1. Introduction {#sec1}
===============

T-type Ca^2+^ currents crucially determine neuronal excitability. They are located in the somatodendritic compartment of many types of neurons ([@bib4]; [@bib24]) and have a low threshold of activation. This renders them capable of firing low-threshold Ca^2+^ spikes ([@bib11]; [@bib14], [@bib15]) and can switch the firing mode of cells from normal firing behaviour to burst firing ([@bib18]; [@bib23]). On a network level, they are involved in the generation of intrinsic rhythms ([@bib12]). Their role in neurological functions and diseases like pain perception and hyperalgesia ([@bib13]; [@bib17]), epilepsy ([@bib23]; [@bib25]), mechanoreceptor function ([@bib21]), to olfaction ([@bib16]), as well as the maintenance of sleep states ([@bib1]) was demonstrated by pharmacological and genetic inhibition.

Besides their low threshold of activation, T-type Ca^2+^ channels have a steep voltage dependent inactivation in the vicinity of the resting membrane potential ([@bib26]). Therefore, the availability of T-type Ca^2+^ channels depends on slight changes in membrane potential. However, inactivation and recovery from inactivation are dynamic processes. Following membrane depolarization, onset of inactivation of T-type Ca^2+^ channels reaches steady-state within seconds. The time-course of recovery from inactivation was shown to be dependent of the duration of the previous depolarization ([@bib26]). As a consequence, availability of T-type Ca^2+^ channels would not only reflect the actual membrane potential but integrate prior alterations. This was thought to provide a mechanism for intrinsic short-term plasticity.

However, the voltage steps examined in ([@bib26]) were far more pronounced than membrane potential changes observed in physiological conditions. Since a large fraction of T-type Ca^2+^ channels is inactivated at resting membrane potential, hyperpolarization - as it occurs during inhibitory post synaptic potentials - is required to enable them to recover from inactivation, a process also termed de-inactivation.

In this study we address the question, if scaling of recovery rates occurs following slight changes of membrane potential and if this influences the de-inactivation of T-type Ca^2+^ channels during inhibitory potentials.

2. Materials and methods {#sec2}
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2.1. Stably transfected HEK-293 cells {#sec2.1}
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The generation of stable cell lines expressing human Ca~v~3.1, Ca~v~3.2 and Ca~v~3.3 has been described previously. The following stably transfected HEK-293 cell lines were used in this study: hα1G-Q39, containing the human α1G channel, Ca~v~3.1a (GenBank accession number [AF190860](http://molpharm.aspetjournals.org/cgi/external_ref?access_num=AF190860&link_type=GEN){#intref0010}, ([@bib8])); hh8-5, containing the Hh8 plasmid construct of human α1H, Ca~v~3.2a (GenBank accession number [AF051946](ncbi-n:AF051946){#intref0015}, ([@bib9])); and Lt9-8, containing the LT9 plasmid construct of α1I, Ca~v~3.3b, ([@bib10]), GenBank accession number [AF393329](ncbi-n:AF393329){#intref0020}). Cells were maintained in DMEM media (4.5 g/l glucose, 584 mg/l L-glutamine) supplemented with 1 mg/mL of geneticin, 10% heat-inactivated foetal bovine serum, 100 units/mL penicillin and 100 μg/mL streptomycin.

2.2. Patch-clamp recording {#sec2.2}
--------------------------

Patch-clamp recordings were obtained from ∼350 HEK cells expressing Ca~v~3 Ca^2+^ channels. Patch pipettes with a resistance of 3--4 MΩ were fabricated from borosilicate glass capillaries and filled with an intracellular solution containing (in mM): Cs-methanesulfonate 87.5, MgCl~2~ 5, CaCl~2~ 0.5, tetraethylammonium 20, HEPES 10, bis-(o-aminophenoxy)-N,N,N',N'-tetraacetic acid (BAPTA) 5, sucrose 16, adenosine-5\'-triphosphate (Na^+^~2~-ATP) 10, guanosine-5\'-triphosphate (GTP) 0.5 and glucose 10 (pH 7.2, 300 mosmol). BAPTA was used to avoid effects of intracellular Calcium to address the biophysical properties of the channels. Patch-clamp recordings from HEK cells were performed in a bath solution containing (in mM): sodiummethanesulfonate 125, KCl 3, MgCl~2~ 1, CaCl~2~ 5, 4-AP 4, tetraethylammonium 20, HEPES 10, glucose 10 (pH 7.4, 315 mosmol). Tight-seal whole-cell recordings were obtained at room temperature (21--24 °C) according to standard techniques ([@bib22]). 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%) so that the maximal residual voltage error did not exceed 1.5 mV ([@bib22]). 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 -70 mV.

2.3. Voltage protocols and data analysis {#sec2.3}
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The onset of inactivation of T-type Ca^2+^ currents was described by holding the membrane potential to -60 mV for varying durations (t~pre~) and a subsequent step to -25 mV ([Fig. 1](#fig1){ref-type="fig"}a). The peak current amplitude elicited ([Fig. 1](#fig1){ref-type="fig"}b) was normalized to the maximal amplitude elicited without a prepulse to --60 mV. The relation between the normalized peak amplitude and the prepulse duration was best fit by a biexponential equation of the form:$$\text{I}\left( \text{t}_{\text{pre}} \right) = \text{A}_{\text{0}} + \text{A}_{1}\text{*exp}\left( {{- \text{t}}_{\text{pre}}/\text{τ}_{1}} \right){+ \text{A}}_{2}\text{*exp}\left( {{- \text{t}}_{\text{pre}}/\text{τ}_{2}} \right)$$where I(t~pre~) is the current amplitude following a prepulse duration of t~pre~, A~0~ is a constant offset, and τ~1~and τ~2~ the time constants of inactivation with the corresponding amplitudes A~1~ and A~2~, respectively.Fig. 1The onset of inactivation is similar for all three Ca~V~3 subtypes. Onset of inactivation was examined using standard protocols (panel a, representative current traces in panel b). Slight depolarizations from -70 to -60 mV were sufficient to inactivate most T-type Ca^2+^ channels (remaining fraction given as A~steadystate~ in [Table 1](#tbl1){ref-type="table"}). The time-course was similar for all three subtypes (panel c~1~-c~3~) and best described by a biexponential function (time constants τ~fast~ and τ~slow~ and the relative proportion of τ~fast~ (A~fast~) are given in [Table 1](#tbl1){ref-type="table"}, n ≥ 7).Fig. 1

Recovery from inactivation was examined with double pulse experiments ([Fig. 2](#fig2){ref-type="fig"}a). We addressed recovery of T-type Ca^2+^ channels following continuous step depolarizations to -60 mV of varying durations (t~pre~:1--100 s). Recovery of T-type Ca^2+^ channels following these conditioning prepulses was examined by stepping the membrane potential back to --70 mV holding potential for a varying recovery interval (Δt, 40 ms to 20.5 seconds) and subsequently applying a brief (300 ms) test pulse to --25 mV. In all experiments, an equivalent normalization test pulse to --25 mV (300 ms) was applied before each double pulse. Normalization of the recovery data was then carried out with the amplitude of the current elicited during this normalization test pulse.Fig. 2The recovery rates depend on the duration of the inactivating depolarization. T-type Ca^2+^ channels were inactivated by a voltage step from -70 to -60 mV of varying duration (t~pre~: 1--100s). Following subsequent steps to -70 mV of increasing duration (40 ms--20 s) to allow channels to recover from inactivation, channel availability was assessed with a test pulse to -25mV (panel a, representative current traces in panel b). Current amplitude was normalized to the maximum current elicited by a test pulse not preceded by an inactivating stimulus and depicted versus the recovery interval (panel c~1~-c~3~, circles, squares and triangles correspond to prepulse durations of 1, 10 and 100s, respectively, n = 5--8). Datasets for all prepulse durations were fit simultaneously with a biexponential function (for Ca~v~3.2 monoexponential, see methods section). The amplitude proportion of fast and slow recovering fractions were linked (Fits depicted as solid lines superimposed on datapoints in panels c~1~-c~3~). Prolonged prepulse durations resulted in increased time constants in all three subtypes (panel d~1~-d~3~, significant when comparing 1s to 100s, indicated by asterisks).Fig. 2

We were concerned that rundown of Ca^2+^ current amplitudes might contaminate our results. Therefore, we excluded all experiments in which the Ca^2+^ current amplitudes elicited by the normalization test pulse (see description of double-pulse protocols above) were reduced by more than 20% over 1.5 hours of recording from further analysis. We also excluded experiments in which the input resistance measured in recording solution was \<1GΩ, or cells in which a transient change in passive membrane properties was observed. The time constants of recovery τ~fast~ and τ~slow~ were extracted by fitting with a biexponential equation of the form:$$\text{I(t)} = \text{A}_{\text{0}} + \text{A}_{\text{fast}}\text{*}\left( {1 - \text{exp}\left( {- {{\Delta\text{t}}/\text{τ}_{\text{fast}}}} \right)} \right) + \text{A}_{\text{slow}}\text{*}\left( {1 - \text{exp}\left( {- {{\Delta\text{t}}/\text{τ}_{\text{slow}}}} \right)} \right)$$

The amplitude proportion of the fast (A~fast~) and the slow (A~slow~) component were linked in a simultaneous fit and thereby identical for all prepule durations.

In some cases, fitting was carried out with a monoexponential equation of an identical form when a biexponential equation resulted in equal time-constants or a corresponding amplitude proportion \<10%.

The recovery from inactivation during physiological hyperpolarizations was examined by application of an inactivating depolarization, a subsequently applied mock IPSP that mimics a recorded IPSP, and a test-pulse to -25 mV (400 ms) to assess the fraction of available T-type Ca^2+^ channels ([Fig. 3](#fig3){ref-type="fig"}a).Fig. 3Slowing of recovery reduces T-type Ca^2+^ channel availability following IPSPs. T-type Ca^2+^ channels were activated with a depolarizing voltage step to -25mV (panel a~1~, representative current trace in a~1~). Subsequently, channel availability was measured following a depolarizing step (1--100 s) to -60mV (panel a~2~) to determine the inactivated fraction (panel b~2~). Finally, the same inactivating voltage step was applied followed by a mock IPSP and the test-pulse to -25mV (panel a~3~). The recovering fraction was defined as the increase of the current amplitude compared to panel b~2~ (see panel b~3~). This fraction was normalized to the inactivated fraction and plotted versus the duration of the inactivating stimulus (panel c~1~-c~3~, n ≤ 7). Prolonged depolarization slows down the recovery (see [Fig. 2](#fig2){ref-type="fig"}) resulting in a smaller fraction recovering during the IPSP for Ca~v~3.1 and Ca~v~3.2 channels (panel c~1~and c~2~, significant when comparing 1s to 100s, indicated by asterisks). For Ca~v~3.3 the recovering fraction was independent of the prepulse duration (panel c~3~).Fig. 3

Data was fit using Origin (OriginLab Corp, Northhampton). All results are shown as the mean ± S.E.M. Statistical comparison was carried out with a two-tailed Student\'s t-test.

3. Results {#sec3}
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3.1. Onset of inactivation {#sec3.1}
--------------------------

First we examined the time course of the onset of inactivation of cloned Ca^2+^ T-type channels (Ca~v~3.1 - Ca~v~3.3) expressed in HEK293 cells. A test-pulse to -25 mV (300 ms) was applied following a preceding depolarization of varying duration (3 ms--59 s) to -60 mV from a holding potential of -70 mV ([Fig. 1](#fig1){ref-type="fig"}a). The peak amplitude of the elicited current ([Fig. 1](#fig1){ref-type="fig"}b) was normalized to the peak amplitude of the current elicited by a test-pulse without previous depolarization. The relative amplitude was averaged for all recorded cells and depicted versus the duration of the preceding depolarization for all three T-type Ca^2+^ channel subtypes examined ([Fig. 1](#fig1){ref-type="fig"}c~1~-c~3~ for Ca~v~3.1-Ca~v~3.3 respectively). This reveals that a relevant fraction of channels inactivates within a time period \< 1s and a steady state inactivation of ∼80% of the channels available at the holding potential (-70 mV) is reached within 10--100 s in all three T-type Ca^2+^ channel subtypes (see [Table 1](#tbl1){ref-type="table"}).Table 1Biexponential fit of the onset of inactivation of the three T-type Ca^2+^ channel isoforms.Table 1Ca~V~3.1Ca~V~3.2Ca~V~3.3A~steadystate~0.16 ± 0.050.24 ± 0.030.27 ± 0.05τ~fast~ (s)0.64 ± 0.060.25 ± 0.030.28 ± 0.08A~fast~ (%)3.9 ± 0.59.5 ± 2.212.6 ± 4.5τ~slow~ (s)0.19 ± 0.010.50 ± 0.050.45 ± 0.06

3.2. Recovery from inactivation {#sec3.2}
-------------------------------

Previous studies ([@bib26]) have shown that the time-course of recovery from inactivation depends on the duration of the depolarizing voltage step that induces the inactivation. In a similar set of experiments we addressed the question, if this scaling of recovery rates also occurs following small changes in membrane potential as observed during physiological processes. We applied a small depolarizing step to -60 mV (from a holding potential of -70 mV) of varying duration (t~pre~: 1--100 s) to inactivate the T-type Ca^2+^ channels (relative current amplitude interpolated according to the recordings in [Fig. 1](#fig1){ref-type="fig"} are given in [Table 2](#tbl2){ref-type="table"}). Subsequently we enabled the channels to recover from inactivation during an increasing period (Δt: 80 ms to 20 s) at -70 mV. Finally a test-pulse to -25 mV was applied ([Fig. 2](#fig2){ref-type="fig"}a). The amplitude of the elicited current increased with prolonged recovery intervals ([Fig. 2](#fig2){ref-type="fig"}b). The fraction of available T-type Ca^2+^ channels was quantified relative to the amount of channels available at holding potential (-70 mV) obtained by a test-pulse without preceding depolarization, averaged for all recorded cells and depicted versus the recovery interval (Δt) for all three T-type Ca^2+^ channel subtypes ([Fig. 2](#fig2){ref-type="fig"}c~1~-c~3~ for Ca~v~3.1-Ca~v~3.3 respectively). Consistent with existing data ([@bib26]), the time-course of recovery from inactivation is dependent on the duration of the inactivating depolarization even in the more physiological range of membrane potential changes used in this study. The time course of recovery was fit with a biexponential equation (see Methods section) for each individual cell. The slowing of recovery of Ca~v~3.1 and Ca~v~3.3 channels apparent in [Fig. 2](#fig2){ref-type="fig"}c~1~ and c~3~ was mainly represented by an increase of the slow time-constant as depicted in [Fig. 2](#fig2){ref-type="fig"}d~1~ and d~3~. In the case of Ca~v~3.2 the amplitude proportion of one time constant turned out to be negligible and a monoexponential equation obtained a proper fit of the data with an increasing time-constant with prolonged inactivating stimulus.Table 2Relative amplitude of I~Ca~ following the prepulses applied in Figs. [2](#fig2){ref-type="fig"} and [3](#fig3){ref-type="fig"}.Table 2Ca~V~3.1Ca~V~3.2Ca~V~3.31s0.380.680.5410 s0.200.320.29100 s0.170.240.27

Taken together the data confirm that even slight changes in membrane potential induce scaled dynamics of recovery from inactivation.

3.3. Recovery during IPSPs {#sec3.3}
--------------------------

Physiological changes of membrane potential are frequently caused by post synaptic potentials. Particularly for the T-type Ca^2+^ channel which is located mainly on the dendrites modulating the neuronal response to synaptic input, hyperpolarization as a consequence of inhibitory GABAergic input is essential to remove inactivation. To address the question, whether scaling of recovery rates influences the availability of T-type Ca^2+^ channels following inhibitory postsynaptic potentials (IPSP) we first assessed the maximal fraction of T-type Ca^2+^ channels available (representative current trace in [Fig. 3](#fig3){ref-type="fig"}b~1~). Therefore, we applied a test-pulse to -25 mV (400 ms) from a holding potential of -70 mV ([Fig. 3](#fig3){ref-type="fig"}a~1~). Then we preceded the test-pulse by a depolarization of varying duration analog to the experiments described before (t~pre~: 1--100 s, [Fig. 3](#fig3){ref-type="fig"}a~2~) to inactivate T-type Ca^2+^ channels ([Fig. 3](#fig3){ref-type="fig"}b~2~, f~inactiv~). Finally, the depolarizing voltage step was followed by a mock IPSP to enable T-type Ca^2+^ channels to recover from inactivation and a subsequent test-pulse to asses the fraction of channels available ([Fig. 3](#fig3){ref-type="fig"}a~3~). The fraction of T-type Ca^2+^ channels that recover during the mock IPSP (f~recovery~, [Fig. 3](#fig3){ref-type="fig"}b~3~) relative to the fraction of inactivated channels (f~inactiv~, [Fig. 3](#fig3){ref-type="fig"}b~2~) is obtained for each individual cell, averaged and depicted versus the duration of the inactivating stimulus ([Fig. 3](#fig3){ref-type="fig"}c~1-3~). In all T-type Ca^2+^ channel subtypes ∼10--25% of the channels that inactivated during the depolarization recovered during the mock IPSP. For Ca~v~3.1 and Ca~v~3.2 the magnitude of this fraction was reduced with more prolonged depolarizations ([Fig. 3](#fig3){ref-type="fig"}c~1~ and c~3~, asterisks indicate p-value\<0.05). This is likely due to the slower recovery from inactivation following more prolonged depolarizations. For Ca~v~3.3 no significant changes in the recovery of T-type Ca^2+^ channels during the mock IPSP could be observed ([Fig. 3](#fig3){ref-type="fig"}c~3~).

Our data suggest that the scaling of recovery results in an altered availability of T-type Ca^2+^ channels following IPSPs and suggest that this channel intrinsic property has implications for modulating the availability of T-type channels during physiological activity.

4. Discussion {#sec4}
=============

The integration of incoming inhibitory and excitatory inputs to an action potential output is a key feature of neurons in the context of a network. This process is determined by the properties of excitatory and inhibitory synapses, but is also importantly determined by intrinsic neuronal excitability ([@bib2]). In particular, the expression of voltage-gated ion channels is a key determinant both of dendritic integration and somatic action potential output generation. The presence of voltage-gated channels confer complex electrical properties on somatodendritic neuronal compartments, due to the time- and voltage-dependent gating of these conductances. In this context, slower voltage-dependent inactivation processes have been recognized as important in modulating the availability of many channels, amongst them sodium and calcium channels. For both of the ion channel types, scaling of recovery rates can constitute an intriguing mechanism for complex activity-dependent modulation of channel availability, and has been discussed as an intrinsic mechanism of short term plasticity ([@bib26]). However, many of these studies have utilized strong depolarizations to induce slow inactivation, which are unlikely to occur in a physiological context. In this study, we demonstrate that even slight membrane potential changes within a physiological range (-70 to -60 mV) are sufficient to inactivate a relevant fraction of T-type Ca^2+^ channels (∼80%, [Fig. 1](#fig1){ref-type="fig"}) on a timescale of seconds. Consistent with previous findings the recovery from this inactivated state depends on the duration (1--100 s) of the preceding depolarizing step. ([Fig. 2](#fig2){ref-type="fig"}). Such depolarizations likely occur under physiological circumstances in-vivo. In many cells up- and down states can be observed, in which the membrane potential switches in a bistable manner between more hyperpolarized and more depolarized levels. These depolarizations are within the range that would induce substantial inactivation of T-type Ca^2+^ channels ([Fig. 1](#fig1){ref-type="fig"}).

Since recent work indicates that the inactivation behavior of T-type Ca^2+^ channels is modulated by intracellular Ca^2+^ levels ([@bib5]; [@bib6]) the demonstrated effects could be due to this secondary mechanism instead of the intrinsic electrophysiological properties. To minimize this effect we applied a high concentration of intracellular Ca^2+^ buffer (BAPTA).

The availability of T-type channels in turn controls burst firing and low-threshold Ca^2+^ spike generation ([@bib11]; [@bib15]). In different brain regions, such as the cerebellum, thalamus and brain stem, a modulation of T-type channel availability was shown to contribute to rhythmogenesis ([@bib12]). In addition, an important role of T-type Ca^2+^ channels has been demonstrated for sensory sytems ([@bib13]; [@bib17]), mechanoreceptor function ([@bib21]), olfaction ([@bib16]) and the maintainance of sleep states ([@bib1]).

In many neurons expressing T-type Ca^2+^ channels, they are located in dendrites ([@bib24]) and modulate the propagation of postsynaptic potentials from the distant dendrites to the soma ([@bib7]; [@bib19]; [@bib20]). In these compartments, a scaled recovery behavior during physiological hyperpolarizations - dependent on the duration of preceding depolarizations -- would affect temporal integration of incoming excitatory and inhibitory input. When applying mock IPSPs following a prolonged depolarized period to mimic this physiological process a relevant fraction of the inactivated channels recovered during this mock IPSP. In fact, this fraction was smaller with increasing duration of the preceding depolarization ([Fig. 3](#fig3){ref-type="fig"}). This suggests that scaling of recovery rates can contribute to the modulation of postsynaptic excitability, making it dependent on prior alterations of the membrane potential. However, the behavior of the three isoforms is quite divers: In our findings only Ca~V~3.1 and 3.1 display a de-inactivation dependent on the duration of the preceding depolarization. Interestingly, these two isoforms require more pronounced hyperpolarization to de-inactivate. In contrast, Ca~V~3.2 has the slowest time-scale of recovery from inactivation (summarized in ([@bib3]), see also [Fig. 2](#fig2){ref-type="fig"}c~2~ and d~2~).

Thus, this biophysical property of T-type Ca^2+^ channels may provide an intrinsic mechanism of short term plasticity and temporal integration of synaptic inputs, an could be modulated by expression patterns of the Ca~V~ isoforms. However, the relevance for different neuronal and sensory systems was not addressed in this study and remains issue for further investigation.

Declarations {#sec5}
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Author contribution statement {#sec5.1}
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Mischa Uebachs: Conceived and designed the experiments; Performed the experiments; Analyzed and interpreted the data; Contributed reagents, materials, analysis tools or data; Wrote the paper.

Christina Schaub: Performed the experiments; Analyzed and interpreted the data; Contributed reagents, materials, analysis tools or data; Wrote the paper.

Funding statement {#sec5.2}
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This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

Competing interest statement {#sec5.3}
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The authors declare no conflict of interest.

Additional information {#sec5.4}
----------------------

No additional information is available for this paper.

We thank Edward Perze-Reyes for providing the HEK293 cell lines used in this study.
