T-type Ca2+ channels encode prior neuronal activity as modulated recovery rates
1 Department of Epileptology, University of Bonn Medical Center, Sigmund-Freud-Strasse 25, 53105 Bonn, Germany
2 Department of Pharmacology, University of Virginia, Charlottesville, VA 22908, USA
Abstract
T-type Ca2+ channels give rise to low-threshold inward currents that are central determinants of neuronal excitability. The availability of T-type Ca2+ channels is strongly influenced by voltage-dependent inactivation and recovery from inactivation. Here, we show that native and cloned T-type Ca2+ channel subunits selectively encode specific aspects of prior membrane potential changes via a powerful modulation of the rates with which these channels recover from inactivation. Increasing the duration of subthreshold (–70 to –55 mV) conditioning depolarizations caused a pronounced slowing of subsequent recovery from inactivation of both cloned (Cav3.1–3.3) and native T-type channels (thalamic neurones). The scaling of recovery rates with increasing duration of conditioning depolarizations could be well described by a power law function. Different T-type channel isoforms exhibited overlapping but complementary ranges of recovery rates. Intriguingly, scaling of recovery rates was dramatically reduced in Cav3.2 and Cav3.3, but not Cav3.1 subunits, when mock action potentials were superimposed on conditioning depolarizations. Our results suggest that different T-type channel subunits exhibit dramatic differences in scaling relationships, in addition to well-described differences in other biophysical properties. Furthermore, the availability of T-type channels is powerfully modulated over time, depending on the patterns of prior activity that these channels have encountered. These data provide a novel mechanism for cellular short-term plasticity on the millisecond to second time scale that relies on biophysical properties of specific T-type Ca2+ channel subunits.
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Introduction
T-type Ca2+ currents are central determinants of neuronal excitability that are present in the somatodendritic compartment of many types of neurones (Carbone & Lux, 1984; Talley et al. 1999). Genetic and pharmacological inhibition of T-type Ca2+ currents has demonstrated the importance of these currents in various sensory systems, ranging from pain perception and hyperalgesia (Kim et al. 2003; Ikeda et al. 2003), mechanoreceptor function (Shin et al. 2003), to olfaction (Kawai & Miyachi, 2001), as well as the maintenance of sleep states (Anderson et al. 2005). On a cellular level, T-type currents are essential for the generation of burst discharges and the generation of intrinsic rhythms in subsets of CNS neurones (for review see Huguenard, 1996). Furthermore, T-type Ca2+ channels underlie low-threshold Ca2+ spikes that are observed in many types of neurones (Jahnsen & Llinás, 1984a,b; Greene et al. 1986).
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The availability of T-type Ca2+ channels is strongly dependent on membrane voltage, because all known T-type channels display a steep voltage-dependent inactivation in the vicinity of resting membrane potential. As a consequence, bursting neurones expressing T-type Ca2+ channels can switch to a nonbursting regular firing mode when T-type Ca2+ channels are inactivated by subtle depolarizations from resting membrane potential (Kim et al. 2001; Su et al. 2002). However, recovery from inactivation following membrane depolarizations is a dynamic process. As a consequence, the availability of T-type channels over time following repolarization will also critically depend on the rates with which these channel types recover from inactivation. It has been recently appreciated that recovery rates from inactivation of individual voltage-gated membrane channels may vary considerably. In the case of voltage-gated Na+ channels, the recovery rates have been shown to be dependent on the duration of preceding depolarizations, with longer depolarizations giving rise to markedly slower recovery rates (Toib et al. 1998; Ellerkmann et al. 2001). The relationship between the duration of the conditioning depolarization and the recovery rate has been well described by a power law relation. Such scaling relationships (Bassingthwaighte et al. 1994) imply that there is no single characteristic recovery rate, but that the recovery rate reflects the time allowed for inactivation. As a consequence, this mechanism may be considered as a mechanism of short-term plasticity that preserves a trace of certain aspects of prior neuronal activity. Unlike Na+ channels (Toib et al. 1998; Ellerkmann et al. 2001), such a mechanism might already be invoked in T-type Ca2+ channels by subtle depolarizations from the resting membrane potential, and would be expected to critically influence availability of these channels during repolarization.
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In the present study, we have meticulously examined recovery of cloned and native T-type channels following different patterns of activity. Our results suggest that T-type Ca2+ channel subunits differentially encode specific aspects of prior membrane potential changes as modulated recovery rates and provide a novel mechanism for cellular short–term plasticity.
Methods
HEK 293 cells
The generation of stable cell lines expressing human Cav3.1, Cav3.2 and Cav3.3 has been previously described. The following stably transfected HEK 293 cell lines were used in this study: h1G-Q39, containing the human 1G channel, Cav3.1a (GenBank accession no. AF190860; Cribbs et al. 2000); hh8-5, containing the Hh8 plasmid construct of human 1H, Cav3.2a (GenBank accession no. AF051946; Cribbs et al. 1998); and Lt9–8, containing the LT9 plasmid construct of 1I, Cav3.3b (Gomora et al. 2002; GenBank accession no. AF393329). Cells were maintained in Dulbecco's modified Eagle's medium (DMEM) medium (4.5 g l–1 glucose, 584 mg l–1L-glutamine), supplemented with 1 mg ml–1 geneticin, 10% heat-inactivated fetal bovine serum, 100 units ml–1 penicillin and 100 g ml–1 streptomycin.
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Preparation of dissociated neurones from the lateral geniculate nucleus of the thalamus
Male Wistar rats (postnatal day 12–20) were decapitated under deep ether anaesthesia. A block of the brain containing the thalamic nuclei was rapidly removed and placed in oxygenated chilled (–4°C) solution containing (mM): 20 Pipes, 2.4 KCl, 10 MgSO4, 0.5 CaCl2, 10 glucose, 195 sucrose (pH 7.25) (Pipes1). Coronal 500 μm slices containing the lateral geniculate nucleus (LGN) were made with a vibratome (Leica VT1000S, Wetzlar, Germany). The LGN was subsequently dissected under stereoscopic observation in Pipes1 solution (see above). LGN microslices were then placed in an incubation chamber containing a slightly altered Pipes buffered solution (Pipes2; mM): 20 Pipes, 5 KCl, 3 MgCl2, 25 glucose, 120 NaCl and 0.5 CaCl2 (pH 7.35; 100% O2), and gradually warmed to 30°C over a period of 25 min. After warming, trypsin (1 mg ml–1) was added to the Pipes2 solution, and microslices were incubated for 30 min. The enzymic reaction was terminated by washing in enzyme-free Pipes2 solution. After allowing slices to cool to room temperature for 10–30 min, LGN neurones were dissociated by trituration with fire-polished Pasteur pipettes. Only those dissociated cells with a morphology reminiscent of LGN projection neurones were included in this study, as described in detail elsewhere (Pape et al. 1994).
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Patch-clamp recording
Patch-clamp recordings were obtained from 350 HEK cells expressing Cav3 Ca2+ channels, and 33 native LGN neurones. Patch pipettes with a resistance of 3–4 M were fabricated from borosilicate glass capillaries and filled with an intracellular solution containing (mM): 87.5 caesium methanesulphonate, 5 MgCl2, 0.5 CaCl2, 20 tetraethylammonium, 10 Hepes, 5 1,2-bis-(o-aminophenoxy)ethane-N,N,N',N'-tetraacetic acid (BAPTA), 16 sucrose, 10 adenosine 5'-triphosphate (Na+2-ATP), 0.5 guanosine 5'-triphosphate (GTP), and 10 glucose (pH 7.2, 300 mosmol kg–1). Patch-clamp recordings from native LGN neurones and HEK cells were performed in a bath solution containing (mM): 125 sodium methanesulphonate, 3 KCl, 1 MgCl2, 5 CaCl2, 4 4-aminopyridine (4-AP), 20 tetraethylammonium, 10 Hepes, 10 glucose (pH 7.4, 315 mosmol kg–1). Tight-seal whole-cell recordings were obtained at room temperature (21–24°C) according to standard techniques. Membrane currents were recorded using a patch-clamp amplifier (EPC9, HEKA Elektronik, Lambrecht/Pfalz, Germany) and collected online with the Pulse acquisition and analysis program (HEKA Elektronik, Lambrecht/Pfalz, Germany). Series resistance compensation was employed to improve the voltage-clamp control (>80% for HEK cells, >50% for dissociated LGN neurones) so that the maximal residual voltage error did not exceed 1.5 mV (Sigworth et al. 1995). A liquid junction potential of 5 mV was measured between the intra- and extracellular solution, and corrected on-line such that without correction the voltages given in this paper would be 5 mV more positive. Holding potential was –95 and –85 mV for recordings in HEK cells and dissociated LGN neurones, respectively.
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Voltage protocols and data analysis
The voltage dependence of activation and inactivation was characterized using standard protocols (see Supplemental material, Fig. S1A and C, representative current traces in panels B and D). The voltage-dependent activation was fit by the product of a Boltzmann function, reflecting voltage-dependent activation (eqn (1)), and the general constant field equation (eqn (2)).
(1)
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(2)
where ICa(V) denotes the Ca2+ current amplitude, PCa denotes the Ca2+ permeability, [Ca2+]in and [Ca2+]out denote the internal and external Ca2+ concentrations, respectively. V corresponds to the command voltage, V is the voltage of half-maximal inactivation or activation. The PCa for each potential was derived, normalized to the maximal value and averaged (see supplemental Fig. S1E). The voltage dependence of inactivation was derived by converting peak current to PCa and fitting these values with eqn (1).
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The onset of inactivation of T-type Ca2+ currents was described by holding the membrane potential to –55 mV for varying durations (tpre) and a subsequent step to –25 mV (see Fig. 1A). The peak current amplitude elicited (see Fig. 1B) was normalized to the maximal amplitude elicited without a prepulse to –55 mV. The relation between the normalized peak amplitude and the prepulse duration was best fit by a biexponential equation (see Fig. 1C) of the form:
(3)
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where I(tpre) is the current amplitude following a prepulse duration of tpre, A0 is a constant offset, and 1 and 2 are the time constants of inactivation with the corresponding amplitudes A1 and A2, respectively.
A, a hyperpolarizing voltage step was applied to remove inactivation completely (–115 mV, 2 s), followed by a prepulse of variable duration (–55 mV, tpre) to induce inactivation. The fraction of available current was determined with a subsequent 100 ms test pulse (–25 mV). B, representative currents mediated by Cav3.1 (), Cav3.2 () and Cav3.3 subunits (). Currents are progressively reduced with increases in tpre. C, normalized peak amplitude of the Ca2+ currents was plotted versus the duration of the inactivating prepulse (tpre, see C) for all three subunits. Continuous lines superimposed on the data points represent biexponential fits (n= 7, 8 and 8 for Cav3.1, Cav3.3 and Cav3.3, respectively). Error bars represent S.E.M.
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Recovery from inactivation was examined with double-pulse experiments. The first set of experiments addressed recovery of T-type channels following continuous step depolarizations (see, for instance, Fig. 2A). The voltage of these conditioning pulses was varied from –70 to –10 mV (see supplemental Fig. S3A and C) and their duration (tpre) ranged from 0.3 to 300 s (i.e. Fig. 2A). Recovery of T-type Ca2+ channels following these conditioning prepulses was examined by stepping the membrane potential back to –95 mV holding potential for a varying recovery interval (t, 5 ms to 20.5 s) and subsequently applying a brief (100 ms) test pulse to –25 mV. In all experiments, an equivalent normalization test pulse to –25 mV (100 ms) was applied 5 s before each double pulse. To ensure 100% recovery of the current prior to application of the normalization test pulse, an interval was interspersed between individual double pulses and the subsequent normalization pulse that was at least threefold larger than the time required for full recovery of the current amplitudes (–95 mV). Thus, this interval varied depending on the subunit examined and the prepulse duration employed (ranging from 10 to 90 s). Normalization of the recovery data was then carried out with the amplitude of the current elicited during this normalization test pulse. As expected, these protocols revealed a full recovery of T-type current amplitudes following the longest recovery interval (20 s), even for the longest prepulses for which recovery rates were slowest (recovery to 99.7 ± 0.3, 99.2 ± 0.4 and 99.7 ± 0.5% for the Cav3.1, Cav3.2 and Cav3.3 subunits, respectively, following 300 s prepulses).
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A, the duration of conditioning prepulses was systematically varied (tpre 0.3–300 s). Subsequent recovery from inactivation was assessed with a 100 ms test pulse to –25 mV, separated from the conditioning prepulse by a variable interpulse interval (t). B, representative current traces for two different prepulse durations (tpre 1 and 300 s) are depicted for each of the cloned T-type channels (Ba–c correspond to Cav3.1–3.3 as indicated). The leftmost traces correspond to currents elicited by a normalization test pulse to –25 mV (100 ms), which was applied 10 s before each double pulse. To ensure that currents were 100% recovered prior to application of the normalization test pulse, an interval was interspersed between individual double pulses and the subsequent normalization pulse that was at least threefold larger than the time required for full recovery of the current amplitudes (ranging from 10 to 90 s, see Methods). C, recovery time course, currents were normalized to the peak current during the normalization test pulse (leftmost traces in Ba–c. The recovery time course shows a progressive slowing with more prolonged prepulses (tpre 1, 3, 10, 30 and 100 s, indicated by asterisks, triangles, diamonds, squares and circles, respectively). Ca–c correspond to Cav3.1 (n= 8–10), Cav3.2 (n= 5–9) and Cav3.3 (n= 5–11 for each data point), respectively. The time course of recovery for Cav3.1–3.3 was well described with a biexponential equation superimposed on the data points. D, the fast time constant fast (triangles) and a slower time constant slow (squares) are plotted versus the duration of the conditioning depolarization tpre (Cav3.1–3.3 in Da–c, respectively). The relationship between these parameters could be fit with a power law relation of the form (tpre) =a(tpre/a)b (where where a is a constant kinetic setpoint, and b is a scaling power), which is superimposed on the data points (see Table 2 for values). The change in with increasing tpre was highly significant for Cav3.1 (F6,59= 18.88, P < 0.001, and F6,59= 39.69, P < 0.001, for fast and slow, respectively), Cav3.2 (F6,45= 7.15, P < 0.001, and F6,45= 11.17, P < 0.001, for fast and slow, respectively) and Cav3.3 (F6,59= 15.18, P < 0.001, and F6,59= 29.52, P < 0.001, for fast and slow, respectively). Error bars represent S.E.M.
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Similar experiments were carried out with conditioning trains of mock action potentials (APs; i.e. Fig. 6A). Each individual mock AP had a linear upstroke of 1 ms and a linear downstroke of 2 ms duration, with a peak at +25 mV. This corresponds roughly to the range of AP durations observed for developing LGN neurones (White & Sur, 1992). We varied either the duration of AP trains (from 0.1 to 100 s, at a constant frequency of 30 Hz), or their frequency (from 1 to 100 Hz, with a constant duration of 30 s, see Fig. 6A). In some experiments, mock AP trains were superimposed on continuous depolarizing prepulses (to –55 mV) of varying durations (see Fig. 4A). Normalization of the recovery data was carried out as for continuous conditioning stimuli. For a given conditioning stimulus, the total duration of double-pulse protocols ranged from 3 to 75 min. We were concerned that rundown of Ca2+ current amplitudes might contaminate our results. Therefore, we excluded all experiments in which the Ca2+ current amplitudes elicited by the normalization test pulse (see description of double-pulse protocols above) were reduced by more than 20% over 1.5 h of recording. We also excluded experiments in which the input resistance measured in recording solution was <1G, or cells in which a transient change in passive membrane properties was observed. The time constants of recovery fast and slow were extracted by fitting with a biexponential equation of the form:
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(4)
In some cases, fitting was carried out with a monoexponential or a triexponential equation of an identical form for purposes of comparison to biexponential fits.
A, mock AP trains were applied from hyperpolarized (–95 mV) membrane potentials (depolarization to +25 mV, rising and falling phase, 1 and 2 ms, respectively; frequency 0.3–100 Hz). B, cumulative inactivation induced by mock AP trains at 30 Hz for Cav3 subunits. Cav3.1 and 3.2 undergo powerful cumulative inactivation, while inactivation of Cav3.3 by such trains is negligible. Representative current traces elicited by the 1st, 3rd, 10th, 30th and 100th mock AP (applied with 30 Hz) are depicted in Ba–Bc for Cav3.1–3.3, respectively. Rising and falling phases of the mock AP are indicated by hatched and open bars, respectively. As in Fig. 4, the normalized and averaged amplitudes of peak Ca2+ current elicited by the first 30 APs for Cav3.1–3.3 channels are shown (Ca–Cc, n= 7, 10 and 6 for Cav3.1, Cav3.3 and Cav3.3, respectively). The normalized amplitudes during the 91st to 100th mock AP in a train are summarized in D for different mock AP train frequencies. Error bars represent S.E.M.
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A, conditioning trains consisted of concatenated APs (rising and falling phase, 1 and 2 ms, respectively, to a peak voltage of +25 mV, rising and falling phase indicated by hatched and open bar, respectively, in Ba–c) at various frequencies (3–100 Hz), superimposed on the conditioning depolarization to –55 mV. B, representative current traces elicited by the 1st, 3rd, 10th, 30th and 100th mock AP of a train of 30 Hz are depicted in Ba–c for Cav3.1–3.3, respectively. C, the peak amplitudes of the inward current were normalized to the peak amplitudes during the first mock action potential. The normalized and averaged (n= 5, 5 and 6 for Cav3.1, Cav3.2 and Cav3.3, respectively). The amplitudes are shown for the first 30 APs for Cav3.1–3.3 (Ca–c). D, the data from Ca–c is replotted on a time x-axis. For the sake of comparison, the onset of inactivation during a continuous depolarization as depicted in Fig 1 is superimposed as a red dashed line. Error bars represent S.E.M.
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The relationship between the recovery time constants fast and slow and the duration of the preceding depolarization (tpre) was fitted by a power law function of the following form:
(5)
where a is a constant kinetic setpoint, and b is a scaling power. Data were fit using a Levenberg Marquard algorithm (Origin, Microcal, Northhampton, USA).
All results are shown as the means ±S.E.M. Statistical comparison was carried out with a two-tailed Student's t test or ANOVA where appropriate. Results of ANOVA are given as Fx,y, where x and y correspond to the degrees of freedom between groups and within groups, respectively. Comparison of the goodness of fit for different models was carried out with an F test. This test was used to evaluate whether an improvement in 2 values in a more complex model is greater than the improvement that would be expected by chance. It can thus be used to compare models that differ with respect to their degrees of freedom, and is appropriate in the case of nested models (Horn, 1987). It was carried out by calculating an F ratio, defined in general terms as:
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(6)
where 2null and 2alt are the sum of squares values for the simpler (null hypothesis) and more complex model (alternative hypothesis), respectively. dfnull and dfalt correspond to the degrees of freedom of the two models. F ratios are given as Fx,y, where x and y correspond to dfnull– dfalt, and dfalt, respectively. Subsequently, a P value was determined from the F ratio.
All animal experiments were conducted in accordance with the guidelines of the University of Bonn Animal Care Committee, and were approved by the board of proper use of experimental animals of the state Nordrhein-Westfalen.
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Results
The steady-state voltage dependence of the cloned T-type Ca2+ channels was consistent with previously published data (see supplemental Fig. S1). Importantly, all Cav3 subunits displayed a steep voltage-dependent inactivation at voltages within the range of the resting membrane potential (see supplemental Fig. S1E, and Table 1). This common feature of T-type Ca2+ channels subunits renders their availability exquisitely sensitive to changes in membrane voltage. In addition to membrane voltage per se, T-type Ca2+ channel availability over time will also depend critically on the time course with which these channels first inactivate during membrane depolarizations, and subsequently recover from inactivation during repolarization of the neuronal membrane.
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The time course of recovery from inactivation is strongly dependent on the duration of the preceding membrane depolarization
We therefore first examined the onset of inactivation during conditioning voltage steps to –55 mV of varying duration (1 ms to 32 s, see Fig. 1A; representative experiments for Cav3.1–3.3 in Fig. 1B). During conditioning steps within this voltage range, Ca2+ channels undergo predominant closed state inactivation, i.e. they inactivate without having previously opened. The onset of inactivation for Cav3 channels followed a biexponential time course, with one time constant in the range of 300–700 ms and a second time constant in the range of 3–7 s (Fig. 1C; see Table 1 for values).
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We then determined whether the time course of recovery from inactivation is altered when the duration of a prior conditioning depolarization is varied (tpre: 0.3–300 s, –55 mV for Cav3.1 and Cav3.2, –65 mV for Cav3.3 subunits because prepulse facilitation was already observed at –55 mV). The time course of subsequent recovery from inactivation of the three cloned subunits was investigated by systematically varying the interval (t) between the conditioning depolarization and a test pulse to –25 mV (Fig. 2A). It was immediately apparent that the recovery process was significantly slower following more prolonged conditioning depolarizations (compare tpre of 1 and 300 s, Fig. 2Ba–c). The time course of recovery was well described with a biexponential equation for all three T-type subunits (Fig. 2Ca–c), with a fast time constant fast in the range of hundreds of milliseconds and a slower time constant slow in the range of seconds. Fitting datasets simultaneously with a monoexponential equation produced worse fits (F7,47= 8.29, P < 0.0001; F7,47= 24.51, P < 0.0001; and F7,47= 3.88, P= 0.0021; for Cav3.1, Cav3.2 and Cav3.3, respectively).
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The magnitude of both fast and slow proved to be quantitatively related to the duration of the conditioning depolarization tpre (Fig. 2Da–c, triangles and squares correspond to fast and slow, respectively). The relationship between these parameters could be fit with a power law relation of the form (tpre) =a(tpre/a)b, where a is a constant kinetic setpoint and b is a scaling power (fits superimposed on datapoints in Fig. 2Da–c, see Table 2 for values). This relationship translates to a dramatic and highly significant increase in the magnitude of recovery time constants over the range of prepulse durations examined (P < 0.001, ANOVA; for detailed information on significance see Fig. 2 legend). For instance, fast displayed a 2.4-, 3.5- and 4.9-fold change for Cav3.1–Cav3.3 channels, respectively. Similarly, slow was augmented 5.6-, 5.1- and 8.3-fold for Cav3.1–Cav3.3 channels, respectively.
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In these experiments, the slowing of recovery rates was not due to a change in the proportion of channels recovering with fastversusslow. If we compared the fraction of inactivated channels recovering with slow after brief (0.3 s) and prolonged (300 s) prepulses, this fraction was unchanged or even decreased with more prolonged prepulses (Cav3.1: 0.498 compared with 0.388, P < 0.05; Cav3.2: not significant; Cav3.3: 0.474 compared with 0.225, P < 0.05). It is of note that one published study did not observe a slowing of recovery rates for the Cav3.1 channel when two different conditioning prepulse durations were tested. Instead, an increase in the relative proportion of slowly recovering channels was assumed (Hering et al. 2004), whereas we did not find a consistent change in this proportion. We therefore formally examined the quality of fitting with these two models. To this end, we have simultaneously fitted full datasets (all recovery intervals, prepulse durations of 1–300 s) with a simultaneous fitting procedure, separately for each Cav3 subunit. We have compared two models. Firstly, we have fitted with the amplitudes of fast and slow components free to differ for each prepulse duration, but the time constants fast and slow constrained to be the same (see supplemental Fig. S2 – fits to averaged datapoints are shown for all three subunits and two prepulse durations of 3 and 300 s, superimposed on datapoints as red dashed lines). Secondly, we have fitted with the amplitudes of fast and slow components constrained to be the same, but the time constants free to differ for different prepulse durations (supplemental Fig. S2, black lines, panels Aa–c, Ba–c). Fits obtained with varying the time constants fast and slow, but not the amplitudes, were better than those obtained with the converse model. We compared the quality of fit with both models with an F test. This yielded F ratios of F5,47= 2.53, F5,47= 12.39 and F5,47= 2.53, and P values of 0.0418, 0.0001 and 0.0418, for Cav3.1, Cav3.2 and Cav3.3, respectively. Thus, a model with the time constants fast and slow free to vary for different prepulse durations is significantly better for all three subunits. It should be noted that this difference was most apparent for Cav3.2, less so for Cav3.1 and Cav3.3. It is therefore perhaps not surprising that Hering et al. (2004) obtained reasonable fitting results with a variation of the amplitudes, and thought this model to be most appropriate in the absence of a formal comparison between models. Additionally, there could be a potentially large impact of differences in recording conditions (for instance predominantly Na+ instead of K+ in the intracellular solution, as opposed to 20 mM in our study, and differing intracellular free-Ca2+ concentrations).
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We also used simultaneous fitting of full datasets (all recovery intervals, prepulse durations of 1–300 s) to evaluate whether recovery can be fit with the sum of three exponential equations, with the slowing of recovery attributed to changes in the amplitude contributions of these three components. We accordingly fit the dataset with a triexponential equation, with time constants constrained to be the same for all prepulse durations. We compared this model to the biexponential model with the amplitude contributions of the two components constrained to be the same for all prepulse durations. For Cav3.1 and Cav3.2, these determinations showed that 2 values increased when fitting with the triexponential models, despite the decrease in the degrees of freedom, resulting in negative F ratios. For Cav3.3, an F ratio of F2,45= 1.0, P= 0.38 was obtained. This is also apparent from supplemental Fig. S2, in which triexponential fits (dashed blue lines, panels Aa–c, Ba–c) did not approximate the data as well as a biexponential model with time constants constants fast and slow free to vary. These results indicate that slowing of recovery from inactivation can be best explained by a model in which time constants vary with prepulse duration.
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We also investigated scaling following conditioning prepulses to more depolarized potentials (to –25 mV, tpre ranging from 0.1 to 300 s, see supplemental Fig. S3A). Cav3.1 and 3.2 subunits exhibited powerful scaling of recovery rates similar to that observed in Fig. 2B–D (supplemental Fig. S3Ba and b, and Table 2, see also Fig. S3C–E for systematic variation of prepulse voltage). As above, the slowing of recovery from inactivation was not due to an enhanced amplitude contribution of slow (relative fraction of channels recovering with slow, Cav3.1: 0.452 compared with 0.536, P < 0.05; Cav3.2: not significant; prepulse durations of 0.3 and 300 s, respectively). Analogous to the analysis described above for recovery following subthreshold prepulses, we tested formally whether variation of constants fast and slow account best for slowing of recovery. Indeed, the data were approximated significantly better with the amplitudes of the fast and slow component constrained to be the same, and the time constants fast and slow free to differ for different prepulse durations than vice versa (F5,47= 2.66, P= 0.0337; and F5,47= 6.74, P < 0.0001; for Cav3.1 and Cav3.2, respectively).
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For Cav3.3, recovery from inactivation was distorted by a pronounced prepulse facilitation as previously described for the LT9 isoform of Cav3.3 used in this study (Gomora et al. 2002), and therefore this subunit was not further examined (not shown).
We next tested whether T-type Ca2+ channels in native neurones exhibit scaling relationships similar to T-type channels in expression systems. Thalamic relay neurones express a large T-type current that is most probably mediated by Cav3.1 subunits (Talley et al. 1999; Kim et al. 2001). We therefore isolated thalamic relay neurones from the LGN (see Methods) and examined recovery from inactivation following different conditioning prepulses (1, 10, 30 and 100 s, –70 mV, Fig. 3A). In order to avoid contamination by high-threshold Ca2+ currents, test pulses were applied to –45 mV (see Fig. 3A). This resulted in a Ca2+ current mediated mainly by T-type Ca2+ channels, as evidenced by the nearly complete inactivation of the Ca2+ current during a 100 ms test pulse (see Fig. 3B, leftmost traces). The recovery from inactivation of T-type currents in LGN neurones was also well described by a biexponential function. Similar to Cav3 subunits, a pronounced and highly significant slowing of recovery rates was also observed for T-type channels in LGN neurones with increasing prepulse durations (exemplary traces for tpre of 1 and 100 s depicted in Fig. 3B, see also Fig. 3C, F43,4= 13.01, P < 0.001; and F43,4= 11.60, P < 0.001; for fast and slow, respectively, ANOVA). This slowing of recovery rates manifested as a 1.88-fold increase in the magnitude of fast and a 6.50-fold increase in slow when tpre was increased from 1 to 100 s (Fig. 3D, parameters of the power law function describing scaling of native T-type currents are given in Table 2). Interestingly, the range of recovery rates exhibited by T-type currents in LGN neurones was consistent with those observed for Cav3.1 subunits (see Fig. 2Da). As for the Cav3 subunits, we carried out an F test for formal comparison of the quality of fit for the two biexponential models in which either time constants or amplitude contributions were constrained to be the same for different prepulse durations. As for cloned Cav3 subunits, varying the magnitude of the time constants with increasing prepulse durations turned out to provide the best fit (F5,7= 14.10, P= 0.0015). It should be noted that the fits of the recovery from inactivation in native cells rely on less datapoints than those performed in expression systems, due to the difficulty in obtaining stable very long-term recordings from these cells. We should therefore add a cautionary note that the absolute values of the time constants may be subject to some experimental error. Nevertheless, the data show that in principle, scaling is likely to exist also in native neurones.
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A and B, the dependence of recovery rates on prepulse duration was examined with a voltage protocol similar to that described in Fig. 2A. The leftmost traces in B correspond to currents elicited by brief (100 ms) voltage steps to –45 mV following complete recovery of the current amplitude. Because long-term recordings >1 h were difficult to carry out in native lateral geniculate nucleus (LGN) neurones, the number of different t intervals was reduced. Likewise, experiments with 300 s prepulses could not be carried out. C, nonetheless, pronounced slowing of both fast (F4,43= 13.01, P < 0.001) and slow (F4,43= 11.60, P < 0.001) was observed when tpre was prolonged (C). D, relationship of fast and slow to the duration of conditioning prepulses tpre (n= 8–10 for each data point). Error bars represent S.E.M.
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Taken together, these data indicate that the recovery rates of both cloned T-type channel subunits and native T-type channels are strongly modulated by the duration of a subthreshold conditioning depolarization. This phenomenon is likely to be physiologically relevant because it is also invoked following predominant closed state inactivation which occurs close to the resting membrane potential of neuronal cells. Intriguingly, all three T-type Ca2+ channels exhibited overlapping but complementary ranges of fast and slow, covering an extensive range of recovery rates (See Table 2, and compare Fig. 2Da–c).
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Scaling of recovery rates is abolished by superimposing mock action potentials on conditioning depolarizations
The complex behaviour of T-type channels described so far provides a mechanism that conserves a trace of prior membrane potential as a modulated recovery rate of T-type Ca2+ channels. We next tested whether the presence of APs superimposed on continuous depolarizations could modify scaling relationships. To this end, we used conditioning trains in which mock APs (linear upstroke and downstroke of 1 and 2 ms, respectively, to +25 mV) were superimposed on a continuous depolarization to –55 mV (Fig. 4A, frequencies of mock APs ranging from 3 to 100 Hz). This conditioning stimulation caused a potent inactivation of Cav3.1–3.3 channels during the first 30 mock APs (Fig. 4Ba–c, duration of the upstroke and downstroke of mock APs indicated by hatched and open bars; 1st, 3rd, 10th, 30th and 100th mock AP currents during a 30 Hz train are shown). The time course of Ca2+ peak currents invoked by mock APs during such combined trains is depicted in Fig. 4Ca–c. Notably, Cav3.3 channels displayed a pronounced facilitation during the first mock APs at higher stimulation frequencies (100 Hz), similar to previous reports (Kozlov et al. 1999), and thereafter inactivated (Fig. 4Cc). The amount of inactivation reached steady-state within 100 mock APs for all three subunits. In order to compare the inactivation during combined trains to the amount of inactivation induced by conditioning depolarizations to –55 mV alone, we replotted data in Fig. 4Ca–c on a time x-axis and superimposed the onset of inactivation depicted in Fig. 1 as a dashed red line (Fig. 4Da–c).
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We next examined recovery of Cav3.1-Cav3.3 channels following inactivation by combined conditioning trains (mock APs at 30 Hz superimposed on a depolarization to –55 mV) using double-pulse experiments (Fig. 5A). The results of these experiments are shown in Fig. 5Ba–c. For Cav3.1 channels, combined conditioning pulses caused a slowing of the recovery over the whole range of prepulse durations for both fast and slow (Fig. 5Ba). However, both time constants still exhibited pronounced scaling with increasing tpre (P < 0.001, ANOVA; for further fit parameters see figure legend). Surprisingly, superimposing APs on continuous prepulses had a completely different effect in Cav3.2 and Cav3.3 channels. Here, scaling relationships were largely abolished by addition of APs (Fig. 5Bb and c). This effect became even clearer when fast and slow were plotted versus the duration of the conditioning train (Fig. 5C, black datapoints and lines). The experiments with continuous conditioning depolarizations are shown for the sake of comparison (red datapoints and dashed lines, data taken from Fig. 2Da–c).
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A, the conditioning train consisted of mock APs (upstroke 1 ms, downstroke 2 ms, to +25 mV, at 30 Hz) superimposed on a continuous depolarization to –55 mV. The duration of this conditioning train ranged from 0.3 to 100 s. As in Fig. 2, the recovery interval t until a subsequent test pulse to –25 mV was varied to examine the time course of recovery. B, Cav3.1 still exhibited slowing of recovery rates with more prolonged tpre (Ba, n= 8–11). In contrast, scaling appeared to be abolished for Cav3.2 and 3.3 subunits (Bb and c, n= 6–8 and n= 5–7, respectively). Note that the fraction of Cav3.3 inactivated at short t is smaller that that shown in Fig. 4. This difference arises because availability of Cav3.3 channels was measured with mock APs applied from depolarized (–55 mV) potentials in Fig. 4, whereas even the leftmost datapoints in Bc refer to experiments with a brief recovery interval t at –95 mV. C, relation of tpre to fast and slow. Significant scaling is still observed for Cav3.1 subunits (black symbols, continuous lines, F3,30= 10.09, P < 0.001, and F3,30= 14.30, P < 0.001, for fast and slow, respectively), but recovery is slowed compared with continuous conditioning depolarizations alone (Ca, red dashed lines and red squares show the data from Fig. 2 for comparison in Ca–c). For Cav3.2, scaling was powerfully reduced by superimposing APs, even though changes in fast with increasing tpre were still significant (Cb, F3,25= 7.074, P < 0.005, and F3,25= 0.34, n.s., for fast and slow, respectively). No significant scaling for either fast or slow was observed for Cav3.3 subunits (Cc). Error bars represent S.E.M.
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Scaling is not observed following mock AP trains from hyperpolarized membrane potentials
These experiments raised the question of whether inactivation of Ca2+ channels by APs also invokes scaling of recovery rates. Cav3.1 and 3.2 channels undergo powerful cumulative inactivation during trains of AP waveforms applied from hyperpolarized holding potentials (Fig. 6A; see Kozlov et al. 1999). This phenomenon is depicted in Fig. 6Ba and b (1st, 3rd, 10th, 30th and 100th mock AP currents during a 30 Hz train are shown, duration of the upstroke and downstroke of mock APs is indicated by hatched and open bars). Cumulative inactivation of Cav3.1 and Cav3.2 during mock AP trains from –95 mV saturated during the first 30–40 mock APs (Fig. 6Ca and b, respectively). The inactivation obtained at the end of a conditioning train consisting of 100 mock APs at different frequencies is depicted in Fig. 6D. As expected, higher frequencies resulted in an increasing fraction of inactivated channels at the end of the conditioning train for Cav3.1 and Cav3.2 subunits. It is also apparent from Fig. 6Bc and D that Cav3.3 subunits did not display strong inactivation during such conditioning trains, as previously described. This is most probably due to the slow kinetics of activation and the fast deactivation of this subunit. These properties cause Cav3.3 channels to be inefficiently opened by short depolarizations, and induce them to preferentially deactivate after opening (instead of inactivating, see also Kozlov et al. 1999). As a consequence of this behaviour, we were not able to further investigate recovery of Cav3.3 channels following such conditioning trains. It should be noted that we did not observe facilitation of Cav3.3 channels during spike trains as in Fig. 4Cc, most probably due to the more hyperpolarized interspike voltage.
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For Cav3.1 and 3.2 channels, we were then able to examine recovery from inactivation following trains of AP-like waveforms of varying frequencies (1–100 Hz, tpre 30 s) or durations (30 Hz, tpre 0.1–100 s, see Fig. 7A). Following these trains, the proportion of channels recovering with slow was <10% in many cases. As a consequence, the behaviour of slow when varying the duration or frequency of prior AP trains could not be quantified. However, fast could be determined with the different conditioning protocols. When the duration of a conditioning train of mock APs (30 Hz) was systematically varied from 0.1 to 100 s (30 Hz, see Fig. 7A), fast was not significantly affected (Cav3.1 and Cav3.2 shown in Fig. 7Ba and b, respectively, ANOVA, n.s.). Similarly, altering the frequency of a 30 s conditioning train (from 1 to 100 Hz) caused no appreciable change in fast (Fig. 7Ca and b, ANOVA, n.s.). These results indicate that, even though AP trains cause inactivation of Cav3.1 and Cav3.2 channels, recovery from inactivation is not altered by changing the frequency or duration of the train.
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Since Cav3.3 did not undergo strong inactivation during mock AP trains elicited from hyperpolarized potentials, this subunit was not investigated further. A, mock AP trains used to induce inactivation of Cav3 channels. Both the duration and the frequency of the conditioning train were systematically varied. Test pulses to –25 mV were applied following various recovery times (t). B, influence of changing the duration of a conditioning train of mock APs (30 Hz) from 0.1 to 100 s on the rate of recovery from inactivation (Cav3.1 and 3.2 shown in Ba and c, n= 8–12 and n= 5–9, respectively). For both Cav3.1 (Ba) and Cav3.2 (Bb), the contribution of the slow time constant slow to the recovery process was small (<10%) following mock AP trains. Therefore, only fast is shown in Ba and b, and Ca and b. The change in fast with different prepulse durations tpre was not significant for Cav3.1 (F4,43= 2.08, n.s.) and Cav3.2 (F4,34= 0.35, n.s.). C, equivalent experiments to those in B, but with a systematic variation of the frequency of a 30 s conditioning train from 1 to 100 Hz. No scaling is observed for either Cav3.1 (F4,51= 1.31, n.s., n= 9–13) or Cav3.2 (F4,32= 0.78, n.s., n= 6–9). Error bars represent S.E.M.
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The scaling of recovery rates for different types of conditioning stimuli is summarized in Fig. 8 for Cav3.1–3.3 channels. For the sake of clarity, the three conditioning stimuli are depicted in Fig. 8A (black squares, continuous depolarization only; white squares, mock APs superimposed on continuous depolarizations; red cross-hatched squares, mock APs only). In order to summarize the data, scaling of recovery rates is expressed more simply as the fold increase in over a range of prepulse durations (0.3–100 s). Clearly, continuous depolarizations have dramatic effects on fast and slow for all three channel subtypes (black bars), as described in Fig. 2. Superimposing APs on conditioning depolarizations only slightly affects scaling in Cav3.1 (Fig. 8Ba), but dramatically reduces or even completely abolishes it in Cav3.2 and Cav3.3 channels (Fig. 8Bb and c, respectively, open bars). Application of conditioning trains consisting only of mock APs did not induce significant scaling of recovery rates (Fig. 8Ba and c, red cross-hatched bars; significance of ANOVA over the range of tpre examined is indicated by asterisks in Fig. 8Ba–c). In summary, these results indicate that AP firing and subthreshold membrane depolarizations have very different consequences for subsequent availability of specific T-type Ca2+ channel subunits (summarized in Fig. 8C, ‘+’ and ‘–’ indicate presence and absence of significant scaling, respectively. n.i., not investigated).
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A, summary of the different types of conditioning stimuli used to induce inactivation of Cav3 channels: continuous depolarizations (to –55 mV) of different durations (uppermost voltage protocol, identical to those used in Fig. 2A, filled squares), 30 Hz AP trains superimposed on continuous depolarizations (–55 mV, –65 mV for Cav3.3 subunits, middle voltage protocol, identical to those used in Fig. 5A, open squares), 30 Hz AP trains of different durations directly from hyperpolarized membrane potentials (– 95 mV, lowermost voltage protocol, as depicted in Fig. 7A, hatched squares). Ba–c, summary of the fold increase in fast and slow over the range of prepulse durations examined (0.3–100 s). Continuous depolarizations have dramatic effects on fast and slow for all three channel subtypes (filled bars, see also Fig. 2; single asterisk, P < 0.005; two asterisks, P < 0.001; throughout the figure). Superimposing APs on conditioning depolarizations only slightly affects scaling in Cav3.1 (open bars, Ba), but strongly reduces or completely abolishes it in Cav3.2 and Cav3.3 channels (open bars, Bb and c, respectively). AP trains applied directly from hyperpolarized membrane potentials do not induce significant scaling.
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Discussion
In addition to activity-dependent facilitation or depression of synaptic input, temporal integration in neurones is also powerfully influenced by the availability of voltage-gated ion channels in the somatodendritic neuronal membrane. In the present study, we show that the availability of both native and cloned T-type channels is powerfully modulated by the duration and the nature of a preceding inactivating stimulus.
, http://www.100md.com Recovery rates of T-type channels reflect the duration of prior depolarizations
Our first finding was that the rate constants with which channels recover from inactivation are steeply dependent on the duration of the preceding conditioning depolarization. Intriguingly, Ca2+ channels exhibited this scaling of recovery rates following subthreshold conditioning depolarizations, suggesting that this mechanism is likely to be invoked under physiological conditions by subtle depolarizations from resting membrane potential. This is unlike the behaviour of voltage-gated Na+ channels, which exhibit scaling only following strong depolarizations or prolonged high-frequency AP trains (Toib et al. 1998; Ellerkmann et al. 2001). Nevertheless, the power law function describing scaling revealed roughly similar scaling power for voltage-gated Na+ and Ca2+ channels (Toib et al. 1998; Ellerkmann et al. 2001). This finding has the intriguing consequence that neurones retain a trace of slow subthreshold membrane depolarizations, encoded as a modulated recovery rate of T-type Ca2+ channels.
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Our findings suggest that it is the slowing of recovery rates that accounts for the slowing of the recovery from inactivation. Could an increase in the relative amplitude of the component recovering with slow also adequately describe slowing of the recovery process, as suggested by Hering et al. (2004) for Cav3.1 We believe that this is not the case. We carried out a comparison of these two models, first fitting the recovery time course with the relative amplitude contribution of slow kept constant, and then with the time constants fast and slow kept constant. We first fit the recovery time course following long (300 s) prepulses, and extracted time constants and the corresponding amplitude contributions from these fits (described in detail in Results). For all three subunits, variation of the time constants produced a significantly better fit. The reason for the discrepancy to the interpretation of Hering et al. (2004) is unclear, even though this group appears not to have compared the two models in a quantitative manner. It could be due to the large differences in recording conditions (i.e. composition of the intracellular solution), if so, this would be a potentially interesting issue for further investigation.
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T-type channels selectively encode action potential firing and subthreshold depolarizations
A particularly fascinating property of T-type channels emerged when inactivation was induced with different types of mock AP trains. The powerful scaling of Cav3.2 and Cav3.3 channels following continuous subthreshold depolarizations was mostly or even completely abolished if mock APs were superimposed on the conditioning depolarization. This appears not to be true for Cav3.1 channels: scaling was observed regardless of whether slow inactivation was induced with or without superimposed mock APs. The key findings regarding scaling of Cav3 channels are summarized in a qualitative manner in Fig. 8C. These results have two major implications. First, in addition to the undoubted differences between individual Cav3 subunits regarding fast gating properties (Kozlov et al. 1999; Klckner et al. 1999), clear differences in slow recovery and scaling have also emerged. Intriguingly, the range of recovery rates was overlapping but complementary for all three channel subunits (compare Fig. 2Da–c), allowing the generation of T-type currents displaying diverse scaling properties in native neurones. This is particularly interesting in view of the distinctive expression pattern of Cav3 subunits in the CNS (Talley et al. 1999). A second major implication of our experiments is that availability of T-type channels is differentially modulated on a time scale of many seconds, depending on whether the neurone has previously encountered subthreshold depolarizations, AP firing or both (see Fig. 8B and C). Because the availability of T-type Ca2+ channels is a crucial determinant of neuronal firing (reviewed in Huguenard, 1996; Perez-Reyes, 2003), such properties may constitute an important mechanism for short-term plasticity of intrinsic membrane properties.
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How can scaling be interpreted biophysically In principle, both Markovian and fractal models have been used to describe ion channel behaviour (for discussion of the relation between these types of models see Liebovitch, 1989; Bassingthwaighte et al. 1994; Toib et al. 1998). As put forward in Toib et al. (1998), one way in which the occurrence of scaling relationships may be explained is by collapsing a complex Markovian scheme into a single scaled effective rate. This notion is illustrated by the following kinetic scheme:
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(Scheme 1)
where R denotes the resting state of the channel, and I1–In are pools of linearly interlinked inactivated states. In this model, more prolonged depolarization would cause channels to accumulate in more remote inactivated states. As a consequence, recovery rates become slower, because recovery from remote inactivated states requires a transition through a higher number of intermediate inactivated states. Indeed, such one-dimensional diffusion models can give rise to power law relationships (Millhauser et al. 1988).
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In the case of Na+ channels, two types of inactivation processes can be clearly discriminated. A fast inactivation mechanism does not display scaling, whereas much slower inactivation mechanisms show powerful scaling (Toib et al. 1998). Accordingly, it has been argued that fast and slow inactivation relies on distinct molecular processes. This is supported by several additional lines of evidence. Firstly, selective pharmacological effects on slow, but not fast recovery from inactivation have been demonstrated (Remy et al. 2004). Additionally, whereas the structural correlate of fast Na+ channel inactivation has been clearly identified (Stühmer et al. 1989; West et al. 1992), the structural basis of slow inactivation is most probably complex (Cummins & Sigworth, 1996; Hayward et al. 1997; Melamed-Frank & Marom, 1999; Mitrovic et al. 2000; Alekov et al. 2001; Vilin & Ruben, 2001).
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Could there also be two different types of inactivation that coexist for T-type channels In contrast to Na+ channels, not much is known regarding the molecular basis of T-type Ca2+ channel inactivation that would allow us to structurally separate two mechanisms. Nevertheless, upon closer inspection of Fig. S3, it appears as if fast and slow do not scale for a range of prepulse durations, and then start scaling for prepulse durations >1 s. This could imply that there are inactivation mechanisms corresponding to the classical scheme (no scaling, Frazier et al. 2001). The second (scaling) mechanism could be accessed from closed states during prolonged depolarizations. This mechanism may involve inactivation via linearly coupled inactivated states (as depicted in Scheme 1), thereby giving rise to scaling relationships. For brief prepulses, the rate constants for scaling and nonscaling inactivation might be in the same range. As prepulses are prolonged, inactivation processes showing scaling would become slower, dominating the macroscopic recovery rates. This concept would explain why scaling emerges when continuous conditioning pulses are prolonged. Likewise, the lack of scaling seen following action potential trains is most probably due to the fact that slow inactivation requires prolonged depolarization, and is thus not invoked by trains of brief depolarizations.
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The assumption of distinct scaling and nonscaling inactivation mechanisms alone, however, does not explain why superimposing APs on continuous depolarizations almost completely abolishes scaling, at least for the Cav3.2 and Cav3.3 subunits. The most parsimonious explanation for this finding is that the classical, nonscaling inactivation mechanism (as induced by superimposing mock APs) inhibits the scaling inactivation process. In this scenario, superimposing APs on continuous depolarizations would cause powerful cumulative inactivation via the open state, which would not take place in the absence of mock APs. In this case, inactivation via the scaling mechanism would be impaired, and the recovery time course would be less affected by varying the duration of the conditioning train. The existence of such a mechanism would imply that interactions between two gating mechanisms are highly relevant for Cav3.2 and Cav3.3 channels, but perhaps less so for Cav3.1 channels. Indeed, an interaction between fast (nonscaling) and slow (scaling) inactivation is observed for some voltage-gated Na+ channels. Firstly, introduction of mutations or intracellular application of proteolytic enzymes which completely remove fast gating strongly affect slow inactivation processes (Valenzuela & Bennett, 1994; Featherstone et al. 1996; Kontis & Goldin, 1997; Hilber et al. 2002). Conversely, manipulations that stabilize fast inactivation inhibit entry into slow inactivation (Hilber et al. 2002). The idea that different gating mechanisms interact is also in line with the observation that the amplitude contributions of fast, intermediate and slow inactivating Na+ channel components appear to change in a highly hierarchical manner when conditioning prepulses are prolonged (Toib et al. 1998; Hayward et al. 1997).
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Functional implications of T-type channel scaling
Regardless of the mechanisms involved, the complex properties of T-type channels we describe have obvious consequences for the regulation of channel availability by prior activity. T-type Ca2+ channels are crucial in mediating Ca2+-dependent burst responses that are prominent in subsets of neurones from various brain regions including the cerebellum, thalamus and brain stem (Huguenard, 1996). In thalamic neurones, the T-type Ca2+ channel plays a key role in the phase-locked firing of thalamic neurones during both seizures and spindle oscillations, which occur normally during slow-wave sleep. During both types of oscillations, thalamic relay neurones are hyperpolarized by rhythmic inhibitory postsynaptic potentials, which deinactivate the T current, sometimes resulting in rebound bursts. Scaling of T-type channels that we also demonstrated in native LGN neurones is likely to modulate this phenomenon. Scaling of T-type channels may also be important in other neurones, or even neuronal subcompartments. For instance, T-type Ca2+ channels are highly expressed in dendrites, where they powerfully modulate the propagation of synaptic potentials from distal dendrites to the soma (Christie et al. 1995; Magee & Johnston, 1995; Magee et al. 1995). Dendritic Ca2+ electrogenesis may therefore also be powerfully modulated by intrinsic properties of T-type Ca2+ channels. It should also be noted that scaling phenomena may become particularly relevant during epileptic seizures, in which long-lasting depolarizations in conjunction with high-frequency firing occur. It will also be important to consider the behaviour of T-type channels in concert with other nonscaling channels, such as certain A-type K+ channels (Toib et al. 1998). Clearly, the recovery rates of both types of channels profoundly affect the balance in the availability of these channels over time after repolarization. Changing the recovery rates of T-type, but not A-type channels, may therefore strongly impact the relative availability of both channel types following membrane repolarization.
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Supplemental material
The online version of this paper can be accessed at:
DOI: 10.1113/jphysiol.2005.103614
http://jp.physoc.org/cgi/content/full/jphysiol.2005.103614/DC1
and contains supplemental material consisting of three figures:
Supplemental Figure S1. Voltage-dependent activation and inactivation of cloned T-type channels.
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Supplemental Figure S2. Comparison of different models to approximate the recovery time course of T-type channels.
Supplemental Figure S3. Recovery from inactivation of T-type channels following conditioning prepulses to depolarized voltages.
This material can also be found as part of the full-text HTML version available from http://www.blackwell-synergy.com
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2 Department of Pharmacology, University of Virginia, Charlottesville, VA 22908, USA
Abstract
T-type Ca2+ channels give rise to low-threshold inward currents that are central determinants of neuronal excitability. The availability of T-type Ca2+ channels is strongly influenced by voltage-dependent inactivation and recovery from inactivation. Here, we show that native and cloned T-type Ca2+ channel subunits selectively encode specific aspects of prior membrane potential changes via a powerful modulation of the rates with which these channels recover from inactivation. Increasing the duration of subthreshold (–70 to –55 mV) conditioning depolarizations caused a pronounced slowing of subsequent recovery from inactivation of both cloned (Cav3.1–3.3) and native T-type channels (thalamic neurones). The scaling of recovery rates with increasing duration of conditioning depolarizations could be well described by a power law function. Different T-type channel isoforms exhibited overlapping but complementary ranges of recovery rates. Intriguingly, scaling of recovery rates was dramatically reduced in Cav3.2 and Cav3.3, but not Cav3.1 subunits, when mock action potentials were superimposed on conditioning depolarizations. Our results suggest that different T-type channel subunits exhibit dramatic differences in scaling relationships, in addition to well-described differences in other biophysical properties. Furthermore, the availability of T-type channels is powerfully modulated over time, depending on the patterns of prior activity that these channels have encountered. These data provide a novel mechanism for cellular short-term plasticity on the millisecond to second time scale that relies on biophysical properties of specific T-type Ca2+ channel subunits.
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Introduction
T-type Ca2+ currents are central determinants of neuronal excitability that are present in the somatodendritic compartment of many types of neurones (Carbone & Lux, 1984; Talley et al. 1999). Genetic and pharmacological inhibition of T-type Ca2+ currents has demonstrated the importance of these currents in various sensory systems, ranging from pain perception and hyperalgesia (Kim et al. 2003; Ikeda et al. 2003), mechanoreceptor function (Shin et al. 2003), to olfaction (Kawai & Miyachi, 2001), as well as the maintenance of sleep states (Anderson et al. 2005). On a cellular level, T-type currents are essential for the generation of burst discharges and the generation of intrinsic rhythms in subsets of CNS neurones (for review see Huguenard, 1996). Furthermore, T-type Ca2+ channels underlie low-threshold Ca2+ spikes that are observed in many types of neurones (Jahnsen & Llinás, 1984a,b; Greene et al. 1986).
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The availability of T-type Ca2+ channels is strongly dependent on membrane voltage, because all known T-type channels display a steep voltage-dependent inactivation in the vicinity of resting membrane potential. As a consequence, bursting neurones expressing T-type Ca2+ channels can switch to a nonbursting regular firing mode when T-type Ca2+ channels are inactivated by subtle depolarizations from resting membrane potential (Kim et al. 2001; Su et al. 2002). However, recovery from inactivation following membrane depolarizations is a dynamic process. As a consequence, the availability of T-type channels over time following repolarization will also critically depend on the rates with which these channel types recover from inactivation. It has been recently appreciated that recovery rates from inactivation of individual voltage-gated membrane channels may vary considerably. In the case of voltage-gated Na+ channels, the recovery rates have been shown to be dependent on the duration of preceding depolarizations, with longer depolarizations giving rise to markedly slower recovery rates (Toib et al. 1998; Ellerkmann et al. 2001). The relationship between the duration of the conditioning depolarization and the recovery rate has been well described by a power law relation. Such scaling relationships (Bassingthwaighte et al. 1994) imply that there is no single characteristic recovery rate, but that the recovery rate reflects the time allowed for inactivation. As a consequence, this mechanism may be considered as a mechanism of short-term plasticity that preserves a trace of certain aspects of prior neuronal activity. Unlike Na+ channels (Toib et al. 1998; Ellerkmann et al. 2001), such a mechanism might already be invoked in T-type Ca2+ channels by subtle depolarizations from the resting membrane potential, and would be expected to critically influence availability of these channels during repolarization.
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In the present study, we have meticulously examined recovery of cloned and native T-type channels following different patterns of activity. Our results suggest that T-type Ca2+ channel subunits differentially encode specific aspects of prior membrane potential changes as modulated recovery rates and provide a novel mechanism for cellular short–term plasticity.
Methods
HEK 293 cells
The generation of stable cell lines expressing human Cav3.1, Cav3.2 and Cav3.3 has been previously described. The following stably transfected HEK 293 cell lines were used in this study: h1G-Q39, containing the human 1G channel, Cav3.1a (GenBank accession no. AF190860; Cribbs et al. 2000); hh8-5, containing the Hh8 plasmid construct of human 1H, Cav3.2a (GenBank accession no. AF051946; Cribbs et al. 1998); and Lt9–8, containing the LT9 plasmid construct of 1I, Cav3.3b (Gomora et al. 2002; GenBank accession no. AF393329). Cells were maintained in Dulbecco's modified Eagle's medium (DMEM) medium (4.5 g l–1 glucose, 584 mg l–1L-glutamine), supplemented with 1 mg ml–1 geneticin, 10% heat-inactivated fetal bovine serum, 100 units ml–1 penicillin and 100 g ml–1 streptomycin.
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Preparation of dissociated neurones from the lateral geniculate nucleus of the thalamus
Male Wistar rats (postnatal day 12–20) were decapitated under deep ether anaesthesia. A block of the brain containing the thalamic nuclei was rapidly removed and placed in oxygenated chilled (–4°C) solution containing (mM): 20 Pipes, 2.4 KCl, 10 MgSO4, 0.5 CaCl2, 10 glucose, 195 sucrose (pH 7.25) (Pipes1). Coronal 500 μm slices containing the lateral geniculate nucleus (LGN) were made with a vibratome (Leica VT1000S, Wetzlar, Germany). The LGN was subsequently dissected under stereoscopic observation in Pipes1 solution (see above). LGN microslices were then placed in an incubation chamber containing a slightly altered Pipes buffered solution (Pipes2; mM): 20 Pipes, 5 KCl, 3 MgCl2, 25 glucose, 120 NaCl and 0.5 CaCl2 (pH 7.35; 100% O2), and gradually warmed to 30°C over a period of 25 min. After warming, trypsin (1 mg ml–1) was added to the Pipes2 solution, and microslices were incubated for 30 min. The enzymic reaction was terminated by washing in enzyme-free Pipes2 solution. After allowing slices to cool to room temperature for 10–30 min, LGN neurones were dissociated by trituration with fire-polished Pasteur pipettes. Only those dissociated cells with a morphology reminiscent of LGN projection neurones were included in this study, as described in detail elsewhere (Pape et al. 1994).
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Patch-clamp recording
Patch-clamp recordings were obtained from 350 HEK cells expressing Cav3 Ca2+ channels, and 33 native LGN neurones. Patch pipettes with a resistance of 3–4 M were fabricated from borosilicate glass capillaries and filled with an intracellular solution containing (mM): 87.5 caesium methanesulphonate, 5 MgCl2, 0.5 CaCl2, 20 tetraethylammonium, 10 Hepes, 5 1,2-bis-(o-aminophenoxy)ethane-N,N,N',N'-tetraacetic acid (BAPTA), 16 sucrose, 10 adenosine 5'-triphosphate (Na+2-ATP), 0.5 guanosine 5'-triphosphate (GTP), and 10 glucose (pH 7.2, 300 mosmol kg–1). Patch-clamp recordings from native LGN neurones and HEK cells were performed in a bath solution containing (mM): 125 sodium methanesulphonate, 3 KCl, 1 MgCl2, 5 CaCl2, 4 4-aminopyridine (4-AP), 20 tetraethylammonium, 10 Hepes, 10 glucose (pH 7.4, 315 mosmol kg–1). Tight-seal whole-cell recordings were obtained at room temperature (21–24°C) according to standard techniques. Membrane currents were recorded using a patch-clamp amplifier (EPC9, HEKA Elektronik, Lambrecht/Pfalz, Germany) and collected online with the Pulse acquisition and analysis program (HEKA Elektronik, Lambrecht/Pfalz, Germany). Series resistance compensation was employed to improve the voltage-clamp control (>80% for HEK cells, >50% for dissociated LGN neurones) so that the maximal residual voltage error did not exceed 1.5 mV (Sigworth et al. 1995). A liquid junction potential of 5 mV was measured between the intra- and extracellular solution, and corrected on-line such that without correction the voltages given in this paper would be 5 mV more positive. Holding potential was –95 and –85 mV for recordings in HEK cells and dissociated LGN neurones, respectively.
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Voltage protocols and data analysis
The voltage dependence of activation and inactivation was characterized using standard protocols (see Supplemental material, Fig. S1A and C, representative current traces in panels B and D). The voltage-dependent activation was fit by the product of a Boltzmann function, reflecting voltage-dependent activation (eqn (1)), and the general constant field equation (eqn (2)).
(1)
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(2)
where ICa(V) denotes the Ca2+ current amplitude, PCa denotes the Ca2+ permeability, [Ca2+]in and [Ca2+]out denote the internal and external Ca2+ concentrations, respectively. V corresponds to the command voltage, V is the voltage of half-maximal inactivation or activation. The PCa for each potential was derived, normalized to the maximal value and averaged (see supplemental Fig. S1E). The voltage dependence of inactivation was derived by converting peak current to PCa and fitting these values with eqn (1).
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The onset of inactivation of T-type Ca2+ currents was described by holding the membrane potential to –55 mV for varying durations (tpre) and a subsequent step to –25 mV (see Fig. 1A). The peak current amplitude elicited (see Fig. 1B) was normalized to the maximal amplitude elicited without a prepulse to –55 mV. The relation between the normalized peak amplitude and the prepulse duration was best fit by a biexponential equation (see Fig. 1C) of the form:
(3)
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where I(tpre) is the current amplitude following a prepulse duration of tpre, A0 is a constant offset, and 1 and 2 are the time constants of inactivation with the corresponding amplitudes A1 and A2, respectively.
A, a hyperpolarizing voltage step was applied to remove inactivation completely (–115 mV, 2 s), followed by a prepulse of variable duration (–55 mV, tpre) to induce inactivation. The fraction of available current was determined with a subsequent 100 ms test pulse (–25 mV). B, representative currents mediated by Cav3.1 (), Cav3.2 () and Cav3.3 subunits (). Currents are progressively reduced with increases in tpre. C, normalized peak amplitude of the Ca2+ currents was plotted versus the duration of the inactivating prepulse (tpre, see C) for all three subunits. Continuous lines superimposed on the data points represent biexponential fits (n= 7, 8 and 8 for Cav3.1, Cav3.3 and Cav3.3, respectively). Error bars represent S.E.M.
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Recovery from inactivation was examined with double-pulse experiments. The first set of experiments addressed recovery of T-type channels following continuous step depolarizations (see, for instance, Fig. 2A). The voltage of these conditioning pulses was varied from –70 to –10 mV (see supplemental Fig. S3A and C) and their duration (tpre) ranged from 0.3 to 300 s (i.e. Fig. 2A). Recovery of T-type Ca2+ channels following these conditioning prepulses was examined by stepping the membrane potential back to –95 mV holding potential for a varying recovery interval (t, 5 ms to 20.5 s) and subsequently applying a brief (100 ms) test pulse to –25 mV. In all experiments, an equivalent normalization test pulse to –25 mV (100 ms) was applied 5 s before each double pulse. To ensure 100% recovery of the current prior to application of the normalization test pulse, an interval was interspersed between individual double pulses and the subsequent normalization pulse that was at least threefold larger than the time required for full recovery of the current amplitudes (–95 mV). Thus, this interval varied depending on the subunit examined and the prepulse duration employed (ranging from 10 to 90 s). Normalization of the recovery data was then carried out with the amplitude of the current elicited during this normalization test pulse. As expected, these protocols revealed a full recovery of T-type current amplitudes following the longest recovery interval (20 s), even for the longest prepulses for which recovery rates were slowest (recovery to 99.7 ± 0.3, 99.2 ± 0.4 and 99.7 ± 0.5% for the Cav3.1, Cav3.2 and Cav3.3 subunits, respectively, following 300 s prepulses).
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A, the duration of conditioning prepulses was systematically varied (tpre 0.3–300 s). Subsequent recovery from inactivation was assessed with a 100 ms test pulse to –25 mV, separated from the conditioning prepulse by a variable interpulse interval (t). B, representative current traces for two different prepulse durations (tpre 1 and 300 s) are depicted for each of the cloned T-type channels (Ba–c correspond to Cav3.1–3.3 as indicated). The leftmost traces correspond to currents elicited by a normalization test pulse to –25 mV (100 ms), which was applied 10 s before each double pulse. To ensure that currents were 100% recovered prior to application of the normalization test pulse, an interval was interspersed between individual double pulses and the subsequent normalization pulse that was at least threefold larger than the time required for full recovery of the current amplitudes (ranging from 10 to 90 s, see Methods). C, recovery time course, currents were normalized to the peak current during the normalization test pulse (leftmost traces in Ba–c. The recovery time course shows a progressive slowing with more prolonged prepulses (tpre 1, 3, 10, 30 and 100 s, indicated by asterisks, triangles, diamonds, squares and circles, respectively). Ca–c correspond to Cav3.1 (n= 8–10), Cav3.2 (n= 5–9) and Cav3.3 (n= 5–11 for each data point), respectively. The time course of recovery for Cav3.1–3.3 was well described with a biexponential equation superimposed on the data points. D, the fast time constant fast (triangles) and a slower time constant slow (squares) are plotted versus the duration of the conditioning depolarization tpre (Cav3.1–3.3 in Da–c, respectively). The relationship between these parameters could be fit with a power law relation of the form (tpre) =a(tpre/a)b (where where a is a constant kinetic setpoint, and b is a scaling power), which is superimposed on the data points (see Table 2 for values). The change in with increasing tpre was highly significant for Cav3.1 (F6,59= 18.88, P < 0.001, and F6,59= 39.69, P < 0.001, for fast and slow, respectively), Cav3.2 (F6,45= 7.15, P < 0.001, and F6,45= 11.17, P < 0.001, for fast and slow, respectively) and Cav3.3 (F6,59= 15.18, P < 0.001, and F6,59= 29.52, P < 0.001, for fast and slow, respectively). Error bars represent S.E.M.
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Similar experiments were carried out with conditioning trains of mock action potentials (APs; i.e. Fig. 6A). Each individual mock AP had a linear upstroke of 1 ms and a linear downstroke of 2 ms duration, with a peak at +25 mV. This corresponds roughly to the range of AP durations observed for developing LGN neurones (White & Sur, 1992). We varied either the duration of AP trains (from 0.1 to 100 s, at a constant frequency of 30 Hz), or their frequency (from 1 to 100 Hz, with a constant duration of 30 s, see Fig. 6A). In some experiments, mock AP trains were superimposed on continuous depolarizing prepulses (to –55 mV) of varying durations (see Fig. 4A). Normalization of the recovery data was carried out as for continuous conditioning stimuli. For a given conditioning stimulus, the total duration of double-pulse protocols ranged from 3 to 75 min. We were concerned that rundown of Ca2+ current amplitudes might contaminate our results. Therefore, we excluded all experiments in which the Ca2+ current amplitudes elicited by the normalization test pulse (see description of double-pulse protocols above) were reduced by more than 20% over 1.5 h of recording. We also excluded experiments in which the input resistance measured in recording solution was <1G, or cells in which a transient change in passive membrane properties was observed. The time constants of recovery fast and slow were extracted by fitting with a biexponential equation of the form:
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(4)
In some cases, fitting was carried out with a monoexponential or a triexponential equation of an identical form for purposes of comparison to biexponential fits.
A, mock AP trains were applied from hyperpolarized (–95 mV) membrane potentials (depolarization to +25 mV, rising and falling phase, 1 and 2 ms, respectively; frequency 0.3–100 Hz). B, cumulative inactivation induced by mock AP trains at 30 Hz for Cav3 subunits. Cav3.1 and 3.2 undergo powerful cumulative inactivation, while inactivation of Cav3.3 by such trains is negligible. Representative current traces elicited by the 1st, 3rd, 10th, 30th and 100th mock AP (applied with 30 Hz) are depicted in Ba–Bc for Cav3.1–3.3, respectively. Rising and falling phases of the mock AP are indicated by hatched and open bars, respectively. As in Fig. 4, the normalized and averaged amplitudes of peak Ca2+ current elicited by the first 30 APs for Cav3.1–3.3 channels are shown (Ca–Cc, n= 7, 10 and 6 for Cav3.1, Cav3.3 and Cav3.3, respectively). The normalized amplitudes during the 91st to 100th mock AP in a train are summarized in D for different mock AP train frequencies. Error bars represent S.E.M.
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A, conditioning trains consisted of concatenated APs (rising and falling phase, 1 and 2 ms, respectively, to a peak voltage of +25 mV, rising and falling phase indicated by hatched and open bar, respectively, in Ba–c) at various frequencies (3–100 Hz), superimposed on the conditioning depolarization to –55 mV. B, representative current traces elicited by the 1st, 3rd, 10th, 30th and 100th mock AP of a train of 30 Hz are depicted in Ba–c for Cav3.1–3.3, respectively. C, the peak amplitudes of the inward current were normalized to the peak amplitudes during the first mock action potential. The normalized and averaged (n= 5, 5 and 6 for Cav3.1, Cav3.2 and Cav3.3, respectively). The amplitudes are shown for the first 30 APs for Cav3.1–3.3 (Ca–c). D, the data from Ca–c is replotted on a time x-axis. For the sake of comparison, the onset of inactivation during a continuous depolarization as depicted in Fig 1 is superimposed as a red dashed line. Error bars represent S.E.M.
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The relationship between the recovery time constants fast and slow and the duration of the preceding depolarization (tpre) was fitted by a power law function of the following form:
(5)
where a is a constant kinetic setpoint, and b is a scaling power. Data were fit using a Levenberg Marquard algorithm (Origin, Microcal, Northhampton, USA).
All results are shown as the means ±S.E.M. Statistical comparison was carried out with a two-tailed Student's t test or ANOVA where appropriate. Results of ANOVA are given as Fx,y, where x and y correspond to the degrees of freedom between groups and within groups, respectively. Comparison of the goodness of fit for different models was carried out with an F test. This test was used to evaluate whether an improvement in 2 values in a more complex model is greater than the improvement that would be expected by chance. It can thus be used to compare models that differ with respect to their degrees of freedom, and is appropriate in the case of nested models (Horn, 1987). It was carried out by calculating an F ratio, defined in general terms as:
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(6)
where 2null and 2alt are the sum of squares values for the simpler (null hypothesis) and more complex model (alternative hypothesis), respectively. dfnull and dfalt correspond to the degrees of freedom of the two models. F ratios are given as Fx,y, where x and y correspond to dfnull– dfalt, and dfalt, respectively. Subsequently, a P value was determined from the F ratio.
All animal experiments were conducted in accordance with the guidelines of the University of Bonn Animal Care Committee, and were approved by the board of proper use of experimental animals of the state Nordrhein-Westfalen.
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Results
The steady-state voltage dependence of the cloned T-type Ca2+ channels was consistent with previously published data (see supplemental Fig. S1). Importantly, all Cav3 subunits displayed a steep voltage-dependent inactivation at voltages within the range of the resting membrane potential (see supplemental Fig. S1E, and Table 1). This common feature of T-type Ca2+ channels subunits renders their availability exquisitely sensitive to changes in membrane voltage. In addition to membrane voltage per se, T-type Ca2+ channel availability over time will also depend critically on the time course with which these channels first inactivate during membrane depolarizations, and subsequently recover from inactivation during repolarization of the neuronal membrane.
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The time course of recovery from inactivation is strongly dependent on the duration of the preceding membrane depolarization
We therefore first examined the onset of inactivation during conditioning voltage steps to –55 mV of varying duration (1 ms to 32 s, see Fig. 1A; representative experiments for Cav3.1–3.3 in Fig. 1B). During conditioning steps within this voltage range, Ca2+ channels undergo predominant closed state inactivation, i.e. they inactivate without having previously opened. The onset of inactivation for Cav3 channels followed a biexponential time course, with one time constant in the range of 300–700 ms and a second time constant in the range of 3–7 s (Fig. 1C; see Table 1 for values).
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We then determined whether the time course of recovery from inactivation is altered when the duration of a prior conditioning depolarization is varied (tpre: 0.3–300 s, –55 mV for Cav3.1 and Cav3.2, –65 mV for Cav3.3 subunits because prepulse facilitation was already observed at –55 mV). The time course of subsequent recovery from inactivation of the three cloned subunits was investigated by systematically varying the interval (t) between the conditioning depolarization and a test pulse to –25 mV (Fig. 2A). It was immediately apparent that the recovery process was significantly slower following more prolonged conditioning depolarizations (compare tpre of 1 and 300 s, Fig. 2Ba–c). The time course of recovery was well described with a biexponential equation for all three T-type subunits (Fig. 2Ca–c), with a fast time constant fast in the range of hundreds of milliseconds and a slower time constant slow in the range of seconds. Fitting datasets simultaneously with a monoexponential equation produced worse fits (F7,47= 8.29, P < 0.0001; F7,47= 24.51, P < 0.0001; and F7,47= 3.88, P= 0.0021; for Cav3.1, Cav3.2 and Cav3.3, respectively).
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The magnitude of both fast and slow proved to be quantitatively related to the duration of the conditioning depolarization tpre (Fig. 2Da–c, triangles and squares correspond to fast and slow, respectively). The relationship between these parameters could be fit with a power law relation of the form (tpre) =a(tpre/a)b, where a is a constant kinetic setpoint and b is a scaling power (fits superimposed on datapoints in Fig. 2Da–c, see Table 2 for values). This relationship translates to a dramatic and highly significant increase in the magnitude of recovery time constants over the range of prepulse durations examined (P < 0.001, ANOVA; for detailed information on significance see Fig. 2 legend). For instance, fast displayed a 2.4-, 3.5- and 4.9-fold change for Cav3.1–Cav3.3 channels, respectively. Similarly, slow was augmented 5.6-, 5.1- and 8.3-fold for Cav3.1–Cav3.3 channels, respectively.
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In these experiments, the slowing of recovery rates was not due to a change in the proportion of channels recovering with fastversusslow. If we compared the fraction of inactivated channels recovering with slow after brief (0.3 s) and prolonged (300 s) prepulses, this fraction was unchanged or even decreased with more prolonged prepulses (Cav3.1: 0.498 compared with 0.388, P < 0.05; Cav3.2: not significant; Cav3.3: 0.474 compared with 0.225, P < 0.05). It is of note that one published study did not observe a slowing of recovery rates for the Cav3.1 channel when two different conditioning prepulse durations were tested. Instead, an increase in the relative proportion of slowly recovering channels was assumed (Hering et al. 2004), whereas we did not find a consistent change in this proportion. We therefore formally examined the quality of fitting with these two models. To this end, we have simultaneously fitted full datasets (all recovery intervals, prepulse durations of 1–300 s) with a simultaneous fitting procedure, separately for each Cav3 subunit. We have compared two models. Firstly, we have fitted with the amplitudes of fast and slow components free to differ for each prepulse duration, but the time constants fast and slow constrained to be the same (see supplemental Fig. S2 – fits to averaged datapoints are shown for all three subunits and two prepulse durations of 3 and 300 s, superimposed on datapoints as red dashed lines). Secondly, we have fitted with the amplitudes of fast and slow components constrained to be the same, but the time constants free to differ for different prepulse durations (supplemental Fig. S2, black lines, panels Aa–c, Ba–c). Fits obtained with varying the time constants fast and slow, but not the amplitudes, were better than those obtained with the converse model. We compared the quality of fit with both models with an F test. This yielded F ratios of F5,47= 2.53, F5,47= 12.39 and F5,47= 2.53, and P values of 0.0418, 0.0001 and 0.0418, for Cav3.1, Cav3.2 and Cav3.3, respectively. Thus, a model with the time constants fast and slow free to vary for different prepulse durations is significantly better for all three subunits. It should be noted that this difference was most apparent for Cav3.2, less so for Cav3.1 and Cav3.3. It is therefore perhaps not surprising that Hering et al. (2004) obtained reasonable fitting results with a variation of the amplitudes, and thought this model to be most appropriate in the absence of a formal comparison between models. Additionally, there could be a potentially large impact of differences in recording conditions (for instance predominantly Na+ instead of K+ in the intracellular solution, as opposed to 20 mM in our study, and differing intracellular free-Ca2+ concentrations).
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We also used simultaneous fitting of full datasets (all recovery intervals, prepulse durations of 1–300 s) to evaluate whether recovery can be fit with the sum of three exponential equations, with the slowing of recovery attributed to changes in the amplitude contributions of these three components. We accordingly fit the dataset with a triexponential equation, with time constants constrained to be the same for all prepulse durations. We compared this model to the biexponential model with the amplitude contributions of the two components constrained to be the same for all prepulse durations. For Cav3.1 and Cav3.2, these determinations showed that 2 values increased when fitting with the triexponential models, despite the decrease in the degrees of freedom, resulting in negative F ratios. For Cav3.3, an F ratio of F2,45= 1.0, P= 0.38 was obtained. This is also apparent from supplemental Fig. S2, in which triexponential fits (dashed blue lines, panels Aa–c, Ba–c) did not approximate the data as well as a biexponential model with time constants constants fast and slow free to vary. These results indicate that slowing of recovery from inactivation can be best explained by a model in which time constants vary with prepulse duration.
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We also investigated scaling following conditioning prepulses to more depolarized potentials (to –25 mV, tpre ranging from 0.1 to 300 s, see supplemental Fig. S3A). Cav3.1 and 3.2 subunits exhibited powerful scaling of recovery rates similar to that observed in Fig. 2B–D (supplemental Fig. S3Ba and b, and Table 2, see also Fig. S3C–E for systematic variation of prepulse voltage). As above, the slowing of recovery from inactivation was not due to an enhanced amplitude contribution of slow (relative fraction of channels recovering with slow, Cav3.1: 0.452 compared with 0.536, P < 0.05; Cav3.2: not significant; prepulse durations of 0.3 and 300 s, respectively). Analogous to the analysis described above for recovery following subthreshold prepulses, we tested formally whether variation of constants fast and slow account best for slowing of recovery. Indeed, the data were approximated significantly better with the amplitudes of the fast and slow component constrained to be the same, and the time constants fast and slow free to differ for different prepulse durations than vice versa (F5,47= 2.66, P= 0.0337; and F5,47= 6.74, P < 0.0001; for Cav3.1 and Cav3.2, respectively).
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For Cav3.3, recovery from inactivation was distorted by a pronounced prepulse facilitation as previously described for the LT9 isoform of Cav3.3 used in this study (Gomora et al. 2002), and therefore this subunit was not further examined (not shown).
We next tested whether T-type Ca2+ channels in native neurones exhibit scaling relationships similar to T-type channels in expression systems. Thalamic relay neurones express a large T-type current that is most probably mediated by Cav3.1 subunits (Talley et al. 1999; Kim et al. 2001). We therefore isolated thalamic relay neurones from the LGN (see Methods) and examined recovery from inactivation following different conditioning prepulses (1, 10, 30 and 100 s, –70 mV, Fig. 3A). In order to avoid contamination by high-threshold Ca2+ currents, test pulses were applied to –45 mV (see Fig. 3A). This resulted in a Ca2+ current mediated mainly by T-type Ca2+ channels, as evidenced by the nearly complete inactivation of the Ca2+ current during a 100 ms test pulse (see Fig. 3B, leftmost traces). The recovery from inactivation of T-type currents in LGN neurones was also well described by a biexponential function. Similar to Cav3 subunits, a pronounced and highly significant slowing of recovery rates was also observed for T-type channels in LGN neurones with increasing prepulse durations (exemplary traces for tpre of 1 and 100 s depicted in Fig. 3B, see also Fig. 3C, F43,4= 13.01, P < 0.001; and F43,4= 11.60, P < 0.001; for fast and slow, respectively, ANOVA). This slowing of recovery rates manifested as a 1.88-fold increase in the magnitude of fast and a 6.50-fold increase in slow when tpre was increased from 1 to 100 s (Fig. 3D, parameters of the power law function describing scaling of native T-type currents are given in Table 2). Interestingly, the range of recovery rates exhibited by T-type currents in LGN neurones was consistent with those observed for Cav3.1 subunits (see Fig. 2Da). As for the Cav3 subunits, we carried out an F test for formal comparison of the quality of fit for the two biexponential models in which either time constants or amplitude contributions were constrained to be the same for different prepulse durations. As for cloned Cav3 subunits, varying the magnitude of the time constants with increasing prepulse durations turned out to provide the best fit (F5,7= 14.10, P= 0.0015). It should be noted that the fits of the recovery from inactivation in native cells rely on less datapoints than those performed in expression systems, due to the difficulty in obtaining stable very long-term recordings from these cells. We should therefore add a cautionary note that the absolute values of the time constants may be subject to some experimental error. Nevertheless, the data show that in principle, scaling is likely to exist also in native neurones.
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A and B, the dependence of recovery rates on prepulse duration was examined with a voltage protocol similar to that described in Fig. 2A. The leftmost traces in B correspond to currents elicited by brief (100 ms) voltage steps to –45 mV following complete recovery of the current amplitude. Because long-term recordings >1 h were difficult to carry out in native lateral geniculate nucleus (LGN) neurones, the number of different t intervals was reduced. Likewise, experiments with 300 s prepulses could not be carried out. C, nonetheless, pronounced slowing of both fast (F4,43= 13.01, P < 0.001) and slow (F4,43= 11.60, P < 0.001) was observed when tpre was prolonged (C). D, relationship of fast and slow to the duration of conditioning prepulses tpre (n= 8–10 for each data point). Error bars represent S.E.M.
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Taken together, these data indicate that the recovery rates of both cloned T-type channel subunits and native T-type channels are strongly modulated by the duration of a subthreshold conditioning depolarization. This phenomenon is likely to be physiologically relevant because it is also invoked following predominant closed state inactivation which occurs close to the resting membrane potential of neuronal cells. Intriguingly, all three T-type Ca2+ channels exhibited overlapping but complementary ranges of fast and slow, covering an extensive range of recovery rates (See Table 2, and compare Fig. 2Da–c).
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Scaling of recovery rates is abolished by superimposing mock action potentials on conditioning depolarizations
The complex behaviour of T-type channels described so far provides a mechanism that conserves a trace of prior membrane potential as a modulated recovery rate of T-type Ca2+ channels. We next tested whether the presence of APs superimposed on continuous depolarizations could modify scaling relationships. To this end, we used conditioning trains in which mock APs (linear upstroke and downstroke of 1 and 2 ms, respectively, to +25 mV) were superimposed on a continuous depolarization to –55 mV (Fig. 4A, frequencies of mock APs ranging from 3 to 100 Hz). This conditioning stimulation caused a potent inactivation of Cav3.1–3.3 channels during the first 30 mock APs (Fig. 4Ba–c, duration of the upstroke and downstroke of mock APs indicated by hatched and open bars; 1st, 3rd, 10th, 30th and 100th mock AP currents during a 30 Hz train are shown). The time course of Ca2+ peak currents invoked by mock APs during such combined trains is depicted in Fig. 4Ca–c. Notably, Cav3.3 channels displayed a pronounced facilitation during the first mock APs at higher stimulation frequencies (100 Hz), similar to previous reports (Kozlov et al. 1999), and thereafter inactivated (Fig. 4Cc). The amount of inactivation reached steady-state within 100 mock APs for all three subunits. In order to compare the inactivation during combined trains to the amount of inactivation induced by conditioning depolarizations to –55 mV alone, we replotted data in Fig. 4Ca–c on a time x-axis and superimposed the onset of inactivation depicted in Fig. 1 as a dashed red line (Fig. 4Da–c).
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We next examined recovery of Cav3.1-Cav3.3 channels following inactivation by combined conditioning trains (mock APs at 30 Hz superimposed on a depolarization to –55 mV) using double-pulse experiments (Fig. 5A). The results of these experiments are shown in Fig. 5Ba–c. For Cav3.1 channels, combined conditioning pulses caused a slowing of the recovery over the whole range of prepulse durations for both fast and slow (Fig. 5Ba). However, both time constants still exhibited pronounced scaling with increasing tpre (P < 0.001, ANOVA; for further fit parameters see figure legend). Surprisingly, superimposing APs on continuous prepulses had a completely different effect in Cav3.2 and Cav3.3 channels. Here, scaling relationships were largely abolished by addition of APs (Fig. 5Bb and c). This effect became even clearer when fast and slow were plotted versus the duration of the conditioning train (Fig. 5C, black datapoints and lines). The experiments with continuous conditioning depolarizations are shown for the sake of comparison (red datapoints and dashed lines, data taken from Fig. 2Da–c).
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A, the conditioning train consisted of mock APs (upstroke 1 ms, downstroke 2 ms, to +25 mV, at 30 Hz) superimposed on a continuous depolarization to –55 mV. The duration of this conditioning train ranged from 0.3 to 100 s. As in Fig. 2, the recovery interval t until a subsequent test pulse to –25 mV was varied to examine the time course of recovery. B, Cav3.1 still exhibited slowing of recovery rates with more prolonged tpre (Ba, n= 8–11). In contrast, scaling appeared to be abolished for Cav3.2 and 3.3 subunits (Bb and c, n= 6–8 and n= 5–7, respectively). Note that the fraction of Cav3.3 inactivated at short t is smaller that that shown in Fig. 4. This difference arises because availability of Cav3.3 channels was measured with mock APs applied from depolarized (–55 mV) potentials in Fig. 4, whereas even the leftmost datapoints in Bc refer to experiments with a brief recovery interval t at –95 mV. C, relation of tpre to fast and slow. Significant scaling is still observed for Cav3.1 subunits (black symbols, continuous lines, F3,30= 10.09, P < 0.001, and F3,30= 14.30, P < 0.001, for fast and slow, respectively), but recovery is slowed compared with continuous conditioning depolarizations alone (Ca, red dashed lines and red squares show the data from Fig. 2 for comparison in Ca–c). For Cav3.2, scaling was powerfully reduced by superimposing APs, even though changes in fast with increasing tpre were still significant (Cb, F3,25= 7.074, P < 0.005, and F3,25= 0.34, n.s., for fast and slow, respectively). No significant scaling for either fast or slow was observed for Cav3.3 subunits (Cc). Error bars represent S.E.M.
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Scaling is not observed following mock AP trains from hyperpolarized membrane potentials
These experiments raised the question of whether inactivation of Ca2+ channels by APs also invokes scaling of recovery rates. Cav3.1 and 3.2 channels undergo powerful cumulative inactivation during trains of AP waveforms applied from hyperpolarized holding potentials (Fig. 6A; see Kozlov et al. 1999). This phenomenon is depicted in Fig. 6Ba and b (1st, 3rd, 10th, 30th and 100th mock AP currents during a 30 Hz train are shown, duration of the upstroke and downstroke of mock APs is indicated by hatched and open bars). Cumulative inactivation of Cav3.1 and Cav3.2 during mock AP trains from –95 mV saturated during the first 30–40 mock APs (Fig. 6Ca and b, respectively). The inactivation obtained at the end of a conditioning train consisting of 100 mock APs at different frequencies is depicted in Fig. 6D. As expected, higher frequencies resulted in an increasing fraction of inactivated channels at the end of the conditioning train for Cav3.1 and Cav3.2 subunits. It is also apparent from Fig. 6Bc and D that Cav3.3 subunits did not display strong inactivation during such conditioning trains, as previously described. This is most probably due to the slow kinetics of activation and the fast deactivation of this subunit. These properties cause Cav3.3 channels to be inefficiently opened by short depolarizations, and induce them to preferentially deactivate after opening (instead of inactivating, see also Kozlov et al. 1999). As a consequence of this behaviour, we were not able to further investigate recovery of Cav3.3 channels following such conditioning trains. It should be noted that we did not observe facilitation of Cav3.3 channels during spike trains as in Fig. 4Cc, most probably due to the more hyperpolarized interspike voltage.
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For Cav3.1 and 3.2 channels, we were then able to examine recovery from inactivation following trains of AP-like waveforms of varying frequencies (1–100 Hz, tpre 30 s) or durations (30 Hz, tpre 0.1–100 s, see Fig. 7A). Following these trains, the proportion of channels recovering with slow was <10% in many cases. As a consequence, the behaviour of slow when varying the duration or frequency of prior AP trains could not be quantified. However, fast could be determined with the different conditioning protocols. When the duration of a conditioning train of mock APs (30 Hz) was systematically varied from 0.1 to 100 s (30 Hz, see Fig. 7A), fast was not significantly affected (Cav3.1 and Cav3.2 shown in Fig. 7Ba and b, respectively, ANOVA, n.s.). Similarly, altering the frequency of a 30 s conditioning train (from 1 to 100 Hz) caused no appreciable change in fast (Fig. 7Ca and b, ANOVA, n.s.). These results indicate that, even though AP trains cause inactivation of Cav3.1 and Cav3.2 channels, recovery from inactivation is not altered by changing the frequency or duration of the train.
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Since Cav3.3 did not undergo strong inactivation during mock AP trains elicited from hyperpolarized potentials, this subunit was not investigated further. A, mock AP trains used to induce inactivation of Cav3 channels. Both the duration and the frequency of the conditioning train were systematically varied. Test pulses to –25 mV were applied following various recovery times (t). B, influence of changing the duration of a conditioning train of mock APs (30 Hz) from 0.1 to 100 s on the rate of recovery from inactivation (Cav3.1 and 3.2 shown in Ba and c, n= 8–12 and n= 5–9, respectively). For both Cav3.1 (Ba) and Cav3.2 (Bb), the contribution of the slow time constant slow to the recovery process was small (<10%) following mock AP trains. Therefore, only fast is shown in Ba and b, and Ca and b. The change in fast with different prepulse durations tpre was not significant for Cav3.1 (F4,43= 2.08, n.s.) and Cav3.2 (F4,34= 0.35, n.s.). C, equivalent experiments to those in B, but with a systematic variation of the frequency of a 30 s conditioning train from 1 to 100 Hz. No scaling is observed for either Cav3.1 (F4,51= 1.31, n.s., n= 9–13) or Cav3.2 (F4,32= 0.78, n.s., n= 6–9). Error bars represent S.E.M.
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The scaling of recovery rates for different types of conditioning stimuli is summarized in Fig. 8 for Cav3.1–3.3 channels. For the sake of clarity, the three conditioning stimuli are depicted in Fig. 8A (black squares, continuous depolarization only; white squares, mock APs superimposed on continuous depolarizations; red cross-hatched squares, mock APs only). In order to summarize the data, scaling of recovery rates is expressed more simply as the fold increase in over a range of prepulse durations (0.3–100 s). Clearly, continuous depolarizations have dramatic effects on fast and slow for all three channel subtypes (black bars), as described in Fig. 2. Superimposing APs on conditioning depolarizations only slightly affects scaling in Cav3.1 (Fig. 8Ba), but dramatically reduces or even completely abolishes it in Cav3.2 and Cav3.3 channels (Fig. 8Bb and c, respectively, open bars). Application of conditioning trains consisting only of mock APs did not induce significant scaling of recovery rates (Fig. 8Ba and c, red cross-hatched bars; significance of ANOVA over the range of tpre examined is indicated by asterisks in Fig. 8Ba–c). In summary, these results indicate that AP firing and subthreshold membrane depolarizations have very different consequences for subsequent availability of specific T-type Ca2+ channel subunits (summarized in Fig. 8C, ‘+’ and ‘–’ indicate presence and absence of significant scaling, respectively. n.i., not investigated).
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A, summary of the different types of conditioning stimuli used to induce inactivation of Cav3 channels: continuous depolarizations (to –55 mV) of different durations (uppermost voltage protocol, identical to those used in Fig. 2A, filled squares), 30 Hz AP trains superimposed on continuous depolarizations (–55 mV, –65 mV for Cav3.3 subunits, middle voltage protocol, identical to those used in Fig. 5A, open squares), 30 Hz AP trains of different durations directly from hyperpolarized membrane potentials (– 95 mV, lowermost voltage protocol, as depicted in Fig. 7A, hatched squares). Ba–c, summary of the fold increase in fast and slow over the range of prepulse durations examined (0.3–100 s). Continuous depolarizations have dramatic effects on fast and slow for all three channel subtypes (filled bars, see also Fig. 2; single asterisk, P < 0.005; two asterisks, P < 0.001; throughout the figure). Superimposing APs on conditioning depolarizations only slightly affects scaling in Cav3.1 (open bars, Ba), but strongly reduces or completely abolishes it in Cav3.2 and Cav3.3 channels (open bars, Bb and c, respectively). AP trains applied directly from hyperpolarized membrane potentials do not induce significant scaling.
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Discussion
In addition to activity-dependent facilitation or depression of synaptic input, temporal integration in neurones is also powerfully influenced by the availability of voltage-gated ion channels in the somatodendritic neuronal membrane. In the present study, we show that the availability of both native and cloned T-type channels is powerfully modulated by the duration and the nature of a preceding inactivating stimulus.
, http://www.100md.com Recovery rates of T-type channels reflect the duration of prior depolarizations
Our first finding was that the rate constants with which channels recover from inactivation are steeply dependent on the duration of the preceding conditioning depolarization. Intriguingly, Ca2+ channels exhibited this scaling of recovery rates following subthreshold conditioning depolarizations, suggesting that this mechanism is likely to be invoked under physiological conditions by subtle depolarizations from resting membrane potential. This is unlike the behaviour of voltage-gated Na+ channels, which exhibit scaling only following strong depolarizations or prolonged high-frequency AP trains (Toib et al. 1998; Ellerkmann et al. 2001). Nevertheless, the power law function describing scaling revealed roughly similar scaling power for voltage-gated Na+ and Ca2+ channels (Toib et al. 1998; Ellerkmann et al. 2001). This finding has the intriguing consequence that neurones retain a trace of slow subthreshold membrane depolarizations, encoded as a modulated recovery rate of T-type Ca2+ channels.
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Our findings suggest that it is the slowing of recovery rates that accounts for the slowing of the recovery from inactivation. Could an increase in the relative amplitude of the component recovering with slow also adequately describe slowing of the recovery process, as suggested by Hering et al. (2004) for Cav3.1 We believe that this is not the case. We carried out a comparison of these two models, first fitting the recovery time course with the relative amplitude contribution of slow kept constant, and then with the time constants fast and slow kept constant. We first fit the recovery time course following long (300 s) prepulses, and extracted time constants and the corresponding amplitude contributions from these fits (described in detail in Results). For all three subunits, variation of the time constants produced a significantly better fit. The reason for the discrepancy to the interpretation of Hering et al. (2004) is unclear, even though this group appears not to have compared the two models in a quantitative manner. It could be due to the large differences in recording conditions (i.e. composition of the intracellular solution), if so, this would be a potentially interesting issue for further investigation.
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T-type channels selectively encode action potential firing and subthreshold depolarizations
A particularly fascinating property of T-type channels emerged when inactivation was induced with different types of mock AP trains. The powerful scaling of Cav3.2 and Cav3.3 channels following continuous subthreshold depolarizations was mostly or even completely abolished if mock APs were superimposed on the conditioning depolarization. This appears not to be true for Cav3.1 channels: scaling was observed regardless of whether slow inactivation was induced with or without superimposed mock APs. The key findings regarding scaling of Cav3 channels are summarized in a qualitative manner in Fig. 8C. These results have two major implications. First, in addition to the undoubted differences between individual Cav3 subunits regarding fast gating properties (Kozlov et al. 1999; Klckner et al. 1999), clear differences in slow recovery and scaling have also emerged. Intriguingly, the range of recovery rates was overlapping but complementary for all three channel subunits (compare Fig. 2Da–c), allowing the generation of T-type currents displaying diverse scaling properties in native neurones. This is particularly interesting in view of the distinctive expression pattern of Cav3 subunits in the CNS (Talley et al. 1999). A second major implication of our experiments is that availability of T-type channels is differentially modulated on a time scale of many seconds, depending on whether the neurone has previously encountered subthreshold depolarizations, AP firing or both (see Fig. 8B and C). Because the availability of T-type Ca2+ channels is a crucial determinant of neuronal firing (reviewed in Huguenard, 1996; Perez-Reyes, 2003), such properties may constitute an important mechanism for short-term plasticity of intrinsic membrane properties.
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How can scaling be interpreted biophysically In principle, both Markovian and fractal models have been used to describe ion channel behaviour (for discussion of the relation between these types of models see Liebovitch, 1989; Bassingthwaighte et al. 1994; Toib et al. 1998). As put forward in Toib et al. (1998), one way in which the occurrence of scaling relationships may be explained is by collapsing a complex Markovian scheme into a single scaled effective rate. This notion is illustrated by the following kinetic scheme:
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(Scheme 1)
where R denotes the resting state of the channel, and I1–In are pools of linearly interlinked inactivated states. In this model, more prolonged depolarization would cause channels to accumulate in more remote inactivated states. As a consequence, recovery rates become slower, because recovery from remote inactivated states requires a transition through a higher number of intermediate inactivated states. Indeed, such one-dimensional diffusion models can give rise to power law relationships (Millhauser et al. 1988).
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In the case of Na+ channels, two types of inactivation processes can be clearly discriminated. A fast inactivation mechanism does not display scaling, whereas much slower inactivation mechanisms show powerful scaling (Toib et al. 1998). Accordingly, it has been argued that fast and slow inactivation relies on distinct molecular processes. This is supported by several additional lines of evidence. Firstly, selective pharmacological effects on slow, but not fast recovery from inactivation have been demonstrated (Remy et al. 2004). Additionally, whereas the structural correlate of fast Na+ channel inactivation has been clearly identified (Stühmer et al. 1989; West et al. 1992), the structural basis of slow inactivation is most probably complex (Cummins & Sigworth, 1996; Hayward et al. 1997; Melamed-Frank & Marom, 1999; Mitrovic et al. 2000; Alekov et al. 2001; Vilin & Ruben, 2001).
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Could there also be two different types of inactivation that coexist for T-type channels In contrast to Na+ channels, not much is known regarding the molecular basis of T-type Ca2+ channel inactivation that would allow us to structurally separate two mechanisms. Nevertheless, upon closer inspection of Fig. S3, it appears as if fast and slow do not scale for a range of prepulse durations, and then start scaling for prepulse durations >1 s. This could imply that there are inactivation mechanisms corresponding to the classical scheme (no scaling, Frazier et al. 2001). The second (scaling) mechanism could be accessed from closed states during prolonged depolarizations. This mechanism may involve inactivation via linearly coupled inactivated states (as depicted in Scheme 1), thereby giving rise to scaling relationships. For brief prepulses, the rate constants for scaling and nonscaling inactivation might be in the same range. As prepulses are prolonged, inactivation processes showing scaling would become slower, dominating the macroscopic recovery rates. This concept would explain why scaling emerges when continuous conditioning pulses are prolonged. Likewise, the lack of scaling seen following action potential trains is most probably due to the fact that slow inactivation requires prolonged depolarization, and is thus not invoked by trains of brief depolarizations.
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The assumption of distinct scaling and nonscaling inactivation mechanisms alone, however, does not explain why superimposing APs on continuous depolarizations almost completely abolishes scaling, at least for the Cav3.2 and Cav3.3 subunits. The most parsimonious explanation for this finding is that the classical, nonscaling inactivation mechanism (as induced by superimposing mock APs) inhibits the scaling inactivation process. In this scenario, superimposing APs on continuous depolarizations would cause powerful cumulative inactivation via the open state, which would not take place in the absence of mock APs. In this case, inactivation via the scaling mechanism would be impaired, and the recovery time course would be less affected by varying the duration of the conditioning train. The existence of such a mechanism would imply that interactions between two gating mechanisms are highly relevant for Cav3.2 and Cav3.3 channels, but perhaps less so for Cav3.1 channels. Indeed, an interaction between fast (nonscaling) and slow (scaling) inactivation is observed for some voltage-gated Na+ channels. Firstly, introduction of mutations or intracellular application of proteolytic enzymes which completely remove fast gating strongly affect slow inactivation processes (Valenzuela & Bennett, 1994; Featherstone et al. 1996; Kontis & Goldin, 1997; Hilber et al. 2002). Conversely, manipulations that stabilize fast inactivation inhibit entry into slow inactivation (Hilber et al. 2002). The idea that different gating mechanisms interact is also in line with the observation that the amplitude contributions of fast, intermediate and slow inactivating Na+ channel components appear to change in a highly hierarchical manner when conditioning prepulses are prolonged (Toib et al. 1998; Hayward et al. 1997).
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Functional implications of T-type channel scaling
Regardless of the mechanisms involved, the complex properties of T-type channels we describe have obvious consequences for the regulation of channel availability by prior activity. T-type Ca2+ channels are crucial in mediating Ca2+-dependent burst responses that are prominent in subsets of neurones from various brain regions including the cerebellum, thalamus and brain stem (Huguenard, 1996). In thalamic neurones, the T-type Ca2+ channel plays a key role in the phase-locked firing of thalamic neurones during both seizures and spindle oscillations, which occur normally during slow-wave sleep. During both types of oscillations, thalamic relay neurones are hyperpolarized by rhythmic inhibitory postsynaptic potentials, which deinactivate the T current, sometimes resulting in rebound bursts. Scaling of T-type channels that we also demonstrated in native LGN neurones is likely to modulate this phenomenon. Scaling of T-type channels may also be important in other neurones, or even neuronal subcompartments. For instance, T-type Ca2+ channels are highly expressed in dendrites, where they powerfully modulate the propagation of synaptic potentials from distal dendrites to the soma (Christie et al. 1995; Magee & Johnston, 1995; Magee et al. 1995). Dendritic Ca2+ electrogenesis may therefore also be powerfully modulated by intrinsic properties of T-type Ca2+ channels. It should also be noted that scaling phenomena may become particularly relevant during epileptic seizures, in which long-lasting depolarizations in conjunction with high-frequency firing occur. It will also be important to consider the behaviour of T-type channels in concert with other nonscaling channels, such as certain A-type K+ channels (Toib et al. 1998). Clearly, the recovery rates of both types of channels profoundly affect the balance in the availability of these channels over time after repolarization. Changing the recovery rates of T-type, but not A-type channels, may therefore strongly impact the relative availability of both channel types following membrane repolarization.
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Supplemental material
The online version of this paper can be accessed at:
DOI: 10.1113/jphysiol.2005.103614
http://jp.physoc.org/cgi/content/full/jphysiol.2005.103614/DC1
and contains supplemental material consisting of three figures:
Supplemental Figure S1. Voltage-dependent activation and inactivation of cloned T-type channels.
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Supplemental Figure S2. Comparison of different models to approximate the recovery time course of T-type channels.
Supplemental Figure S3. Recovery from inactivation of T-type channels following conditioning prepulses to depolarized voltages.
This material can also be found as part of the full-text HTML version available from http://www.blackwell-synergy.com
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