Abstract
One form of the short QT syndrome (SQT3) has been linked to the D172N gain-in-function mutation to Kir2.1, which preferentially increases outward current through channels responsible for inward rectifier K+ current (IK1). This study investigated mechanisms by which the Kir2.1 D172N mutation facilitates and perpetuates ventricular arrhythmias.
The ten Tusscher et al. model for human ventricular action potentials (APs) was modified to incorporate changes to IK1 based on experimentally observed changes to Kir2.1 function: both heterozygous (WT-D172N) and homozygous (D172N) mutant scenarios were studied. Cell models were incorporated into heterogeneous one-dimensional (1D), 2D tissue, and 3D models to compute the restitution curves of AP duration (APD-R), effective refractory period (ERP-R), and conduction velocity (CV). Temporal and spatial vulnerability of ventricular tissue to re-entry was measured and dynamic behaviour of re-entrant excitation waves (lifespan and dominant frequency) in 2D and 3D models of the human ventricle was characterized. D172N ‘mutant’ IK1 led to abbreviated APD and ERP, as well as steeper APD-R and ERP-R curves. It reduced tissue excitability at low excitation rates but increased it at high rates. It increased tissue temporal vulnerability for initiating re-entry, but reduced the minimal substrate size necessary to sustain re-entry. SQT3 ‘mutant’ IK1 also stabilized and accelerated re-entrant excitation waves, leading to sustained rapid re-entry.
Increased IK1 due to the Kir2.1 D172N mutation increases arrhythmia risk due to increased tissue vulnerability, shortened ERP, and altered excitability, which in combination facilitate initiation and maintenance of re-entrant circuits.
1. Introduction
A number of potassium channel currents contribute to ventricular action potential (AP) repolarization, including transient outward current (ITO), rapid and slow delayed rectifier K+ currents (IKr and IKs), and inward rectifier K+ current (IK1).1 Comparatively little IK1 flows at depolarized voltages during the ventricular AP plateau, but as IKr declines during late repolarization IK1 increases, making it important for terminal AP repolarization.1–3KCNJ2-encoded Kir2.1 protein is expressed in both atria and ventricles of the human heart and is implicated in the channels that underlie IK1.4,5 Changes in IK1 can be arrhythmogenic.5 For example, up-regulation of IK1 in Kir2.1-overexpressing mice increases ventricular arrhythmia risk by producing a substrate that facilitates high-frequency rotor development and stability.6 On the other hand, loss-of-function Kir2.1 mutations have been implicated in Andersen–Tawil syndrome, the cardiac manifestations of which include delayed ventricular repolarization and ventricular arrhythmia.7,8
The short QT syndrome (SQTS) is associated with accelerated ventricular repolarization and with an increased incidence of cardiac arrhythmias and of sudden death.9 A recent review of 61 identified SQTS cases10 reported a mean rate-corrected QT (QTc) interval of ∼307 ms, while 99% of the normal population have QTc intervals >360–370 ms. K+ channel mutations have been identified in some SQTS families10 and, while rare, the SQTS has been suggested to offer a useful paradigm for elucidating the role of K+ channels in ventricular fibrillation (VF).11 A gain-of-function KCNJ2 mutation has been identified in one form (SQT3) of the syndrome,12 with a juvenile proband and her father exhibiting QTc intervals of 315 and 320 ms, respectively, and an abnormal (narrow, peaked) T-wave morphology.12 Programmed electrical stimulation was able to elicit VF.12 Genetic analysis identified a single-base substitution in KCNJ2, giving rise to an aspartate to asparagine substitution at position 172 (D172N) of the Kir2.1 protein. Whole-cell patch-clamp recordings of Kir2.1 current at ambient and physiological temperatures have shown preferential augmentation of outward but not inward current through D172N-Kir2.1 channels.12,13 Ventricular AP clamp experiments have demonstrated a marked increase in outward Kir2.1 during terminal repolarization,13 while simulations based on the Priebe–Beuckelmann model14 predict AP abbreviation and changes to T-wave morphology consistent with those seen clinically.12 However, while the observed changes to Kir2.1 current in SQT3 have been suggested to increase the likelihood of re-entrant arrhythmia,12 this remains to be demonstrated directly. At present, there is no phenotypically accurate experimental model of SQT3; consequently, this study was undertaken in order to investigate the arrhythmogenic substrate in SQT3 by using ventricular cell and tissue models that incorporate ventricular transmural cell and structural [two-dimensional (2D) and 3D] heterogeneity.
2. Methods
2.1 Recombinant Kir2.1 channel electrophysiology and IK1 simulation
IK1 formulations were modified based on the experimentally determined properties of D172N-Kir2.1 channels expressed alone or co-expressed with WT Kir2.1 in order to reflect homozygous and heterozygous conditions, respectively. WT and D172N-Kir2.1 constructs (kindly provided by Matsuda et al.15) were expressed in Chinese Hamster Ovary cells and recordings made at 37°C as described previously.13 Experimentally derived current–voltage (I–V) data based on absolute current magnitudes (Figure 1Ai) for WT, WT-D172N, and D172N IKir2.113 were used to modify IK1 formulations from the ten Tusscher and Panfilov (TNNP)16 ventricular cell model. This was achieved by simulating the experimental voltage-clamp protocol13 and simultaneously minimizing the error between the simulated and experimental data using the Broyden–Fletcher–Goldfarb–Shanno optimization algorithm. Relative current proportions for WT, heterozygous, and homozygous conditions were then scaled using relative proportions of peak IKir2.1 obtained previously from AP clamp experiments13 (Vhold of −80 mV and Erev of approximately −88 to −89 mV) (Figure 1Aii). Peak outward D172N and WT-D172N IK1 was, respectively, ∼4.6- and ∼2.2-fold that for WT IKir2.1 (Figure 1B). The simulated AP clamp data in Figure 1B match closely prior experimental observations.13 Equations and parameters of IK1 for WT, WT-D172N, and D172N conditions are detailed in the accompanying Supplementary material online.
(Ai and Aii) Model fit to normalized experimental I–V relations (Ai) for WT, WT-D172N, and D172N conditions and model-derived IK1 current densities (Aii) based on the original TNNP IK1 channel current density. (Bi, Bii, and Biii) Profile of IK1 for WT (Bi), WT-D172N (Bii), and D172N (Biii) during an epicardial ventricular AP command. (Ci, Cii, and Ciii) Epicardial simulation of APs (Ci), time course and amplitude of IK1 (Cii), and instantaneous I–V relations (Ciii) under WT, WT-D172N, and D172N conditions. (Di, Dii, and Diii) Mid-myocardial simulation of APs (Di), time course and amplitude of IK1 (Dii), and instantaneous I–V relations (Diii) under WT, WT-D172N, and D172N conditions. (Ei, Eii, and Eiii) Endocardial simulation of APs (Ei), time course and amplitude of IK1 (Eii), and instantaneous I–V relations (Eiii) under WT, WT-D172N, and D172N conditions.
2.2 Cellular and tissue models
The IK1 model formulations were then incorporated into the ten Tusscher and Panfilov1,6 model for human ventricular cell APs. The cellular model was then incorporated into 1D, 2D, and 3D anatomical models of human ventricle based on the mono-domain equation.17,18 In the tissue models, the ventricular wall was composed of three regions containing: EPI, MIDDLE, and ENDO cells (with respective proportions of 25%:35%:40%). These proportions are similar to those used in other studies18–21 and reproduced a positive T-wave on the electrocardiogram (ECG) in the WT condition. Although some studies report no transmural difference in APD across the human ventricular wall,22 others have reported the presence of MIDDLE cells23–25 in the deep subendocardium of the human heart.26 Our models also implemented a five-fold decrease in gap junctional conductance between the MIDDLE and EPI region. This followed the approach of Gima and Rudy19 (and our previous studies on SQT118 and SQT227), which was based on experimental data of Yan et al.,28 indicating a sharp transition of tissue resistance in a left ventricular wedge model.
Details are provided in Supplementary material online regarding multiscale model development, as well as methods for simulating pseudo-ECG, protocols used for measuring restitution of AP duration (APD-R), effective refractory period (ERP-R), conduction velocity (CV-R), tissue excitability, initiation of re-entrant excitation waves, measuring tissue temporal vulnerability, and minimal substrate size for sustaining re-entry. Dynamics of re-entry and numerical methods have been documented in detail in our previous studies.18,27,29
3. Results
Changes in IK1 due to the Kir2.1 D172N mutation abbreviated human ventricular APD are shown in Figure 1C–E. The measured APD90 was 311, 430, and 312 ms for the EPI, MIDDLE, and ENDO cells, respectively, under the WT condition, which were shortened, respectively, to 283, 382, and 283 ms for the WT-D172N condition and to 264, 353, and 265 ms for the D172N condition. The abbreviated APD resulted from increased IK1 during the AP repolarization phase as shown by the time course of IK1 and the I–V phase plot during AP repolarization in Figure 1Ciii–Eiii. The observed resting potential values were −86.2, −86.4, and −86.5 mV for the WT, WT-D172N, and D172N conditions, respectively.
The APD reduction was rate-dependent (Figure 2A–C) for EPI, MIDDLE, and ENDO cells, respectively. Across the range of diastolic intervals studied, the measured APD90 was smaller in the WT-D172N and the D172N conditions than in the WT condition. In addition, the APD-R relationships were steepened by the mutation, as indicated by the observed increase in the maximal slope of the APD-R curves (Figure 2D). In the EPI and ENDO cells, the computed maximal slope of the APD-R curves was significantly increased in the WT-D172N and the D172N conditions. However, in the MIDDLE cell, the measured maximal slope of the APD-R curves was reduced slightly by the WT-D172N mutation, but significantly increased by the D172N mutation.
(A–C) APD restitution curves for EPI (A), MIDDLE (B), and ENDO (C) cells, respectively, for the WT, WT-D172N, and D172N conditions. (D) Measured slopes of APD-R curves for EPI, MIDDLE, and ENDO cells in WT, WT-D172N, and D172N conditions. (E–G) ERP-R curves for EPI (E), MIDDLE (F), and ENDO (G) cells, respectively, for the WT, WT-D172N, and D172N conditions. (H) Measured slopes of ERP-R curves for EPI, MIDDLE, and ENDO cells for WT, WT-D172N, and D172N conditions.
The measured ERP was also reduced in the WT-D172N and the D172N mutation conditions compared with WT. The ERP reduction was also rate-dependent as shown in Figure 2E–G. Across a range of basic stimulus cycle lengths (BCL; see Supplementary material online, Methods), the measured ERP in the WT-D172N and the D172N conditions was smaller than that in the WT condition. The D172N mutation also steepened the ERP-R curves as indicated by the increased maximal slope of the ERP-R curve (Figure 2H) in the mutation conditions. As an increased steepness of APD-R and ERP-R curves is believed to be associated with increased instability of re-entrant excitation waves,30 predisposing to breakup of re-entrant excitation waves and leading to formation of multiple re-entrant excitation wavelets,30–32 these simulation results indicated proarrhythmic effects of the Kir2.1 D172N mutation. The mutation also shifted the ERP-R curves of the WT-D172N and D172N conditions leftwards, indicating that the Kir2.1 mutation enabled ventricular cells to support higher rate electrical activity [as normally seen during ventricular tachycardia (VT) and VF conditions].
Using a 1D-strand model, a pseudo-ECG was computed for the WT, WT-D172N, and D172N mutation conditions (Figure 3). The results are shown in Figure 3A–C for an excitation wave propagating from ENDO towards MIDDLE and EPI parts of the strand. In each panel, space runs vertically from ENDO at the bottom to EPI at the top while time runs horizontally from left to right. From this propagating excitation wave, ECG traces were simulated for WT (Figure 3D), WT-D172N (Figure 3E), and D172N (Figure 3F) conditions and the QT intervals were calculated (Figure 3G). In these simulations, the QT interval was shortened progressively from 363 (WT) to 319 (WT-D172N) and 295 ms (D172N) and T-wave amplitude increased. T-wave width (measured as the time interval between Tpeak and Tend) also changed from 51 (WT) to 39 (WT-D172N) and 33 ms (D172N). Since the only difference between these simulation conditions was the change of IK1 channel kinetics, the observed changes in respect of the QT interval shortening and T-wave height and width can be attributed with confidence to the effect on the simulations of the parameters corresponding to the D172N mutation.
(A–C) Colour mapping of membrane potential of cells along the 1D strand from blue (−86 mV) to red (+42 mV) (see colour key, in mV). Space runs vertically from the ENDO end to the EPI end at the top. Time runs horizontally. (A) WT condition. (B) WT-D172N condition. (C) D172N condition. (D–F) Pseudo-ECGs corresponding to the WT, WT-D172N, and D172N conditions, respectively. (G) Superimposed pseudo-ECGs for the WT, WT-D172N, and D172N conditions, respectively, and their associated QT intervals. (H) CV-R under WT (blue), WT-D172N (green), and D172N (red) conditions.
Figure 3H plots the rate dependence of ventricular CV. It shows that the mutation decreased ventricular conduction at low rates (BCL > 560 ms; rate < 107 b.p.m.), but facilitated conduction at high rates. At a rate of 60 b.p.m. (Pacing Cycle Length [PCL] = 1000 ms), the measured CV was 66 cm/s for the WT, 64 cm/s for the WT-D172N and 62 cm/s for the D172N condition. The decreased CV was due to reduced tissue excitability as shown in Supplementary material online, Figure S1, as no change in the intercellular electrical coupling was considered. However, at a rate between 158 and 196 b.p.m. (i.e. 305 ms < PCL < 380 ms), the measured CV was much higher in the WT-D172N or D172N conditions than in the WT condition. This is likely due to a shorter ERP in the two mutant simulation conditions compared with the WT condition. When the stimulus rate was above 167 b.p.m. (BCL < 360 ms), conduction failed in the WT condition, but was sustained in the WT-D172N and D172N conditions. The highest rate for ventricular tissue to support conduction was 183 b.p.m. (BCL = 327 ms) under the WT-D172N condition and 201 b.p.m. (BCL = 298 ms) for the D172N condition. Thus, the increased IK1 facilitated ventricular conduction at high rates close to those observed in clinical VT.33
We further measured transmural ventricular APD dispersion across the strand and the temporal vulnerability of tissue under the WT, WT-D172N, and D172N conditions. Figure 4 shows the measured spatial distribution of APD90 (Figure 4A), the spatial gradient of APD90 (Figure 4B), and its absolute value (Figure 4C) across the strand. Compared with the WT condition, although the APD across the strand was reduced by the WT-D172N and D172N conditions (Figure 4A), the APD gradient was markedly increased at some local regions across the transmural strand (Figure 4B and C).
(A) Spatial distribution of APD90 in the 1D transmural strand for WT (blue), WT-D172N (green), and D172N (red). (B) Actual spatial gradient of APD90 in the 1D transmural strand for WT (blue), WT-D172N (green), and D172N (red). (C) Absolute spatial gradient of APD90 in the 1D transmural strand for WT (blue), WT-D172N (green), and D172N (red). (D–F) Measured vulnerable window for WT, WT-D172N, and D172N along the 1D strand. Vertical dotted lines indicate boundary between different cell types along the strand.
The temporal vulnerability of ventricular tissue to unidirectional conduction block was measured in response to a premature stimulus applied during the refractory period of a previous excitation wave. Figure 4D–F represents the measured width of vulnerable time window across the tissue in the WT, WT-D172N, and D172N conditions, respectively. In the figure, the measured T1 [upper envelope; denoting the maximal time interval between the S1 and the S2 stimulus such that the excitation wave evoked by the S2 stimulus propagated uni-directionally in the strand (see Supplementary material online)] and T2 (lower envelope; denoting the minimal time interval between the S1 and the S2 stimulus such that the excitation wave evoked by the S2 stimulus propagated uni-directionally in the strand) are plotted against space from the ENDO (0 mm) end to the EPI (15 mm) end of the strand. As the difference between T1 and T2 (T1–T2) gives a measure of the temporal vulnerability of the tissue, it is clear that the tissue's temporal vulnerability is increased across the whole strand in the D172N mutation condition, but only at the border region between EPI and MIDDLE in the WT-D172N condition.
The spatial vulnerability of ventricular tissue was quantified by measuring the minimal spatial length of S2 that sustains re-entry for WT, WT-D172N, and D172N conditions in idealized 2D models. The measured minimal (critical) length was 49, 21, and 18 mm for the WT, WT-D172N, and D172N conditions, respectively. There was a significant reduction in the critical size necessary to support the formation and maintenance of re-entry in the WT-D172N and the D172N conditions (by 57 and 64%, respectively), reflecting the likely impact of this mutation in terms of predisposition towards ventricular arrhythmia.
Figure 5 shows that D172N-altered IK1 stabilized re-entrant spiral waves, which led to sustained multiple re-entrant wavelets in a realistic 2D ventricular tissue model. In the figure, snapshots of re-entrant excitation waves at different time points are shown for the WT (Figure 5Ai–Di), WT-D172N (Figure 5Aii–Dii), and the D172N mutation (Figure 5Aiii–Diii) conditions. Figure 5Ei–Eiii shows time traces of APs recorded from a left ventricular cell for the WT, WT-D172N, and D172N conditions. In the WT condition (Figure 5Ai–Di), the initiated spiral wave was unstable, with its tip meandering around in the transmural tissue, leading to self-termination when it meandered out of the boundary of the tissue. The measured lifespan of spiral waves was 0.7 s (Figure 5F). Power spectrum analysis of the recorded whole-field averaged electrical activity from the tissue revealed a peak frequency of 2.8 Hz. In the WT-D172N and D172N conditions (Figure 5Aii–Dii and Aiii–Diii), the tip of spiral wave also meandered, but in a smaller region when compared with the WT condition. In both cases, re-entrant activity continued throughout the 10 s simulation period (Figure 5F). Power spectrum analysis of the recorded electrical activity from the tissue revealed a peak frequency of 3.1 and 3.6 Hz for the WT-D172N and D172N conditions, respectively (Figure 5G).
(Ai, Aii, and Aiii) Application of a premature S2 stimulus into the refractory and partially recovered region of an excitation wave after a delay of 335 ms for WT, 301 ms for WT-D172N, and 285 ms for D172N condition from the initial wave stimulus. (Bi, Bii, and Biii) Developed spiral wave from the S2 stimulus. Snapshot at time = 500 ms. (Ci, Cii, and Ciii) Snapshot of spiral wave at time = 750 ms. The induced spiral wave transited from transmural re-entry with tip rotating within the ventricle wall to anatomical re-entry with tip rotating around the ventricle boundary in WT and WT-D172N conditions. However, transmural re-entry persisted in the D172N condition and broke-up forming regenerative multiple re-entrant wavelets. (Di, Dii, and Diii) Snapshot of spiral wave at time = 1000 ms. Spiral wave self-terminated in WT before this recording point, but persisted in WT-D172N and D172N conditions. (Ei, Eii, and Eiii) Recorded time series of the AP of a cell in the left ventricle for the WT, WT-D172N, and D172N conditions. (F) Measured lifespan of re-entry scroll wave in WT, WT-D172N, and D172N conditions. (G) Computed dominant frequency of electrical activity recorded from ventricle in WT, WT-D172N, and D172N conditions (2.8 Hz for WT, 3.1 Hz for WT-D172N, and 3.6 Hz for D172N condition).
Due to the complex geometry and anisotropic properties of ventricular tissue, it cannot be assumed that sustained re-entry in a 2D tissue model under the mutation conditions necessarily translates into similar activity in a 3D tissue model. Therefore, further simulations were performed using 3D anatomical human ventricle geometry. Results are shown in Figure 6, which shows snapshots of evolution of re-entrant scroll waves (WT: Figure 6Ai–Di; WT-D172N: Figure 6Aii–Dii; and D172N: Figure 6Aiii–Diii) arising from a response to a premature stimulus (see Section 2). For the WT condition, the scroll wave self-terminated with a lifespan of 0.7 s (Figure 6F). However, with the WT-D172N and D172N mutation conditions, the scroll wave broke-up forming multiple wavelets that were sustained throughout the simulation period of 10 s (Figure 6F). Power spectrum analysis on the registered pseudo-ECG shows the dominant frequency of ventricle excitation to be ∼2.3 Hz for the WT condition, ∼4.8 Hz for the WT-D172N mutation condition, and 6.0 Hz for the D172N mutation condition (Figure 6G). Figure 6Ei–Eiii shows a recording of the evolution of the AP of a cell in the left ventricle for the WT, WT-D172N, and D172N conditions. These 3D results concur with the 2D simulations, further illustrating the proarrhythmic effects of the Kir2.1 D172N mutation. Video files showing re-entry in 2D and 3D models are included in Supplementary material online.
(Ai, Aii, and Aiii) Application of a S2 premature stimulus in a local region at refractory period of a previous conditioning excitation wave after a time delay of 380 ms for WT, 350 ms for WT-D172N, and 343 ms for D172N conditions from the initial conditioning wave stimulus. (Bi, Bii, and Biii) Developed scroll wave from the S2 stimulus for the WT, WT-D172N, and D172N conditions. Snapshot at time = 500 ms. (Ci, Cii, and Ciii) Snapshot of scroll wave at time = 750 ms for the WT, WT-D172N, and D172N conditions. (Di, Dii, and Diii) Snapshot of scroll wave at time = 1000 ms. The scroll wave self-terminated in WT, but persisted and broke-up forming regenerative wavelets in WT-D172N and D172N conditions. (Ei, Eii, and Eiii) Recorded time series of the AP of a cell in the left ventricle for WT, Wt-D172N, and D172N conditions. (F) Measured lifespan of re-entry scroll wave in WT, WT-D172N, and D172N conditions. (G) Computed dominant frequency of electrical activity recorded from ventricle in WT, WT-D172N, and D172N conditions (2.3 Hz for WT, 4.8 Hz for WT-D172N, and 6.0 Hz for D172N condition).
4. Discussion
4.1 Summary of major findings
The proband in whom the D172N mutation was identified was heterozygotic for the SQT3 mutation (WT-D172N).12 She had a QTc interval of 315 ms, while her father had one of 320 ms.12 It is of particular note that with our WT-D172N expression model, mimicking the heterozygous state of the proband, we found the reconstructed QT interval shorten from 363 ms in WT condition to 319 ms in the WT-D172N condition (∼12% shortening). It shortened to 295 ms in the D172N condition (∼19% shortening). In addition, the risk of arrhythmogenesis as measured by the vulnerability of tissue and lifespan of re-entry was increased. Our results indicate that the Kir2.1 D172N mutation: (i) abbreviates the APD90 and steepens the APD-R and ERP-R curves, thus increasing susceptibility to arrhythmia; (ii) shortens the QT interval and alters T-wave morphology, which are tall, peaked, and asymmetric similar to that of the proband;12 (iii) augments the transmural dispersion of APD90 across the ventricular wall, which leads to the increase, at some localized regions of the temporal vulnerability of the tissue to the genesis of uni-directional conduction by a premature excitation; (iv) reduces the minimal substrate size of tissue required to initiate and maintain re-entry; and (v) stabilizes and accelerates re-entrant excitation waves.
The simulation data in this study constitute novel evidence that the proarrhythmic effects of augmented IK1 associated with Kir2.1 D172N mutation involve both increased tissue susceptibility to the initiation of re-entry and the stabilization and acceleration of re-entry (leading to sustained VF). In first reporting the existence of the Kir2.1 D172N mutation in a patient with the SQTS, Priori et al.12 used a Priebe–Beuckelmann14 ventricular cell AP model to demonstrate AP shortening, abbreviated QT interval, alteration to T-wave morphology, and steeper APD-R and ERP-R curves with the mutation condition. However, the present study has examined for the first time the effects of the D172N mutation at 2D tissue and 3D organ levels, showing not only QT interval shortening under WT-D172N and D172N expression conditions, but also an increased susceptibility to and stability of re-entry.
4.2 Pro-fibrillatory mechanisms of the Kir2.1 D172N mutation
The SQTS is associated with malignant tachycardias9,34–36 and some patients may have an episode of VF.37 In the SQT3 setting, VF could be elicited by programmed electrical stimulation, and though a prior history of cardiac arrhythmias had not been noted in the proband, her father had a history of palpitations and presyncopal events.12 It was hypothesized that APD and ERP abbreviation would be anticipated to provide a substrate for increased risk of re-entrant arrhythmias.12
Our simulations provide evidence for the proarrhythmic effects of the KCNJ2-D172N mutation in perpetuating and facilitating re-entrant excitation waves. They support the notion that the APD and ERP shortening as a result of the KCNJ2-D172N mutation is proarrhythmic. This is due to the fact that the shortened APD (ERP), together with a reduced cardiac excitability and therefore a reduced CV, reduces the wavelength of excitation waves [equal to the product of APD (ERP) and the CV]. This consequently reduces the critical mass of tissue necessary to accommodate re-entrant excitation waves, facilitating the initiation and maintenance of re-entry. With the WT-D172N and D172N mutation conditions, the measured minimal substrate size of tissue for maintaining re-entrant excitation wave was reduced by 57 and 64%, respectively, compared with the WT condition. Thus, re-entry in 2D and 3D models in the WT tissue self-terminated shortly after initiation. This is due to the longer ERP and thus a larger wavelength of re-entry, which could not be sustained in a limited mass of tissue. However, in the mutation conditions, re-entry was sustained in the same-sized tissue due to the shorter ERP and smaller wavelength of re-entry. Our findings also indicate that the KCNJ2-D172N mutation augments transmural heterogeneity of APD90 and ERP, due to differential APD and ERP abbreviation among EPI, MIDDLE, and ENDO cells. This led to an augmented APD/ERP dispersion in some regions of the transmural strand. This in turn is proarrhythmic as it increased the tissue's vulnerable time window in which uni-directional conduction block could occur as shown in Figure 4.
Our simulations indicate that the proarrhythmic effect of the KCNJ2-D172N mutation is also reflected by the increased stability and acceleration of re-entry in the ‘mutant’ tissue. This is compatible with observations from previous studies,5,6,38 in which increased IK1 was associated with increased stability and acceleration of ‘rotor’ activities. However, there are notable differences in the effects of altered IK1 on the dynamics of re-entry between the present study and previous studies.5,6,38 In previous studies,5,6,38 situations were considered in which both inward and outward components of IK1 were proportionally increased. In such cases, there was a steep slope of the augmented IK1I–V curve at membrane potentials close to the potassium equilibrium potential (EK), which would act to shift resting potential towards EK. In turn, this would increase recovery of sodium current (INa) during high-rate excitation and, thereby, help stabilize re-entry.38 In contrast, the KCNJ2-D172N mutation preferentially augmented the outward component of IK1, so that at membrane potentials close to EK, the effect on the slope of the augmented IK1I–V relation is reduced in comparison to situations in which proportionately similar increases in inward and outward IK1 occur, resulting in only very slight changes to resting membrane potential. In this case, the increased stability and acceleration of re-entry is not via increased recovery of INa, but is attributable to the increased tissue excitability at high excitation rates (see Supplementary material online, Figure S1) due to decreased ERP (Figure 2). Reduction in ERP also results in decreased wavelength of ventricular excitation waves, allowing higher activation frequencies of re-entrant excitation waves (Figure 6). We found that once formed, re-entrant excitation waves were more stationary and persistent under conditions with the KCNJ2-D172N mutation, with their tips meandering in smaller regions, thereby leading to sustained re-entry.
In our simulations, while, as for the 2D models, increased IK1 also helped to stabilize re-entrant excitation waves leading to persistent re-entry in the 3D model, re-entrant wave behaviour was not identical at the 2D and 3D levels. In the 3D situation—presumably due to complicated structures of ventricular tissue, such as anisotropic fibre orientation and layered structure of ventricular tissue and irregular thickness of ventricular wall—re-entrant excitation waves with augmented IK1 had a greater dominant frequency and longer lifespan when compared with those seen at the 2D tissue level. Our data highlight the potential value of using a 3D human ventricle anatomical model, with which it is possible to simulate activity in a more complex fashion than is possible with a 2D sheet. The results from our 3D model support the proarrhythmic effects of the mutation identified in the 2D simulations, providing data that complement and extend those obtained from the 2D simulations.
4.3 Relevance to previous studies
Dysfunction of IK1 channels predisposes to cardiac arrhythmias associated with Andersen's syndrome,39,40 long QT syndrome,41–43 and SQTS.41–43 Augmented IK1 has previously been implicated in VF genesis and maintenance in experimental animal models.44–46 Over-expression of Kir2.1 in the transgenic mouse heart up-regulated IK1, which helped to initiate and stabilize VF.6 Significantly, previous studies44,45 have reported a determinant role of IK1 in rotor dynamics, and blockade of it terminated VF in guinea pig hearts. Recently, there has been increasing awareness of the role of malfunctioning IK1 on contributing to cardiac arrhythmias.5 Our data indicate that in the case of the Kir2.1 D172N mutant, the resulting increase in outward IK1 not only helps to stabilize re-entry (consistent with previous studies of hearts with overexpressed Kir2.16), but also increases the susceptibility of human ventricular tissue to the ‘genesis’ of re-entry. Our study therefore adds to the growing weight of evidence implicating increased IK1 in cardiac arrhythmia initiation and perpetuation5,44–47 and, by extension, to the possibility that IK1 may offer a potential therapeutic target for cardiac arrhythmia treatment.
4.4 Potential limitations of these simulations
Limitations of the ten Tusscher et al. model have been discussed in detail elsewhere.16,18,48,49 In the multicellular tissue model—due to a lack of detailed experimental data—the proportion of each region composed of each distinct cell type and intercellular electrical coupling was chosen to produce a positive T-wave and a CV of a planar solitary excitation wave close to the experimental data, similar to those used in other studies.19–21
Care must be exercised in the interpretation of results from the 2D model, as it is based on a single slice of the ventricle wall. Although we considered anisotropic intracellular electrical coupling in the 2D and realistic anatomical structure, the 2D model nevertheless represents only a cross-sectional slice through the ventricle; it therefore lacks features of an anatomically realistic 3D ventricular geometry such as the irregular thickness of the wall structure across the entire geometry, layered structure of ventricular tissue, and more realistic anisotropy, all of which could influence maintenance of ventricular arrhythmias in the D172N mutation conditions. These potential limitations predicated our additional use of 3D simulations. Though the 3D model incorporates ‘realistic’ ventricular anatomical geometry, it lacks inclusion of a Purkinje fibre network, which may play a role in arrhythmogenesis in the SQTS.31 In addition, the tissue models in this study do not consider the effect of cardiac mechanics on tissue geometry, which feasibly might influence re-entry,50–52 particularly for SQT patients.50
Another potential limitation of the present study is lack of consideration of parameter uncertainty for a particular human heart, such as variation in model parameters, pacing frequency and inhomogeneous APD-R properties, each of which may play an important role in the genesis of VF. Also the present model implemented a mono-domain approach, rather than a bi-domain representation. However, previous studies have reported insignificant differences between the solutions from the mono-domain and bi-domain models,53–55 visually indistinguishable influence on simulated ECG55 and negligible differences with convergence analyses.56
While it is important that potential limitations of the models used in this study are made explicit, these do not influence fundamentally the conclusions that can be drawn on likely mechanisms by which the KCNJ2 D172N mutation facilitates arrhythmia induction and maintenance. Moreover, it is striking that in our simulations, despite differing levels of complexity, the 2D and 3D simulations yielded qualitatively if not quantitatively similar findings in terms of identifying mechanisms that can account for increased arrhythmia susceptibility in SQT3. This highlights the likely importance of the proarrhythmic mechanisms identified in this study. Very recently, a second SQT3 variant has been identified in which a heterozygous KCNJ2 mutant (M301K) has been associated with markedly abbreviated QTc intervals and inducibility of VF.57 The characteristics of heterologously expressed WT-M301K Kir2.1 current show markedly impaired inward rectification, increasing outward current over a wide range of voltages (a more extensive Kir2.1 current change than seen for the D172N mutation). It is possible that adoption of a similar approach to that used in the present study, incorporating into our 1D–3D tissue models suitably modified IK1 formulations, may provide insight into arrhythmogenic mechanisms of this new SQT3 variant.
5. Conclusions
The findings of this study both substantiate a causal link between the KCNJ2-D172N mutation and QT interval shortening and offer a novel explanation for increased susceptibility to re-entry and perpetuation of re-entrant arrhythmia in this form of SQTS. Our data substantiate the notion that the KCNJ2-D172N mutation leads to accelerated ventricular repolarization and QT interval shortening.12 Additionally, on the basis of our findings, we propose that the KCNJ2-D172N mutation: (i) leads to an increased transmural APD dispersion that increases tissue vulnerability to the genesis of re-entry with premature excitation; (ii) shortens ventricular tissue ERP, which facilitates the maintenance of re-entry once this has been initiated.
Supplementary material
Supplementary material is available at Cardiovascular Research online.
Conflict of interest: none declared.
Funding
This work was supported by British Heart Foundation (FS/08/021 to H.Z. and J.C.H. for I.A.). The authors also thank the British Heart Foundation for additional project grant support.
