A computational model of Purkinje fibre single cell electrophysiology: implications for the long QT syndrome

Computational modeling of cardiac electrophysiology and arrhythmogenesis: toward clinical translation

The complexity of cardiac electrophysiology, involving dynamic changes in numerous components across multiple spatial (from ion channel to organ) and temporal (from milliseconds to days) scales, makes an intuitive or empirical analysis of cardiac arrhythmogenesis challenging. Multiscale mechanistic computational models of cardiac electrophysiology provide precise control over individual parameters, and their reproducibility enables a thorough assessment of arrhythmia mechanisms. This review provides a comprehensive analysis of models of cardiac electrophysiology and arrhythmias, from the single cell to the organ level, and how they can be leveraged to better understand rhythm disorders in cardiac disease and to improve heart patient care. Key issues related to model development based on experimental data are discussed, and major families of human cardiomyocyte models and their applications are highlighted. An overview of organ-level computational modeling of cardiac electrophysiology and its clinical applications in personalized arrhythmia risk assessment and patient-specific therapy of atrial and ventricular arrhythmias is provided. The advancements presented here highlight how patient-specific computational models of the heart reconstructed from patient data have achieved success in predicting risk of sudden cardiac death and guiding optimal treatments of heart rhythm disorders. Finally, an outlook toward potential future advances, including the combination of mechanistic modeling and machine learning/artificial intelligence, is provided. As the field of cardiology is embarking on a journey toward precision medicine, personalized modeling of the heart is expected to become a key technology to guide pharmaceutical therapy, deployment of devices, and surgical interventions.

Long-term memory in Staphylococcus aureus α-hemolysin ion channel kinetics

The kinetics of an ion channel are classically understood as a random process. However, studies have shown that in complex ion channels, formed by multiple subunits, this process can be deterministic, presenting long-term memory. Staphylococcus aureus α-hemolysin (α-HL) is a toxin that acts as the major factor in Staphylococcus aureus virulence. α-HL is a water-soluble protein capable of forming ion channels into lipid bilayers, by insertion of an amphipathic  β-barrel. Here, the α-HL was used as an experimental model to study memory in ion channel kinetics. We applied the approximate entropy (ApEn) approach to analyze randomness and the Detrended Fluctuation Analysis (DFA) to investigate the existence of long memory in α-HL channel kinetics. Single-channel currents were measured through experiments with α-HL channels incorporated in planar lipid bilayers. All experiments were carried out under the following conditions: 1 M NaCl solution, pH 4.5; transmembrane potential of + 40 mV and temperature 25 ± 1 °C. Single-channel currents were recorded in real-time in the memory of a microcomputer coupled to an A/D converter and a patch-clamp amplifier. The conductance value of the α-HL channels was 0.82 ± 0.0025 nS (n = 128). The DFA analysis showed that the kinetics of α-HL channels presents long-term memory ([Formula: see text] = 0.63 ± 0.04). The ApEn outcomes showed low complexity to dwell times when open (ApEno = 0.5514 ± 0.28) and closed (ApEnc = 0.1145 ± 0.08), corroborating the results of the DFA method.

Memory in Ion Channel Kinetics

Ion channels are transport proteins present in the lipid bilayers of biological membranes. They are involved in many physiological processes, such as the generation of nerve impulses, hormonal secretion, and heartbeat. Conformational changes in the ion channel-forming protein allow the opening or closing of pores to control the ionic flux through the cell membranes. The opening and closing of the ion channel have been classically treated as a random kinetic process, known as a Markov process. Here the time the channel remains in a given state is assumed to be independent of the condition it had in the previous state. More recently, however, several studies have shown that this process is not random but a deterministic one, where both the open and closed dwell-times and the ionic current flowing through the channel are history-dependent. This property is called long memory or long-range correlation. However, there is still much controversy regarding how this memory originates, which region of the channel is responsible for this property, and which models could best reproduce the memory effect. In this article, we provide a review of what is, where it is, its possible origin, and the mathematical methods used to analyze the long-term memory present in the kinetic process of ion channels.

Model Systems for Addressing Mechanism of Arrhythmogenesis in Cardiac Repair

PURPOSE OF REVIEW

Cardiac cell-based therapy represents a promising approach for cardiac repair. However, one of the main challenges is cardiac arrhythmias associated with stem cell transplantation. The current review summarizes the recent progress in model systems for addressing mechanisms of arrhythmogenesis in cardiac repair.

RECENT FINDINGS

Animal models have been extensively developed for mechanistic studies of cardiac arrhythmogenesis. Advances in human induced pluripotent stem cells (hiPSCs), patient-specific disease models, tissue engineering, and gene editing have greatly enhanced our ability to probe the mechanistic bases of cardiac arrhythmias. Additionally, recent development in multiscale computational studies and machine learning provides yet another powerful tool to quantitatively decipher the mechanisms of cardiac arrhythmias. Advancing efforts towards the integrations of experimental and computational studies are critical to gain insights into novel mitigation strategies for cardiac arrhythmias in cell-based therapy.

Cardiac transmembrane ion channels and action potentials: cellular physiology and arrhythmogenic behavior

Cardiac arrhythmias are among the leading causes of mortality. They often arise from alterations in the electrophysiological properties of cardiac cells and their underlying ionic mechanisms. It is therefore critical to further unravel the pathophysiology of the ionic basis of human cardiac electrophysiology in health and disease. In the first part of this review, current knowledge on the differences in ion channel expression and properties of the ionic processes that determine the morphology and properties of cardiac action potentials and calcium dynamics from cardiomyocytes in different regions of the heart are described. Then the cellular mechanisms promoting arrhythmias in congenital or acquired conditions of ion channel function (electrical remodeling) are discussed. The focus is on human-relevant findings obtained with clinical, experimental, and computational studies, given that interspecies differences make the extrapolation from animal experiments to human clinical settings difficult. Deepening the understanding of the diverse pathophysiology of human cellular electrophysiology will help in developing novel and effective antiarrhythmic strategies for specific subpopulations and disease conditions.

Reduced Na+ current in Purkinje fibers explains cardiac conduction defects and arrhythmias in Duchenne muscular dystrophy

Dystrophic cardiac Purkinje fibers have abnormally reduced Na+ current densities. This explains impaired ventricular conduction in the dystrophic heart.

Human Purkinje in silico model enables mechanistic investigations into automaticity and pro-arrhythmic abnormalities

Cardiac Purkinje cells (PCs) are implicated in lethal arrhythmias caused by cardiac diseases, mutations, and drug action. However, the pro-arrhythmic mechanisms in PCs are not entirely understood, particularly in humans, as most investigations are conducted in animals. The aims of this study are to present a novel human PCs electrophysiology biophysically-detailed computational model, and to disentangle ionic mechanisms of human Purkinje-related electrophysiology, pacemaker activity and arrhythmogenicity. The new Trovato2020 model incorporates detailed Purkinje-specific ionic currents and Ca²⁺ handling, and was developed, calibrated and validated using human experimental data acquired at multiple frequencies, both in control conditions and following drug application. Multiscale investigations were performed in a Purkinje cell, in fibre and using an experimentally-calibrated population of PCs to evaluate biological variability. Simulations demonstrate the human Purkinje Trovato2020 model is the first one to yield: (i) all key AP features consistent with human Purkinje recordings; (ii) Automaticity with funny current up-regulation (iii) EADs at slow pacing and with 85% hERG block; (iv) DADs following fast pacing; (v) conduction velocity of 160 cm/s in a Purkinje fibre, as reported in human. The human in silico PCs population highlights that: (1) EADs are caused by I_CaL reactivation in PCs with large inward currents; (2) DADs and triggered APs occur in PCs experiencing Ca²⁺ accumulation, at fast pacing, caused by large L-type calcium current and small Na⁺/Ca²⁺ exchanger. The novel human Purkinje model unlocks further investigations into the role of cardiac Purkinje in ventricular arrhythmias through computer modeling and multiscale simulations.

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A human in silico AP model was developed to investigate arrhythmia in cardiac Purkinje.

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The new Purkinje model enables multiscale investigations from single cell to tissue.

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Populations of human Purkinje models reproduce and explain experimental variability.

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Ca²⁺-current reactivation triggers EADs in virtual Purkinje cells with weak repolarisation reserve.

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Ca²⁺ accumulation caused by increased Ca²⁺ and NCX currents triggers DADs.

Rapid Characterization of hERG Channel Kinetics II: Temperature Dependence

Ion channel behavior can depend strongly on temperature, with faster kinetics at physiological temperatures leading to considerable changes in currents relative to room temperature. These temperature-dependent changes in voltage-dependent ion channel kinetics (rates of opening, closing, inactivating, and recovery) are commonly represented with Q₁₀ coefficients or an Eyring relationship. In this article, we assess the validity of these representations by characterizing channel kinetics at multiple temperatures. We focus on the human Ether-à-go-go-Related Gene (hERG) channel, which is important in drug safety assessment and commonly screened at room temperature so that results require extrapolation to physiological temperature. In Part I of this study, we established a reliable method for high-throughput characterization of hERG1a (Kv11.1) kinetics, using a 15-second information-rich optimized protocol. In this Part II, we use this protocol to study the temperature dependence of hERG kinetics using Chinese hamster ovary cells overexpressing hERG1a on the Nanion SyncroPatch 384PE, a 384-well automated patch-clamp platform, with temperature control. We characterize the temperature dependence of hERG gating by fitting the parameters of a mathematical model of hERG kinetics to data obtained at five distinct temperatures between 25 and 37°C and validate the models using different protocols. Our models reveal that activation is far more temperature sensitive than inactivation, and we observe that the temperature dependency of the kinetic parameters is not represented well by Q₁₀ coefficients; it broadly follows a generalized, but not the standardly-used, Eyring relationship. We also demonstrate that experimental estimations of Q₁₀ coefficients are protocol dependent. Our results show that a direct fit using our 15-s protocol best represents hERG kinetics at any given temperature and suggests that using the Generalized Eyring theory is preferable if no experimental data are available to derive model parameters at a given temperature.

Na+ microdomains and sparks: Role in cardiac excitation-contraction coupling and arrhythmias in ankyrin-B deficiency

Cardiac sodium (Na⁺) potassium ATPase (NaK) pumps, neuronal sodium channels (I_Na), and sodium calcium (Ca²⁺) exchangers (NCX1) may co-localize to form a Na⁺ microdomain. It remains controversial as to whether neuronal I_Na contributes to local Na⁺ accumulation, resulting in reversal of nearby NCX1 and influx of Ca²⁺ into the cell. Therefore, there has been great interest in the possible roles of a Na⁺ microdomain in cardiac Ca²⁺-induced Ca²⁺ release (CICR). In addition, the important role of co-localization of NaK and NCX1 in regulating localized Na⁺ and Ca²⁺ levels and CICR in ankyrin-B deficient (ankyrin-B^+/-) cardiomyocytes has been examined in many recent studies. Altered Na⁺ dynamics may contribute to the appearance of arrhythmias, but the mechanisms underlying this relationship remain unclear. In order to investigate this, we present a mechanistic canine cardiomyocyte model which reproduces independent local dyadic junctional SR (JSR) Ca²⁺ release events underlying cell-wide excitation-contraction coupling, as well as a three-dimensional super-resolution model of the Ca²⁺ spark that describes local Na⁺ dynamics as governed by NaK pumps, neuronal I_Na, and NCX1. The model predicts the existence of Na⁺ sparks, which are generated by NCX1 and exhibit significantly slower dynamics as compared to Ca²⁺ sparks. Moreover, whole-cell simulations indicate that neuronal I_Na in the cardiac dyad plays a key role during the systolic phase. Rapid inward neuronal I_Na can elevate dyadic [Na⁺] to 35-40 mM, which drives reverse-mode NCX1 transport, and therefore promotes Ca²⁺ entry into the dyad, enhancing the trigger for JSR Ca²⁺ release. The specific role of decreased co-localization of NaK and NCX1 in ankyrin-B^+/- cardiomyocytes was examined. Model results demonstrate that a reduction in the local NCX1- and NaK-mediated regulation of dyadic [Ca²⁺] and [Na⁺] results in an increase in Ca²⁺ spark activity during isoproterenol stimulation, which in turn stochastically activates NCX1 in the dyad. This alteration in NCX1/NaK co-localization interrupts the balance between NCX1 and NaK currents in a way that leads to enhanced depolarizing inward current during the action potential plateau, which ultimately leads to a higher probability of L-type Ca²⁺ channel reopening and arrhythmogenic early-afterdepolarizations.

A Heart for Diversity: Simulating Variability in Cardiac Arrhythmia Research

In cardiac electrophysiology, there exist many sources of inter- and intra-personal variability. These include variability in conditions and environment, and genotypic and molecular diversity, including differences in expression and behavior of ion channels and transporters, which lead to phenotypic diversity (e.g., variable integrated responses at the cell, tissue, and organ levels). These variabilities play an important role in progression of heart disease and arrhythmia syndromes and outcomes of therapeutic interventions. Yet, the traditional in silico framework for investigating cardiac arrhythmias is built upon a parameter/property-averaging approach that typically overlooks the physiological diversity. Inspired by work done in genetics and neuroscience, new modeling frameworks of cardiac electrophysiology have been recently developed that take advantage of modern computational capabilities and approaches, and account for the variance in the biological data they are intended to illuminate. In this review, we outline the recent advances in statistical and computational techniques that take into account physiological variability, and move beyond the traditional cardiac model-building scheme that involves averaging over samples from many individuals in the construction of a highly tuned composite model. We discuss how these advanced methods have harnessed the power of big (simulated) data to study the mechanisms of cardiac arrhythmias, with a special emphasis on atrial fibrillation, and improve the assessment of proarrhythmic risk and drug response. The challenges of using in silico approaches with variability are also addressed and future directions are proposed.

An atlas- and data-driven approach to initializing reaction-diffusion systems in computer cardiac electrophysiology

The cardiac electrophysiology (EP) problem is governed by a nonlinear anisotropic reaction-diffusion system with a very rapidly varying reaction term associated with the transmembrane cell current. The nonlinearity associated with the cell models requires a stabilization process before any simulation is performed. More importantly, when used in a 3-dimensional (3D) anatomy, it is not sufficient to perform this stabilization on the basis of isolated cells only, since the coupling of the different cells through the tissue greatly modulates the dynamics of the system. Therefore, stabilization of the system must be performed on the entire 3D model. This work develops a novel procedure for the initialization of reaction-diffusion systems for numerical simulations of cardiac EP from steady-state conditions. We exploit surface point correspondence to establish volumetric point correspondence. Upon introduction of a new 3D anatomy with surface point correspondence, a prediction of the cell model steady states is derived from the set of earlier biophysical simulations. We show that the prediction error is typically less than 10% for all model variables, with most variables showing even greater accuracy. When initializing simulations with the predicted model states, it is demonstrated that simulation times can be cut by at least two-thirds and potentially more, which saves hours or days of high-performance computing. Overall, these results increase the clinical applicability of detailed computational EP studies on personalized anatomies.

Early somatic mosaicism is a rare cause of long-QT syndrome

Somatic mosaicism, the occurrence and propagation of genetic variation in cell lineages after fertilization, is increasingly recognized to play a causal role in a variety of human diseases. We investigated the case of life-threatening arrhythmia in a 10-day-old infant with long QT syndrome (LQTS). Rapid genome sequencing suggested a variant in the sodium channel Na_V1.5 encoded by SCN5A, NM_000335:c.5284G > T predicting p.(V1762L), but read depth was insufficient to be diagnostic. Exome sequencing of the trio confirmed read ratios inconsistent with Mendelian inheritance only in the proband. Genotyping of single circulating leukocytes demonstrated the mutation in the genomes of 8% of patient cells, and RNA sequencing of cardiac tissue from the infant confirmed the expression of the mutant allele at mosaic ratios. Heterologous expression of the mutant channel revealed significantly delayed sodium current with a dominant negative effect. To investigate the mechanism by which mosaicism might cause arrhythmia, we built a finite element simulation model incorporating Purkinje fiber activation. This model confirmed the pathogenic consequences of cardiac cellular mosaicism and, under the presenting conditions of this case, recapitulated 2:1 AV block and arrhythmia. To investigate the extent to which mosaicism might explain undiagnosed arrhythmia, we studied 7,500 affected probands undergoing commercial gene-panel testing. Four individuals with pathogenic variants arising from early somatic mutation events were found. Here we establish cardiac mosaicism as a causal mechanism for LQTS and present methods by which the general phenomenon, likely to be relevant for all genetic diseases, can be detected through single-cell analysis and next-generation sequencing.

Optogenetic versus Electrical Stimulation of Human Cardiomyocytes: Modeling Insights

Optogenetics provides an alternative to electrical stimulation to manipulate membrane voltage, and trigger or modify action potentials (APs) in excitable cells. We compare biophysically and energetically the cellular responses to direct electrical current injection versus optical stimulation mediated by genetically expressed light-sensitive ion channels, e.g., Channelrhodopsin-2 (ChR2). Using a computational model of ChR2(H134R mutant), we show that both stimulation modalities produce similar-in-morphology APs in human cardiomyocytes, and that electrical and optical excitability vary with cell type in a similar fashion. However, whereas the strength-duration curves for electrical excitation in ventricular and atrial cardiomyocytes closely follow the theoretical exponential relationship for an equivalent RC circuit, the respective optical strength-duration curves significantly deviate, exhibiting higher nonlinearity. We trace the origin of this deviation to the waveform of the excitatory current-a nonrectangular self-terminating inward current produced in optical stimulation due to ChR2 kinetics and voltage-dependent rectification. Using a unifying charge measure to compare energy needed for electrical and optical stimulation, we reveal that direct electrical current injection (rectangular pulse) is more efficient at short pulses, whereas voltage-mediated negative feedback leads to self-termination of ChR2 current and renders optical stimulation more efficient for long low-intensity pulses. This applies to cardiomyocytes but not to neuronal cells (with much shorter APs). Furthermore, we demonstrate the cell-specific use of ChR2 current as a unique modulator of intrinsic activity, allowing for optical control of AP duration in atrial and, to a lesser degree, in ventricular myocytes. For self-oscillatory cells, such as Purkinje, constant light at extremely low irradiance can be used for fine control of oscillatory frequency, whereas constant electrical stimulation is not feasible due to electrochemical limitations. Our analysis offers insights for designing future new energy-efficient stimulation strategies in heart or brain.

Isolation and characterization of embryonic stem cell-derived cardiac Purkinje cells

The cardiac Purkinje fiber network is composed of highly specialized cardiomyocytes responsible for the synchronous excitation and contraction of the ventricles. Computational modeling, experimental animal studies, and intracardiac electrical recordings from patients with heritable and acquired forms of heart disease suggest that Purkinje cells (PCs) may also serve as critical triggers of life-threatening arrhythmias. Nonetheless, owing to the difficulty in isolating and studying this rare population of cells, the precise role of PC in arrhythmogenesis and the underlying molecular mechanisms responsible for their proarrhythmic behavior are not fully characterized. Conceptually, a stem cell-based model system might facilitate studies of PC-dependent arrhythmia mechanisms and serve as a platform to test novel therapeutics. Here, we describe the generation of murine embryonic stem cells (ESC) harboring pan-cardiomyocyte and PC-specific reporter genes. We demonstrate that the dual reporter gene strategy may be used to identify and isolate the rare ESC-derived PC (ESC-PC) from a mixed population of cardiogenic cells. ESC-PC display transcriptional signatures and functional properties, including action potentials, intracellular calcium cycling, and chronotropic behavior comparable to endogenous PC. Our results suggest that stem-cell derived PC are a feasible new platform for studies of developmental biology, disease pathogenesis, and screening for novel antiarrhythmic therapies.

Modeling our understanding of the His-Purkinje system

The His-Purkinje System (HPS) is responsible for the rapid electric conduction in the ventricles. It relays electrical impulses from the atrioventricular node to the muscle cells and, thus, coordinates the contraction of ventricles in order to ensure proper cardiac pump function. The HPS has been implicated in the genesis of ventricular tachycardia and fibrillation as a source of ectopic beats, as well as forming distinct portions of reentry circuitry. Despite its importance, it remains much less well characterized, structurally and functionally, than the myocardium. Notably, important differences exist with regard to cell structure and electrophysiology, including ion channels, intracellular calcium handling, and gap junctions. Very few computational models address the HPS, and the majority of organ level modeling studies omit it. This review will provide an overview of our current knowledge of structure and function (including electrophysiology) of the HPS. We will review the most recent advances in modeling of the system from the single cell to the organ level, with considerations for relevant interspecies distinctions.

Myokit: A simple interface to cardiac cellular electrophysiology

Myokit is a new powerful and versatile software tool for modeling and simulation of cardiac cellular electrophysiology. Myokit consists of an easy-to-read modeling language, a graphical user interface, single and multi-cell simulation engines and a library of advanced analysis tools accessible through a Python interface. Models can be loaded from Myokit's native file format or imported from CellML. Model export is provided to C, MATLAB, CellML, CUDA and OpenCL. Patch-clamp data can be imported and used to estimate model parameters. In this paper, we review existing tools to simulate the cardiac cellular action potential to find that current tools do not cater specifically to model development and that there is a gap between easy-to-use but limited software and powerful tools that require strong programming skills from their users. We then describe Myokit's capabilities, focusing on its model description language, simulation engines and import/export facilities in detail. Using three examples, we show how Myokit can be used for clinically relevant investigations, multi-model testing and parameter estimation in Markov models, all with minimal programming effort from the user. This way, Myokit bridges a gap between performance, versatility and user-friendliness.

Purkinje Cells as Sources of Arrhythmias in Long QT Syndrome Type 3

Long QT syndrome (LQTS) is characterized by ventricular arrhythmias and sudden cardiac death. Purkinje cells (PC) within the specialized cardiac conduction system have unique electrophysiological properties that we hypothesize may produce the primary sources of arrhythmia in heritable LQTS. LQTS type 3 (LQT3) transgenic mice harboring the ΔKPQ^+/− mutation were crossed with Contactin2-EGFP BAC transgenic mice, which express a fluorescent reporter gene within the Purkinje fiber network. Isolated ventricular myocytes (VMs) (EGFP⁻) and PCs (EGFP⁺) from wild type and ΔKPQ mutant hearts were compared using the whole-cell patch clamp technique and microfluorimetry of calcium transients. Increased late sodium current was seen in ΔKPQ-PCs and ΔKPQ-VMs, with larger density in ΔKPQ-PCs. Marked prolongation of action potential duration of ΔKPQ-PCs was seen compared to ΔKPQ-VMs. ΔKPQ-PCs, but not ΔKPQ-VMs, exhibited frequent early afterdepolarizations, which corresponded to repetitive oscillations of intracellular calcium. Abnormalities in cell repolarization were reversed with exposure to mexiletine. We present the first direct experimental evidence that PCs are uniquely sensitive to LQT3 mutations, displaying electrophysiological behavior that is highly pro-arrhythmic.

Computational modeling of cardiac optogenetics: Methodology overview & review of findings from simulations

Cardiac optogenetics is emerging as an exciting new potential avenue to enable spatiotemporally precise control of excitable cells and tissue in the heart with low-energy optical stimuli. This approach involves the expression of exogenous light-sensitive proteins (opsins) in target heart tissue via viral gene or cell delivery. Preliminary experiments in optogenetically-modified cells, tissue, and organisms have made great strides towards demonstrating the feasibility of basic applications, including the use of light stimuli to pace or disrupt reentrant activity. However, it remains unknown whether techniques based on this intriguing technology could be scaled up and used in humans for novel clinical applications, such as pain-free optical defibrillation or dynamic modulation of action potential shape. A key step towards answering such questions is to explore potential optogenetics-based therapies using sophisticated computer simulation tools capable of realistically representing opsin delivery and light stimulation in biophysically detailed, patient-specific models of the human heart. This review provides (1) a detailed overview of the methodological developments necessary to represent optogenetics-based solutions in existing virtual heart platforms and (2) a survey of findings that have been derived from such simulations and a critical assessment of their significance with respect to the progress of the field.

Exploring susceptibility to atrial and ventricular arrhythmias resulting from remodeling of the passive electrical properties in the heart: a simulation approach

Under diseased conditions, remodeling of the cardiac tissue properties (“passive properties”) takes place; these are aspects of electrophysiological behavior that are not associated with active ion transport across cell membranes. Remodeling of the passive electrophysiological properties most often results from structural remodeling, such as gap junction down-regulation and lateralization, fibrotic growth infiltrating the myocardium, or the development of an infarct scar. Such structural remodeling renders atrial or ventricular tissue as a major substrate for arrhythmias. The current review focuses on these aspects of cardiac arrhythmogenesis. Due to the inherent complexity of cardiac arrhythmias, computer simulations have provided means to elucidate interactions pertinent to this spatial scale. Here we review the current state-of-the-art in modeling atrial and ventricular arrhythmogenesis as arising from the disease-induced changes in the passive tissue properties, as well as the contributions these modeling studies have made to our understanding of the mechanisms of arrhythmias in the heart. Because of the rapid advance of structural imaging methodologies in cardiac electrophysiology, we chose to present studies that have used such imaging methodologies to construct geometrically realistic models of cardiac tissue, or the organ itself, where the regional remodeling properties of the myocardium can be represented in a realistic way. We emphasize how the acquired knowledge can be used to pave the way for clinical applications of cardiac organ modeling under the conditions of structural remodeling.

In silico ischaemia-induced reentry at the Purkinje-ventricle interface

AIMS

This computational modelling work illustrates the influence of hyperkalaemia and electrical uncoupling induced by defined ischaemia on action potential (AP) propagation and the incidence of reentry at the Purkinje-ventricle interface in mammalian hearts.

METHODS AND RESULTS

Unidimensional and bidimensional models of the Purkinje-ventricle subsystem, including ischaemic conditions (defined as phase 1B) in the ventricle and an ischaemic border zone, were developed by altering several important electrophysiological parameters of the Luo-Rudy AP model of the ventricular myocyte. Purkinje electrical activity was modelled using the equations of DiFrancesco and Noble. Our study suggests that an extracellular potassium concentration [K(+)]o >14 mM and a slight decrease in intercellular coupling induced by ischaemia in ventricle can cause conduction block from Purkinje to ventricle. Under these conditions, propagation from ventricle to Purkinje is possible. Thus, unidirectional block (UDB) and reentry can result. When conditions of UDB are met, retrograde propagation with a long delay (320 ms) may re-excite Purkinje cells, and give rise to a reentrant pathway. This induced reentry may be the origin of arrhythmias observed in phase 1B ischaemia.

CONCLUSION

In a defined setting of ischaemia (phase 1B), a small amount of uncoupling between ventricular cells, as well as between Purkinje and ventricular tissue, may induce UDBs and reentry. Hyperkalaemia is also confirmed to be an important factor in the genesis of reentrant rhythms, since it regulates the range of coupling in which UDBs may be induced.

Uniformization method for solving cardiac electrophysiology models based on the Markov-chain formulation

This paper compares different numerical methods for the solution of myocyte models of cardiac electrophysiology. In particular, it presents how the technique called uniformization method substantially increases the stability of simple first-order methods such as Euler explicit method and Rush-Larsen (RL) method, for the solution of modern electrophysiology models that are based on continuous-time Markov chains (MCs) for the description of subcellular structures, such as ion channels. The MCs are often associated with stiff ordinary differential equations that severely limit the time step used by these traditional methods. By using the uniformization method, we could significantly increase the time steps for the solution of different cardiac electrophysiology models and improve the computational performance up to 150 times compared to the performance of Euler's and RL's methods.

Continuous-time control of alternans in long Purkinje fibers

Alternans-an arrhythmic response of cardiac tissue to periodic pacing-often serves as a precursor to a more dangerous, and potentially lethal, state of fibrillation. Suppression of alternans using feedback control may be a plausible method to prevent fibrillation. Several approaches based on impulsive control have been proposed previously, where feedback is applied for a brief instance of time during each pacing interval. This paper presents a continuous-time approach, where feedback current is applied at all times, which is capable of suppressing alternans in fibers of significantly greater length (up to at least 4 cm), compared with impulsive control (less than 1 cm), and for a wide range of pacing cycle lengths.

Modeling tissue- and mutation- specific electrophysiological effects in the long QT syndrome: role of the Purkinje fiber

Congenital long QT syndrome is a heritable family of arrhythmias caused by mutations in 13 genes encoding ion channel complex proteins. Mounting evidence has implicated the Purkinje fiber network in the genesis of ventricular arrhythmias. In this study, we explore the hypothesis that long QT mutations can demonstrate different phenotypes depending on the tissue type of expression. Using computational models of the human ventricular myocyte and the Purkinje fiber cell, the biophysical alteration in channel function in LQT1, LQT2, LQT3, and LQT7 are modeled. We identified that the plateau potential was important in LQT1 and LQT2, in which mutation led to minimal action potential prolongation in Purkinje fiber cells. The phenotype of LQT3 mutation was dependent on the biophysical alteration induced as well as tissue type. The canonical ΔKPQ mutation causes severe action potential prolongation in both tissue types. For LQT3 mutation F1473C, characterized by shifted channel availability, a more severe phenotype was seen in Purkinje fiber cells with action potential prolongation and early afterdepolarizations. The LQT3 mutation S1904L demonstrated striking effects on action potential duration restitution and more severe action potential prolongation in Purkinje fiber cells at higher heart rates. Voltage clamp simulations highlight the mechanism of effect of these mutations in different tissue types, and impact of drug therapy is explored. We conclude that arrhythmia formation in long QT syndrome may depend not only on the basis of mutation and biophysical alteration, but also upon tissue of expression. The Purkinje fiber network may represent an important therapeutic target in the management of patients with heritable channelopathies.

Advances in modeling ventricular arrhythmias: from mechanisms to the clinic

Modern cardiovascular research has increasingly recognized that heart models and simulation can help interpret an array of experimental data and dissect important mechanisms and interrelationships, with developments rooted in the iterative interaction between modeling and experimentation. This article reviews the progress made in simulating cardiac electrical behavior at the level of the organ and, specifically, in the development of models of ventricular arrhythmias and fibrillation, as well as their termination (defibrillation). The ability to construct multiscale models of ventricular arrhythmias, representing integrative behavior from the molecule to the entire organ, has enabled mechanistic inquiry into the dynamics of ventricular arrhythmias in the diseased myocardium, in understanding drug-induced proarrhythmia, and in the development of new modalities for defibrillation, to name a few. In this article, we also review the initial use of ventricular models of arrhythmia in personalized diagnosis, treatment planning, and prevention of sudden cardiac death. Implementing individualized cardiac simulations at the patient bedside is poised to become one of the most thrilling examples of computational science and engineering approaches in translational medicine.

Computational optogenetics: empirically-derived voltage- and light-sensitive channelrhodopsin-2 model

Channelrhodospin-2 (ChR2), a light-sensitive ion channel, and its variants have emerged as new excitatory optogenetic tools not only in neuroscience, but also in other areas, including cardiac electrophysiology. An accurate quantitative model of ChR2 is necessary for in silico prediction of the response to optical stimulation in realistic tissue/organ settings. Such a model can guide the rational design of new ion channel functionality tailored to different cell types/tissues. Focusing on one of the most widely used ChR2 mutants (H134R) with enhanced current, we collected a comprehensive experimental data set of the response of this ion channel to different irradiances and voltages, and used these data to develop a model of ChR2 with empirically-derived voltage- and irradiance- dependence, where parameters were fine-tuned via simulated annealing optimization. This ChR2 model offers: 1) accurate inward rectification in the current-voltage response across irradiances; 2) empirically-derived voltage- and light-dependent kinetics (activation, deactivation and recovery from inactivation); and 3) accurate amplitude and morphology of the response across voltage and irradiance settings. Temperature-scaling factors (Q₁₀) were derived and model kinetics was adjusted to physiological temperatures. Using optical action potential clamp, we experimentally validated model-predicted ChR2 behavior in guinea pig ventricular myocytes. The model was then incorporated in a variety of cardiac myocytes, including human ventricular, atrial and Purkinje cell models. We demonstrate the ability of ChR2 to trigger action potentials in human cardiomyocytes at relatively low light levels, as well as the differential response of these cells to light, with the Purkinje cells being most easily excitable and ventricular cells requiring the highest irradiance at all pulse durations. This new experimentally-validated ChR2 model will facilitate virtual experimentation in neural and cardiac optogenetics at the cell and organ level and provide guidance for the development of in vivo tools.

Optogenetics, the use of light-sensitive ion channels for stimulation of mammalian cells and tissues, offers specificity and superior precision of control compared to traditional chemical or electrical means of stimulation. In particular, Channelrhodospin-2 (ChR2), a light-sensitive ion channel, originally derived from algae, has found wide-spread application in neuroscience for controlled stimulation of different brain regions. More recently, this work was extended to other organs, including the heart, where it opens the possibility for a new generation of optical pacemakers. The development of new optogenetic tools that allow for more efficient optical stimulation can be guided by computational prediction of the response of different cells and tissues to light. In this report, we provide a new computational model of ChR2 that was empirically validated and can be inserted into different cell types – neurons or heart cells – for virtual optical stimulation and prediction of optimal light-delivery arrangements, minimum energy needs etc. Overall, virtual optogenetics can accelerate the development of new optical stimulation tools for better understanding and control of brain and heart function.

Establishing in vitro to clinical correlations in the evaluation of cardiovascular safety pharmacology

Preclinical studies are vital in establishing the efficacy and safety of a new chemical entity (NCE) in humans. To deliver meaningful information, experiments have to be well defined and provide outcome that is relevant and translatable to humans. This review briefly surveys the various preclinical experiments that are frequently conducted to assess drug effects on cardiac conductivity in early drug development. We examine the different approaches used to establish correlations between non-clinical and clinical settings and discuss their value in the evaluation of cardiovascular risk.

Induced pluripotent stem cells used to reveal drug actions in a long QT syndrome family with complex genetics

Understanding the basis for differential responses to drug therapies remains a challenge despite advances in genetics and genomics. Induced pluripotent stem cells (iPSCs) offer an unprecedented opportunity to investigate the pharmacology of disease processes in therapeutically and genetically relevant primary cell types in vitro and to interweave clinical and basic molecular data. We report here the derivation of iPSCs from a long QT syndrome patient with complex genetics. The proband was found to have a de novo SCN5A LQT-3 mutation (F1473C) and a polymorphism (K897T) in KCNH2, the gene for LQT-2. Analysis of the biophysics and molecular pharmacology of ion channels expressed in cardiomyocytes (CMs) differentiated from these iPSCs (iPSC-CMs) demonstrates a primary LQT-3 (Na⁺ channel) defect responsible for the arrhythmias not influenced by the KCNH2 polymorphism. The F1473C mutation occurs in the channel inactivation gate and enhances late Na⁺ channel current (I_NaL) that is carried by channels that fail to inactivate completely and conduct increased inward current during prolonged depolarization, resulting in delayed repolarization, a prolonged QT interval, and increased risk of fatal arrhythmia. We find a very pronounced rate dependence of I_NaL such that increasing the pacing rate markedly reduces I_NaL and, in addition, increases its inhibition by the Na⁺ channel blocker mexiletine. These rate-dependent properties and drug interactions, unique to the proband’s iPSC-CMs, correlate with improved management of arrhythmias in the patient and provide support for this approach in developing patient-specific clinical regimens.

Unique cardiac Purkinje fiber transient outward current β-subunit composition: a potential molecular link to idiopathic ventricular fibrillation

RATIONALE

A chromosomal haplotype producing cardiac overexpression of dipeptidyl peptidase-like protein-6 (DPP6) causes familial idiopathic ventricular fibrillation. The molecular basis of transient outward current (I(to)) in Purkinje fibers (PFs) is poorly understood. We hypothesized that DPP6 contributes to PF I(to) and that its overexpression might specifically alter PF I(to) properties and repolarization.

OBJECTIVE

To assess the potential role of DPP6 in PF I(to).

METHODS AND RESULTS

Clinical data in 5 idiopathic ventricular fibrillation patients suggested arrhythmia origin in the PF-conducting system. PF and ventricular muscle I(to) had similar density, but PF I(to) differed from ventricular muscle in having tetraethylammonium sensitivity and slower recovery. DPP6 overexpression significantly increased, whereas DPP6 knockdown reduced, I(to) density and tetraethylammonium sensitivity in canine PF but not in ventricular muscle cells. The K(+)-channel interacting β-subunit K(+)-channel interacting protein type-2, essential for normal expression of I(to) in ventricular muscle, was weakly expressed in human PFs, whereas DPP6 and frequenin (neuronal calcium sensor-1) were enriched. Heterologous expression of Kv4.3 in Chinese hamster ovary cells produced small I(to); I(to) amplitude was greatly enhanced by coexpression with K(+)-channel interacting protein type-2 or DPP6. Coexpression of DPP6 with Kv4.3 and K(+)-channel interacting protein type-2 failed to alter I(to) compared with Kv4.3/K(+)-channel interacting protein type-2 alone, but DPP6 expression with Kv4.3 and neuronal calcium sensor-1 (to mimic PF I(to) composition) greatly enhanced I(to) compared with Kv4.3/neuronal calcium sensor-1 and recapitulated characteristic PF kinetic/pharmacological properties. A mathematical model of cardiac PF action potentials showed that I(to) enhancement can greatly accelerate PF repolarization.

CONCLUSIONS

These results point to a previously unknown central role of DPP6 in PF I(to), with DPP6 gain of function selectively enhancing PF current, and suggest that a DPP6-mediated PF early-repolarization syndrome might be a novel molecular paradigm for some forms of idiopathic ventricular fibrillation.

An image-based model of the whole human heart with detailed anatomical structure and fiber orientation

Many heart anatomy models have been developed to study the electrophysiological properties of the human heart. However, none of them includes the geometry of the whole human heart. In this study, an anatomically detailed mathematical model of the human heart was firstly reconstructed from the computed tomography images. In the reconstructed model, the atria consisted of atrial muscles, sinoatrial node, crista terminalis, pectinate muscles, Bachmann's bundle, intercaval bundles, and limbus of the fossa ovalis. The atrioventricular junction included the atrioventricular node and atrioventricular ring, and the ventricles had ventricular muscles, His bundle, bundle branches, and Purkinje network. The epicardial and endocardial myofiber orientations of the ventricles and one layer of atrial myofiber orientation were then measured. They were calculated using linear interpolation technique and minimum distance algorithm, respectively. To the best of our knowledge, this is the first anatomically-detailed human heart model with corresponding experimentally measured fibers orientation. In addition, the whole heart excitation propagation was simulated using a monodomain model. The simulated normal activation sequence agreed well with the published experimental findings.

How the Hodgkin-Huxley equations inspired the Cardiac Physiome Project

Early modelling of cardiac cells (1960-1980) was based on extensions of the Hodgkin-Huxley nerve axon equations with additional channels incorporated, but after 1980 it became clear that processes other than ion channel gating were also critical in generating electrical activity. This article reviews the development of models representing almost all cell types in the heart, many different species, and the software tools that have been created to facilitate the cardiac Physiome Project.

Models of HERG gating

HERG (Kv11.1, KCNH2) is a voltage-gated potassium channel with unique gating characteristics. HERG has fast voltage-dependent inactivation, relatively slow deactivation, and fast recovery from inactivation. This combination of gating kinetics makes study of HERG difficult without using mathematical models. Several HERG models have been developed, with fundamentally different organization. HERG is the molecular basis of I(Kr), which plays a critical role in repolarization. We programmed and compared five distinct HERG models. HERG gating cannot be adequately replicated using Hodgkin-Huxley type formulation. Using Markov models, a five-state model is required with three closed, one open, and one inactivated state, and a voltage-independent step between some of the closed states. A fundamental difference between models is the presence/absence of a transition directly from the proximal closed state to the inactivated state. The only models that effectively reproduce HERG data have no direct closed-inactivated transition, or have a closed-inactivated transition that is effectively zero compared to the closed-open transition, rendering the closed-inactivation transition superfluous. Our single-channel model demonstrates that channels can inactivate without conducting with a flickering or bursting open-state. The various models have qualitative and quantitative differences that are critical to accurate predictions of HERG behavior during repolarization, tachycardia, and premature depolarizations.

Biophysical properties of slow potassium channels in human embryonic stem cell derived cardiomyocytes implicate subunit stoichiometry

Human embryonic stem cells (hESCs) are an important cellular model for studying ion channel function in the context of a human cardiac cell and will provide a wealth of information about both heritable arrhythmias and acquired electrophysiological disorders. However, detailed electrophysiological characterization of the important cardiac ion channels has been so far overlooked. Because mutations in the gene for the I(Ks) α subunit, KCNQ1, constitute the majority of long QT syndrome (LQT-1) cases, we have carried out a detailed biophysical analysis of this channel expressed in hESCs to establish baseline I(Ks) channel biophysical properties in cardiac myocytes derived from hESCs (hESC-CMs). I(Ks) channels are heteromultimeric proteins consisting of four identical α-subunits (KCNQ1) assembled with auxiliary β-subunits (KCNE1). We found that the half-maximal I(Ks) activation voltage in hESC-CMs and in myocytes derived from human induced pluripotent stems cells (hiPSC-CMs) falls between that of KCNQ1 channels expressed alone and with full complement of KCNE1, the major KCNE subunit expressed in hESC-CMs as shown by qPCR analysis. Overexpression of KCNE1 by transfection of hESC-CMs markedly shifted and slowed native I(Ks) activation implying assembly of additional KCNE1 subunits with endogenous channels. Our results in hESC-CMs, which indicate an I(Ks) subunit stoichiometry that can be altered by variable KCNE1 expression, suggest the possibility for variable I(Ks) function in the developing heart, in different tissues in the heart, and in disease. This establishes a new baseline for I(Ks) channel properties in myocytes derived from pluripotent stem cells and will guide future studies in patient-specific hiPSCs.

Unique properties of the ATP-sensitive K⁺ channel in the mouse ventricular cardiac conduction system

Background- The specialized cardiac conduction system (CCS) expresses a unique complement of ion channels that confer a specific electrophysiological profile. ATP-sensitive potassium (K(ATP)) channels in these myocytes have not been systemically investigated. Methods and Results- We recorded K(ATP) channels in isolated CCS myocytes using Cntn2-EGFP reporter mice. The CCS K(ATP) channels were less sensitive to inhibitory cytosolic ATP compared with ventricular channels and more strongly activated by MgADP. They also had a smaller slope conductance. The 2 types of channels had similar intraburst open and closed times, but the CCS K(ATP) channel had a prolonged interburst closed time. CCS K(ATP) channels were strongly activated by diazoxide and less by levcromakalim, whereas the ventricular K(ATP) channel had a reverse pharmacological profile. CCS myocytes express elevated levels of Kir6.1 but reduced Kir6.2 and SUR2A mRNA compared with ventricular myocytes (SUR1 expression was negligible). SUR2B mRNA expression was higher in CCS myocytes relative to SUR2A. Canine Purkinje fibers expressed higher levels of Kir6.1 and SUR2B protein relative to the ventricle. Numeric simulation predicts a high sensitivity of the Purkinje action potential to changes in ATP:ADP ratio. Cardiac conduction time was prolonged by low-flow ischemia in isolated, perfused mouse hearts, which was prevented by glibenclamide. Conclusions- These data imply a differential electrophysiological response (and possible contribution to arrhythmias) of the ventricular CCS to K(ATP) channel opening during periods of ischemia.

Model-based control of cardiac alternans in Purkinje fibers

This paper describes a systematic approach to suppressing cardiac alternans in simulated Purkinje fibers using localized current injections. We investigate the controllability and observability of the periodically paced Noble model for different locations of the recording and control electrodes. In particular, we show that the loss of controllability causes the failure of the control approach introduced by Echebarria and Karma [Chaos 12, 923 (2002)] for longer fiber lengths. Furthermore, we explain how the optimal locations for the recording and control electrodes and the timing of the feedback current can be selected, accounting for both linear and nonlinear effects, effectively doubling the length of fibers that can be controlled with previous methods.

Considerations for the use of cellular electrophysiology models within cardiac tissue simulations

The use of mathematical models to study cardiac electrophysiology has a long history, and numerous cellular scale models are now available, covering a range of species and cell types. Their use to study emergent properties in tissue is also widespread, typically using the monodomain or bidomain equations coupled to one or more cell models. Despite the relative maturity of this field, little has been written looking in detail at the interface between the cellular and tissue-level models. Mathematically this is relatively straightforward and well-defined. There are however many details and potential inconsistencies that need to be addressed, in order to ensure correct operation of a cellular model within a tissue simulation. This paper will describe these issues and how to address them. Simply having models available in a common format such as CellML is still of limited utility, with significant manual effort being required to integrate these models within a tissue simulation. We will thus also discuss the facilities available for automating this in a consistent fashion within Chaste, our robust and high-performance cardiac electrophysiology simulator. It will be seen that a common theme arising is the need to go beyond a representation of the model mathematics in a standard language, to include additional semantic information required in determining the model's interface, and hence to enhance interoperability. Such information can be added as metadata, but agreement is needed on the terms to use, including development of appropriate ontologies, if reliable automated use of CellML models is to become common.

A model of canine purkinje cell electrophysiology and Ca(2+) cycling: rate dependence, triggered activity, and comparison to ventricular myocytes

Purkinje cells (Pcell) are characterized by different electrophysiological properties and Ca(2+) cycling processes than ventricular myocytes (Vcell) and are frequently involved in ventricular arrhythmias. Yet, the mechanistic basis for their arrhythmic vulnerability is not completely understood. The objectives were to: (1) characterize Pcell electrophysiology, Ca(2+) cycling, and their rate dependence; (2) investigate mechanisms underlying Pcell arrhythmogenicity; and compare Pcell and Vcell electrophysiology, Ca(2+) cycling, and arrhythmic properties. We developed a new mathematical model of Pcell. The Ca(2+) subsystem includes spatial organization and receptors distribution unique to Pcell. Results were: (1) in Pcell and Vcell, Na(+) accumulation via its augmentation of repolarizing I(NaK) dominates action potential duration adaptation and, in Pcell, I(NaL) contributes additional action potential duration shortening at short cycle length; (2) steep Pcell restitution is attributable to slow recovery of I(NaL); (3) biphasic Ca(2+) transients of Pcell reflect the delay between Ca(2+) release from junctional sarcoplasmic reticulum and corbular sarcoplasmic reticulum; (4) Pcell Ca(2+) alternans, unlike Vcell, can develop without inducing action potential alternans; (5) Pcell action potential alternans develops at a shorter cycle length than Vcell, with increased subcellular heterogeneity of Ca(2+) cycling attributable to refractoriness of Ca(2+) release from corbular sarcoplasmic reticulum and junctional sarcoplasmic reticulum; (6) greater Pcell vulnerability to delayed afterdepolarizations is attributable to higher sarcoplasmic reticulum Ca(2+) content and ionic currents that reduce excitation threshold and promote triggered activity; and (7) early after depolarizations generation in Pcell is mostly attributable to reactivation of I(NaL2), whereas I(CaL) plays this role in Vcell. Steeper rate dependence of action potential and Ca(2+) transients, central peripheral heterogeneity of Ca(2+) cycling, and distinct ion channel profile underlie greater arrhythmic vulnerability of Pcell compared to Vcell.

Ionic mechanisms of electrophysiological properties and repolarization abnormalities in rabbit Purkinje fibers

Purkinje cells play an important role in drug-induced arrhythmogenesis and are widely used in preclinical drug safety assessments. Repolarization abnormalities such as action potential (AP) prolongation and early afterdeploarizations (EAD) are often observed in vitro upon pharmacological interventions. However, because drugs do not act on only one defined target, it is often difficult to fully explain the mechanisms of action and their potential arrhythmogenicity. Computational models, when appropriately detailed and validated, can be used to gain mechanistic insights into the mechanisms of action of certain drugs. Nevertheless, no model of Purkinje electrophysiology that is able to reproduce characteristic Purkinje responses to drug-induced changes in ionic current conductances such as AP prolongation and EAD generation currently exists. In this study, a novel biophysically detailed model of rabbit Purkinje electrophysiology was developed by integration of data from voltage-clamp and AP experimental recordings. Upon validation, we demonstrate that the model reproduces many key electrophysiological properties of rabbit Purkinje cells. These include: AP morphology and duration, both input resistance and rate dependence properties as well as response to hyperkalemia. Pharmacological interventions such as inward rectifier K(+) current and rapid delayed rectifier K(+) current block as well as late Na(+) current increase result in significant AP changes. However, enhanced L-type Ca(2+) current (i(CaL)) dominates in EAD genesis in Purkinje fibers. In addition, i(CaL) inactivation dynamics and intercellular coupling in tissue strongly modulate EAD formation. We conclude that EAD generation in Purkinje cells is mediated by an increase in i(CaL) and modulated by its inactivation kinetics.

Quantitative prediction of the arrhythmogenic effects of de novo hERG mutations in computational models of human ventricular tissues

Mutations to hERG which result in changes to the rapid delayed rectifier current I(Kr) can cause long and short QT syndromes and are associated with an increased risk of cardiac arrhythmias. Experimental recordings of I(Kr) reveal the effects of mutations at the channel level, but how these changes translate to the cell and tissue levels remains unclear. We used computational models of human ventricular myocytes and tissues to predict and quantify the effects that de novo hERG mutations would have on cell and tissue electrophysiology. Mutations that decreased I(Kr) maximum conductance resulted in an increased cell and tissue action potential duration (APD) and a long QT interval on the electrocardiogram (ECG), whereas those that caused a positive shift in the inactivation curve resulted in a decreased APD and a short QT. Tissue vulnerability to re-entrant arrhythmias was correlated with transmural dispersion of repolarisation, and any change to this vulnerability could be inferred from the ECG QT interval or T wave peak-to-end time. Faster I(Kr) activation kinetics caused cell APD alternans to appear over a wider range of pacing rates and with a larger magnitude, and spatial heterogeneity in these cellular alternans resulted in discordant alternans at the tissue level. Thus, from channel kinetic data, we can predict the tissue-level electrophysiological effects of any hERG mutations and identify how the mutation would manifest clinically, as either a long or short QT syndrome with or without an increased risk of alternans and re-entrant arrhythmias.