Ca²⁺-dependent components of inactivation of unitary cardiac L-type Ca²⁺ channels

Abstract

A Ca²⁺ ion-dependent inactivation (CDI) of L-type Ca²⁺ channels (LCC) is vital in limiting and shaping local Ca²⁺ ion signalling in a variety of excitable cell types. However, under physiological conditions the unitary LCC properties that underlie macroscopic inactivation are unclear. Towards this end, we have probed the gating kinetics of individual cardiac LCCs recorded with a physiological Ca²⁺ ion concentration (2 mm) permeating the channel, and in the absence of channel agonists. Upon depolarization the ensemble-averaged LCC current decayed with a fast and a slow exponential component. We analysed the unitary behaviour responsible for this biphasic decay by means of a novel kinetic dissection of LCC gating parameters. We found that inactivation was caused by a rapid decrease in the frequency of LCC reopening, and a slower decline in mean open time of the LCC. In contrast, with barium ions permeating the channel ensemble-averaged currents displayed only a single, slow exponential decay and little time dependence of the LCC open time. Our results demonstrate that the fast and slow phases of macroscopic inactivation reflect the distinct time courses for the decline in the frequency of LCC reopening and the open dwell time, both of which are modulated by Ca²⁺ influx. Analysis of the evolution of CDI in individual LCC episodes was employed to examine the stochastic nature of the underlying molecular switch, and revealed that influx on the order of a thousand Ca²⁺ ions may be sufficient to trigger CDI. This is the first study to characterize both the unitary kinetics and the stoichiometry of CDI of LCCs with a physiological Ca²⁺ concentration. These novel findings may provide a basis for understanding the mechanisms regulating unitary LCC gating, which is a pivotal element in the local control of Ca²⁺-dependent signalling processes.

Introduction

The influx of Ca²⁺ ions through L-type Ca²⁺ channels (LCCs) triggers numerous critical cellular functions, including excitation–contraction coupling in cardiac muscle (Stern, 1992; Cheng et al. 1993), excitation–secretion coupling in neurons (Rettig & Neher, 2002), and excitation–transcription coupling in gene expression (Dolmetsch, 2003). A Ca²⁺-dependent inactivation (CDI) of LCCs limits the amount and defines the timing of Ca²⁺ ion entry during depolarization (Brehm & Eckert, 1978; Brown et al. 1981; Josephson et al. 1984; Lee et al. 1985; Yue et al. 1990; Imredy & Yue, 1994; reviewed by McDonald et al. 1994; and Budde et al. 2002). It is commonly thought that voltage-dependent inactivation (VDI) of LCCs is a slower process, and is mechanistically distinct from CDI. However, single LCC studies probing CDI and differentiating it from VDI are lacking, especially under physiological conditions. Thus, the unitary characteristics of LCC inactivation have remained elusive.

We have previously shown that the unitary LCC currents can be analysed using a physiological Ca²⁺ ion concentration (Guia et al. 2001). We have also found that voltage modulates both the time-dependent kinetics (Josephson et al. 2002a) and the conductance of the Ca²⁺-conducting unitary LCC (Guia et al. 2001, Josephson et al. 2002b). Here we address LCC inactivation and analyse the signature of CDI registered by unitary LCC currents recorded with 2 mm Ca²⁺ ions permeating the channel, and in the absence of LCC agonists. A novel kinetic dissection of LCC gating provides direct evidence that inactivation of the ensemble current results from time-dependent changes in two unitary parameters. In addition, an analysis based on individual episodes reveals the relationship between the amount of prior Ca²⁺ ion entry and the extent of CDI. The present results help to clarify the physiological role of Ca²⁺ and voltage in producing unitary LCC inactivation, and support an emerging picture of the molecular mechanisms underlying this critical process.

Methods

Myocyte preparation

Male Sprague–Dawley rats (250 to 300 g; 2 to 3 months old) were killed by intraperitoneal injection of pentobarbital (80 to 100 mg kg⁻¹); hearts were rapidly removed and retrogradely perfused. All procedures for animal use were in strict accordance with the NIH Guide for the Care and Use of Laboratory Animals and met the standards of The Journal of Physiology as set out by Drummond (2008), and were approved by the Institutional Animal Care and Use Committee. Ventricular myocytes were isolated enzymatically as described previously (Guia et al. 2001).

Single channel recording

Recording of unitary L-type Ca²⁺ channels was performed as previously described (Guia et al. 2001). The myocytes were superfused with a high potassium depolarizing solution (HiK) at a rate of 2–3 ml min⁻¹. The HiK solution (in mm: 120 potassium aspartate; 25 KCl; 10 Hepes; 10 glucose; 2 MgCl₂; 1 CaCl₂; 2 EGTA; 6 KOH, pH 7.2, 290 mosmol l⁻¹) was used to depolarize the cells to near 0 mV so that V_m was equal to the patch potential, inverted (–V_patch). The free calcium concentration in the HiK solution was calculated to be approximately 80 nm. The cells were allowed to stabilize in the HiK solution for at least 20 min before unitary current measurements were conducted. In the present experiments the possibility that Ca²⁺ ions released from the sarcoplasmic reticulum (SR) via Ca²⁺-induced Ca²⁺ release (CICR) produced CDI was considered unlikely. The experiments were conducted using myocytes that were conditioned (for at least 15–20 min) in a depolarizing medium containing a high K⁺ concentration with the Ca²⁺ concentration buffered to 80 nm; these conditions may lead to (at least partial) depletion of SR Ca²⁺ ions. In addition, it is commonly thought that the formation of the gigaseal alters the submembrane micro-architecture, and disrupts the communication between the LCC and the SR Ca²⁺-release channels. Thus, it is most likely that the present results reflect the actions of Ca²⁺ ions that are passing through the LCC, and not via Ca²⁺ ions released from internal stores.

Borosilicate patch pipettes made from Corning no. 7052 glass (1.5 mm OD, 0.86 mm ID, Model 5968, A-M Systems, Inc., Carlsborg, WA, USA). The pipette tips were fire-polished (model MF-83, Narishige Instrument Lab., Tokyo, Japan) to produce 8–15 MΩ tip resistances when filled with the pipette solutions, and the shanks were painted with a thick layer of silicone elastomer (Sylgard 184, Dow-Corning, Midland, MI, USA, polymerized under a heat gun) to within 100 μm of the tip. Pipettes were filled with a solution containing 2 mm CaCl₂ or 2 mm BaCl₂, 10 mm CsCl and 5 mm 4-aminopyridine to block K⁺ currents, 10 mm Hepes, and TEA-OH to pH 7.4, with sucrose added to maintain normal osmolarity (290 mOsm/l). Seal resistances of 50 – >300 GΩ were obtained by applying slight pressure with the pipette tip on the membrane then applying gentle suction inside the pipette using a gas-tight glass syringe. No corrections were made for junction potentials. Membrane and pipette capacitances were corrected electronically. All experiments were performed at room temperature (22.5–23.5°C).

Current amplification was accomplished with an Axopatch 200B patch clamp (Axon Instruments/Molecular Devices, Union City, CA, USA) and recorded on a computer hard disk using pCLAMP software (v. 6 and v. 8, Axon Instruments) via a Digidata 1200A (Axon Instruments) signal acquisition system. Data was filtered at 2 kHz (−3 dB, 4-pole Bessel) and digitized at 10 kHz sampling rate. Voltage steps were applied (at 1 Hz) from holding potentials −50 mV to test potentials for 300 ms in duration. The protocol was repeated 200 times.

Single channel analysis

The single channel current traces were corrected for leakage and capacity currents by subtraction of an average of episodes devoid of single channel activity during the test voltage step (null sweeps). The identification of single channel opening and closing transitions using a 50% amplitude threshold was accomplished using Clampfit v. 9.2 (pCLAMP, Axon Instruments). The extent of artifactual lengthening of the observed open time as a result of missed brief closures was estimated according to the equation τ_O=τ_O,obsexp(−τ_d/τ_C), where τ_O is the corrected open-state lifetime, τ_O,obs is the open-state lifetime obtained from histogram fitting, τ_d is the system dead time (0.09 ms), and τ_C is the lifetime of the shortest fitted component in the dwell-state histogram (Colquhoun & Hawkes, 1995). Estimates of τ_O were within 6% of τ_O,obs. Grouped data are reported as means ±s.e.m. Testing for statistical significance was accomplished using an analysis of variance (ANOVA) or Student's t test, as appropriate.

The presence of a single active Ca²⁺ channel in a given patch was assessed by the absence of overlapping currents recorded upon depolarization to 0 mV; only single channel patches were used for analysis. To verify that only one active channel was present we used an estimator for the exact number of channels in a patch as employed in Herzig et al. (2007). P_MAX (maximum of simultaneously open channels) is an estimator for n, the ‘real’ number of channels in a patch with k simultaneous detected openings (overlapping current levels). The P_MAX probability Prob(channel n = k) is then given by:

where k is the number of simultaneous openings (observed channels), n is the real number of active channels, P_o,all is the open probability calculated over the entire recording time, and M is the total number of sweeps. In the present experiments k was always 1, and M was 200.

For −30 mV, P_o,all was an average value of 0.0228, so that

For −10 mV, P_o,all was an average value of 0.079, so that:

Thus, there was <1% chance that the patch recordings analysed contained >1 active LCC.

Results

We analysed the time-, and voltage-dependent gating kinetics of unitary LCC currents, using an external Ca²⁺ ion concentration of 2 mm and in the absence of channel agonists, to gain insight into the physiological gating mechanisms underlying LCC inactivation Fig. 1 shows representative examples of unitary LCC currents recorded in response to depolarizing steps from a holding potential of −50 mV. At potentials just above threshold (−30 mV, Fig. 1A), LCCs opened infrequently and sparse reopenings were randomly distributed throughout the duration (300 ms) of the voltage step. Correspondingly, at this potential the ensemble average current (bottom trace, labelled ‘AVG’) was small and showed little inactivation. However, as the magnitude of the depolarization was increased (e.g. −10 mV, Fig. 1B), LCC openings tended to occur early in the voltage step, and were less frequent at longer latencies. Thus, at depolarized potentials the ensemble-average current displayed a rapid phase of inactivation followed by a smaller slower phase. The time course for this biphasic decay of the ensemble-average current was fitted with a sum of two exponential functions, yielding a fast time constant of 17.6 ± 1.5 ms; and a slow time constant of 85.9 ± 14.9 ms; n= 6 cells). These findings confirm that CDI can be triggered by the Ca²⁺ ion influx through a single LCC (Yue et al. 1990), even with a physiological concentration of Ca²⁺ ions (2 mm) permeating the channel.

Figure 1. Unitary LCC currents recorded with 2 mm Ca²⁺ ions permeating the channel.

Step potentials of −30 mV (A) and −10 mV (B) were applied from a holding potential of −50 mV. Displayed are five cell-attached patch recordings containing unitary LCC openings, at each potential (corrected for leakage and capacity currents as in Methods). The traces displayed are consecutively recorded and derived from the same patch. The traces in the bottom row (labelled ‘AVG’) are the ensemble-average currents of 200 consecutive patch recordings. Note the different magnitude of the current calibrations in (A) and (B) for both the individual traces and the ensemble averages. Data shown are representative of six independent experiments.

A Ca²⁺-dependent mechanism is clearly implicated in LCC inactivation, but how is it manifest in the kinetic behaviour of the single channel? We sought functional evidence of CDI by analysing, in detail, the gating parameters of the unitary LCC currents. First, to visualize the overall gating behaviour of the unitary currents we constructed scatter-plots of event open time vs. latency (i.e. time from beginning of the voltage step), recorded at test potentials of −30 mV (shown in Fig. 2A) and −10 mV (shown in Fig. 2B). A striking difference in the appearance of the scatter-plots is immediately obvious at these two potentials. Whereas the distribution of event open times remained relatively constant at threshold potentials (Fig. 2A), there was an dramatic decrease in LCC open time with increasing latency at depolarized potentials (Fig. 2B).

Figure 2. Scatter-plots of event open times vs. latency.

Recorded at step potentials of −30 mV (A) and −10 mV (B), with 2 mm Ca²⁺ ions permeating the channel. Scatter-plots were constructed from LCC event lists from the analysis of 200 episodes at each potential. Event detection was performed as described in Methods. Each data point represents one opening of the LCC. Data shown are representative of six independent experiments.

To quantitatively explore unitary LCC inactivation we dissected it into its two contributing processes: the frequency of channel opening vs. time, and open dwell time vs. time. An example of this novel analysis is shown in Fig. 3. Representative data are presented for the average frequency of channel opening (Fig. 3A), and for average open dwell time (Fig. 3B) for single LCC events recorded with 2 mm Ca²⁺ ions, as a function of latency (time) during voltage steps to −10 mV. Consistent with the inactivation of the ensemble-average currents at depolarized potentials (Fig. 1B), the average frequency of LCC opening was markedly diminished with increasing latency, and was dramatically reduced to only 15% of its initial value by the end of the step (Fig. 3A, grey line). The time course for the decay of the average frequency of opening at −10 mV was estimated by fitting with an exponential function (pale, smooth curve), yielding an average time constant of 30.2 ± 0.7 ms (n= 5 cells).

Figure 3. The kinetic dissection of unitary LCC parameters at depolarized potentials.

Plots of the average frequency of channel opening (A, top panel), and average channel open time (B, bottom panel) vs. latency during a voltage step to −10 mV, recorded with 2 mm Ca²⁺ ions. The plots were constructed by latency-averaging LCC event parameters over 200 episodes, using a 0.1 ms time bin increment. The individual data points are mean values for each time bin. The grey lines show the average time course of each parameter (adjacent averaging, 100 pts). The decay phase of the average time course was fitted with an exponential function (pale, smooth curve). The time constant for decay of the average frequency of opening (A) was 37.2 ± 0.6 ms, and for the average open time (B) was 137 ± 5.9 ms. The inset (upper right) shows the time course for the probability of opening, fitted with a bi-exponential decay (τ₁, 24 ms; τ₂, 127 ms). Data shown are representative of five independent experiments.

However, a reduction in the frequency of LCC opening is not conclusively diagnostic for the type of inactivation, as this finding might be consistent with either Ca²⁺-dependent, or voltage-dependent mechanisms. How then can the Ca²⁺-dependent and voltage-dependent forms of inactivation be differentiated at the single channel level?

To approach this question the quantitative behaviour of the LCC open time during voltage steps to −10 mV was assessed across an ensemble of episodes by sorting opening event lists by their latency of occurrence during the voltage step, and then averaging, to yield plots of the mean open time vs. latency, as shown in Fig. 3B. The mean open time was greatest at the beginning of the voltage step (approaching 1 ms) and falling to a minimum value (0.2–0.3 ms) by the end of the voltage step. Exponential fits to the decline of the mean open time vs. latency (pale, smooth curve) provided an estimate of the time course, which at −10 mV had an average time constant of 167 ± 11.8 ms (n= 5 cells). Thus, the biphasic time course for the ensemble LCC inactivation reflects the distinct time courses for the latency-dependent decline in the mean open time, as well as the frequency of opening of the LCC.

In comparison with the results at depolarized potentials, Fig. 4 presents the analysis of single LCC events recorded near threshold potentials (i.e. −30 mV), using 2 mm Ca²⁺. At this potential the mean frequency of opening of the LCC (Fig. 4A) displayed only a slight decline with increasing latency. Moreover, the mean open time (Fig. 4B) remained relatively constant throughout the duration of the voltage step. The average open time at −30 mV was 0.52 ± 0.02 ms at the beginning of the step, as compared with 0.41 ± 0.02 ms at the end of the step (n= 6 cells). Thus, the behaviour of both unitary parameters was consistent with the ensemble-averaged currents, which displayed little inactivation at this potential. This lack of inactivation at threshold potentials may be related to the sparse channel openings. We can speculate that these sparse openings do not permit sufficient numbers of Ca²⁺ ions to enter to produce CDI, and/or permit sufficient time for the channel to recover from CDI.

Figure 4. The kinetic dissection of unitary LCC parameters at threshold potentials.

Plots of the average frequency of channel opening (A, top panel) and average channel open time (B, bottom panel) vs. latency during voltage steps to −30 mV, recorded with 2 mm Ca²⁺ ions. The plots were constructed by latency-averaging LCC event parameters over 200 episodes, using a 0.1 ms time bin increment. The individual data points are mean values for each time bin. The grey curves show the average time course of each parameter (adjacent averaging, 100 pts). Data shown are representative of six independent experiments.

The substitution of Ba²⁺ ions for Ca²⁺ ions has been widely used to test for the presence of CDI of the macroscopic LCC currents, as Ba²⁺ ions produce little or no ion-dependent inactivation (Brehm & Eckert, 1978; Josephson et al. 1984; Ferreira et al. 1997). We hypothesized that if the progressive shortening of LCC open time during a voltage step was related to a specific action of Ca²⁺ ions, it would not be mimicked by Ba²⁺ ions. As shown in Fig. 5A, single LCC currents recorded (at −10 mV) with 2 mm Ba²⁺ ions permeating the channel exhibited a pattern of openings quite different from those recorded using Ca²⁺ ions. In contrast to the results with Ca²⁺, single LCC currents carried by Ba²⁺ ions show repeated reopenings throughout the time course of the voltage step. The ensemble-averaged Ba²⁺ ion current (AVG) displayed a much slower rate of inactivation and was well-fitted with only a single exponential function (average time constant of 176 ± 55 ms, n= 5 cells). A slow decline in the frequency of LCC opening with increasing latency was observed in the Ba²⁺ ion recordings (Fig. 5B), which can account for the slow rate of inactivation of the Ba²⁺ ensemble-average currents. However, the mean open time of the LCC was unchanged with latency during depolarizing voltage steps with 2 mm Ba²⁺ ions permeating the channel (Fig. 5C), in marked contrast with the results obtained using Ca²⁺ ions. These differences in LCC gating between Ca²⁺ and Ba²⁺ ions suggest that a latency-dependent shortening of the mean LCC open time with Ca²⁺ permeating the channel is a unique feature of CDI.

Figure 5. Single LCC currents recorded with 2 mm Ba²⁺ ions.

A, five representative current traces recorded at −10 mV. The traces displayed are consecutively recorded and derived from the same patch. The ensemble average of 200 episodes is shown in the bottom trace (labelled ‘AVG’). B, plot of the average frequency of channel opening vs. latency during voltage steps to −10 mV. The decay phase of the frequency of opening in A was fitted with an exponential function with a time constant of 103 ± 6.2 ms. C, plot of the average channel open time vs. latency during voltage steps to −10 mV. Note the lack of latency dependence of the mean open time with 2 mm Ba²⁺ ions. Data shown are representative of five independent experiments.

For whole-cell LCC currents, the extent of CDI is related to the magnitude of the prior Ca²⁺ influx through LCCs (Brehm & Eckert, 1978; Peterson et al. 2000). Accordingly, if the extent of unitary LCC inactivation is determined by the amount of prior Ca²⁺ ion influx through individual LCCs then the open dwell time should display an inverse relationship with the amount of prior Ca²⁺ ion influx during each voltage step. Figure 6 shows the relationship between the prior cumulative open time and the next LCC open time in that episode, across an ensemble of episodes. At −30 mV (Fig. 6A) there was, on average, no open time shortening of the subsequent event with increasing prior cumulative open time. However, at −10 mV (Fig. 6B) and to a greater extent at 0 mV (Fig. 6C), increasing prior cumulative open time was associated with a decrease in open time of the subsequent event. Thus, the predicted inverse relationship between prior Ca²⁺ ion influx and the next event open time was evident. This figure also suggests that the open time shortening was not solely a function of the amount of prior Ca²⁺ entry, as similar amounts of cumulative prior open time that did not produce shortening at −30 mV did so at −10 mV and at 0 mV.

Figure 6. The relationship between cumulative prior LCC open time and the subsequent (next) LCC event open time.

Recorded at step potentials of −30 mV (A), −10 mV (B) and 0 mV (C) with 2 mm Ca²⁺ ions. Cumulative prior open time was calculated during a time window of the first 100 ms of each episode, across ensembles of 200 episodes. The mean open time was calculated for all events with a given cumulative prior open time, using a 0.1 ms time bin increment. The grey curves show the adjacent averaging (20 pts) of the data points. Data shown are representative of four independent experiments.

However, it should be noted that the metric ‘prior cumulative open time’ as used in Fig. 6 may also be a surrogate for latency. To circumvent this complication we tested the prior Ca²⁺ entry hypothesis using an isochronal analysis to determine the relationship between the prior Ca²⁺ ion influx and the shortening of the mean open time (the hallmark of CDI), as evaluated in individual episodes. Each episode was divided into two time windows: an ‘early’ window 1 (0–100 ms) and a ‘late’ window 2 (100–300 ms). For the isochronal analysis of individual episodes, an initial window duration of 100 ms, and a second window duration of 200 ms were determined to be optimal, over the voltage range studied, from our analyses of ensemble latency vs. frequency and latency vs. open time. The cumulative number of Ca²⁺ ions entering during openings in window 1 was correlated with the degree of shortening of the open time (i.e. the ratio of the mean open time during window 2 divided by the mean open time during window 1 (MOT2/MOT1). The relationship between these parameters was assessed by means of a scatter-plot, in which each data point represents one episode in an ensemble of recordings.

Figure 7 displays the application of this analysis for episodes recorded at 0 mV, using 2 mm Ca²⁺ ions (Fig. 7A), or 2 mm Ba²⁺ ions (Fig. 7B). With Ca²⁺ permeation (Fig. 7A), episodes with a larger cumulative number of Ca²⁺ ions entering during openings in window 1 resulted in a decrease in the ratio of MOT2/MOT1. Note that for the majority of episodes the ratio was significantly less than unity, indicating a substantial shortening of open times. The relationship between prior Ca²⁺ ion entry and open time shortening suggests that as little as a few LCC openings (i.e. an influx on the order of a thousand Ca²⁺ ions) may suffice to produce the conformational change(s) responsible for CDI. Thus, for individual episodes, the relative shortening of the mean open time in the second window was more likely with increasing numbers of Ca²⁺ ions during the first window. The apparent stochasticity of the relationship may be related to the nature of the local Ca²⁺ environment. The vast majority of Ca²⁺ ions entering during an LCC opening are rapidly buffered (i.e. <1 ms), so that there may remain only a few free Ca²⁺ ions available to bind to the site that initiates the conformational changes involved in CDI. We believe that it is this highly probabilistic Ca²⁺ environment that contributes to the unitary time course for CDI.

Figure 7. The relationship between prior ion influx and the shortening of the LCC mean open time, in individual episodes.

Recorded with 2 mm Ca²⁺ ions (A) or 2 mm Ba²⁺ ions (B). Individual episodes were recorded at 0 mV and were parsed into two time windows: 0–100 ms (window 1), and 100–300 ms (window 2). For each episode the ratio of the mean open time for window 2 divided by the mean open time for window 1 (MOT2/MOT1) is plotted (semi-logarithmically) as a function of the cumulative number of ions entering during window 1 of that trace (individual data symbols represent one episode of 200). Data below the dotted line at MOT2/MOT1 = 1 indicates ion-dependent shortening of the mean open time for that episode. Data shown are representative of six independent experiments.

The Ca²⁺ ion specificity of the shortening of open times was tested in experiments in which Ba²⁺ ions were substituted for Ca²⁺ ions, and the episodic analysis (as described above) was applied to the unitary LCC currents carried by 2 mm Ba²⁺ ions. In Fig. 7B, MOT2/MOT1 is plotted vs. prior cumulative Ba²⁺ ion entry per episode. Note that the ratio is near unity, regardless of the cumulative Ba²⁺ ion entry. Thus, on average, prior Ba²⁺ ion influx through the LCC during window 1 did not result in a significant shortening of the LCC open time. These results (confirmed in a total of 6 cells) indicate that the decrease in LCC open time is due to a specific action of Ca²⁺ ions, at the level of individual episodes.

To confirm the prior Ca²⁺ ion dependency of the LCC open time, established in the episodic analysis of Fig. 7A, we employed histogram plotting of LCC open times. Figure 8 displays histograms showing LCC event open time distributions with varying prior cumulative Ca²⁺ ion influx. In Fig. 8A the grey columns show the distribution of events with a prior cumulative open time of <5 ms, as compared with all events (black columns). In Fig. 8B the grey columns show the distribution of events with a prior cumulative open time of >40 ms, as compared with all events (black columns). In Fig. 8A and B the event distributions were normalized to allow for a graphical comparison. It is apparent that there is an enhancement in the proportion of longer-duration events in Fig. 8A, where the cumulative prior LCC open time was relatively small (i.e. <5 ms). Conversely, shorter-duration events predominate when the cumulative prior LCC open time was relatively large (>40 ms).

Figure 8. LCC open time histograms (recorded at −10 mV) showing the dependency of event open time on prior cumulative LCC open time, across an ensemble of episodes.

In A the grey columns show the histogram for events from episodes with a prior cumulative open time of <5 ms, as compared with all events (black columns). In B the grey columns show the histogram for events with a prior cumulative open time of >40 ms, as compared with all events (black columns). In A and B both distributions were normalized to allow for a graphical comparison. Data shown are representative of five independent experiments.

We next extended the episodic analysis of open times as a function of prior Ca²⁺ ion entry to determine the effect of voltage. Figure 9 shows representative results of this analysis, comparing data obtained at 0 mV (Fig. 9A) with −30 mV (Fig. 9B). With strong depolarization to 0 mV (Fig. 9A), open time shortening occurred in episodes having a cumulative prior Ca²⁺ entry greater than ∼1000 ions. However, at a weakly depolarizing potential of −30 mV (Fig. 9B), the ratio MOT2/MOT1 approached unity. On average, no open time shortening was observed at this potential, even in episodes with equivalent amounts of prior Ca²⁺ entry. When the single channel amplitude (i) is varied by voltage, the larger amplitude at negative potentials (e.g. −30 mV) is counterbalanced by a shorter open time, so that the total Ca²⁺ entry per opening is, on average, approximately the same as at depolarized potentials (e.g. 0 mV). Thus, this is a test of varying voltage, with a near-constant total Ca²⁺ entry per opening. These results suggest that it is the combined actions of Ca²⁺ and voltage that are necessary to produce inactivation.

Figure 9. Voltage dependence of the effect of prior Ca²⁺ ion entry on LCC open time.

Episodic analysis as described in Fig. 7, recorded at 0 mV (A) and −30 mV (B). The data are plotted on linear axes, and are fitted with a single exponential of the form: y=Aexp(−x/t) +y₀; where y₀ is the offset, A is the amplitude, and t is the ‘apparent binding constant’ (number of Ca²⁺ ions). The best-fit parameters for A were y₀, 0.39 ± 0.06; A, 7.7 ± 1.8; t, 1122 ± 211; with an R² value of 0.53. The best-fit parameters for B were y₀, 1.18 ± 0.10; A, 4.5 ± 0.77; t, 500 ± 117; with an R² value of 0.51. Data shown are representative of four independent experiments.

Lastly, we applied the ‘prior Ca²⁺ entry’ hypothesis to the frequency of opening, and determined the Ca²⁺ ion sensitivity of this parameter. Figure 10 shows the relationship between cumulative prior Ca²⁺ ion influx and the frequency of LCC opening at −10 mV (Fig. 10A), as compared with the shortening of the LCC mean open time (Fig. 10B), using the episodic isochronal analysis. In Fig. 10A for each episode the frequency of opening for window 2 is divided by the frequency of opening for window 1, and is plotted as a function of the cumulative number of Ca²⁺ ions entering during window 1 of that episode (i.e. individual data symbols represent one episode). As evident in the scatter-plot, the majority of episodes fall below the line at Frequency = 1, indicating a reduction in the ratio of frequency of (re)-opening for that episode. The average ratio (frequency 2/frequency 1) was 0.36 ± 0.021 (n= 6 cells). The data were quantified by fitting with a simple one-site binding model, yielding an apparent ‘binding constant’ of 1353 Ca²⁺ ions. In Fig. 10B the scatter-plot shows the ratio of the mean open time for window 2 divided by the mean open time for window 1 (MOT2/MOT1) as a function of the cumulative number of ions entering during window 1 of that episode. Data points below the dotted line at MOT2/MOT1 = 1 indicate Ca²⁺ ion-dependent shortening of the mean open time for that episode. The average ratio MOT2/MOT1 was 0.59 ± 0.08 (n= 6 cells). The data were quantified by fitting with a simple one-site binding model, with an apparent ‘binding constant’ of 1146 Ca²⁺ ions. Thus, both the mean open time shortening (Fig. 10B) and the frequency of (re)-opening (Fig. 10A) displayed a similar sensitivity to the prior Ca²⁺ ion entry.

Figure 10. The relationship between cumulative prior Ca²⁺ ion influx and the frequency of LCC opening (A) and the shortening of the LCC mean open time (B).

Episodes were recorded at a step potential of −10 mV (with 2 mm Ca²⁺ ions) and were parsed into two time windows: 0–100 ms (window 1), and 100–300 ms (window 2). A, for each episode the frequency of opening for window 2 is divided by the frequency of opening for window 1 (FREQ2/2/FREQ1), and is plotted as a function of the cumulative number of Ca²⁺ ions entering during window 1 of that trace (individual data symbols represent one episode). Data points below the line at FREQ2/2/FREQ1 = 1 indicate a reduction in frequency of (re)-opening for that episode. B, for each episode the ratio of the mean open time for window 2 divided by the mean open time for window 1 (MOT2/MOT1) is plotted as a function of the cumulative number of ions entering during window 1 of that trace (individual data symbols represent one episode). Data points below the dotted line at MOT2/MOT1 = 1 indicate Ca²⁺ ion-dependent shortening of the mean open time for that episode. The data are fitted with a single exponential of the form: y=Aexp(−x/t) +y₀; where y₀ is the offset, A is the amplitude, and t is the ‘apparent binding constant’ (number of Ca²⁺ ions). The best-fit parameters for A were y₀, 0.31 ± 0.02; A, 1.19 ± 0.21; t, 1353 ± 277; with an R² value of 0.22. The best-fit parameters for B were y₀, 0.38 ± 0.07; A, 7.59 ± 1.76; t, 1146 ± 213; with an R² value of 0.54. Data shown are representative of six independent experiments.

Discussion

The present results show that the inactivation of the ensemble LCC current results from a Ca²⁺-sensitive decrease in both the frequency of LCC reopening and LCC open time, each parameter displaying a distinct time course. These findings are novel, and have physiological relevance, as this is the first study of unitary LCC inactivation conducted using a permeant Ca²⁺ ion concentration of 2 mm, in the absence of any Ca²⁺ channel agonists.

The extent of unitary LCC inactivation was markedly reduced and its time course slowed when Ba²⁺ ions were substituted on an equimolar basis for Ca²⁺ ions as the permeant species. With Ba²⁺ permeating the channel, individual episodes displayed repeated reopenings throughout the depolarization, with only a modest reduction in the frequency of opening. Moreover, the latency-dependent decrease in open time was absent using Ba²⁺ ions, indicating the ionic specificity of this process.

The present findings also shed light on the inter-dependent roles of Ca²⁺-dependent and voltage- dependent mechanisms in synergistically producing the decay of the ensemble LCC current. This information is not directly available from macroscopic (whole-cell) recordings of I_Ca, for which it has been widely assumed that the initial fast phase of decay represents Ca²⁺-dependent inactivation, and the slower phase represents voltage-dependent inactivation (see reviews by Budde et al. 2002 and McDonald et al. 1994; but see Findlay, 2003 for a novel view of macroscopic inactivation). The present results indicate that both fast and slow phases of LCC current decay are related to CDI. Thus, the deterministic time course for inactivation of the ensemble LCC current (evolving over tens to hundreds of milliseconds) results from stochastic, Ca²⁺-dependent (and voltage-dependent) conformational changes governing both the frequency of opening and open time of the unitary LCC.

In addition, the present results address the stoichiometry of CDI at the unitary LCC current level. We derive this information from the relationship between prior Ca²⁺ ion entry and subsequent unitary LCC mean open time within individual episodes. Using that analysis we found that the cumulative Ca²⁺ ion influx during several LCC openings was sufficient to induce the conformational changes that produce CDI. With a physiological external Ca²⁺ concentration (2 mm) that influx is on the order of a thousand ions. However, a flux of this magnitude may actually result in only a very few free Ca²⁺ ions near the inner mouth of the channel, with the vast majority being rapidly buffered (Bers, 2001).

Our findings may be compared with those of earlier studies of single Ca²⁺ channel inactivation. For Ca²⁺ channels of invertebrate neuronal cell bodies (recorded using 40 mm Ca²⁺) a correlation between Ca²⁺ entry and subsequent Ca²⁺ channel closed times was absent, and it was concluded that Ca²⁺ entry did not produce inactivation (Lux & Brown, 1984). In contrast, for LCCs in guinea-pig heart cells Yue et al. (1990) found that Ca²⁺ entering during LCC openings (recorded using 160 mm Ca²⁺, and an LCC agonist, 8-br-cAMP) produced alterations in gating transition rates (as detected by an ensemble conditional open probability analysis) that evolved over hundreds of milliseconds. However, underlying time courses for the changes in single LCC gating parameters were not explicitly identified in their analysis. Moreover, the high concentration of external Ca²⁺ ions and the addition of an LCC agonist that were used in that study are conditions known to affect LCC gating (Findlay, 2003), and may have altered the physiological properties of CDI.

Subsequently, Imredy & Yue (1994) reported that prepulses eliciting Ca²⁺ entry resulted in a slow component in the distribution of LCC first latencies during a second, test pulse (using 150 mm Ca²⁺, 10 mm Ba²⁺ and 8-br-cAMP). This feature was interpreted as a transition from a basal gating mode (termed ‘mode 1’) into a mode characterized by a long-lived closed state, leading to a brief open state (termed ‘mode Ca²⁺’). However, the time course for the transition into mode Ca²⁺ was not measured in those experiments, nor was any correlation made between the amount of Ca²⁺ entry during the prepulse, and the prolongation of first latency during the test pulse in individual episodes. Also using guinea-pig heart cells (and 10 mm Ca²⁺), Rose et al. (1992) proposed that multiple distinct gating patterns underlie the transient and maintained components of I_Ca. Thus, the present experiments, conducted with a physiological Ca²⁺ ion concentration and in the absence of any Ca²⁺ channel agonists, have explicitly identified the time course for each of the Ca²⁺-dependent components of unitary LCC inactivation that were presciently suggested by those pioneering single channel studies.

Recently, the key molecular structures involved in this crucial negative-feedback regulation of the LCC have been elucidated (de Leon, 1995; Soldatov et al. 1998; Peterson et al. 1999, 2000; Zuhlke et al. 1999; Pitt et al. 2001; Soldatov, 2003). Our findings may be further interpreted within the framework of a proposed molecular model of LCC inactivation. Ca²⁺ entry (and its binding to calmodulin (CaM) on the carboxy-tail of the α1 subunit of the LCC) is thought to trigger the removal of an inhibition of inactivation mediated by the carboxy-tail, thereby allowing a rapid, voltage-dependent closure (collapse) of the pore region of the channel (Soldatov et al. 1998; Pitt et al. 2001; Soldatov, 2003). The present results are consistent with this novel view of inactivation in which Ca²⁺ binding triggers the removal of a resident ‘brake’ that prevents pore collapse. In that model apoCaM is tethered to the c-terminal tail and signals actively to slow inactivation. When the c-terminal lobe of CaM binds to the nearby CaM effector sequence, the braking effect is relieved, thereby facilitating the constriction of the pore and inactivation is accelerated. This rapid phase of inactivation of the Ca²⁺-conducting LCC is not always complete (i.e. absorbing) and can lead to a channel conformation that still permits brief, albeit infrequent, reopenings. We speculate that the shift to brief, infrequent reopenings is a result of the removal of a stabilizing influence of the c-terminal tail on the open state of the LCC. Thus, when the c-terminal tail is interacting with the pore, LCC open times are relatively long and reopenings are frequent. Removal of the interaction favours pore closure, although a brief open conformation can be occasionally reached. We anticipate that the future application of the kinetic analysis of unitary channel gating described in the present study will further the identification of specific molecular determinants and channel mechanisms that govern CDI.

In cardiac myocytes the strength and timing of contraction is controlled by local Ca²⁺-induced Ca²⁺ release, which is determined by the properties of the unitary LCC currents (Stern, 1992; Santana et al. 1996; Soeller & Cannell, 2004). In this physiological context what might be the significance of the shortening of LCC open time during CDI? Perhaps the significance of this feature of CDI is that it prolongs the final inactivation of the LCC, which otherwise might inactivate rapidly and completely by a purely voltage-dependent mechanism. Thus, CDI may allow a small component of inward current to be maintained for the electrogenesis of the AP plateau, but with a lower probability of eliciting Ca²⁺ sparks. In the future it will be of importance to investigate how the physiological gating of the unitary LCC impacts upon local Ca²⁺ signalling, not only for cardiac myocytes, but also for the diverse physiological functions governed by Ca²⁺ ions across a wide range of cell types.

Glossary

Abbreviations

CDI

Ca²⁺-dependent inactivation

CICR

Ca²⁺-induced Ca²⁺ release

FREQ

frequency of opening

LCC

L-type Ca²⁺ channel

MOT

mean open time

SR

sarcoplasmic reticulum

VDI

voltage-dependent inactivation

Author contributions

I.J., A.G., M.S., Conception and design of the experiments. I.J., A.G., M.S. Collection, analysis and interpretation of data. I.J., E.G., J.L., M.S. Drafting the article or revising it critically for important intellectual content. All authors approved the final manuscript. The experiments were conducted at the NIA/NIH.

Author's present address

A. Guia: Aviva Biosciences, San Diego, CA, USA.