In silico investigation of a KCNQ1 mutation associated with short QT syndrome

Short QT syndrome (SQTS) is a rare condition characterized by abnormally ‘short’ QT intervals on the ECG and increased susceptibility to cardiac arrhythmias and sudden death. This simulation study investigated arrhythmia dynamics in multi-scale human ventricle models associated with the SQT2-related V307L KCNQ1 ‘gain-of-function’ mutation, which increases slow-delayed rectifier potassium current (IKs). A Markov chain (MC) model recapitulating wild type (WT) and V307L mutant IKs kinetics was incorporated into a model of the human ventricular action potential (AP) for investigation of QT interval changes and arrhythmia substrates. In addition, the degree of simulated IKs inhibition necessary to normalize the QT interval and terminate re-entry in SQT2 conditions was quantified. The developed MC model accurately reproduced AP shortening and reduced effective refractory period associated with altered IKs kinetics in homozygous (V307L) and heterozygous (WT-V307L) mutation conditions, which increased the lifespan and dominant frequency of re-entry in 3D human ventricle models. IKs reductions of 58% and 65% were sufficient to terminate re-entry in WT-V307L and V307L conditions, respectively. This study further substantiates a causal link between the V307L KCNQ1 mutation and pro-arrhythmia in human ventricles, and establishes partial inhibition of IKs as a potential anti-arrhythmic strategy in SQT2.

consequences of realistic ventricular anatomical geometry in two and three dimensions, which play important roles in initiation and maintenance of arrhythmic excitation waves 18,19 .
One aim of this study was to address the above limitations of the previous study using a HH model of SQT2 16 . We conducted the present study in order to: (i) develop a novel biophysically-accurate and validated Markov chain (MC) model to recapitulate the kinetic changes to I Ks in the SQT2 V307L KCNQ1 mutation based on available experimental data at physiological temperature; (ii) determine the functional consequences of the SQT2 V307L mutation on AP repolarisation and the QT interval by incorporating it into a well-established human ventricular cell model 20 ; (iii) explore the arrhythmogenic substrate in the SQT2 V307L mutation by using "realistic" 2D tissue and 3D organ-scale simulations; and, moreover; (iv) investigate theoretically the degree of I Ks inhibition required to normalise the QT interval as a pseudo-pharmacological therapeutic intervention.
The multi-scale cardiac modelling approach taken in this study has been employed successfully in our previous studies to dissect ionic mechanisms underlying QT interval shortening and pro-arrhythmia in variants 1 and 3 of the SQTS 18,19 . The developed MC model represents a significant advance over previous studies 10, 16 in SQT2 modelling and the reported results further understanding of the mechanisms by which the SQT2 V307L mutation enhances susceptibility to reentrant arrhythmia. Furthermore, a theoretical basis for pharmacological intervention in SQT2 is proposed.

Results
Simulation of single cell I Ks under control and V307L mutation conditions. First, we tested the ability of the I Ks MC model to reproduce the previously published experimental data 17 on the voltage dependence of wild type (WT) and V307L KCNQ1+KCNE1 I Ks at physiological temperature. Figures 1Aii and 1Bii show the voltage clamp protocol used which is the same as that used for the experimental data 17 and the generated I Ks current traces ( Fig. 1Ai and Bi) from which the I-V relationships were reconstructed ( Fig. 1Aiii and Biii). The simulated I-V relationships for both the WT and KCNQ1 V307L conditions match those recorded experimentally 17 . The simulated current traces match experimental recordings; under the V307L mutation condition, the slower deactivation rate and faster activation rate of the I Ks channel 17 compared to the WT condition were reproduced ( Fig. 1Ai and Bi).
To validate the MC model formulations, we next simulated AP voltage clamps to test their ability to reproduce the dynamic properties of WT and V307L KCNQ1 mutant I Ks channels. Figure 1Aiv and Biv show the results of the simulated AP clamp experiments compared to those obtained in vitro 17 . The MC model reproduced the profile of I Ks during imposed AP commands with a high degree of accuracy, both in the WT condition and with augmented I Ks in simulations incorporating the KCNQ1 V307L mutation.
Following incorporation of the WT and V307L MC models into the 2006 model of ten Tusscher et al. (TNNP) 20 , Fig. 2 shows simulated APs (Ai), I Ks profile (Aii) and I Ks instantaneous I-V relationship for an epicardial (EPI) cell (Aiii). The mid-myocardial (MIDDLE) and endocardial (ENDO) counterparts are shown in Fig. 2B and C, respectively. WT I Ks increased progressively following the upstroke of the AP and reached maximal amplitude very late during the plateau phase before declining rapidly during terminal repolarisation. WT-V307L I Ks activated earlier than WT and increased in amplitude more rapidly. Compared to WT current, it reached significantly higher maximal amplitude early during the plateau leading to abbreviation of the AP duration (APD). V307L I Ks activated even earlier than WT-V307L I Ks , increased even more rapidly, and attained higher maximal amplitude. Consequently, it abbreviated the APD to a greater extent. Under the WT condition, the computed APD 90 was 326 ms, 454 ms and 327 ms for EPI, MIDDLE and ENDO cells respectively. These were shortened respectively to 233 ms, 355 ms and 234 ms under the WT-V307L condition, and to 194 ms, 306 ms and 194 ms under the V307L mutation condition. The APD 90 values for all the conditions are summarised in Table 1. The APD shortening resulted from the augmented I Ks early during the plateau phase of the AP as shown by the time course of I Ks (Fig. 2Aii-Cii) and the I-V phase plots in Fig. 2Aiii-Ciii. The greatest APD shortening was observed for the MIDDLE cell model ( Table 1).
The APD abbreviation was rate-dependent as shown by the APD restitution (APD-R) curves in Fig. 3A-C for the EPI, MIDDLE and ENDO cell types, respectively. Over the range of diastolic intervals (DI) studied, the APD was smaller in the WT-V307L and V307L mutant conditions than in the WT condition. The mutations also steepened the APD-R curves in each cell type as shown by the computed maximal slopes for each APD-R curve in Fig. 3D. In the EPI cell, the maximal slopes of the WT-V307L and V307L conditions were similar, while there was a progressive increase in steepness of the slopes in the MIDDLE cell type. In the ENDO cell, while the slopes under the WT-V307L and V307L conditions were steeper than WT, the slope of the WT-V307L condition was steeper than that of the V307L mutant.
The ERP reduction was also rate-dependent. It was reduced under the WT-V307L and V307L mutation conditions compared to the WT condition across the range of basic stimulus cycle lengths (BCL) as shown in ERP-R curves in Fig. 3E-G for the EPI, MIDDLE and ENDO cell types, respectively. In the EPI and ENDO cells, there was little difference in the slopes of the ERP-R curves between the WT, WT-V307L and V307L conditions (Fig. 3H). The slope was steeper for the mutation conditions in the MIDDLE cell compared to WT but the slope for the WT-V307L condition was slightly steeper than that for the V307L mutant alone. The mutations also shifted the ERP-R curve leftwards implying that the KCNQ1 V307L mutation enabled ventricular cells to support higher rate electrical activity (as normally seen during VT and VF conditions).

Simulation of the ECG with WT and SQT2 mutant I Ks .
Using a 1D strand model of the ventricular wall, we computed a pseudo-ECG under the WT, WT-V307L and V307L KCNQ1 conditions (Fig. 4D-F). These were extracted from a propagating wave from the ENDO end of the strand towards the EPI end ( Fig. 4A-C). Time runs horizontally from left to right in Fig. 4A-C while space runs vertically from the ENDO end at the bottom to the EPI end at the top. The QT interval was shortened from 351 ms in the WT condition to 292 ms in the WT-V307L condition and to 262 ms in the V307L condition (Fig. 4G). T wave width (measured as the time interval between T peak and T end ) also changed from 49 ms (WT) to 60 ms (WT-V307L) and 64 ms (V307L). These simulations thus reproduce the key features observed in the ECGs of SQTS patients; abbreviated QT interval, tall and peaked T-waves and wider T peak to T end 2, [4][5][6][7] . As the only difference between these simulations is the altered kinetics of I Ks resulting from the mutation, the observed changes in the QT interval, T wave height and width can be confidently attributed to the parameters corresponding to the V307L mutation.
Gima and Rudy 21 showed that increased spatial gradient of membrane potential was responsible for the increase in T-wave amplitude during simulated hyperkalaemia. In order to determine if the same effect was responsible for the taller T wave amplitudes in the WT-V307L and V307L ECGs (Fig. 4D-G), we examined the effects of this KCNQ1 mutation on membrane potential heterogeneity (δV) in supplementary simulations. Supplementary Figure S2 shows the pairwise differences between EPI, MIDDLE and ENDO cells during an AP. Under the KCNQ1 WT-V307L and V307L mutation conditions, the maximal δV between EPI-MIDDLE and ENDO-MIDDLE cells were greater than under the WT condition, which contributed to the augmented T-wave and V307L (Biii) conditions. I Ks profile during AP clamp using a ventricular AP waveform voltage command in WT (Aiv) and V307L (Biv) conditions. All experimental data, including insets shown in panels Ai and Bi, are taken from El Harchi et al. 17 . amplitude 16,18,21 . Also shown is the spatial distribution of APD 90 , the spatial gradient of APD 90 , and the absolute value of the spatial gradient of APD 90 . The spatial gradient of APD 90 was augmented across the strand but markedly so in the ENDO region.
Investigating the arrhythmogenic substrate in SQT2 -1D simulations. In further supplementary simulations using the 1D strand, we investigated the vulnerability of WT, WT-V307L and V307L tissue to unidirectional block in response to a premature stimulus applied during the refractory tail of a previous excitation wave. During such conduction block tissue is rendered more susceptible to re-entrant arrhythmia. Supplementary Figure S3 shows the percentage increase compared to the WT condition in the temporal vulnerable window to conduction block, measured at a location 5.0 mm away from the epicardial end of the 1D strand. The width of the vulnerable window was increased by 37% and 82% with respect to the WT in WT-V307L and V307L conditions, respectively.
Investigating the arrhythmogenic substrate in SQT2 -2D and 3D simulations with realistic geometry. In a realistic human ventricle cross-sectional slice (    Table 1. Action potential duration in WT, WT-V307L and V307L conditions. Action potential duration (APD) was measured in all transmural cell types; epicardial (EPI), mid-myocardial (MIDDLE), and endocardial (ENDO) at a frequency of 1 Hz. ΔAPD is measured relative to WT.
re-entry self-terminated after 1.  (Fig. 5F). These 2D simulation results illustrate that the KCNQ1 V307L mutation increases tissue susceptibility to arrhythmogenesis by maintaining re-entrant excitation waves.
Realistically, the ventricles are three-dimensional and have a much more complex anisotropic geometry compared to the 2D ventricular slice. Therefore, one cannot necessarily assume that sustained reentry in the 2D tissue model translates to similar activity in 3D tissue. Consequently, we performed further simulations with a 3D anatomical human ventricle geometry. The results are shown in Fig. 6, which shows snapshots of the evolution of re-entrant scroll waves (WT: Fig. 6Ai-Di, Supplementary Videos S4 and S5; WT-V307L: Fig. 6Aii-Dii, Supplementary Videos S6 and S7; V307L: Fig. 6Aiii-Diii, Supplementary Videos S8 and S9) developing as a response to a premature stimulus. For the WT condition, the scroll wave self-terminated with a lifespan of 0.5 s (Fig. 6F). However, under WT-V307L and V307L mutation conditions, the scroll wave broke up forming multiple re-entrant wavelets that self-terminated within 2.5 s in WT-V307L tissue but were sustained throughout the 5 s simulation period in V307L tissue (Fig. 6F). Power spectrum analysis of the registered pseudo-ECG shows the dominant frequency of ventricle excitation to be 2.34 Hz for the WT condition, 3.13 Hz for the WT-V307L mutation condition and 7.42 Hz for the V307L mutation condition (Fig. 6G). Investigating I Ks as a potential therapeutic target in SQT2. As a pseudo-pharmacological approach to treating patients with SQT2, we mimicked I Ks channel blockade by drugs in order to determine the extent of blockade required to normalise the QT interval. To investigate this, maximal channel conductance of mutant I Ks was reduced in the EPI, MIDDLE and ENDO single cell types. Figure 7A-E show the results for an EPI cell in the TNNP model under the WT-V307L (Fig. 7A-B) and V307L (Fig. 7D-E) conditions. In all three cell types, approximately 60% simulated I Ks blockade was required to make the APD comparable to that of WT under the WT-V307L mutation condition while approximately 76% I Ks blockade was necessary under the V307L mutation condition.
Using the intact 1D strand, we performed a similar investigation on the normalization of the QT interval. In tissue, due to the electrical coupling between cells via gap junctions, APD differences between different cell types are reduced. Thus, for the WT-V307L mutation condition, 59% I Ks reduction (Fig. 7C) was needed to normalise the QT interval to that of WT while under the V307L mutation condition, approximately 75% I Ks reduction was necessary (Fig. 7F). These results are similar to the single cell situation. Finally, we investigated whether simulated I Ks blockade could terminate re-entrant activity under the mutation conditions (Fig. 8) in the 3D anatomical human ventricles. Figure 8A shows the WT condition with a premature stimulus applied during the tissue's vulnerable window at 355 ms. If I Ks reduction under the mutation conditions normalises the QT interval, then the application of a premature stimulus at this same time (355 ms) should produce somewhat similar activity to WT. Figure 8Bi and Ci show WT-V307L and V307L mutant tissue with no I Ks reduction, i.e. the pure heterozygote and homozygote mutant conditions respectively with a premature stimulus applied at 315 ms for WT-V307L and 260 ms for V307L leading to re-entrant activity that persists beyond the WT reentry lifespan. It transpired that 58% I Ks reduction was sufficient to make the WT-V307L reentry lifespan (Fig. 8Bii) comparable to that of WT while 65% I Ks reduction was adequate under the V307L mutation condition (Fig. 8Cii). These simulations illustrate the possibility of I Ks as a relevant drug target to treat tachyarrhythmia in the SQT2 setting.

Discussion
In this study, we have developed a MC model of I Ks incorporating the SQT2 V307L KCNQ1 mutation in order to elucidate possible pro-arrhythmic effects of this KCNQ1 gene mutation, and investigate in silico the possibility of I Ks inhibition as a treatment for SQT2. The major findings of the present study are summarised as follows: (i) a novel biophysically-detailed MC model formulation that reproduces accurately the dynamic properties of the KCNQ1 V307L mutation; (ii) the V307L mutation abbreviates the APD and steepens the APD restitution curve; (iii) the V307L mutation shortens the QT interval, increases T wave amplitude and T peak − T end duration, all of which are concordant with clinical observations regarding the SQTS; (iv) significantly reduced ERP in all transmural cell types in the KCNQ1 V307L mutation accelerates re-entrant excitation waves in human ventricles; (v) augmented membrane potential (δV) differences and transmural APD dispersion associated with the KCNQ1 V307L mutation contributes to increased T-wave amplitude and increased temporal vulnerability to uni-directional conduction block by a premature excitation at some localised regions of the ventricles; (vi) I Ks blockade is a potential therapeutic means of normalizing the QT interval and terminating re-entrant activity in the SQT2 setting. These results provide increased insight into understanding the causal link between the KCNQ1 V307L mutation and QT interval shortening and tachyarrhythmia.
In the first report of the KCNQ1 V307L mutation in a patient with the SQTS, Bellocq et al. 10 used a Priebe-Beuckelmann ventricular cell AP model 22 to demonstrate AP shortening. In our previous study 16 , we used the 2004 TNNP human ventricular AP cell model 23 with modified HH I Ks formulations reproducing V307L KCNQ1+KCNE1 kinetics available at that time to also demonstrate AP abbreviation, QT interval shortening, T wave morphology changes, reduced minimal substrate size for re-entry and reentrant activity in idealised 2D geometry. However, the current study is the first to reproduce the subsequently identified slower deactivation of V307L KCNQ1+KCNE1 I Ks and to examine the mutation's functional consequences in realistic 2D and 3D anatomical geometries. The present study is also the first to investigate the blockade of I Ks as a potential pharmacological intervention for treating SQT2 patients.  The MC structure used in this study 24 was previously employed in the study of O'Hara et al. 25 , in which effects of the "silent" Q357R KCNQ1 mutation in the long QT syndrome (LQT1) were probed in silico. That study 25 found that multiple insults to the repolarization reserve were required to reproduce the complex arrhythmic phenotype associated with the Q357R mutation, highlighting the need for a more kinetically-accurate description of I Ks channel kinetics than can be achieved with traditional HH formulations. This study builds on the approach employed by O'Hara et al. 25 , incorporating a detailed MC description of I Ks kinetics associated with a KCNQ1 channelopathy into anatomically-detailed human ventricle tissue simulations.
The SQTS is associated with malignant tachycardias 2, 4, 10, 26 and some patients present with ventricular fibrillation episodes 10,27 including the SQT2 proband 10 , who was successfully resuscitated from ventricular fibrillation. In our simulations we found that the KCNQ1 V307L mutation reduces ERP at all rates (Fig. 3). This helps to maintain re-entrant activity in tissue, as it decreases the wavelength of ventricular excitation waves, allowing higher activation frequencies of re-entrant excitation waves. This is evident in the increased lifespan and dominant frequency associated with the WT-V307L and V307L mutation conditions in both 2D and 3D simulations (Figs 5  and 6). Furthermore, we found that the SQT2 mutation increases vulnerability to initiation of re-entrant activity through localized increases in transmural heterogeneity of membrane potential, which leads to an increased temporal window of vulnerability to uni-directional conduction (Supplementary Figure S3). These findings are qualitatively in accord with our previous study 16 using the HH model of SQT2 with idealized tissue geometrical structures, demonstrating the elucidated arrhythmogenenic mechanisms of SQT2 are model independent and further solidify the causative link between KCNQ1 V307L mutation and ventricular arrhythmogenesis.
The use of Implantable Cardioverter Defibrillators (ICDs) is the current preferred treatment for the SQTS 2, 4, 28, 29 . However, as the SQTS is characterised by tall and peaked T-waves, there is the risk of inappropriate shocks to the patient due to T-wave over-sensing 2,4,28 . Additionally, ICDs do not restore the QT interval to its normal duration and are not suitable for all patients (e.g. infants). Therefore, pharmacological alternatives that can restore the normal duration of the QT interval and offer protection from arrhythmias are being actively pursued 2,4,30,31 . Hydroquinidine has been found to be effective in prolonging the QT interval and preventing episodes of VF, but its effect is greater in patients with identified SQT1 (hERG) mutations than in those without SQT1 mutations 32 . At present, there is no selective I Ks blocker in clinical use. In vitro experiments have shown that although I Ks is selectively blocked by chromanol 293B 33,34 , the blocking potency of this agent is reduced for recombinant channels containing the V307L KCNQ1 mutation 17,34 . In contrast, I Ks channels incorporating the V307L KCNQ1 mutation were inhibited by the quinolone agent mefloquine with a similar potency to that for WT channels 17 .
Our simulations mimicked selective pharmacological block of the I Ks channel in the SQT2 setting through reductions in I Ks magnitude. These showed that in the heterozygotic WT-V307L KCNQ1 condition, a blockade of I Ks by ~58% is sufficient to restore the QT interval to its original duration and make the tissue behave like WT tissue whereas under the V307L homozygote condition, a blockade of I Ks by ~65% is sufficient to achieve the same result. In our simulations, a high degree of I Ks block was required in the setting of SQT2 to 'correct' the cellular level APD and QT interval in tissue as well as to reduce tissue vulnerability and lifespan of reentry to those of normal tissue. This is consistent with the extent of I Ks augmentation arising from SQT2 conditions, however. This is demonstrated in Supplementary Figure S13. In these simulations, increasing maximal I Ks channel conductance in the WT condition by an amount equal to the inverse of that required to normalise the AP in SQT2 mutant conditions led to comparable shortening of the APD, and thus corresponded approximately to the amount of increased I Ks due to SQT2 mutant conditions. Although simulated I Ks block is a theoretical consideration (in the absence of clinically used selective I Ks inhibitors), and involves a simple current reduction rather than modification of kinetics, our study is nonetheless the first to provide proof-of-concept that I Ks block has the potential to be effective in the SQT2 setting. Furthermore, whilst the important role of I Ks in repolarization reserve means that I Ks blockade can lead to torsade de pointes 33,35,36 , this risk is likely to be greatest against a background of a normal, rather than abbreviated QT interval.
Inhibition of I Ks as a potential therapeutic strategy was further tested in another form of SQT2 caused by the KCNQ1 V141M mutation, which differs from the V307L mutation in that it induces a constitutively active voltage-independent current component 11 . Briefly, the MC was further modified to recapitulate kinetics of the V141M KCNQ1 mutation (shown in Supplementary Figure S11), including presence of a voltage-independent component, shifted voltage dependence of activation to less depolarized potentials, and significantly slowed deactivation 37 . We found that the heterozygous WT-V141M condition produced a significant shortening of the APD and QT interval, consistent with the SQTS phenotype. Simulation of a substantial degree of I Ks block (79%) resulted in normalization of the AP, as shown in Supplementary Figure S12. These supplementary simulations help to justify and validate our modelling approach, whilst providing further evidence that I Ks block may, in principle, be an effective therapeutic strategy in the setting of SQT2.
In order to determine whether or not the principal results obtained in this study pertaining to the KCNQ1 V307L mutation were model-dependent, single cell and 1D simulations performed in the TNNP model were also carried out in the more recently-developed O'Hara-Rudy dynamic (ORd) human ventricular cell model 38 . At the single cell level, the major findings reported using the TNNP model were matched qualitatively by the ORd model, i.e. the SQT2 mutations significantly reduced the APD, affecting transmural regions of the ventricles differentially (Supplementary Figure S4), and increased maximum slope of APD restitution (Supplementary Figure S5). In the ORd model intact 1D strand, the MC formulation of the KCNQ1 V307L mutation accurately reproduced QT interval shortening and an increase in T-wave amplitude -two hallmarks of the SQTS (Supplementary Figure S6) 2,[4][5][6][7] . The underlying mechanisms contributing to increased T-wave amplitude due to the SQT2 mutations were the same as in the TNNP model, i.e. augmented maximal membrane potential difference, δV, between coupled cells in tissue (Supplementary Figure S7) due to increased spatial gradient of APD across the transmural strand (Supplementary Figure S8). Furthermore, tissue temporal vulnerability to uni-directional conduction in the ORd model 1D transmural strand (measured at the MIDDLE-EPI border) was increased by the SQT2 mutations (Supplementary Figure S9). I Ks reductions of 50% and 65% in WT-V307L and V307L conditions respectively were required to normalize the APD in single cell ORd model simulations (Supplementary Figure S10). These values are comparable to the TNNP values of 60% and 76%. Similar to the single cell situation, the degrees of I Ks blockade necessary to normalise the QT interval in SQT2 mutation conditions in the ORd model were slightly lower but still fairly close to those in the TNNP model. The model independence of these results is significant. Obtaining qualitative agreement between two distinct human ventricle cell models shows that the fundamental mechanisms by which the SQT2 mutations affect ventricular electrophysiology are the same even when there are differences in ion channel kinetics, as in the TNNP and ORd models.
Limitations of the main human ventricular cell model used (TNNP 2006) have been discussed in detail elsewhere 18,20,39 . In the multicellular tissue model -due to a lack of detailed experimental data -the proportion of each region comprised each distinct cell type and intercellular electrical coupling was chosen to produce a positive T-wave and a conduction velocity of a planar solitary excitation wave close to experimental data, similar to those used in other studies 16,21,40 . The heterozygote formulation used in this study relies on the simplifying assumption that V307L I Ks behaves similar to a 50:50 mixture of WT and mutant channels. The channel population may be more complex in reality, with each channel comprising both WT and mutant KCNQ1 subunits. That said, our previous study 16 investigated the effects of varying mutant subunit composition in SQT2 based on different expression/co-expression ratios used in experiments in the original paper describing the V307L KCNQ1 mutation 10 , and found that the degree of APD and QT interval shortening increased progressively with the level of V307L expression. Thus, the simplifying assumption adopted in the present study is unlikely to affect adversely the simulation results: our heterozygote formulation reproduced QT interval shortening and increased T wave amplitude associated with the SQTS phenotype 2, 4-7 .
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 V307L 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 40 . 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 41,42 , particularly for SQTS patients [43][44][45] .
Whilst it is important that both assumptions and 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 KCNQ1 V307L mutation facilitates arrhythmia induction and maintenance, and the possibility of I Ks inhibition as pharmacological modulation in the setting of SQT2. 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 SQT2. This highlights the likely importance of the pro-arrhythmic mechanisms identified in this study.
The simulations in this study substantiate that the KCNQ1 V307L mutation is causally linked to QT interval shortening and increased tissue vulnerability to arrhythmogenesis in this form of the SQTS. In addition, we have shown that I Ks blockade normalises the QT interval and successfully terminates re-entry during tachyarrhythmias. Thus, the findings of this study provide a comprehensive explanation for clinical consequences of this form of the SQTS in terms of abbreviation of repolarisation and susceptibility to arrhythmia and it provides a potential pharmacological approach in designing therapeutic interventions for this form of the SQTS. It is notable that the more recently reported R259H 13 and F279I 46 KCNQ1 SQT2 mutations produce similar changes to recombinant channel I Ks to those of V307L KCNQ1. The results reported here may therefore also have relevance to SQT2 associated with these mutations. Additionally, the multi-scale ventricular models developed and employed in this study may have further utility for probing the basis of arrhythmia, both in other forms of the SQTS and other repolarisation disorders.

Methods
Development of I Ks Markov chain model. The MC model of I Ks incorporating the V307L KCNQ1 mutation was based on the work of Silva and Rudy 24 , who developed it using experimental data at physiological temperature (37 °C) including data from human ventricular myocytes representing I Ks activation and deactivation kinetics (MC scheme shown in Supplementary Figure S1). The model was modified to reflect the experimentally observed kinetic properties of WT and V307L-mutant "I Ks " (KCNQ1+KCNE1) channels. These kinetic properties include: (i) the profound leftward shift (−36 mV) of channel activation for the V307L mutation compared to WT 17 , (ii) slower channel deactivation in the V307L mutation 17 , (iii) the increased repolarising current during ventricular AP clamp 17 , and (iv) accelerated activation as seen with the V307L mutation 10,17 .
To obtain the transition rates of the MC model that reproduced the experimentally observed kinetic properties of WT and V307L, we simulated the experimental current-voltage (I-V) relationships for WT and V307L KCNQ1 + KCNE1 using the voltage clamp protocol from El-Harchi et al. 17 (Fig. 1Aii-Bii). The membrane potential was held at −80 mV and then depolarised briefly to −40 mV for 50 ms, followed by 3 s depolarisations to a range of potentials from −70 mV to +60 mV (in 10 mV increments); finally, tail currents were elicited by repolarisation to −40 mV for 5 s. The currents obtained at the end of the depolarising steps were normalised and compared to experimental data (Fig. 1Aiii-Biii). The elicited current traces from the voltage clamp protocol are shown in Fig. 1Ai-Bi. By minimising the least-squared difference between the experimental data and the simulation, the variables representing the transition rates that produced the best fit and behaviour of macroscopic currents relative to the experimental data were obtained (Fig. 1Aiii-Biii). The minimisation was performed using the Nelder-Mead Simplex algorithm 47 . Relative current proportions for WT and V307L KCNQ1 conditions were then scaled using relative proportions of peak I Ks obtained from AP clamp experiments 17 . AP clamp and model validation. The MC model was validated by comparing simulated results with those observed experimentally during ventricular AP clamp (Fig. 1Aiv-Biv). The same digitised ventricular AP used to generate the experimental AP clamp 17 was used in the simulation.
Heterozygote formulation. To mimic the heterozygous state of the proband, we constructed a heterozygous formulation (WT-V307L) consisting of 50% WT and 50% V307L channels. We used this formulation to also investigate the effects of the KCNQ1 V307L mutation in this heterozygous condition.
Cellular and tissue models. The developed I Ks MC model was incorporated into the 2006 version of the TNNP 20 model of the human ventricular cell AP for consistency with our previous in silico studies on the SQTS 18,19,44 . Single cell models were then incorporated into 1D, 2D and 3D multicellular models with a monodomain tissue representation 18,19,48 of realistic human ventricular geometries. The realistic human geometries were reconstructed as described previously 18,19 with a spatial resolution of 0.2 mm. The anatomical model was segmented into three distinct regions: 25% EPI, 35% MIDDLE and 40% ENDO cells. These proportions are similar to those used in other studies 16,18,21,40 and were chosen as they produced a positive T-wave on the ECG under the WT condition.
Further details regarding multi-scale model development, including methods for simulating the pseudo-ECG, protocols used for measuring restitution of the APD and ERP, initiation of re-entrant excitation waves, dynamics of re-entry, and numerical methods have been documented in detail in our previous studies 16,18,19,49 and are provided in the Supplement.