Shaping a new Ca²⁺ conductance to suppress early afterdepolarizations in cardiac myocytes

Abstract

Non-technical summary

Diseases, genetic defects, or ionic imbalances can alter the normal electrical activity of cardiac myocytes causing an anomalous heart rhythm, which can degenerate to ventricular fibrillation (VF) and sudden cardiac death. Well-recognized triggers for VF are aberrations of the cardiac action potential, known as early afterdepolarizations (EADs). In this study, combining mathematical modelling and experimental electrophysiology in real-time (dynamic clamp), we investigated the dependence of EADs on the biophysical properties of the L-type Ca²⁺ current (I_Ca,L) and identified modifications of I_Ca,L properties which effectively suppress EAD. We found that minimal changes in the voltage dependence of activation or inactivation of I_Ca,L can dramatically reduce the occurrence of EADs in cardiac myocytes exposed to different EAD-inducing conditions. This work assigns a critical role to the L-type Ca²⁺ channel biophysical properties for EADs formation and identifies the L-type Ca²⁺ channel as a promising therapeutic target to suppress EADs and their arrhythmogenic effects.

Abstract

Sudden cardiac death (SCD) due to ventricular fibrillation (VF) is a major world-wide health problem. A common trigger of VF involves abnormal repolarization of the cardiac action potential causing early afterdepolarizations (EADs). Here we used a hybrid biological–computational approach to investigate the dependence of EADs on the biophysical properties of the L-type Ca²⁺ current (I_Ca,L) and to explore how modifications of these properties could be designed to suppress EADs. EADs were induced in isolated rabbit ventricular myocytes by exposure to 600 μmol l⁻¹ H₂O₂ (oxidative stress) or lowering the external [K⁺] from 5.4 to 2.0–2.7 mmol l⁻¹ (hypokalaemia). The role of I_Ca,L in EAD formation was directly assessed using the dynamic clamp technique: the paced myocyte's V_m was input to a myocyte model with tunable biophysical parameters, which computed a virtual I_Ca,L, which was injected into the myocyte in real time. This virtual current replaced the endogenous I_Ca,L, which was suppressed with nifedipine. Injecting a current with the biophysical properties of the native I_Ca,L restored EAD occurrence in myocytes challenged by H₂O₂ or hypokalaemia. A mere 5 mV depolarizing shift in the voltage dependence of activation or a hyperpolarizing shift in the steady-state inactivation curve completely abolished EADs in myocytes while maintaining a normal Ca_i transient. We propose that modifying the biophysical properties of I_Ca,L has potential as a powerful therapeutic strategy for suppressing EADs and EAD-mediated arrhythmias.

Introduction

Early afterdepolarizations (EADs) are transient reversals of normal repolarization (i.e. positive dV/dt), occurring in late phase 2 or phase 3 of the cardiac action potential (AP). These events, observable both at the cellular and tissue level, are recognized as triggers of cardiac arrhythmias (Sato et al. 2009; Weiss et al. 2010b). When EADs propagate through cardiac tissue, they can generate premature heart beats, ventricular tachycardia (VT) and ventricular fibrillation (VF), common causes of sudden cardiac death in a variety of clinical settings.

EADs classically occur during bradycardia under conditions of reduced repolarization reserve, due to either abnormally decreased outward currents, or increased inward currents, or both. The predominant inward currents in ventricular myocytes which have been implicated in EAD genesis are the persistent I_Na (Maltsev et al. 1998), I_NCX (Volders et al. 1997; Szabo et al. 1994) and I_Ca,L (January & Riddle, 1989). Previous work has shown that reactivation of the L-type Ca²⁺ current (I_Ca,L) during phase 2 and 3 of the action potential (AP) plateau plays a major role in EAD formation (January et al. 1988), although other factors are also important (Weiss et al. 2010a). Most EADs are initiated between −40 and 0 mV (Fig. 1), corresponding to the range of membrane potentials where the steady-state activation and inactivation curves of I_Ca,L overlap, often referred to as the ‘window current’ region (January & Riddle, 1989; Antoons et al. 2007a). As the AP repolarizes into this voltage ‘window’, a fraction of the L-type Ca²⁺ channels not inactivated may be available for reactivation to generate the upstroke of the EAD. In this study, we sought to determine the relevance of I_Ca,L in EAD formation, and investigated whether EAD suppression can be achieved solely by manipulating I_Ca,L without altering other ionic conductances or signalling pathways. We analysed whether EAD formation can be suppressed by minimal perturbation of the biophysical properties of L-type Ca²⁺ channels affecting the I_Ca,L window voltage region. Since it is difficult to control these properties experimentally with any degree of precision, we adopted a hybrid biological–computational approach using the dynamic clamp technique (Dorval et al. 2001; Berecki et al. 2005, 2006, 2007; Wilders, 2006). This allowed us to replace the native I_Ca,L of the myocyte with a computed virtual I_Ca,L with programmable properties. Our findings show that EAD formation is highly sensitive to I_Ca,L properties and properties of the window region (such as the slopes of the activation and inactivation curves (Tran et al. 2009)), such that subtle shifts in the voltage dependence of steady-state I_Ca,L activation or inactivation can abolish EADs. Moreover, these changes are predicted to have no significant effects on the amplitude or kinetics of the intracellular Ca²⁺ transient, suggesting that pharmacological or genetic manipulation of the voltage-dependent properties of I_Ca,L could have therapeutic potential for suppressing EAD-mediated arrhythmias without adversely affecting excitation–contraction coupling.

Figure 1. Oxidative stress and hypokalaemia generate EADs in dissociated rabbit cardiomyocytes.

A, representative AP recordings in current-clamped ventricular myocytes stimulated at a pacing cycle length of 5 s. EADs, absent in control conditions, were consistently induced by addition of 600 μmol l⁻¹ H₂O₂ to the bath solution or by reducing extracellular [K⁺] from 5.4 mmol l⁻¹ to 2.7 mmol l⁻¹ (hypokalaemia). The histogram to the left of each trace shows the distribution of action potential duration measured at 90% repolarization (APD₉₀) for each condition. B, action potentials in the dotted box in A are shown on an expanded scale (arrows point to EADs). C, percent of action potentials displaying EADs in Control, H₂O₂ and hypokalaemia conditions.

Methods

Ethical approval

All animal protocols were approved by the UCLA Institutional Animal Care and Use Committee and conformed to the Guide for the Care and Use of Laboratory Animals published by the US National Institutes of Health.

Electrophysiology

Ventricular myocytes were isolated from New Zealand White rabbits as previously described (Mahajan et al. 2008a). All animals were anaesthetized with 50 mg ml⁻¹ intravenous pentobarbital, before excision of the hearts, which were subsequently submerged in Ca²⁺-free Tyrode solution containing (in mmol l⁻¹): 136 NaCl, 5.4 KCl, 1 MgCl₂, 0.33 NaH₂PO₄, 10 glucose, and 10 Hepes, adjusted to pH 7.4. The hearts were cannulated and perfused retrogradely on a Langendorff apparatus with Ca²⁺-free Tyrode buffer containing 1.65 mg ml⁻¹ collagenase and 0.8 mg ml⁻¹ bovine serum albumin for 30–40 min. After washing out the enzyme solution, the hearts were swirled in a beaker to dissociate cells. The Ca²⁺ concentration was gradually increased to 1.8 mmol l⁻¹, and the cells were stored at room temperature. This procedure typically yielded 50% rod-shaped Ca²⁺-tolerant myocytes. Only Ca²⁺-tolerant, rod-shaped ventricular myocytes with clear striations were randomly selected for electrophysiological studies within 8 h of isolation. All recordings were measured with AxoPatch 200B (Axon Instruments). Whole-cell patch-clamp recordings (in current or voltage clamp mode) were performed at 34–36°C using pipettes of 1–2 MΩ. The intracellular solution contained (in mmol l⁻¹): 110 potassium aspartate, 30 KCl, 5 NaCl, 10 Hepes, 0.1 EGTA, 5 MgATP, 5 creatine phosphate, 0.05 cAMP adjusted to pH 7.2. For I_Ca,L recordings the solutions were as described above, except that K⁺ was replaced with Cs⁺ to abolish K⁺ conductance and 10 μmol l⁻¹ TTX was added to the extracellular solution to block Na⁺ conductance. The L-type-specific Ca²⁺ current was determined by subtracting the current after 20 μmol l⁻¹ nifedipine from the total current. Data were acquired and analysed using custom-made software (G-Patch, Analysis). Currents were filtered at 1/5 of the sampling frequency. The steady-state activation curves were constructed by dividing the peak I–V curve by the driving force to calculate conductance (G) and dividing G by G_max. The inactivation curves were constructed by plotting the normalized peak current during a test pulse at 10 mV following a 300 ms inactivating pulse at various voltages. The slope and half-activation/inactivation potential of these curves were estimated by fitting to a Boltzmann distribution, and these parameters were used to constrain the dynamic clamp model for both control and H₂O₂ conditions. These two versions of the model were then implemented for Dynamic Clamp in RTXI (http://www.rtxi.org) (Lin et al. 2010). Sampling/computation frequency was 10 kHz.

Intracellular calcium measurements

Myocytes were loaded with 10 μmol l⁻¹ Fluo4-AM (Molecular probes) for 30 min at room temperature. Cells were then washed twice in regular Tyrode solution and placed in a heated chamber at 34–36°C for fluorescence and electrophysiology measurements. Intracellular calcium (Ca_i) transients were recorded using a CMOS camera (Silicon Imaging SI-1300, Niskayuna, NY, USA).

Dynamic clamp

The ionic conductances included in the model are I_Ca,L, the fast sodium current I_Na, the Na⁺–K⁺ pump current I_NaK, the Na⁺–Ca²⁺ exchange current I_NCX, and the Ca²⁺-dependent slow component of the delayed rectifier potassium channel I_Ks. The intracellular Ca²⁺ concentration was divided into four compartments, i.e. submembrane Ca²⁺ (C_s), cytosolic Ca²⁺ (C_i) and network SR Ca²⁺ and junctional SR Ca²⁺. The average submembrane Ca²⁺ concentration, C_s, is used to compute Ca²⁺-dependent inactivation in the I_Ca,L formulation. The Ca²⁺ flux into the cell due to I_Ca,L is given by (Mahajan et al. 2008b):

(1)

where J_Ca is the current flux into the cell via L-type Ca²⁺ channels, g_Ca is determined by fitting to the nifedipine-sensitive current traces measured under voltage clamp, P_o is the probability of finding an L-type Ca²⁺ channel in the open state, and i_Ca is the driving force for Ca²⁺ given by:

(2)

where C_s is the submembrane concentration in units of mmol l⁻¹, P_Ca (0.00054 cm/s) is the Ca channel permeability and V is the membrane voltage, F is the Faraday constant, and T is temperature. In order to facilitate shifts of the activation and inactiation curves, we replaced the Markovian calcium channel open probability P_o (Mahajan et al. 2008b) with the Hodgkin–Huxley formulation from the Luo–Rudy dynamic model (Luo & Rudy, 1994), where P_o is formulated as:

where d is the voltage-dependent activation gate, f is the voltage-dependent inactivation gate and q is the Ca²⁺-dependent inactivation gate. The steady states of these gating variables as functions of voltage are formulated in the following manner:

(3)

(4)

(5)

(6)

(7)

where τ_d and τ_f are the time constants of d gate and f gate respectively, d_half is the voltage at half maximum of activation/inactivation (f_half), d_slope is the slope factor of the activation curve, p_dest is the non-inactivating pedestal of the inactivation gate, C_s is the submembrane Ca concentration in units of mM, Cst is the affinity for Ca of the inactivation gate, and a1, a2, b1, b2, b3, and b4 are additional factors used for fitting. All the parameters listed in the equations are fitted to our experimental data (the fitting parameters are shown in online supplemental materials). The Ca²⁺ cycling is the same as that in the rabbit ventricular myocyte model (Mahajan et al. 2008b).

Results

Oxidative stress-induced and hypokalaemia-induced EADs in isolated rabbit ventricular myocytes

To determine the relevance of I_Ca,L biophysical properties to EAD formation and/or suppression, we used two methods to induce EAD in whole-cell patch-clamped isolated rabbit ventricular myoyctes: (i) oxidative stress, by exposure to 600 μmol l⁻¹ H₂O₂ (Xie et al. 2009), or (ii) hypokalaemia, by lowering extracellular [K⁺] (from 5.4 to 2.0–2.7 mmol l⁻¹). Myocytes were superfused in the recording chamber at 34–36°C, and stimulated at a pacing cycle length (PCL) of 5 s (Fig. 1). Under current clamp, both H₂O₂ (n = 14) and hypokalaemia (n = 8) prolonged the APD significantly and consistently produced EADs in ∼70% of paced APs (Fig. 1A and B) within 5–10 min. In our analysis, we individually inspected each action potential for EAD occurrence, defined as well-resolved deflections of the voltage with a positive dV/dt during late phase 2 or phase 3 of the AP. EAD morphology varied among experiments and also within the same action potential as in Fig. 1B (under hypokalaemia). Typically, EADs exhibited a positive voltage deflection of ≥5 mV with durations (from inflection point to peak) between 30 and 150 ms).

Among other effects, oxidative stress with H₂O₂ is known to promote EADs by activating Ca²⁺–calmodulin-dependent protein kinase II (CaMKII) (Xie et al. 2009), which alters I_Ca,L (Dzhura et al. 2000) and induces late I_Na (Wagner et al. 2006; Wagner et al. 2011). To characterize how H₂O₂ altered I_Ca,L properties under our experimental conditions, we recorded the nifedipine-sensitive Ca²⁺ current in voltage-clamped isolated myocytes before and after exposure to 600 μmol l⁻¹ H₂O₂ (n = 5) (Fig. 2): in addition to an overall slowing of inactivation (Fig. 2A and B), H₂O₂ shifted the peak of the current–voltage (I–V) relationship by −5 mV as shown in Fig. 2C. By constructing steady-state activation and inactivation curves, we found that H₂O₂ produced an ∼−5 mV shift of the steady state half-activation potential (V_1/2,act), accompanied by an ∼+5 mV shift in the steady state half-inactivation potential (V_1/2,inact) (Fig. 2D). Effectively, H₂O₂ increased the height of the I_Ca,L window current region, changes which are expected to promote EAD formation (Antoons et al. 2007b; Qi et al. 2009; Tran et al. 2009).

Figure 2. H₂O₂ alters both the time-dependent and steady-state properties of I_Ca,L in rabbit ventricular myocytes.

A, voltage clamp recordings of nifedipine (20 μmol l⁻¹) sensitive I_Ca,L in response to depolarizing pulses from −40 mV (HP = −80 mV), under control conditions (black) or after 2 min of exposure to 600 μmol l⁻¹ H₂O₂ (red). B, voltage clamp recordings of nifedipine-sensitive I_Ca,L in response to a two-pulse protocol from a holding potential of −90mV, under control conditions (black) or after 2 min of exposure to 600 μmol l⁻¹ H₂O₂ (red). The inactivating pulse was 300 ms to approximate the duration of a normal action potential. C, the I–V relationship for I_Ca,L (normalized to the peak current) under control conditions (black circles, n = 4) and H₂O₂ (red circles, n = 5). Note the negative shift of the I–V curve in H₂O₂. D, mean steady-state activation and inactivation curves for I_Ca,L in control (black circles, n = 4) and H₂O₂ conditions (red diamonds, n = 5). Note that the H₂O₂-induced shift of steady-state curves results in a higher I_Ca,L window area. External solution (mmol l⁻¹): 136 NaCl, 5.4 CsCl, 1 MgCl₂, 0.33 NaH₂PO₄, 1.8 CaCl₂, 10 glucose, 10 Hepes, and 10 μmol l⁻¹ TTX, pH 7.4. Pipette solution (in mmol l⁻¹): 100 caesium aspartate, 30 CsCl, 5 NaCl, 10 Hepes, 0.1 EGTA, 5 MgATP, 5 creatine phosphate, 0.05 cAMP, pH 7.2. Temperature = 35–37°C.

Role of oxidative stress-mediated I_Ca,L alterations in EAD generation

To understand how the H₂O₂-induced changes in I_Ca,L described above contributed to EAD formation, we next used the dynamic clamp technique (Tan & Joyner, 1990) to replace the myocyte's native I_Ca,L with a virtual I_Ca,L with programmable properties. The principle of the dynamic clamp operation is illustrated in Fig. 3A. The recorded membrane potential of a current-clamped myocyte (V_m) is fed into a Linux-based computer with the Real-time Experimental Interface (RTXI) software (Dorval et al. 2001) running the UCLA ventricular myocyte AP model (Mahajan et al. 2008b). The model computes, in real time, the macroscopic L-type Ca²⁺ channel current, which is injected continuously into the myocyte, in turn changing its membrane potential. This cycle (V_m sampling →I_Ca,L computation →I_Ca,L injection →V_m sampling …) is iterated at 10 kHz, creating a dynamic, bidirectional relationship between the model and the cell.

Figure 3. The dynamic patch clamp implements a virtual Ca²⁺ current computed with detailed Ca²⁺ cycling dynamics.

A, diagram of the dynamic clamp system. A ventricular myocyte is whole-cell patch-clamped with an amplifier in current-clamp mode. The myocyte's V_m signal (red arrow) is digitized and input to a computer running a cardiac action potential model (Mahajan et al. 2008) containing macroscopic Hodgin–Huxley (HH)-type formulations for five conductances (I_Ca,L; the fast Na⁺ channel I_Na; the Na⁺/K⁺ pump I_NaK; the Na⁺/Ca²⁺ exchanger I_NCX; and the Ca²⁺-dependent K⁺ rectifier I_Ks) and [Ca²⁺] in four discrete cellular compartments (C_s, C_i, C_jp and C_j). Ionic conductances and concentrations can be fine-tuned by altering model parameters online. The calculated ionic conductances can be output in any combination to produce I_Command. In this case, I_Command = I_Ca,L (blue arrow). I_Command is combined with a pacing AP stimulus and converted to analog before being input to the amplifier to be injected into the clamped myocyte. This alters the myocyte V_m, which is in turn sampled for the next computation. Thus, there is a dynamic, bidirectional relationship between V_m and model conductance output, at a sampling/computation frequency of 10 kHz. B, the predicted I_Ca,L conductance from the model in panel A (red) accurately predicts a current similar in amplitude and kinetics to experimentally recorded I_Ca,L from rabbit cardiomyocytes (black) in response to depolarizing pulses from a holding potential of −40 mV.

The virtual I_Ca,L computed in the AP model was tuned to fit experimental recordings of native I_Ca,L recorded from rabbit ventricular myocytes (Fig. 3B). In addition to computing I_Ca,L, the model also computes all other elements of Ca_i cycling in the UCLA rabbit ventricular myocyte model (Mahajan et al. 2008b), which is critical for simulating the effects of intracellular Ca²⁺ on Ca²⁺-dependent inactivation of the virtual I_Ca,L being injected into the myocyte. Thus, this model also generates a virtual intracellular Ca²⁺ transient, which showed good agreement with the intracellular Ca²⁺ transient recorded directly from a myocyte under control conditions (Fig. S1). The model computes Ca²⁺ concentrations in four discrete subcellular compartments (Fig. 3A), with the average submembrane Ca²⁺ concentration (C_s) used for the calculation of Ca²⁺-dependent inactivation of I_Ca,L, as described previously (Mahajan et al. 2008b). Although we initially used a seven-state Markovian description of I_Ca,L, we achieved equivalent accuracy of fitting the experimental I_Ca,L data with a Hodgkin–Huxley type I_Ca,L formulation, with the advantage that the biophysical parameters relevant to this work could be directly modified, such as V_1/2,act and V_1/2,inact, which determine the steady-state activation and inactivation properties of the injected virtual I_Ca,L.

In our experimental protocol utilizing the dynamic clamp technique, we first paced a rabbit ventricular myocyte to record the AP in the current clamp mode (Fig. 4A, trace 1). The recorded AP waveform was used to compute a virtual Ca_i transient, displayed below the AP trace (Fig. 4B, trace 1). The myocyte was then exposed to 600 μmol l⁻¹ H₂O₂ until EADs appeared consistently (Fig. 4A, trace 2). Nifedipine (20 μmol l⁻¹) was then added to block the native I_Ca,L, which markedly shortened APD and abolished EADs (Fig. 4, trace 3). Current injection by the dynamic clamp was then turned on, adding the virtual I_Ca,L computed from the UCLA rabbit ventricular AP cell model (Mahajan et al. 2008b), whose properties had been adjusted to simulate the previously analysed effects of H₂O₂ on I_Ca,L gating properties shown in Fig. 2. Injection of this ‘H₂O₂-modified’ virtual I_Ca,L effectively restored the electrical properties of the myocyte membrane, resulting in AP prolongation and the reappearance of EADs (Fig. 4, trace 4). The associated computed virtual Ca_i transients are shown in Fig. 4B.

Figure 4. Reconstitution of EADs by a virtual I_Ca,L and their suppression by shifting I_Ca,L V_1/2 activation.

A, APs from rabbit ventricular myocytes recorded at a pacing cycle length of 5 s at 36–37°C in control conditions (1). Addition of 600 μmol l⁻¹ H₂O₂ to the bath solution induced EADs within 5–10 min (2). Addition of 20 μmol l⁻¹ nifedipine blocked the native I_Ca,L, shortened APD and abolished EADs (3). The dynamic clamp was then turned on to inject a virtual ‘I_Ca,L’ computed in real time (red trace), which restored EADs (4). Varying a single I_Ca,L parameter (V_1/2 activation) by +5 mV to effectively reduce the ‘I_Ca,L window region’ abolished EADs, despite the presence of H₂O₂ (5). B, representative action potentials from each condition (numbered) in A and their corresponding virtual Ca_i transients. Note that both action potential duration and the shape and amplitude of the computed Ca_i transient in conditions (1) and (5) are similar. C, graphical representation of the change in the overlap of the activation and steady-state inactivation curves upon a +5 mV shift in the V_1/2 of activation.

To investigate the sensitivity of EAD formation to the properties of the virtual I_Ca,L, we then shifted the voltage dependence of I_Ca,L activation (V_1/2,act) by +5 mV, to resemble the normal steady activation curve prior to H₂O₂ exposure. This small shift, which effectively suppressed the I_Ca,L‘window’ current by reducing the overlap between the steady state activation and inactivation curves to (Fig. 4C), abolished EADs and restored the AP duration towards the control value (Fig. 4, trace 5). Moreover, the virtual Ca_i transient (Fig. 4B, trace 5) had similar amplitude and kinetics to that computed for the normal control AP (Fig. 4B, trace 1). Similar results were also achieved by shifting the voltage dependence of I_Ca,L inactivation (V_1/2,inact) in the negative direction to reduce the window current region (not shown).

The overall results, summarized in Fig. 5, demonstrate that the small shifts in the V_1/2 of steady-state activation and inactivation of I_Ca,L strongly suppress EAD formation. A +4 mV shift of the V_1/2,act from −5 mV to −1 mV (Fig. 5A) shortened APD₉₀ from 1197 ± 112 (n = 7) to 373 ± 15 ms (n = 4) (Fig. 5B) and suppressed EAD occurrence from 91 ± 4% to 24 ± 20% of paced APs (Fig. 5C). An additional +1 mV shift to 0 mV (Fig. 5A) shortened APD₉₀ to 331 ± 15 ms (n = 6) (Fig. 5B) and further suppressed EAD occurrence to ∼2% (Fig. 5C). Similar results were achieved with small hyperpolarizing shifts in the V_1/2,inact. A −3 mV shift from −17 mV to −20 mV (Fig. 5D) reduced APD₉₀ to 696 ± 42 ms (n = 3) (Fig. 5E) and EAD occurrence to 52% (Fig. 5F). Further shifting V_1/2,inact by an additional −2 mV to −22 mV (Fig. 5D) reduced APD₉₀ to 488 ± 21 ms (n = 4) (Fig. 5E) and EAD occurrence to 10%.

Figure 5. EADs induced by oxidative stress are steeply dependent on V_1/2 of activation and inactivation.

A, steady-state activation and inactivation of the virtual I_CaL under control conditions (black) and with the V_1/2 activation shifted by −1 (blue) or −5 mV (red) to partially simulate the effects of oxidative stress increasing the I_CaL window region (cross-hatched). B and C, APD₉₀ (B) and the percentage of AP's exhibiting EADs (C) corresponding to the virtual I_Ca,L activation/inactivation properties in A, when the respective currents were injected by the dynamic clamp into ventricular myocytes in the presence of 0.6 mmol l⁻¹ H₂O₂ and 20 μmol l⁻¹ nifedipine. The virtual I_Ca,L simulating oxidative stress caused marked AP prolongation and EADs, which were suppressed by returning the V_1/2 activation towards normal (blue and black). D, steady-state activation and inactivation of the virtual I_Ca,L under control conditions (black) and with the V_1/2 inactivation shifted by +3 (blue) or +5 mV (red) to partially simulate the effects of oxidative stress increasing the I_Ca,L window region (cross-hatched). E and F, APD₉₀ (E) and the percentage of APs exhibiting EADs (F) corresponding to the virtual I_Ca,L activation/inactivation properties in A, when the respective currents were injected by the dynamic clamp into ventricular myocytes in the presence of 0.6 mmol l⁻¹ H₂O₂ and 20 μmol l⁻¹ nifedipine. The virtual I_Ca,L corresponding to the red curve simulating oxidative stress caused marked AP prolongation and EADs, which were suppressed by returning the V_1/2 inactivation towards normal (blue and black).

Reducing I_Ca,L window current also suppresses hypokalaemia-induced EADs

To demonstrate that the results described above are not unique to H₂O₂-induced EADs, we also assessed the effectiveness of shifting V_1/2,act or V_1/2,inact at suppressing hypokalaemia-induced EADs. Lowering extracellular K⁺ from 5.4 to 2.0 mmol l⁻¹ hyperpolarized the resting membrane potential to nearly −100 mV and induced EADs within 5 min (Fig. 1 and 6). As with H₂O₂-induced EADs, blocking I_Ca,L with 20 μmol l⁻¹ nifedipine abolished EADs and shortened the action potential (not shown). Adding a virtual I_Ca,L with dynamic clamp prolonged APD₉₀ to 2170 ± 190 ms (n = 6) (Fig. 6C and E, hatched bars) and reconstituted EADs in 83% of APs (Fig. 6D and F, hatched bars). A +5 mV depolarizing shift in the steady state activation curve from −1 to +4 mV shortened APD₉₀ to 476 ± 39 ms (n = 3) (Fig. 6C, open bar) and reduced EAD occurrence to 0% (Fig. 6D, open bar). Similarly, a hyperpolarizing shift in the steady state inactivation curve from −18 to −23 mV shortened APD₉₀ to 869 ± 167 ms (n = 3) and reduced EAD occurrence to 10% of APs.

Figure 6. EADs induced by hypokalemia are steeply dependent on V_1/2 of activation and inactivation.

A, Under hypokalemic conditions (2.0 mM external K⁺), EADs (blue) were reconstituted in the presence of 20 mM nifedipine by injecting via the dynamic clamp a virtual I_Ca,L, with normal activation (blue) and inactivation (black) properties. Shifting the V_1/2 of activation by +5 mV (black) to reduce the I_Ca,L window region reversed AP prolongation and abolished EADs. B, Similar effects were observed when V_1/2 of inactivation was shifted by −5 mV to reduce the I_Ca,L window region. C, The +5 mV shift in the activation curve shortened and D, abolished EADs. E, The −5 mV shift in the inactivation curve also shortened APD90 and F, dramatically reduced EAD occurrence.

Discussion

It is widely accepted that EADs are important cellular triggers for VT and VF when repolarization reserve is reduced, as can occur clinically in acquired and congenital long QT syndromes and heart failure (Huffaker et al. 2004; Maruyama et al. 2011). In the present study, we used two different conditions, oxidative stress (H₂O₂) and hypokalaemia (Fig. 1), which reliably induce bradycardia-dependent EADs (positive dV/dt during phase 2 or 3) by different mechanisms in >90% of rabbit ventricular myocytes within 5–10 min of exposure. After blocking the native I_Ca,L with nifedipine, we used the dynamic clamp technique to inject a virtual I_Ca,L, which successfully reconstituted EADs. Moreover, the biophysical properties of the virtual I_Ca,L could be reprogrammed to explore its role in EAD formation. Our major findings are: (i) EAD formation is very sensitive to small shifts in the voltage sensitivity of steady state activation and inactivation of I_Ca,L, such that a +5 mV depolarizing shift in V_1/2,act, or a −5 mV hyperpolarizing shift in V_1/2,inact powerfully suppressed EAD formation (Figs 4–6); (ii) these small shifts were predicted to have minimal effects on peak I_Ca,L during the AP, such that the Ca_i transient, hence excitation–contraction coupling and contractility, remain normal (Fig. 4B); (iii) the same strategy was effective at suppressing EADs generated by two different mechanisms (Figs 4 and 6): oxidative stress in which CaMKII activation potentiating inward Na⁺ and Ca²⁺ currents plays a critical role (Dzhura et al. 2000; Anderson, 2004; Wagner et al. 2006; Xie et al. 2009; Koval et al. 2010; Wagner et al. 2011), and hypokalaemia, in which decreased outward K⁺ currents play the major role (Sato et al. 2010). Moreover, the degree of hypokalaemia used in this study is clinically relevant to values associated with EAD-mediated arrhythmias in patients (Osadchii, 2010).

These findings have therapeutic implications, namely that novel agents which alter the voltage dependence and/or kinetics of I_Ca,L could be developed to suppress EAD-mediated arrhythmias without adversely depressing excitation–contraction coupling.

Sensitivity of EADs to I_Ca,L properties

In the present study, we analysed the effects of small shifts in the V_1/2,act and V_1/2,inact on EAD formation, as a convenient way to suppress I_Ca,L reactivation in the window voltage region. However, I_Ca,L reactivation causing EADs during AP repolarization is not solely dependent on V_1/2,act and V_1/2,inact, but instead is a complex function of many I_Ca,L parameters juxtaposed with other factors, such as K⁺ currents influencing the speed of repolarization (Tran et al. 2009). With respect to I_Ca,L, other parameters in addition to V_1/2,act and V_1/2,inact influence I_Ca,L reactivation during repolarization, including the maximal L-type Ca²⁺ current conductance; the steepness (slope factor) of voltage-dependent activation and inactivation; the time constants of activation, inactivation (both Ca²⁺ dependent and voltage dependent), and recovery from inactivation; and the amplitude of the non-inactivating pedestal current. These factors can be combined into a single mathematical expression giving a necessary condition for EADs (Tran et al. 2009). In the present study, our modifications to the virtual I_Ca,L assumed that all of these other factors remained constant, allowing us to examine the isolated effects of V_1/2,act and V_1/2,inact. Thus, a major advantage of the dynamic clamp approach is that the virtual I_Ca,L can be programmed to simulate all of the effects that a candidate agent has on these I_Ca,L properties, once they have been characterized experimentally. The appropriately reshaped virtual I_Ca,L can then be evaluated to determine whether or not it suppresses EADs in real myocytes when introduced by the dynamic clamp technique.

Limitations

Although the dynamic clamp provides a technique to systematically dissect the role of key ionic currents such as I_Ca,L in EAD formation, an important limitation is that a virtual I_Ca,L does not trigger SR Ca²⁺ release, so it is not possible to directly test the effects of a modified virtual I_Ca,L on the Ca_i transient or cell shortening. This limitation was partially offset by using an AP model incorporating detailed Ca²⁺ cycling dynamics which allowed us to make predictions about the Ca_i transient, validated by experimental recordings of the Ca_i transient in rabbit ventricular myocytes using a Ca²⁺-sensitive fluorescent dye (Fig. S1). In fact, the lack of Ca²⁺ entering the cell during the virtual I_Ca,L injection also provides an advantage, allowing us to distinguish the purely electrical effects of ionic currents from their biochemical consequences (Ca²⁺-mediated signalling). Thus, these results demonstrate that EADs can occur in the absence of Ca²⁺ influx or SR Ca²⁺ release and can be a purely electrical phenomenon. For example, we computed the virtual Na⁺–Ca²⁺ exchange current accompanying the virtual Ca_i transient in our model, but chose not to inject this current into the myocyte via the dynamic clamp, since our initial goal was to investigate whether I_Ca,L alone was sufficient to reconstitute EADs without other Ca²⁺-sensitive currents. Furthermore, through the dynamic clamp, the contributions of other currents to EAD formation can be analysed systematically, assuming they have been accurately formulated in the model.

Therapeutic implications

Our study demonstrates ‘proof-of-concept’ for a hybrid biological–computational approach designed to predict how modifications of ion channel properties affect cellular arrhythmogenic phenomena such as EADs. Thus, in this study, the dynamic clamp has highlighted potential therapeutic targets (i.e. I_Ca,L properties such as V_1/2,act, V_1/2,inact) for new drugs or genetic interventions to suppress EAD-mediated arrhythmias.

Interstingly, whereas pharmacological agents may have off-target effects in both cardiac and non-cardiac tissue, a specific way to target I_Ca,L could be to take advantage of the modulatory accessory subunits of the L-type Ca²⁺ channel (Birnbaumer et al. 1998; Davies et al. 2007; Dolphin, 2009) such as α₂δ or β subunits. These accessory subunits are highly specific for the channel and are known to modulate its biophysical properties (Birnbaumer et al. 1998; Olcese et al. 1994; Platano et al. 2000). Thus, genetic interventions to tune the biophysical properties of I_Ca,L by altering its subunit composition could be a promising approach to suppress EAD formation in a highly specific manner.

Glossary

Abbreviations

AP

action potential

APD

action potential duration

CaMKII

Ca²⁺–calmodulin-dependent protein kinase II

EAD

early afterdepolarization

I_Ca,L

L-type Ca²⁺ current

RTXI

real-time experimental interface

SR

sarcoplasmic reticulum

VF

ventricular fibrillation

VT

ventricular tachycardia

Author contributions

R.V.M. performed research. Y.X. and A.P. provided analytical tools. R.V.M. and R.O. analyzed data. R.V.M, A.G., Z.Q., J.N.W, and R.O. designed research. R.V.M, A.P., A.G., Z.Q., J.N.W and R.O. wrote the paper. All authors have approved the final version of the paper for publication. The authors have no disclosures.

Supplementary material

Supplementary Fig. S1

Supplementary Table. S1

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