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J Physiol Volume 555, Number 2, 331-344, March 1, 2004 DOI: 10.1113/jphysiol.2003.054361
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Slow inactivation of the CaV3.1 isotype of T-type calcium channels

Julien Hering, Anne Feltz and Régis C. Lambert

Laboratoire de neurobiologie, Ecole Normale Supérieure, 46, rue d'Ulm, 75005 Paris, France


    Abstract
 Top
 Abstract
 Introduction
 Methods
 Results
 Discussion
 References
 
T-type calcium channels (the CaV3 channel family) are involved in defining the resting membrane potential and in neuronal activities such as oscillations and rebound depolarization. Their physiological roles depend upon the channel activation and inactivation kinetics. A fast inactivation that stops the ionic flux of calcium in tens of milliseconds has already been described in both native and heterologously expressed channels. Here, using HEK 293 cells expressing the rat CaV3.1 channel and whole-cell voltage clamp, we investigate an additional inactivation process, which can be distinguished from the previously described fast inactivation by its slow time course of recovery from inactivation ({tau}= 1 s) and by its sensitivity to external calcium. Steady-state slow inactivation is voltage dependent around the resting membrane potential (the potential of half-inactivation (V0.5) =-70 mV, slope factor = 7.4 mV) and can reduce the calcium current by up to 50%. Near resting potential, the slow inactivation displays a half-time of induction of tens of seconds. The slow inactivation therefore modulates the availability of T-type calcium channels depending upon recent cell history, providing a mechanism to store information in a time scale of seconds.

(Received 12 September 2003; accepted after revision 12 December 2003; first published online 19 December 2003)
Corresponding author R. C. Lambert: Laboratoire de neurobiologie, Ecole Normale Supérieure, 46, rue d'Ulm, 75005 Paris, France. Email: rlambert{at}wotan.ens.fr


    Introduction
 Top
 Abstract
 Introduction
 Methods
 Results
 Discussion
 References
 
The CaV3 family of calcium channels (T-type channels; Perez-Reyes et al. 1998; Cribbs et al. 1998; Lee et al. 1999) are characterized by their low threshold of activation and their fast inactivation. This inactivation occurs at hyperpolarized voltages, in a range that partially overlaps their activation. It has been known for many years that T-type channels are involved in numerous physiological processes, especially in the central nervous system (for review see Huguenard, 1996; Perez-Reyes, 2003). Indeed, the interplay between channel activation and inactivation, which occurs between -80 mV and -50 mV, depending on the T-type channel isotypes and the neuronal population (Perez-Reyes, 2003), can cause non-linear responses to variations in membrane potential around its resting value. This explains why these channels play a central role in calcium-dependent burst firing, oscillations and, more generally, in transitions between different firing patterns. Their role in shaping neuronal activity is therefore linked to the properties of the channel inactivation, such as its voltage dependence, and its kinetics of onset and recovery. The fast inactivation process of the T-type channel has been extensively characterized, especially for the CaV3.1 isotype (Serrano et al. 1999). In addition, previous results obtained on both native (Bossu & Feltz, 1986; Herrington & Lingle, 1992; and review in Chen & Hess, 1990; Perez-Reyes, 2003) and cloned (Klöckner et al. 1999; Frazier et al. 2001; Talavera et al. 2003) channels have shown that the recovery from inactivation of T-type channels can display slow kinetics. This suggests the existence of a slow inactivation process in addition to the fast inactivation already characterized. However, this slow process, which influences the physiological function of T-type channels by defining their availability, has been ignored in models and has never been characterized in detail.

In this paper, we provide evidence that rat CaV3.1 channels expressed in the HEK 293 cell line undergo slow inactivation. We show that the slow inactivation mechanism operates on a time scale of seconds and that up to half of the population of CaV3.1 channels can be driven into slow-inactivated states at the resting potential or during burst firing. The entry into the slow inactivation is characterized by a different apparent voltage dependence from the fast inactivation, reaching its maximal effect at more depolarized potentials than fast inactivation. In addition, slow inactivation is sensitive to the concentration of the divalent charge carrier. These results are compared to the numerous investigations of slow inactivation of sodium and potassium voltage-gated channels.

Since the pore-forming {alpha}1-subunit of cloned T-type channels generates currents similar to native currents, the description and quantification of the slow inactivation process performed here on expressed CaV3.1 channels should help us to understand better the involvement of these channels in neuronal activity. Indeed, slow inactivation may provide a mechanism for this channel population to store information about previous neuronal activity on a time scale of seconds, endowing the neurone with the ability to integrate its own activity for especially long periods.


    Methods
 Top
 Abstract
 Introduction
 Methods
 Results
 Discussion
 References
 
Cell culture

HEK 293 cells were cultured in Dulbecco's modified Eagle's medium (DMEM) complemented with 10% fetal bovine serum, 100 U ml-1 penicillin, and 100 µg ml-1 streptomycin. The stably transfected rat Cav3.1 ({alpha}1G) cell line was kindly provided by Dr. E. Perez-Reyes. The sequence of the rat CaV3.1 transcript used (Lee et al. 1999) is accessible under GenBank accession no. AF027984. Selection was maintained by adding 250 µg ml-1 G-418 to the culture medium. Cells were dissociated using enzymatic digestion with 0.25% trypsin-1 mM EDTA and mechanical trituration. Cells were then split in 35 mm Petri dishes and used during the 1–3 days following the dissociation. All products were purchased from Gibco–Life Technology–Invitrogen.

Transient transfections were also performed using either the calcium-phosphate method or the GeneJammer kit (Stratagene), with a mixture of the CaV3.1 plasmid and the EGFP plasmid to identify the transfected cells. No significant differences were observed between results obtained with stably or transiently transfected cells.

Electrophysiology

Currents were recorded in the whole-cell configuration of the patch-clamp technique using an Axopatch 200A and pCLAMP 8.1 software (Axon Instruments, Union City, CA, USA), filtered at 5 kHz and sampled at 10 kHz. Pipettes were pulled from borosilicate glass capillaries (TW150F-6, WPI, USA) and had a resistance of 1–2 M{Omega} when filled with the recording solution. At least 75% of the series resistance (typically < 10 M{Omega}) and cell capacitance (typically 20 pF) was compensated. Leak currents and capacity transients were subtracted using a P/4 protocol.

To isolate Ca2+ currents, solutions were designed to suppress endogenous K+ and Cl- currents and to fix the Na+ reversal potential close to 0 mV. The pipette solution contained (mM): 10 Hepes, 2.5 CaCl2, 2 MgCl2, 60 methanesulphonic acid, 10 TEA-OH, 70 N-methyl-D-gluconate, 100 NaOH, and 40 BAPTA, 4 Mg-ATP, 15 phosphocreatine and 25 U ml-1 phosphocreatine kinase; pH was adjusted to 7.2 with TEA-OH (solution osmolality was 300 mosmol kg-1). Recording was only started 5 min after rupturing the patch, to allow dialysis of the intracellular medium by the pipette solution.

In most cases, the external solution contained (mM): 10 Hepes, 2 CaCl2, 1 MgCl2, 130 methanesulphonate, 20 TEA-OH, 20 N-methyl-D-glucamine (NMDG) and 120 NaOH, 10 glucose; pH was adjusted to 7.4 with TEA-OH (osmolality was 310 mosmol kg-1).

For concentrations of external calcium higher than 2 mM, NMDG concentration was reduced to maintain solution osmolality. The absence of any endogenous current activated by the various protocols used in the present work was checked on wild-type HEK cells (not shown). All chemicals were purchased from Sigma-Aldrich.

Experiments were carried out at room temperature: 22–24°C.

Protocols

We explain here the principle of the double-pulse protocols. A proportion of the population of the channels was inactivated by the first depolarizing voltage pulse of variable potential and duration. This inactivating pulse was followed by an interpulse interval with specific durations ({Delta}T) at hyperpolarized potentials to allow a proportion of channels to recover from inactivation. Finally, a second depolarizing voltage pulse (the test pulse) to -20 mV was applied to test the number of available channels. We refer to the corresponding evoked current as Itest. The amplitude of Itest was not compared to the amplitude of the current evoked during the inactivating pulse, in order to avoid any accumulation of inactivation when applying successive double-pulses or possible run down of the current, which may happen even in the presence of ATP during very long protocols (i.e. recovery from inactivation with 1 min inactivating pulses lasts around 25 min). Instead, each Itest was compared to a specific consecutive control current (Icontrol) evoked at -20 mV after 5 s at the -100 mV holding potential. The ratio Itest/Icontrol was then calculated.

In Fig. 6, the inactivating pulses were applied at different voltages to compensate for the shift of the potential of half-activation (V0.5) of the activation curves that occurs when external calcium is changed (data not shown). The potential of the inactivating pulse, Vip, was -20 mV for 0.5 and 2 mM Ca2+, -10 mV and -5 mV for 10 and 20 mM Ca2+, respectively.



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Figure 6.  Modulation of slow inactivation by external calcium
A, diagram of the protocol. Currents evoked by a test pulse to -20 mV were conditioned successively by 100 ms and 1 min inactivating pulses to a potential, Vip, depending on the external solution (see Methods), followed by a 350 ms recovery phase at the holding potential, in the presence of an increasing concentration of calcium. For each ionic condition, evoked responses have been scaled and with respect to the current amplitude obtained with a 100 ms inactivating pulse. B, induction of slow inactivation with increasing concentrations of calcium in the bath solution. The percentage of slow inactivation induced in the different concentrations of calcium was: 31.1, 38.7, 41.5 and 41.1% for 0.5, 2, 10 and 20 mM of [Ca2+]o, respectively (currents recorded in the same cell). The dashed and dotted lines indicate the minimum and the maximum, respectively, of the current amplitude.

 
Analysis

For analysis with Clampfit v6.0.3 (Axon Instruments), current traces were numerically low-pass filtered at 1 kHz. All curve fitting was carried out with KyPlot v2.09 (developed by Dr. K. Yoshioka, KyensLab Inc., Tokyo, Japan) using a least-squares routine (Quasi-Newton). The I–V plot was described by a modified Boltzmann function:


(1)
where I is the current, G the conductance, Erev the reversal potential, V0.5 the potential of half-activation, and k the slope factor. The voltage dependence of inactivation was described with a Boltzmann equation:


(2)
where V0.5 is the potential of half-inactivation. To evaluate the onset kinetics of slow inactivation, data were fitted with a bi-exponential function:


(3)
where E is the minimum proportion of activable channels, A1 and A2 the relative amplitudes of the different components, and {tau}1 and {tau}2 the time constants. The curves of recovery from inactivation were described by a bi-exponential function:


(4)
where {tau}1 and {tau}2 are the time constants of the fast and slow exponentials and Af is the relative amplitude of the fast component. An additional scaling factor, a, was used when the recovery from inactivation was not complete after 10 s:


(5)
A factor k was introduced when studying potentials at which initial inactivation at the end of the prepulse was not complete (Fig. 4B):


(6)
where a+k= 1. The curve fitting was performed for each cell and the mean and standard deviation were then obtained by averaging the values from each cell.



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Figure 4.  Voltage dependence of entry in the slow inactivation
A, steady-state fast and slow inactivation. Inactivating pulses of 1 min or 500 ms to different voltages were applied (see diagrams). The current ratios Itest/Icontrol were scaled so that they spanned from 1 to 0, between -100 and -20 mV (see the non-normalized data in the inset) and were fitted with a Boltzmann function (see Methods). For prepulse depolarizations above -20 mV, the values were constant and are not illustrated. Fit parameters for 500 ms and 1 min inactivating pulses, respectively, were: V0.5=-69.0 ± 4.9 and -65.7 ± 2.4 mV, k= 4.3 ± 0.5 and 7.4 ± 0.8, n= 4 and 3. The fit of the steady-state inactivation curve of Fig. 1C is presented as a dotted line for comparison. B, the dependence of the kinetics of recovery from slow inactivation upon inactivating pulse potential. Each data set was fitted with a double-exponential function. For the data obtained with inactivating pulses at -70 mV, inactivation was incomplete and a constant of 0.68 ± 0.06 was added to the function. Fit parameters for an inactivating prepulse potential of -70, -50, -20 and +20 mV were, respectively: {tau}fast= 150 ± 13, 150 ± 25, 120 ± 25 and 147 ± 25 ms; {tau}slow= 0.92 ± 0.26, 1.16 ± 0.11, 1.18 ± 0.45 and 1.25 ± 0.30 s; relative amplitude of the fast component (Af) = 0.76 ± 0.04, 0.77 ± 0.07, 0.55 ± 0.07 and 0.55 ± 0.06; n= 4, 3, 9 and 3. C, voltage dependence of the induction of slow inactivation. The same protocol as in Fig. 3 was applied with inactivating pulses to -20, -50 and -70 mV. Fit parameters obtained with double-exponential functions were, respectively: minimum ratio (E) = 0.66 ± 0.05, 0.62 ± 0.04 and 0.73 ± 0.08; {tau}1= 4.50 ± 4.05, 16.44 ± 8.48 and 12.53 ± 5.20 s; relative amplitude of the first component (A1) = 0.08 ± 0.05, 0.18 ± 0.07 and 0.16 ± 0.06; {tau}2= 18.54 ± 8.89, 34.90 ± 26.24 and 40.79 ± 38.213; relative amplitude of the second component (A2) = 0.21 ± 0.5, 0.13 ± 0.08 and 0.09 ± 0.06; 6 < n < 13, n= 4 and n= 3.

 
The requirement for a second exponential component when fitting the data of the recovery from fast inactivation (inactivating pulse of 500 ms, Fig. 1Dc) and the onset kinetics of slow inactivation (Fig. 3C) was tested statistically with an F test performed on the sum of squared residuals according to Motulsky & Ransnas (1987). The significance of the effect of the external concentration of calcium on the induction of slow inactivation was tested with the multiple-comparison test of Tukey–Kramer.



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Figure 1.  Fast inactivation of CaV3.1 channels
A, typical I–V curve obtained in a HEK 293 cell expressing CaV3.1 channels. Current traces evoked from a holding potential of -100 mV by successive depolarizations ranging from -70 to +60 mV with 5 mV increments are illustrated in the inset. The data obtained with depolarizations between -70 and 0 mV were fitted with a modified Boltzmann function (see Methods). The voltage of half-activation, the slope factor and the reversal potential are -43 mV, 5.0 and +28 mV, respectively. B, time constant of the onset of fast inactivation. Current traces obtained when varying the depolarizing step potential were fitted with a double-exponential function (rise and decay phases). Average time constants of the fast inactivation are presented as a function of the depolarizing potential; a minimum of 18.0 ± 1.5 ms (n= 9) is reached around -10 mV. The typical current trace presented in the inset was evoked by a step depolarization from -100 mV to -20 mV. The decay phase of the current was fitted with a single exponential function for illustration (dotted line) with a time constant of 22 ms. C, voltage dependence of steady-state inactivation. Currents were evoked by step depolarizations to -30 mV preceded by a 1 s prepulse to potentials ranging from -120 to -15 mV with 5 mV increments. Typical current are shown in the inset. The average values of the voltage of half-inactivation and the slope factor of the Boltzmann fit of individual curves are -69.5 ± 4.3 mV and 4.5 ± 03 (n= 4), respectively. D, recovery from the fast inactivation. a, diagram of the double pulse protocol using a 500 ms inactivating pulse at -20 mV (see Methods). The recovery from inactivation was measured with an interval ({Delta}T) ranging from 20 ms to 10 s. b, specimen current traces (left trace: example of an Icontrol). c, recovery from fast inactivation. Ratios Itest/Icontrol are plotted as a function of the interpulse duration (note the logarithmic scale of the x-axis). The data were fitted with both single (dashed line) and double (continuous line) exponential functions. The mean time constant obtained with a single exponential fit was 137 ± 11 ms (n= 10). Using a double-exponential fit, the average values of the first and the second time constants and relative amplitude of the fast component were 51 ± 32 ms, 199 ± 21 ms and 0.36 ± 0.20 (n= 10), respectively.

 


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Figure 3.  Development of the slow inactivation
A, diagram of the double-pulse protocol with inactivating pulses of different durations and a 350 ms interpulse interval at the holding potential of -100 mV. B, current traces evoked by the test pulses (Itest) while increasing the duration of the inactivating pulses from 100 ms to 240 s are superimposed with an example of a control current. C, the ratio Itest/Icontrol is plotted against the duration of the inactivating pulse (6 < n < 13). Five complete sets of data were fitted with a bi-exponential function (see Methods). The parameters obtained were: minimum ratio Itest/Icontrol; (E) 0.66 ± 0.05; time constants {tau}1 and {tau}2, 4.50 ± 4.05 and 18.54 ± 8.89 s with relative amplitude of 0.08 ± 0.05 (A1) and 0.21 ± 0.05 (A2), respectively. The average value of the maximal ratios observed with short inactivating pulses is 0.92 ± 0.04, since full recovery from fast inactivation is not achieved in 350 ms (see Fig. 1Dc).

 
Data are given as means ±S.D. However, in order to facilitate the reading of long numerical series, only mean values are given in the main body of the results and the standard deviations are indicated in the figure legends.


    Results
 Top
 Abstract
 Introduction
 Methods
 Results
 Discussion
 References
 
Fast inactivation of CaV3.1 channels

Using a depolarizing-step protocol over a range of potentials from –70 to +60 mV and a holding potential of -100 mV, families of CaV3.1 currents were recorded from HEK 293 cells; a typical I–V curve is presented in Fig. 1A. As illustrated in the inset, the most noticeable property of the currents generated by this protocol is their very fast decay. Indeed, CaV3.1 channels display the fastest inactivation among all the low voltage-activated calcium channels. With a step depolarization to -10 mV, inactivation occurs with a time constant of 18 ms (n= 9, Fig. 1B). This time constant is not reduced by stronger depolarizations. The involvement of these channels in neuronal activity is strictly dependent upon their steady-state inactivation. Thus, Fig. 1C shows that only a small proportion of the population of the channels is available at -60 mV, a common resting potential in neurones, whereas a hyperpolarization to -100 mV can fully deinactivate the whole population. Moreover, the availability of these channels is highly time-dependent and is determined by the kinetics of their recovery from the inactivation. To examine this property, a double-pulse protocol (see Methods and Fig. 1D) was performed with an inactivating pulse at -20 mV lasting 500 ms, in order to completely inactivate the channels. The proportion of channels recovering from inactivation during periods at -100 mV of various durations (from 20 ms to 10 s) was estimated from the relative amplitude of the current evoked at -20 mV. The description of the recovery kinetics by a single exponential yielded an unsatisfactory fit (dashed line in Fig. 1Dc); a bi-exponential function gave a significantly better fit (continuous line, Fig. 1Dc, P < 0.0001, see Methods). The average values of the time constants are 51 and 199 ms with a relative amplitude of the fast component of 0.36 (n= 10). The presence of two components appeared to be independent of the duration of the inactivating pulse, since in two cells in which inactivation was induced by shorter depolarizations (100 ms), a bi-exponential function with similar time constants was also necessary to fit the data (the time constants for the two cells were, respectively, 25 and 203 ms; and 32 and 235 ms).

Slow inactivation of CaV3.1

Previous investigations in our laboratory have suggested the existence of an additional slower inactivation process that can be induced by long depolarizations in native T-type channels of neurones of nodosus ganglion (Bossu & Feltz, 1986). Other studies have also suggested that T-type channels display slow kinetics of inactivation (Herrington & Lingle, 1992; Klöckner et al. 1999; Frazier et al. 2001; Talavera et al. 2003; and see review in Chen & Hess, 1990; Perez-Reyes, 2003). We therefore investigated the recovery from inactivation induced by long depolarizations of 1 min at -20 mV. As illustrated in Fig. 2B and C, the recovery from inactivation after 1-min-long depolarizations is clearly slower than after prepulses of 500 ms. After inactivation of the channels with long pulses, a hyperpolarization lasting more than 3 s at -100 mV was required to record a peak current of similar amplitude to the control current. The recovery time course was satisfactorily described with the sum of two exponentials. The two time constants obtained from the fit are 110 ms and 1.2 s, with relative amplitude of the fast component of 0.55 (n= 9). Note that the fast time constant of 110 ms is similar to the value of 137 ms estimated when fitting with a single exponential the recovery curve from the fast inactivation induced by 500 ms inactivating pulses (Fig. 1D). We thus concluded that the fast component describes the kinetics of the recovery from the fast-inactivated states and that an additional slow process of recovery, with a time constant around 1 s at -100 mV, appears following long depolarizations. This slow inactivation affects about half of the population of CaV3.1 channels.



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Figure 2.  Slow kinetics of the recovery from inactivation induced by long depolarizations
A, diagram of the protocols used to monitor the recovery from inactivation induced with short (500 ms), intermediate (10 s) or long (1 min) inactivating prepulses (see Methods). B, current traces recorded for the different values of the interpulse interval ({Delta}T) ranging from 20 ms to 10 s with conditioning prepulses of 1 min (left trace: example of an Icontrol). C, recovery from inactivation induced by a 1 min prepulse (•). Data points obtained with {Delta}T= 4, 5 and 8 s were omitted on the graph but were used for the curve-fitting processes. Fits of the data with double-exponential functions yield time constants of 110 ± 20 ms and 1.18 ± 0.45 s, with a relative amplitude of the fast component of 0.55 ± 0.07 (n= 9). Data obtained with a 500 ms prepulse are illustrated for comparison ({circ}, see detail in Fig. 1D). D, recovery from a 10 s inactivating prepulse. The time constants estimated by double-exponential fits were 130 ± 20 ms and 1.10 ± 0.34 s with a relative amplitude of the fast component of 0.80 ± 0.10 (n= 5). Fit of the data obtained with 500 ms (dashed line) and 1 min (dotted line) inactivating pulses are shown for comparison.

 
For voltage-gated sodium channels, the kinetics of the slow inactivation depends upon the duration of the inactivating pulse (Toib et al. 1998). We therefore applied inactivating pulses of intermediate duration to check if the recovery from slow inactivation of CaV3.1 channels shares this property. In Fig. 2D we present the recovery curve established with inactivating pulses of 10 s. The time constants given by the fit were 130 ms and 1.1 s, with a relative amplitude of the fast component of 0.80 (n= 5). The time constants were identical to those obtained with 1 min pulses, with only the relative proportions of fast and slow components modified, indicating that fewer channels had entered into the slow-inactivated states during the 10 s depolarizations than during 1 min pulse. This demonstrates that the kinetics of recovery from inactivation do not depend upon the duration of the inactivating pulse.

Because fast inactivation is complete within a few hundred milliseconds, other inactivated states with much slower kinetics do not participate in the definition of the decay of the current evoked by depolarization. Therefore, the entry into other slower inactivation processes cannot be observed directly. Since no molecular approach has succeeded in preventing the development of the fast inactivation in T-type channels, we decided to use an indirect method to measure the onset of slow inactivation. Increasing durations of the inactivating pulse were used to induce progressively slow inactivation of the channels (Fig. 3A). A 350 ms period at the holding potential was subsequently applied to allow most of the channels in the fast-inactivated state to recover. The peak current evoked at -20 mV (Fig. 3B) following this hyperpolarization was thus inversely related to the number of channels accumulated in the slow-inactivated state. Figure 3C shows that for inactivating pulse durations below about 1 s, the ratio Itest/Icontrol was quite stable at 0.92, showing that only around 8% of channels are still in the fast-inactivated state after the 350 ms recovery period. Note that above 1 s, this incompleteness of the recovery from fast inactivation also exists, but becomes negligible when the slow inactivation is induced. For prepulse durations longer than 1 s, the ratio decreases until it plateaus at 0.66 with inactivating prepulses longer than 2 min. Inactivating pulses of more than 4 min were tested and the ratios displayed no further decrease (data not shown). The onset of slow inactivation occurred with a time of half-induction of around 10 s. Although the values of the time constants varied from cell to cell a bi-exponential function was necessary to fit the kinetics of the onset of slow inactivation in each cell (Fig. 3C, P < 0.001, see Methods). Mean values of the time constants were 4.5 and 18.5 s with relative amplitude of each component of 0.08 and 0.21, respectively. More than 30% of Cav3.1 channels enter into the slow-inactivated states when depolarizations last more than 1 min. Note that the discrepancy between the 30% slow inactivation estimated with this protocol and the 50% estimated by the recovery from long inactivation pulses is due to the fact that some slow-inactivated channels recover during the 350 ms interpulse at -100 mV. Since the ratio is never zero even for inactivating pulses even longer than 1 min, we suggest that the slow-inactivated state is not an absorbing state and that there exists an equilibrium between fast- and slow-inactivated channels.

Voltage dependence of the slow inactivation

The voltage dependence of entry into slow inactivation was characterized using a double-pulse protocol with 1 min inactivating pulses to different potentials (see diagrams of the protocols in Fig. 4A). We compared the resulting voltage dependence with that of fast inactivation probed with 500 ms pulses in an analogous protocol. We fitted the steady-state inactivation relations with Boltzmann functions. The V0.5 values were quite similar for fast (500 ms pulse) and slow (1 min pulse) inactivation: -69.0 (n= 4) and -65.7 mV (n= 3), respectively. In contrast, the slope factor for slow inactivation, 7.4 mV, was markedly greater than that for fast inactivation, 4.3 mV. Thus, fast and slow inactivations have different apparent voltage dependences. The principal difference is that slow inactivation is less voltage sensitive or, in other words, is sensitive to voltage over a greater range of potentials. This means that slow inactivation can occur at the resting potentials, at which some silent neurones are likely to remain for several seconds.

Figure 4B shows the recovery from the slow inactivation that had been induced at different potentials and addresses the question of the influence of the inactivating prepulse on the recovery rate. For depolarizations at 20 and -20 mV, the recovery from slow inactivation displayed similar time constants and relatives amplitudes (see legend of Fig. 4 for details). For inactivating pulses to -50 and -70 mV, the recovery from long inactivating pulses is faster. However, the change is due to the shift between the two exponential component rather than any change of the time constants: 150 ms in both cases for the fast component and 0.92 and 1.2 s for the slow component when induced at -50 and -70 mV, respectively. The kinetics of recovery from either fast or slow inactivations are therefore independent of the potential at which the channels enter these inactivated states. However, the relative amplitude of the fast component is increased to 0.80 with inactivating pulses below -20 mV compared to the value of 0.55 estimated for pulses above -20 mV. The dependence of the relative amplitudes of these components upon the potential of the inactivating pulse suggests that the fast-inactivated state is favoured at weakly depolarized potentials. This is in agreement with the differences in apparent voltage dependence of the fast and slow inactivations shown in Fig. 4A. This may indicate a slowing of the entry into the slow-inactivated state at less depolarized potentials.

To investigate the effect of membrane potential on the kinetics of entry into slow inactivation, we employed a double-pulse protocol similar to the one described in Fig. 3 but using inactivating prepluses to -20, -50 and -70 mV (Fig. 4C). The minimal value of the ratios Itest/Icontrol for inactivating pulses at -50 and -20 mV were similar, 0.62 and 0.66, respectively, but reached 0.73 at -70 mV, suggesting that fewer channels had entered into the slow-inactivated states. It is worth noting that with inactivating pulses at -70 mV the minimum of the ratio is higher than with -20 mV prepulse, due to the fact that fast inactivation is not complete at this potential. In addition, there is a shift of the half-maximal induction of slow inactivation towards longer values of the prepulse durations when more hyperpolarized inactivating pulses are applied (Fig. 4C). Accordingly, the corresponding time constants of the bi-exponential fit also increase with the hyperpolarization of the inactivating pulse: 5, 16 and 13 s for the first component, and 19, 35 and 41 s for the second, for -20, -50 and -70 mV, respectively. These results suggest that at hyperpolarized potentials both the rate of slow inactivation and its extent are reduced. Moreover, a near-steady-state is achieved at every potential with 1 min inactivating pulses. This confirms that no shift in the ratios estimated in our previous protocols was introduced because steady state of inactivations had not been reached.

The voltage dependence of recovery from slow inactivation was investigated by applying a double-pulse protocol (see Methods), with varying interpulse potentials ranging from -120 to -50 mV (see diagram of the protocol in Fig. 5A). This protocol is not a direct measurement of the voltage sensitivity of recovery from slow inactivation, because fast inactivation is induced during the 350 ms interpulse at various potentials. However, the plateau observed below -90 mV, when no fast inactivation is induced, indicates that a constant number of channels recover from slow inactivation during a 350 ms hyperpolarization between -20 and -90 mV. This suggests that the recovery from slow inactivation is not intrinsically voltage dependent.



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Figure 5.  Voltage dependence of recovery from slow inactivation
A, recovery from slow inactivation at hyperpolarized potentials. Same protocol as Fig. 4A with the interpulse potentials ranging from -120 to -50 mV (see diagram in the inset). Note the constant number of channels recovering from slow inactivation between -120 mV and -90 mV. B, kinetics of the recovery from inactivation at different voltages. The data obtained with an interpulse interval at -70 mV (and compared to a control pulse from a holding potential of -70 mV) were fitted with the sum of two exponentials and scaled because inactivation is not complete in 10 s (see Methods). The times constants were: 130 ± 45 and 110 ± 20 ms for the first exponential; 2.38 ± 1.01 and 1.18 ± 0.45 s for the second; with a relative amplitude of the fast component of 0.58 ± 0.08 and 0.55 ± 0.07; n= 6 and 9 for interpulse epochs at -70 and -100 mV, respectively. The scaling factor (a) is 0.96 ± 0.03 (n= 6).

 
We compared the kinetics of the recovery from slow inactivation at -70 and -100 mV (see protocols in inset of Fig. 5B). The results obtained clearly show that recovery at -70 mV is less complete after 3 s than recovery at -100 mV. The fits of the data yielded time constants of recovery from slow inactivation that are slightly slower at -70 mV (2.4 s, n= 6) than at -100 mV (1.2 s, n= 9).

Modulation of slow inactivation properties by external calcium concentration

In contrast to HVA calcium channels, T-type channels undergo a fast inactivation that is calcium independent. However, numerous studies of the voltage-gated Na+ (Townsend & Horn, 1997) and K+ channels (Demo & Yellen, 1991; Pardo et al. 1992; Gomez-Lagunas & Armstrong, 1994; Levy & Deutsch., 1996a,b; Kiss & Korn, 1998) have shown modulation of their slow inactivation processes by permeant cations. To address this question for the CaV3.1 channel, we induced slow inactivation in different extracellular concentrations of calcium (0.5, 2, 10 and 20 mM). As illustrated for a typical cell in Fig. 6B, the extent of slow inactivation induced by 1 min inactivating prepulses increased with calcium concentration from 29 ± 2% at 0.5 mM[Ca2+]o to 40 ± 3% at 10 mM (P < 0.005 for 2 and 20 mM compared to 0.5 mM and P < 0.001 for 10 mM compared to 0.5 mM; n= 5) with saturation above 10 mM[Ca2+]o.

Slow inactivation occurs during neuronal activity

We have seen that induction of (Fig. 4A) and recovery from slow inactivation (Fig. 5A) occurs at physiological potentials. To estimate whether slow inactivation can also be induced by sustained neuronal activity, repetitive depolarizations to +20 mV were performed, initially from a -100 mV holding potential. The use of such a hyperpolarized holding potential, although non-physiological, was motivated by the need to isolate the effect of the repetitive brief depolarizations from any inactivation arising before or between depolarization at the holding potential. In this protocol, stimulation had to be maintained at high frequency (200 Hz) in order to observe the entry into slow inactivation (Fig. 7A). We then simulated bursting activity with partial repolarization to -50 mV between brief depolarizations to activate Cav3.1 channels in a more physiological way. In this situation, slow inactivation could be observed at much lower frequency (50 Hz in the example presented in Fig. 7A). However, as already mentioned, since slow inactivation is induced when cells are maintained at -50 mV without any activity (see below and Fig. 4A), the consequence of the repetitive depolarizations on the slow inactivation process is difficult to assess in this latter protocol. In these two protocols, the fits of the entry into slow inactivation are similar to those obtained in Fig. 3C with a sustained inactivating pulse to -20 mV, in agreement with the constant properties of the slow inactivation above -20 mV as shown in Fig. 4.



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Figure 7.  Slow inactivation and neuronal activity
A, activity can induce slow inactivation. a, double-pulse protocols similar to those in Fig. 3 were used. The inactivating pulses were constructed with series of short pulses of 2 ms to +20 mV mimicking a neuronal firing. The frequencies tested were 50, 100 and 200 Hz, with the interpulse membrane potential kept at -100 mV (protocols 1–3). In a fourth protocol, consecutive depolarizations at 50 Hz and +20 mV were intersected with repolarizations at -50 mV to mimic neuronal bursting firing superimposed upon a plateau depolarization (protocol 4). b, slow inactivation was induced in two (protocols 3 and 4) of the four protocols tested in four different cells. Data from protocols 3 and 4 were fitted as in Fig. 3. The fit parameters for the 50 Hz/-50 mV protocol 4 and the 200 Hz/-100 mV protocol 3, respectively, were: minimum ratio (E) = 0.61 and 0.69; fast time constants ({tau}1) = 3.97 and 2.48 s with relative amplitude (A1) of 0.05 and 0.08; slow time constants ({tau}2) = 25.41 and 17.63 with relative amplitude (A2) of 0.25 and 0.19. B, successive hyperpolarizations allow recovery from slow inactivation induced at the resting potential. a, an inactivating prepulse of 500 ms or 1 min at -50 mV were first applied to mimic short and long resting periods, which induce fast inactivation (F.i.) and fast and slow inactivation (S.i.), respectively. Recovery was then allowed to proceed at -100 mV, with 50 ms depolarizations to -20 mV every 400 ms. Current traces show that the current amplitude was 20% smaller after a 1 min inactivating pulse to -50 mV than after a 500 ms pulse, indicating the presence of slow inactivation. After the fifth pulse, 12% of the channels have recovered from the slow inactivation. b, to further mimic neuronal activity, we simulated successive bursts of inhibitory inputs by shortening the interpulse intervals to 200 ms and by holding the potential during the interpulses at -80 mV with test pulses at -50 mV. Using this protocol, 6% of the current has recovered after the fifth hyperpolarizing period, compared to the initial 20% slow inactivation.

 
We next studied how channels recover from the slow inactivation induced near resting potential. As illustrated in Fig. 7Ba, a significant number of channels enter the slow inactivated state when cells are maintained for 1 min at -50 mV, and cannot be recruited after a single hyperpolarization lasting a few hundred milliseconds, even at a very hyperpolarized potential. We then tested if these channels can recover from the slow inactivation during repetitive hyperpolarized episodes, which mimic bursts of inhibitory inputs (Fig. 7Bb). The progressive increase in the current amplitude evoked after a few 200 ms hyperpolarizations to -80 mV separated by 10 ms at -50 mV clearly suggests that the channels accumulated into the slow inactivated state during prolonged period at -50 mV can deinactivate during successive transient hyperpolarizations and thus be returned to the pool of activatable channels.


    Discussion
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 Abstract
 Introduction
 Methods
 Results
 Discussion
 References
 
We demonstrate that the rat CaV3.1 channel displays at least two types of inactivation that can be distinguished by their kinetics, the voltage dependence of their onset and their sensitivity to external calcium.

Fast inactivation of CaV3.1 channels

The present study did not focus upon fast inactivation, which has already been characterized (Serrano et al. 1999; Burgess et al. 2002). Our protocols were therefore not optimally designed to characterize this process. Nevertheless, we observed that the recovery from fast inactivation is best described by the sum of two exponentials in our recording conditions. Although unusual, this is in agreement with the data reported by Monteil et al. (2000) who also found a bi-exponential recovery from fast inactivation with similar time constants in human T-type channel isotypes. Does the slower component reflect the slow inactivation process described here? Since the bi-exponential recovery was observed when channel inactivation was induced with 100 ms inactivating pulses, which induce very little slow inactivation in our hands and since their slow recovery component ({tau}= 200 ms) was significantly faster than the recovery from slow inactivation we measure ({tau}= 1.2 s), we conclude that fast inactivation has two distinct recovery components that are unrelated to the slow inactivation characterized here.

Slow inactivation of CaV3.1 channels

Previous work on native T-type channels has already described slow kinetics of the recovery from inactivation. This was performed in different preparations with very different recording conditions (Bossu & Feltz, 1986; Herrington & Lingle, 1992; for review see Chen & Hess, 1990; Perez-Reyes, 2003) before the cloning of the T-type channels. The results were interpreted as suggesting the existence of different T-type channels. The subsequent characterization of the three cloned isotypes (Perez-Reyes et al. 1998; Cribbs et al. 1998; Lee et al. 1999) confirmed the existence of channels with different kinetics. However, each of them displays both fast and slow inactivations (Klöckner et al. 1999; Frazier et al. 2001; and the authors' unpublished data).

In this study, we describe the properties of slow inactivation of the CaV3.1 channel. This slow inactivation occurs with a half-time of 10 s during maintained depolarizations at -20 mV (see Fig. 3C). Entry into slow inactivation displays two time constants: a few seconds for the faster one and tens of seconds for the slower one. In contrast, the recovery at -100 mV from slow inactivation induced by long inactivating pulses can be described with a single time constant of 1.1 s. This suggests that although the onset of the slow inactivation appears to be a multistep process, the channels use a common pathway to recover from this inactivation, as we will discuss further below. Moreover, the time to recover from this inactivation is not related to the duration of the previous depolarization (see Fig. 2C). For the slow (C-type) inactivation of voltage-gated potassium channels (Choi et al. 1991), similar observations were made with the Shaker B channels, for which the recovery is also virtually insensitive to the duration of previous stimuli (Toib et al. 1998). In contrast, kinetics of the recovery from the slow inactivation of voltage-gated sodium channels (Rudy, 1978; for review see Goldin, 2003) is related to duration of previous activation (Toib et al. 1998).

Conditions in which the fast and slow inactivations are observable vary, however, from one study to another. When investigating the relationship between deactivation and fast inactivation of CaV3.1 channels, Burgess et al. (2002) reported data of recovery from inactivation after 10 s-long prepulses, a value corresponding to the midpoint of induction of slow inactivation in our conditions. However, the recovery from inactivation appeared to be complete after 1 s at -100 mV (see Fig. 4A in Burgess et al. 2002), which suggests that no component with a slow time constant contributes to this recovery. Talavera et al. (2003) have recently reported fast and a slow time constants in the recovery kinetics of CaV3.1 with values close to our results. However, these kinetics were observed in the recovery from inactivation induced by a short prepulse (200 ms), which would not induce slow inactivation in our recording condition. The differences in the concentration of external ions used may explain these discrepancies of slow inactivation properties and it will be further discussed below.

When depolarized, CaV3.1 channels gradually enter into the slow-inactivated states. Although depolarizations were applied for long durations, slow inactivation was never complete. It reaches a maximum with half of the channels in the slow-inactivated states. The incompleteness of the slow inactivation may reflect a partitioning of the channels during the long prepulse into slow- and fast-inactivated states according to their respective kinetics, and/or the ability of these two inactivation processes to interfere. This latter mechanism occurs in sodium channels in which the slow and fast inactivation gates allosterically interfere, there being competition between the pore conformation for slow inactivation and the docking of the fast inactivating particle in the C-termini of the S6 segments of domain I and IV (Wang et al. 2003; but see also Hilber et al. 2001, 2002). Slow inactivation processes also occur in HVA calcium channels and Shi & Soldatov (2002) have similarly suggested that the slow and fast inactivation gates of the CaV2.1 channel interfere, via a mechanism involving a structural motif at the cytoplasmic end of the S6 segments (for review see Soldatov, 2003). The evidence provided by Staes et al. 2001) and Marksteiner et al. (2001) suggests that the fast inactivation gate in the T-type channel could be localized in the vicinity of the C-termini of the S6 segments and the initial part of the C-terminus of the protein. Similarly to what occurs in sodium and HVA calcium channels, the closure of the fast inactivation gate in the intracellular part of CaV3.1 may allosterically impair the development of the structural conformational changes required to reach slow-inactivated states.

Voltage dependence of slow inactivation

Macroscopic fast inactivation is voltage dependent mainly because it is kinetically linked to the activation processes (Droogmans & Nilius, 1989; Chen & Hess, 1990; Serrano et al. 1999). For instance, this is directly observable in Fig. 1C, in which the decay of the current is relatively slow at more negative potentials where activation is incomplete. Similar characteristics were estimated using both our standard protocol with a 1 s inactivating prepulse (Fig. 1B) and the 500 ms inactivating pulse also used in the present study (Fig. 4A). Another protocol was adapted for the slow inactivation properties, with a 1 min prepulse and 350 ms interpulse (see protocol in the inset of Fig. 4A), and thus the results obtained suggests that this inactivation is also coupled to activation (Fig. 4A). However it requires greater depolarizations to reach its maximal effect than the fast inactivation (see Fig. 4A). Similar characteristics are encountered with the slow inactivation of other voltage-dependent channels, in which the requirement of stronger depolarization was related to structural rearrangements. In sodium channels, the absence of an effect of modification in the S5–S6 linkers on the voltage dependence of slow inactivation suggests that the sensitivity to voltage resides outside the pore (Vilin et al. 2001). Indeed, the specific enhancement of the entry into slow-inactivated states induced by mutations in the voltage sensor of domain IV (Mitrovic et al. 2000) provides evidence that the displacement of the voltage sensor and its associated charge movement plays an important role in the slow inactivation processes. Similarly, in Shaker potassium channels, a model of protein rearrangement has been proposed that postulates a molecular coupling of the voltage sensor to the slow-inactivation gate (Olcese et al. 1997; Loots & Isacoff, 1998, 2000). Whether similar structural rearrangements are involved in slow inactivation of CaV3.1 channels and can explain the more depolarized potentials required to induce this inactivation is still to be determined.

Slow inactivation is impaired for small depolarizations at which its onset kinetics are very slow (tens of seconds). One hypothesis to account for this observation is that the slow-inactivated states are reached from the open state and thus tiny depolarizations induce less slow inactivation, with a slower on-rate because activation is limited and slow at those potentials. As a consequence of the fast decay of CaV3.1 current, this pathway would be limited by the availability of the open state during a long depolarization. However, Serrano et al. (1999) have shown that a residual current can be observed during a sustained depolarization as low as -80 mV due to the activation of at most 2% of the channels. Therefore, channels might reach the slow-inactivated state through the open state during sustained depolarizations. An alternative explanation is that a different pathway may exist to reach the slow-inactivated states from non-conducting states such as the closed or fast-inactivated states. During small depolarizations an intermediate conformation with an incomplete charge movement would be favoured, reducing occupation of these slow-inactivated states.

The recovery from fast inactivation is not considered to be intrinsically voltage dependent (Serrano et al. 1999) and Fig. 5A suggests the same property for slow inactivation. Burgess et al. (2002) provided evidence that the channel must deactivate first (with movement of gating charges) before the recovery from inactivation can occur (see also Satin & Cribbs, 2000; Kuo & Yang, 2001). Similarly, the recovery from slow inactivation is probably under the control of the deactivation pathway. Because we measured only a single time constant of recovery from slow inactivation, the microscopic rate of recovery is probably the limiting step in the whole process and is devoid of an intrinsic voltage dependence. Moreover, we have shown that the potential at which the slow-inactivated states are reached has no effect on the time constant of recovery from long inactivating pulses. In conclusion, we suggest that the recovery from slow inactivation always follows the same pathway to leave the slow-inactivated states whatever the pathway used to reach them.

Modulation of slow inactivation by external Ca2+

When the concentration of external calcium is raised, the maximum degree of slow inactivation is increased by 10% between 0.5 and 20 mM. Since our internal solution contains 40 mM BAPTA, an efficient calcium chelator, an intracellular effect of this cation on the induction of slow inactivation is improbable.

Our results may be explained by a change in the equilibrium between the fast and slow inactivations in favour of the latter. In both voltage-gated sodium and potassium channels, the effect of external cations is the opposite. In voltage-gated sodium channels, an increase of the external sodium concentration shifts the steady-state slow inactivation curve in the depolarized direction and accelerates the recovery from this inactivation (Townsend et al. 1997). Similarly, in potassium channels, ions that bind in or near the external mouth of the pore impede the C-type inactivation conformation change (López-Barneo et al. 1993; Baukrowitz & Yellen, 1996; Kiss & Korn, 1998; Kiss et al. 1999) and speed the recovery from this inactivation (Levy & Deutsch, 1996b).

In CaV3.1, the increase in slow inactivation by external calcium saturates at 10–20 mM. Previous studies on native T-type channels have provided evidence that currents saturate when increasing calcium concentration with a KD between 0.33 and 10 mM (Bossu et al. 1985; Carbone & Lux, 1987; Takahashi et al. 1989; Lux et al. 1990; Herrington & Lingle, 1992). Therefore, the saturation of the pore is expected around 20 mM of external calcium. We may hence hypothesize that the selectivity filter is involved in the slow inactivation processes and that the calcium occupancy of the pore stabilizes the slow inactivation conformation of the channel and slows the kinetics of recovery from these inactivated states. Analogously, Talavera et al. (2003) have shown that the mutations of the amino acids EEDD that form the selectivity filter strongly modified the equilibrium between the slow and fast inactivation states. If the ionic occupancy of the pore affects slow inactivation, varying extracellular concentrations of cations that compete for the pore accessibility may explain the apparent discrepancies in inactivation properties of the CaV3.1 channels reported by different teams using various Ca2+ and Na+ extracellular concentration (Burgess et al. 2002; Talavera et al. 2003).

Modulation of neuronal excitability by slow inactivation of CaV3.1 channel

Although the CaV3.1 channel has a limited ability to sustain currents at high frequencies (>20 Hz), and the channels stop conducting after a few spikes (Kozlov et al. 1999), slow inactivation can occur during high-frequency bursting activity. The frequency of spikes within a burst will directly affect the ability to induce slow inactivation and the duration of a burst will determined the extent of slow inactivation. This provides a memory mechanism able to retain information about burst characteristics for several seconds. Furthermore, we provide evidence that in inactive neurones channels can enter slow-inactivated states at the resting potential. Conversely, recovery from slow inactivation will require either prolonged hyperpolarization or repeated bursts of inhibitory events. Because slow inactivation of up to half of the channels can be observed, it is crucial to include this process in our view of the physiological role of CaV3.1 channels in different kinds of neuronal activities, such as the generation of rhythmic activities, rebound potentials and bistability-mediated activities related to the window-current (for review see Huguenard, 1996; Perez-Reyes, 2003).


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    Acknowledgements
 
We thank Dr Edward Perez-Reyes for his gift of the Cav3.1 cell line and plasmid. This work was supported by a PhD grant from the Ministère de l'Education Nationale de la Recherche et de la Technologie (M.N.R.T).




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