Two components of the delayed rectifier K+ current in ventricular myocytes of the guinea pig type. Theoretical formulation and their role in repolarization

ST segment and T wave abnormalities: A narrative review

INTRODUCTION

The electrocardiogram (ECG) is a valuable tool for interpreting ventricular repolarization. This article aims to broaden the diagnostic scope beyond the conventional ischemia-centric approach, integrating an understanding of pathophisiological influences on ST-T wave changes.

METHODS

A review was conducted on the physiological underpinnings of ventricular repolarization and the pathophisiological processes that can change ECG patterns. The research encompassed primary repolarization abnormalities due to uniform variations in ventricular action potential, secondary changes from electrical or mechanical alterations, and non-ischemic conditions influencing ST-T segments.

RESULTS

Primary T waves are characterized by symmetrical waves with broad bases and variable QT intervals, indicative of direct myocardial action potential modifications due to ischemia, electrolyte imbalances, and channelopathies. Secondary T waves are asymmetric and often unassociated with significant QT interval changes, suggesting depolarization alterations or changes in cardiac geometry and contractility.

CONCLUSION

We advocate for a unified ECG analysis, recognizing primary and secondary ST-T changes, and their clinical implications. Our proposed analytical framework enhances the clinician's ability to discern a wide array of cardiac conditions, extending diagnostic accuracy beyond myocardial ischemia.

Intracellular ion accumulation in the genesis of complex action potential dynamics under cardiac diseases

Intracellular ions, including sodium (Na^{+}), calcium (Ca^{2+}), and potassium (K^{+}), etc., accumulate slowly after a change of the state of the heart, such as a change of the heart rate. The goal of this study is to understand the roles of slow ion accumulation in the genesis of cardiac memory and complex action-potential duration (APD) dynamics that can lead to lethal cardiac arrhythmias. We carry out numerical simulations of a detailed action potential model of ventricular myocytes under normal and diseased conditions, which exhibit memory effects and complex APD dynamics. We develop a low-dimensional iterated map (IM) model to describe the dynamics of Na^{+}, Ca^{2+}, and APD and use it to uncover the underlying dynamical mechanisms. The development of the IM model is informed by simulation results under the normal condition. We then use the IM model to perform linear stability analyses and computer simulations to investigate the bifurcations and complex APD dynamics, which depend on the feedback loops between APD and intracellular Ca^{2+} and Na^{+} concentrations and the steepness of the APD response to the ion concentrations. When the feedback between APD and Ca^{2+} concentration is positive, a Hopf bifurcation leading to periodic oscillatory behavior occurs as the steepness of the APD response to the ion concentrations increases. The negative feedback loop between APD and Na^{+} concentration is required for the Hopf bifurcation. When the feedback between APD and Ca^{2+} concentration is negative, period-doubling bifurcations leading to high periodicity and chaos occurs. In this case, Na^{+} accumulation plays little role in the dynamics. Finally, we carry out simulations of the detailed action potential model under two diseased conditions, which exhibit steep APD responses to ion concentrations. Under both conditions, Hopf bifurcations leading to slow oscillations or period-doubling bifurcations leading to high periodicity and chaotic APD dynamics occur, depending on the strength of the ion pump-Na^{+}-Ca^{2+} exchanger. Using functions reconstructed from the simulation data, the IM model accurately captures the bifurcations and dynamics under the two diseased conditions. In conclusion, besides using computer simulations of a detailed high-dimensional action-potential model to investigate the effects of slow ion accumulation and short-term memory on bifurcations and genesis of complex APD dynamics in cardiac myocytes under diseased conditions, this study also provides a low-dimensional mathematical tool, i.e., the IM model, to allow stability analyses for uncovering the underlying mechanisms.

The electrical restitution of the non-propagated cardiac ventricular action potential

Sudden changes in pacing cycle length are frequently associated with repolarization abnormalities initiating cardiac arrhythmias, and physiologists have long been interested in measuring the likelihood of these events before their manifestation. A marker of repolarization stability has been found in the electrical restitution (ER), the response of the ventricular action potential duration to a pre- or post-mature stimulation, graphically represented by the so-called ER curve. According to the restitution hypothesis (ERH), the slope of this curve provides a quantitative discrimination between stable repolarization and proneness to arrhythmias. ER has been studied at the body surface, whole organ, and tissue level, and ERH has soon become a key reference point in theoretical, clinical, and pharmacological studies concerning arrhythmia development, and, despite criticisms, it is still widely adopted. The ionic mechanism of ER and cellular applications of ERH are covered in the present review. The main criticism on ERH concerns its dependence from the way ER is measured. Over the years, in fact, several different experimental protocols have been established to measure ER, which are also described in this article. In reviewing the state-of-the art on cardiac cellular ER, I have introduced a notation specifying protocols and graphical representations, with the aim of unifying a sometime confusing nomenclature, and providing a physiological tool, better defined in its scope and limitations, to meet the growing expectations of clinical and pharmacological research.

Facilitation of hERG Activation by Its Blocker: A Mechanism to Reduce Drug-Induced Proarrhythmic Risk

Modulation of the human Ether-à-go-go-Related Gene (hERG) channel, a crucial voltage-gated potassium channel in the repolarization of action potentials in ventricular myocytes of the heart, has significant implications on cardiac electrophysiology and can be either antiarrhythmic or proarrhythmic. For example, hERG channel blockade is a leading cause of long QT syndrome and potentially life-threatening arrhythmias, such as torsades de pointes. Conversely, hERG channel blockade is the mechanism of action of Class III antiarrhythmic agents in terminating ventricular tachycardia and fibrillation. In recent years, it has been recognized that less proarrhythmic hERG blockers with clinical potential or Class III antiarrhythmic agents exhibit, in addition to their hERG-blocking activity, a second action that facilitates the voltage-dependent activation of the hERG channel. This facilitation is believed to reduce the proarrhythmic potential by supporting the final repolarizing of action potentials. This review covers the pharmacological characteristics of hERG blockers/facilitators, the molecular mechanisms underlying facilitation, and their clinical significance, as well as unresolved issues and requirements for research in the fields of ion channel pharmacology and drug-induced arrhythmias.

Local Control Model of a Human Ventricular Myocyte: An Exploration of Frequency-Dependent Changes and Calcium Sparks

Calcium (Ca2+) sparks are the elementary events of excitation-contraction coupling, yet they are not explicitly represented in human ventricular myocyte models. A stochastic ventricular cardiomyocyte human model that adapts to intracellular Ca2+ ([Ca2+]i) dynamics, spark regulation, and frequency-dependent changes in the form of locally controlled Ca2+ release was developed. The 20,000 CRUs in this model are composed of 9 individual LCCs and 49 RyRs that function as couplons. The simulated action potential duration at 1 Hz steady-state pacing is ~0.280 s similar to human ventricular cell recordings. Rate-dependence experiments reveal that APD shortening mechanisms are largely contributed by the L-type calcium channel inactivation, RyR open fraction, and [Ca2+]myo concentrations. The dynamic slow-rapid-slow pacing protocol shows that RyR open probability during high pacing frequency (2.5 Hz) switches to an adapted "nonconducting" form of Ca2+-dependent transition state. The predicted force was also observed to be increased in high pacing, but the SR Ca2+ fractional release was lower due to the smaller difference between diastolic and systolic [Ca2+]SR. Restitution analysis through the S1S2 protocol and increased LCC Ca2+-dependent activation rate show that the duration of LCC opening helps modulate its effects on the APD restitution at different diastolic intervals. Ultimately, a longer duration of calcium sparks was observed in relation to the SR Ca2+ loading at high pacing rates. Overall, this study demonstrates the spontaneous Ca2+ release events and ion channel responses throughout various stimuli.

Improving the hERG model fitting using a deep learning-based method

The hERG channel is one of the essential ion channels composing the cardiac action potential and the toxicity assay for new drug. Recently, the comprehensive in vitro proarrhythmia assay (CiPA) was adopted for cardiac toxicity evaluation. One of the hurdles for this protocol is identifying the kinetic effect of the new drug on the hERG channel. This procedure included the model-based parameter identification from the experiments. There are many mathematical methods to infer the parameters; however, there are two main difficulties in fitting parameters. The first is that, depending on the data and model, parametric inference can be highly time-consuming. The second is that the fitting can fail due to local minima problems. The simplest and most effective way to solve these issues is to provide an appropriate initial value. In this study, we propose a deep learning-based method for improving model fitting by providing appropriate initial values, even the right answer. We generated the dataset by changing the model parameters and trained our deep learning-based model. To improve the accuracy, we used the spectrogram with time, frequency, and amplitude. We obtained the experimental dataset from https://github.com/CardiacModelling/hERGRapidCharacterisation. Then, we trained the deep-learning model using the data generated with the hERG model and tested the validity of the deep-learning model with the experimental data. We successfully identified the initial value, significantly improved the fitting speed, and avoided fitting failure. This method is useful when the model is fixed and reflects the real data, and it can be applied to any in silico model for various purposes, such as new drug development, toxicity identification, environmental effect, etc. This method will significantly reduce the time and effort to analyze the data.

Models of the cardiac L-type calcium current: A quantitative review

The L-type calcium current (I CaL ) plays a critical role in cardiac electrophysiology, and models ofI CaL are vital tools to predict arrhythmogenicity of drugs and mutations. Five decades of measuring and modelingI CaL have resulted in several competing theories (encoded in mathematical equations). However, the introduction of new models has not typically been accompanied by a data-driven critical comparison with previous work, so that it is unclear which model is best suited for any particular application. In this review, we describe and compare 73 published mammalianI CaL models and use simulated experiments to show that there is a large variability in their predictions, which is not substantially diminished when grouping by species or other categories. We provide model code for 60 models, list major data sources, and discuss experimental and modeling work that will be required to reduce this huge list of competing theories and ultimately develop a community consensus model ofI CaL . This article is categorized under: Cardiovascular Diseases > Computational Models Cardiovascular Diseases > Molecular and Cellular Physiology.

Quantifying arrhythmic long QT effects of hydroxychloroquine and azithromycin with whole-heart optical mapping and simulations

Background

In March 2020, hydroxychloroquine (HCQ) alone or combined with azithromycin (AZM) was authorized as a treatment for COVID-19 in many countries. The therapy proved ineffective with long QT and deadly cardiac arrhythmia risks, illustrating challenges to determine the new safety profile of repurposed drugs.

Objective

To investigate proarrhythmic effects and mechanism of HCQ and AZM (combined and alone) with high doses of HCQ as in the COVID-19 clinical trials.

Methods

Proarrhythmic effects of HCQ and AZM are quantified using optical mapping with voltage-sensitive dyes in ex vivo Langendorff-perfused guinea pig (GP) hearts and with numerical simulations of a GP Luo-Rudy and a human O’Hara-Virag-Varro-Rudy models, for Epi, Endo, and M cells, in cell and tissue, incorporating the drug’s effect on cell membrane ionic currents.

Results

Experimentally, HCQ alone and combined with AZM leads to long QT intervals by prolonging the action potential duration and increased spatial dispersion of action potential (AP) repolarization across the heart, leading to proarrhythmic discordant alternans. AZM alone had a lesser arrhythmic effect with less triangulation of the AP shape. Mathematical cardiac models fail to reproduce most of the arrhythmic effects observed experimentally.

Conclusions

During public health crises, the risks and benefits of new and repurposed drugs could be better assessed with alternative experimental and computational approaches to identify proarrhythmic mechanisms. Optical mapping is an effective framework suitable to investigate the drug’s adverse effects on cardiac cell membrane ionic channels at the cellular level and arrhythmia mechanisms at the tissue and whole-organ level.

Non-Coding RNAs in the Cardiac Action Potential and Their Impact on Arrhythmogenic Cardiac Diseases

Cardiac arrhythmias are prevalent among humans across all age ranges, affecting millions of people worldwide. While cardiac arrhythmias vary widely in their clinical presentation, they possess shared complex electrophysiologic properties at cellular level that have not been fully studied. Over the last decade, our current understanding of the functional roles of non-coding RNAs have progressively increased. microRNAs represent the most studied type of small ncRNAs and it has been demonstrated that miRNAs play essential roles in multiple biological contexts, including normal development and diseases. In this review, we provide a comprehensive analysis of the functional contribution of non-coding RNAs, primarily microRNAs, to the normal configuration of the cardiac action potential, as well as their association to distinct types of arrhythmogenic cardiac diseases.

Multiphysics computational modelling of the cardiac ventricles

Development of cardiac multiphysics models has progressed significantly over the decades and simulations combining multiple physics interactions have become increasingly common. In this review, we summarise the progress in this field focusing on various approaches of integrating ventricular structures. electrophysiological properties, myocardial mechanics, as well as incorporating blood hemodynamics and the circulatory system. Common coupling approaches are discussed and compared, including the advantages and shortcomings of each. Currently used strategies for patient-specific implementations are highlighted and potential future improvements considered.

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.

Antiarrhythmic drug effects on premature beats are partly determined by prior cardiac activation frequency in perfused guinea-pig heart

NEW FINDINGS

What is the central question of this study? Can antiarrhythmic drug effects on repolarization, conduction time and excitation wavelength in premature beats be determined by prior cardiac activation frequency? What is the main finding and its importance? In premature beats induced after a series of cardiac activations at a slow rate, antiarrhythmics prolong repolarization but evoke little or no conduction delay, thus increasing the excitation wavelength, which indicates an antiarrhythmic effect. Fast prior activation rate attenuates prolongation of repolarization, while amplifying the conduction delay induced by drugs, which translates into the reduced excitation wavelength, indicating proarrhythmia. These findings suggest that a sudden increase in heart rate can shape adverse pharmacological profiles in patients with ventricular ectopy.

ABSTRACT

Antiarrhythmic drugs used to treat atrial fibrillation can occasionally induce ventricular tachyarrhythmia, which is typically precipitated by a premature ectopic beat through a mechanism related, in part, to the shortening of the excitation wavelength (EW). The arrhythmia is likely to occur when a drug induces a reduction, rather than an increase, in the EW of ectopic beats. In this study, I examined whether the arrhythmic drug profile is shaped by the increased cardiac activation rate before ectopic excitation. Ventricular monophasic action potential durations, conduction times and EW values were assessed during programmed stimulations applied at long (S₁ -S₁ [basic drive cycle length] = 550 ms) and short (S₁ -S₁  = 200 ms) cycle lengths in perfused guinea-pig hearts. The premature activations were induced with extrastimulus application immediately upon termination of the refractory period. With dofetilide, a class III antiarrhythmic agent, a prolongation in action potential duration and the resulting increase in the EW obtained at S₁ -S₁  = 550 ms were significantly attenuated at S₁ -S₁  = 200 ms, in both the regular (S₁ ) and the premature (S₂ ) beats. With class I antiarrhythmic agents (quinidine, procainamide and flecainide), fast S₁ -S₁ pacing was found to attenuate the drug-induced increase in action potential duration, while amplifying drug-induced conduction slowing, in both S₁ and S₂ beats. As a result, although the EW was increased (quinidine and procainamide) or not changed (flecainide) at the long S₁ -S₁ intervals, it was invariably reduced by these agents at the short S₁ -S₁ intervals. These findings indicate that the increased heart rate before ectopic activation shapes the arrhythmic profiles by facilitating drug-induced EW reduction.

Modulation of hERG K+ Channel Deactivation by Voltage Sensor Relaxation

The hERG (human-ether-à-go-go-related gene) channel underlies the rapid delayed rectifier current, I_kr, in the heart, which is essential for normal cardiac electrical activity and rhythm. Slow deactivation is one of the hallmark features of the unusual gating characteristics of hERG channels, and plays a crucial role in providing a robust current that aids repolarization of the cardiac action potential. As such, there is significant interest in elucidating the underlying mechanistic determinants of slow hERG channel deactivation. Recent work has shown that the hERG channel S4 voltage sensor is stabilized following activation in a process termed relaxation. Voltage sensor relaxation results in energetic separation of the activation and deactivation pathways, producing a hysteresis, which modulates the kinetics of deactivation gating. Despite widespread observation of relaxation behaviour in other voltage-gated K⁺ channels, such as Shaker, Kv1.2 and Kv3.1, as well as the voltage-sensing phosphatase Ci-VSP, the relationship between stabilization of the activated voltage sensor by the open pore and voltage sensor relaxation in the control of deactivation has only recently begun to be explored. In this review, we discuss present knowledge and questions raised related to the voltage sensor relaxation mechanism in hERG channels and compare structure-function aspects of relaxation with those observed in related ion channels. We focus discussion, in particular, on the mechanism of coupling between voltage sensor relaxation and deactivation gating to highlight the insight that these studies provide into the control of hERG channel deactivation gating during their physiological functioning.

Short-Long Heart Rate Variation Increases Dispersion of Action Potential Duration in Long QT Type 2 Transgenic Rabbit Model

The initiation of polymorphic ventricular tachycardia in long QT syndrome type 2 (LQT2) has been associated with a characteristic ECG pattern of short-long RR intervals. We hypothesize that this characteristic pattern increases APD dispersion in LQT2, thereby promoting arrhythmia. We investigated APD dispersion and its dependence on two previous cycle lengths (CLs) in transgenic rabbit models of LQT2, LQT1, and their littermate controls (LMC) using random stimulation protocols. The results show that the short-long RR pattern was associated with a larger APD dispersion in LQT2 but not in LQT1 rabbits. The multivariate analyses of APD as a function of two previous CLs (APD_n = C + α₁CL_n−1 + α₂CL_n−2) showed that α₁ (APD restitution slope) is largest and heterogeneous in LQT2 but uniform in LQT1, enhancing APD dispersion under long CL_n−1 in LQT2. The α₂ (short-term memory) was negative in LQT2 while positive in LQT1, and the spatial pattern of α₁ was inversely correlated to α₂ in LQT2, which explains why a short-long combination causes a larger APD dispersion in LQT2 but not in LQT1 rabbits. In conclusion, short-long RR pattern increased APD dispersion only in LQT2 rabbits through heterogeneous APD restitution and the short-term memory, underscoring the genotype-specific triggering of arrhythmias in LQT syndrome.

Rapid Characterization of hERG Channel Kinetics I: Using an Automated High-Throughput System

Predicting how pharmaceuticals may affect heart rhythm is a crucial step in drug development and requires a deep understanding of a compound’s action on ion channels. In vitro hERG channel current recordings are an important step in evaluating the proarrhythmic potential of small molecules and are now routinely performed using automated high-throughput patch-clamp platforms. These machines can execute traditional voltage-clamp protocols aimed at specific gating processes, but the array of protocols needed to fully characterize a current is typically too long to be applied in a single cell. Shorter high-information protocols have recently been introduced that have this capability, but they are not typically compatible with high-throughput platforms. We present a new 15 second protocol to characterize hERG (Kv11.1) kinetics, suitable for both manual and high-throughput systems. We demonstrate its use on the Nanion SyncroPatch 384PE, a 384-well automated patch-clamp platform, by applying it to Chinese hamster ovary cells stably expressing hERG1a. From these recordings, we construct 124 cell-specific variants/parameterizations of a hERG model at 25°C. A further eight independent protocols are run in each cell and are used to validate the model predictions. We then combine the experimental recordings using a hierarchical Bayesian model, which we use to quantify the uncertainty in the model parameters, and their variability from cell-to-cell; we use this model to suggest reasons for the variability. This study demonstrates a robust method to measure and quantify uncertainty and shows that it is possible and practical to use high-throughput systems to capture full hERG channel kinetics quantitatively and rapidly.

Effects of antiarrhythmics on the electrical restitution in perfused guinea-pig heart are critically determined by the applied cardiac pacing protocol

NEW FINDINGS

What is the central question of this study? Are modifications in the restitution of ventricular action potential duration induced by antiarrhythmic drugs the same when assessed with premature extrastimulus application at variable coupling intervals (the standard stimulation protocol) and with steady state pacing at variable rates (the dynamic stimulation protocol)? What is the main finding and its importance? With class I and class III antiarrhythmics, the effects on electrical restitution determined with the standard stimulation protocol dissociate from those obtained during dynamic pacing. These findings indicate a limited value of the electrical restitution assessments based on extrasystolic stimulations alone, as performed in the clinical studies, in estimating the outcomes of antiarrhythmic drug therapies.

ABSTRACT

A steep slope of the ventricular action potential duration (APD) to diastolic interval (DI) relationships (the electrical restitution) can precipitate tachyarrhythmia, whereas a flattened slope is antiarrhythmic. The derangements in APD restitution responsible for transition of tachycardia to ventricular fibrillation can be assessed with cardiac pacing at progressively increasing rates (the dynamic stimulation protocol). Nevertheless, this method is not used clinically owing to the risk of inducing myocardial ischaemia. Instead, the restitution kinetics is determined with a premature extrastimulus application at variable coupling intervals (the standard stimulation protocol). Whether the two protocols are equivalent in estimating antiarrhythmic drug effects is uncertain. In this study, dofetilide and quinidine, the agents blocking repolarizing K⁺ currents, increased epicardial APD in perfused guinea-pig hearts, with effects being greater at long vs. short DIs. These changes were more pronounced during dynamic pacing compared to premature extrastimulations. Accordingly, although both agents markedly steepened the dynamic restitution, there was only a marginal increase in the standard restitution slope with dofetilide, and no effect with quinidine. Lidocaine and mexiletine, selective Na⁺ channel blockers, prolonged the effective refractory period without changing APD, and increased the minimum DI that enabled ventricular capture during extrastimulations. No change in the minimum DI was noted during dynamic pacing. Consequently, although lidocaine and mexiletine reduced the standard restitution slope, they failed to flatten the dynamic restitution. Overall, these findings imply a limited value of the electrical restitution assessments with premature extrastimulations alone in discriminating arrhythmic vs. antiarrhythmic changes during drug therapies.

The influence of hERG1a and hERG1b isoforms on drug safety screening in iPSC-CMs

The human Ether-à-go-go Related Gene (hERG) encodes the pore forming subunit of the channel that conducts the rapid delayed rectifier potassium current I_Kr. I_Kr drives repolarization in the heart and when I_Kr is dysfunctional, cardiac repolarization delays, the QT interval on the electrocardiogram (ECG) prolongs and the risk of developing lethal arrhythmias such as Torsade de Pointes (TdP) increases. TdP risk is incorporated in drug safety screening for cardiotoxicity where hERG is the main target since the I_Kr channels appear highly sensitive to blockage. hERG block is also included as an important read-out in the Comprehensive in Vitro Proarrhythmia Assay (CiPA) initiative which aims to combine in vitro and in silico experiments on induced pluripotent stem cell-derived cardiomyocytes (iPSC-CMs) to screen for cardiotoxicity. However, the hERG channel has some unique features to consider for drug safety screening, which we will discuss in this study. The hERG channel consists of different isoforms, hERG1a and hERG1b, which individually influence the kinetics of the channel and the drug response in the human heart and in iPSC-CMs. hERG1b is often underappreciated in iPSC-CM studies, drug screening assays and in silico models, and the fact that its contribution might substantially differ between iPSC-CM and healthy but also diseased human heart, adds to this problem. In this study we show that the activation kinetics in iPSC-CMs resemble hERG1b kinetics using Cs⁺ as a charge carrier. Not including hERG1b in drug safety testing might underestimate the actual role of hERG1b in repolarization and drug response, and might lead to inappropriate conclusions. We stress to focus more on including hERG1b in drug safety testing concerning I_Kr.

Facilitation of I Kr current by some hERG channel blockers suppresses early afterdepolarizations

Some hERG channel blockers are clinically safe, but others cause fatal cardiac arrhythmias. Furutani et al. show that safe blockers facilitate channel opening in ventricular myocytes and provide a repolarization reserve at precisely the voltages and times needed to suppress arrhythmias.

Drug-induced block of the cardiac rapid delayed rectifying potassium current (I_Kr), carried by the human ether-a-go-go-related gene (hERG) channel, is the most common cause of acquired long QT syndrome. Indeed, some, but not all, drugs that block hERG channels cause fatal cardiac arrhythmias. However, there is no clear method to distinguish between drugs that cause deadly arrhythmias and those that are clinically safe. Here we propose a mechanism that could explain why certain clinically used hERG blockers are less proarrhythmic than others. We demonstrate that several drugs that block hERG channels, but have favorable cardiac safety profiles, also evoke another effect; they facilitate the hERG current amplitude in response to low-voltage depolarization. To investigate how hERG facilitation impacts cardiac safety, we develop computational models of I_Kr block with and without this facilitation. We constrain the models using data from voltage clamp recordings of hERG block and facilitation by nifekalant, a safe class III antiarrhythmic agent. Human ventricular action potential simulations demonstrate the ability of nifekalant to suppress ectopic excitations, with or without facilitation. Without facilitation, excessive I_Kr block evokes early afterdepolarizations, which cause lethal arrhythmias. When facilitation is introduced, early afterdepolarizations are prevented at the same degree of block. Facilitation appears to prevent early afterdepolarizations by increasing I_Kr during the repolarization phase of action potentials. We empirically test this prediction in isolated rabbit ventricular myocytes and find that action potential prolongation with nifekalant is less likely to induce early afterdepolarization than action potential prolongation with dofetilide, a hERG channel blocker that does not induce facilitation. Our data suggest that hERG channel blockers that induce facilitation increase the repolarization reserve of cardiac myocytes, rendering them less likely to trigger lethal ventricular arrhythmias.

Control of voltage-driven instabilities in cardiac myocytes with memory

Sudden cardiac death is known to be associated with dynamical instabilities in the heart, and thus control of dynamical instabilities is considered a potential therapeutic strategy. Different control methods were developed previously, including time-delayed feedback pacing control and constant diastolic interval pacing control. Experimental, theoretical, and simulation studies have examined the efficacy of these control methods in stabilizing action potential dynamics. In this study, we apply these control methods to control complex action potential (AP) dynamics under two diseased conditions: early repolarization syndrome and long QT syndrome, in which voltage-driven instabilities occur in the presence of short-term cardiac memory. In addition, we also develop a feedback pacing method to stabilize these instabilities. We perform theoretical analyses using iterated map models and carry out numerical simulations of AP models. We show that under the normal condition where the memory effect is minimal, all three methods can effectively control the action potential duration (APD) dynamics. Under the two diseased conditions where the memory effect is exacerbated, constant diastolic pacing control is least effective, while the feedback pacing control is most effective. Under a very strong memory effect, all three methods fail to stabilize the voltage-driven instabilities. The failure of effective control is due to memory and the all-or-none AP dynamics which results in very steep changes in APD.

A response surface optimization approach to adjust ionic current conductances of cardiac electrophysiological models. Application to the study of potassium level changes

Cardiac electrophysiological computational models are often developed from previously published models. The new models may incorporate additional features to adapt the model to a different species or may upgrade a specific ionic formulation based on newly available experimental data. A relevant challenge in the development of a new model is the estimation of certain ionic current conductances that cannot be reliably identified from experiments. A common strategy to estimate those conductances is by means of constrained non-linear least-squares optimization. In this work, a novel methodology is proposed for estimation of ionic current conductances of cardiac electrophysiological models by using a response surface approximation-based constrained optimization with trust region management. Polynomial response surfaces of a number of electrophysiological markers were built using statistical sampling methods. These markers included action potential duration (APD), triangulation, diastolic and systolic intracellular calcium concentration, and time constants of APD rate adaptation. The proposed methodology was applied to update the Carro et al. human ventricular action potential model after incorporation of intracellular potassium ([K⁺]_i) dynamics. While the Carro et al. model was well suited for investigation of arrhythmogenesis, it did not allow simulation of [K⁺]_i changes. With the methodology proposed in this study, the updated Carro et al. human ventricular model could be used to simulate [K⁺]_i changes in response to varying extracellular potassium ([K⁺]_o) levels. Additionally, it rendered values of evaluated electrophysiological markers within physiologically plausible ranges. The optimal values of ionic current conductances in the updated model were found in a notably shorter time than with previously proposed methodologies. As a conclusion, the response surface optimization-based approach proposed in this study allows estimating ionic current conductances of cardiac electrophysiological computational models while guaranteeing replication of key electrophysiological features and with an important reduction in computational cost with respect to previously published approaches. The updated Carro et al. model developed in this study is thus suitable for the investigation of arrhythmic risk-related conditions, including those involving large changes in potassium concentration.

Transient Outward K+ Current (Ito) Underlies the Right Ventricular Initiation of Polymorphic Ventricular Tachycardia in a Transgenic Rabbit Model of Long-QT Syndrome Type 1

BACKGROUND

Sudden death in long-QT syndrome type 1 (LQT1), an inherited disease caused by loss-of-function mutations in KCNQ1, is triggered by early afterdepolarizations (EADs) that initiate polymorphic ventricular tachycardia (pVT). We investigated ionic mechanisms that underlie pVT in LQT1 using a transgenic rabbit model of LQT1.

METHODS

Optical mapping, cellular patch clamping, and computer modeling were used to elucidate the mechanisms of EADs in transgenic LQT1 rabbits.

RESULTS

The results showed that shorter action potential duration in the right ventricle (RV) was associated with focal activity during pVT initiation. RV cardiomyocytes demonstrated higher incidence of EADs under 50 nmol/L isoproterenol. Voltage-clamp studies revealed that the transient outward potassium current (Ito) magnitude was 28% greater in RV associated with KChiP2 but with no differences in terms of calcium-cycling kinetics and other sarcolemmal currents. Perfusing with the Ito blocker 4-aminopyridine changed the initial focal sites of pVT from the RV to the left ventricle, corroborating the role of Ito in pVT initiation. Computer modeling showed that EADs occur preferentially in the RV because of the larger conductance of the slow-inactivating component of Ito, which repolarizes the membrane potential sufficiently rapidly to allow reactivation of ICa,L before IKr has had sufficient time to activate.

CONCLUSIONS

Ito heterogeneity creates both triggers and an arrhythmogenic substrate in LQT1. In the absence of IKs, Ito interactions with ICa,L and IKr promote EADs in the RV while prolonging action potential duration in the left ventricle. This heterogeneity of action potential enhances dispersion of refractoriness and facilitates conduction blocks that initiate pVTs.

Sinusoidal voltage protocols for rapid characterisation of ion channel kinetics

Key points

Ion current kinetics are commonly represented by current–voltage relationships, time constant–voltage relationships and subsequently mathematical models fitted to these. These experiments take substantial time, which means they are rarely performed in the same cell.

Rather than traditional square‐wave voltage clamps, we fitted a model to the current evoked by a novel sum‐of‐sinusoids voltage clamp that was only 8 s long.

Short protocols that can be performed multiple times within a single cell will offer many new opportunities to measure how ion current kinetics are affected by changing conditions.

The new model predicts the current under traditional square‐wave protocols well, with better predictions of underlying currents than literature models. The current under a novel physiologically relevant series of action potential clamps is predicted extremely well.

The short sinusoidal protocols allow a model to be fully fitted to individual cells, allowing us to examine cell–cell variability in current kinetics for the first time.

Abstract

Understanding the roles of ion currents is crucial to predict the action of pharmaceuticals and mutations in different scenarios, and thereby to guide clinical interventions in the heart, brain and other electrophysiological systems. Our ability to predict how ion currents contribute to cellular electrophysiology is in turn critically dependent on our characterisation of ion channel kinetics – the voltage‐dependent rates of transition between open, closed and inactivated channel states. We present a new method for rapidly exploring and characterising ion channel kinetics, applying it to the hERG potassium channel as an example, with the aim of generating a quantitatively predictive representation of the ion current. We fitted a mathematical model to currents evoked by a novel 8 second sinusoidal voltage clamp in CHO cells overexpressing hERG1a. The model was then used to predict over 5 minutes of recordings in the same cell in response to further protocols: a series of traditional square step voltage clamps, and also a novel voltage clamp comprising a collection of physiologically relevant action potentials. We demonstrate that we can make predictive cell‐specific models that outperform the use of averaged data from a number of different cells, and thereby examine which changes in gating are responsible for cell–cell variability in current kinetics. Our technique allows rapid collection of consistent and high quality data, from single cells, and produces more predictive mathematical ion channel models than traditional approaches.

Ion current kinetics are commonly represented by current–voltage relationships, time constant–voltage relationships and subsequently mathematical models fitted to these. These experiments take substantial time, which means they are rarely performed in the same cell.

Rather than traditional square‐wave voltage clamps, we fitted a model to the current evoked by a novel sum‐of‐sinusoids voltage clamp that was only 8 s long.

Short protocols that can be performed multiple times within a single cell will offer many new opportunities to measure how ion current kinetics are affected by changing conditions.

The new model predicts the current under traditional square‐wave protocols well, with better predictions of underlying currents than literature models. The current under a novel physiologically relevant series of action potential clamps is predicted extremely well.

The short sinusoidal protocols allow a model to be fully fitted to individual cells, allowing us to examine cell–cell variability in current kinetics for the first time.

Memory-induced nonlinear dynamics of excitation in cardiac diseases

Excitable cells, such as cardiac myocytes, exhibit short-term memory, i.e., the state of the cell depends on its history of excitation. Memory can originate from slow recovery of membrane ion channels or from accumulation of intracellular ion concentrations, such as calcium ion or sodium ion concentration accumulation. Here we examine the effects of memory on excitation dynamics in cardiac myocytes under two diseased conditions, early repolarization and reduced repolarization reserve, each with memory from two different sources: slow recovery of a potassium ion channel and slow accumulation of the intracellular calcium ion concentration. We first carry out computer simulations of action potential models described by differential equations to demonstrate complex excitation dynamics, such as chaos. We then develop iterated map models that incorporate memory, which accurately capture the complex excitation dynamics and bifurcations of the action potential models. Finally, we carry out theoretical analyses of the iterated map models to reveal the underlying mechanisms of memory-induced nonlinear dynamics. Our study demonstrates that the memory effect can be unmasked or greatly exacerbated under certain diseased conditions, which promotes complex excitation dynamics, such as chaos. The iterated map models reveal that memory converts a monotonic iterated map function into a nonmonotonic one to promote the bifurcations leading to high periodicity and chaos.

Inhibitory Effect of Vascular Endothelial Growth Factor on the Slowly Activating Delayed Rectifier Potassium Current in Guinea Pig Ventricular Myocytes

Background

Vascular endothelial growth factor (VEGF) exerts a number of beneficial effects on ischemic myocardium via its angiogenic properties. However, little is known about whether VEGF has a direct effect on the electrical properties of cardiomyocytes. In the present study, we investigated the effects of different concentrations of VEGF on delayed rectifier potassium currents (I_K) in guinea pig ventricular myocytes and their effects on action potential (AP) parameters.

Methods and Results

I_K and AP were recorded by the whole‐cell patch clamp method in ventricular myocytes. Cells were superfused with control solution or solution containing VEGF at different concentrations for 10 minutes before recording. Some ventricular myocytes were pretreated with a phosphatidylinositol 3‐kinase inhibitor for 1 hour before the addition of VEGF. We found that VEGF inhibited the slowly activating delayed rectifier potassium current (I_Ks) in a concentration‐dependent manner (18.13±1.04 versus 12.73±0.34, n=5, P=0.001; 12.73±0.34 versus 9.05±1.20, n=5, P=0.036) and prolonged AP duration (894.5±36.92 versus 746.3±33.71, n=5, P=0.021). Wortmannin, a phosphatidylinositol 3‐kinase inhibitor, eliminated these VEGF‐induced effects. VEGF had no significant effect on the rapidly activating delayed rectifier potassium current (I_Kr), resting membrane potential, AP amplitude, or maximal velocity of depolarization.

Conclusions

VEGF inhibited I_Ks in a concentration‐dependent manner through a phosphatidylinositol 3‐kinase–mediated signaling pathway, leading to AP prolongation. The results indicate a promising therapeutic potential of VEGF in prevention of ventricular tachyarrhythmias under conditions of high sympathetic activity and ischemia.

Arrhythmogenic drugs can amplify spatial heterogeneities in the electrical restitution in perfused guinea-pig heart: An evidence from assessments of monophasic action potential durations and JT intervals

Non-uniform shortening of the action potential duration (APD90) in different myocardial regions upon heart rate acceleration can set abnormal repolarization gradients and promote arrhythmia. This study examined whether spatial heterogeneities in APD90 restitution can be amplified by drugs with clinically proved proarrhythmic potential (dofetilide, quinidine, procainamide, and flecainide) and, if so, whether these effects can translate to the appropriate changes of the ECG metrics of ventricular repolarization, such as JT intervals. In isolated, perfused guinea-pig heart preparations, monophasic action potentials and volume-conducted ECG were recorded at progressively increased pacing rates. The APD90 measured at distinct ventricular sites, as well as the JTpeak and JTend values were plotted as a function of preceding diastolic interval, and the maximum slopes of the restitution curves were determined at baseline and upon drug administration. Dofetilide, quinidine, and procainamide reverse rate-dependently prolonged APD90 and steepened the restitution curve, with effects being greater at the endocardium than epicardium, and in the right ventricular (RV) vs. the left ventricular (LV) chamber. The restitution slope was increased to a greater extent for the JTend vs. the JTpeak interval. In contrast, flecainide reduced the APD90 restitution slope at LV epicardium without producing effect at LV endocardium and RV epicardium, and reduced the JTpeak restitution slope without changing the JTend restitution. Nevertheless, with all agents, these effects translated to the amplified epicardial-to-endocardial and the LV-to-RV non-uniformities in APD90 restitution, paralleled by the increased JTend vs. JTpeak difference in the restitution slope. In summary, these findings suggest that arrhythmic drug profiles are partly attributable to the accentuated regional heterogeneities in APD90 restitution, which can be indirectly determined through ECG assessments of the JTend vs. JTpeak dynamics at variable pacing rates.

Kv4.3 Modulates the Distribution of hERG

This study examines the interaction between hERG and Kv4.3. The functional interaction between hERG and Kv4.3, expressed in a heterologous cell line, was studied using patch clamp techniques, western blot, immunofluorescence, and co-immunoprecipitation. Co-expression of Kv4.3 with hERG increased hERG current density (tail current after a step to +10 mV: 26 ± 3 versus 56 ± 7 pA/pF, p < 0.01). Kv4.3 co-expression also increased the protein expression and promoted the membrane localization of hERG. Western blot showed Kv4.3 increased hERG expression by Hsp70. hERG and Kv4.3 co-localized and co-immunoprecipitated in cultured 293 T cells, indicating physical interactions between hERG and Kv4.3 proteins in vitro. In addition, Hsp70 interacted with hERG and Kv4.3 respectively, and formed complexes with hERG and Kv4.3. The α subunit of I_to Kv4.3 can interact with and modify the localization of the α subunit of I_Kr hERG, thus providing potentially novel insights into the molecular mechanism of the malignant ventricular arrhythmia in heart failure.

Role of abnormal repolarization in the mechanism of cardiac arrhythmia

In cardiac patients, life-threatening tachyarrhythmia is often precipitated by abnormal changes in ventricular repolarization and refractoriness. Repolarization abnormalities typically evolve as a consequence of impaired function of outward K⁺ currents in cardiac myocytes, which may be caused by genetic defects or result from various acquired pathophysiological conditions, including electrical remodelling in cardiac disease, ion channel modulation by clinically used pharmacological agents, and systemic electrolyte disorders seen in heart failure, such as hypokalaemia. Cardiac electrical instability attributed to abnormal repolarization relies on the complex interplay between a provocative arrhythmic trigger and vulnerable arrhythmic substrate, with a central role played by the excessive prolongation of ventricular action potential duration, impaired intracellular Ca²⁺ handling, and slowed impulse conduction. This review outlines the electrical activity of ventricular myocytes in normal conditions and cardiac disease, describes classical electrophysiological mechanisms of cardiac arrhythmia, and provides an update on repolarization-related surrogates currently used to assess arrhythmic propensity, including spatial dispersion of repolarization, activation-repolarization coupling, electrical restitution, TRIaD (triangulation, reverse use dependence, instability, and dispersion), and the electromechanical window. This is followed by a discussion of the mechanisms that account for the dependence of arrhythmic vulnerability on the location of the ventricular pacing site. Finally, the review clarifies the electrophysiological basis for cardiac arrhythmia produced by hypokalaemia, and gives insight into the clinical importance and pathophysiology of drug-induced arrhythmia, with particular focus on class Ia (quinidine, procainamide) and Ic (flecainide) Na⁺ channel blockers, and class III antiarrhythmic agents that block the delayed rectifier K⁺ channel (dofetilide).

Beat-to-beat ECG restitution: A review and proposal for a new biomarker to assess cardiac stress and ventricular tachyarrhythmia vulnerability

BACKGROUND

Cardiac restitution is the ability of the heart to recover from one beat to the next. Ventricular arrhythmia vulnerability can occur when the heart does not properly adjust to sudden changes in rate or in hemodynamics leading to excessive temporal and/or spatial heterogeneity in conduction or repolarization. Restitution has historically been used to study, by invasive means, the dynamics of the relationship between action potential duration (APD) and diastolic interval (DI) in sedated subjects using various pacing protocols. Even though the analogous measures of APD and DI can be obtained using the surface ECG to acquire the respective QT and TQ intervals for ECG restitution, this methodology has not been widely adopted for a number of reasons.

METHODS

Recent development of more advanced software algorithms enables ECG intervals to be measured accurately, on a continuous beat-to-beat basis, in an automated manner, and under highly dynamic conditions (i.e., ambulatory or exercise) providing information beyond that available in the typical resting state.

RESULTS

Current breakthroughs in ECG technology will allow ECG restitution measures to become a practical approach for providing quantitative measures of the risks for ventricular arrhythmias as well as cardiac stress in general.

CONCLUSIONS

In addition to a review of the underlying principles and caveats of ECG restitution, a new approach toward an advancement of more integrated restitution biomarkers is proposed.

Quantitative analysis of the Ca2+ -dependent regulation of delayed rectifier K+ current IKs in rabbit ventricular myocytes

KEY POINTS

[Ca²⁺ ]_i enhanced rabbit ventricular slowly activating delayed rectifier K⁺ current (I_Ks ) by negatively shifting the voltage dependence of activation and slowing deactivation, similar to perfusion of isoproterenol. Rabbit ventricular rapidly activating delayed rectifier K⁺ current (I_Kr ) amplitude and voltage dependence were unaffected by high [Ca²⁺ ]_i . When measuring or simulating I_Ks during an action potential, I_Ks was not different during a physiological Ca²⁺ transient or when [Ca²⁺ ]_i was buffered to 500 nm.

ABSTRACT

The slowly activating delayed rectifier K⁺ current (I_Ks ) contributes to repolarization of the cardiac action potential (AP). Intracellular Ca²⁺ ([Ca²⁺ ]_i ) and β-adrenergic receptor (β-AR) stimulation modulate I_Ks amplitude and kinetics, but details of these important I_Ks regulators and their interaction are limited. We assessed the [Ca²⁺ ]_i dependence of I_Ks in steady-state conditions and with dynamically changing membrane potential and [Ca²⁺ ]_i during an AP. I_Ks was recorded from freshly isolated rabbit ventricular myocytes using whole-cell patch clamp. With intracellular pipette solutions that controlled free [Ca²⁺ ]_i , we found that raising [Ca²⁺ ]_i from 100 to 600 nm produced similar increases in I_Ks as did β-AR activation, and the effects appeared additive. Both β-AR activation and high [Ca²⁺ ]_i increased maximally activated tail I_Ks , negatively shifted the voltage dependence of activation, and slowed deactivation kinetics. These data informed changes in our well-established mathematical model of the rabbit myocyte. In both AP-clamp experiments and simulations, I_Ks recorded during a normal physiological Ca²⁺ transient was similar to I_Ks measured with [Ca²⁺ ]_i clamped at 500-600 nm. Thus, our study provides novel quantitative data as to how physiological [Ca²⁺ ]_i regulates I_Ks amplitude and kinetics during the normal rabbit AP. Our results suggest that micromolar [Ca²⁺ ]_i , in the submembrane or junctional cleft space, is not required to maximize [Ca²⁺ ]_i -dependent I_Ks activation during normal Ca²⁺ transients.

Potassium currents in the heart: functional roles in repolarization, arrhythmia and therapeutics

This is the second of the two White Papers from the fourth UC Davis Cardiovascular Symposium Systems Approach to Understanding Cardiac Excitation-Contraction Coupling and Arrhythmias (3-4 March 2016), a biennial event that brings together leading experts in different fields of cardiovascular research. The theme of the 2016 symposium was 'K⁺ channels and regulation', and the objectives of the conference were severalfold: (1) to identify current knowledge gaps; (2) to understand what may go wrong in the diseased heart and why; (3) to identify possible novel therapeutic targets; and (4) to further the development of systems biology approaches to decipher the molecular mechanisms and treatment of cardiac arrhythmias. The sessions of the Symposium focusing on the functional roles of the cardiac K⁺ channel in health and disease, as well as K⁺ channels as therapeutic targets, were contributed by Ye Chen-Izu, Gideon Koren, James Weiss, David Paterson, David Christini, Dobromir Dobrev, Jordi Heijman, Thomas O'Hara, Crystal Ripplinger, Zhilin Qu, Jamie Vandenberg, Colleen Clancy, Isabelle Deschenes, Leighton Izu, Tamas Banyasz, Andras Varro, Heike Wulff, Eleonora Grandi, Michael Sanguinetti, Donald Bers, Jeanne Nerbonne and Nipavan Chiamvimonvat as speakers and panel discussants. This article summarizes state-of-the-art knowledge and controversies on the functional roles of cardiac K⁺ channels in normal and diseased heart. We endeavour to integrate current knowledge at multiple scales, from the single cell to the whole organ levels, and from both experimental and computational studies.

Limitations in electrophysiological model development and validation caused by differences between simulations and experimental protocols

Models of ion channel dynamics are usually built by fitting isolated cell experimental values of individual parameters while neglecting the interaction between them. Another shortcoming regards the estimation of ionic current conductances, which is often based on quantification of Action Potential (AP)-derived markers. Although this procedure reduces the uncertainty in the calculation of conductances, many studies evaluate electrophysiological AP-derived markers from single cell simulations, whereas experimental measurements are obtained from tissue preparations. In this work, we explore the limitations of these approaches to estimate ion channel dynamics and maximum current conductances and how they could be overcome by using multiscale simulations of experimental protocols. Four human ventricular cell models, namely ten Tusscher and Panfilov (2006), Grandi et al. (2010), O'Hara et al. (2011), and Carro et al. (2011), were used. Two problems involving scales from ion channels to tissue were investigated: 1) characterization of L-type calcium voltage-dependent inactivation I_Ca,L; 2) identification of major ionic conductance contributors to steady-state AP markers, including APD₉₀, APD₇₅, APD₅₀, APD₂₅, Triangulation and maximal and minimal values of V and dV/dt during the AP (V_max, V_min, dV/dt_max, dV/dt_min). Our results show that: 1) I_Ca,L inactivation characteristics differed significantly when calculated from model equations and from simulations reproducing the experimental protocols. 2) Large differences were found in the ionic currents contributors to APD₂₅, Triangulation, V_max, dV/dt_max and dV/dt_min between single cells and 1D-tissue. When proposing any new model formulation, or evaluating an existing model, consistency between simulated and experimental data should be verified considering all involved effects and scales.

Spontaneous initiation of premature ventricular complexes and arrhythmias in type 2 long QT syndrome

The occurrence of early afterdepolarizations (EADs) and increased dispersion of repolarization are two known factors for arrhythmogenesis in long QT syndrome. However, increased dispersion of repolarization tends to suppress EADs due to the source-sink effect, and thus how the two competing factors cause initiation of arrhythmias remains incompletely understood. Here we used optical mapping and computer simulation to investigate the mechanisms underlying spontaneous initiation of arrhythmias in type 2 long QT (LQT2) syndrome. In optical mapping experiments of transgenic LQT2 rabbit hearts under isoproterenol, premature ventricular complexes (PVCs) were observed to originate from the steep spatial repolarization gradient (RG) regions and propagated unidirectionally. The same PVC behaviors were demonstrated in computer simulations of tissue models of rabbits. Depending on the heterogeneities, these PVCs could lead to either repetitive focal excitations or reentry without requiring an additional vulnerable substrate. Systematic simulations showed that cellular phase 2 EADs were either suppressed or confined to the long action potential region due to the source-sink effect. Tissue-scale phase 3 EADs and PVCs occurred due to tissue-scale dynamical instabilities caused by RG and enhanced L-type calcium current (I_Ca,L), occurring under both large and small RG. Presence of cellular EADs was not required but potentiated PVCs when RG was small. We also investigated how other factors affect the dynamical instabilities causing PVCs. Our main conclusion is that tissue-scale dynamical instabilities caused by RG and enhanced I_Ca,L give rise to both the trigger and the vulnerable substrate simultaneously for spontaneous initiation of arrhythmias in LQT2 syndrome.

Rabbit-specific computational modelling of ventricular cell electrophysiology: Using populations of models to explore variability in the response to ischemia

Computational modelling, combined with experimental investigations, is a powerful method for investigating complex cardiac electrophysiological behaviour. The use of rabbit-specific models, due to the similarities of cardiac electrophysiology in this species with human, is especially prevalent. In this paper, we first briefly review rabbit-specific computational modelling of ventricular cell electrophysiology, multi-cellular simulations including cellular heterogeneity, and acute ischemia. This mini-review is followed by an original computational investigation of variability in the electrophysiological response of two experimentally-calibrated populations of rabbit-specific ventricular myocyte action potential models to acute ischemia. We performed a systematic exploration of the response of the model populations to varying degrees of ischemia and individual ischemic parameters, to investigate their individual and combined effects on action potential duration and refractoriness. This revealed complex interactions between model population variability and ischemic factors, which combined to enhance variability during ischemia. This represents an important step towards an improved understanding of the role that physiological variability may play in electrophysiological alterations during acute ischemia.

A computational modelling approach combined with cellular electrophysiology data provides insights into the therapeutic benefit of targeting the late Na+ current

KEY POINTS

The ventricular action potential plateau is a phase of high resistance, which makes ventricular myocytes vulnerable to small electrical perturbations. We developed a computationally based model of GS-458967 interaction with the cardiac Na+ channel, informed by experimental data recorded from guinea pig isolated single ventricular myocytes. The model predicts that the therapeutic potential of GS-458967 derives largely from the designed property of significant potent selectivity for INaL.

ABSTRACT

Selective inhibition of the slowly inactivating or late Na(+) current (INaL) in patients with inherited or acquired arrhythmia syndrome may confer therapeutic benefit by reducing the incidence of triggers for arrhythmia and suppressing one component of arrhythmia-promoting cardiac substrates (e.g. prolonged refractoriness and spatiotemporal dispersion of action potential duration). Recently, a novel compound that preferentially and potently reduces INaL, GS-458967 (IC50 for block of INaL = 130 nM) has been studied. Experimental measurements of the effects of GS-458967 on endogenous INaL in guinea pig ventricular myocytes demonstrate a robust concentration-dependent reduction in action potential duration (APD). Using experimental data to calibrate INaL and the rapidly activating delayed rectifier K(+) current, IKr, in the Faber-Rudy computationally based model of the guinea pig ventricular action potential, we simulated effects of GS-458967 on guinea pig ventricular APD. GS-458967 (0.1 μM) caused a 28.67% block of INaL and 12.57% APD shortening in experiments, while the model predicted 10.06% APD shortening with 29.33% block of INaL. An additional effect of INaL block is to reduce the time during which the membrane potential is in a high resistance state (i.e. the action potential plateau). To test the hypothesis that targeted block of INaL would make ventricular myocytes less susceptible to small electrical perturbations, we used the computational model to test the degree of APD prolongation induced by small electrical perturbations in normal cells and in cells with simulated long QT syndrome. The model predicted a substantial dose-dependent reduction in sensitivity to small electrical perturbations as evidenced by action potential duration at 90% repolarization variability in the presence of GS-458967-induced INaL block. This effect was especially potent in the 'disease setting' of inherited long QT syndrome. Using a combined experimental and theoretical approach, our results suggest that INaL block is a potent therapeutic strategy. This is because reduction of INaL stabilizes the action potential waveform by reducing depolarizing current during the plateau phase of the action potential. This reduces the most vulnerable phase of the action potential with high membrane resistance. In summary, by reducing the sensitivity of the myocardial substrate to small electrical perturbations that promote arrhythmia triggers, agents such as GS-458967 may constitute an effective antiarrhythmic pharmacological strategy.

Spatially Discordant Alternans and Arrhythmias in Tachypacing-Induced Cardiac Myopathy in Transgenic LQT1 Rabbits: The Importance of IKs and Ca2+ Cycling

BACKGROUND

Remodeling of cardiac repolarizing currents, such as the downregulation of slowly activating K+ channels (IKs), could underlie ventricular fibrillation (VF) in heart failure (HF). We evaluated the role of Iks remodeling in VF susceptibility using a tachypacing HF model of transgenic rabbits with Long QT Type 1 (LQT1) syndrome.

METHODS AND RESULTS

LQT1 and littermate control (LMC) rabbits underwent three weeks of tachypacing to induce cardiac myopathy (TICM). In vivo telemetry demonstrated steepening of the QT/RR slope in LQT1 with TICM (LQT1-TICM; pre: 0.26±0.04, post: 0.52±0.01, P<0.05). In vivo electrophysiology showed that LQT1-TICM had higher incidence of VF than LMC-TICM (6 of 11 vs. 3 of 11, respectively). Optical mapping revealed larger APD dispersion (16±4 vs. 38±6 ms, p<0.05) and steep APD restitution in LQT1-TICM compared to LQT1-sham (0.53±0.12 vs. 1.17±0.13, p<0.05). LQT1-TICM developed spatially discordant alternans (DA), which caused conduction block and higher-frequency VF (15±1 Hz in LQT1-TICM vs. 13±1 Hz in LMC-TICM, p<0.05). Ca2+ DA was highly dynamic and preceded voltage DA in LQT1-TICM. Ryanodine abolished DA in 5 out of 8 LQT1-TICM rabbits, demonstrating the importance of Ca2+ in complex DA formation. Computer simulations suggested that HF remodeling caused Ca2+-driven alternans, which was further potentiated in LQT1-TICM due to the lack of IKs.

CONCLUSIONS

Compared with LMC-TICM, LQT1-TICM rabbits exhibit steepened APD restitution and complex DA modulated by Ca2+. Our results strongly support the contention that the downregulation of IKs in HF increases Ca2+ dependent alternans and thereby the risk of VF.

Three-dimensional computer model of the right atrium including the sinoatrial and atrioventricular nodes predicts classical nodal behaviours

The aim of the study was to develop a three-dimensional (3D) anatomically-detailed model of the rabbit right atrium containing the sinoatrial and atrioventricular nodes to study the electrophysiology of the nodes. A model was generated based on 3D images of a rabbit heart (atria and part of ventricles), obtained using high-resolution magnetic resonance imaging. Segmentation was carried out semi-manually. A 3D right atrium array model (∼3.16 million elements), including eighteen objects, was constructed. For description of cellular electrophysiology, the Rogers-modified FitzHugh-Nagumo model was further modified to allow control of the major characteristics of the action potential with relatively low computational resource requirements. Model parameters were chosen to simulate the action potentials in the sinoatrial node, atrial muscle, inferior nodal extension and penetrating bundle. The block zone was simulated as passive tissue. The sinoatrial node, crista terminalis, main branch and roof bundle were considered as anisotropic. We have simulated normal and abnormal electrophysiology of the two nodes. In accordance with experimental findings: (i) during sinus rhythm, conduction occurs down the interatrial septum and into the atrioventricular node via the fast pathway (conduction down the crista terminalis and into the atrioventricular node via the slow pathway is slower); (ii) during atrial fibrillation, the sinoatrial node is protected from overdrive by its long refractory period; and (iii) during atrial fibrillation, the atrioventricular node reduces the frequency of action potentials reaching the ventricles. The model is able to simulate ventricular echo beats. In summary, a 3D anatomical model of the right atrium containing the cardiac conduction system is able to simulate a wide range of classical nodal behaviours.

Exponential integrators for a Markov chain model of the fast sodium channel of cardiomyocytes

The modern Markov chain models of ionic channels in excitable membranes are numerically stiff. The popular numerical methods for these models require very small time steps to ensure stability. Our objective is to formulate and test two methods addressing this issue, so that the timestep can be chosen based on accuracy rather than stability. Both proposed methods extend Rush-Larsen technique, which was originally developed to Hogdkin-Huxley type gate models. One method, "matrix Rush-Larsen" (MRL) uses a matrix reformulation of the Rush-Larsen scheme, where the matrix exponentials are calculated using precomputed tables of eigenvalues and eigenvectors. The other, "hybrid operator splitting" (HOS) method exploits asymptotic properties of a particular Markov chain model, allowing explicit analytical expressions for the substeps. We test both methods on the Clancy and Rudy (2002) I(Na)Markov chain model. With precomputed tables for functions of the transmembrane voltage, both methods are comparable to the forward Euler method in accuracy and computational cost, but allow longer time steps without numerical instability. We conclude that both methods are of practical interest. MRL requires more computations than HOS, but is formulated in general terms which can be readily extended to other Markov chain channel models, whereas the utility of HOS depends on the asymptotic properties of a particular model. The significance of the methods is that they allow a considerable speed-up of large-scale computations of cardiac excitation models by increasing the time step, while maintaining acceptable accuracy and preserving numerical stability.

Multiscale computational analysis of the bioelectric consequences of myocardial ischaemia and infarction

Ischaemic heart disease is considered as the single most frequent cause of death, provoking more than 7 000 000 deaths every year worldwide. A high percentage of patients experience sudden cardiac death, caused in most cases by tachyarrhythmic mechanisms associated to myocardial ischaemia and infarction. These diseases are difficult to study using solely experimental means due to their complex dynamics and unstable nature. In the past decades, integrative computational simulation techniques have become a powerful tool to complement experimental and clinical research when trying to elucidate the intimate mechanisms of ischaemic electrophysiological processes and to aid the clinician in the improvement and optimization of therapeutic procedures. The purpose of this paper is to briefly review some of the multiscale computational models of myocardial ischaemia and infarction developed in the past 20 years, ranging from the cellular level to whole-heart simulations.

Computational modeling of inhibition of voltage-gated Ca channels: identification of different effects on uterine and cardiac action potentials

The uterus and heart share the important physiological feature whereby contractile activation of the muscle tissue is regulated by the generation of periodic, spontaneous electrical action potentials (APs). Preterm birth arising from premature uterine contractions is a major complication of pregnancy and there remains a need to pursue avenues of research that facilitate the use of drugs, tocolytics, to limit these inappropriate contractions without deleterious actions on cardiac electrical excitation. A novel approach is to make use of mathematical models of uterine and cardiac APs, which incorporate many ionic currents contributing to the AP forms, and test the cell-specific responses to interventions. We have used three such models-of uterine smooth muscle cells (USMC), cardiac sinoatrial node cells (SAN), and ventricular cells-to investigate the relative effects of reducing two important voltage-gated Ca currents-the L-type (ICaL) and T-type (ICaT) Ca currents. Reduction of ICaL (10%) alone, or ICaT (40%) alone, blunted USMC APs with little effect on ventricular APs and only mild effects on SAN activity. Larger reductions in either current further attenuated the USMC APs but with also greater effects on SAN APs. Encouragingly, a combination of ICaL and ICaT reduction did blunt USMC APs as intended with little detriment to APs of either cardiac cell type. Subsequent overlapping maps of ICaL and ICaT inhibition profiles from each model revealed a range of combined reductions of ICaL and ICaT over which an appreciable diminution of USMC APs could be achieved with no deleterious action on cardiac SAN or ventricular APs. This novel approach illustrates the potential for computational biology to inform us of possible uterine and cardiac cell-specific mechanisms. Incorporating such computational approaches in future studies directed at designing new, or repurposing existing, tocolytics will be beneficial for establishing a desired uterine specificity of action.

Nonlinear and Stochastic Dynamics in the Heart

In a normal human life span, the heart beats about 2 to 3 billion times. Under diseased conditions, a heart may lose its normal rhythm and degenerate suddenly into much faster and irregular rhythms, called arrhythmias, which may lead to sudden death. The transition from a normal rhythm to an arrhythmia is a transition from regular electrical wave conduction to irregular or turbulent wave conduction in the heart, and thus this medical problem is also a problem of physics and mathematics. In the last century, clinical, experimental, and theoretical studies have shown that dynamical theories play fundamental roles in understanding the mechanisms of the genesis of the normal heart rhythm as well as lethal arrhythmias. In this article, we summarize in detail the nonlinear and stochastic dynamics occurring in the heart and their links to normal cardiac functions and arrhythmias, providing a holistic view through integrating dynamics from the molecular (microscopic) scale, to the organelle (mesoscopic) scale, to the cellular, tissue, and organ (macroscopic) scales. We discuss what existing problems and challenges are waiting to be solved and how multi-scale mathematical modeling and nonlinear dynamics may be helpful for solving these problems.

Novel Timothy syndrome mutation leading to increase in CACNA1C window current

BACKGROUND

Timothy syndrome (TS) is a rare multisystem genetic disorder characterized by a myriad of abnormalities, including QT prolongation, syndactyly, and neurologic symptoms. The predominant genetic causes are recurrent de novo missense mutations in exon 8/8A of the CACNA1C-encoded L-type calcium channel; however, some cases remain genetically elusive.

OBJECTIVE

The purpose of this study was to identify the genetic cause of TS in a patient who did not harbor a CACNA1C mutation in exon 8/A, and was negative for all other plausible genetic substrates.

METHODS

Diagnostic exome sequencing was used to identify the genetic substrate responsible for our case of TS. The identified mutation was characterized using whole-cell patch-clamp technique, and the results of these analyses were modeled using a modified Luo-Rudy dynamic model to determine the effects on the cardiac action potential.

RESULTS

Whole exome sequencing revealed a novel CACNA1C mutation, p.Ile1166Thr, in a young male with diagnosed TS. Functional electrophysiologic analysis identified a novel mechanism of TS-mediated disease, with an overall loss of current density and a gain-of-function shift in activation, leading to an increased window current. Modeling studies of this variant predicted prolongation of the action potential as well as the development of spontaneous early afterdepolarizations.

CONCLUSION

Through expanded whole exome sequencing, we identified a novel genetic substrate for TS, p.Ile1166Thr-CACNA1C. Electrophysiologic experiments combined with modeling studies have identified a novel TS mechanism through increased window current. Therefore, expanded genetic testing in cases of TS to the entire CACNA1C coding region, if initial targeted testing is negative, may be warranted.

An in silico case study of idiopathic dilated cardiomyopathy via a multi-scale model of the cardiovascular system

Mathematical modelling has been used to comprehend the pathology and the assessment of different treatment techniques such as heart failure and left ventricular assist device therapy in the cardiovascular field. In this study, an in-silico model of the heart is developed to understand the effects of idiopathic dilated cardiomyopathy (IDC) as a pathological scenario, with mechanisms described at the cellular, protein and organ levels. This model includes the right and left atria and ventricles, as well as the systemic and pulmonary arteries and veins. First, a multi-scale model of the whole heart is simulated for healthy conditions. Subsequently, the model is modified at its microscopic and macroscopic spatial scale to obtain the characteristics of IDC. The extracellular calcium concentration, the binding affinity of calcium binding proteins and the maximum and minimum elastances have been identified as key parameters across all relevant scales. The modified parameters cause a change in (a) intracellular calcium concentration characterising cellular properties, such as calcium channel currents or the action potential, (b) the proteins being involved in the sliding filament mechanism and the proportion of the attached crossbridges at the protein level, as well as (c) the pressure and volume values at the organ level. This model allows to obtain insight and understanding of the effects of the treatment techniques, from a physiological and biological point of view.

Mathematical modeling of physiological systems: an essential tool for discovery

Mathematical models are invaluable tools for understanding the relationships between components of a complex system. In the biological context, mathematical models help us understand the complex web of interrelations between various components (DNA, proteins, enzymes, signaling molecules etc.) in a biological system, gain better understanding of the system as a whole, and in turn predict its behavior in an altered state (e.g. disease). Mathematical modeling has enhanced our understanding of multiple complex biological processes like enzyme kinetics, metabolic networks, signal transduction pathways, gene regulatory networks, and electrophysiology. With recent advances in high throughput data generation methods, computational techniques and mathematical modeling have become even more central to the study of biological systems. In this review, we provide a brief history and highlight some of the important applications of modeling in biological systems with an emphasis on the study of excitable cells. We conclude with a discussion about opportunities and challenges for mathematical modeling going forward. In a larger sense, the review is designed to help answer a simple but important question that theoreticians frequently face from interested but skeptical colleagues on the experimental side: "What is the value of a model?"

Beta-adrenergic stimulation reverses the I Kr-I Ks dominant pattern during cardiac action potential

β-Adrenergic stimulation differentially modulates different K(+) channels and thus fine-tunes cardiac action potential (AP) repolarization. However, it remains unclear how the proportion of I Ks, I Kr, and I K1 currents in the same cell would be altered by β-adrenergic stimulation, which would change the relative contribution of individual K(+) current to the total repolarization reserve. In this study, we used an innovative AP-clamp sequential dissection technique to directly record the dynamic I Ks, I Kr, and I K1 currents during the AP in guinea pig ventricular myocytes under physiologically relevant conditions. Our data provide quantitative measures of the magnitude and time course of I Ks, I Kr, and I K1 currents in the same cell under its own steady-state AP, in a physiological milieu, and with preserved Ca(2+) homeostasis. We found that isoproterenol treatment significantly enhanced I Ks, moderately increased I K1, but slightly decreased I Kr in a dose-dependent manner. The dominance pattern of the K(+) currents was I Kr > I K1 > I Ks at the control condition, but reversed to I Kr < I K1 < I Ks following β-adrenergic stimulation. We systematically determined the changes in the relative contribution of I Ks, I Kr, and I K1 to cardiac repolarization during AP at different adrenergic states. In conclusion, the β-adrenergic stimulation fine-tunes the cardiac AP morphology by shifting the power of different K(+) currents in a dose-dependent manner. This knowledge is important for designing antiarrhythmic drug strategies to treat hearts exposed to various sympathetic tones.

Change of short-term memory effect in acute ischemic ventricular myocardium: a computational study

The ionic mechanism of change in short-term memory (STM) during acute myocardial ischemia has not been well understood. In this paper, an advanced guinea pig ventricular model developed by Luo and Rudy was used to investigate STM property of ischemic ventricular myocardium. STM response was calculated by testing the time to reach steady-state action potential duration (APD) after an abrupt shortening of basic cycling length (BCL) in the pacing protocol. Electrical restitution curves (RCs), which can simultaneously visualize multiple aspects of APD restitution and STM, were obtained from dynamic and local S1S2 restitution portrait (RP), which consist of a longer interval stimulus (S1) and a shorter interval stimulus (S2). The angle between dynamic RC and local S1S2 RC reflects the amount of STM. Our results indicated that compared with control (normal) condition, time constant of STM response in the ischemic condition decreased significantly. Meanwhile the angle which reflects STM amount is less in ischemic model than that in control model. By tracking the effect of ischemia on intracellular ion concentration and membrane currents, we declared that changes in membrane currents caused by ischemia exert subtle influences on STM; it is only the decline of intracellular calcium concentration that give rise to the most decrement of STM.

Reduced Na⁺ current density underlies impaired propagation in the diabetic rabbit ventricle

Diabetes is associated with an increased risk of sudden cardiac death, but the underlying mechanisms remain unclear. Our goal was to investigate changes occurring in the action potential duration (APD) and conduction velocity (CV) in the diabetic rabbit ventricle, and delineate the principal ionic determinants. A rabbit model of alloxan-induced diabetes was utilized. Optical imaging was used to record electrical activity in isolated Langendorff-perfused hearts in normo-, hypo- and hyper-kalemia ([K(+)]o=4, 2, 12 mM respectively). Patch clamp experiments were conducted to record Na(+) current (I(Na)) in isolated ventricular myocytes. The mRNA/protein expression levels for Nav1.5 (the α-subunit of I(Na)) and connexin-43 (Cx43), as well as fibrosis levels were examined. Computer simulations were performed to interpret experimental data. We found that the APD was not different, but the CV was significantly reduced in diabetic hearts in normo-, hypo-, and, hyper-kalemic conditions (13%, 17% and 33% reduction in diabetic vs. control, respectively). The cell capacitance (Cm) was increased (by ~14%), and the density of INa was reduced by ~32% in diabetic compared to control hearts, but the other biophysical properties of I(Na) were unaltered. The mRNA/protein expression levels for Cx43 were unaltered. For Nav1.5, the mRNA expression was not changed, and though the protein level tended to be less in diabetic hearts, this reduction was not statistically significant. Staining showed no difference in fibrosis levels between the control and diabetic ventricles. Computer simulations showed that the reduced magnitude of I(Na) was a key determinant of impaired propagation in the diabetic ventricle, which may have important implications for arrhythmogenesis.