HOME HELP FEEDBACK SUBSCRIPTIONS ARCHIVE SEARCH TABLE OF CONTENTS		QUICK SEARCH:   [advanced] Author: Keyword(s): Year:  Vol:  Page:

This Article Abstract Full Text (PDF) All Versions of this Article: 293/3/H1805    most recent 01160.2006v1 Alert me when this article is cited Alert me if a correction is posted Citation Map Services Email this article to a friend Similar articles in this journal Similar articles in Web of Science Similar articles in PubMed Alert me to new issues of the journal Download to citation manager Citing Articles Citing Articles via Web of Science (1) Citing Articles via Google Scholar Google Scholar Articles by Gudzenko, V. Articles by Olcese, R. Search for Related Content PubMed PubMed Citation Articles by Gudzenko, V. Articles by Olcese, R.

Influence of channel subunit composition on L-type Ca²⁺ current kinetics and cardiac wave stability

¹Department of Anesthesiology, Division of Molecular Medicine, ²Department of Medicine, Division of Cardiology, and ³Cardiovascular Research Laboratory, David Geffen School of Medicine at the University of California Los Angeles, Los Angeles; ⁴Department of Physics, California State University Northridge, Northridge, California

Submitted 22 October 2006 ; accepted in final form 29 May 2007

	ABSTRACT

TOP ABSTRACT MATERIALS AND METHODS RESULTS DISCUSSION GRANTS REFERENCES

 
Previous studies have demonstrated that the slope of the function relating the action potential duration (APD) and the diastolic interval, known as the APD restitution curve, plays an important role in the initiation and maintenance of ventricular fibrillation. Since the APD restitution slope critically depends on the kinetics of the L-type Ca²⁺ current, we hypothesized that manipulation of the subunit composition of these channels may represent a powerful strategy to control cardiac arrhythmias. We studied the kinetic properties of the human L-type Ca²⁺ channel (Ca_v1.2) coexpressed with the ₂-subunit alone (_1C + ₂) or in combination with _2a, _2b, or ₃ subunits (_1C + ₂ + ), using Ca²⁺ as the charge carrier. We then incorporated the kinetic properties observed experimentally into the L-type Ca²⁺ current mathematical model of the cardiac action potential to demonstrate that the APD restitution slope can be selectively controlled by altering the subunit composition of the Ca²⁺ channel. Assuming that _2b most closely resembles the native cardiac L-type Ca²⁺ current, the absence of , as well as the coexpression of _2a, was found to flatten restitution slope and stabilize spiral waves. These results imply that subunit modification of L-type Ca²⁺ channels can potentially be used as an antifibrillatory strategy.

Ca²⁺ channel; restitution; cardiac action potential; spiral waves; beta subunit

The APD restitution curve depends on the time course of ion currents that regulate the voltage across the cell membrane. The predominant inward current during the plateau of the AP is the L-type Ca²⁺ current, which plays an important role in regulating the shape and kinetics of the AP (5, 21). Critical aspects of the L-type Ca²⁺ current that influence the APD restitution properties are its rate and degree of inactivation during the AP plateau, and also the rate of recovery from inactivation at the resting membrane potential. Accordingly, we hypothesized that manipulation of the subunit composition of the L-type Ca²⁺ channel may provide a highly selective means to control the APD restitution characteristics in a therapeutically desirable manner. In this work, we combined experimental and computational approaches to identify components of the Ca²⁺ channel that can be genetically manipulated to reduce restitution slope.

To explore this possibility we took advantage of the structural composition of the L-type Ca²⁺ channel in the heart (Ca_v1.2), which consists of a pore-forming _1C-subunit and the regulatory subunits and ₂ (16, 31, 32). Studies have shown that -subunits [thought to be _2b in the heart (2)], which bind to the intracellular linker between domains I and II of the ₁-subunit (17, 18), participate in the trafficking of the pore-forming _1C-subunit and modulate its biophysical and kinetic properties (1, 10, 13, 14). Although the modulation of voltage-dependent inactivation by -subunits has been extensively investigated, their modulatory effects under conditions relevant to the shape of the APD restitution curve, using Ca²⁺ as charge carrier, have not been explored. Thus we present novel data using Ca²⁺ as charge carrier to preserve Ca²⁺-dependent inactivation, to investigate the inactivation and recovery kinetics of four different subunits compositions of L-type channels (_1C + ₂, _1C + ₂ + _2a, _1c + ₂ + _2b, and _1c + ₂ + ₃) of the human Ca_v1.2 channel expressed in Xenopus laevis oocytes. Although -subunits have been successfully expressed in adult cardiac myocytes by recombinant adenovirus infection (2, 31), we used the oocyte expression system to be able to precisely control specific channel compositions, including the lack of any endogenous -subunits (_1C + ₂), without the confounding influences of native L-type Ca²⁺ channel subunits present in cardiac myocytes. To estimate the influence of the subunit composition on the APD restitution properties, we developed a phenomenological model of the L-type Ca²⁺ current, in which all kinetic properties could be fitted directly to the experimental measurements. Incorporating this model into an established mathematical model of the ventricular AP, we explored the relationship between APD restitution and the kinetics of different subunit compositions, assuming that the _2b-subunit mostly closely resembles the native L-type Ca²⁺ current (2). On the basis of these studies, we find that the shape of the APD restitution curve is sensitive to subunit composition of the L-type Ca²⁺ channel, as a consequence of the strong -subunit modulation of the degree of Ca²⁺ and voltage-dependent inactivation. Using this AP model we also explored the relationship between spiral wave stability and L-type Ca²⁺ current kinetics, to show that spiral wave breakup can be eliminated by manipulating the subunit composition of the L-type channels.

	MATERIALS AND METHODS

TOP ABSTRACT MATERIALS AND METHODS RESULTS DISCUSSION GRANTS REFERENCES

 
Molecular Biology and Oocyte Preparation

We have used the human L-type Ca²⁺ channel _1C,₇₇ (26, 27, 37) and the accessory subunits ₂, ₃, _2a, _2b in pBluescript, pAGA2, and pAGA3 vectors (courtesy of N. Qin and N. M. Soldatov). The mRNAs were transcribed in vitro (mMESSAGE mMACHINE, AMBION) and injected in Xenopus laevis oocytes. Oocytes were obtained from adult Xenopus laevis. Xenopus laevis were handled in compliance with the US Public Health Service Policy on Humane Care and Use of Laboratory Animals and the National Institutes of Health Guide for the Care and Use of Laboratory Animals. Protocols were approved by the University of California, Los Angeles Institutional Animal Care and Use Committee. The frogs were anesthetized by 40-min immersion in 0.1% tricaine, a portion of the ovary was removed, and stage V and VI oocytes were selected, according to the procedures. One day before mRNA injection, the oocyte follicular layer was removed by collagenase treatment. Frogs were euthanized in 1% tricaine. A 50-nl dose of cRNA containing 0.2 mg/ml of each subunit was injected per oocyte. We produced four different composition of L-type Ca²⁺ channel: _1c + ₂, _1c + ₂ + _2a, _1c + ₂ + _2b, and _1c + ₂ + ₃. The oocytes were maintained at 17–19°C in modified Barth's solution supplemented with 100 U/ml penicillin, 50 U/ml gentamicin, and 2.5 mM pyruvate. Ca²⁺ channel currents were recorded after incubation for 4–8 days.

Electrophysiology

The cut-open oocyte voltage-clamp technique (29) was used to record Ca²⁺ currents from oocytes expressing _1C,₇₇ in combination with the regulatory ₂, _2a, _2b, and ₃ Ca²⁺ channel subunits. The composition of the external solution (recording chamber and guard compartments) was 10 mM Ca²⁺, 96 mM Na⁺, 10 mM HEPES, titrated to pH 7.0 with methanesulfonic acid. The lower chamber in contact with the fraction of the oocyte permeabilized with 0.1% saponin, contained 110 mM K-glutamate and 10 mM HEPES titrated to pH 7.0 with NaOH. Before recording, all the oocytes were injected with 100 nl of BAPTA-Na₄ 50 mM titrated to pH 7.0 with methanesulfonic acid, to prevent activation of endogenous Ca²⁺-activated Cl^– channels (12). To remove contaminating nonlinear charge movement related to the oocytes endogenous Na-K-ATPase (22), 0.1 mM ouabain was added to all external solutions. Leakage and linear capacity currents were compensated analogically and subtracted online using p/-4 and p/-6 subtraction protocol from –90 mV holding potential. Ca²⁺ current recordings used to estimate the recovery from inactivation were acquired unsubtracted. Current traces were filtered at 1/5 of the sampling frequency.

Mathematical Modeling

A phenomenological model of the L-type Ca²⁺ channel. To evaluate the effects on the AP of different L-type Ca²⁺ channel subunit modifications, we have developed a simplified mathematical model of the L-type Ca²⁺ current and incorporated it into an established ionic model (3) (Fox AP model) of the membrane voltage dynamics, modified to include the Ca²⁺ cycling model of Shiferaw et al. (24), which more realistically represents Ca²⁺ cycling dynamics at fast heart rates relevant to tachyarrhythmias. The key feature of this model is that it incorporates our experimentally measured time constants of Ca²⁺ and voltage-dependent inactivation and recovery, as well as the observation that recovery occurs via a biexponential time course. Furthermore, the kinetic parameters of this model can be chosen to modify the properties of the L-type Ca²⁺ current formulation in the Fox AP model, which is based on cardiac myocyte data assumed to represent the native _2b-subunit (2). Thus our L-type Ca²⁺ current model can be used to assess how a given change from the native _2b to another type of -subunit influences the voltage dynamics of a simulated cardiac myocyte.

The L-type Ca²⁺ current is formulated as

(1)

where N is the number of channels in the cell, d is the voltage-dependent activation gate variable, f_VCa is a voltage- and Ca²⁺-dependent inactivation gate, and i_Ca is the single channel current. To model Ca²⁺ and voltage-dependent inactivation and recovery from inactivation, we treat f_VCa as a sum of two independent gate variables

(2)

where w is a weight factor adjusted to fit the relative amplitude of the two experimentally measured recovery components. The gate variables f_VCa¹ and f_VCa² model inactivation and recovery from inactivation via a fast and slow pathway, respectively. The time dependence of these gates is written in the usual way

(3)

with i = 1,2, and where the steady-state inactivation gates are chosen to have the mathematical form

(4)

where f_Ca and f_V are the Ca²⁺- and voltage-dependent threshold functions implemented in the Fox AP model. These functions are

(5)

where _s is the threshold for Ca²⁺-dependent inactivation. The variable f₀ is a constant that fixes the minimum steady-state value of f_VCa and determines the pedestal L-type Ca²⁺ current after inactivation. The two time constants for inactivation and recovery are governed by

(6)

so that inactivation occurs with a time constant _in, whereas recovery occurs via a fast and slow time constant given by _R^fast and _R^slow, respectively. Since we observed only one time constant of inactivation we have chosen _VCa¹ and _VCa² to be the same (_in) above the activation threshold (voltage V > –40 mV). The L-type Ca²⁺ current formulation in the Fox AP model can be achieved by setting w = 1, and f₀ = 0, with _in = _R^slow = _R^fast = 40 ms so that inactivation is complete (there is no pedestal current) and recovery from inactivation occurs via a single exponential time course.

Hereafter, we will refer to model results using these parameters as the wild-type case (WT), since these parameters reflect Ca current kinetics under physiological conditions. All model parameters, aside from the modified L-type Ca current parameters, are taken directly from Shiferaw et al. (24) and from the Fox AP formulation (3).

S1-S2 restitution. The S1-S2 restitution curve was computed by pacing the cell to steady state at an S1 pacing cycle length of 400 ms and then delivering the S2 stimulus at varying coupling intervals. The APD after the last stimulus was then graphed vs. the DI of the previous beat.

Two-dimensional tissue simulations. We modeled a two-dimensional (6.75 x 6.75 cm²) monodomain tissue using the reaction-diffusion equation

(7)

where C_m = 1 µF/cm² is the transmembrane capacitance, D = 5 x 10^–4 cm²/ms is the effective diffusion coefficient of membrane voltage in cardiac tissue, and I_ion is the total single cell ionic current density. The reaction diffusion equation was integrated with an operator splitting method and adaptive time step method (19). The space step was 0.015 cm and the time step varied from 0.1 to 0.01 ms.

	RESULTS

TOP ABSTRACT MATERIALS AND METHODS RESULTS DISCUSSION GRANTS REFERENCES

 
Functional Expression of _1C,77 and Accessory Subunits

Using the cut-open oocyte voltage clamp technique, we investigated the steady-state and time-dependent properties of the Ca²⁺ current elicited by coexpressing the pore-forming -subunit of the L-type channel (Ca_v1.2) with the modulatory subunits ₂, alone or in combination with _2a, _2b, or ₃ subunits. It is well documented that -subunits [thought to be the _2b in native cardiac L-type Ca²⁺ channels (2)] modulate the voltage-dependent inactivation of the Ca²⁺ channel and facilitate channel opening. However, the influence of -subunit composition on the Ca²⁺-induced Ca²⁺ inactivation properties of the L-type Ca²⁺ channel has not been fully explored. Here, we have investigated the role of three different -subunits on those kinetic properties of the L-type Ca²⁺ current most relevant to APD restitution, namely the inactivation and recovery kinetics.

The functional expression of the modulatory -subunits was confirmed by the leftward shift in the voltage dependence of activation revealed by the current-voltage relationship (I-V) in all the + combinations, as shown in Fig. 1. Coexpression of any of the -subunits tested produced on average a 10-mV shift of the I-V curve toward more negative potentials, compared with _1C + ₂ channels. This voltage shift is well known as a signature of the functional expression of -subunits (1, 13, 15). The saturating expression of -subunits was confirmed injecting cRNA encoding for _2b, at 50 and 200% of the concentration used in this study (0.2 mg/ml). Also, we found no significant difference in the peak current I_peak amplitude and inactivation kinetics when the cRNA encoding for _2b was injected at 50% (0.1 mg/ml) or 200% (0.4 mg/ml) of the concentration used in this study. I_peak (0.1 mg/ml) = 108.1 ± 4.6 nA; I_peak (0.2 mg/ml) = 94.1 ± 18.6 nA; I_peak (0.4 mg/ml) = 102.2 ± 24.7 nA. Similarly, no significant difference was observed in the time constant of the Ca²⁺ current inactivation during 400 ms depolarization (_inact) for the three concentration of _2b-subunits. At +10 mV, _inact (0.1 mg/ml) = 92.0 ± 7.8 ms, _inact (0.2 mg/ml) = 82.6 ± 3.5 ms, and _inact (0.4 mg/ml) = 85.6 ± 3.6 (n = 4 for each concentration ratio, same day, same batch of oocytes), demonstrating that under our conditions (0.2 mg/ml) the experiments are performed at the saturating part of the dose-response curve for -subunit effect. In fact, _2b is the largest of the -subunits used in this study (628aa), giving the smallest (most unfavorable) : molar ratio when coexpressed with _1C (see MATERIALS AND METHODS).

View larger version (13K): [in this window] [in a new window]   Fig. 1. Coexpression of different -subunits modulates the voltage dependence of channel activation. Superimposed current-voltage (I-V) relationship for different L-type Ca2+ channel subunit combinations consisting of 1C + 2 and either 2a, 2b, or 3. I/Ipeak, Normalized calcium current. Extracellular solution contained 10 mM Ca2+. Note that coexpression of any -subunit produces the typical left shift of the I-V curve on the voltage axis.

The _1C-subunit undergoes Ca²⁺-induced inactivation, which dominates over voltage-induced inactivation as a consequence of a conformational change of the protein mediated by calmodulin (for a recent review, see Ref. 11). Most studies investigating the effects of Ca²⁺ channel modulatory subunits on inactivation have examined only voltage-induced inactivation and have not characterized recovery from inactivation in detail. Using Ca²⁺ as a charge carrier to preserve the Ca²⁺-induced inactivation, we studied the effect of different -subunits, as well as the absence of a -subunit, on the inactivation properties of _1C + ₂. Depolarizing pulses (400 ms, slightly longer than a typical physiological cardiac action potential) from a –90 mV holding potential (HP) were used to quantify the effects of the subunit composition on the inactivation properties of the L-type Ca²⁺ current.

The decay of the macroscopic conductance was well fit by a monoexponential function of the form I(t) = A·exp(–t/) + B where t is the time, A is the amplitude of the inactivating component of the current, is the time constant of the decay, and B is the steady-state noninactivating current. The time-dependent component reflected mainly Ca²⁺-induced inactivation, since the voltage-dependent inactivation component measured with Ba²⁺ replacing Ca²⁺ as the charge carrier was much slower (data not shown). Over 400 ms, a duration relevant to the cardiac APD, the second voltage-dependent component was well approximated by a time-independent pedestal.

Representative current recordings during depolarization to –20, 0, and 30 mV are shown in Fig. 2 for _1C + ₂ expressed alone (A) and with _2a (B), _2b (C), or ₃ (D), with the fits superimposed as continuous lines. The rate of inactivation was strongly dependent on the subunit composition of the channels. Figure 3 summarizes the rates (A) and amplitudes (B) of the Ca²⁺-induced inactivation during 400-ms depolarizing pulses. Inactivation rates could be reliably estimated starting from –20 mV for the _1C + ₂ and _2a channels and from –10 mV and above in _2b and ₃ channels. For more negative voltages the Ca²⁺ current was too small to yield reliable kinetics measurements. On average, at +10 mV, the slowest rate of inactivation was observed in _1C+₂ (5.4 ± 0.2 s^–1), whereas the fastest rate was recorded with _2b (12.5 ± 0.3 s^–1). Coexpression of _2a, _2b, or ₃ subunits accelerated Ca²⁺ current inactivation kinetics for potentials relevant to the end of the action potential (0–20 mV).

View larger version (30K): [in this window] [in a new window]   Fig. 2. Subunit composition controls the rate of inactivation of the L-type Ca2+ current. Ca2+ current recordings from oocytes expressing 1C + 2 (A) and 1C + 2 + 2a (B), 2b (C), and 3 (D), by the cut-open oocyte voltage-clamp technique. Representative traces are shown for a 400-ms step depolarization to the indicated potentials. Current traces were fit to a monoexponential function ICa = A·e–t/ + B (solid lines shown superimposed) where ICa is calcium current, A is the amplitude of the inactivating component of the current, t is the time from the beginning of the depolarizing step, is the time constant of inactivation, and B is the noninactivating (pedestal) component of the current.

View larger version (15K): [in this window] [in a new window]   Fig. 3. Rate and extent of Ca2+-induced inactivation depend on the subunit composition of the L-type Ca2+ channel. Rate (1/; A) and amplitude (B) of Ca2+-induced inactivation for 4 different compositions of L-type Ca2+ channels. Percent of inactivation is computed as 100·A/(A + B). Data are averages of 9–12 experiments ± SE. The rate of inactivation vs. membrane potential for all subunit compositions displayed the bell-shaped relation, typical of a Ca2+-dependent process.

2

Recovery from Inactivation of L-type Ca²⁺ Current

To investigate the effects of -subunits on recovery from inactivation, which has not been previously characterized in detail for -subunits with Ca²⁺ as the charge carrier, we used a two-pulse protocol. From a holding potential of –90 mV, an inactivating (1-s) pulse to +10 mV (P1) was followed, after a variable duration of repolarization, by a short (100-ms) test pulse (P2) of the same amplitude. The time interval between P1 and P2 was progressively increased to monitor channel recovery. The interval between every repetitive cycle (between P2 and P1) was 20 s to avoid accumulation of inactivation. Representative experiments for the different subunit composition are shown in Fig. 4, A–D. The corresponding time course of the recovery from inactivation is shown in Fig. 4, E–H. The recovery kinetics were well fit by a biexponential function (fit superimposed, solid line). The averages of the fitting parameters for the fast and slow components of recovery are reported in Table 1. The fastest time constant of recovery from inactivation (37.8 ± 3 ms) was observed for the _1C + ₂ combination. However, this component only accounted for 53% of the total current recovery. Coexpression of any -subunit significantly slowed this fast component of the recovery, and the fraction of the current undergoing faster recovery from inactivation was significantly larger: for _2a, _fast = 112 ± 10 ms (75 ± 2%), _slow = 2,018 ± 201 ms; for _2b, _fast = 108 ± 7 ms (82 ± 1.5%), _slow = 1,830 ± 13 ms; and for ₃, _fast = 85 ± 4 ms (77 ± 2%), _slow = 1,224 ± 76 ms. These results show that the -subunit composition of the L-type channels can differentially modulate the kinetics of recovery from inactivation.

View larger version (18K): [in this window] [in a new window]   Fig. 4. Recovery from inactivation of the L-type Ca2+ current is dependent on the channel subunit composition. A–D: Ca2+ current traces for 4 different subunit compositions of L-type Ca2+ channels, elicited by a 2-pulse protocol [10 mM external Ca2+, holding potential (HP) = –90 mV] used to estimate the time course of recovery from inactivation. All Ca2+ currents were recorded unsubtracted. The pulse protocol is shown at top. An inactivating (1-s) pulse to +10 mV (P1) was followed by a short test pulse (P2) of the same amplitude. The time interval between P1 and P2, at –90 mV, was progressively increased to monitor channel recovery. The time course of the recovery from inactivation for each of the subunit composition studied was estimated by plotting the peak current during the test pulse (P2) as a function of the interpulse duration. E–H: plot of the ratio of the peak current during the test pulse P2 and the peak current during P1 vs. the interpulse duration. Data points were fit to the sum of 2 exponential functions (continuous lines). The averaged fast and slow time constants (fast and slow) of recovery and their relative amplitudes (Ampfast and Ampslow) are shown.

To study how the -subunit composition of the L-type Ca²⁺ channel is predicted to modulate the APD and the shape of the APD restitution curve, we simulated the effect of a given subunit modification on the kinetics of the L-type Ca²⁺ current as formulated in the Fox AP action potential model (3) modified to include our dynamic Calcium current (Ca_i) cycling model (24). Our strategy is as follows: on the basis of the findings that the Ca²⁺ current in cardiac myocytes is most similar to _1C + ₂ + _2b channels (2), we simulated different subunit compositions by changing proportionately the kinetics of the L-type Ca²⁺ current in the Fox AP model by the same factor by which that subunit composition changed the _1C + ₂ + _2b current kinetics in the oocyte experiments. Thus, if _myocyte is the time of inactivation of the Ca²⁺ current measured at physiological temperatures, as implemented in the Fox AP model, and if _myocyte³ is that same time constant for the ₃ composition measured in our experiment, then

(8)

where _oocyte³ and _oocyte^2b are found by estimating that same time constant directly from our current measurements of _1C + ₂ + ₃ and _1C + ₂ + _2b. Thus we can estimate the time constant of inactivation when ₃ is expressed in the cardiac myocyte as . In this way we could systematically evaluate how a given subunit modification should influence the kinetics of the L-type Ca²⁺ current under physiological conditions. Note that this approach assumes that the ratio of time constants, for different subunit compositions, is independent of temperature. A minor caveat is that the recovery from inactivation of the L-type Ca²⁺ current, as represented in the Fox model, only has one time constant of recovery, in contrast to our measurements of _1C+₂+_2b. For this time constant we used the same time constants measured experimentally. The model parameters used are given in Table 2.

View this table: [in this window] [in a new window]   Table 2. L-type Ca2+ current parameters as formulated in the Fox AP model, and the corresponding -subunit modifications

View larger version (20K): [in this window] [in a new window]   Fig. 5. Simulated cardiac action potentials (APs) with different subunit compositions. A: AP simulation using the Shiferaw-Fox AP model with corresponding subunit modifications. Subunit modifications were modeled by scaling the rate constants of the L-type Ca2+ current as described in RESULTS. All modifications prolonged the AP duration (APD). All voltage traces are taken after 20 beats of stimulation at 1-s pacing. B: Ca2+ transients corresponding to the subunit modifications and pacing protocol in A. WT, wild type. C: APD restitution curves obtained using an S1-S2 pacing protocol in the Shiferaw-Fox AP model, with various subunit modifications, and using S1 = 1 s. The maximum conductance of the L-type Ca2+ current was adjusted so that the APD was comparable at a diastolic interval (DI) of 350 ms. D: corresponding slopes of the APD restitution curves for the different subunit modifications shown in B. E and F: APs and Ca2+ transients after steady-state pacing at 400 ms, for the subunit modifications as in C. Dotted line represents the AP and Ca2+ transient for a simulated effect of a Ca2+ channel blocker (e.g., verapamil), when conductance of the Ca2+ current in the Shiferaw-Fox AP model is decreased by 50%. Note the dramatic reduction in AP duration and Ca2+ transient.

To characterize the effects of the changes in APD restitution produced by various subunit compositions on the stability of reentry, we initiated reentry using a cross-field stimulation in simulated two-dimensional tissue (6.75 x 6.75 cm²). Figure 6A shows voltage snapshots at 400 and 800 ms using the Shiferaw-Fox AP model, which had steep S1-S2 restitution (dashed black line in Fig. 5B). As shown, a spiral wave that was initiated in the tissue was unstable and broke up into several wave fronts typical of a VF-like state. This breakup occurred after four spiral wave rotations. The spiral wave meandered in a chaotic fashion and as the wave tip followed the wave back. After 2 s, the fractionated wave fronts self-terminated by meandering to and colliding with borders of the tissue. Figure 6B shows the effects of the _1C + ₂-subunit composition, which had the greatest effect at flattening APD restitution slope. In this case the initiated spiral wave remained intact as a single reentrant wave rotating around a stable circular core and did not break up into VF-like state over the full 3-s duration (20 spiral wave rotations) of the simulation. Similarly, Fig. 6C shows the spiral wave evolution at 600 ms and 3 s for the _2a-subunit parameters, again showing that the spiral wave was stabilized. It is interesting to note that the spiral wave tip morphology was different for each subunit composition tested. For the _1C + ₂-subunit composition, the wavelength of the spiral wave was shortened at short DI, which led to an increase in the excitable area near the spiral tip. This effect tended to stabilize the spiral wave as the propensity for wave break was decreased. On the other hand, the _2a case led to a blunted spiral tip with a larger wavelength. However, in this case the waveback was smooth and did not induce wave break.

View larger version (57K): [in this window] [in a new window]   Fig. 6. Effect of subunit composition on reentrant spiral wave dynamics in simulated 2D tissue. A: voltage snapshots at 400 and 800 ms after the initiation of the spiral wave, for the WT L-type Ca2+ current as formulated in the Shiferaw-Fox AP model. The spiral wave broke up after 5 rotations into multiple wavelets, before spontaneously terminating after 2 s. Note that initial conditions in the tissue were the same as after 1-s pacing to steady state. B: voltage snapshots after 600 ms and 3 s (20 rotations) after the initiation of the spiral wave by using the 1C + 2-subunit modification. Reentry remained stable without spiral wave breakup. C: same as above using the 2a composition parameters. As shown, reentry remained stable for up to 3 s (20 rotations).

	DISCUSSION

TOP ABSTRACT MATERIALS AND METHODS RESULTS DISCUSSION GRANTS REFERENCES

Whereas APD is sensitive to both the time constant and extent of Ca²⁺-induced inactivation, APD restitution at short DI primarily depends on the rate of L-type Ca²⁺ current recovery from inactivation. In oocytes, we found that the time course of recovery was biexponential. For all the -subunits studied, the fast component of recovery from inactivation had a time constant in the 100-ms range, whereas the slower component had a time constant in the 1- to 2-s range. A double exponential time course of recovery from inactivation has also been described in human ventricular myocytes (9). The amplitudes of the recovery components were similar for all the -subunit compositions we tested, with the fast component accounting for 75–80% of the total current recovery. However, in the absence of any -subunit the channel recovery kinetics were significantly different. In this case, the fast and slow components each accounted for 50% of recovery, and both time constants were accelerated by a factor of 2, compared with when a -subunit was present. These results demonstrate that the recovery kinetics of the L-type Ca²⁺ current were relatively insensitive to -subunits but changed dramatically when -subunits were eliminated.

To predict the physiological effects of different subunit compositions of the L-type Ca²⁺ channel on the cardiac AP and APD restitution properties, we incorporated the measured kinetic properties of the L-type Ca²⁺ current into a detailed ventricular AP model. To evaluate the effect of subunit composition changes on AP properties, we rescaled the WT Ca²⁺ current kinetics, using _1c + ₂ + _2b as reference. Implementing these kinetic changes, we found that all subunit modifications increased the pedestal current of the L-type Ca²⁺ current, which, in the model, increased net inward current during the AP plateau. In particular, the coexpression with _2a and _1C + ₂ modifications prolonged APD dramatically to >500 ms, which may be proarrhythmic if not corrected by shortening APD back to control levels. Indeed, a defective L-type Ca²⁺ channel inactivation is considered the underlying mechanism in the Timothy Syndrome, a congenital form of long QT (28). Thus this study also emphasizes that to take advantage of the potency of the kinetic effects derived by the subunit modifications in preventing wave break, a control of the total Ca²⁺ entry has to be taken into consideration to prevent proarrhythmic consequences of APD prolongation and intracellular Ca²⁺ overload. To study the effects on APD restitution and spiral wave stability in the model, we made the latter adjustment for all of the modified subunit compositions by reducing the maximum conductance of the L-type Ca²⁺ current sufficiently to return APD back to its control value near 250 ms. As shown in Fig. 5C, APD restitution slope for the native L-type Ca²⁺ current was relatively steep (slope >1) at short DI, leading to spiral wave breakup into a VF-like state in two-dimensional tissue, as shown in Fig. 6A. Both of these properties, APD restitution slope >1 and spontaneous spiral wave breakup, are characteristic features of ventricular muscle from many mammalian species, including humans (7, 30, 36). All other subunit combinations exhibited flatter APD restitution slopes. In ₃, the effect was only modest and not sufficient to flatten APD restitution slope to <1. On the other hand, the _2a and _1C + ₂ cases flattened APD restitution slope to <1 everywhere. So both of these subunit modifications prevented spiral wave breakup, as demonstrated in Fig. 6, B and C.

Our simulation results showed that both the _2a and _1C + ₂ compositions, along with a reduction of Ca²⁺ current amplitude, led to a flattened APD restitution curve. To understand the underlying mechanism for this effect, in Fig. 7A we have plotted the Ca²⁺ current during the S1-S2 protocol used to compute the restitution curves shown in Fig. 5C. Families of superimposed Ca²⁺ currents for the last S1 beat and for a wide range of S2 intervals are shown for both the WT and the _1C + ₂ composition. As expected the WT Ca²⁺ current completely inactivates and subsequently recovers from a small peak value (–10 pA/pF) to a significantly higher value (–30 pA/pF) as the S1-S2 interval is increased. On the other hand, the _1C + ₂ composition recovers from a current amplitude of –10 pA/pF to about –15 pA/pF, since lesser inactivation occurred in the last S1 beat. To confirm that Ca²⁺ current entry indeed dictates APD restitution, in Fig. 7B we plot the integrated Ca²⁺ current elicited by S2 beat as a function of DI. Indeed, the integral of the Ca²⁺ current closely resembles the APD restitution curve (for WT and _1C + ₂) shown in Fig. 5C. Thus in this case the flattening of the restitution is directly related to the fact that recovery from inactivation is diminished since the overall extent of inactivation was reduced.

View larger version (22K): [in this window] [in a new window]   Fig. 7. Effect of Ca2+ current kinetics on APD restitution during simulated S1-S2 protocol. A: WT (top) and 1C + 2 (bottom) Ca2+ current during the last S1 beat and during the following S2 beat. The stimulation protocol was identical to that used to determine the S1-S2 restitution curve in Fig. 5C. B: time integral of the Ca2+ current as a function of DI for both the WT and the 1C + 2 parameters. Note the striking similarity with the APD restitution curves shown in Fig. 5C. C: plot of the S1-S2 restitution curve for the WT and 1C + 2 channel composition, with Ca2+ current conductance held fixed. To prevent an unphysiologically long AP in this case, the time-independent potassium current (IKp) is increased by a factor of 8. The S1-S2 restitution protocol is the same as that used in Fig. 5C. D: slope of the restitution curves shown in C.

An interesting finding of this study is that the modulation of Ca²⁺ current kinetics seems to be potentially applicable for therapy only if the subunit changes are implemented in conjunction with a reduction of the current amplitude. For both the _2a and _1C + ₂ compositions, inactivation of the Ca²⁺ current was dramatically altered so that the APD and Ca²⁺ current entry was increased to unphysiological levels. However, we found that if the current amplitude was reduced, as for instance when a Ca²⁺ channel blocker such as verapamil is applied, it is then possible both to flatten APD restitution and to maintain physiological Ca²⁺ levels. In effect, the Ca²⁺ entry due to the larger pedestal current allows the current amplitude to be decreased, which in effect reduces the contribution of Ca²⁺ current kinetics and also returns the Ca²⁺ transient back to physiological levels (Fig. 5, E and F). Thus, in this case the detrimental effects of the subunit composition changes could be countered by simply decreasing the current amplitude. These results highlight the complex interplay of various components of the cell electrophysiology, so that targeting the ion channel kinetics leads to downstream changes that must be balanced by at least one more independent change.

Some studies (8) have argued that the dynamic rather than S1-S2 restitution curve is predictive of spiral wave breakup. The dynamic restitution curve is found by measuring the steady-state APD as a function DI at a fixed pacing cycle length. Since this is a steady-state measurement, the dynamic restitution is sensitive to a variety of slow ionic processes, such as Na⁺ and Ca²⁺ ion accumulation regulated by ion exchangers and pumps. Consequently, the Shiferaw-Fox model using the WT parameters reached steady state only after about 20 beats. Since this time is much longer than the roughly three to five spiral wave rotations needed for an intact spiral wave to break up, the dynamic restitution, in this case, is less directly relevant to spiral wave stability. On the other hand, the S1-S2 restitution curve reflects the immediate response of the APD to variations in DI induced by a change in cycle length. Hence a steep S1-S2 restitution slope leads to large APD variations along the spiral wave, which leads to a nonuniform waveback distribution that induces wave break. Indeed, this is consistent with our simulation results since the _2a and _1C + ₂ compositions directly influenced Ca²⁺ current recovery and thus S1-S2 restitution slope.

It is important to stress that the approach presented here is distinct from previous studies (4, 23) showing that marked reduction of the L-type current, via a Ca²⁺ channel blocker such as verapamil, can flatten restitution slope and prevent spiral wave breakup. In those studies, the reduction of the L-type current led to a large decrease in Ca²⁺ entry and thus markedly suppressed contractility. In our numerical study, Ca²⁺ entry is preserved since the reduction of the L-type current is introduced only to compensate for the overall reduced inactivation observed with the "_2a" and _1C + ₂ composition. Therefore, flattening of APD restitution is achieved while preserving normal and preventing excessive Ca²⁺ entry into the cell. In Fig. 5, E and F, we simulated the effect of a direct decrease of the Ca²⁺ current conductance (50% reduction) and indeed found that the peak Ca²⁺ transient is reduced by almost a factor of 5, whereas the APD is decreased by roughly a factor of 2. The dramatic decrease in peak Ca²⁺ occurs over several paced beats, since a new equilibrium point must be reached, in which the efflux due to the Na/Ca exchanger current will balance the current influx due to the reduced Ca²⁺ current. In general, this leads to a marked reduction of the sarcoplasmic reticulum content since Ca²⁺ influx is essentially cut in half. The advantage of decreasing the expression levels of ₃ and _2b or overexpressing _2a along with a reduction in the current conductance is that Ca²⁺ entry over one beat can be preserved. Thus control of -subunit expression offers an alternative way of controlling restitution slope and wave stability.

Given the results in this study, it is worth asking whether Ca²⁺ channel subunit modifications can be developed to the point of being a viable therapeutic strategy. A particular limitation of current gene therapy approaches is that expression levels tend to be heterogeneous. However, it is important to point out that electrotonic coupling dramatically smoothes out cell-to-cell heterogeneities. Thus, the challenge is to modify "enough" cardiac cells to change the electrophysiology of cardiac tissue over a tissue scale that is relevant to the dynamics of a spiral wave. With improved vector technology, this may be achievable in the foreseeable future.

Limitations

One important limitation predicted by this study is that the -subunit modifications yield therapeutic effects only if the Ca²⁺ current amplitude is adjusted to keep transsarcolemmal Ca²⁺ entry roughly constant in the face of different inactivation kinetics. This is essential for avoiding either excessive suppression of the Ca²⁺ transient or Ca²⁺ overload, which can be directly arrhythmogenic. The Ca²⁺ current amplitude is, however, a tractable target, since different Ca²⁺ current blockers are available and can be dosed to achieve a desired level of current block. In the broader perspective, it is likely that any therapeutic strategy that targets current kinetics will likely inflict side effects that will have to be controlled by an independent mechanism. This issue certainly deserves careful attention because it is likely to complicate any therapeutic proposal to modulate cell electrophysiology.

Intracellular Ca²⁺ cycling is another important dynamic factor influencing wave stability in addition to APD restitution (33), and the L-type Ca²⁺ current has a major influence on intracellular Ca_i cycling dynamics. Although the Shiferaw-Fox model contains dynamically active Ca_i cycling, the effects of the L-type Ca²⁺ current modifications simulated in this study did not exacerbate Ca_i-cycling-mediated wave instabilities to the point that they interfered with the ability of flattening of APD restitution slope to prevent spiral wave breakup. However, this issue needs to be studied in more detail. Finally, the kinetic parameters of reconstituted L-type Ca²⁺ channels in oocytes may not be the same as that as in cardiac myocytes. A mammalian cell line studied at 37°C under perforated patch-clamp conditions would be preferable for characterizing different subunit compositions. Nevertheless, our results represent a starting point for further exploration of gene-based therapeutic strategies in mammalian hearts.

With recognition of the limitations discussed above, these results offer a first proof of concept that a nonpharmacological tool (i.e., the use of modulatory subunit specific for Ca²⁺ channels) might be strategically applied to control cardiac wave stability to prevent spiral wave breakup in the heart.

	GRANTS

TOP ABSTRACT MATERIALS AND METHODS RESULTS DISCUSSION GRANTS REFERENCES

 
This research was supported by National Institutes of Health Grants R01 NS-043240, P50 HL-53219, and P01 HL-078931 and by Laubisch and Kawata Endowments.

	ACKNOWLEDGMENTS

 
We thank Nikolai Soldatov for constructive discussions and providing the human _1C clone and Ning Qin for providing the ₂- and -subunits.

	FOOTNOTES

 

Address for reprint requests and other correspondence: R. Olcese, Division of Molecular Medicine, BH 570 CHS, Dept. of Anesthesiology, David Geffen School of Medicine, Univ. of California Los Angeles, Box 957115, Los Angeles, CA 90095-7115 (e-mail: rolcese{at}ucla.edu)

The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.

^* V. Gudzenko and Y. Shiferaw contributed equally to this work.

	REFERENCES

TOP ABSTRACT MATERIALS AND METHODS RESULTS DISCUSSION GRANTS REFERENCES

 

1. Birnbaumer L, Qin N, Olcese R, Tareilus E, Platano D, Costantin J, Stefani E. Structures and functions of calcium channel beta subunits. J Bioenerg Biomembr 30: 357–375, 1998.[CrossRef][Web of Science][Medline]
2. Colecraft HM, Alseikhan B, Takahashi SX, Chaudhuri D, Mittman S, Yegnasubramanian V, Alvania RS, Johns DC, Marban E, Yue DT. Novel functional properties of Ca(2+) channel beta subunits revealed by their expression in adult rat heart cells. J Physiol 541: 435–452, 2002.[Abstract/Free Full Text]
3. Fox JJ, McHarg JL, Gilmour RF Jr. Ionic mechanism of electrical alternans. Am J Physiol Heart Circ Physiol 282: H516–H530, 2002.[Abstract/Free Full Text]
4. Garfinkel A, Kim YH, Voroshilovsky O, Qu Z, Kil JR, Lee MH, Karagueuzian HS, Weiss JN, Chen PS. Preventing ventricular fibrillation by flattening cardiac restitution. Proc Natl Acad Sci USA 97: 6061–6066, 2000.[Abstract/Free Full Text]
5. Goldhaber JI, Xie LH, Duong T, Motter C, Khuu K, Weiss JN. Action potential duration restitution and alternans in rabbit ventricular myocytes: the key role of intracellular calcium cycling. Circ Res 96: 459–466, 2005.[Abstract/Free Full Text]
6. Karma A. Electrical alternans and spiral wave breakup in cardiac tissue. Chaos 4: 461–472, 1994.[CrossRef][Web of Science][Medline]
7. Kim BS, Kim YH, Hwang GS, Pak HN, Lee SC, Shim WJ, Oh DJ, Ro YM. Action potential duration restitution kinetics in human atrial fibrillation. J Am Coll Cardiol 39: 1329–1336, 2002.[Abstract/Free Full Text]
8. Koller ML, Riccio ML, Gilmour RF Jr. Dynamic restitution of action potential duration during electrical alternans and ventricular fibrillation. Am J Physiol Heart Circ Physiol 275: H1635–H1642, 1998.[Abstract/Free Full Text]
9. Li GR, Nattel S. Properties of human atrial I_Ca at physiological temperatures and relevance to action potential. Am J Physiol Heart Circ Physiol 272: H227–H235, 1997.[Abstract/Free Full Text]
10. Lory P, Varadi G, Slish DF, Varadi M, Schwartz A. Characterization of beta subunit modulation of a rabbit cardiac L-type Ca²⁺ channel alpha 1 subunit as expressed in mouse L cells. FEBS Lett 315: 167–172, 1993.[CrossRef][Web of Science][Medline]
11. Morad M, Soldatov N. Calcium channel inactivation: possible role in signal transduction and Ca²⁺ signaling. Cell Calcium 38: 223–231, 2005.[CrossRef][Web of Science][Medline]
12. Neely A, Olcese R, Wei X, Birnbaumer L, Stefani E. Ca²⁺-dependent inactivation of a cloned cardiac Ca²⁺ channel alpha 1 subunit (alpha 1C) expressed in Xenopus oocytes. Biophys J 66: 1895–1903, 1994.[Web of Science][Medline]
13. Neely A, Wei X, Olcese R, Birnbaumer L, Stefani E. Potentiation by the beta subunit of the ratio of the ionic current to the charge movement in the cardiac calcium channel. Science 262: 575–578, 1993.[Abstract/Free Full Text]
14. Olcese R, Neely A, Qin N, Wei X, Birnbaumer L, Stefani E. Coupling between charge movement and pore opening in vertebrate neuronal alpha 1E calcium channels. J Physiol 497: 675–686, 1996.[Abstract/Free Full Text]
15. Olcese R, Qin N, Schneider T, Neely A, Wei X, Stefani E, Birnbaumer L. The amino terminus of a calcium channel beta subunit sets rates of channel inactivation independently of the subunit's effect on activation. Neuron 13: 1433–1438, 1994.[CrossRef][Web of Science][Medline]
16. Perez-Garcia MT, Kamp TJ, Marban E. Functional properties of cardiac L-type calcium channels transiently expressed in HEK293 cells. Roles of alpha 1 and beta subunits. J Gen Physiol 105: 289–305, 1995.[Abstract/Free Full Text]
17. Pragnell M, De Waard M, Mori Y, Tanabe T, Snutch TP, Campbell KP. Calcium channel beta-subunit binds to a conserved motif in the I-II cytoplasmic linker of the alpha 1-subunit. Nature 368: 67–70, 1994.[CrossRef][Medline]
18. Qin N, Olcese R, Zhou J, Cabello OA, Birnbaumer L, Stefani E. Identification of a second region of the beta-subunit involved in regulation of calcium channel inactivation. Am J Physiol Cell Physiol 271: C1539–C1545, 1996.[Abstract/Free Full Text]
19. Qu Z, Garfinkel A. An advanced algorithm for solving partial differential equation in cardiac conduction. IEEE Trans Biomed Eng 46: 1166–1168, 1999.[CrossRef][Web of Science][Medline]
20. Qu Z, Karagueuzian HS, Garfinkel A, Weiss JN. Effects of Na⁺ channel and cell coupling abnormalities on vulnerability to reentry: a simulation study. Am J Physiol Heart Circ Physiol 286: H1310–H1321, 2004.[Abstract/Free Full Text]
21. Qu Z, Xie F, Garfinkel A, Weiss JN. Origins of spiral wave meander and breakup in a two-dimensional cardiac tissue model. Ann Biomed Eng 28: 755–771, 2000.[CrossRef][Web of Science][Medline]
22. Rakowski RF. Charge movement by the Na/K pump in Xenopus oocytes. J Gen Physiol 101: 117–144, 1993.[Abstract/Free Full Text]
23. Riccio ML, Koller ML, Gilmour RF Jr. Electrical restitution and spatiotemporal organization during ventricular fibrillation. Circ Res 84: 955–963, 1999.[Abstract/Free Full Text]
24. Shiferaw Y, Watanabe MA, Garfinkel A, Weiss JN, Karma A. Model of intracellular calcium cycling in ventricular myocytes. Biophys J 85: 3666–3686, 2003.[Web of Science][Medline]
25. Solberg LE, Singer DH, Ten Eick RE, Duffin EG Jr. Glass microelectrode studies on intramural papillary muscle cells. Description of preparation and studies on normal dog papillary muscle. Circ Res 34: 783–797, 1974.[Abstract/Free Full Text]
26. Soldatov NM. Molecular diversity of L-type Ca²⁺ channel transcripts in human fibroblasts. Proc Natl Acad Sci USA 89: 4628–4632, 1992.[Abstract/Free Full Text]
27. Soldatov NM, Bouron A, Reuter H. Different voltage-dependent inhibition by dihydropyridines of human Ca²⁺ channel splice variants. J Biol Chem 270: 10540–10543, 1995.[Abstract/Free Full Text]
28. Splawski I, Timothy KW, Decher N, Kumar P, Sachse FB, Beggs AH, Sanguinetti MC, Keating MT. Severe arrhythmia disorder caused by cardiac L-type calcium channel mutations. Proc Natl Acad Sci USA 102: 8089–8096; discussion 8086–8088, 2005.[Abstract/Free Full Text]
29. Stefani E, Bezanilla F. Cut-open oocyte voltage-clamp technique. Methods Enzymol 293: 300–318, 1998.[Web of Science][Medline]
30. Taggart P, Sutton P, Chalabi Z, Boyett MR, Simon R, Elliott D, Gill JS. Effect of adrenergic stimulation on action potential duration restitution in humans. Circulation 107: 285–289, 2003.[Abstract/Free Full Text]
31. Takahashi M, Seagar MJ, Jones JF, Reber BF, Catterall WA. Subunit structure of dihydropyridine-sensitive calcium channels from skeletal muscle. Proc Natl Acad Sci USA 84: 5478–5482, 1987.[Abstract/Free Full Text]
32. Wang MC, Collins RF, Ford RC, Berrow NS, Dolphin AC, Kitmitto A. The three-dimensional structure of the cardiac L-type voltage-gated calcium channel: comparison with the skeletal muscle form reveals a common architectural motif. J Biol Chem 279: 7159–7168, 2004.[Abstract/Free Full Text]
33. Weiss JN, Karma A, Shiferaw Y, Chen PS, Garfinkel A, Qu Z. From pulsus to pulseless: the saga of cardiac alternans. Circ Res 98: 1244–1253, 2006.[Abstract/Free Full Text]
34. Weiss JN, Qu Z, Chen PS, Lin SF, Karagueuzian HS, Hayashi H, Garfinkel A, Karma A. The dynamics of cardiac fibrillation. Circulation 112: 1232–1240, 2005.[Abstract/Free Full Text]
35. Wu TJ, Lin SF, Weiss JN, Ting CT, Chen PS. Two types of ventricular fibrillation in isolated rabbit hearts: importance of excitability and action potential duration restitution. Circulation 106: 1859–1866, 2002.[Abstract/Free Full Text]
36. Wu TJ, Yashima M, Doshi R, Kim YH, Athill CA, Ong JJ, Czer L, Trento A, Blanche C, Kass RM, Garfinkel A, Weiss JN, Fishbein MC, Karagueuzian HS, Chen PS. Relation between cellular repolarization characteristics and critical mass for human ventricular fibrillation. J Cardiovasc Electrophysiol 10: 1077–1086, 1999.[Web of Science][Medline]
37. Zuhlke RD, Bouron A, Soldatov NM, Reuter H. Ca²⁺ channel sensitivity towards the blocker isradipine is affected by alternative splicing of the human alpha1C subunit gene. FEBS Lett 427: 220–224, 1998.[CrossRef][Web of Science][Medline]

This Article Abstract Full Text (PDF) All Versions of this Article: 293/3/H1805    most recent 01160.2006v1 Alert me when this article is cited Alert me if a correction is posted Citation Map Services Email this article to a friend Similar articles in this journal Similar articles in Web of Science Similar articles in PubMed Alert me to new issues of the journal Download to citation manager Citing Articles Citing Articles via Web of Science (1) Citing Articles via Google Scholar Google Scholar Articles by Gudzenko, V. Articles by Olcese, R. Search for Related Content PubMed PubMed Citation Articles by Gudzenko, V. Articles by Olcese, R.