The currents show strong cumulative inactivation in response to repetitive depolarizations, consistent with continued inactivation from the open state even after repolarization.

Generation of the stable HEK 293 cell line expressing rat α1G (sequence data available from EMBL/GenBank/DDBJ under accession no. AF027984) has been described previously (Lee et al. 1999). Cells were cultured in MEM supplemented with 10% fetal bovine serum and 600 μg/ml G418, at 37°C in 95% O₂, 5% CO₂. Cell culture media and reagents were from GIBCO BRL. The cells were passaged every 3–4 d. Before recording, cells were harvested from the culture dish by trypsinization, washed with MEM, and stored in the supplemented medium. Cells were used for patch clamp recording 1–4 d after trypsinization.

Currents were recorded using conventional whole-cell patch clamp recording, with an Axopatch 200A amplifier and the Clampex program of pClamp v. 6.0.3 (Axon Instruments). The extracellular solution was 140 mM NaCl, 2 mM CaCl₂, 1 mM MgCl₂, and 10 mM HEPES, adjusted to pH 7.2 with NaOH. The intracellular solution contained 140 mM NaCl, 11 mM EGTA, 2 mM CaCl₂, 4 mM MgATP, 1 mM MgCl₂, and 10 mM HEPES, pH 7.2 with NaOH. The pipets filled with intracellular solution had resistances of 2–4 MΩ. The series resistance in the whole-cell configuration (measured from optimal compensation of capacity transients with the amplifier circuitry) was 5.7 ± 0.3 MΩ, with cell capacitance of 15.3 ± 0.5 pF

The holding potential was −100 mV. Currents were recorded on two channels, with on-line leak subtraction using the P/−4 method on one channel, and raw data during depolarizations on the other, to assess the holding current and cell stability. When this is done, Clampex v. 6 incorrectly sets the current to zero at the end of each leak-subtracted record, so all protocols included a significant period of time at the holding potential at the beginning of each record, and the current during that first holding level was set to zero when the leak-subtracted data were analyzed (using Analyze Adjust Baseline for Epoch A in Clampfit).

Most data analysis used Clampfit v. 6. Exponential fits to data records used the Simplex or Mixed methods of Clampfit. Other curve fitting was done with the Solver function of Microsoft Excel v. 5 or Excel 97. Unless noted otherwise, values are mean ± SEM. For figures showing averaged data, error bars (±SEM) are shown when larger than the symbols.

Since the currents recorded could be >1 nA, data were examined closely for signs of series resistance error. Clamp speed was assessed by the rise time of tail currents, and steady state accuracy by the effect of partial inactivation on the time course of tail currents. For cells used for kinetic analysis of tail currents (e.g., Fig. 3), the 10–90% rise time was 0.15–0.35 ms after 10-kHz analogue filtering. Prepulses that caused ∼70% inactivation (using the protocol illustrated in the inset to Fig. 11) affected the time constant for deactivation at −100 mV by ≤15%. Since the measured time constants changed 37% per 10 mV near −100 mV (see Fig. 5), this suggests ≤5 mV error.

Kinetic models were simulated using SCoP (v. 3.51; Simulation Resources). Simulated data were analyzed further using spreadsheets, or were converted to binary files and analyzed with Clampfit.

Currents with the properties expected of T-type calcium currents were recorded from HEK 293 cells stably expressing α1G cDNA. Depolarizations in 10-mV increments from a holding potential of −100 mV elicited transient inward and outward currents (Fig. 1 A). Currents showed voltage-dependent macroscopic activation and inactivation, with faster kinetics at more depolarized voltages. At intermediate voltages, the currents “cross over” as typically observed for Na⁺ currents and T-currents (Randall and Tsien 1997; Perez-Reyes et al. 1998). The current–voltage (I–V) relationship, measured at the time of peak current during each record, is shown in Fig. 1 B. Detectable current was first observed near −70 mV, with peak inward current near −40 mV.

The ionic conditions used in this study were essentially normal (see materials and methods), including 2 mM Ca²⁺_o, except that K⁺_i was replaced by Na⁺_i to minimize currents through any endogenous K⁺ channels that might be present. HEK 293 cells have occasionally been reported to have endogenous ion channels (Berjukow et al. 1996; Zhu et al. 1998), which could interfere with study of heterologously expressed channels. Especially since the outward currents at positive voltages were unexpectedly large (Fig. 1), we evaluated the presence of contaminating currents using the “envelope” of tail currents produced by depolarizations of different durations. If the recorded currents reflect activity of a single class of channel, the peak amplitude of a tail current must be proportional to the amplitude of the current at the end of the preceding voltage step (Hodgkin and Huxley 1952a). Fig. 2 demonstrates that the tail currents change in parallel with the step current, and that the tail current amplitudes multiplied by a constant scaling factor superimpose on the time course of the current recorded during the step, for steps to −20 or +60 mV. These data indicate that the α1G currents are well isolated in our experimental conditions.

The I–V curve, measured as in Fig. 1 B, is affected both by gating (activation and inactivation) and by permeation (the voltage dependence of ion flow through an open channel). The protocol of Fig. 3 A was used to begin to separate those processes. Channels were first activated by a 2-ms pulse to +60 mV, designed to rapidly activate the channels while minimizing inactivation. This protocol allows us to examine permeation, from the instantaneous I–V relation measured immediately after repolarization (Fig. 3 B). Assuming that the brief step to +60 mV activates the same number of channels each time (consistent with the constancy of the current recorded during the step to +60 mV), the shape of the instantaneous I–V should reflect the voltage dependence of current flow through an open channel. This I–V is distinctly nonlinear, suggesting complex interactions among permeant ions in the α1G pore. The reversal potential was +24.4 ± 1.3 mV

Division of the I–V curve (Fig. 1 B) by the instantaneous I–V curve (Fig. 3 B) was used to evaluate the voltage dependence of activation of α1G channels (Fig. 4 A). That ratio (P_O,r) should be proportional to the number of channels open at the time of peak current at each voltage. Compared with the usual procedure of measuring tail current amplitudes after depolarizations of fixed duration, this method has the advantage of measuring activation at the maximal value for each voltage. The data at ≤0 mV were fitted to a single Boltzmann function, with half-maximal activation at −48 mV. The data deviate from that function at positive voltages, in part because the current ratios become discontinuous at the reversal potential, but the measured activation was consistently ∼20% greater near +60 mV than near 0 mV. For a rapidly inactivating channel, some channels will inactivate before the point of peak inward current, and the extent of that “hidden” inactivation may vary with voltage. Therefore, the activation curve (Fig. 4 A) should be considered an empirical measurement, which may not fully describe the true voltage dependence of the microscopic activation process.

The time course of channel activation was nonexponential. At negative voltages, there was a clear sigmoid delay, which could be approximated by m²h or m³h kinetics (not shown). At positive voltages, the initial time course was not well resolved because of a transient outward current, possibly a gating current, which lasted <1 ms at the T-current reversal potential. The time to peak was voltage dependent, changing approximately fourfold over 100 mV from −30 to +70 mV (Fig. 4 B).

Macroscopic inactivation was measured by single exponential fits to the time course of current decay using the protocol of Fig. 1 (filled symbols, Fig. 5 A). Inactivation was relatively slow at more negative voltages (−60 to −40 mV), but varied little with voltage between −30 and +70 mV. One explanation is that the microscopic inactivation process is voltage independent, as proposed for Na⁺ channels (Armstrong and Bezanilla 1977), but macroscopic inactivation is voltage dependent because of kinetic coupling to the activation process, especially at relatively negative voltages where activation is incomplete. To test that idea, time constants were also measured for the relaxations from the protocol of Fig. 3 (open symbols, Fig. 5 A). The decay of current in that case reflects a combination of channel closing (deactivation) and inactivation. From −120 to −70 mV, where channels would be expected to deactivate, the time constants varied exponentially with voltage

The rate of T-channel deactivation reaches a voltage-independent limiting rate at extreme negative voltages in some studies (Chen and Hess 1990) but not others (Herrington and Lingle 1992; Todorovic and Lingle 1998). To test this for α1G, we examined tail currents at voltages as negative as −150 mV. The time constants showed no detectable deviation from exponential voltage dependence (Fig. 5 B).

Substantial inactivation was observed at voltages as negative as −80 mV (Fig. 6 A). Pulses to −120 mV had little effect, implying that there is little resting fast inactivation at our holding potential of −100 mV. At −80 mV, inactivation proceeded with

We examined the time and voltage dependence of recovery from inactivation (Fig. 6 B), using the protocol illustrated in Fig. 6 C. Recovery from inactivation was complete at −100 and −120 mV. Strikingly, the time course was essentially identical at those voltages (Table), suggesting voltage-independent recovery from inactivation at voltages where recovery is complete. Recovery was incomplete, but only slightly slower, at −90 and −80 mV (Table).

Fig. 6 suggests that inactivation should reach a steady state by ∼1 s. To test that, and to measure the properties of steady state inactivation, voltage steps lasting 1 s were given either directly from −100 mV, or after 60-ms steps to −20 mV to inactivate most of the channels (Fig. 7). At steady state, the measured channel availability should depend only on the tested voltage, i.e., the channel should have “forgotten” whether the inactivating pulse to −20 mV had been given. This comparison can only be done in a narrow voltage range, near the midpoint of the steady state inactivation curve, where the amplitudes of inactivation and recovery are both measurable. The two protocols gave almost identical availability curves:

The time course of inactivation and recovery showed no clear deviation from exponential kinetics for steps lasting up to ∼1 s (Fig. 6 A). This is consistent with the existence of a single inactivation process for α1G in that time scale. It is possible that separate slow inactivation processes occur in the second-to-minute time scale, as reported for many voltage-dependent channels, so the “steady state” inactivation curve reported here pertains only to the primary “fast” inactivation process.

The inactivation curve could be described well by a single Boltzmann relation, assuming that channels inactivate fully at depolarized voltages (Fig. 7). The currents recorded during depolarizations do decay to near zero, but small currents are consistently observed at the end of the pulse (Fig. 1 A). This was observed even after depolarizations lasting 120 ms (Fig. 8 A). If the inactivated state is fully absorbing, only 0.0003 of the channels should remain open after 120 ms

The completeness of inactivation was evaluated further using longer (300-ms) depolarizations (Fig. 8 B). The averaged record shows a small steady state current at −20 mV, followed by a tail current with a fast component appropriate for channel closing at −100 mV. For the five cells included in that record, from a single exponential fit to the first ∼30 ms of the tail current,

Another possible source of incomplete inactivation is a “window current” produced by overlap of the steady state activation and inactivation curves. Roughly speaking, that current should be maximal halfway between the midpoint voltages of the two curves (approximately −70 mV for α1G). Tail currents after 600-ms pulses to −70 mV were very small

As noted above, single exponential fits to tail currents from the protocol of Fig. 8 B yielded an apparently nondeactivating component of 10 ± 2 pA, which corresponds to P_O,r = 0.002.

For comparison, we calculated the resurgent current expected if all of the channels must recover through the open state. We used a three-state scheme: C ← O ↔ I, assuming that channel closing is irreversible at −100 mV. The inactivation (k_I) and recovery (k_−I) rates can be estimated from the limiting time constants for inactivation

Another argument that inactivation and activation are not strictly coupled is that a C … C ↔ O ↔ I scheme predicts much less complete inactivation than observed. If the rate constants for inactivation and recovery are truly voltage independent with the values estimated above,

Fig. 7 demonstrates that there is considerable inactivation at quite negative voltages, below the range where channel activation is detectable (see Fig. 1 B and Fig. 4). This observation suggests that channels can inactivate directly from closed states. However, it is possible that open-state inactivation could slowly accumulate even if P_O is low, perhaps undetectably low. To examine this quantitatively, we calculated the amount of inactivation expected if channels can inactivate only from the open state. That can be done in a model-independent manner, if we make two assumptions: (a) the microscopic rate constant for inactivation k_I (O → I) is the reciprocal of the nearly voltage-independent time constant measured at more than −30 mV, and (b) recovery from inactivation can be neglected (i.e., inactivation is absorbing). We do not mean to imply that these assumptions are true, but they allow simple calculation of the amount of inactivation expected to be produced by a voltage protocol, and deviations from the “predicted” inactivation are likely to be informative.

The predicted inactivation was calculated as follows: first, after measuring the instantaneous I–V relation for a cell (Fig. 3 B), currents are converted to relative P_O values (P_O,r), by dividing the observed current by the instantaneous current at the same voltage. This gives P_O,r as a function of time (relative to that at +60 mV). The expected open-state inactivation is then calculated by integrating

during the protocol. Note that this calculation does not make any assumptions about the kinetic scheme for channel activation; i.e., it is independent of number and arrangement of closed states. Similar analyses have been done by Bean 1981 for Na⁺ channels, and Herrington and Lingle 1992 for T-channels of GH₃ cells.

At −70 mV, where channel opening was clearly detectable, the observed inactivation was approximately twice the predicted value (Fig. 9 A). The difference was larger at −80 mV (Fig. 9 B), where inward currents were visible in one or two of the four cells analyzed. If recovery from inactivation were considered, the predicted inactivation would be reduced further, increasing the discrepancy. We conclude that there is excess inactivation that cannot be accounted for by inactivation from the open state, presumably indicating inactivation directly from closed states.

To determine whether inactivation from closed states is a fundamentally different kinetic process from open-state inactivation, we examined recovery from inactivation after 600-ms steps to −70 mV (Fig. 10). Recovery from inactivation was similar, whether inactivation was produced primarily from open or closed states (Table). Notably, there was little voltage dependence to recovery (varying approximately twofold from −120 to −80 mV), and recovery could be quite rapid (τ ∼ 100 ms at −120 mV). These results suggest that the inactivated states reached from open and closed states interconvert rapidly. Alternatively, it is possible that a single inactivated state is accessed from both open and closed states.

The results described above demonstrate that inactivation can occur from closed states, at least for long, weak depolarizations to voltages near the midpoint of the inactivation curve. But what about brief, strong depolarizations? Fig. 11 compares the measured and predicted open-state inactivation produced by the protocol of Fig. 3. (Inactivation was measured from an additional test pulse to +60 mV, given 20 ms after each record; see Fig. 11, inset.) At negative potentials, there is a good match between measured and predicted inactivation. At positive potentials, the predicted inactivation is larger, possibly due to the observed tendency of inactivation to slow slightly at positive voltages, or to some amount of recovery from inactivation.

Most of the inactivation observed at −120 to −100 mV in Fig. 11 can be attributed to the predicted open-state inactivation produced during the initial 2-ms step to +60 mV

State-dependent inactivation is often associated with cumulative inactivation, a phenomenon where repetitive pulses produce significant inactivation, even when little or no inactivation is visible during each depolarization (Neher and Lux 1971; Aldrich 1981). We do observe strong cumulative inactivation for brief trains of pulses for α1G, either using square voltage steps (Fig. 12 A) or action potential–like depolarizations (Fig. 12 B).

Cumulative inactivation results from “hidden” inactivation, which can occur either “on the way up” (during activation, before the point of peak current), or “on the way down” (during the tail current). Inactivation “on the way up” is favored if inactivation occurs primarily from intermediate closed states (Aldrich 1981; Klemic et al. 1998), while inactivation occurs from open states “on the way down” if channel deactivation is slow (DeCoursey 1990). As might be expected for slowly deactivating T-channels, the cumulative inactivation in Fig. 12 A can be accounted for by open-state inactivation, with much of the predicted inactivation occurring during the tail currents (see lower trace). The actual measured current amplitudes at the end of the second to fourth pulses were 51 ± 2, 31 ± 2, and 21 ± 2% of the first pulse current, comparable to the predicted inactivation of 58 ± 2, 36 ± 3, and 22 ± 4%

Another sign of state-dependent inactivation is “nonmonotonic recovery from inactivation” (Neher and Lux 1971; Marom and Levitan 1994). For pairs of brief depolarizations, channels continue to inactivate during the initial part of the interpulse interval, before recovery from inactivation begins, producing a U-shaped time course for the current measured during the second pulse (Fig. 13). However, apparent nonmonotonic recovery can be observed for interpulse intervals that are not long enough to fully close the channel, if that leads to more channel activation during the second pulse (Gillespie and Meves 1980). That is, a larger test pulse current could result from greater channel activation, rather than less inactivation, for very brief intervals. To exclude this possibility, we delivered a third pulse, after allowing 20 ms for complete channel closing. Currents during the third pulse also showed a U-shaped time dependence (Fig. 13), although inactivation during the 20-ms tail current (and at early times during the third pulse) made the U shape less dramatic. Since nonmonotonic recovery would not occur at all if inactivation were strictly voltage dependent, this is good evidence for state-dependent inactivation.

A model for channel gating can be useful both as an empirical description and as a testable hypothesis for the underlying mechanism. We wanted to develop a model that could reproduce the major experimental results of this study: inactivation is state dependent, fastest from open states, but detectable from closed states. Deactivation is strongly voltage dependent, compared with channel opening (measured as time to peak). Inactivation is strong, but there is a sustained current, corresponding to a P_O,r of 1–2%, over a wide voltage range. Inactivation and recovery reach voltage-independent limiting rates. Repetitive depolarizations produce cumulative inactivation, but inactivation is stronger during a single maintained depolarization.

We considered a model where inactivation is coupled allosterically to voltage sensor activation (Fig. 14 A), which has proven successful for describing inactivation for several voltage-dependent channels (Kuo and Bean 1994; Klemic et al. 1998; Patil et al. 1998). The model involves sequential activation of four voltage sensors (presumably the S4 regions), followed by a distinct channel opening step with less voltage dependence. This can describe the observed delay before channel opening, but voltage-independent channel opening (k_O) limits the voltage dependence of the time to peak. Channel closing (k_−O) must have significant voltage dependence, however, to produce the observed exponential voltage dependence of deactivation (Fig. 5 A). Inactivation is allowed from any of the closed or open states, as in the Hodgkin and Huxley 1952b Na⁺ channel model, but channel activation favors inactivation (and slows recovery). The rate constants for inactivation and recovery are state dependent, but do not depend directly on voltage.

We began by assuming that all four voltage sensors are allosterically coupled to inactivation. Simulations initially appeared to be successful, but close examination revealed an interesting discrepancy. At voltages near the threshold for significant activation, the sustained current was larger than observed experimentally. Although the true steady state P_O did increase monotonically with depolarization, after depolarizations producing partial inactivation (e.g., 60–120 ms), the simulated tail currents were approximately twice as large at near-threshold negative voltages than at positive voltages. This was not seen experimentally (Fig. 8 A; even more clear for 60-ms depolarizations, where the tail currents were larger and more easily measurable; data not shown). In fact, although the characteristic “crossover” (Randall and Tsien 1997) of T-current records was clear in the current–voltage curve (Fig. 1 A), it was barely detectable when the experimental records were converted to P_O (Fig. 14 B). This occurred even though the measured time constants for macroscopic inactivation were slower at more negative voltages (Fig. 5 A), as expected when slow, rate-limiting channel opening is followed by relatively fast inactivation.

The crossover exhibited by the simulations suggested that the model underestimated the rate of inactivation at more negative voltages, which presumably must occur from closed states. We thus modified the scheme, so that activation of only the first three voltage sensors affects the inactivation rate. That is, the last voltage sensor to move (C₃–C₄) has no further effect on the inactivation rate, and the open channel inactivates at the same rate as closed channels in C₃ and C₄. This is arbitrary, but there is precedent for differential coupling of voltage sensors to inactivation of Na⁺ channels (Mitrovic et al. 1998). Faster inactivation from the intermediate closed state C₃ significantly reduced the sustained current at negative voltages, and reduced the crossover (Fig. 14 C). Allowing only the first two voltage sensors to affect the inactivation rate eliminated crossover of P_O records, but degraded the quality of the fit in other ways, notably weakening the voltage dependence of steady state inactivation.

The scheme of Fig. 14 A can accurately describe many aspects of the experimental data (Fig. 15). Current records cross over at negative voltages (Fig. 15 A) and activate in the appropriate voltage range (Fig. 15B and Fig. C). The sum of two Boltzmann distributions was required for accurate description of the simulated activation curve (Fig. 15 C; compare with Fig. 4 A). The voltage dependence of the time to peak (Fig. 15 D) resembled the experimental data (Fig. 4 B), approaching 1 ms at strongly positive voltages. Tail currents from the protocol of Fig. 3 A decayed nearly monoexponentially (Fig. 15E and Fig. F), although the model does not describe the small increase in time constant at positive voltages (Fig. 5 A). The model reproduces cumulative inactivation (Fig. 15 G), with considerable inactivation occurring during tail currents. Nonmonotonic recovery from inactivation occurs after brief (5-ms) steps, although this is barely visible in the P3/P1 ratio (Fig. 15 H).

It is noteworthy that the tail currents could be described by single exponentials (Fig. 15E and Fig. F), even in the intermediate voltage range (near −60 mV) where some channels inactivate and others deactivate. If both processes were effectively irreversible, a single exponential would result (⁠

The model also produced appropriate steady state inactivation, including its steep voltage dependence

Functional expression of the α1G clone in HEK 293 cells produced currents with the essential kinetic properties of T-type calcium currents. Specifically, the voltage dependence of activation (V_1/2 ∼ −50 mV) is clearly in the LVA range, and inactivation (V_1/2 ∼ −80 mV) also occurs at more negative voltages than for most HVA channels. Inactivation is not only rapid (τ ∼ 15 ms at −40 mV and above), but also nearly complete. α1G deactivates ∼10-fold slower than HVA channels

The main goal of this study was to characterize the kinetics of inactivation in α1G channels. We conclude that inactivation is state dependent, with little intrinsic voltage dependence. For brief strong depolarizations, inactivation occurs primarily from the open state, but long weak depolarizations produce inactivation from partially activated closed states. We will next discuss the evidence for these conclusions.

The macroscopic inactivation and recovery processes reach essentially voltage-independent time constants at extreme voltages, above −50 mV for inactivation and below −90 mV for recovery (Fig. 5 and Fig. 7). This can be described by intrinsically voltage-dependent inactivation, if rate constants depend nonexponentially on voltage, as for β_h in the original Hodgkin and Huxley 1952b model, but a voltage-independent rate-limiting step is a more attractive explanation. Furthermore, open-state inactivation at a voltage-independent rate can account for the inactivation observed for brief depolarizations and the subsequent tail currents (Fig. 11). Most notably, there was more inactivation during tail currents at −80 to −60 mV than at more negative voltages, as predicted by open-state inactivation, since channels deactivate slowly in that range. The observation of nonmonotonic recovery from inactivation (Fig. 13) confirms that inactivation can continue to occur after repolarization, as expected for state-dependent but not voltage-dependent inactivation.

Although open-state inactivation can account for the effects of brief depolarization (Fig. 11), inactivation also occurred slowly during depolarizations to −90 mV (Fig. 7), where no channel opening was detectable. At −70 or −80 mV, the amount of observed inactivation considerably exceeded that predicted by voltage-independent open-state inactivation (Fig. 9). Unless the rate for open-state inactivation increases more than twofold at these hyperpolarized voltages, which is unlikely, inactivation must also occur from closed states. The simplest explanation for the inactivation observed below −60 mV is that activation of voltage sensors favors inactivation, even if the channel does not open (Fig. 14 A). For α1G, inactivation is faster from the open state than from some of the intermediate closed states, since macroscopic inactivation slowed below −40 mV, and a maintained depolarization produced more inactivation than repetitive pulses (Fig. 13 A).

Open- and closed-state inactivation of α1G appear to be closely linked processes, since recovery from inactivation is similar after procedures that favor open-state inactivation (60-ms pulses to −20 mV) or closed-state inactivation (600-ms pulses to −70 mV). The absence of a significant inward current during recovery from inactivation (Fig. 8) demonstrates that the primary pathway for recovery from inactivation is via closed states.

It is possible that what we describe as open-state inactivation actually occurs from a closed state that is in rapid, voltage-independent equilibrium with the open state (Marom and Levitan 1994). Since this can be difficult to distinguish from inactivation directly from the open state, even with single channel data, we retain the expression “open-state inactivation” to emphasize that this form of inactivation is closely coupled kinetically to channel opening. Although our model assumes that inactivation occurs at the same rate from certain closed states (C₃ and C₄) as from the open state, open-state inactivation is the predominant pathway except at the most negative voltages, mainly because the C₄ ↔ O equilibrium is strongly to the right for the parameters used, so occupancy of C₃ and C₄ is generally low.

Although our model describes well many qualitative and quantitative features of the experimental data, it should be considered preliminary. The model parameters were found by trial and error, rather than rigorous parameter estimation procedures based on quantitative error minimization. We have not systematically tested alternative models. Our data do not include information from single-channel or gating current experiments, which have proven important for modeling gating of other channels. We believe it is useful to present this model at this time, as a possible basis for future studies on the gating of both cloned and native T-channels.

α1G is likely to underlie native T-currents in some but not all cells. Notably, it is highly expressed in the thalamus (Perez-Reyes et al. 1998). Two other α1 subunits (α1H and α1I) produce T-currents in expression systems (Cribbs et al. 1998; Perez-Reyes et al. 1998; Lee et al. 1999), and the existence of additional α1 genes cannot be excluded. Other sources of diversity in channel properties, including accessory subunits and posttranslational modifications, remain to be fully explored for T-channels. It has been suggested that α₁ subunits normally associated with HVA channels can produce T-like activity under some conditions (Soong et al. 1993; Meir and Dolphin 1998), but the cloning of three indisputable T-channels makes this possibility less attractive as a general explanation for native T-currents (Randall and Tsien 1997; Bean and McDonough 1998; Lambert et al. 1998; Nakashima et al. 1998).

Kinetic and pharmacological diversity among T-channels is well established (Huguenard 1996). One feature with possible implications for mechanisms of channel gating is the voltage dependence at extreme voltages, which could reveal voltage-independent limiting rates (Chen and Hess 1990). We found clear evidence for voltage independence of the inactivation process (above −50 mV) and recovery (below −90 mV). This agrees well with some studies (Chen and Hess 1990; Herrington and Lingle 1992), although a limiting voltage-independent rate for recovery is not always clear (Huguenard and McCormick 1992). In contrast, channel deactivation remained strongly voltage dependent even at −150 mV (Herrington and Lingle 1992; Todorovic and Lingle 1998; but see Chen and Hess 1990). We have not examined activation kinetics closely in this study, but channel opening became quite rapid at depolarized voltages, with time to peak 1.4 ± 0.1 ms at +60 mV

Our data for α1G are consistent with single exponential kinetics both for development of inactivation and for recovery, on a time scale up to 1 s. This is consistent with most previous work on native T-channels, although some studies have reported multiexponential kinetics (Bossu and Feltz 1986; Herrington and Lingle 1992). A preliminary report suggests that α1G may also exhibit a second inactivation process, on a longer time scale (Martin et al. 1998).

There are some similarities among inactivation processes for different voltage-dependent channels. Fast inactivation of Na⁺ channels and N-type inactivation of K⁺ channels reach a limiting rate at positive voltages. At intermediate voltages, macroscopic inactivation is voltage dependent due to kinetic coupling to the activation process, which is relatively slow at such voltages. Inactivation is strong but not necessarily 100% complete. Inactivation of α1G channels shares these properties.

One striking difference from Na⁺ channels is that recovery from inactivation shows little voltage dependence for T-current (Table; Chen and Hess 1990). This suggests a voltage-independent rate-limiting step for recovery, consistent with the view that the microscopic inactivation and recovery rates are both independent of voltage. In one study, recovery became voltage independent for Na⁺ channels, but only below −160 mV (Kuo and Bean 1994). Further work will be necessary to determine whether these differences are merely quantitative, or reflect qualitatively different inactivation mechanisms.

Inactivation of α1G was strong but incomplete, with 98–99% inactivation over a wide voltage range. There is considerable variability in the extent of inactivation of Na⁺ channels, 70–97% in the squid giant axon (Vandenberg and Bezanilla 1991) but 99.9% in mammalian skeletal muscle (Cannon and Corey 1993). In squid axon, the extent of inactivation decreases with strong depolarization (Chandler and Meves 1970), which may be true to a lesser extent for α1G (Fig. 8). This effect is not clearly associated with a slower macroscopic inactivation rate in squid axon (Chandler and Meves 1970), but an ∼20% decrease in the inactivation rate was detectable above +50 mV for α1G (Fig. 5 A). The decreased inactivation with strong depolarization was voltage dependent in squid axon (Bezanilla and Armstrong 1977), but effects of permeant ions on gating should also be considered for T-channels (Carbone and Lux 1987; Shuba et al. 1991), since in our ionic conditions the primary charge carriers are Ca²⁺ for inward currents and Na⁺ for outward currents.

Fast inactivation of Na⁺ and K⁺ channels is believed to occur primarily but not exclusively from open states (Bean 1981; Aldrich and Stevens 1983; Hoshi et al. 1990), as we find here for α1G. This contrasts with slower inactivation processes of some K⁺ (Aldrich 1981; Klemic et al. 1998, Klemic et al. 1999) and HVA Ca²⁺ channels (Patil et al. 1998), where inactivation from closed states appears to be the predominant pathway even at positive voltages.

One of the clearest functional roles of native T-channels is generation of the low threshold spike that underlies bursts of action potentials in (e.g.) thalamic relay neurons (Huguenard 1996). In those cells, T-channels are inactivated at the normal resting potential (near −60 mV). But inactivation can be rapidly removed by hyperpolarizations, such as inhibitory postsynaptic potentials (IPSPs). This allows rebound activation of T-channels and a low threshold spike, terminated in part by T-channel inactivation. The properties of α1G currents are fully consistent with such a scheme.

α1G exhibited a sustained current, with 1–2% of the channels remaining open at all voltages above −70 mV (Fig. 8). Our kinetic model accounts for that current with a finite, voltage-independent rate of recovery from inactivation. This differs from the “window current” predicted from an overlap between the activation and inactivation curves, which has a bell-shaped P_O versus voltage relation (if inactivation is complete at positive voltages, as often assumed), peaking near the foot of the activation curve (Williams et al. 1997). But in either case, there would be a steady state T-current at voltages near the resting potential, which could have interesting consequences for neuronal integration and calcium homeostasis (Williams et al. 1997; Bean and McDonough 1998). We are not aware of direct evidence for such a current from previous voltage clamp studies of T-current, although current clamp studies on thalamic neurons do suggest existence of a window current (Williams et al. 1997). Our results could overestimate the steady state T-current if additional slow inactivation processes exist, but the time scale we have examined (up to ∼1 s) is sufficient to predict that there should be significant T-channel activity during hyperpolarized intervals during a burst of action potentials.

It is not possible to extrapolate directly from results in an expression system to the situation in vivo, but several kinetic properties of α1G could have important physiological consequences. Activation is quite rapid at positive voltages, so any α1G channels not already activated in a low threshold spike might be activated significantly by a single Na⁺-dependent action potential. After repolarization, slow deactivation will keep the channels open for a few milliseconds, producing maintained Ca²⁺ entry (as noted by Huguenard 1996). In addition, a significant fraction of channels will inactivate (rather than deactivate) after repolarization. This contributes to the strong cumulative inactivation observed for α1G during action potential–like depolarizations (Fig. 13).

The cumulative inactivation critically depends on the state dependence of inactivation, combined with the characteristic slow deactivation of T-channels. Previous models for thalamic T-currents resemble the original Hodgkin and Huxley 1952b model for Na⁺ current, with inactivation depending on voltage but not on the state of activation of the channel. Some degree of cumulative inactivation does occur with Hodgkin-Huxley models, as some channels inactivate without opening in response to brief depolarizations, but recovery from inactivation begins immediately upon repolarization. Correspondingly, the models of Wang et al. 1991 and Huguenard and McCormick 1992 for thalamic T-current produce much less cumulative inactivation than observed here (simulations not shown). It is sometimes assumed that Hodgkin-Huxley models are valid as operational descriptions of macroscopic ionic currents, even if they are not mechanistically correct. However, state-dependent inactivation can produce effects that are not describable by such models, notably in response to repetitive depolarizations (Klemic et al. 1998; Patil et al. 1998). Future studies will be necessary to determine whether T-channels natively expressed in neurons also exhibit strong cumulative inactivation during a burst of action potentials, and to explore the consequences for the role of T-channels in neuronal excitability.

We thank Drs. Leanne L. Cribbs and Toni Schneider for preparation of the α1G cell line, and Dr. Christopher J. Lingle for helpful comments on a draft of this paper.

This work was supported in part by National Institutes of Health grant NS24471 to S.W. Jones and HL58728 to E. Perez-Reyes, and by a Howard Hughes Medical Institute grant to Case Western Reserve University School of Medicine.