In silico investigation of the mechanisms underlying atrial fibrillation due to impaired Pitx2.

Atrial fibrillation (AF) is the most common sustained cardiac arrhythmia and is a major cause of stroke and morbidity. Recent genome-wide association studies have shown that paired-like homeodomain transcription factor 2 (Pitx2) to be strongly associated with AF. However, the mechanisms underlying Pitx2 modulated arrhythmogenesis and variable effectiveness of antiarrhythmic drugs (AADs) in patients in the presence or absence of impaired Pitx2 expression remain unclear. We have developed multi-scale computer models, ranging from a single cell to tissue level, to mimic control and Pitx2-knockout atria by incorporating recent experimental data on Pitx2-induced electrical and structural remodeling in humans, as well as the effects of AADs. The key findings of this study are twofold. We have demonstrated that shortened action potential duration, slow conduction and triggered activity occur due to electrical and structural remodelling under Pitx2 deficiency conditions. Notably, the elevated function of calcium transport ATPase increases sarcoplasmic reticulum Ca2+ concentration, thereby enhancing susceptibility to triggered activity. Furthermore, heterogeneity is further elevated due to Pitx2 deficiency: 1) Electrical heterogeneity between left and right atria increases; and 2) Increased fibrosis and decreased cell-cell coupling due to structural remodelling slow electrical propagation and provide obstacles to attract re-entry, facilitating the initiation of re-entrant circuits. Secondly, our study suggests that flecainide has antiarrhythmic effects on AF due to impaired Pitx2 by preventing spontaneous calcium release and increasing wavelength. Furthermore, our study suggests that Na+ channel effects alone are insufficient to explain the efficacy of flecainide. Our study may provide the mechanisms underlying Pitx2-induced AF and possible explanation behind the AAD effects of flecainide in patients with Pitx2 deficiency.

Introduction

Atrial fibrillation (AF), the most common sustained heart rhythm disorder, affects more than 33 million people worldwide and represents a growing cause of stroke and morbidity[1, 2]. Although the prevalence of AF increases with age and with the context of concomitant cardiac pathologies such as myocardial ischemia, hypertension and heart failure, genome-wide association studies (GWAS) have shown that one-third of AF patients carry common genetic variants, suggesting that AF has a heritable component[3-5]. These single nucleotide polymorphisms rs2200733 and rs10033464 were firstly identified in European, Chinese and Japanese populations on chromosome 4q25[6]. The gene-poor 4q25 region harbors the Pitx2 homeobox gene, which has been implicated in AF predisposition[3, 4, 7].

Pitx2 plays an important role in a left-sided signalling pathway that establishes the left-right asymmetry of the heart[8, 9]. Pitx2 encodes 3 isoforms (Pitx2a, Pitx2b and Pitx2c) and the Pitx2c isoform promotes the embryonic development of cardiac left–right asymmetry, with levels in right and left atriums being 1:100[10]. The atrial-selective transcription factor Pitx2 is an upstream transcriptional regulator of atrial electric function and cardiogenesis[11, 12]. Complete loss of Pitx2 function can result in malformation of the pulmonary veins that are well-known sites for ectopic activity promoting spontaneous AF[9]. Pitx2 loss-of-function mouse mutants displayed abnormal electrocardiograms with atrioventricular block, irregular R-R intervals and low voltage P waves[13, 14]. In the Pitx2-mutant atrial myocytes, a significantly more depolarized resting membrane potential (RMP)[14, 15], action potential duration (APD) shortening[10, 16, 17], and abnormalities in calcium handling[18, 19] were observed. Furthermore, expression array analyses identified genes related to calcium handling, gap junctions and ion channels affected by the reduced expression of Pitx2, mediating AF risk in carriers of common gene variants[10, 13, 14, 16, 19–21]. However, the precise AF pathophysiology under reduced Pitx2 remains unclear. Population-based studies have assessed the influence of common SNPs related to AF on the response to antiarrhythmic drug (AAD) therapies and showed that carriers of the variant allele at rs10033646 on chromosome 4q25 (Pitx2) responded favourably to the class I AAD (flecainide)[22-26]. The possible reasons behind this remain elusive.

In this study, we aimed to utilize virtual human atrial models to investigate the functional role of Pitx2-induced remodeling in atrial arrhythmogenesis and to examine the mechanism underlying the efficacy of flecainide for patients with Pitx2-induced AF. To achieve this, we adopted the previously modified and validated Courtemanche-Ramirez-Nattel model (CRN-TPA) for the human atrial cell by incorporating formulations of intracellular calcium dynamics from the ten Tusscher-Panfilov model to reproduce triggered activity[24, 27]. We then modified the model to produce four distinct models of Pitx2-induced electrical remodeling based on grouping existing literature. Furthermore, regional cellular heterogeneity between RA and LA, as well as Pitx2-induced structural remodeling including cell-cell coupling and fibrosis, was integrated into the computer models. Lastly, the antiarrhythmic action of flecainide was systematically simulated by integrating the block effects of flecainide on the sodium channel I, rapidly activating delayed rectifier potassium channel I and ryanodine receptor (RyR) into atrial cell models.

Methods

An overview of our multi-scale human atrial models are provided in . The downregulation of Pitx2 in membrane effector genes (the magenta circles) and alterations in ion channels and gap junction encoded by these genes were integrated into the multi-scale atrial models (). The developed models included single cells, 1D atrial strands and 2D atrial tissue. These Pitx2-mutant models were then incorporated with the actions of flecainide on ion channels (the red circles) to assess its efficacy.

Multi-scale computer models to investigate the mechanism underlying Pitx2-induced AF and the effects of class Ic AAD (flecainide).

a, The computer models incorporated Pitx2-induced electrical and structural remodeling, and flecainide interactions with ion channels. Remodeled targets (magenta circles) included gap junction, IK1, IKs, INa, ICaL, RyR and SERCA. Drug targets of flecainide (red circles) were IKr, INa and RyR. Under the control condition, heterogeneity in Pitx2 expressions (b) and AP (c) between LA and RA was included in the computer models. d, Based on experimental and clinical studies up to date, four Pitx2 deficiency-induced human atrial cell models were developed: Pitx2-1 with remodeled IK1 (green), Pitx2-2 with remodelled IKs and ICaL (magenta), Pitx2-3 with remodelled ICaL, RyR and SERCA (red) and Pitx2-4 with remodelled IK1, IKs, INa, ICaL, RyR and SERCA (blue). Abbreviations: AF–atrial fibrillation; AAD–antiarrhythmic drug; LA–left atrium; RA–right atrium; AP–action potential; RyR–ryanodine receptor; SERCA–calcium transport ATPase.

Human atrial cell model

At the single cell level, a recent human atrial cellular kinetics model (CRN-TPA) () developed by our group was further adapted to simulate control and Pitx2 deficiency-induced AF conditions[24]. Cellular heterogeneity between LA and RA was modeled by taking into account differences in mRNA level for Pitx2 and in I current density (). Under control conditions, Pitx2 level in human LA is almost 100-fold higher in the LA as compared to that in RA[10] ( and I current density in LA cells is 1.6-fold of that in RA cells[28, 29] (.

Pitx2-induced electrophysiological remodeling

To study the effect of the Pitx2-dependent gene regulatory network in human atrial myocytes, we incorporated alterations in the ion channel properties due to Pitx2 deficiency into the CRN-TPA model. These Pitx2-induced changes in ion channels and cell-to-cell coupling have been characterized in many animal studies. Although these studies have shown SR calcium overload, RMP elevation and APD abbreviation in Pitx2-mutant mice atrial myocytes[10, 14–16, 18, 19], the identified remodeled ion channels are different in these studies: remodeling in I was identified among some studies[14, 15]; whereas remodeling in other channels, such as I, I and I are present in others[16, 19–21]. Recent studies also characterized changes to the subcellular calcium handling properties and alterations to the tissue structure (i.e., fibrosis and gap junctions)[14, 21]. To incorporate such variations in experimental data into the computer models, four different scenarios (Pitx2-1, Pitx2-2, Pitx2-3 and Pitx2-4) () were considered here for simulating Pitx2-induced remodeling (). Pitx2-1 included the remodeled inward-rectifier potassium current (I) (green)[15], while Pitx2-2 included the remodeled L-type calcium current (I) and slow delayed rectifier potassium current (I) (magenta)[16]. Pitx2-3 has incorporated with remodelled key regulators associated with calcium handling, i.e., I, RyR and calcium transport ATPase (SERCA) (red)[19]. The Pitx2-4 model took into account all identified regulators and best represented Pitx2 deficiency-induced electrical remodeling by including remodeled I, I, I, I, RyR and SERCA[15, 16, 19, 21] (blue). Furthermore, based on the assumption that the extent of electrical remodelling in atrial cells is dependent on mRNA level for Pitx2, Pitx2-modulated targets in LA cells have a 100 times greater change compared to those in RA cells. This enabled us to: (1) consider a broad range of experimental data on identified ion channel remodeling; (2) investigate the effects of varying degrees of remodeling to reproduce phenomenon observed in animal experiments; and (3) ascertain mechanisms underlying Pitx2-induced AF.

Actions of flecainide on ion channels

To investigate the anti-arrhythmic effects of the class Ic drug flecainide, we integrated the actions of flecainide on ion channels and RyR into the Pitx2-mutant computer models. According to experimental/clinical data[26, 30], modifications to ion channels provoked by flecainide were modeled by using the standard sigmoid dose-response curve ( parametrized with IC and Hill coefficient (nH = 1). The values of IC for inhibition of I, I and RyR open probability were 84, 1.5[30] and 55 μM[26], respectively.

1D multicellular models

To study the effect of Pitx2-induced remodelling and flecainide on spatiotemporal behavior of electrical waves, we designed a 1D RA-LA strand model in which it has 75 RA myocytes and the other 75 LA cells. The diffusion coefficient (D) was set to a value of 0.1 cm2/s that gave a CV of a planar wave at 48.61 cm/s, within the physiological ranges (Slow: 30 to 40 cm/s, Normal: 60 to 75 cm/s, Fast: 150 to 200 cm/s). In Pitx2-mutant models, D in the LA was reduced by 50% to simulate the reduction in CV resulting from Pitx2-induced structural remodeling. Electrical waves in the strand model were evoked by the supra-threshold stimuli applied to three myocytes at the RA end. VW of unidirectional conduction block, an index to quantify the temporal vulnerability of cardiac tissue to re-entry, was quantified by varying the S1-S2 interval in the 1D homogeneous atrial strand. The protocol included 10 S1 stimuli applied at the end of the atrial strand and an S2 stimulus applied at the central segment of the atrial strand. Furthermore, VWRA-LA of unidirectional conduction block was measured to quantify the RA-to-LA electrical heterogeneity[31, 32] by varying the S1-S2 interval in the RA-to-LA strand model with 250 RA myocytes and the other 250 LA cells.

2D multicellular models

To illuminate the spatiotemporal dynamics of triggered activity, a 500×500 square tissue model with randomly distributed normal myocytes, Pitx2-4 cells and fibrosis was designed to simulate synchronization of triggered beats and investigate the conditions of arrhythmia induction. Five different scenarios (#1, #2, #3, #4 and #5) were considered here for investigating effects of Pitx2-4 cells, fibrosis and cell-to-cell uncoupling on the inducibility of ectopic activity. D was set to be 100% for the #1, #2 and #3 conditions, and 30% for the #4 and #5 conditions, respectively. The ratios of normal cells, Pitx2-4 cells and fibrosis were set to be 80:20:0, 40:60:0, 78:20:2, 80:20:0 and 78:20:2, for the #1, #2, #3, #4 and #5 conditions, respectively. AP synchronization in the tissue model was simulated by a stimulus applied to the entire tissue at the beginning according to de Lang’s method[33]. In addition, the spatiotemporal behavior of spiral waves in the drug-free Pitx2 setting versus in the presence of flecainide was investigated in the 500×500 homogeneous LA tissue. The spiral wave was initiated by a standard S1-S2 protocol. The S1 was applied to the left surface to evoke a planar excitation wave propagating towards the right part. The S2 was applied to a local area of the tissue within the VW to evoke unidirectional propagation that can lead to re-entry.

Code availability

The ionic models for RA and LA atrial cells (Control, Pitx2-1, Pitx2-2, Pitx2-3 and Pitx2-4) and mathematical models of drug-channel interactions are freely available from the repository CellML (http://models.cellml.org/workspace/5c7). The electrophysiology codes developed by our team and can be obtained from GitHub (https://github.com/aspirerabbit).

Results

Pitx2-induced triggered activity in the single cell models

The ionic mechanisms of Pitx2 deficiency-induced AF were investigated by examining calcium transient (Cai) and action potentials (APs) using the computer models of control and four different scenarios of Pitx2-deficiency (Pitx2-1, Pitx2-2, Pitx2-3 and Pitx2-4) (. At 1Hz pacing frequency, the Pitx2 deficiency-induced electrical remodeling produced augmented Cai under Pitx2-3 and Pitx2-4 conditions, and delayed afterdepolarizations (DADs) under the Pitx2-3 condition (). Furthermore, we observed an increase in RMP (Pitx2-1 and Pitx2-4), large overshoot and maximum upstroke velocity (dVdtmax) (Pitx2-4), and APD abbreviation (Pitx2-2, Pitx2-3 and Pitx2-4) in Pitx2-deficient LA cells, compared with controls (). However, these changes were absent in Pitx2-deficient RA cells (grey color). Thus, the augmented alterations in APs between RA and LA in the Pitx2-deficient settings, particularly in Pitx2-3 and Pitx2-4, significantly increased regional electrical heterogeneity. Additional simulations at 2Hz pacing frequency were performed to investigate the effects of pacing frequency on APs and Cai. The amplitude of Cai was increased under all four conditions and triggered APs occurred in Pitx2-deficient LA cells (Pitx2-3 and Pitx2-4) when pacing frequency was increased ().

Simulated action potentials (AP, Vm) and calcium transients (Cai) of left atrial (LA) and right atrial (RA) cells under controls and Pitx2-induced remodelling conditions.

At a pacing frequency of 1Hz, AP and Cai (a), RMP (b), overshoot (c), dVdtmax (d) and APD (e) under control, Pitx2-1, Pitx2-2, Pitx2-3 and Pitx2-4 conditions. Black and grey markers were used for LA and RA cells, respectively. Similar key indicators (f-j) at a pacing frequency of 2Hz were displayed. Blue arrows indicated delayed afterdepolarizations, triggered action potentials and spontaneous calcium transients. Abbreviations: RMP–resting membrane potential; dVdtmax−maximum upstroke velocity; APD–action potential duration.

To further evaluate the contribution of each remodelled target to the abnormalities in AP under Pitx2-4 condition, we conducted computer simulations by incorporating each ionic remodelling of Pitx2-4. Compared with the control AP, remodelled I resulted in a more positive RMP, increased I contributed to greater overshot and dVdtmax, altered I, I or SERCA caused a reduction in APD90, and enhanced SERCA increased sarcoplasmic reticulum calcium content (CaSR) and resulted in triggered APs ().

To further explore the putative targets among the remodelled cellular components that contribute to the Pitx2-4 phenotype, a series of simulations with modified Pitx2-4 models were performed by reversing each remodelled target separately. Compared with triggered APs in Pitx2-4 atrial cells, reversing SERCA remodelling rescued spontaneous depolarizations, but not in other conditions (.

Effects of flecainide on Pitx2-induced arrhythmias at the single cell level

To assess the class Ic AAD flecainide, we have performed computer simulations with modelled the interaction of flecainide with I, I and RyR. shows APs of Pitx2-deficient LA cells in the absence or presence of 2μM flecainide. In all cases of Pitx2-deficient LA myocytes, the flecainide therapy rescued abnormal depolarizations (Pitx2-3 and Pitx2-4), RMP elevation, increased overshoot, dVdtmax acceleration, and APD abbreviation. To investigate exactly how the flecainide therapy contributes to the antiarrhythmic effects, we conducted additional simulations by including flecainide actions on each ionic target (i.e., I, I or RyR) separately in the Pitx2-4 model. Compared with APs in the presence of 2μM flecainide on all targets (), triggered APs were still observed in Pitx2-4 cells with the action of flecainide on I or I only ( but not in LA myocytes with the effect of flecainide on RyR alone (.

Antiarrhythmic effects of flecainide on action potentials (AP, Vm).

a, Comparison of APs of LA cells in the presence or absence of 2 μM Fle. The main AP parameters included RMP (b), overshoot (c), dVdtmax (d) and APD (e). Simulated effects of 2 μM Fle on all targets (f), and on INa (g), on Ikr (h) and on RyR (i) respectively. Blue arrows indicate delayed afterdepolarizations. Abbreviations: LA–left atrium; Fle–flecainide; RMP–resting membrane potential; dVdtmax−maximum upstroke velocity; APD–action potential duration; RyR–ryanodine receptor.

Further simulations were conducted to examine whether the flecainide therapy can reduce the heterogeneity in AP features between RA and LA caused by Pitx2 deficiency-induced electrical remodelling. In presence of 2μM flecainide, our results indicate that heterogeneity in AP features (including AP profile, RMP, overshoot, dVdtmax and APD90) between RA and LA increased to varying degrees, compared to those in the absence of flecainide (). With the increase of flecainide concentration within the therapeutic range (0.5–2 μM), dVdtmax decreased and APD90 increased in both RA and LA cells. However, their differences between RA and LA cells were not reduced ().

Arrhythmogenesis of Pitx2 deficiency in 1D computer model

We then examined the effect of Pitx2-induced remodeling on electrical excitation and heterogeneity of conduction in a 1D strand model with a total of 150 atrial cells (#1 - #75 for RA and #76 - #150 for LA). Under the control condition, pacing at the RA end (cell #1) using an extra stimulus led to electrical propagation from RA to LA. AP and Cai along the control RA-LA strand had no obvious difference, while significant heterogeneities in AP and Cai and triggered APs originating from LA were observed under Pitx2-deficient conditions (Pitx2-3 and Pitx2-4) (). After administration of 2 μM flecainide, these heterogeneities in the Pitx2-deficient strand still existed, but atrial ectopic beats were suppressed (). Similar to the single cell modelling results, these ectopic beats remained in Pitx2-4 cells with the action of flecainide on I or I only, but were suppressed by the block effect of flecainide on RyR alone ().

Simulated electrical (Vm) and calcium (Cai) waves in a 1D RA-LA strand.

a, Simulated Vm and Cai waves in the drug-free settings (a) and in the presence of 2 μM flecainide (b). Comparison of CV(c) and WL (d) of LA (black) versus RA (grey) strands in the drug-free settings. In the presence of 2 μM flecainide, CV (e) and WL (f) are compared between RA and LA strands. The 1D strand contains 75 RA (#1-#75) cells and 75 LA (#76-#150) cells. Electrical waves were elicited by an extra stimulus at the RA end and propagated from RA to LA. Blue arrows indicate spontaneous delayed afterdepolarizations, triggered action potentials and calcium transients. Abbreviations: 1D –one-dimensional; RA–right atrium; LA–left atrium; CV–conduction velocity; WL–Wavelength.

To further quantify potential substrates of re-entrant arrhythmias, we measured conduction velocity (CV) and wavelength (WL) in both RA and LA. Compared with those under the control condition, reduction in CV and WL was observed in the four Pitx2-deficient LA strand models but not in the RA model (), leading to increased dispersion of repolarization and elevated susceptibility to re-entry. After administration of flecainide, for the control and four Pitx2-deficient LA cases, CV and the differences between RA and LA remained ( and ), while prolongation of WL occurred in both the LA and RA ( and ), thereby reducing the incidence of arrhythmias induced by Pitx2 deficiency.

Structural remodelling promoting abnormal electrical activity at the tissue level

To further investigate focal arrhythmia arising from spatiotemporal synchronization of triggered APs due to Pitx2 deficiency as well as structural remodelling (fibrosis and cell-to-cell coupling), we designed a 2D tissue model (500×500) in which normal LA myocytes (white), Pitx2-4 remodeled LA cells (gray) and fibrosis (black) were randomly distributed (). The entire tissue was preconditioned at the beginning to produce AP synchronization according to de Lang’s method[33]. In the well-coupled tissue, 20% Pitx2-4 cells could not overcome the sink-source mismatch to produce excitation waves (). However, increased number of Pitx2-4 cells, reduced cell-to-cell coupling or upregulated fibrosis ( can produce triggered waves (). Furthermore, persistently triggered activity was observed in the model with both cell-to-cell uncoupling and fibrosis (). Thus, in addition to Pitx2 deficiency-induced electrical remodeling, structural remodeling can further increase susceptibility to ectopic beats at the tissue level.

Simulated spontaneous ectopic activity and re-entry.

a, A 500×500 square tissue model includes normal atrial myocytes, Pitx2-4 remodelled LA cells, fibrosis, and gap junctions. Simulated spontaneous ectopic activity in the tissue model with 20% Pitx2-4 cells (b), with further increased Pitx2-4 cells (c), with enhanced cell-to-cell uncoupling (d), with increased fibrosis (e), and with increased cell-to-cell uncoupling and fibrosis (f). Re-entrant waves in the drug-free Pitx2-4 settings (g) and in the presence of 2 μM flecainide (h). Note: For the #1 scenario, the diffusion coefficient (D) was set to be 100% and the ratio of normal cells, Pitx2-4 cells and fibrosis was set to be 80:20:0. For the #2 scenario, the number of Pitx2-4 cells was increased to 40% and thereby the ratio of different cell types was 40:60:0. And D was set to be 100%. For the #3 scenario, D was reduced to 30% to model cell-to-cell uncoupling and the ratio of different cell types was set to be 80:20:0. For the #4 scenario, fibrosis was increased to 2% and thereby the ratio of different cell types was 78:20:2. And D was set to be 100%. For the #5 scenario, fibrosis was increased to 2% and D was reduced to 30%. And the ratio of different cell types was 78:20:2.

We also investigated spiral wave dynamics and re-entry initiated from unidirectional conduction within the vulnerable window (VW) using an S1-S2 protocol. Under the drug-free Pitx2-4 condition, a spiral wave was initiated within its VW (230–232 ms) ( and and transformed into fibrillated-like waves. Furthermore, it facilitated the development of triggered activity and interacted with ectopic beats (. In the presence of 2 μM flecainide, a planar wave slowly propagated and then produced a spiral wave within a shorter VW (294.7–296 ms) ( and However, this re-entrant wave self-terminated at 8450 ms and no triggered activity occurred ( Thus, the efficacy of flecainide in suppressing Pitx2-induced AF may be attributed to its effects on triggered activity and WL.

A quantitative summary of electrophysiology characteristics is listed in .

Discussion

Pitx2 plays a critical role in heart development and left-right atrial asymmetry, and its deficiency is associated with a 65% increased risk of AF[3]. Flecainide therapy for patients with Pitx2 deficiency seems promising, though its mechanism remains elusive[15, 25, 34]. To our knowledge, this is the first systematic in silico study to improve our understanding of the mechanism underlying Pitx2 deficiency induced AF by employing novel bio-physics based multi-scale computer models. More specifically, we have developed and studied a family of human atrial cellular models grouped by different levels of electrical remodelling due to Pitx2 deficiency, and at a single cell, 1D strand and 2D tissue level. Furthermore, we have included structural remodelling (fibrosis and cell-to-cell coupling) into our modelling study as well.

The key findings of this study are twofold. Firstly, we found that shortened APD, elevated RMP and slow conduction occur in LA cells with Pitx2 deficiency due to the identified remodelled vital channels. Notably, the elevated function of SERCA increases SR Ca2+ concentration, thereby enhancing susceptibility to triggered activity. Furthermore, heterogeneity is further elevated due to Pitx2 deficiency: 1) Electrical heterogeneity between RA and LA increases; and 2) Increased fibrosis and decreased cell-cell coupling due to structural remodelling slow electrical propagation and provide obstacles to attract re-entry, facilitating the initiation of re-entrant circuits. Secondly, our study suggests that the interaction of flecainide with RyR prevents spontaneous calcium release and reduces VW (or increases WL), contributing to the efficacy of the class Ic AADs. In contrast with existing studies, our study suggests that Na+ channel effect alone is insufficient to explain the effectiveness of flecainide. Additionally, the introduction of flecainide fails to reverse the RA-to-LA electrical heterogeneity.

Ionic basis of Pitx2 insufficiency-induced AP phenotype

Electrical remodelling due to Pitx2 insufficiency accounts for ectopic depolarizations[21, 24] and abbreviated APs[14], contributing to AF, but the ionic mechanisms underlying these changes in AP characteristics remain unclear. In the present study, we incorporated variations in experimental data into four computer models (Pitx2-1, Pitx2-2, Pitx2-3 and Pitx2-4). In these models, the Pitx2-4 model took into account all identified regulators and best represented Pitx2 deficiency-induced electrical remodelling. Ionic mechanisms underlying Pitx2 insufficiency-induced AP phenotype in different Pitx2 models were investigated by incorporating each ionic remodelling into the control model and reversing each remodelled target separately in the Pitx2-4 model. Consistent with experimental data on Pitx2 insufficiency-induced electrical remodelling[16, 19–21], remodelled targets considered in the Pitx2-4 model include I, I, I, I, RyR and SERCA. In these remodelled targets, we observed that downregulated I resulted in a more positive RMP and a prolonged APD, upregulated I contributed to a high overshoot and dVdtmax, the I increase and (or) the I decrease led to a reduction in APD, and increased SR calcium load due to enhanced SERCA function caused triggered APs. On the one hand, our simulated results support the notion that down-regulation of I and up-regulation of I are hallmarks of electrical remodelling in AF patients and mainly cause APD shortening[35, 36]. On the other hand, our results demonstrate that enhanced SERCA function can increase the incidence of spontaneous SR calcium release events, in line with the experimental observation in AF patients[37, 38]. The calcium extrusion due to the spontaneous SR calcium release via I can contribute to phase-4 depolarizations. In addition to the inward I due to enhanced SERCA function, the remodelled I and I modulate RMP and membrane excitability[24], but our data and other studies[37, 38] suggest that triggered APs are mainly due to SR calcium load resulted from enhanced SERCA function.

Role of remodelling under Pitx2-deficiency in arrhythmogenesis

Increased electrical heterogeneity between RA and LA due to down-regulated Pitx2 expression implicated in the initiation and maintenance of re-entrant arrhythmias.[39] Since the ratio of Pitx2 between LA and RA is 100:1 in the human atria,[10] we assumed that the extent of remodelling after Pitx2 deletion is dependent on the amount of Pitx2. In this study, increased electrical heterogeneity may result from the difference in Pitx2-induced remodelling between LA and RA. In our study, we observed that electrical remodeling induced by Pitx2 deficiency causes APD abbreviation and ectopic depolarizations in LA myocytes, but not in RA myocytes. Thus, Pitx2 insufficiency can cause an elevated difference in electrical properties between RA and LA cells, increasing repolarization dispersion in tissue and thereby susceptibility to the development of re-entry[32, 40, 41]. Furthermore, Pitx2 deficiency can also cause LA structural remodeling by regulating cardiac structural genes, increasing electrical and structural heterogeneity between the two atrial chambers. Finally, our computer simulation studies suggest that the introduction of flecainide can suppress triggered activity but fail to reverse the RA-to-LA electrical heterogeneity. The presence of increased fibrosis and decreased cell-to-cell coupling under structural remodelling further facilitates slow conduction, WL abbreviation, triggered activity and the initiation of re-entrant drivers, increasing susceptibility to AF. It is known that Pitx2-dependent network regulates cardiac structural genes (Gja1, Gja5 and Dsp)[21] and Pitx2-induced structural remodeling leads to fibrosis and cell-cell uncoupling[42]. Also, structural remodeling due to the left-sided Pitx2 expression increases the intrinsic heterogeneity (i.e., CV and WL) between RA and LA, facilitating the development of re-entry ().

Mechanisms underlying Pitx2 deficiency-induced AF and ionic mechanisms of anti-arrhythmic effects of flecainide in AF patients with Pitx2 down-regulation.

a, Pitx2 regulates calcium handling genes Atp2a2, Ryr2 and Sln, electrical remodelling genes Scn5a, Kcnj2, Kcnj4, Kcnj11, Kcnj12, Kcnq1 Cacna1d, Cacna2d2, and Cav1, and structural remodelling genes Gja1, Gja5 and Dsp. Pitx2 down-regulation in the LA leads calcium handling abnormities, electrical remodelling and structural remodelling, contributing to APD abbreviation, slowed atrial conduction and DAD, leading to AF triggers and substrates. b, Flecainide has block effects on RyR, INa and IKr. Flecainide can reduce spontaneous calcium waves and triggered activity, and prolong the APD, thereby suppressing Pitx2 deficiency-induced AF. Abbreviations: AF–atrial fibrillation; LA–left atrium; DAD–delayed afterdepolarization; APD–action potential duration; RyR–ryanodine receptor.

Antiarrhythmic effects of flecainide

The class Ic AAD flecainide has antiarrhythmic effects on triggered activity by suppressing spontaneous SR calcium release via RyR, and on re-entrant arrhythmia by prolonging WL in Pitx2-induced AF. Population-based studies have established that the two SNPs, rs2200733 and rs10033464, from chromosome 4q25 near Pitx2 are associated with high incidence of AF[25]. Furthermore, there exists evidence that carriers of the variant allele at rs10033646 respond favourably to class Ic AADs including flecainide. The possible mechanism, as Syeda et al. suggest, is the inhibition of I in the presence of flecainide, therefore increasing post-repolarization refractory and suppressing arrhythmias in LA with Pitx2 deficiency.[15] Some experimental studies also suggest that the interaction of flecainide with I and RyR plays an important role[26, 30]. The precise antiarrhythmic mechanism of flecainide on Pitx2-induced AF remains unsettled. In this study, our results provide novel mechanistic insights on the crucial role of actions of flecainide on I and RyR in its antiarrhythmic effect. Our simulation study suggests inhibition of I alone in the presence of flecainide plays a minor role in suppressing AF. It is known that the action of flecainide on RyR can suppress triggered activity, for example, the previous studies on the flecainide therapy in catecholaminergic polymorphic ventricular tachycardia.[22, 26] Furthermore, flecainide had antiarrhythmic effects on Pitx2-induced AF due to its action on I by prolonging WL, decreasing susceptibility of tissue to re-entrant arrhythmias ().

However, flecainide also had adverse effects in Pitx2-induced AF. On the one hand, both of Pitx2-induced structural remodelling and the action of flecainide on I can slow CV and facilitate re-entry. On the other hand, both of Pitx2-induced electrical remodelling and the actions of flecainide on ion channels may increase the RA-to-LA electrical heterogeneity, promoting APD dispersion and thereby unidirectional conduction block indexed by VWRA-LA[31, 32]. These findings support the notion that flecainide is not recommended in patients with structural heart disease due to high proarrhythmic risk based on the clinical findings[43]. Thus, flecainide may be an effective antiarrhythmic drug for the treatment of Pitx2-induced AF patients without the structural disease[42, 44, 45].

Limitations

Although the CRN model is based on human measurements, it cannot reproduce DADs due to overloaded calcium in the SR[46]. Therefore, the CRN model was modified and validated to generate our basal model (CRN-TPA) developed by our group[24]. In this study, the modified Grandi model and the CRN-TPA model were chosen as they are able to reproduce human AP morphology, triggered activity (, APD rate dependence and excitation dynamics for studying re-entrant arrhythmias in human atrial tissue[24, 47, 48]. There are several limitations special to this study here. Firstly, effects of Pitx2 insufficiency were assumed to be qualitatively similar between human and animal atria. Furthermore, in agreement with an experimental study[21] in which the extent of remodelling due to Pitx2 deletion was found to be dependent on the amount of Pitx2 expression, the ratio of remodelling between LA and RA was set to be 100:1. These assumptions warrant further investigations. Secondly, although we predicted Pitx2-induced AF phenotypes, including DADs in LA myocytes and ectopic beats and re-entry in LA tissues, these models do not explicitly represent subcellular calcium dynamics to simulate calcium sparks and the effects of the drugs on them[37, 38]. These ectopic beats in LA tissues were simulated by synchronizing LA cells and this protocol was based on experimental studies showing that spontaneous calcium releases are synchronous and overcome source-sink mismatch to generate focal arrhythmias in intact hearts[49-51]. Therefore, the mechanisms underlying spatiotemporal synchronization of SR calcium release in atrial tissue should be further explored. Thirdly, fibrosis was modelled as nonconducting tissue in this study as consistent with our previous studies[52, 53] and others[54]. In contrast, fibrosis was electrically coupled with healthy myocytes in some modelling studies[55]. Although different methodologies were used to model fibrosis in the past, they all draw the similar conclusions with regard to the role of fibrosis in AF[52, 56–58]. Finally, the precise spatial distribution of Pitx2 throughout human atria was unknown, therefore the regional difference in the cellular properties and remodelling was not investigated. Furthermore, we modelled atrial heterogeneity in the RA-LA tissue by considering the difference in I[28]. However, the ionic differences between the RA and LA are more diverse [59, 60], and this intrinsic heterogeneity should be considered. In addition, our idealized RA-LA tissue model did not include transition regions between RA and LA, electrical properties of transition regions, realistic geometry of these subregions, and fibre orientation. These limitations lead to a sharp transition between the RA and LA in our idealized tissue model. Special attention should be paid to explain our simulated results, and the effects of these factors on perpetuation and maintenance of re-entrant excitation should be further investigated[52]. Therefore, how the Pitx2-dependent gene regulatory network affects calcium homeostasis, intrinsic electrical heterogeneity, tissue structure, and atrial rhythm provide opportunities for further studies.

Conclusions

Electrical and structural remodelling due to Pitx2 deficiency promoted arrhythmogenesis, leading to the development of after-depolarizations and re-entrant excitation. Effects of the class Ic AAD flecainide on AP morphology and tissue dynamics under Pitx2 deletion conditions, particularly its interaction with RyR for preventing spontaneous calcium release, demonstrated that flecainide is effective for the treatment of Pitx2-induced AF patients without structural diseases. We expect that these and analogous efforts will contribute to improved platforms for AF risk determination and therapeutic stratification.

Intracellular structures of the Courtemanche et al. model (CRN), our human atrial (TPA) model and a new human atrial model (CRN_TPA) constructed by integrating the calcium dynamics of our TPA model into the CRN model.

The CRN_TPA model was developed by combining the calcium handling formulations from the TPA model and the transmembrane currents of the CRN model. The cell space includes a sub-cellular compartment dyadic cleft (SS), the sarcoplasmic reticulum (SR), the cytoplasm and cell membrane.

(DOCX)

Click here for additional data file.

Interactions of Class Ic AAD flecainide with ion channels.

Dose-response for the inhibitory effects of flecainide on INa, IKr, and RyR showed that IC50 values are 84±4 μM, 1.5±0.1 μM, and 55±8 μM, respectively. Abbreviations: AAD–antiarrhythmic drug; RyR–ryanodine receptor; IC half-maximal inhibitory concentration.

(DOCX)

Click here for additional data file.

Role of individual remodelled targets in the Pitx2 deficiency-induced atrial fibrillation.

Effects of individual remodelled targets (IK1, INa, IKs, ICaL, RyR or SERCA) on AP (a), RMP (b), overshoot (c), dVdtmax (d), APD (e) and CaSR (f). Effects of reversing remodelled individual targets on key indicators (g-l). haBlue arrows indicate spontaneous delayed afterdepolarization (DAD). Abbreviations: RyR–ryanodine receptor; SERCA–calcium transport ATPase; AP–Action potential; RMP–resting membrane potential; dVdtmax–maximum upstroke velocity; APD–action potential duration; CaSR–sarcoplasmic reticulum calcium content.

(DOCX)

Click here for additional data file.

Antiarrhythmic effects of flecainide on action potentials (AP, Vm) of LA and RA cells under control, Pitx2-1, Pitx2-2, Pitx2-3 and Pitx2-4 conditions.

a, Comparison of APs of LA (red) versus RA (gray) cells in the presence of 2μM flecainide under control and four Pitx2-deficiency conditions. The main AP parameters included RMP (b), overshoot (c), dVdtmax (d) and APD (e). Within clinical dose (0.5~2 μM), flecainide reduced dVdtmax (f) and prolonged APD (g). Abbreviations: LA–left atrium; RA–right atrium; Fle–flecainide; RMP–resting membrane potential; dVdtmax–maximum upstroke velocity; APD–action potential duration.

(DOCX)

Click here for additional data file.

Antiarrhythmic effects of flecainide on electrical (Vm) and calcium (Cai) waves.

Compared with Vm and Cai waves in the drug-free Pitx2-4 settings (a), these waves in the presence of 2 μM flecainide on targeting INa (b), on Ikr (c) and on RyR alone (d) respectively. Blue arrows indicate spontaneous delayed afterdepolarizations, triggered action potentials and calcium transients. Within clinical dose (0.5~2 μM), flecainide reduced CV (e) and prolonged WL (f). Abbreviations: RyR–ryanodine receptor; CV–conduction velocity; WL–Wavelength.

(DOCX)

Click here for additional data file.

Effects of fibrosis and cell-to-cell uncoupling on ectopic beats.

a, Simulated spontaneous ectopic activity and re-entrant waves in the tissue model with increased fibrosis. b, Simulated ectopic activity and re-entrant waves in the tissue model with cell-to-cell uncoupling.

(DOCX)

Click here for additional data file.

Vulnerable window (VW) of unidirectional block from premature stimulation.

Bidirectional conduction block, unidirectional conduction block and bidirectional conduction in the drug-free Pitx2-4 settings (a) versus in the presence of 2 μM flecainide (b). VW under Pitx2-1, Pitx2-2, Pitx2-3 and Pitx2-4 conditions in the drug-free Pitx2-4 settings (c) versus in the presence of 2μM flecainide (d).

(DOCX)

Click here for additional data file.

Simulated action potentials (AP) of left atrial (LA) and right atrial (RA) cells under controls and Pitx2-induced remodelling conditions.

At a pacing frequency of 2Hz, AP under control, Pitx2-1, Pitx2-2, Pitx2-3 and Pitx2-4 conditions. Black and grey markers were used for LA and RA cells, respectively. Blue arrows indicate spontaneous delayed afterdepolarizations and triggered action potentials.

(DOCX)

Click here for additional data file.

Effects of Pitx2-induced remodelling on action potential duration (APD) restitution properties.

(a-e) APD restitution curves for control, Pitx2-1, Pitx2-2, Pitx2-3 and Pitx2-4 conditions. Black and grey markers were used for LA and RA cells, respectively. Abbreviations: APD–action potential duration; DI–diastolic interval; LA–left atrial cell; RA–right atrial cell.

(DOCX)

Click here for additional data file.

Simulated action potentials (AP) of left atrial (LA) and pulmonary vein (PV) cells under controls and Pitx2-induced remodelling conditions.

At a pacing frequency of 2Hz, AP under control, Pitx2-1, Pitx2-2, Pitx2-3 and Pitx2-4 conditions. Black and red markers were used for LA and PV cells, respectively. Blue arrows indicate spontaneous delayed afterdepolarizations and triggered action potentials.

(DOCX)

Click here for additional data file.

Ionic differences in regional cell models.

(DOCX)

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A quantitative summary of electrophysiology characteristics for left atrial (LA) and pulmonary vein (PV) cells under controls and Pitx2-induced remodelling conditions.

(DOCX)

Click here for additional data file.

Re-entry in 2D idealized geometry under the drug-free Pitx2-4 condition.

(AVI)

Click here for additional data file.

Re-entry in 2D idealized geometry under the Pitx2-4 condition in the presence of 2 μM flecainide.

(AVI)

Click here for additional data file.

Supplementary Methods and Results.

(DOCX)

Click here for additional data file.

13 Sep 2019

Dear Dr Zhao,

Thank you very much for submitting your manuscript, 'Resolving the mechanism underlying increased susceptibility to atrial fibrillation in patients with impaired Pitx2', to PLOS Computational Biology. As with all papers submitted to the journal, yours was fully evaluated by the PLOS Computational Biology editorial team, and in this case, by independent peer reviewers. The reviewers appreciated the attention to an important topic but identified some aspects of the manuscript that should be improved.

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Reviewer's Responses to Questions

Comments to the Authors:

Please note here if the review is uploaded as an attachment.

Reviewer #1: This is an interesting modelling study of the role of genetic factors in the role of atrial fibrillation (AF). Specifically, the study focuses on mechanisms underlying Pitx2 deficiency-induced AF, as well as effects of anti-arrhythmic drug (AAD) flecainide in AF patients with Pitx2 down-regulation. Pitx2 deficiency promoted AF arrhythmogenesis in single-cell and tissue atrial models through to the development of after-depolarizations and re-entrant excitations, whereas flecainide prevents both. Overall, the work is novel and interesting, but the paper could benefit from clarification and a better presentation of some of the results. Please see my specific comments and suggestions below.

1) The paper claims that “the introduction of flecainide fails to reverse the RA-to-LA electrical heterogeneity”. However, it also stated that “in the presence of 2 μM flecainide, a planar wave … produced a spiral wave within a shorter VW” (compared to the flecainide-free case, by less than 1 ms). It has been shown in several studied that shorter VW is a sign of reduced electrical heterogeneity (Colman et al., 2014; 16: 416-23, Varela et al., 2016; 12: e1005245). Hence, I would expect that APD dispersion under flecainide should be reduced by 1-2 ms – was this measured? From the figures presented this is impossible to conclude, would it be possible to provide the actual numbers? It is also worth referencing the aforementioned studies, as they demonstrate the important role of increased atrial heterogeneity in AF arrhythmogenesis, and the modulating effects of AADs on the APD and APD dispersion. If flecainide in this study indeed reduces atrial heterogeneity even by a few ms, it should contribute to its anti-arrhythmic effect, as shown in the studies by Colman and Varela.

2) Four genetic variants Pitx2-1, -2, -3, -4 are considered in single-cell, 1D and 2D tissue models and multiple electrophysiology characteristics are measured in each case. Due do the large number of cases considered, it’s not easy to see the general picture. The paper could benefit from one or more tables summarizing these multiple characteristics and their inter-relations (e.g., APD and VW increased/decreased, triggered activity or re-entry present/absent, etc).

3) Atrial heterogeneity itself is modelled quite simplistically, which is a major limitation. First, there is a sharp transition between the RA and LA, which is non-physiological, since there is no direct conduction between the chambers (and even if there was, it would not have been a sharp charge). Moreover, RA-LA differences are accounted for by changing only one ionic current, IKr. However, ionic difference between the RA and LA are more diverse (Colman et al., J Physiol. 2013; 591: 4249-72). This should at least be mentioned in Limitations.

4) Whereas all four Pitx2 models are characterised by shorter APD in the LA compared to RA, other AP characteristics change differently between the chambers and Pitx2 models. For example, RMP is higher in the LA in Pitx2-1 and Pitx2-4, but higher in the RA in Pitx2-2 and Pitx2-3; moreover, these difference are rate-dependent (Figure 2). It’s worth discussing what are ionic mechanisms of such differences, and which Pitx2 model may be most physiological.

5) I think some phrasing throughout the paper can be improved. First, the title “Resolving the mechanism…” makes an excessively strong statement and should be toned downed. Similarly, a statement about “demystifying” the role of Pitx2 in Introduction should be moderated. Then the second para of Introduction uses a lot of terms and jargon specific to a narrow research field and is difficult to follow – please re-write using more general terms. Finally, in what sense are rs2200733 and rs10033464 “the most important variants”?

6) Figure 5d and f are difficult to interpret (f in particular). Are we looking at the voltage? Do all cells in panels f fire at once (going from blue to yellow) and then become desynchronised (mixture of blue and yellow in the last two panels)? These patterns look non-physiological. Why in panels d the patterns are different, with desynchrony seen already in the second panel? Please also see comment 2 above about better systemising all results in the paper.

Reviewer #2: This study by Bai et al. uses computational simulations to investigate the effects of impaired Pitx2 properties on atrial fibrillation susceptibility and reentry properties. The study uses single cell, 1D and 2D simulations to investigate these effects, comparing four different Pitx2 cell model representations. The effects of flecainide are then simulated on one of the cell model variants. This represents a nice and well-designed use of simulation to investigate AF mechanisms, incorporating available experimental data. I have a few main comments, and some minor comments for improving the presentation of the study.

Main comments:

1) The results of this study may be highly dependent on the choice of atrial cell model. The authors show that calcium dynamics are important in predicting the effects of pitx2. Please could the authors justify their choice of cell model, and if possible predict how their findings would change with the use of a different atrial cell model?

2) How do you think pulmonary vein cell response would compare to the left atrial cell model findings here? Could you perform a subset of simulations for a cell model with ionic properties modified to match pulmonary vein cells and see how DAD incidence and action potential properties change?

3) The parameter changes for the different Pitx2 cell models should be included in the main body of the text rather than just in the supplement as this is fundamental to the study.

4) It would be helpful to have more quantitative results in the text and not simply in the figures.

Minor comments:

Abstract:

• “Secondly, our study suggests...” It isn’t clear whether this finding is with or without Pitx2 changes, and which of the parameter sets it refers to.

Introduction:

• “The lack of Pitx2 can alter right-left atrium…” this sentence is very unclear.

Results:

• Are there are reported differences between Pitx2 level in the appendages or pulmonary veins compared to the atrial body?

• Section 3.1 is methods not results. It might be clearer to include the methods section first and then the results section.

• Why did you decide to use 1Hz and 2Hz pacing? Is 2Hz fast enough to test restitution properties? Please could you test the restitution properties of each cell model?

• The text says heterogeneity in AP features between RA and LA increased to varying degrees, and then later it says differences between RA and LA cells remained unchanged. Please clarify.

• Please include values in the text to support your statements. How much did APD decrease by etc.

• How did the Pitx2-3 cells respond to the block effect of flecainide?

• It would be very interesting to see how these differences in LA vs RA response affect AF simulations in a realistic bi atrial model.

• “Persistently triggered activity was observed in the model with both cell-to-cell uncoupling and fibrosis”. Could you quantify this in terms of frequency of triggers, amount of uncoupling and degree of fibrosis?

• Please comment on the magnitude of the change in vulnerable window size. It seems like a small change with flecanide?

Discussion:

• Key finding 2: Increased fibrosis and decreased cell-to-cell coupling…” Did you show these anchor reentry in this paper?

• High “accidence” of AF – should be “incidence”

• Limitations: Please discuss the choice of cell model.

• Limitations: The effect of fibrosis modeling methodology has been shown to affect simulated AF dynamics in previous studies.

Methods:

• Please include more details on how this model differs from the original CRN model and also on % changes in conductances for each Pitx2 model.

• Please include a reference for IC50 values.

• How much did CV change by for the reduced diffusion coefficient simulations?

• What % of cells were normal, Pitx2-4 and fibrosis in the simulations? Did you investigate the sensitivity of simulation outcome to this?

• Please include a link to your github.

Figure 1: Make subfigure d larger

Figure 4: Are any changes significantly different?

Figure 5: Not clear what b-f show?

**********

Have all data underlying the figures and results presented in the manuscript been provided?

Large-scale datasets should be made available via a public repository as described in the PLOS Computational Biology data availability policy, and numerical data that underlies graphs or summary statistics should be provided in spreadsheet form as supporting information.

Reviewer #1: Yes

Reviewer #2: Yes

**********

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Reviewer #1: Yes: Oleg Aslanidi

Reviewer #2: No

15 Dec 2019

Submitted filename: RebuttalLetter_15Dec_2019_Final.pdf

Click here for additional data file.

22 Jan 2020

Dear Dr Zhao,

We are pleased to inform you that your manuscript 'In silico investigation of the mechanisms underlying atrial fibrillation due to impaired Pitx2' has been provisionally accepted for publication in PLOS Computational Biology.

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Daniel Beard

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Reviewer's Responses to Questions

Comments to the Authors:

Please note here if the review is uploaded as an attachment.

Reviewer #1: The authors did a great job revising the manuscript and carefully addressing all the reviewers' comments. All points raised previously have been clarified and the new figures and tables are highly informative. I can only congratulate the authors.

Reviewer #2: Thank you for responding to all of my comments. Congratulations on an interesting and thorough study.

**********

Have all data underlying the figures and results presented in the manuscript been provided?

Large-scale datasets should be made available via a public repository as described in the PLOS Computational Biology data availability policy, and numerical data that underlies graphs or summary statistics should be provided in spreadsheet form as supporting information.

Reviewer #1: Yes

Reviewer #2: Yes

**********

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Reviewer #1: Yes: Oleg Aslanidi

Reviewer #2: No

20 Feb 2020

PCOMPBIOL-D-19-01121R1

In silico investigation of the mechanisms underlying atrial fibrillation due to impaired Pitx2

Dear Dr Zhao,

I am pleased to inform you that your manuscript has been formally accepted for publication in PLOS Computational Biology. Your manuscript is now with our production department and you will be notified of the publication date in due course.

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Thank you again for supporting PLOS Computational Biology and open-access publishing. We are looking forward to publishing your work!

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Table 1

Review of Pitx2-insufficiency induced remodelling data and model parameters in human left atrium.

Process	Experimental observation	Control	Pitx2-1	Pitx2-2	Pitx2-3	Pitx2-4
INa	-60% (SCN5A & SCN1B) (Chinchilla et al., 2011); -40% (SCN5A & SCN1B) (Lozano-Velasco et al., 2017); +95% SCN5A (Nadadur et al., 2016); No Change (Syeda et al., 2016)	—	—	—	—	+10%
IKs	+150% KCNQ1(Tao et al., http://circgenetics.ahajournals.org/2014); +100% (Pérez-Hernández et al., 2015); Increased volt-dependent potassium current (Kirchhof et al., 2011)	—	—	+100%	—	+150%
IK1	-20% (KCNJ2 & KCNJ12) (Chinchilla et al., 2011); +30 (KCNJ2 & KCNJ12) (Lozano-Velasco et al., 2017); -25% (Syeda et al., 2016)	—	-25%	—	—	-30%
ICaL	+500% CACNA1D (Tao et al., 2014); -50% (Pérez-Hernández et al., 2015); -50% (Lozano-Velasco et al., 2015); -30% CACNA1C (Lozano-Velasco et al., 2017); Decreased CACNA1C (Kirchhof et al., 2011)	—	—	-50%	-50%	-30%
SERCA	+50% ATP2A2(Tao et al., 2014); +1000% ATP2A2(Lozano-Velasco et al., 2015); +100% ATP2A2(Lozano-Velasco et al., 2017); +12% ATP2A2 (Nadadur et al., 2016)	—	—	—	+200%	+100%
RyR	+145% RyR2 (Tao et al., 2014); +30% RyR2 (Lozano-Velasco et al., 2015); +30% RyR2 (Lozano-Velasco et al., 2017); +10% RyR2 (Nadadur et al., 2016)	—	—	—	+30%	+30%
Gap junctions	-55% GJA1(Chinchilla et al., 2011); -5% GJA1(Nadadur et al., 2016); +100% GJA1 (Tao et al., 2014); +1000% (Pérez-Hernández et al., 2015); -50% (Pérez-Hernández et al., 2015);-58% (Kirchhof et al., 2011)	—	-50%	-50%	-50%	-50%

Note: The remodelling in human right atrium is %1 of that in human left atrium. Abbreviations: RyR–ryanodine receptor; SERCA–calcium transport ATPase.

Table 2

A quantitative summary of electrophysiology characteristics.

			Control	Pitx2-1	Pitx2-2	Pitx2-3	Pitx2-4	Control+F	Pitx2-1+F	Pitx2-2+F	Pitx2-3+F	Pitx2-4+F
Cell	RMP	RA	-79.89	-79.81	-79.87	-79.97	-79.86	-81.62	-81.59	-81.63	-81.77	-81.67
		LA	-80.97	-77.45	-82.05	-84.38	-83.23	-82.10	-78.90	-83.23	-85.94	-82.82
	OS	RA	24.25	24.23	24.24	24.29	24.25	24.15	24.14	24.16	24.23	24.20
		LA	24.73	22.75	24.86	25.33	27.73	24.45	22.45	24.56	24.94	27.01
	dVdtmax	RA	205.7	205.3	205.6	206.0	205.7	205.6	205.5	205.6	206.2	205.9
		LA	209.1	193.8	211.9	215.8	231.4	207.6	192.9	210.2	212.9	226.3
	TA	RA	No	No	No	No	No	No	No	No	No	No
		LA	No	No	No	Yes	Yes	No	No	No	No	No
	APD	RA	292.5	292.7	292.0	290.6	291.5	358.9	359.1	358.3	356.8	357.5
		LA	246.5	258.7	221.1	204.2	224.5	333.4	354.9	280.8	237.5	261.6
	ΔAPD		46.0	34.0	70.9	86.4	67.0	25.5	4.2	77.5	119.3	95.9
1D	CV	RA	48.61	48.62	48.60	48.59	48.63	47.24	47.27	47.25	47.23	47.28
		LA	48.48	34.56	33.27	33.01	35.59	47.22	33.46	32.45	32.25	34.53
	ΔCV		0.13	14.06	15.33	15.58	13.04	0.02	13.81	14.8	14.98	12.75
	WL	RA	13.69	13.70	13.66	13.65	13.66	18.57	18.59	18.54	18.44	18.50
		LA	11.49	8.571	7.087	6.735	7.295	17.11	13.36	9.791	7.887	9.641
	ΔWL		2.2	5.129	6.573	6.915	6.365	1.46	5.23	8.749	10.553	8.859
	TA		No	No	No	Yes	Yes	No	No	No	No	No
	VWRA-LA		293.8–294.5	324.8–327.8	293.8–295.8	291.8–298.8	291.8–294.8	359.8–360.8	398.8–402.8	332.8–349.8	332.8–352.8	332.8–349.8
2D	Re-entry		-	-	-	-	Yes	-	-	-	-	No
	TA		-	-	-	-	Yes	-	-	-	-	No

Note: In order to evaluate the RA-to-LA electrical heterogeneity, VWRA-LA of unidirectional conduction block, an index to quantify the RA-to-LA electrical heterogeneity, was quantified by varying the S1-S2 interval in the RA-to-LA strand model with 250 RA myocytes and the other 250 LA cells. The protocol included 10 S1 stimuli applied at the end of the RA part and an S2 stimulus applied at the end segment of the atrial strand.