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Differential Modulation of Cardiac Ca²⁺ Channel Gating by ß-Subunits

Igor Dzhura ^* and Alan Neely ^* 

^* Department of Physiology, Texas Tech University, Lubbock, Texas USA; and Centro de Neurosciencias de Valparaíso, University of Valparaíso, Valparaíso, Chile

Correspondence: Address reprint requests to Alan Neely, Centro de Neurociencias de Valparaíso, Universidad de Valparaíso, Gran Bretaña 1111, Valparaíso, Chile. Tel.: 56-32-50-8054; Fax: 56-32-28-3320; E-mail: alan.neely{at}uv.cl.

	ABSTRACT

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION ACKNOWLEDGEMENTS REFERENCES

 
To investigate the mechanisms that increase ionic currents when Ca²⁺ channels' ₁ subunits are co-expressed with the ß-subunits, we compared channel activity of Ca_V1.2 (_1C) co-expressed with ß_1a and ß_2a in Xenopus oocytes. Normalized by charge movement, ionic currents were near threefold larger with ß_2a than with ß_1a. At the single-channel level, the open probability (P_o) was over threefold larger with ß_2a, and traces with high P_o were more frequent. Among traces with P_o > 0.1, the mean duration of burst of openings (MBD) were nearly twice as long for _1Cß_2a (15.1 ± 0.7 ms) than for _1Cß_1a (8.4 ± 0.5 ms). Contribution of endogenous ß_3xo was ruled out by comparing MBDs with _1C-cRNA alone (4.7 ± 0.1 ms) with ß_3xo (14.3 ± 1.1 ms), and with ß_1b (8.2 ± 0.5 ms). Open-channel current amplitude distributions were indistinguishable for _1Cß_1a and _1Cß_2a, indicating that opening and closing kinetics are similar with both subunits. Simulations with constant opening and closing rates reproduced the microscopic kinetics accurately, and therefore we conclude that the conformational change-limiting MBD is differentially regulated by the ß-subunits and contributes to the larger ionic currents associated with ß_2a, whereas closing and opening rates do not change, which should reflect the activity of a separate gate.

	INTRODUCTION

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION ACKNOWLEDGEMENTS REFERENCES

 
High-voltage Ca²⁺ channels are multisubunit membrane proteins composed of four nonhomologous subunits: the ₁ subunit, encompassing all the structural elements of a functional voltage-activated channel; and three regulatory subunits: ₂/, ß, and . Co-expression of ₂/- and/or ß-subunits with the ₁ subunit increases macroscopic currents, suggesting that these subunits may regulate channel abundance (Wei et al., 1991; Williams et al., 1992). However, increased ionic currents often displayed significant alteration in time and voltage dependence (Stea et al., 1993; Singer et al., 1991), indicating that the function of the channel may also be modulated by the regulatory subunit. Through gating current measurements we showed that co-expression of ß_2a augments ionic conductance fivefold without changing the maximum gating charge movement (Neely et al., 1993). The coupling efficiency of charge movement to pore opening is also increased by the ß-subunit in a neuronal Ca²⁺ channel (Ca_V2.3) expressed in Xenopus oocytes (Olcese et al., 1996).

Further insight in the functional changes associated with co-expression of the ß-subunit was gained by comparing single-channel activity of Ca_V1.2 expressed with or without ß_2a (Wakamori et al., 1993; Neely et al., 1995; Costantin et al., 1998). All these studies rule out changes in single-channel conductance and report increases in the frequency of long openings to explain, at least partially, how ionic currents may be increased by the ß-subunit. Since native Ca²⁺ channels activate in different gating modes with characteristic open probability (P_o) (Cavalie et al., 1986; Hess et al., 1984), the frequency of long openings may be increased by ß if the interaction with ₁ promotes modes of higher P_o. Shift in gating modes with different subunit combinations has been shown to occur in the acetylcholine-activated channel (Naranjo and Brehm, 1993). However, rather than an increase in the fraction of time spent in the high P_o mode, co-expression of ß_2a with _1C was correlated instead with an increase in the frequency of mode switching (Costantin et al., 1998). Co-expression of the neuronal isoform of ß with Ca_V2.1 led to an increase in the mean open-time also, with no evidence of mode shifting (Wakamori et al., 1999).

A common assumption in these co-expression experiments was that contribution of endogenous subunits is negligible. Today this view is no longer tenable since we know that ß releases ₁ from the endoplasmic reticulum (Bichet et al., 2000) and is required for the expression (Tareilus et al., 1997) and proper targeting of channels (Chien et al., 1995; Brice et al., 1997). This combined effect on expression and function was suggested to reflect the binding of multiple ß-subunits: association with one ß would be required for expression whereas functional changes would come about with additional ß-subunits. In this scheme, lower coupling efficiencies may arise from channels with an incomplete complement of ß, as it would be the case if, for example, ß_1a expresses less efficiently than ß_2a (Birnbaumer et al., 1998). Here we compare the gating behavior of channels from oocytes co-expressing _1C with two different ß-subunits: the cardiac (ß_2a) and the skeletal (ß_1a) muscle isoform. We show that oocytes expressing _1Cß_2a display higher ionic-to-gating current ratio than the ones expressing _1Cß_1a. At the single-channel level, we found that the P_o for channels from _1Cß_2a expressing oocytes is severalfold higher than for _1Cß_1a, with an increase in the number of sweeps with higher P_o. Among traces with P_o > 0.1, MBD was nearly twice as long for _1Cß_2a than for _1Cß_1a, suggesting that the ß-subunit modulates gating within a mode. We also analyzed oocytes expressing other subunit combinations to rule out channel heterogeneity as the source of this functional difference.

The duration of burst of openings is determined by the transition rate to long-lived closed state and the ratio between opening and closing rates (Colquhoun and Sakmann, 1985). When opening and closing events are well-resolved, all these rates can be obtained directly from dwell-time histograms. In the presence of the dihydropyridine agonist Bay K 6844, as used here, most openings appear well-resolved, but they are often interrupted by brief closures that, when missed, lead to an overestimation of the open state's lifetime. This error cannot be corrected for in a model-independent manner (McManus and Magleby, 1991). To test for differences in opening and closing rates in a detection-independent manner, we compared the distribution of current amplitudes of _1Cß_2a and _1Cß_1a and found no difference. Opening and closing rates derived directly from these distributions (Marks and Jones, 1992; Prodhom et al., 1989) were over 10-fold faster than predicted from dwell-time histograms. Simulated single-channel activity with these faster rates reproduced open-time and burst-duration histograms for both subunit combinations when only the rate leading to long-lived closed states was changed. Changes in fast gating that increase MBD visibly alter the open-channel amplitude distribution, indicating that a conformational change leading to long-lived closed state is being differentially regulated by the ß-subunits and that modulation of this transition partially accounts for the increases in coupling efficiencies. In contrast, closing and opening rates do not appear to sense the presence of the ß-subunit, indicating that a separate gating mechanism is involved.

	METHODS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION ACKNOWLEDGEMENTS REFERENCES

 
RNA synthesis and oocytes preparation
The cardiac Ca²⁺ channel ₁ subunit was an amino terminal deletion mutant of the rabbit Ca_V1.2 (N60) that yields larger ionic and gating currents without changes in kinetics or sensitivity to the modulation by the ß-subunit (Wei et al., 1996). The ß_2a (Wei et al., 1991) and ß_1b (Pragnell et al., 1991) subunits were from rat, the ß_1a was from rabbit (Ruth et al., 1989) and ß_3xo is a ß₃-like subunit cloned from Xenopus oocytes (Tareilus et al., 1997). N60, ß_2a, and ß_3xo subunits were subcloned into pAGA2 (Sanford et al., 1991), ß_1a in pGEM-3, and ß_1b in pBS. pAGAN60, pAGAß_2a and pAGAß_3xo cDNA were linearized with HindIII; pBSß_1b with NotI and pGEMß_1a with XbaI (New England Biolabs, Beverly, MA). RNAs were synthesized in vitro with the mMESSAGE MACHINE (Ambion, Austin, TX) according to the manufacturer instructions and resuspended in 10 µl of water at 4–6 µg/µl. Stock solutions were diluted from 10- to 100-fold and the dilutions yielding larger expression and maximal functional changes were chosen for subsequent experiments. For the oocytes included in the article, cRNA were diluted as follows: ß_2a 1:40, ß_1a 1:20, ß_1b 1:20, ß_3xo 1:60, and N60 1:20. 50 nl of cRNA were injected per oocyte using a 10-µl automatic injector (Drummond Scientific, Broomall, PA).

Large Xenopus female frogs (Nasco, Modesto, CA) were anaesthetized by immersion in 0.15% tricaine for 15 min. One or two lobes of an ovary were removed through a 10- to 12-mm abdominal incision under sterile conditions. Oocytes were harvested from the same frog up to five times, allowing at least six weeks of recovery. This procedure, general care, and handling of Xenopus frogs were carried out according to a protocol approved by the Institutional Animal Care Committee of Texas Tech University Health Sciences Center. Oocytes were defolliculated by collagenase treatment (2 mg/ml, type II from Worthington Biochemical, Lakewood, NJ) for 30 min in Ca²⁺-free solution (82.5 mM NaCl, 2.5 mM KCl, 1 mM MgCl₂, and 5 mM HEPES titrated to pH 7.6 with NaOH). Collagenase treatment was stopped by repeated rinses with Ca²⁺-free media that was then replaced by SOS (100 mM NaCl, 2 mM KCl, 1.8 mM CaCl₂, 1 mM MgCl₂, and 5 mM HEPES titrated to pH 7.6 with NaOH) in several partial dilution steps over a period of 1 h. Oocytes were maintained at 19.5°C in SOS supplemented with Na-pyruvate (2.5 mM), gentamycin (50 or 200 µg/ml), and Verapamil (10 µM). The latter appears to increase survival of oocytes expressing large Ca²⁺ currents, although a systematic survey was not carried out.

Recording techniques
Macroscopic currents were recorded using the cut-open oocyte voltage-clamp technique (Taglialatela et al., 1992) with a CA-1 amplifier (Dagan, Minneapolis, MN). Oocyte membrane exposed to the bottom chamber was permeabilized by a brief treatment with 0.1% saponin. The voltage pipettes were filled with 2 M tetramethylammonium-methanesulfonate, 50 mM NaCl, and 10 mM EGTA and had tip resistance from 600–1200 k. Data acquisition and analysis were performed using the pCLAMP6 system (Axon Instruments, Foster City, CA). The external solution contained 10 mM Ba²⁺, 96 mM n-methylglucamine, and 10 mM HEPES, and the pH was adjusted to 7.0 with methanesulfonic acid (MES). The internal solution contained 120 mM n-methylglucamine, 10 mM EGTA, and 10 mM HEPES and the pH was adjusted to 7.0 with MES.

Patch-clamp recordings of single channels were performed with an Axopatch-200A with an integrating headstage (Axon Instruments, Foster City, CA). Patch pipettes were pulled from aluminum silicate capillary (Sutter Instrument, Novato, CA) and filled with a solution containing 76 mM Ba²⁺, 10 mM HEPES, and 100 nM S(-)Bay K 8644 (Research Biochemical International, Natick, MA). The pH was adjusted to 7.0 with MES. Pipette resistance ranged from 4 to 7 M. Vitelline membranes were removed manually after exposure to a hyperosmotic solution (2–5 min) containing 200 mM K-glutamate, 20 mM KCl, 1 mM MgCl₂, 10 mM EGTA, 10 mM HEPES, and 100 nM S(-) Bay K 8644 and titrated to pH 7.2 with KOH. Oocytes were then placed in the recording chamber with a depolarizing solution of the following composition: 110 mM K⁺, 10 mM HEPES titrated to pH 7.0 with MES. Channels were activated by 185-ms pulses to 0 mV at 1 Hz from a holding potential of -70 mV sampled at 20 kHz and filtered at 2 kHz.

Unless noted otherwise, all chemical and reagents were from Sigma-Aldrich (St. Louis, MO).

Data analysis
Dwell-time histograms
Dwell-time histograms were constructed with the dedicated software TRANSIT (Van Dongen, 1996) from traces corrected for capacitive transients and leakage currents by subtracting the average of traces without openings. This software also yields a P_o estimate by calculating the fraction of time spent in the open state. The number of samples was reduced by one-half before the analysis resulting in an effective sampling rate of 10 kHz. Multiexponential probability density functions (PDF) were adjusted to fit dwell-time histograms displayed in Sigworth-Sine coordinates using a maximum likelihood algorithm (Sigworth and Sine, 1987). The first bin included for the analysis of closed and open-time histograms was from 0.36 to 0.44 ms that corresponds to the first bin followed by a nonempty bin. This eliminates events shorter than three times the dead time of the system (0.1 ms).

A burst was defined as a series of consecutive openings separated by closures briefer than _crit, such that

(1)

Here, _L and _S correspond to the mean duration of long and short closures respectively obtained from fitting closed-duration histograms with a double-exponential PDF. Shut intervals pertaining to either long- or short-lived closed states will have the same probability of being misclassified if their duration is equal to _crit (Colquhoun and Sakmann, 1985).

All-points histograms
Opening and closing rate constants were extracted from all-point histograms according to a method introduced by Fitzhugh (1983) and Yellen (1984) and later adapted for Ca²⁺ channels by Marks and Jones (1992). Briefly, the filtered flicker of a channel between a single open and closed state is described by a ß-distribution in the absence of noise,

(2)

where ^* = k_O and ß^* = k_C, k_O and k_C are the opening and closing rates, respectively, is the time constant of the filters, and x is the normalized current amplitude (open = 1 and closed = 0). The value of was calculated as in Marks and Jones (1992). Background noise was included as a convolution of B(x) with a Normal distribution describing baseline fluctuations (Villarroel et al., 1988),

(3)

where µ and are the mean and standard deviation of the baseline noise, respectively.

To eliminate capacitive transients, a multiexponential function that best described the transient at the beginning of the test pulse was subtracted from each pulse. After this subtraction, the beginning and end of the traces were forced to ‘0’ eliminating any remaining capacitive component. The data was then filtered digitally at 300 Hz with a Gaussian filter. Traces whose baseline deviated from zero were readjusted by eye. All-point histograms were then constructed with FETCHAN6 (Axon Instrument) and exported to an Excel (Microsoft, Seattle, WA) spreadsheet for further analysis. Bins between -0.3 and +0.3 pA were normalized to a total area of ‘1’ and a Normal distribution adjusted. The theoretical Normal distribution was then convolved to B(x) to obtain A(x), which was then compared to the open-channel amplitude PDF (APDF). The convolution was performed with a program originally written in QuickBasic by Marks and Jones (1992), later adapted as an Excel macro. Amplitude bins of all-points histograms were divided by the single-channel current amplitude and the area normalized by the total count between 70% and 150% of the amplitude to generate the APDF. Single-channel current amplitudes were first measured in prolonged openings and then adjusted (±5%) to improve the quality of the fit of the APDF.

Simulation of single-channel activity
The program CSIM 2.0 (Axon Instruments) was used to simulate single-channel activity. The single-channel conductance was set to 17 pS and the reversal potential to +70 mV. Sampling rate was set at 10 kHz, the filter at 1.7 kHz, and 0.18 pA of noise was added. The cutoff frequency was determined by measuring the rise time (10–90% in 200 µs) of single-channel openings from the experimental records.

	RESULTS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION ACKNOWLEDGEMENTS REFERENCES

 
Macroscopic currents
Fig. 1 compares voltage-clamp traces and current-voltage plots from oocytes expressing either _1cß_2a or _1cß_1a. To separate differences in function and expression for each oocyte, we normalized inward currents measured at the end of each pulse by the amount of charge movement measured at the onset of a depolarizing step (Q_on) to the current reversal potential (+55 to +67 mV, Fig. 1 B). At these voltages, contribution of ionic current is negligible (Fig. 1 B) and charge movement is expected to have reached their maximum for the different subunit combinations of Ca⁺² channels expressed in oocytes (Neely et al., 1993). Channel expression, as assayed by Q_on, was highly variable and not significantly different for the two subunit combinations. In 10 mM Ba²⁺ the average Q_on was 503 ± 129 nC (n = 8) and 283 ± 117 nC (n = 7) for _1cß_1a and _1cß_2a respectively. On the other hand, when ionic currents were normalized by Q_on, we observed that _1C combined with ß_2a yields larger ionic currents (-2.61 ± 0.62 nA/pC at +10 mV, with n = 7) than when combined with ß_1a (-0.97 ± 0.26 nA/pC at +20 mV, with n = 8). Such an increase in coupling efficiency between charge movement and ionic current can occur through an increase in the single-channel conductance and/or the P_o of the channel. Since these issues are addressed through single-channel recordings taken in the presence of channel agonist and high external Ba²⁺ to overcome bandwidth and noise limitations, we also compared normalized ionic currents in 0.1 µM S(-) Bay K 8644 and 76 mM external Ba²⁺. In these recording conditions, _1cß_2a expressing oocytes yield -5.56 nA/pC (at +20 mV, with n = 7) compared to -1.92 nA/pC (at +25 mV, with n = 8) for _1cß_1a. (Fig. 1 D) and Q_on was 205 ± 21 nC (n = 8) for _1cß_1a and 250 ± 92 nC (n = 7) for _1cß_2a.

View larger version (29K): [in this window] [in a new window]   FIGURE 1  Current-voltage relationship normalized by charge movement for oocytes expressing 1Cß1a or 1Cß2a. (A) Superimposed voltage-clamp traces during 60-ms depolarizing steps from -40 mV to +55 mV in 5-mV increments from two oocytes; one expressing 1Cß1a (top) and the other 1Cß2a (bottom) in 10 mM external Ba+2. Membranes were held at -80 mV between depolarizing pulses and linear components were subtracted by the p/-4 protocol from the same holding voltage. Currents were sampled at 5 kHz and filtered at 1 kHz. (B) Example of charge-movement measurement (shaded area) at the onset of a depolarization to the current reversal potential from an oocyte expressing 1Cß2a. (C) Average IV plots normalized by charge-movement from eight oocytes expressing 1Cß1a () and seven oocytes expressing 1Cß2a (•). Error bars represent SE. (D) Normalized IV plots in the presence of 0.1 µM (-)Bay K 8644 and 76 mM external Ba2+ from eight oocytes expressing 1Cß1a () and seven oocytes expressing 1Cß2a (•).

View larger version (61K): [in this window] [in a new window]   FIGURE 2  Single-channel recordings (top) and dairy plots (bottom) from oocytes expressing either 1Cß1a (A) or 1Cß2a (B). The patch from the oocyte expressing 1Cß1a was interrupted after 500 traces whereas 1000 traces were collected from the oocyte expressing 1Cß2a. Traces with Po > 0.1 are labeled by *. Shaded rectangles over the dairy plots point to traces selected for display. Channels were activated at 1 Hz by 185-ms pulses to 0 mV from a holding potential of -70 mV. Recordings were sampled at 20 kHz and filtered at 2 kHz.

View larger version (39K): [in this window] [in a new window]   FIGURE 3  Mean current and Po distribution from oocytes expressing 1Cß1a (cross-hatched) and 1Cß2a (shaded) subunits. (A) Mean current traces constructed with 2628 traces from seven single-channel patches from four oocytes expressing 1Cß1a (dotted line) and 1514 traces from four single-channel patches from four oocytes expressing 1Cß2a (continuous line). Traces were smoothed by averaging of window of 5 ms. (B) Po frequency histograms constructed from the same records used in A expressed as a percent of the total number of traces. (C) Po frequency histograms as in B but using logarithmic binning. (D) Cumulative Po distributions. For 1Cß2a, on average, 77.4 ± 3.1% of the traces have Po ≤ 0.06, while 23.8 ± 3.1% have Po > 0.06; 18.0 ± 1.9% Po > 0.1; 4.8% ± 0.3% Po > 0.3; and 1.7 ± 0.3% Po > 0.5. For 1Cß1a, 92.0 ± 2.7% of the traces have Po ≤ 0.06, while 8.0 ± 2.7% of the traces have Po > 0.06; 4.4 ± 1.6% Po > 0.1; 0.3 ± 0.1% Po > 0.3; and 0.03 ± 0.03% Po > 0.5. The differences are statistically significant for all bins in D (P < 0.05, two-tailed t-test).

To sort out the extent to which changes in gating modes or in gating within each mode contributed to this difference, we compared the P_o distributions through P_o histograms combining all traces. Although we found a high degree of overlap (Fig. 3 B), the Mann-Whitney-Wilcoxon test (Bancroft and Han, 1981) indicates that there is more than a 95% probability that the two histograms originated from different populations and that P_o for ß_2a is higher than for ß_1a. The average P_o calculated from these histograms yields 0.008 ± 0.003 for _1Cß_1a and 0.020 ± 0.007 for _1Cß_2a. We also noted that the sum of two exponential distributions approximated the P_o distributions and thus resorted to logarithmic binning to resolve different gating modes. Indeed, with this transformation, P_o histograms of active traces appear clearly bimodal, with a peak at low P_o 0.003 for both subunit combinations, and a second peak at 0.1 for _1Cß_1a and at 0.2 for _1Cß_2a (Fig. 3 C). Also, the relative frequency of traces with P_o > 0.1 was several fold larger for _1Cß_2a (18.0 ± 2.3%) than for _1Cß_1a (4.4 ± 1.6%), whereas traces with no or very low activity (P_o ≤ 0.06) were more frequent with _1Cß_1a (92.0 ± 2.7%) than with _1Cß_2a (77.4 ± 3.1%; Fig. 3 D). These results indicate that increased frequency of high P_o sweeps contribute to the augmented currents observed in oocytes expressing _1Cß_2a.

Unfortunately, patch-to-patch variability, the relatively short duration of runs and difficulties in separating each mode, prevented us from establishing whether this increase is due to a higher chance of entering the high P_o mode or larger stability of this state. On the other hand, the shift in the mode of the high P_o sweeps revealed in the log-binned P_o histograms suggests that channel kinetics within gating modes may also contribute to increases in P_o mediated by co-expression of ß_2a.

Dwell-time histograms
For the analysis of dwell-times, recordings from patches with a few isolated double openings were also included to improve our estimates of mean open times and MBD by raising the number of experiments to 14 for _1Cß_2a and 12 for _1Cß_1a. However, the lifetime of long closed states may be underestimated, since even for sweeps without overlapping openings there is a chance that two channels became active simultaneously. Another shortcoming of adding patches known to have more than one channel is that sweeps selected by mode may also include some activity of channels in different modes. Bearing these limitations in mind, only the changes in the major components of dwell-time histograms were considered.

Open-time histograms constructed with all traces in a recording often required the sum of up to three exponential distributions to adequately describe the data, even for channels with seemingly mono-modal P_o distribution (Fig. 4). On the other hand, contribution of brief openings (_fast < 0.5 ms) to open-time histograms was greatly reduced, and often no longer detectable when traces with P_o ≤ 0.1 were excluded, even for clearly bimodal channels, as illustrated in Fig. 4. Average time constants and relative amplitudes of each component for histograms constructed with all traces or only with traces with P_o > 0.1 or P_o ≤ 0.1 are summarized in Table 2. We only found a significant difference in the time constant of the fast component measured in the histograms built from traces with P_o > 0.1. However, this component turns out to be shorter for _1Cß_2a (1.54 ± 0.33 ms compared to 2.60 ± 0.56 ms for _1Cß_1a) and thus, would contribute to a decrease in P_o for _1Cß_2a. We also noted that events with open-time < 0.6 ms were more frequent than predicted by the exponential distributions, suggesting that the combined effect of noise and limited bandwidth was giving rise to nonexponential distributions (McManus et al., 1987). This problem was further aggravated by the small number of events in each recording (562 ± 177 and 1402 ± 299 events for _1Cß_1a and _1Cß_2a, respectively). As an alternative, we compared the time constants defining the single exponential distribution that best described the open-time histograms constructed from traces with P_o > 0.1. With this simplification, we were able to detect a modest (26%) but statistically significant increase in _open with ß_2a (Table 4).

View larger version (42K): [in this window] [in a new window]   FIGURE 4  Open-time histograms and Po distributions from oocytes expressing 1Cß1a and 1Cß2a. (A) Po histograms with logarithmic binning from an oocyte expressing 1Cß1a (top). The middle and bottom panels illustrate two 1Cß2a examples that differ in the relative contribution of low Po traces. (B) Open-time histograms using all traces, and (C) open-time histograms from traces with Po > 0.1. Histograms were fitted by a single exponential distribution (thick lines) or to the sum of two or three components (dashed lines). The thin lines show the contribution of individual exponential distributions. See Table 4 for parameters used.

View this table: [in this window] [in a new window]   TABLE 2  Multiexponential distributions describing open-time histograms for 1Cß1a and 1Cß2a

View this table: [in this window] [in a new window]   TABLE 4  Dwell-times from oocytes expressing either 1Cß1a or 1Cß2a

View larger version (38K): [in this window] [in a new window]   FIGURE 5  Closed-time histograms from oocytes expressing 1Cß1a and 1Cß2a. Same patches as in Fig. 4 with A and B corresponding to patches showing a single peak in the Po frequency histogram and C from the oocyte expressing 1Cß2a in which the Po frequency histogram reveals two modes of activity. The left panel shows a closed-time histogram using all traces, whereas in the right panel only traces with Po > 0.1 were selected. The sum of two exponential distributions was used to fit the data (thick line). The thin lines show the contribution of individual exponential distributions. See Table 3 for parameters used.

Burst-durations analysis
A potential mechanism that may increase the P_o within a gating mode is by reducing the exit rate to long-lived closed states. This should be reflected in an increase in MBD. Burst-duration histograms for patches from oocytes expressing _1Cß_1a or _1Cß_2a are compared in Fig. 6. When all traces were included in the analysis, often single exponential distributions did not yield an adequate fit (Fig. 6 C), whereas burst-duration histograms from traces with P_o > 0.1 appeared well-described by single exponential distributions (Fig. 6, A and B, and Table 4). The time constant defining this single exponential distribution was taken as the MBD. For a few patches, we systematically varied the minimum P_o of the traces included in the burst-duration histograms and found no changes in MBD from P_o > 0.05 to P_o < 0.3; selecting sweeps with higher P_o resulted in a sharp increase in MBD. We also found that adding a second exponential component improved the quality of the fit only marginally, and the duration of the slowest component remained within 15% of the time constant obtained from the fit with a single exponential distribution. The slow component of double-exponential distributions used to adjust burst-duration histograms from all traces had average time constants of 9.5 ± 1.1 ms and 12.0 ± 1.0 ms for _1Cß_1a and _1Cß_2a, respectively.

View larger version (38K): [in this window] [in a new window]   FIGURE 6  Burst-duration histograms from oocytes expressing 1Cß1a and 1Cß2a. Burst-duration histograms from all traces (left) are compared to histograms containing only burst from traces with Po > 0.1 (right). Same patches as in Figs. 4 and 5. Patches in which the distribution of Po show a single peak (A and B), burst-durations followed a single exponential distribution when either all or only Po > 0.1 traces are included. In contrast, burst-durations histograms from patches with two modes of activity can be described by a single exponential distribution only when traces with Po > 0.1 are used (C). Time constants (ms) defining the exponential distribution that best fitted the data are shown next to each histogram.

View larger version (24K): [in this window] [in a new window]   FIGURE 7  Burst-duration histogram from oocytes expressing 1C alone or combined with ß1b or ß3xo. Representative traces (top) and burst-duration histograms from traces with Po > 0.1 (bottom) of patches containing a single channel from Xenopus oocytes injected with mRNA encoding the 1C subunit alone (A), combined with mRNA for ß1b (B) or for ß3xo (C). Continuous lines depict the single exponential distributions that best fitted the burst-duration histograms; the time constants (ms) are shown next to each plot.

View this table: [in this window] [in a new window]   TABLE 5  Dwell-times from oocytes expressing 1C, 1Cß3XO or 1Cß1b

(4)

where

(5)

and

(6)

By reversing S and O, a similar set of equations yields _true(O) and _true(S).

Assuming T_d = 0.1 ms and _obs(O) and _obs(S) from Table 4 (open-time and short closed-time respectively), we numerically solved the complete set of equations for _1Cß_1a and _1Cß_2a. As expected, two sets of solutions were obtained for each subunit combination; for _1Cß_1a, _true(O) and _true(S) can take the values of 4.10 ms and 0.66 ms or 0.039 ms and 0.023 ms, respectively, whereas _1Cß_2a, 5.07 ms and 0.57 ms, or 0.041 ms and 0.022 ms, constitute solutions for _true(O) and _true(S), respectively. To determine which of the two possible solutions is a better approximation of _true(O) and _true(S), we used the distribution of current amplitudes within a burst of openings (APDF) to obtain a detection-independent estimate of the channel opening and closing rate (Pietrobon et al., 1989; Prodhom et al., 1989; Villarroel et al., 1988; Yellen, 1984). Here, to simplify the analysis we neglected the contributions from transitions at the beginning and end of bursts and constructed all-points histograms from whole traces with P_o > 0.1 (see Methods). One of the advantages of this approach is that information on baseline noise can be extracted from the same histogram. Fig. 8 compares APDF from two patches expressing _1Cß_1a and _1Cß_2a, chosen for having the same baseline noise and open-channel current amplitudes, and shows that they are nearly identical. This match suggests that opening and closing rates for both subunit combinations are the same. To extract opening and closing rates from APDF, we systematically varied k_O and k_C and found that when the ratio k_O/k_C was kept at 10 and k_O > 10,000 s^-1, A(x) fit the experimental APDF extremely well. The thick line in Fig. 8 C corresponds to A(x) when k_O = 25,000 s^-1 and k_C = 2500 s^-1. This indicates that _true(S) and _true(O) are near 10-fold shorter than predicted by dwell-time histograms, and also that the P_o within bursts is close to 0.9. The latter would also be consistent with the slowest solution of _true(S) and _true(O) for _1Cß_2a (k_O = 1762 s^-1 and k_C = 197 s^-1 ), but A(x) is visibly sharper than the data (thin line in Fig. 8 C). On the other hand, the fast solution ( k_O = 43,478 s^-1 and k_C = 25,651 s^-1) yields a rather wide and symmetrical A(x) that reaches a maximum near a normalized amplitude of 0.6 that is inconsistent with the expected P_o within bursts (not shown). From these comparisons, it would appear, then, that _true(S) and _true(O) are near 10-fold shorter than predicted by dwell-time histograms, and cannot be corrected for by the equations proposed for a two-states model.

View larger version (18K): [in this window] [in a new window]   FIGURE 8  Open-channel amplitudes PDF. (A) Representative traces from on-cell patches after digitally filtering at 300 Hz and eliminating capacitive transients and baseline fluctuations (see Methods). The left and right panels are from oocytes expressing 1Cß1a and 1Cß2a, respectively. (B) All-points histograms from traces with Po > 0.1. The baseline standard deviations, as defined by the Normal distributions that best fitted the baseline (shaded area), were 0.039 pA and 0.041 pA for 1Cß1a and 1Cß2a, respectively. (C) APDF for 1Cß1a () and 1Cß2a (•). The continuous thick line depicts an A(x) with kC = 25,000 s-1 and kO = 2500 s-1. For comparison, we also included A(x) distributions for different values for kO and kC, as indicated in this figure.

(7)

In this case, the MBD depends on the rate connecting C₁ to C₂ (k_-1) and the relative time spent on C₁ according to the following equation (Colquhoun and Hawkes, 1981):

(8)

Assuming k_O = 25,000 s^-1 and k_C = 2500 s^-1, as in the APDF that fitted the data in Fig. 8 C (continuous line), this equation predicts that an exit rate to long-lived closed state (k_-1) of 748 s^-1 yields a MBD of 15.1 ms, as the one measured for _1Cß_2a. MBD can be shortened to 8.40 ms, like _1Cß_1a, by increasing k_-1 to 1369 s^-1. The same change in MBD should be obtained if k_O is reduced to 12,597 s^-1 or k_C is raised to 4848 s^-1. However, in both cases the predicted APDF from a two-states model visibly deviates from the experimental data (Fig. 8 C). These large changes in the shapes of the APDF can be intuitively foreseen since, in contrast to modifying the transition rate out of the burst, decreasing the opening rate or increasing the closing rate by 50% will go along with large changes in the P_o and the number of transitions within a burst. Thus, the similarity of APDF for both subunit combinations indicates that the exit rate to the long-lived closed state is the chief transition being modulated differentially by the two ß-subunits whereas fast openings and closing within a burst remain virtually unchanged.

The issue to be addressed now is whether channels with opening and closing rates 10-fold faster than the system's dead-time yield dwell-time histograms with apparent open-time in the ms range. To this end, we simulated single-channel activity using the same sampling rate, filter, and noise as in the recordings. These simulations were then analyzed using the same detection parameters as for the experimental data, and dwell-time and burst-duration histograms were constructed from traces with P_o > 0.1. We tested the different values of k_O, k_C, and k_-1 that mimic the changes in MBD. The forward rate between C₂ and C₁ (k₁) was set at 50 s^-1 to approximate the value obtained from closed-time histograms. Representative traces and burst-duration histograms of simulated channels are shown in Fig. 9. Single-channel activity from these simulations was characterized by burst of openings lasting several ms and traces within bursts appeared with increased noise. For the rates chosen to mimic _1Cß_2a activity, the measured MBD were remarkably close to the calculated value (15.2 ms). Also simulation with k_O, k_C, or k_-1 modified individually to reduce the MBD to 8.4 ms produced burst-duration histograms with mean values that approached the expected value. It is noteworthy that, in all cases, very few shut intervals could be resolved within a burst, illustrating how one can be easily misled to conclude that all openings are well-resolved. On the other hand, despite the fact that most brief closures go undetected, burst-durations histograms appear to be accurate. This stands in contrast with open-time histograms that predict lifetimes an order-of-magnitude longer than expected from the closing rates used in the simulation (Fig. 10). Interestingly, open-time histograms from the simulated data labeled ß2a and ß1a_1 were nearly identical to the experimental data from _1Cß_2a and _1Cß_1a, respectively. Moreover, even though closing and opening rates were the same in these two simulations, _open decreases from 5.44 ms (ß2a) to 4.81 ms (ß1a_1; Fig. 10 A); a difference that compares with the one that separates _1Cß_2a from _1Cß_1a. These simulations also show that slowing the opening rate (ß1a_2) or increasing the closing rate (ß1a_3) by near twofold to reduce the MBD, shortens the apparent _open significantly and should have been detected experimentally. Changing these rates also has a significant impact in the APDF (Fig. 10 C). For comparison, we also included the distribution (continuous line) that fit the experimental APDF in Fig. 8 C; it nearly perfectly superimposes to the APDF from simulation ß2a and ß1a_1. The only deviations occur at lower amplitude bins where transitions to and from long closures come into play. The effect of decreasing the opening rate (k_O = 12,600 s^-1) or increasing the closing rate (k_C = 4848 s^-1) on the APDF is illustrated by ß1a_2 and ß1a_3 data, respectively. In summary, the simulated data reproduces remarkably well the properties and differences of open-time histograms and APDF, and provide independent evidence for a large discrepancy between the true and measured dwell-times.

View larger version (38K): [in this window] [in a new window]   FIGURE 9  Simulated single-channel activity and burst-durations histograms. Single-channel activity was simulated assuming a three-states model as described in methods. Left panels show the first five consecutive traces of each simulation. Each simulation was ran for 128 traces and analyzed with TRANSIT using the same parameters as for the experimental data. See Table 6 for rates used. The time constants of the exponential distribution that best fitted the data is shown next to the respective histogram.

View larger version (32K): [in this window] [in a new window]   FIGURE 10  Dwell-time histograms and APDF from simulated channels. (A) Open-time histograms and (B) closed-time histograms generated from the simulated data. Single exponential distributions described open-time histograms whereas the sum of two exponential distributions was used to describe closed-time histograms. Time constants and relative contribution of each exponential distribution are shown next to each histogram. APDF from simulated channels is shown in C. The continuous line is the same B(x) shown in Fig. 11 (kO = 25,000 s-1 and kC = 2500 s-1) convolved to the baseline noise of simulation labeled ß2a.

View larger version (20K): [in this window] [in a new window]   FIGURE 11  Calculated changes in Po associated to a 1.8-fold decrease in MBD. The steady-state Po for different four-states sequential models (inset) was calculated according to and the changes in Po expressed as the ratio between the calculated Po for long bursts models (MBD = 15.1 ms) and the calculated Po for short bursts (MBD = 8.4 ms), and were calculated using Eq. 8 when MBD was set to 8.4 ms and 15.1 ms, respectively. The plot shows the ratio against the number of openings (OPB) in a short burst calculated from Colquhoun and Hawkes (1981), for a series of kO ranging from 1200 s-1 to 80,000 s-1 while kO/kC = 10. The latter is suggested by the experimental APDF. In addition, 1/(k-2 + k1) was also kept constant (20 ms) to approximate the observed mean lifetime of long-lived closed states. With these considerations, when increasing kO, OPB varied from 1.81 to 112.2 for long bursts and from 1.008 to 61.3 for short bursts. Three pairs of k2 and k-2 values were examined. (Model 1) A three-states model obtained by virtually eliminating the sojourn in C3 (k2 = 20,000 s-1 and k-2 = 0.1 s-1). In this case, when kO was varied from 1200 s-1 to 80,000 s-1, the Po for long MBD changed from 0.24 to 0.38, whereas the ratio changed from 89.5 to 1.48 as OPB increases. (Model 2) A four-states model in which the mean lifetime of C3 and C2 was set to 20 ms (k2 = 50 s-1 and k-2 = k1 = 25 s-1). With this model, Po for long MBD varies from 0.1 (kO = 1200 s-1) to 0.18 (kO = 80,000 s-1), whereas the ratio approached 1.67 with large OPB. (Model 3). A four-states model in which the transition from C2 to C3 was decreased to obtain a Po of 0.036 (k2 = 50 s-1, k-2 = 44.8 s-1, and k1 = 5.2 s-1). In this case, the Po for long MBD changed from 0.018 (kO = 1200 s-1) to 0.037 (kO = 80,000 s-1) and the ratio from 98.5 to 1.81.

	DISCUSSION

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION ACKNOWLEDGEMENTS REFERENCES

 
The P_o is differentially modulated by the ß-subunit
To gain new insights on the molecular mechanisms of channel activation we selected two ß-subunits that, when combined with the cardiac _1C subunit, yield Ca²⁺ channels with different coupling efficiency between voltage-sensing and pore-opening. We measured a difference in coupling efficiency of more than twofold between ß_1a and ß_2a when comparing the amplitude of ionic currents normalized by maximal charge movements. We also confirmed that single-channel conductances are the same with both subunits, indicating that a difference in P_o must be the culprit. This appears corroborated by the difference in the mean amplitude of average traces from single-channel recordings. However, the magnitude of such change is less certain, because some of the patches from _1Cß_1a expressing oocytes may have contained more than one channel, even if they never open simultaneously.

An upper limit on the likelihood of not observing double openings from patches with two channels can be estimated from the steady-state P_o. If two channels contributed to the P_o estimated for _1Cß_2a (0.036), then each channel should have a P_o of 0.018. In this case, the probability of observing a double opening at any given time should be 0.018² = 3.24 x 10^-4, and of not observing a double opening in 500 consecutive observations should be (1 - 3.24 x 10^-4)⁵⁰⁰ > 0.80. In other words, there is an 80% chance of not observing a double opening in 500 consecutive trials in a two-channels patch if the P_o of each individual channel is 0.018. However, this approach does not consider that during each sweep each channel may have several opportunities of reaching the open state. For example, if each channel opens on average 100 times per sweep, the likelihood of not observing a double would be (1 - 3.24 x 10^-4)¹⁰⁰ = 0.97 and, in 500 sweeps the likelihood becomes 0.97⁵⁰⁰ < 10^-7. Here, we do not have previous knowledge on how many times a channel opens in a sweep and how many sweeps contain openings. So we approached this issue by simulating several models based on the most reliable information derived from our experiments. In these simulations, 50,000 sweeps were generated in each run and sweeps containing double openings were counted to estimate the probability of observing double openings. Each model was run several times to estimate an error on the number of double openings counted. We consistently found that in models in which more than 12% of the sweeps had each channel staying open at least 10% of the time (P_o > 0.1), the likelihood of not observing double openings in 500 sweeps is less than 1%. Considering that for _1Cß_2a, 18 ± 2% of the sweeps had P_o > 0.1 it is unlikely that patches containing two channels were included in this analysis. On the other hand, in simulations that yield less than a 7% of sweeps with P_o > 0.1, the chances of not observing double openings in two-channels patches surpassed 20%. Thus, it is not unlikely that patches form oocytes expressing _1Cß_1a, having less than 5% of the sweeps with P_o > 0.1, may have held more than one channel. If this is the case, the differences in amplitude in mean currents we observed may be smaller than the true difference in P_o between the two subunit combinations.

Modulation of fast and slow gating
Single-channel activity underlying the expression of _1Cß_2a and _1Cß_1a displayed fluctuations in the P_o