Abstract
Cardiac electrical activity is controlled by the carefully orchestrated activity of more than a dozen different ion conductances. Yet, there is considerable variability in cardiac ion channel expression levels both within and between subjects. In this study we tested the hypothesis that variations in ion channel expression between individuals are not random but rather there are modules of co-expressed genes and that these modules make electrical signaling in the heart more robust.
Meta-analysis of 3653 public RNA-Seq datasets identified a strong correlation between expression of CACNA1c (L-type calcium current, ICaL) and KCNH2 (rapid delayed rectifier K+ current, IKr), which was verified in mRNA extracted from human induced pluripotent stem cell-derived cardiomyocytes. In silico modeling indicates that the co-expression of CACNA1c and KCNH2 limits the variability in action potential duration and reduces susceptibility to early afterdepolarizations, a surrogate marker for pro-arrhythmia.
Introduction
Robust electrical signaling in the heart is critical for co-ordinating the efficient pumping of blood around the body. Failure of cardiac electrical signaling, even for just a few minutes, can have fatal consequences, with sudden cardiac death accounting for up to 10% of deaths in our community (1). Despite decades of research, predicting in advance who is more or less susceptible to sudden cardiac death remains challenging (2).
The action potential (AP) of excitable cells, such as cardiac myocytes and neurons, reflects the orchestrated activity of at least a dozen distinct ion channels and electrogenic transporters (3) (4). In such complex systems, both theoretical and experimental studies have shown that there is considerable inter-individual variability in the combinations of molecular input parameters that can produce very similar integrated outputs (5) (6). This has led to a paradigm shift in computational modeling that relies not on generating idealized outputs based on mean data but rather development of populations of models that account for the observed variability in molecular inputs (7) (8). Such models are already proving useful for interrogating inter-individual variability in response to pathological stimuli (9) (10) (11). Our challenge now is to discern the underlying essence of these complex systems (12,13) so that we may then make rational interventions to treat pathology that takes into account inter-individual variation. Specifically, are there underlying principles regulating cardiac electrical activity that can provide insights into why some people are more susceptible to sudden cardiac death in response to pathological stimuli, such as drug block of the rapid delayed rectifier potassium channel (IKr) which is the underlying basis of drug-induced long QT syndrome (di-LQTS) (14).
A common approach to discern patterns in multi-dimensional biological problems has been to look for co-expression networks (13) (15). Co-expression networks are known to encode functional information (16), with co-expression reflecting co-regulation and co-functionality (17) (18). To help identify robust co-expression modules, it is helpful to use meta-analytical approaches, as the aggregation of large numbers of individual networks across multiple independent experiments averages away noise and reinforces those correlations that reflect real signals (19) (20) (21).
Here, we have used meta-analytic co-expression analysis in large scale human gene expression data sets to identify modules of co-expressed ion channel genes which were then used to constrain population models of cardiac electrical activity. These models were then used to test the hypothesis that co-expression of repolarization and depolarization currents helps prevent irregular action potentials from emerging when human cardiac myocytes are exposed to pro-arrhythmic stimuli. We show that tight coupling of current densities for the L-type calcium current (ICaL) and the rapid component of the delayed rectifier potassium current (IKr) reduced the emergence of pro-arrhythmic early afterdepolarizations (EADs) and this protection persisted in the face of highly variable expression of other ion channels, as well as in the presence of pharmacological block of IKr, a potent pro-arrhythmic stimulus (22). A very important prediction to arise out of our modelling studies is that in the context of drug block of IKr those patients with high expression of ICaL and IKr experience more EADs and are therefore more likely to be susceptible to ventricular arrhythmias.
Results
The shape and duration of action potentials in cardiac myocytes are determined by the orchestrated activity of voltage-gated sodium, calcium and potassium channels, as well as a series of electrogenic transporters that regulate intracellular ion concentrations (See Supplementary data Figure S1). These channels, transporters and related intracellular calcium handling proteins are encoded by a few dozen genes, sometimes referred to as the rhythmonome (23) (see Supplementary data, Table 1).
To determine whether there were any co-expression patterns among the rhythmonome genes we first undertook an untargeted screen for possible expression correlation patterns in publicly available RNA-seq data sets (see list of RNA-seq experiments in supplementary data, Table 2). Ranked correlation coefficients from an aggregate co-expression network that contain data from 3653 samples are illustrated in the heatmap in Figure 1A. High ranked correlations indicate similarity of transcriptional profiles between the genes. A clustering analysis, as shown by the dendrogram in Figure 1A, groups genes according to their correlation similarities, as defined by the Spearman’s correlation coefficients (see color code in Figure 1A). There is a large cluster of yellow/green squares in the bottom left corner indicating that there are significant levels of correlation amongst many of the genes. Furthermore, within this large cluster there are two sub-clusters. The cluster of yellow-green squares corresponding to 13 genes in the bottom left corner (red dashed box in Figure 1A) encode for proteins that regulate calcium fluxes as well as the transient outward K+ current (KCND3), which helps to maintain the plateau potential at a level that maximizes calcium influx (24). A second sub-cluster, in the upper right quadrant of the main cluster, encompasses 10 genes (black dashed box in Figure 1A), including KCNH2, SCN5a, KCNJ12 and KCNIP2, that encode for ion channel proteins important for regulating action potential duration (APD).
Overall, the connectivity within the set of rhythmonome genes is fairly high in comparison to their connectivity to all other genes in the co-expression network (node degree analysis, p∼5.7e-14), with a central gene being CACNA1C, the gene encoding the alpha subunit of the L-type calcium channel (see Supplementary data, Figure S2). Although CACNA1c clusters in the group of calcium handling genes in the bottom left quadrant of the main cluster in Figure 1A, it also shows high levels of correlation with the cluster of ion channel genes in the top right quadrant of Figure 1A. In a similar fashion, the KCNH2 gene, which encodes for IKr, is included in the ion channel cluster but also shows moderate-high correlations with a portion of the calcium handling genes in the bottom left quadrant. The highest ranked co-expression partners for CACNA1C and KCNH2 are highlighted in Figure 1B.
The vast majority of the public RNA-Seq datasets included in our analyses were not heart specific. It is, however, noteworthy that there are no strong correlations between the expression of any of the individual ion channel or calcium handling genes and the cardiac-specific markers included in our analyses: GATA-4, NKX2-5, MYL2 and MYL7. For example, the cardiac marker genes are towards the bottom of the lists in Figure 1B. This suggests that the correlations within the set of rhythmonome genes are not simply a reflection of cardiac specific expression but rather represent intrinsic correlations.
The degree of network connectivity for each rhythmonome gene within the local rhythmonome network (y-axis) versus its connectivity within the whole genome (x-axis). All the rhythmonome genes are more highly connected within the local network (i.e., all the points lie above the line of identity, p∼5.7e-14). CACNA1C is highlighted in red and KCNH2 in yellow.
To investigate whether the meta-analytic co-expression patterns observed in Figure 1 were also seen in human heart cells, we extracted mRNA from human induced pluripotent stem cell-derived cardiomyocytes (hiPSC-CMs) (27) obtained from 10 patients with no known heart disease. All samples contained high levels of cardiac marker genes (MYL7, GATA4 and NKX2.5) (Figure 2A). Furthermore, the levels of expression of the housekeeper genes, GPADH and HRPT1 were similar across samples (see data at right side of Figure 2A). The levels of expression of most rhythmonome genes showed variations between the samples that spanned approximately an order of magnitude. However, similar to the generic tissue RNA-Seq datasets, there were modules of co-expressed genes (e.g., see dashed box in bottom left quadrant of Figure 2B). Most of the 13 genes in the cluster in Figure 2B are present in the modules highlighted by the black and red dashed boxes in Figure 1A. Conversely, many of the ion channel genes contained in the modules highlighted in Figure 1 are not present in the module in Figure 2 (e.g. KCNJ2/KCNJ12, which encodes for IK1; KCND3, which encodes for ITo; and SCN5a, which encodes for INa). These genes are all known to be expressed at lower levels in embryonic hearts and so unsurprisingly they are not well expressed in the hiPSC-CM lines (28).
We next looked to see if there were any specific relationships between genes encoding depolarization and repolarization currents, within the hiPSC-CM expression profiles. In Figure 2C, we have plotted the expression of KCNH2 versus the genes that encode for the depolarization currents that showed the highest levels of correlation with expression of KCNH2 in the generic tissue datasets (see Figure 1B, i.e., CACNA1c, CACNA1H and SCN5a). The most notable correlation that was observed in the hiPSC-CMs was that between KCNH2 and CACNA1c; r2 = 0.89 (Figure 2C).
As the only robust relationship that we observed in both the generic tissue sets and the hiPSC-CM lines was the co-expression of KCNH2 and CACNA1c, we focused on this pair for our subsequent studies. To investigate whether co-expression modules of ion channel genes might influence integrated cardiac electrical function, we used an in silico approach. First, we simulated a population of 1000 human cardiac action potentials where random scalar values, chosen from a log normal distribution with mean 1 and standard deviation of 0.5 (Figure 3A, lower panel), was applied to every conductance in each iteration of the action potential model (see Figure 3A and Supplementary Data, Movie S1).
The baseline action potential produced by this model (black trace in right hand panel of Figure 3A) has a duration at the point of 90% repolarization (APD90) of 264 ms. The population of 1000 cardiac cells generated by randomly scaling the conductances exhibited APD90 values that ranged from ∼120 ms to ∼500 ms (Figure 3A, right panel, and Figure 3B). We next selected those cells with APD90 values that fell within 20% of the mean value (red bars, Figure 3B) to determine if there were any patterns of ion channel co-expression that could contribute to keeping the APD90 within this narrow selected range. The correlation matrix of the conductance scaling factors for the selected cells (Figure 3C) reveals a positive correlation between GKr and GCaL (R=0.36) as well as an inverse correlation for GKr and GKs (R=-0.46). The positive correlation between the conductance scalars GKr and GCaL in the in silico modelling dataset (Figure 3) suggests that the correlation seen between CACNA1c and KCNH2 mRNA expression in both the public RNA-Seq datasets (Figure 1) and the hiPSC-CM dataset (Figure 2) would contribute to reducing the population variability in APD90 values.
We next repeated our previous simulation of 1000 action potentials but forced the conductance scaling factors for IKr and ICaL to be identical in each cell (denoted co-expression in Figure 4, also see Data supplement, Movie S2). The scaling factors for all other conductances remained independent. The distribution of APD90 values for both independent and co-expression cell populations becomes broader as the level of variability is increased (Figure 4A-C). However, the spread of APD90 values in the cells with identical GCaL-GKr scalars is always narrower than in the cell populations with independent GCaL-GKr scalar values. For example, in the case of Figure 4B, the variance of the APD90 values was 0.026 for the co-expression dataset but 0.046 for the independent dataset (see supplementary data Figure S3-C). Another notable feature of the data in Figure 4C is that early afterdepolarisations (EADs) begin to appear in the cell population with independent scalars when the scalar variability, σ2, exceeds 0.20 (also see supplementary data Figure S4). The number of cells with an EAD are indicated in parentheses above each distribution in Figure 4C.
We next investigated whether coupling of the conductance scalars for GKr and GCaL influenced the generation of EADs in response to a pathological stimulus. Specifically, how cells respond to drug block of IKr, the underlying cause of di-LQTS (22). Example populations of action potentials obtained for independent and co-expression populations with IKr block of 0%, 50% and 80% are illustrated in Figure 5. As the extent of IKr block is increased (from A to C), the proportion of simulated action potentials producing EADs increases. It is also clear that at lower levels of IKr block, EADs were more frequent when GCaL and GKr scalars were modulated independently (see Figure 5B and inset to Figure 5D). However, the proportion of simulations developing EADs in both the independent and co-expression populations becomes similar when the extent of IKr block exceeds 80% (Figure 5D).
It is well established that only a subset of patients exposed to drugs that block IKr (29), or with a mutation causing 50% loss of IKr function (30), will develop life threatening arrhythmias. This is consistent with the prediction made by our simulated drug block experiments shown in Figure 5. We therefore asked whether the data from the co-expression datasets could tell us anything about what factors might predispose to the development of EADs in the presence of a drug that blocks IKr. Analysis of the subset of scalars within the co-expression dataset that produced the 50 longest APs without EADs, compared to the subset of scalars that resulted in APs with EADs, is illustrated in Figure 6A and 6B respectively. Notably, the longest APs without EADs had low GCaL scalars (and hence low GKr scalars) before addition of drug block. Conversely, the APs that developed EADs had higher GCaL and GKr scalars. In Figure 6C, we have plotted the APD90 values for cells in the highest (red) and lowest (blue) quartiles of GCal - GKr scalars. As expected, the low GCaL group showed longer APD90 values on average compared to the high GCaL group (see the continuous lines in Figure 6C). Furthermore, for the 70% IKr block scenario, 44% of the high GCaL group have developed EADs whereas only 7% of the low GCaL group have developed EADs (compare red and blue bars at 70% drug block in Figure 6C). Thus, higher GCaL is associated with a greater risk of developing EADs in response to moderate levels of IKr block. A similar pattern of results was observed when GCaL and GKr were allowed to vary independently, except that in this scenario the difference between the high GCaL and low GCaL groups was even more dramatic at lower levels of IKr block (see supplementary data Figure S4).
A corollary of our prediction that patients with high GCaL are more susceptible to EADs when exposed to a drug that blocks IKr, is that co-administration of a drug that blocks ICaL would reduce the incidence of EADs. Magnesium, which is used in the acute management of di-LQTS (14), is a weak calcium channel blocker. Raising plasma [Mg2+] from 1.5 to 2.5 mM would be expected to inhibit ICaL by ∼20% (31), conversely reducing [Mg2+] from 1.5 to 0.5 mM would be expected to increase ICaL by ∼20%. When we increased ICaL by 20%, the incidence of EADs in the high GCaL group increased from 10% to 16% for the 60% IKr block simulation and from 44% to 58% for the 70% IKr block simulations (see Figure 7). A drug that inhibited ICaL by 20% caused a modest decrease in the percentage of cells with EADs and reduction of ICaL by 50% had a correspondingly larger effect, for example, reducing EADs from 44% to 12% in the 70% IKr block scenario (Figure 7).
Discussion
Cardiac electrical activity is regulated by the interdependent activity of a plethora of ion channels, transporters and calcium handling proteins (4). Understanding the precise details of how these conductances interact to control the rhythm of the heart has been an enduring source of fascination. In this study, we have used meta-analytical techniques to interrogate the large numbers of RNASeq datasets that have been deposited in public access databases, to look for patterns of co-expressed genes that might help decipher the control of cardiac electrical activity. The most important pair of co-expressed genes, identified both in the public RNA Seq datasets (Figure 1) and in heart cells derived from hiPSC lines (Figure 2), was that of CACNA1c (ICaL) and KCNH2 (IKr). Using an in silico approach we demonstrated that tight co-expression of CACNA1c and KCNH2, against a background of variability of all other ion channels, helps to control the duration of repolarization (Figure 4). More importantly, the co-expression of CACNA1c and KCNH2 helps to protect the heart from early after depolarizations when they are exposed to drugs that block IKr (Figure 5). Our simulations also suggest that inter-individual differences in pro-arrhythmic responses to IKr drug block can be explained by inter-individual differences in levels of CACNA1c expression (Figure 6).
Over the last few years, numerous groups have shown that there is considerable heterogeneity of ion channel expression amongst excitable cells, including neurons (32) and cardiac myocytes (7,19). Furthermore, since the pioneering work of Eva Marder and colleagues, the presence of modules of co-expressed ion channel genes has also been well appreciated(15). These previous studies, however, relied on patch clamp analysis of isolated cells (15,33) and qPCR analysis (15) of individual ion channel mRNA, which are highly laborious and so have been restricted to only a few important ion channel genes. The advent of high throughput transcriptomic analyses has greatly facilitated the identification of conserved networks of co-expressed gene modules amongst the entire set of expressed genes (21). By applying meta-analytic approaches to a large number of independent datasets one can more readily discern genuine co-expression signals from noise, as well as explore smaller gene modules (21). In our analysis of a subset of rhythmonome genes (35 members, Table S1) within a large library of public RNA Seq datasets, (see Table S2) we identified two clusters of genes: a first subset that predominantly affects calcium handling and a second subset that predominantly affects membrane potential (see Figure 1). The nodes within each of these clusters that are most closely connected within the rhythmonome relative to all other genes are KCNH2 and CACNA1c (Figure S2). This is analogous to a network of networks (34), where the KCNH2-CACNA1c link provides an interconnection of the two networks. Independent evidence to corroborate an important link between calcium handling and regulation of cardiac action potential duration comes from the large genome-wide association studies (GWAS) of QT interval duration which identified SNPs in a number of calcium handling genes as well as KCNH2 as being important determinants of QT interval in the population (35).
Due to the large number of associations we were testing for in our network analyses, it is possible that some would occur by chance. That we were able to confirm the presence of at least some of the co-expression modules in an independent dataset, i.e. the hiPSC-CM (see Figure 2) provides important corroborative evidence that these co-expression patterns are real and therefore likely to have physiological relevance. It should also be noted that many ion channels important for function in adult cardiac myocytes are not expressed at significant levels in immature cardiac myocytes, such as those derived from hiPSC (e.g. SCN5a, KCNQ1, KCNJ12, KCND3, (28)). It is therefore possible that we have underestimated the number of genes within the modules of co-expressed genes in adult cardiac myocytes.
The patterns of co-expressed genes we observed show some important similarities, as well as differences to previous studies. Banyasz et al. (33) and Rees et al. (18) have both demonstrated that the expression of ICaL is correlated with the sum of the major repolarizing ion currents in guinea-pig and mouse respectively. However, the molecular players involved in cardiac electrical activity in rodents are quite distinct to humans (36). In humans, the most important determinant of repolarization duration at baseline is IKr (37), whereas in guinea-pig IKs and IKr play equally important roles (33) and in mice the fast component of the transient outward current (Ito,f) and the ultra-rapid delayed rectifier (IKur) are the major repolarization currents (18). Thus, there is a common factor between our study showing co-expression of KCNH2 and CACNA1c in human and the previous rodent studies, i.e., all studies show a correlation between ICaL and the major repolarizing currents present in that species. Our study, however, is the first to demonstrate the important co-expressed genes in human heart tissue.
Identifying modules of co-expressed genes are the first step in seeking to understand the logic of complex systems (6). Understanding how such modules impact function in health and disease is the next challenge. In neuronal cells, Marder and colleagues have shown that modules of co-expressed ion channels play an important role in regulating action potential firing patterns (38). Rees and colleagues, have demonstrated that modules of co-expressed depolarization and repolarization currents can help to ensure normal amplitude calcium transients, a critical determinant of overall heart function (18). We have extended these studies to show that in normal heart cells, co-expression of KCNH2 (repolarization) and CACNA1c (depolarization) channels help to maintain the plateau duration of the action potential, which in turn likely contributes to regulating the duration and amplitude of the calcium transient. More importantly, our studies provide the first insights into how patterns of co-expressed ion channel genes influence the hearts response to pathological stimuli.
Sudden death due to abnormalities of cardiac electrical signaling is a major cause of mortality (1). Predicting in advance who is more or less susceptible to sudden cardiac death and therefore warrants prophylactic treatment remains challenging (2). A key to being able to predict who is at greatest risk is understanding why different people respond differently to the same pro-arrhythmic stimulus. Based on the results of our in silico studies, we have provided two important insights into the nature of interindividual risk for developing arrhythmias in response to drugs that block IKr, the major cause of drug-induced cardiac arrhythmias (14). First, cells with low GCaL (and hence low GKr at baseline) exhibited the greatest prolongation of AP duration when exposed to IKr drug block. Second, cells with high GCaL (and hence high GKr at baseline) showed greater propensity for development of EADs at moderate levels of IKr drug-block (Figure 6). An important implication of the observation that a high GCaL increases the susceptibility to EADs in response to drug block of IKr is that the co-administration of an ICaL blocker should reduce the risk of EADs (as shown in Figure 7). This is consistent with the observation that the administration of magnesium, which is a mild calcium channel blocker (31), is helpful in the acute management of patients with drug-induced torsades de pointes (14), and conversely that hypomagnesaemia, which would stimulate ICaL, can exacerbate torsades de pointes (39). It is also consistent with the observation that drugs that block ICaL and IKr (e.g., verapamil) are not associated with drug-induced arrhythmias (40) and that verapamil prevented the development of torsades de pointes in rabbit hearts exposed to an IKr blocker (41). However, given that calcium channel blockers are contra-indicated in some ventricular arrhythmias (42), and the likelihood that patients who have drug-induced LQTS may have other underlying cardiac conditions (14), one should be cautious about prescribing calcium channel blockers. Conversely, it would be reasonable to consider using calcium channel blockers to treat patients with LQTS type 2 (i.e. patients with an isolated loss of IKr function) who continue to have cardiac events despite treatment with ß-blockers (43).
In summary, we have demonstrated that meta-analysis of large-scale gene expression data sets is a powerful technique for discerning underlying patterns in gene expression, and that this can provide insights into disease causation at an individual level. Specifically, we have demonstrated that the co-expression of KCNH2 (IKr) and CACNA1c (ICaL) plays an important role in regulating cardiac repolarization both in health and in disease.
Methods
Analysis of public RNASeq datasets
An aggregate co-expression gene network was built from public data, similar to that described previously(44). Briefly, 75 human RNA-seq expression experiments (listed in Supp Table S2) that passed quality control and had a least 10 samples (3653 samples in total) were downloaded from the Gemma database (45). Approximately thirty thousand genes were used for the network, limited only to those with Entrez gene identifiers. A co-expression network was generated for each experiment by calculating Spearman’s correlation coefficients between every gene pair and then ranking these values (44). An aggregate gene co-expression network was then generated by averaging across all the individual networks, and re-ranking the final network. This final aggregate network was then used to determine the co-expression ranking between genes that encode for the set of ion channels and calcium handling proteins that determine the shape and duration of the human ventricular AP, the so-called rhythmonome gene subset (see Supp Table S1). Network connectivity of the gene set was measured by comparing the weighted local node degree to the global node degree(46). Node degrees are the sum of the total connections a node (here gene) has within a network. Local node degree refers to the sum of connections (here the ranked correlation) within the rhythmonome gene set, while global node degree is the sum of connections to that gene across all the genes in the network. Code for the analysis is available at https://github.com/sarbal/hERG-cal
Human induced pluripotent stem cell derived cardiac myoctes
Human iPSC lines, generated from healthy patients by Stanford Cardiovascular Institute Biobank, as previously described (47), were a generous donation from Joseph Wu (Standford Cardiovascular Institute). HiPSC colonies were maintained on Matrigel® (Corning) coated plates in chemically defined medium (mTeSR1™, StemCell technologies), and passaged using Dispase (StemCell technologies). For differentiation, hiPSCs were dissociated by incubating at 37°C for 7 minutes with TrypLE™ Express (ThermoFisher) and seeded at 125000 cells/cm2 on a Matrigel® coated 12 well plate, in mTeSR™1 medium supplemented with StemMACS™ Y27632 (Miltenyi Biotec). Once the cells reached greater than 95% confluency, differentiation was initiated using STEMdiff™ Cardiomyocyte (CM) differentiation and Maintenance Kit (StemCell technologies). At day 15, CMs were dissociated by incubation in Collagenase Type I (ThermoFisher) for 45 minutes at 37°C to break up the matrix and then incubated in 0.25% Trypsin with EDTA for 7 minutes at room temperature followed by filtering through a 40 µm cell strainer (48). The CMs were seeded on a Fibronectin coated 96-well plate (Greiner Bio-One) and maintained in CM maintenance medium for 10-15 days before they were harvested for mRNA expression analysis. Total RNA was obtained from 40,000 hiPSC-CMs lysed using QIAzol Lysis reagent (Qiagen). The RNA was purified using miRNeasy® Mini Kit (Qiagen), and all samples had RIN values >7.5, and were analysed using Agilent Bioanalyzer pico-chip. RNA samples were hybridised with probes designed to detect 35 known rhythmonome genes using nCounter (NanoString Technologies, see Supplementary Table S1), which was performed at the Ramaciotti Centre for Genomics (UNSW).
Computer modelling
Human cardiac APs were simulated using the endocardial configuration of the O’Hara-Rudy (ORD11) model (25) with key conductances modified as described by Krogh-Madsen et al. (26) (See Supp Figure S1). The original ORD11 code was adapted to run in the Brain Dynamics Toolbox for Matlab (49). To incorporate population variability in ion channel expression levels the maximum conductance for each current was multiplied by conductance scalar (Gx), that was drawn from a random log-normal distribution (37), with unit mean and variance that was systematically manipulated from 0.05 to 0.5. All models were paced at 1Hz with a stimulus of −40 mV and duration of 1 ms and allowed to equilibrate for 300 beats. We then analysed the next four beats (to allow for the possibility of development of alternans) after the equilibration stage. The peaks in those APs were identified using the Matlab findpeaks function. Individual beats were classified as ectopic if they had secondary peaks that were separated by more than 100 ms. The set of four beats were further classified as alternans if the profile of any of the APs deviated from each other by more than 1 mV at any time point. In a second set of simulations, we repeated the same method as above except that the random multipliers applied to both ICaL and IKr were identical. This case we denote co-expression whereas the former case we denote independent expression.
Acknowledgements
This work was supported by grants from the National Health and Medical Research Council (NHMRC), App1116948 (to JIV), App1074386 (to JIV), (App1164518 to APH), by the National Institutes of Health (NIH) R01LM012736 (to JAG), R01MH113005 (to JAG), and supported by the Victor Chang Cardiac Research Institute Innovation Centre, funded by the NSW Government. We also thank Terry Campbell, Dan Roden and Raj Subbiah for helpful discussions.