Impact of I_SK Voltage and Ca²⁺/Mg²⁺-Dependent Rectification on Cardiac Repolarization

Abstract

Cardiac small conductance Ca²⁺-activated K⁺ (SK) channels are activated solely by Ca²⁺, but the SK current (I_SK) is inwardly rectified. However, the impact of inward rectification in shaping action potentials (APs) in ventricular cardiomyocytes under β-adrenergic stimulation or in disease states remains undefined. Two processes underlie this inward rectification: an intrinsic rectification caused by an electrostatic energy barrier from positively charged amino acids at the inner pore and a voltage-dependent Ca²⁺/Mg²⁺ block. Thus, Ca²⁺ has a biphasic effect on I_SK, activating at low [Ca²⁺] yet inhibiting I_SK at high [Ca²⁺]. We examined the effect of I_SK rectification on APs in rat cardiomyocytes by simultaneously recording whole-cell apamin-sensitive currents and Ca²⁺ transients during an AP waveform and developed a computer model of SK channels with rectification features. The typical profile of I_SK during AP clamp included an initial peak (mean 1.6 pA/pF) followed by decay to the point that submembrane [Ca²⁺] reached ∼10 μM. During the rest of the AP stimulus, I_SK either plateaued or gradually increased as the cell repolarized and submembrane [Ca²⁺] decreased further. We used a six-state gating model combined with intrinsic and Ca²⁺/Mg²⁺-dependent rectification to simulate I_SK and investigated the relative contributions of each type of rectification to AP shape. This SK channel model replicates key features of I_SK recording during AP clamp showing that intrinsic rectification limits I_SK at high V_m during the early and plateau phase of APs. Furthermore, the initial rise of Ca²⁺ transients activates, but higher [Ca²⁺] blocks SK channels, yielding a transient outward-like I_SK trajectory. During the decay phase of Ca²⁺, the Ca²⁺-dependent block is released, causing I_SK to rise again and contribute to repolarization. Therefore, I_SK is an important repolarizing current, and the rectification characteristics of an SK channel determine its impact on early, plateau, and repolarization phases of APs.

Significance

Ca²⁺-activated K⁺ (SK) channels are expressed in ventricular myocytes, and their influence on action potentials (APs) becomes significant under β-adrenergic stimulation or in cardiac diseases. SK channels are voltage insensitive but show inward rectification caused by local electrostatic influence from positively charged amino acids near the pore and voltage-dependent blockade by Ca²⁺ and Mg²⁺. Using AP clamp data and computer simulation, we found that the rectification kinetics modulate the temporal trajectory of SK currents during an AP to influence both phase 1 and 3 repolarization depending on the degree of intrinsic and Ca²⁺/Mg²⁺-dependent rectification. This study suggests that modulation of the inward rectification properties of SK channels may have significant implications for arrhythmogenesis in various pathophysiological conditions.

Introduction

Small conductance Ca²⁺-activated K⁺ (SK) channels are solely activated by changes in intracellular Ca²⁺ via constitutively bound calmodulin, making the activation rapid within the 5–15-ms timescale (1). This unique characteristic of Ca²⁺-dependent opening determines its important role in integrating intracellular Ca²⁺ handling to membrane voltage. SK channels have been identified in many excitable cells, but the initial confirmation of SK channels in cardiac myocytes was relatively recent (2). Three SK channel isoforms (SK1-3) encoded by the genes KCNN1-3 have been identified (3,4). Expression of SK channels has been shown in various species, including mice, rats, rabbits, dogs, horses, and humans, both in ventricular (2,5, 6, 7, 8, 9, 10, 11, 12) and atrial (2,7,10,11,13) tissue. Recent studies suggest critical roles of SK channels in human atrial and ventricular arrhythmias, making them a potential therapeutic target (14, 15, 16, 17). However, the exact roles of SK channels in different types of arrhythmias are yet to be determined (18, 19, 20, 21, 22, 23, 24, 25, 26, 27).

The single channel conductance of SK channels is ∼10–20 pS (28,29), and it is well characterized that SK channels lack a voltage sensor, which makes their gating voltage insensitive. However, detailed biophysical studies of SK channel kinetics revealed two distinct properties that limit the SK current (I_SK) predominantly at positive membrane voltages, causing inward rectification, and that may significantly modulate I_SK influence on ventricular repolarization. First, an intrinsic rectification (IntR) is caused by two positively charged amino acids (R396 and K397 in rat SK2 (rSK2)) at the inner mouth of the SK channel pore. These residues provide an energy barrier to the entry and exit of K⁺ ions by a local electrostatic mechanism (30). Second, intracellular divalent ions bind near the selectivity filter of SK channels (S359 in rSK2) and block the flow of K⁺ ions. Ca²⁺ and Mg²⁺ ions bind in SK channels with a higher affinity at positive membrane potentials, contributing to Ca²⁺/Mg²⁺-dependent rectification (31,32) under physiological conditions. The amino acids associated with both forms of rectification are conserved in all three mammalian SK channel isoforms (SK1, SK2, and SK3) by PubMed BLAST analysis (33,34). Although most of the studies of SK channel rectification in heterologous expression systems used the rSK2 isoform (30, 31, 32), homomeric human SK1 (35) and SK3 (36,37) also show inward rectification.

Both intrinsic and Ca²⁺/Mg²⁺-dependent rectification may play significant roles in modulating cardiac repolarizations. The current amplitude will be smaller at positive voltages because of intrinsic rectification, particularly during action potential (AP) upstrokes and the phase 1 repolarization period. The rise of Ca²⁺ during the Ca²⁺ transient may have biphasic effects on I_SK. Recent studies showed that SK channels are closely linked to L-type Ca²⁺ channels (LTCCs) (38,39) and also near to ryanodine receptors (RyR2) (39). Because submembrane Ca²⁺ ([Ca²⁺]_SM) in ventricular cardiomyocytes (VCMs) can rise up to ∼100 μM (40,41), SK channels close to LTCCs may also see large influxes of Ca²⁺ that can inhibit the channels via a Ca²⁺/Mg²⁺-dependent block. The available data indicate that ventricular SK channels do not contribute to AP repolarization in normal conditions but become significantly augmented to impact AP repolarization in cardiac diseases or under a β-adrenergic stimulation (5,16,19,20,42,43). We recently showed that phosphorylation of SK channels by protein kinase A (PKA) increases I_SK in the VCMs of healthy animals. Furthermore, this phenomenon underlies the functional recruitment of SK channels in VCMs from a rat model of hypertrophy induced by pressure overload. We proposed that the PKA phosphorylation of the SK channel attenuates I_SK rectification by reducing the Ca²⁺/voltage-dependent inhibition of SK channels without changing their sensitivity to Ca²⁺, resulting in an increase of I_SK (38). In this study, we aim to determine whether changes in intrinsic rectification also play an important role in this process. Understanding the rectification properties and their modulations are important factors in defining the impact of I_SK on cardiac repolarization in addition to the expression level of SK channels.

Our goal in this study is to characterize the I_SK trajectory during an AP under β-adrenergic stimulation and determine how intrinsic and Ca²⁺/Mg²⁺-dependent rectification of I_SK influences this trajectory, thereby modulating AP dynamics. To address the complex role of SK channels in cardiac repolarization, it is crucial to study SK channel physiology under conditions of physiological Ca²⁺ dynamics, yet most isolated cell physiology experiments have been done with [Ca²⁺] clamped to one concentration. We simultaneously recorded apamin-sensitive currents and Ca²⁺ signals in rat VCMs while voltage clamping the cells with an AP stimulus waveform (AP clamp). In addition, we developed a model with rectification properties and incorporated the data from AP clamp to investigate how intrinsic and Ca²⁺/Mg²⁺-dependent rectification of I_SK affects an AP. The model expands upon a previous SK channel model without rectification characteristics (23). Our results indicate that I_SK does not solely follow the rise and decay of intracellular Ca²⁺ transients but shows an initial peak with a rapid decay, followed by a second rise of I_SK during the phase 3 repolarization. This suggests that the rectification properties of SK channels greatly influence their impact on cardiac repolarization over the full range of an AP (phases 1, 2, and 3) and thereby AP dynamics.

Materials and Methods

Ethical approval

All procedures involving animals were approved by The Rhode Island Hospital 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 (Publication No. 85-23, revised 2011).

VCM isolation, cell culture, and viral infection

Whole hearts and VCMs were isolated from male Sprague-Dawley rats purchased either from Charles River Laboratories (Wilmington, MA) as sham-operated rats for thoracic aortic banding or from Harlan Laboratories (Indianapolis, IN). Animals were acclimatized for 3–4 weeks in the Rhode Island Hospital animal facility. Experiments were performed 4–5 weeks after shipping. Rats were injected with 120 mg/kg pentobarbital intraperitoneally. The heart was removed from euthanized rats via bilateral thoracotomy, mounted on a Langendorff apparatus, and retrogradely perfused with Tyrode solution containing collagenase II (Worthington Biochemical, Lakewood, NJ) at 37°C. VCMs were isolated as previously described (44) before plating onto laminin-coated coverslips for AP clamp experiments. VCMs were recorded under a whole-cell patch clamp within 8 h of isolation. For experiments with rSK2 channel overexpression by viral infection, adult rat VCMs were isolated from 9–12-week-old Sprague-Dawley male rats (Rat Genome Database catalog no. 70508, RRID: RGD_70508) from Harlan Laboratories (Indianapolis, IN), as described previously (44). Myocytes were plated in 24-well plates on laminin-coated glass coverslips, cultured in serum-free medium 199 (Thermo Fisher Scientific, Waltham, MA), and supplemented with 25 mmol/L NaHCO₃, 10 mmol/L HEPES, 5 mmol/L creatine, and 5 mmol/L taurine and 10 U/mL penicillin, 10 μg/mL streptomycin, and 10 μg/mL gentamycin (pH 7.3). Unattached cells were removed after 1 h, and the remaining VCMs were infected with adenoviruses at multiplicity of infection (MOI) of 10 for the rSK2 channel. Myocytes were cultured at 37°C in 95% air, 5% CO₂ for 36–48 h before analysis.

Construction of wild-type and mutant SK2 adenoviruses

Adenovirus-carrying recombinant wild-type rSK2 sequence was constructed as described previously (8,44), utilizing the ViraPower Gateway Expression System (Thermo Fisher Scientific). Briefly, the coding region of rSK2 sequence was cloned into pENTR 1A vector, and then recombined into pAd/CMV/V5-DEST with LR recombination reaction. The R396E/K397E mutant viral construct was made the same way using a mutant coding region of rSK2 made as described (30), which was the kind gift of Dr. Weiyan Li. Sequence-verified plasmid was digested with restriction enzyme PacI before transfection into HEK293A cells (RRID: CVCL_6910) using Lipofectamine 2000 (Invitrogen, Carlsbad, CA). The titer of amplified adenoviral stocks was determined using the Adeno-X qPCR Titration Kit (Takara Bio, Mountain View, CA).

Whole-cell patch clamp of VCMs

Whole-cell patch-clamp recordings of currents and membrane potential were carried out using an Axopatch 200B amplifier (Axon Instruments; Molecular Devices, Sunnyvale, CA) as described previously (44). Briefly, to record SK channel currents from rat VCMs, depolarizing voltage steps were applied at 2-s intervals under a voltage clamp at room temperature. The bath solution (pH 7.3) contained 140 mM NaCl, 5.4 mM KCl, 1 mM MgCl₂, 1 mM CaCl₂, 10 mM HEPES, and 5.6 mM glucose. The nominally Ca²⁺-free pipette solution (pH 7.3) contained 90 mmol/L K-aspartate, 50 mmol/L KCl, 5 mmol/L Mg-ATP, 5 mmol/L NaCl, 1 mmol/L MgCl₂, 0.1 mmol/L Tris-GTP, 10 mmol/L HEPES, and 0.1 mmol/L Rhod-2 K⁺-salt (Thermo Fisher Scientific). Free [Mg²⁺] was 1.37 mM (Maxchelator (45)). Apamin, a selective SK1, 2, and 3 polypeptide inhibitor (IC₅₀ < 10 nM, Alomone Labs, Jerusalem, Israel) was used to identify I_SK. For β-adrenergic stimulation, VCMs were treated with isoproterenol (100 nM; MilliporeSigma, Burlington, MA). Whole-cell capacitance and series resistance were compensated, and a mostly 60–70% series resistance compensation correction was applied. For AP clamp experiments, a linear extrapolated leak conductance was calculated using the recorded current at −86 mV (adjusted offline for liquid junctional potential) and assuming zero current at 0 mV. Leak currents calculated from this conductance were subtracted from the difference currents (total current before apamin − current after apamin). A measured liquid junctional potential of 6 mV was used to adjust voltages in I/V plots and calculation of SK conductance.

Confocal imaging and estimation of [Ca²⁺]_i and [Ca²⁺]_SM

During whole-cell voltage clamp experiments, intracellular Ca²⁺ imaging was simultaneously performed at room temperature using a Leica SP5 II confocal microscope (Leica Microsystems, Wetzler, Germany) equipped with 63 × 1.4 numerical aperture oil objective in line-scan mode at a rate of 2.5 ms per line, synchronized with the electrophysiological setup. Rhod-2 was excited using a 543-nm line of HeNe laser, and fluorescence emission was collected at 560–660-nm wavelengths. Dynamical Rhod-2 fluorescence signal during Ca²⁺ transient was converted to [Ca²⁺]_i (46) using the following equation: [Ca²⁺]_i = Kd(F − F_min)/(F_max − F), where Kd Rhod-2 = 1.58 μmol/L (47,48) and F_min = F_max/15. F_max was determined by breaking the patch pipette and measuring the Rhod-2 fluorescence as the dye was exposed to the 1 mM Ca²⁺ bath solution. When possible, F and F_max were normalized to their respective F₀-values before calculation. [Ca²⁺]_SM was estimated based on previous calculations (48,49). Briefly, the [Ca²⁺]_i calculated as above was smoothed by the Savitzky-Golay method, with five points of window. The rise of [Ca²⁺]_SM = [Ca²⁺]_i + γd[Ca²⁺]_i/dt used the smoothed [Ca²⁺]_i and γ = 110 ms. The decay of [Ca²⁺]_SM = [Ca²⁺]_i + Ae^{(-(t-t₀/τ))} (49), where the A = the peak of [Ca²⁺]_i + γd[Ca²⁺]_i/dt and a single exponential decay was fitted to decay of [Ca²⁺]_i.

Rat and human VCM AP and Ca²⁺ handling model

We used the rat ventricular myocyte AP model of Pandit et al. (50) with adjusted parameters of I_CaL and I_to and I_ss to better represent our experimental results from AP clamp. The details of the model formulation are given in Appendix S1. Numerical calculation of different equations were performed by the Euler method with an adaptive time step of t = 0.1 ∼ 10 μs for the Markovian chain formulations and the first-order exponential integrator method for Hodgkin-Huxley formulism with a time step of t = 100 μs. The simulations to investigate the role I_SK rectification properties in different parameter sets were carried out on a multicore graphic processing unit (Quadro P4000; NVIDIA, Santa Clara, CA) with double precision using the CUDA toolkit (https://developer.nvidia.com/cuda-zone). The data visualization was done using Interactive Data Language (L3Harris Geospatial, Broomfield, CO). For the human ventricular AP model, for which we used the model of O’Hara et al. (51), the parameters were left as in the original except for the integration of our simulated I_SK with rectification, as was done for the rat AP model.

Statistics

Statistical analysis of electrophysiological and Ca²⁺ imaging data was performed using OriginPro 8.1 (OriginLab, Northampton, MA). Data are presented as mean ± standard error (SE). The statistical significance between groups was performed using one-way analysis of variance with Bonferroni post hoc test when appropriate. For all analyses, a p-value of less than 0.05 was considered significant.

Results

Formulation of SK channel kinetics and fitting to the experimental data of overexpressed rSK2

For the development of a mathematical I_SK model, we considered I_SK to be the product of three independent processes: Ca²⁺-dependent activation, intrinsic rectification, and Ca²⁺/Mg²⁺-dependent rectification. I_SK is governed by the Goldman-Hodgkin-Katz current equation:

$$I_{SK}=S{K}_{free}\times S{K}_O\times S{K}_{IntR}\times P_{sk}\frac{V{F}^2}{RT}\frac{{\left[K\right]}_i{e}^{VF/RT}-{\left[K\right]}_O}{e^{VF/RT}-1},$$

where p_SK is the total permeability (s⁻¹) of SK channels, SK_O is the open probability of SK channels, SK_IntR is intrinsic rectification by electrostatic permeability reduction, SK_Free is the probability that SK channels are not bound to Ca²⁺/Mg²⁺, V is membrane potential, F is the Faraday constant, R is the universal gas constant, and T is the temperature. [K]_i and [K]_o are the internal and external potassium ion concentrations, respectively (see Table S1 for details and units).

The activation scheme of the SK channel is based on previous studies of the single SK channel physiology of rSK2 channels, showing that activation depends on the level of Ca²⁺ at the SK channel, and the activation scheme was formulated as a Markovian multistate model with four closed states and two independent open states. The first open state, activated by lower levels of Ca²⁺, has a short duration, and the second open state, activated at higher levels of Ca²⁺, has a longer duration at higher levels of Ca²⁺ (Fig. 1 A; (29)). A list of all the corresponding parameters is provided in Table S1.

Figure 1.

Six-state SK channel gating scheme and sources of SK channel rectification. (A) SK channel gating scheme modified from Hirschberg et al. (29). (B) Cartoon of the source of intrinsic rectification (IntR) of the SK current showing two subunits of the SK channel. Two positively charged amino acids in each subunit near the mouth of SK channel pore electrostatically interfere with the K⁺ ion passage. z = charge number; δ = fraction of membrane voltage (V_m) influencing ion; V_m = membrane potential. (C) Scheme to simulate the block of SK channels by Ca²⁺ and Mg²⁺. (D) Predicted I/V plot of the SK current with no rectification (black), IntR only (magenta), or combined IntR and Ca²⁺/Mg²⁺-dependent rectification (CaMgR) (blue). Equimolar concentrations of K⁺ inside and outside are given.

The electrostatic influence on SK conductance was modeled based on studies by Li and Aldrich (30) showing that two positively charged amino acids at the mouth of the inner pore modulate K⁺ conductance of SK channels. In rSK2, R396, K397, and E399 were identified based on comparison with large-conductance, SK channels, which do not show rectification (30). All three amino acids are also conserved in rSK1 and rSK3 by PubMed BLAST analysis (33,34). The positive charges of R396 and K397 are thought to create an energy barrier to K⁺ at the intracellular mouth of the channel pore that is tempered by negative charge E399. Mutating E399 to positive R399 or neutral N399 leads to increased rectification (30). The change in free energy for ions to pass through the mouth of the pore is dependent on membrane voltage (V_m), the fraction of membrane potential acting at the site of these amino acids (δ), and the valence of ion (z) (Fig. 1 B). Because the intrinsic electrostatic mechanism reduces the single channel conductance (30), we modeled it with the following equation:

$$S{K}_{IntR}\left(V_m\right)=\frac{1}{1+k_{IntR}\exp \left(\raisebox{1ex}{$-V_m{\delta }_{IntR}F$}\!\left/ \!\raisebox{-1ex}{$RT$}\right.\right)}.$$

Because Ca²⁺ and Mg²⁺ bind to the pore of SK channels regardless of open or closed states and share the same binding site in the SK channel (32), we developed a Markov chain model of three states: free SK channel without Ca²⁺/Mg²⁺ binding (SK_free), Mg²⁺-bound SK channel (SK_Mg), and Ca²⁺-bound SK channel (SK_Ca), with respective association and dissociation constants (Fig. 1 C). The equations and parameters of the Ca²⁺/Mg²⁺-dependent rectification scheme are provided in Appendix S1 and Table S1. Fig. 1 D shows a predicted I/V plot of I_SK during a voltage ramp from −100 to 100 mV without rectification, intrinsic rectification only, or with both intrinsic and Ca²⁺/Mg²⁺-dependent rectification.

To establish a parameter set for our model, we reanalyzed previously published data (38) from the overexpression of rSK2 in rat VCMs and optimized the modeling parameters for activation and rectification. The I_SK recordings from the overexpressed rSK2 is robust (mean peak current > 19 pA/pF) and does not have to be isolated from other currents, unlike the I_SK measured from native cells, which peaks at only 1–2 pA/pF (38). SK2 and SK3 are the dominant isoforms detected in rat VCM plasma membrane fraction (8).

The overexpression system also allowed us to use data from the rSK2 double mutant R396E/K397E that has reduced intrinsic rectification (30). Previous studies reported that SK channels are expressed in close proximity to LTCCs and RyR2s in native cells (38,39), indicating a Ca²⁺_SM concentration that is much higher than the bulk cytosolic Ca²⁺ concentration. With the overexpression of rSK2, the amplitude of I_SK was ∼13 times greater than that of peak I_SK in native cells at −10 mV (38). Therefore, we assumed that the number of the SK channels at the surface membrane (non-T-tubule) far outnumbers the existing surface membrane LTCCs in rat VCMs. We estimated there were 4500 native and overexpressed SK channels using a single channel current of 0.5 pA (3,52,53), and the current under ISO conditions at −10 mV (38) vs. 750 native LTCCs or a ratio of 6 using the maximal Ca²⁺ current and membrane capacitance of cells treated with formamide to remove T-tubules (54) and the unitary LTCC current of 0.2 pA (55), so the majority of the SK channels may not be close to LTCCs and are exposed to cytosolic bulk Ca²⁺ concentrations rather than the subcellular Ca²⁺ concentration in close proximity to LTCCs. Therefore, for testing the modeling parameters only, we used the cytosolic bulk Ca²⁺ recordings plotted in Fig. 2, A and B (right) rather than [Ca²⁺]_SM near LTCCs as in native cells to calculate and fit the peak I_SK from overexpressed rSK2. Later, all the modeling of SK channels was performed using the Ca²⁺_SM concentrations. The time to peak of I_SK and the Ca²⁺ transient is slower in the overexpression system (I_SK baseline: 29.1 ± 4.6 ms; I_SK ISO: 39.0 ± 4.3 ms; Ca²⁺ baseline: 33.4 ± 1.6 ms; Ca²⁺ ISO: 28.3 ± 2.7 ms; Fig. S1 B). The mean I_SK and Ca²⁺ time to peak in native rat VCMs is 10.3 ± 1.5 and 18.5 ± 1.0 ms, respectively (38). As reported previously, treatment with isoproterenol (ISO) reduces rectification of I_SK (38), similar to the R396E/K397E mutant (30) (Fig. 2, A and B) despite the increase in bulk [Ca²⁺] (Fig. 2, A and B). Using I/V I_SK data and the recorded bulk [Ca²⁺] (shown in Fig. 2, A and B) from cells overexpressing rSK2 for a parameter set in our model, we were able to generate predicted I/V plots that fit our data for four conditions: rSK2 wild-type baseline, rSK2 wild-type treated with ISO (Fig. 2 A), rSK2 R396E/K397E mutant, and rSK2 R396E/K397E mutant with ISO (Fig. 2 B). Note that for the rSK2 wild-type ISO condition, the parameter set with full rectification properties deviates from the experimental data, particularly at higher V_m, whereas the parameter set with reduced intrinsic rectification can fit the data in the full range of V_m (Fig. 2 A, middle panel). For these simulations, the contribution of the Ca²⁺/Mg²⁺-dependent rectification was minimal because the I_SK experimentally measured from the overexpressed SK channels is mostly dependent on cytosolic bulk Ca²⁺ that does not rise sufficiently to block SK channels (IC₅₀ ∼3 μM at 0 mV (56)).

Figure 2.

Fit of I_SK I/V plots from rSK2 overexpressed in rat VCMs with I/V plots predicted from the model. (A) Normalized I_SK/voltage and bulk [Ca²⁺]_int./voltage (right) for VCMs expressing wild-type rSK2 under control conditions (left) or treated with isoproterenol (ISO; 100 nM, middle). I_SK was normalized to the maximal current amplitude for the same cell under ISO conditions. The solid line indicates the I/V plot predicted by the model for the baseline (black) and ISO (red) conditions. I_SK recordings from wild-type rSK2 control show a biphasic relation dependent on V_m reaching a peak at 25–30 mV because of the SK channel’s rectification characteristics. ISO stimulation alleviated the inhibition of I_SK at higher voltages, showing a continuous increase of I_SK with V_m. Note different levels of IntR for the wild-type ISO plot. n = 4–7; N = 4–5; mean ± SE. rSK2 wild-type plots were replotted from raw data published in Hamilton et al. (38). (B) Normalized I_SK/voltage and bulk [Ca²⁺]_int/voltage (right) for VCMs expressing mutant rSK2 (R396E-K397E), which has no IntR (Li and Aldrich (30)). The solid lines indicate predicted the I/V plot for the baseline and ISO conditions as in (A). n = 11; N = 5; mean ± SE.

I_SK rectification influences an I_SK trajectory during a cardiac ventricular AP in native cardiomyocytes under ISO stimulation with Ca²⁺_SM concentration

After confirming that our parameter set for the model yielded I/V predictions that fit the data from the overexpression of rSK2, we analyzed native rat VCM AP clamp. The I_SK in healthy rat VCMs is barely detectable (38), so we recorded in the presence of ISO for all experiments. Accordingly, for the stimulus AP waveform, we used a typical rat VCM AP recording under ISO conditions, which is characteristically longer than a rat VCM AP under basal conditions (38). Total current was recorded before and after apamin, and the traces were subtracted to generate a difference current (Fig. 3 A). To avoid a potential error from beat-to-beat variation of Ca²⁺ transients, only the pair of traces (before and after apamin) with similar evoked Ca²⁺ transients were subtracted (Fig. 3 A, bottom left). The time to peak for I_SK (Fig. 3 B) is faster than for the overexpression system, most likely because of the tighter link between SK channels and LTCCs with normal SK channel expression, as reported previously (38,39). The faster rise of [Ca²⁺]_SM is expected to activate SK channels more rapidly and also reach levels sufficiently high to subsequently block them. We estimated [Ca²⁺]_SM changes based on the diffusion rate of [Ca²⁺]_i as described in the Materials and Methods and used for further analysis of I_SK. Fig. 3 C shows that the mean [Ca²⁺]_SM at peak I_SK and peak [Ca²⁺] is well above the Ca²⁺ IC₅₀ for SK channels (32,56), associated with a rapid decrease of I_SK during phase 1 of the AP. The peak I_SK during AP clamp is in the range of values obtained in rat VCMs with square voltage pulse stimulation (Fig. 3 D; (38)). The calculation of the SK channel charge transferred during the AP reveals that there is a significant amount of I_SK during late phases of the AP compared with the early phase of I_SK despite significantly lower [Ca²⁺]_i during the late phase of the AP (Fig. 3 E).

Figure 3.

A significant portion of I_SK occurs during later stages of AP. (A) Sample AP clamp traces showing voltage stimulus (left), total current before and after apamin with difference current (black minus red trace, blue), Ca²⁺ transient before and after apamin (bottom left), and normalized I_SK and normalized Ca²⁺ transient (F/F₀) showing the correlation of I_SK with Ca²⁺ transient (bottom right). The Ca²⁺ transients were compared before and after apamin to find recordings with similar evoked Ca²⁺ transients to properly isolate the apamin-sensitive current. The corresponding current traces were used to find the difference current. All recordings were obtained in the presence of 100 nM ISO. (B) Time to peak plot for peak I_SK and peak submembrane Ca²⁺ concentration ([Ca²⁺]_SM) during AP clamp. (C) [Ca²⁺]_SM at peak I_SK and peak Ca²⁺ transient. (D) Mean peak I_SK amplitude during AP clamp. (E) Plot of the stimulus voltage showing the division of the AP stimulus into two regions corresponding to early and late stages (left). Plot of percentage of total SK channel charge in the early and late phases of the AP stimulus (right). n = 6; N = 6; mean ± SE for all plots.

The I_SK trajectory during AP clamp typically has an initial peak followed by a decay profile that varies from cell to cell (Fig. 4 A). We used the same AP clamp stimulus for different cells that showed different Ca²⁺ cycling kinetics and found that the I_SK trajectory of decay can be categorized into two prominent groups: a slow decrease of I_SK during AP plateau (Fig. 4 A, middle) or a rapid decrease followed by a sustained level of I_SK (Fig. 4 A, right). A phase-plane plot of mean SK channel conductance (G_SK) versus [Ca²⁺]_SM shows the highest conductance at the first peak during the initial phase of Ca²⁺ upstroke, but there is a secondary rise of SK channel conductance during the later plateau phase as [Ca²⁺]_SM drops to sub-micromolar concentrations (Fig. 4 B). We incorporated the [Ca²⁺]_SM-values into our model to test the effect of various degrees of intrinsic and Ca²⁺/Mg²⁺-dependent rectification on the I_SK profile during the same AP stimulus used in the experiments. The right panel of Fig. 4 C shows a comparison of I_SK for four different degrees of rectification: 1) no rectification, 2) reduced intrinsic rectification only, 3) normal Ca²⁺/Mg²⁺-dependent rectification only, and 4) both reduced intrinsic and Ca²⁺/Mg²⁺-dependent rectification. The simulation demonstrates an I_SK profile similar to the data, with an initial peak rapidly inhibited by Ca²⁺ and then a relief from Ca²⁺-dependent blocking (arrows, Fig. 4 C, right). Ca²⁺/Mg²⁺-dependent rectification has a more profound effect on the shape of I_SK than intrinsic rectification, which mostly just modifies the amplitude of the first peak (Fig. 4 C, right). The plot of simulated SK channel open probability versus [Ca²⁺]_SM shows a shape like the data (Fig. 4 D, right). Ca²⁺/Mg²⁺-dependent rectification dominates the reduction of I_SK as seen in the plot of SK channel open probability through time during the AP (Fig. 4 D, left).

Figure 4.

Ca²⁺/Mg²⁺ inhibition of SK channels has a dominant effect on SK current profile during AP stimulation. (A) Sample traces from two rat VCMs during AP clamp treated with 100 nM ISO. Given are the AP stimulus waveform (left) and apamin-sensitive SK current density (blue) superimposed on [Ca²⁺]_SM transient (orange) (middle and right). (B) Phase-plane plot of mean SK channel conductance (G_SK) versus mean [Ca²⁺]_SM for AP clamp data. The arrows indicate the direction of time through AP. The blue line indicates the phase rising to peak conductance. The SK channel conductance initially increases ((1)) during the AP upstroke and then decreases ((2)) despite high [Ca²⁺]_SM during AP plateau phase, followed by increase again during the early repolarization phase. n = 6; N = 6 mean ± SE. (C) Model simulation of the SK current using the same voltage stimulus as in (A) and [Ca²⁺]_SM from (A) (left trace, orange). The right plot shows SK current density with no IntR or CaMgR (black), with reduced IntR only (ISO condition, magenta), normal CaMgR only (red), and reduced IntR and normal CaMgR (ISO condition, blue). The arrows indicate Ca²⁺-dependent block and unblock. (D) Simulation plots of SK channel open probability (P_O) versus time (left) or [Ca²⁺]_SM (right) comparing different degrees of rectification, suggesting that SK channel block by high [Ca²⁺] underlies the decrease in conductance during AP plateau followed once again by an increase of SK channel conductance near the repolarization phase of APs. The arrows indicate the direction of time during AP stimulus as in (B).

Intrinsic and Ca²⁺/Mg²⁺-dependent rectification of SK channels modulate I_SK trajectory during AP

To determine how fully rectified I_SK influences APD, we used the Pandit model of rat ventricular APs (50). The effect of rectification on APD is evident in comparing no rectification (black line) with the combined intrinsic and Ca²⁺/Mg²⁺-dependent rectification (blue line) stressing the important role of rectification in shaping the AP (Fig. 5 A). Under the combined influence of intrinsic and Ca²⁺/Mg²⁺-dependent rectification, the modeled [Ca²⁺]_SM has a lower amplitude and is wider than with no rectification (Fig. 5 B, blue line). Full rectification of SK channels caused an ∼7-fold reduction in I_SK (Fig. 5 C, blue line), explaining why I_SK is difficult to detect under baseline conditions. Using the rat ventricular AP model, the SK channel open probability dependence on Ca²⁺ was closest to the data simulation profile in Fig. 4 D when both intrinsic and Ca²⁺/Mg²⁺-dependent rectification were incorporated into the model (Fig. 5 D).

Figure 5.

IntR and CaMgR have a significant effect on APD in a model of rat ventricular APs. (A) Simulated baseline AP waveforms using a modified rat ventricular AP model by Pandit et al. (50). The traces compare the AP duration for conditions of no IntR or CaMgR (black) to combined IntR and CaMgR (blue), along with the effect of each individual source of rectification independently, CaMgR (red) or IntR (magenta). (B) Simulated [Ca²⁺]_SM in the rat ventricular AP model (50). (C) Simulated SK currents under conditions in (B). (D) SK channel open probability versus [Ca²⁺]_SM with different combinations of IntR and CaMgR. (E) Simulated AP waveforms a modified rat ventricular AP model by Pandit et al. (50) for baseline as in (A) and ISO conditions in the presence or absence of I_SK. (F) Simulated [Ca²⁺]_SM in the rat ventricular AP model (50) for baseline and ISO conditions with and without I_SK. (G) Simulated I_SK under baseline or ISO conditions. (H) SK channel open probability versus [Ca²⁺]_SM for baseline and ISO conditions.

We previously reported that apamin, a selective SK channel blocker, significantly prolonged APD under β-adrenergic stimulation using ISO in rat hearts (38). We hypothesized that ISO alleviates intrinsic rectification in addition to increasing intracellular Ca²⁺, which causes changes in I_SK to have a greater impact on APDs under β-adrenergic stimulation. The ISO effect on intracellular Ca²⁺ was modeled by increasing LTCC conductance by 61% (G_Ca from 0.031 to 0.05), RyR2 sensitivity for luminal Ca²⁺ by 50% (k_a,plus and k_b,plus to 1.5 times), Ca²⁺ sensitivity of SERCA by 25% (reducing K_m-value from 0.000168 to 0.000126), and steady-state K⁺ current by 40% (G_ss from 0.007 to 0.0098) in the Pandit rat AP model (50). This modification of parameters resulted in APD prolongation comparable with our previous experimental results from rat hearts (38). Fig. 5, E and F shows AP prolongation and increase of Ca²⁺_SM under ISO conditions. Under baseline condition, APD was slightly prolonged by apamin (blocking SK channels by setting p_SK = 0), whereas APD prolongation by apamin is significantly larger under ISO conditions, in line with our previous experimental data (38). Fig. 5, E and G shows that an increase of I_SK during AP peak and plateau through alleviated rectification under ISO conditions, resulting in greater APD shortening. Note that the SK channel P_O dependence on Ca²⁺ under ISO conditions (Fig. 5 H) is similar to the baseline condition with Ca²⁺/Mg²⁺-dependent rectification only (Fig. 5 D, red line).

We next investigated the contribution of each type of rectification on APD over a range of total SK channel permeability (p_SK). Fig. 6 A shows APD at 10% of peak amplitude (APD₉₀) plotted for different p_SK. Under conditions of low or zero p_sk (gray rectangle), the APD₉₀ is prolonged, leading to early afterdepolarizations (EADs) and repolarization failure (see arrow and inset trace, Fig. 6 A). With no rectification, APD₉₀ shortens rapidly because of a full contribution of I_SK. Introducing intrinsic rectification alone prevented APD shortening over a medium range of p_SK, followed by steeper APD shortening above ∼6 × 10⁻¹⁵ s⁻¹ (magenta line, Fig. 6 A). Ca²⁺/Mg²⁺-dependent rectification alone reduced APD shortening by I_SK over a wider range of p_SK, but abrupt APD shortening occurs at p_SK above ∼1.2 × 10⁻¹⁴ s⁻¹ (red line, Fig. 6 A). The incorporation of both intrinsic and Ca²⁺/Mg²⁺-dependent rectification produced a gradual APD shortening over the widest range of p_SK (blue line, Fig. 6 A). Under conditions of both types of rectification, the shape of the modeled AP is most consistent (Fig. 6 B, top left) in traces for the p_SK indicated by arrows in Fig. 6 A. Note the extremely short APD with no rectification at all (Fig. 6 B, bottom right).

Figure 6.

Both IntR and CaMgR significantly influence the efficacy of APD shortening across a wide range of total SK channel permeabilities. (A) Plot of simulated APD at 10% of peak amplitude versus total SK channel permeability (p_SK) for different conditions of IntR or CaMgR. No rectification leads to a steep APD shortening with an increase of p_SK (black). IntR only has some improvement (magenta), and CaMgR only (red) maintains a more gradual shortening of APD until a sudden drop. Both IntR and CaMgR together allow a gradual APD shortening over the full range of p_SK (blue). With little or no SK conductance (gray rectangle), the AP does not repolarize, and EAD-type events occur (arrow and inset trace). (B) Simulated AP traces for different conditions as in (A). For each condition, the three AP traces are simulated at the permeabilities indicated by the magenta arrows in (A).

Intrinsic and Ca²⁺/Mg²⁺-dependent rectification influences different phases of the AP

We further investigated the effects of intrinsic and Ca²⁺/Mg²⁺-dependent rectification of I_SK on APD in the two-dimensional (2D) parameter space of K_IntR and K_dCa for intrinsic and Ca²⁺/Mg²⁺-dependent rectification, respectively. Plotting a 2D color map of APD resulting from increasing levels of intrinsic and Ca²⁺/Mg²⁺-dependent rectification shows, overall, the shallowest gradient when both types of rectification are increasing together (Fig. 7 A). Plotting I_SK amplitude in a similar way for the first and second I_SK peaks shows intrinsic rectification has a dominant effect on the first I_SK peak because the gradient is strongest along the x axis, whereas Ca²⁺/Mg²⁺-dependent rectification has a greater influence on the second I_SK peak (Fig. 7 B). Looking at the I_SK amplitude through time for increasing intrinsic rectification (Fig. 7 C), we see the steepest current gradient at the time of the first I_SK peak (dashed rectangle), and it transitions to a shallow gradient at later stages of the AP. In contrast, increasing Ca²⁺/Mg²⁺-dependent rectification has a limited effect on I_SK amplitude at the first peak but generates a steeper current gradient for the second peak (Fig. 7 D, dashed rectangle), suggesting that Ca²⁺/Mg²⁺-dependent rectification mainly influences the impact of I_SK on the later phases of the AP.

Figure 7.

IntR and CaMgR have distinct contributions to AP shape. (A) Illustration of membrane voltage (V_m) and I_SK for reference showing the first and second peaks of I_SK. Shown is a two-dimensional (2D) color map of APD showing the effect of varying IntR (K_IntR) and CaMgR (Kd_Ca) on APD in the Pandit et al. AP model (50). IntR and CaMgR are shown increasing in the direction of the arrows along the x and y axes, respectively. (B) 2D color map of the amplitude of the first and second peaks of I_SK with increasing levels of Kd_Ca and K_IntR as in (A). The first peak of I_SK is mostly dependent on an x axis K_IntR (left). The second peak of I_SK is influenced by both K_IntR and Kd_Ca. (C) 2D color map of I_SK amplitude (right y axis) varying K_IntR (left y axis) through time during a simulated rat ventricular AP. The first I_SK peak is indicated by a dashed rectangle. Traces at the right are full I_SK traces at the indicated K_IntR-values (arrows). The first peak is indicated by a purple arrow. (D) 2D color map of I_SK amplitude (right y axis) with varying Kd_Ca (left y axis) through time during a simulated rat ventricular AP. Plateau phase and second I_SK peak are indicated by a dashed rectangle. Traces at the right are full I_SK traces at the indicated Kd_Ca-values (arrows). The second peak is indicated by the purple arrow. (E) Illustration of membrane voltage (Vm) and I_SK from the O’Hara et al. human ventricular AP model (51) incorporating I_SK with rectification. Given is a 2D color map of modeled human APD showing the effect of varying IntR (K_IntR) and CaMgR (Kd_Ca) on APD as in (A). (F) 2D color map of the amplitude of the first and second peaks of modeled human I_SK with increasing levels of Kd_Ca and K_IntR as in (B). The first peak of I_SK is mostly dependent on the x axis K_IntR (left). The second peak of I_SK is influenced by both K_IntR and Kd_Ca.

It is well recognized that the repolarization of murine cardiac AP is mainly caused by transient outward K⁺ current (I_to), whereas that of large animals, including humans, is composed of slowly activating inward rectifier K⁺ currents (I_Ks) and rapidly activating inward rectifier K⁺ currents (I_Kr). To investigate the impact of I_SK on human cardiac APs, we integrated our model of SK current into the O’Hara et al. model of human ventricular AP (51). Fig. 7 E shows an example of a simulated human AP and I_SK traces. We see an I_SK trajectory similar to that of Pandit’s rat AP model with the first and second peaks of I_SK. The impact of intrinsic rectification of I_SK on APD is much greater in the human ventricular AP (Fig. 7 E, steep APD changes in x direction compared with the rat ventricular AP in Fig. 7 A). This is mainly because the human ventricular AP has an elevated plateau V_m so the second peak of I_SK becomes larger when the intrinsic rectification is reduced (Fig. 7 F, the map of the second peak), causing an acceleration of repolarization. Ca²⁺/Mg²⁺-dependent rectification characteristics affect APD (Fig. 7 E, y direction) in similar way as seen in the rat model (Fig. 7 A).

Discussion

SK channels, because of their activation by intracellular Ca²⁺, have received recent attention as possible targets to prevent cardiac arrhythmias (17,20,57). However, the effect of SK channels on cardiac ventricular repolarization is complex potentially because of their unique inward rectification properties. In this study, we investigated how the SK channel rectification influences ventricular repolarization and APDs using an AP clamp of native VCMs under ISO conditions and computer simulation. We found that modulation of I_SK rectification kinetics determines its temporal impact on repolarization to modulate APDs over a wide range of AP phases (phase 1–3).

SK channels are expressed in various cell types and critically involved in regulation of many physiological functions through Ca²⁺-dependent repolarization and afterhyperpolarization of membrane potentials, such as vasoregulation (58) and neuronal excitability (28), and also protection from neurodegeneration (59). Although SK channel’s inward rectifying characteristics have been reported in rSK2 overexpression studies (30, 31, 32,38), rat hippocampal neurons (60), and native rat VCMs under physiological conditions (38), other studies have shown less prominent or no rectification of the SK current in cardiac myocytes (19,42,61). These studies kept intracellular [Ca²⁺] fixed at levels that would not block SK channels, so rectification would be limited to intrinsic rectification and block by Mg²⁺. The studies were also done in heart disease models in which phosphorylation of SK channels could be reducing rectification as reported previously (38). Importantly, intracellular Ca²⁺ cycling in cardiac myocytes yields a broad dynamic range of [Ca²⁺], making it especially important to allow intracellular Ca²⁺ to change over its physiological range as we have done in this study. In addition, because VCM SK channels are in close proximity to LTCCs, SK channels can experience fluctuations of Ca²⁺ ranging from sub-micromolar to 10 s of micromolar Ca²⁺ (40,41,62). This concentration of Ca²⁺ can sufficiently block the channel and limit its contribution to repolarization during the cardiac cycle (32,56). Our AP clamp simulations have shown that Ca²⁺/Mg²⁺-dependent rectification has a dominant effect on the trajectory of I_SK (Fig. 4 C). This I_SK profile is not limited to VCMs because a recent study of I_SK in human atrial myocytes under AP clamp demonstrates complex current dynamics with two peaks (63), similar to our data in rat VCMs (Fig. 4 A), further confirming biphasic regulation of SK channels by [Ca²⁺] during the Ca²⁺ transient. To determine how inward rectification of SK currents influences the human ventricular AP, we introduced our simulated SK current into the O’Hara et al. AP model (51). In the human model, the I_SK trajectory during the AP is similar to our results from rat with some key differences. The human APD is more dependent on intrinsic rectification than in the rat model, most likely because of the high plateau of the AP (Fig. 7, E and F). Also, higher levels of Ca²⁺_SM in the human model (51) cause a more rapid decay of the SK current after the initial peak.

In rat VCMs, the peak of I_SK precedes the peak of Ca²⁺ transients during voltage clamp steps, suggesting that I_SK does not merely follow Ca²⁺ levels but is inhibited while Ca²⁺ continues to rise, and its current versus voltage relationship shows diminished amplitude at a high V_m indicative of inward rectification (38). PKA activation by the β-adrenergic agonist, ISO, reduces rectification, causing an increase in channel conductance at high V_m (Fig. 2) (38). Importantly, the phosphorylation of SK channels in VCMs can reduce rectification in pathological conditions such as hypertrophy, increasing I_SK contribution to APD. Our modeling results show that the two independent rectification mechanisms contribute to the I_SK trajectory differently. Intrinsic rectification has a dominant influence on the first I_SK peak amplitude during early repolarization of the AP (phase 1) as well as I_SK during the plateau phase (phase 2) (Fig. 7, B and C). This is mainly because the intrinsic rectification is predominantly voltage dependent, so it would dominate at positive voltages. Because Ca²⁺/Mg²⁺-dependent rectification is dependent on voltage and Ca²⁺ concentration (31,32), which is slower to rise than voltage, it limits I_SK during the plateau phase (phase 2) until Ca²⁺_SM recovers (Figs. 4, C and D and 7 D). These data strongly indicate that the modulation of SK channel rectification can significantly change its impact on cardiac repolarization and alter arrhythmogenesis, which may explain the puzzling fact that SK channels have very limited roles in shortening APD in normal condition, but their roles become significant in pathological conditions (5,16,19,20,42,43). It is possible that, in heart disease, reduced intrinsic rectification because of PKA phosphorylation of SK channels would increase the initial peak of I_SK to counterbalance the reduced repolarization reserve and prevent excessive APD prolongation. In addition, reduced Ca²⁺ transient amplitudes in heart failure would decrease Ca²⁺-dependent blocking of I_SK and decrease the possibility of LTCC reactivation in phases 2 and 3 of the AP, leading to a lower probability of EAD generation.

Despite several studies indicating a role of SK channels in cardiac arrhythmias, there is still no clear consensus on whether SK channels are anti- or proarrhythmic. In VCMs, I_SK or its effects on APs are barely detectable in several animal models and humans and only become prominent in disease or with β-adrenergic stimulation (5,19,20,25,38,42,43,64). Under pathological conditions of prolonged APD or dysregulated Ca²⁺, there are several studies supporting an antiarrhythmic role of SK channels. For instance, enhancing I_SK is protective in human and dog heart failure VCMs because apamin blocking in these cells promotes proarrhythmic behavior in VCMs (5). There is an upregulation of apamin-sensitive potassium currents in patients with heart failure (42). SK channels are also expressed in mitochondria to modulate mitochondrial V_m and ROS production and enhancing mitochondrial SK channels in a rat hypertrophic model of heart failure reduced Ca²⁺-dependent arrhythmias (8). In addition, blocking SK channels with ondansetron increased EADs and vulnerability to ventricular fibrillation in the rabbit model of pacing-induced heart failure (65). In the same model, inhibiting SK channels with apamin in ventricles was shown to generate EADs and polymorphic ventricular tachycardia because of secondary rises in Ca²⁺ (18). These results demonstrate that the presence of I_SK is protective in chronic long QT conditions as a compensatory mechanism to counterbalance prolonged QT interval or proarrhythmic Ca²⁺-dependent depolarizing currents. However, in pathological conditions with shortened APD, SK channels may exacerbate APD shortening and can be proarrhythmic. During acute induction of arrhythmias, blocking SK channels has been shown to be antiarrhythmic. Blocking SK currents with apamin or UCL-1684 reduced spontaneous sustained ventricular tachycardia in rats with acute myocardial infarction (22). Apamin reduced postshock APD shortening-induced recurrent spontaneous ventricular fibrillation in rabbits (19) and reduced pacing-induced ventricular fibrillation under ISO conditions in female rabbit ventricles (6). Finally, pacing-induced ventricular fibrillation in guinea pigs was partially alleviated by negative modulation with NS8395 or blockade with ICA (21).

Our results indicate that SK channels’ rectification properties may contribute to their multifaceted roles in arrhythmias. Fig. 6 shows that SK channels can suppress EADs and repolarization failures (Fig. 6 A, inset), suggesting that the presence of SK channels can be protective in many diseases associated with reduced repolarization reserve and prolonged APD, including long QT syndrome and heart failure in line with the studies just mentioned. The protective effect of SK channels through normalization of prolonged APD and suppression of triggered activity was demonstrated experimentally in rabbit ventricles (18). However, our results also show that increased SK channel conductance may cause excessive APD shortening, especially when both types of rectification are removed, which can increase risks for reentry formation. Enhancing I_SK in rabbit hearts with the SK enhancer CyPPA shortens ventricular APD and leads to phase 2 reentry (66), in line with the prediction from excessive APD shortening by I_SK with reduced rectification as in our simulation. In addition, transgenic mice overexpressing SK3 had an increased rate of sudden cardiac death associated with nearly a threefold greater ventricular APD₈₀ dispersion in the homozygous transgenic mice (25). Interestingly, our simulation predicts that when intrinsic rectification is absent, a sudden APD shortening may occur in a small range of SK conductances (Fig. 6, red line), which may increase risks of APD dispersion. Modulation of the inward rectification properties of SK channels is, therefore, an important factor in determining whether I_SK is anti- or proarrhythmic in normal and pathological conditions.

In addition to inward rectification of SK channels, the modulation of SK channel sensitivity to activation by Ca²⁺ is another important factor that may alter SK channel kinetics and its contribution to AP repolarization, as shown in a modeling study (67). Experimental results have shown that protein kinase CK2 interacts with SK channels and phosphorylates SK-bound calmodulin to reduce the Ca²⁺ sensitivity of SK channels (68,69). In our recordings of rat cardiomyocytes, we do not see a shift in Ca²⁺ sensitivity with the application of ISO (38); however, it is possible certain pathological conditions do result in a shift in Ca²⁺ sensitivity. Further studies are needed to delineate the effect of modulating rectification versus Ca²⁺ sensitivity in arrhythmogenesis.

This study has several limitations that should be noted. First, I_SK was estimated by measuring an apamin-sensitive current between multiple APs under ISO and I_SK here may have been underestimated because of the ISO rundown effect during the recording. Second, the [Ca²⁺]_SM was estimated based on the parameter sets from data from the rabbit VCMs (70,71) because of lack of the parameter sets from the rat VCMs. Third, our SK channel model parameters were optimized to fit the overexpressed SK2 data with assumption that the overexpressed SK2 senses cytosolic Ca²⁺ concentration, and further studies are needed to better understand a relative contribution of SK1, SK2, and SK3 in SK currents in native myocytes. Fourth, the computer model of rat AP used in this study (50) has three Ca²⁺ compartments, which is suitable for studying SK channels and AP dynamics, but this model cannot replicate spontaneous Ca²⁺ release and Ca²⁺ wave propagation, which is often observed in pathological conditions. Further studies using a more realistic stochastic Ca²⁺ release model may reveal a detailed relationship during pathophysiological conditions, such as early or delayed afterdepolarizations.

In conclusion, the evidence in this study points to the requirement for a precisely tuned level of SK channel conductance via rectification properties to prevent cardiac arrhythmias. More studies will need to be done to determine which type of rectification or sites of phosphorylation make the best targets to maintain this tuning under pathological conditions. Dynamic voltage clamp experiments will also be part of future plans to further validate the importance of SK channel rectification by showing the AP dynamics can be modulated with model-based SK currents.

Author Contributions

Experimental design and interpretation were performed by P.B., T.Y.K., D.T., and B.-R.C. AP clamp experiments and analysis were performed by P.B. and D.T. rSK2 overexpression experiments and analysis were performed by I.P., D.T., P.B., S.H., R.T., and K.R. Modeling was performed by T.Y.K. and B.-R.C. Writing and editing the manuscript were performed by P.B., B.-R.C., T.Y.K., D.T., G.K., S.H., R.T., and K.R.

Editor: Andrew Plested