Action potential and contractility changes in [Na(+)](i) overloaded cardiac myocytes: a simulation study

Aconitine in Synergistic, Additive and Antagonistic Approaches

Aconitine is a highly poisonous C19-diterpenoid alkaloid identified and isolated from the species of the genus Aconitum. Aconitine is indicated in the treatment of cardiovascular diseases (CVDs) and, due to its neurotoxic effects, is a very effective drug in pain release. A total of 101 relevant scientific papers were manually searched on the Web of Science, Scopus, Science Direct, Google Scholar, PubMed and Dovepress databases and in the books available in the library of the Department of Natural Sciences, the National University of Science and Technology POLITEHNICA Bucharest, Pitesti University Centre, Romania. In combination treatments, aconitine shows antiarrhythmic and anti-inflammatory activity, a synergistic antiproliferative effect and decreased reactive oxygen species (ROS) generation, an improved biodistribution and bioavailability. Additionally, the entrapment of aconitine in engineered nanoparticles represents a promising method for reducing the toxicity of this alkaloid. This review provides, for the first time, a comprehensive picture of the knowledge and research on the synergistic, additive and antagonistic effects of aconitine in combination treatments applied in vivo or in vitro. The summarized studies represent important clues in addressing the multitude of knowledge, which can find their utility in practical and clinical applications.

Investigative agents for atrial fibrillation: agonists and stimulants, progress and expectations

INTRODUCTION

Atrial fibrillation (AF) is the most common type of cardiac arrhythmia. Its prevalence has increased due to worldwide populations that are aging in combination with the growing incidence of risk factors associated. Recent advances in our understanding of AF pathophysiology and the identification of nodal players involved in AF-promoting atrial remodeling highlights potential opportunities for new therapeutic approaches.

AREAS COVERED

This detailed review summarizes recent developments in the field antiarrhythmic drugs in the field AF.

EXPERT OPINION

The current situation is far than optimal. Despite clear unmet needs in drug development in the field of AF treatment, the current development of new drugs is absent. The need for a molecule with absence of cardiac and non-cardiac toxicity in the short and long term is a limitation in the field. Improvement in the understanding of AF genetics, pathophysiology, molecular alterations, big data and artificial intelligence with the objective to provide a personalized AF treatment will be the cornerstone of AF treatment in the coming years.

Cell-specific models of hiPSC-CMs developed by the gradient-based parameter optimization method fitting two different action potential waveforms

Parameter optimization (PO) methods to determine the ionic current composition of experimental cardiac action potential (AP) waveform have been developed using a computer model of cardiac membrane excitation. However, it was suggested that fitting a single AP record in the PO method was not always successful in providing a unique answer because of a shortage of information. We found that the PO method worked perfectly if the PO method was applied to a pair of a control AP and a model output AP in which a single ionic current out of six current species, such as IKr, ICaL, INa, IKs, IKur or IbNSC was partially blocked in silico. When the target was replaced by a pair of experimental control and IKr-blocked records of APs generated spontaneously in human induced pluripotent stem cell-derived cardiomyocytes (hiPSC-CMs), the simultaneous fitting of the two waveforms by the PO method was hampered to some extent by the irregular slow fluctuations in the Vm recording and/or sporadic alteration in AP configurations in the hiPSC-CMs. This technical problem was largely removed by selecting stable segments of the records for the PO method. Moreover, the PO method was made fail-proof by running iteratively in identifying the optimized parameter set to reconstruct both the control and the IKr-blocked AP waveforms. In the lead potential analysis, the quantitative ionic mechanisms deduced from the optimized parameter set were totally consistent with the qualitative view of ionic mechanisms of AP so far described in physiological literature.

Curvature-mediated source and sink effects on the genesis of premature ventricular complexes in long QT syndrome

Premature ventricular complexes (PVCs) are spontaneous excitations occurring in the ventricles of the heart that are associated with ventricular arrhythmias and sudden cardiac death. Under long QT conditions, PVCs can be mediated by repolarization gradient (RG) and early afterdepolarizations (EADs), yet the effects of heterogeneities or geometry of the RG or EAD regions on PVC genesis remain incompletely understood. In this study, we use computer simulation to systematically investigate the effects of the curvature of the RG border region on PVC genesis under long QT conditions. We show that PVCs can be either promoted or suppressed by negative or positive RG border curvature depending on the source and sink conditions. When the origin of oscillation is in the source region and the source is too strong, a positive RG border curvature can promote PVCs by causing the source area to oscillate. When the origin of oscillation is in the sink region, a negative RG border curvature can promote PVCs by causing the sink area to oscillate. Furthermore, EAD-mediated PVCs are also promoted by negative border curvature. We also investigate the effects of wavefront curvature and show that PVCs are promoted by convex but suppressed by concave wavefronts; however, the effect of wavefront curvature is much smaller than that of RG border curvature. In conclusion, besides the increase of RG and occurrence of EADs caused by QT prolongation, the geometry of the RG border plays important roles in PVC genesis, which can greatly increase the risk of arrhythmias in cardiac diseases.NEW & NOTEWORTHY The effects of the curvature or geometry of the repolarization gradient region and wavefront curvature on the genesis of premature ventricular complexes are systematically investigated using computer modeling and simulation. Premature ventricular complexes can be promoted by either positive or negative curvature of the gradient region depending on the source and sink conditions. The underlying mechanisms of the curvature effects are revealed, which provides mechanistic insights into arrhythmogenesis in cardiac diseases.

Dissecting the roles of calcium cycling and its coupling with voltage in the genesis of early afterdepolarizations in cardiac myocyte models

Early afterdepolarizations (EADs) are abnormal depolarizations during the plateau phase of the action potential, which are known to be associated with lethal arrhythmias in the heart. There are two major hypotheses for EAD genesis based on experimental observations, i.e., the voltage (Vm)-driven and intracellular calcium (Ca)-driven mechanisms. In ventricular myocytes, Ca and Vm are bidirectionally coupled, which can affect each other's dynamics and result in new dynamics, however, the roles of Ca cycling and its coupling with Vm in the genesis of EADs have not been well understood. In this study, we use an action potential model that is capable of independent Vm and Ca oscillations to investigate the roles of Vm and Ca coupling in EAD genesis. Four different mechanisms of EADs are identified, which are either driven by Vm oscillations or Ca oscillations alone, or oscillations caused by their interactions. We also use 5 other ventricular action potential models to assess these EAD mechanisms and show that EADs in these models are mainly Vm-driven. These mechanistic insights from our simulations provide a theoretical base for understanding experimentally observed EADs and EAD-related arrhythmogenesis.

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.

A review on efforts for improvement in medicinally important chemical constituents inAconitum through biotechnological interventions

The genus Aconitum belongs to the family Ranunculaceae, is endowed with more than 350 species on the earth. Medicinally important aconitine type of diterpenoid alkaloids are the characteristic compounds in most of the Aconitum species. The present review endeavored the major research carried out in the field of genetic resource characterization, pharmacological properties, phytochemistry, major factors influencing quantity, biosynthetic pathways and processing methods for recovery of active ingredients, variety improvement, propagation methods, and important metabolite production through cell/organ culture of various Aconitum species. More than 450 derivatives of aconitine-type C19 and C20-diterpenoid alkaloids along with a few other non-alkaloidal compounds, such as phenylpropanoids, flavonoids, terpenoids, and fatty acids, have been identified in the genus. A few Aconitum species and their common diterpenoid alkaloid compounds are also well characterized for analgesic, inflammatory and cytotoxic properties. However, the different isolated compound needs to be validated for supporting other traditional therapeutical uses of the plant species. Aconitine alkaloids shared common biosynthesis pathway, but their diversification mechanism remains unexplored in the genus. Furthermore, the process needs to be developed on secondary metabolite recovery, mass-scale propagation methods, and agro-technologies for maintaining the quality of products. Many species are losing their existence in nature due to over-exploitation or anthropogenic factors; thus, temporal monitoring of the population status in its habitat, and suitable management programs for ascertaining conservation needs to be developed.

Building a search tool for compositely annotated entities using Transformer-based approach: Case study in Biosimulation Model Search Engine (BMSE)

The Transformer-based approaches to solving natural language processing (NLP) tasks such as BERT and GPT are gaining popularity due to their ability to achieve high performance. These approaches benefit from using enormous data sizes to create pre-trained models and the ability to understand the context of words in a sentence. Their use in the information retrieval domain is thought to increase effectiveness and efficiency. This paper demonstrates a BERT-based method (CASBERT) implementation to build a search tool over data annotated compositely using ontologies. The data was a collection of biosimulation models written using the CellML standard in the Physiome Model Repository (PMR). A biosimulation model structurally consists of basic entities of constants and variables that construct higher-level entities such as components, reactions, and the model. Finding these entities specific to their level is beneficial for various purposes regarding variable reuse, experiment setup, and model audit. Initially, we created embeddings representing compositely-annotated entities for constant and variable search (lowest level entity). Then, these low-level entity embeddings were vertically and efficiently combined to create higher-level entity embeddings to search components, models, images, and simulation setups. Our approach was general, so it can be used to create search tools with other data semantically annotated with ontologies - biosimulation models encoded in the SBML format, for example. Our tool is named Biosimulation Model Search Engine (BMSE).

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.

Antiarrhythmic and Inotropic Effects of Selective Na+/Ca2+ Exchanger Inhibition: What Can We Learn from the Pharmacological Studies?

Life-long stable heart function requires a critical balance of intracellular Ca²⁺. Several ion channels and pumps cooperate in a complex machinery that controls the influx, release, and efflux of Ca²⁺. Probably one of the most interesting and most complex players of this crosstalk is the Na⁺/Ca²⁺ exchanger, which represents the main Ca²⁺ efflux mechanism; however, under some circumstances, it can also bring Ca²⁺ into the cell. Therefore, the inhibition of the Na⁺/Ca²⁺ exchanger has emerged as one of the most promising possible pharmacological targets to increase Ca²⁺ levels, to decrease arrhythmogenic depolarizations, and to reduce excessive Ca²⁺ influx. In line with this, as a response to increasing demand, several more or less selective Na⁺/Ca²⁺ exchanger inhibitor compounds have been developed. In the past 20 years, several results have been published regarding the effect of Na⁺/Ca²⁺ exchanger inhibition under various circumstances, e.g., species, inhibitor compounds, and experimental conditions; however, the results are often controversial. Does selective Na⁺/Ca²⁺ exchanger inhibition have any future in clinical pharmacological practice? In this review, the experimental results of Na⁺/Ca²⁺ exchanger inhibition are summarized focusing on the data obtained by novel highly selective inhibitors.

Modeling Calcium Cycling in the Heart: Progress, Pitfalls, and Challenges

Intracellular calcium (Ca) cycling in the heart plays key roles in excitation-contraction coupling and arrhythmogenesis. In cardiac myocytes, the Ca release channels, i.e., the ryanodine receptors (RyRs), are clustered in the sarcoplasmic reticulum membrane, forming Ca release units (CRUs). The RyRs in a CRU act collectively to give rise to discrete Ca release events, called Ca sparks. A cell contains hundreds to thousands of CRUs, diffusively coupled via Ca to form a CRU network. A rich spectrum of spatiotemporal Ca dynamics is observed in cardiac myocytes, including Ca sparks, spark clusters, mini-waves, persistent whole-cell waves, and oscillations. Models of different temporal and spatial scales have been developed to investigate these dynamics. Due to the complexities of the CRU network and the spatiotemporal Ca dynamics, it is challenging to model the Ca cycling dynamics in the cardiac system, particularly at the tissue sales. In this article, we review the progress of modeling of Ca cycling in cardiac systems from single RyRs to the tissue scale, the pros and cons of the current models and different modeling approaches, and the challenges to be tackled in the future.

Gradient-based parameter optimization method to determine membrane ionic current composition in human induced pluripotent stem cell-derived cardiomyocytes

Premature cardiac myocytes derived from human induced pluripotent stem cells (hiPSC-CMs) show heterogeneous action potentials (APs), probably due to different expression patterns of membrane ionic currents. We developed a method for determining expression patterns of functional channels in terms of whole-cell ionic conductance (G_x) using individual spontaneous AP configurations. It has been suggested that apparently identical AP configurations can be obtained using different sets of ionic currents in mathematical models of cardiac membrane excitation. If so, the inverse problem of G_x estimation might not be solved. We computationally tested the feasibility of the gradient-based optimization method. For a realistic examination, conventional 'cell-specific models' were prepared by superimposing the model output of AP on each experimental AP recorded by conventional manual adjustment of G_xs of the baseline model. G_xs of 4-6 major ionic currents of the 'cell-specific models' were randomized within a range of ± 5-15% and used as an initial parameter set for the gradient-based automatic G_xs recovery by decreasing the mean square error (MSE) between the target and model output. Plotting all data points of the MSE-G_x relationship during optimization revealed progressive convergence of the randomized population of G_xs to the original value of the cell-specific model with decreasing MSE. The absence of any other local minimum in the global search space was confirmed by mapping the MSE by randomizing G_xs over a range of 0.1-10 times the control. No additional local minimum MSE was obvious in the whole parameter space, in addition to the global minimum of MSE at the default model parameter.

Developmental differences in myocardial transmembrane Na+ transport: Implications for excitability and Na+ handling

KEY POINTS

Previous studies showed that myocardial preparations from immature rats are less sensitive to electrical field stimulation than adult preparations. Freshly-isolated ventricular myocytes from neonatal rats showed lower excitability than adult cells, e.g., less negative threshold membrane potential and greater membrane depolarization required for action potential triggering. In addition to differences in mRNA levels for Na⁺ channels isoforms and greater Na⁺ current (I_Na ) density, Na⁺ channel voltage-dependence was shifted to the right in immature myocytes, which seems to be sufficient to decrease excitability, according to computer simulations. Only in neonatal myocytes did cyclic activity promote marked cytosolic Na⁺ accumulation, which was prevented by abolition of systolic Ca²⁺ transients by blockade of Ca²⁺ currents. Developmental changes in I_Na may account for the difference in action potential initiation parameters, but not for cytosolic Na⁺ accumulation, which seems to be due mainly to Na⁺ /Ca²⁺ exchanger-mediated Na⁺ influx.

ABSTRACT

Little is currently known about possible developmental changes in myocardial Na⁺ handling, which may have impact on cell excitability and Ca²⁺ content. Resting intracellular Na⁺ concentration ([Na⁺ ]_i ), measured in freshly-isolated rat ventricular myocytes with CoroNa-green, was not significantly different in neonates (3-5 days old) and adults, but electrical stimulation caused marked [Na⁺ ]_i rise only in neonates. Inhibition of L-type Ca²⁺ current by CdCl₂ abolished not only systolic Ca²⁺ transients, but also activity-dependent intracellular Na⁺ accumulation in immature cells. This indicates that the main Na⁺ influx pathway during activity is the Na⁺ /Ca²⁺ exchanger, rather than voltage-dependent Na⁺ current (I_Na ), which was not affected by CdCl₂ . In immature myocytes, I_Na density was 2-fold greater, inactivation was faster, and the current peak occurred at less negative transmembrane potential (E_m ) than in adults. Na⁺ channel steady-state activation and inactivation curves in neonates showed a rightward shift, which should increase channel availability at diastolic E_m , but also require greater depolarization for excitation, which was observed experimentally and reproduced in computer simulations. Ventricular mRNA levels of Na_v 1.1, Na_v 1.4 and Na_v 1.5 pore-forming isoforms were greater in neonate ventricles, while decrease was seen for the β1 subunit. Both molecular and biophysical changes in the channel profile may contribute to the differences in I_Na density and voltage-dependence, and also to the less negative threshold E_m in neonates, compared to adults. The apparently lower excitability in immature ventricle may confer protection against the development of spontaneous activity in this tissue. Abstract figure legend Little is currently known about possible developmental changes in myocardial Na⁺ transport, which may have impact on cell excitability and other physiological aspects. At the mRNA level, neonatal rat ventricle expresses a greater variety of Na⁺ channel isoforms than in adults. In immature ventricular cardiomyocytes, Na⁺ current (I_Na ) density was greater, but voltage-dependence is shifted to less negative potentials than in adults. This should increase channel availability at diastolic membrane potential, but also require greater depolarization for excitation, which was observed experimentally and reproduced in computer simulation. We also observed that electrical stimulation caused marked intracellular Na⁺ accumulation only in neonates, which was abolished when Ca²⁺ transients and the Na⁺ /Ca²⁺ exchanger (NCX) were inhibited by Cd²⁺ + Ni²⁺ . Thus, it seems that the main Na⁺ influx pathway during activity in neonates is the NCX, rather than voltage-dependent I_Na , which was not affected by these blockers. This article is protected by copyright. All rights reserved.

Numerical evaluation of cardiac mechanical markers as estimators of the electrical activation time

Recent advances in the development of noninvasive cardiac imaging technologies have made it possible to measure longitudinal and circumferential strains at a high spatial resolution also at intramural level. Local mechanical activation times derived from these strains can be used as noninvasive estimates of electrical activation, in order to determine, eg, the origin of premature ectopic beats during focal arrhythmias or the pathway of reentrant circuits. The aim of this work is to assess the reliability of mechanical activation time markers derived from longitudinal and circumferential strains, denoted by AT_ell and AT_ecc , respectively, by means of three-dimensional cardiac electromechanical simulations. These markers are compared against the electrical activation time (AT_v ), computed from the action potential waveform, and the reference mechanical activation markers derived from the active tension and fiber strain waveforms, denoted by AT_ta and AT_eff , respectively. Our numerical simulations are based on a strongly coupled electromechanical model, including bidomain representation of the cardiac tissue, mechanoelectric (ie, stretch-activated channels) and geometric feedbacks, transversely isotropic strain energy function for the description of passive mechanics and detailed membrane and excitation-contraction coupling models. The results have shown that, during endocardial and epicardial ectopic stimulations, all the mechanical markers considered are highly correlated with AT_v , exhibiting correlation coefficients larger than 0.8. However, during multiple endocardial stimulations, mimicking the ventricular sinus rhythm, the mechanical markers are less correlated with the electrical activation time, because of the more complex resulting excitation sequence. Moreover, the inspection of the endocardial and epicardial isochrones has shown that the AT_ell and AT_ecc mechanical activation sequences reproduce only some qualitative features of the electrical activation sequence, such as the areas of early and late activation, but in some cases, they might yield wrong excitation sources and significantly different isochrones patterns.

Cardiac Conduction Velocity, Remodeling and Arrhythmogenesis

Cardiac electrophysiological disorders, in particular arrhythmias, are a key cause of morbidity and mortality throughout the world. There are two basic requirements for arrhythmogenesis: an underlying substrate and a trigger. Altered conduction velocity (CV) provides a key substrate for arrhythmogenesis, with slowed CV increasing the probability of re-entrant arrhythmias by reducing the length scale over which re-entry can occur. In this review, we examine methods to measure cardiac CV in vivo and ex vivo, discuss underlying determinants of CV, and address how pathological variations alter CV, potentially increasing arrhythmogenic risk. Finally, we will highlight future directions both for methodologies to measure CV and for possible treatments to restore normal CV.

Research study on the efficiency of a defibrillating biphasic pulse of various durations based on mathematical modeling and simulation of a cardiomyocyte

The paper presents the results of our research study on the impact of different durations of a biphasic rectangular pulse on the efficiency of the defibrillating action based on modeling and simulation of a cardiomyocyte in the framework of Cell Electrophysiology Simulation Environment. We used Luo-Rudy Mammalian Ventricular Model II (dynamic) as the mathematical model of the biochemical processes, which occur both on the surface and inside a cardiomyocyte in a guinea pig. An analysis of the obtained results allowed us to determine the optimal time of the defibrillating pulse. It has been shown that a pulse of 4 ms duration has the highest efficiency. The research has been carried out directly based on the mathematical model and simulation of the cardiomyocyte that makes it possible to minimize errors which may occur in experiments on animals

Evolution of mathematical models of cardiomyocyte electrophysiology

Advanced computational techniques and mathematical modeling have become more and more important to the study of cardiac electrophysiology. In this review, we provide a brief history of the evolution of cardiomyocyte electrophysiology models and highlight some of the most important ones that had a major impact on our understanding of the electrical activity of the myocardium and associated transmembrane ion fluxes in normal and pathological states. We also present the use of these models in the study of various arrhythmogenesis mechanisms, particularly the integration of experimental pharmacology data into advanced humanized models for in silico proarrhythmogenic risk prediction as an essential component of the Comprehensive in vitro Proarrhythmia Assay (CiPA) drug safety paradigm.

The transient outward potassium current plays a key role in spiral wave breakup in ventricular tissue

Spiral wave reentry as a mechanism of lethal ventricular arrhythmias has been widely demonstrated in animal experiments and recordings from human hearts. It has been shown that in structurally normal hearts spiral waves are unstable, breaking up into multiple wavelets via dynamical instabilities. However, many of the second-generation action potential models give rise only to stable spiral waves, raising issues regarding the underlying mechanisms of spiral wave breakup. In this study, we carried out computer simulations of two-dimensional homogeneous tissues using five ventricular action potential models. We show that the transient outward potassium current (Ito), although it is not required, plays a key role in promoting spiral wave breakup in all five models. As the maximum conductance of Ito increases, it first promotes spiral wave breakup and then stabilizes the spiral waves. In the absence of Ito, speeding up the L-type calcium kinetics can prevent spiral wave breakup, however, with the same speedup kinetics, spiral wave breakup can be promoted by increasing Ito. Increasing Ito promotes single-cell dynamical instabilities, including action potential duration alternans and chaos, and increasing Ito further suppresses these action potential dynamics. These cellular properties agree with the observation that increasing Ito first promotes spiral wave breakup and then stabilizes spiral waves in tissue. Implications of our observations to spiral wave dynamics in the real hearts and action potential model improvements are discussed.NEW & NOTEWORTHY Spiral wave breakup manifesting as multiple wavelets is a mechanism of ventricular fibrillation. It has been known that spiral wave breakup in cardiac tissue can be caused by a steeply sloped action potential duration restitution curve, a property mainly determined by the recovery of L-type calcium current. Here, we show that the transient outward potassium current (Ito) is another current that plays a key role in spiral wave breakup, that is, spiral waves can be stable for low and high maximum Ito conductance but breakup occurs for intermediate maximum Ito conductance. Since Ito is present in normal hearts of many species and required for Brugada syndrome, it may play an important role in the spiral wave stability and arrhythmogenesis under both normal condition and Brugada syndrome.

Mechanisms of Premature Ventricular Complexes Caused by QT Prolongation

QT prolongation, due to lengthening of the action potential duration in the ventricles, is a major risk factor of lethal ventricular arrhythmias. A widely known consequence of QT prolongation is the genesis of early afterdepolarizations (EADs), which are associated with arrhythmias through the generation of premature ventricular complexes (PVCs). However, the vast majority of the EADs observed experimentally in isolated ventricular myocytes are phase-2 EADs, and whether phase-2 EADs are mechanistically linked to PVCs in cardiac tissue remains an unanswered question. In this study, we investigate the genesis of PVCs using computer simulations with eight different ventricular action potential models of various species. Based on our results, we classify PVCs as arising from two distinct mechanisms: repolarization gradient (RG)-induced PVCs and phase-2 EAD-induced PVCs. The RG-induced PVCs are promoted by increasing RG and L-type calcium current and are insensitive to gap junction coupling. EADs are not required for this PVC mechanism. In a paced beat, a single or multiple PVCs can occur depending on the properties of the RG. In contrast, phase-2 EAD-induced PVCs occur only when the RG is small and are suppressed by increasing RG and more sensitive to gap junction coupling. Unlike with RG-induced PVCs, in each paced beat, only a single EAD-induced PVC can occur no matter how many EADs in an action potential. In the wide parameter ranges we explore, RG-induced PVCs can be observed in all models, but the EAD-induced PVCs can only be observed in five of the eight models. The links between these two distinct PVC mechanisms and arrhythmogenesis in animal experiments and clinical settings are discussed.

Late INa Blocker GS967 Supresses Polymorphic Ventricular Tachycardia in a Transgenic Rabbit Model of Long QT Type 2

BACKGROUND

Long QT syndrome has been associated with sudden cardiac death likely caused by early afterdepolarizations (EADs) and polymorphic ventricular tachycardias (PVTs). Suppressing the late sodium current (INaL) may counterbalance the reduced repolarization reserve in long QT syndrome and prevent EADs and PVTs.

METHODS

We tested the effects of the selective INaL blocker GS967 on PVT induction in a transgenic rabbit model of long QT syndrome type 2 using intact heart optical mapping, cellular electrophysiology and confocal Ca2+ imaging, and computer modeling.

RESULTS

GS967 reduced ventricular fibrillation induction under a rapid pacing protocol (n=7/14 hearts in control versus 1/14 hearts at 100 nmol/L) without altering action potential duration or restitution and dispersion. GS967 suppressed PVT incidences by reducing Ca2+-mediated EADs and focal activity during isoproterenol perfusion (at 30 nmol/L, n=7/12 and 100 nmol/L n=8/12 hearts without EADs and PVTs). Confocal Ca2+ imaging of long QT syndrome type 2 myocytes revealed that GS967 shortened Ca2+ transient duration via accelerating Na+/Ca2+ exchanger (INCX)-mediated Ca2+ efflux from cytosol, thereby reducing EADs. Computer modeling revealed that INaL potentiates EADs in the long QT syndrome type 2 setting through (1) providing additional depolarizing currents during action potential plateau phase, (2) increasing intracellular Na+ (Nai) that decreases the depolarizing INCX thereby suppressing the action potential plateau and delaying the activation of slowly activating delayed rectifier K+ channels (IKs), suggesting important roles of INaL in regulating Nai.

CONCLUSIONS

Selective INaL blockade by GS967 prevents EADs and abolishes PVT in long QT syndrome type 2 rabbits by counterbalancing the reduced repolarization reserve and normalizing Nai. Graphic Abstract: A graphic abstract is available for this article.

Calibration of ionic and cellular cardiac electrophysiology models

Cardiac electrophysiology models are among the most mature and well-studied mathematical models of biological systems. This maturity is bringing new challenges as models are being used increasingly to make quantitative rather than qualitative predictions. As such, calibrating the parameters within ion current and action potential (AP) models to experimental data sets is a crucial step in constructing a predictive model. This review highlights some of the fundamental concepts in cardiac model calibration and is intended to be readily understood by computational and mathematical modelers working in other fields of biology. We discuss the classic and latest approaches to calibration in the electrophysiology field, at both the ion channel and cellular AP scales. We end with a discussion of the many challenges that work to date has raised and the need for reproducible descriptions of the calibration process to enable models to be recalibrated to new data sets and built upon for new studies. This article is categorized under: Analytical and Computational Methods > Computational Methods Physiology > Mammalian Physiology in Health and Disease Models of Systems Properties and Processes > Cellular Models.

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.

A Computational Pipeline to Predict Cardiotoxicity: From the Atom to the Rhythm

RATIONALE

Drug-induced proarrhythmia is so tightly associated with prolongation of the QT interval that QT prolongation is an accepted surrogate marker for arrhythmia. But QT interval is too sensitive a marker and not selective, resulting in many useful drugs eliminated in drug discovery.

OBJECTIVE

To predict the impact of a drug from the drug chemistry on the cardiac rhythm.

METHODS AND RESULTS

In a new linkage, we connected atomistic scale information to protein, cell, and tissue scales by predicting drug-binding affinities and rates from simulation of ion channel and drug structure interactions and then used these values to model drug effects on the hERG channel. Model components were integrated into predictive models at the cell and tissue scales to expose fundamental arrhythmia vulnerability mechanisms and complex interactions underlying emergent behaviors. Human clinical data were used for model framework validation and showed excellent agreement, demonstrating feasibility of a new approach for cardiotoxicity prediction.

CONCLUSIONS

We present a multiscale model framework to predict electrotoxicity in the heart from the atom to the rhythm. Novel mechanistic insights emerged at all scales of the system, from the specific nature of proarrhythmic drug interaction with the hERG channel, to the fundamental cellular and tissue-level arrhythmia mechanisms. Applications of machine learning indicate necessary and sufficient parameters that predict arrhythmia vulnerability. We expect that the model framework may be expanded to make an impact in drug discovery, drug safety screening for a variety of compounds and targets, and in a variety of regulatory processes.

Improved Computational Identification of Drug Response Using Optical Measurements of Human Stem Cell Derived Cardiomyocytes in Microphysiological Systems

Cardiomyocytes derived from human induced pluripotent stem cells (hiPSC-CMs) hold great potential for drug screening applications. However, their usefulness is limited by the relative immaturity of the cells' electrophysiological properties as compared to native cardiomyocytes in the adult human heart. In this work, we extend and improve on methodology to address this limitation, building on previously introduced computational procedures which predict drug effects for adult cells based on changes in optical measurements of action potentials and Ca2+ transients made in stem cell derived cardiac microtissues. This methodology quantifies ion channel changes through the inversion of data into a mathematical model, and maps this response to an adult phenotype through the assumption of functional invariance of fundamental intracellular and membrane channels during maturation. Here, we utilize an updated action potential model to represent both hiPSC-CMs and adult cardiomyocytes, apply an IC50-based model of dose-dependent drug effects, and introduce a continuation-based optimization algorithm for analysis of dose escalation measurements using five drugs with known effects. The improved methodology can identify drug induced changes more efficiently, and quantitate important metrics such as IC50 in line with published values. Consequently, the updated methodology is a step towards employing computational procedures to elucidate drug effects in adult cardiomyocytes for new drugs using stem cell-derived experimental tissues.

A demonstration of modularity, reuse, reproducibility, portability and scalability for modeling and simulation of cardiac electrophysiology using Kepler Workflows

Multi-scale computational modeling is a major branch of computational biology as evidenced by the US federal interagency Multi-Scale Modeling Consortium and major international projects. It invariably involves specific and detailed sequences of data analysis and simulation, often with multiple tools and datasets, and the community recognizes improved modularity, reuse, reproducibility, portability and scalability as critical unmet needs in this area. Scientific workflows are a well-recognized strategy for addressing these needs in scientific computing. While there are good examples if the use of scientific workflows in bioinformatics, medical informatics, biomedical imaging and data analysis, there are fewer examples in multi-scale computational modeling in general and cardiac electrophysiology in particular. Cardiac electrophysiology simulation is a mature area of multi-scale computational biology that serves as an excellent use case for developing and testing new scientific workflows. In this article, we develop, describe and test a computational workflow that serves as a proof of concept of a platform for the robust integration and implementation of a reusable and reproducible multi-scale cardiac cell and tissue model that is expandable, modular and portable. The workflow described leverages Python and Kepler-Python actor for plotting and pre/post-processing. During all stages of the workflow design, we rely on freely available open-source tools, to make our workflow freely usable by scientists.

We present a computational workflow as a proof of concept for integration and implementation of a reusable and reproducible cardiac multi-scale electrophysiology model that is expandable, modular and portable. This framework enables scientists to create intuitive, user-friendly and flexible end-to-end automated scientific workflows using a graphical user interface. Kepler is an advanced open-source platform that supports multiple models of computation. The underlying workflow engine handles scalability, provenance, reproducibility aspects of the code, performs orchestration of data flow, and automates execution on heterogeneous computing resources. One of the main advantages of workflow utilization is the integration of code written in multiple languages Standardization occurs at the interfaces of the workflow elements and allows for general applications and easy comparison and integration of code from different research groups or even multiple programmers coding in different languages for various purposes from the same group. A workflow driven problem-solving approach enables domain scientists to focus on resolving the core science questions, and delegates the computational and process management burden to the underlying Workflow. The workflow driven approach allows scaling the computational experiment with distributed data-parallel execution on multiple computing platforms, such as, HPC resources, GPU clusters, Cloud etc. The workflow framework tracks software version information along with hardware information to allow users an opportunity to trace any variation in workflow outcome to the system configurations.

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.

Determinants of early afterdepolarization properties in ventricular myocyte models

Early afterdepolarizations (EADs) are spontaneous depolarizations during the repolarization phase of an action potential in cardiac myocytes. It is widely known that EADs are promoted by increasing inward currents and/or decreasing outward currents, a condition called reduced repolarization reserve. Recent studies based on bifurcation theories show that EADs are caused by a dual Hopf-homoclinic bifurcation, bringing in further mechanistic insights into the genesis and dynamics of EADs. In this study, we investigated the EAD properties, such as the EAD amplitude, the inter-EAD interval, and the latency of the first EAD, and their major determinants. We first made predictions based on the bifurcation theory and then validated them in physiologically more detailed action potential models. These properties were investigated by varying one parameter at a time or using parameter sets randomly drawn from assigned intervals. The theoretical and simulation results were compared with experimental data from the literature. Our major findings are that the EAD amplitude and takeoff potential exhibit a negative linear correlation; the inter-EAD interval is insensitive to the maximum ionic current conductance but mainly determined by the kinetics of I_Ca,L and the dual Hopf-homoclinic bifurcation; and both inter-EAD interval and latency vary largely from model to model. Most of the model results generally agree with experimental observations in isolated ventricular myocytes. However, a major discrepancy between modeling results and experimental observations is that the inter-EAD intervals observed in experiments are mainly between 200 and 500 ms, irrespective of species, while those of the mathematical models exhibit a much wider range with some models exhibiting inter-EAD intervals less than 100 ms. Our simulations show that the cause of this discrepancy is likely due to the difference in I_Ca,L recovery properties in different mathematical models, which needs to be addressed in future action potential model development.

Early afterdepolarizations (EADs) are abnormal depolarizations during the plateau phase of action potential in cardiac myocytes, arising from a dual Hopf-homoclinic bifurcation. The same bifurcations are also responsible for certain types of bursting behaviors in other cell types, such as beta cells and neuronal cells. EADs are known to play important role in the genesis of lethal arrhythmias and have been widely studied in both experiments and computer models. However, a detailed comparison between the properties of EADs observed in experiments and those from mathematical models have not been carried out. In this study, we performed theoretical analyses and computer simulations of different ventricular action potential models as well as different species to investigate the properties of EADs and compared these properties to those observed in experiments. While the EAD properties in the action potential models capture many of the EAD properties seen in experiments, the inter-EAD intervals in the computer models differ a lot from model to model, and some of them show very large discrepancy with those observed in experiments. This discrepancy needs to be addressed in future cardiac action potential model development.

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.

The Role of Sodium in Diabetic Cardiomyopathy

Cardiovascular complications are the major cause of mortality and morbidity in diabetic patients. The changes in myocardial structure and function associated with diabetes are collectively called diabetic cardiomyopathy. Numerous molecular mechanisms have been proposed that could contribute to the development of diabetic cardiomyopathy and have been studied in various animal models of type 1 or type 2 diabetes. The current review focuses on the role of sodium (Na⁺) in diabetic cardiomyopathy and provides unique data on the linkage between Na⁺ flux and energy metabolism, studied with non-invasive ²³Na, and ³¹P-NMR spectroscopy, polarography, and mass spectroscopy. ²³Na NMR studies allow determination of the intracellular and extracellular Na⁺ pools by splitting the total Na⁺ peak into two resonances after the addition of a shift reagent to the perfusate. Using this technology, we found that intracellular Na⁺ is approximately two times higher in diabetic cardiomyocytes than in control possibly due to combined changes in the activity of Na⁺–K⁺ pump, Na⁺/H⁺ exchanger 1 (NHE1) and Na⁺-glucose cotransporter. We hypothesized that the increase in Na⁺ activates the mitochondrial membrane Na⁺/Ca²⁺ exchanger, which leads to a loss of intramitochondrial Ca²⁺, with a subsequent alteration in mitochondrial bioenergetics and function. Using isolated mitochondria, we showed that the addition of Na⁺ (1–10 mM) led to a dose-dependent decrease in oxidative phosphorylation and that this effect was reversed by providing extramitochondrial Ca²⁺ or by inhibiting the mitochondrial Na⁺/Ca²⁺ exchanger with diltiazem. Similar experiments with ³¹P-NMR in isolated superfused mitochondria embedded in agarose beads showed that Na⁺ (3–30 mM) led to significantly decreased ATP levels and that this effect was stronger in diabetic rats. These data suggest that in diabetic cardiomyocytes, increased Na⁺ leads to abnormalities in oxidative phosphorylation and a subsequent decrease in ATP levels. In support of these data, using ³¹P-NMR, we showed that the baseline β-ATP and phosphocreatine (PCr) were lower in diabetic cardiomyocytes than in control, suggesting that diabetic cardiomyocytes have depressed bioenergetic function. Thus, both altered intracellular Na⁺ levels and bioenergetics and their interactions may significantly contribute to the pathology of diabetic cardiomyopathy.

Bond graph modelling of the cardiac action potential: implications for drift and non-unique steady states

Mathematical models of cardiac action potentials have become increasingly important in the study of heart disease and pharmacology, but concerns linger over their robustness during long periods of simulation, in particular due to issues such as model drift and non-unique steady states. Previous studies have linked these to violation of conservation laws, but only explored those issues with respect to charge conservation in specific models. Here, we propose a general and systematic method of identifying conservation laws hidden in models of cardiac electrophysiology by using bond graphs, and develop a bond graph model of the cardiac action potential to study long-term behaviour. Bond graphs provide an explicit energy-based framework for modelling physical systems, which makes them well suited for examining conservation within electrophysiological models. We find that the charge conservation laws derived in previous studies are examples of the more general concept of a 'conserved moiety'. Conserved moieties explain model drift and non-unique steady states, generalizing the results from previous studies. The bond graph approach provides a rigorous method to check for drift and non-unique steady states in a wide range of cardiac action potential models, and can be extended to examine behaviours of other excitable systems.

Effects of antiarrhythmics and hypokalemia on the rate adaptation of cardiac repolarization

OBJECTIVES

In normal conditions, sudden heart rate acceleration provokes a rapid reduction in ventricular action potential duration (APD). The protracted APD rate adaptation favors early afterdepolarizations and precipitates arrhythmia. Nevertheless, it is uncertain as to whether the rate-dependent changes of ventricular repolarization can be adversely modified by arrhythmogenic drugs (quinidine and procainamide) and hypokalemia, in comparison to the agents with safe therapeutic profile, such as lidocaine.

DESIGN

The rate adaptation of QT interval and monophasic APD obtained from the left ventricular (LV) and the right ventricular (RV) epicardium was examined during rapid cardiac pacing applied in isolated, perfused guinea-pig heart preparations.

RESULTS

At baseline, an abrupt increase in cardiac activation rate was associated with a substantial reduction of the QT interval and ventricular APD in the first two cardiac cycles, which was followed by a gradual shortening of repolarization over subsequent pacing intervals. The time constants of the fast (τ_fast) and slow (τ_slow) components of the APD dynamics determined from a double exponential fit were longer in RV compared to LV chamber. Quinidine, procainamide, and hypokalemia prolonged ventricular repolarization and delayed the rate adaptation of the QT interval and APD in LV and RV, as evidenced by increased τ_fast and τ_slow values. In contrast, lidocaine had no effect on the dynamic changes of ventricular repolarization upon heart rate acceleration.

CONCLUSIONS

The rate adaptation of ventricular repolarization is delayed by arrhythmogenic interventions, such as quinidine, procainamide, and hypokalemia, but not changed by lidocaine, a clinically safe antiarrhythmic agent.

Determinants of Isoform-Specific Gating Kinetics of hERG1 Channel: Combined Experimental and Simulation Study

I_Kr is the rapidly activating component of the delayed rectifier potassium current, the ion current largely responsible for the repolarization of the cardiac action potential. Inherited forms of long QT syndrome (LQTS) (Lees-Miller et al., 1997) in humans are linked to functional modifications in the Kv11.1 (hERG) ion channel and potentially life threatening arrhythmias. There is little doubt now that hERG-related component of I_Kr in the heart depends on the tetrameric (homo- or hetero-) channels formed by two alternatively processed isoforms of hERG, termed hERG1a and hERG1b. Isoform composition (hERG1a- vs. the b-isoform) has recently been reported to alter pharmacologic responses to some hERG blockers and was proposed to be an essential factor pre-disposing patients for drug-induced QT prolongation. Very little is known about the gating and pharmacological properties of two isoforms in heart membranes. For example, how gating mechanisms of the hERG1a channels differ from that of hERG1b is still unknown. The mechanisms by which hERG 1a/1b hetero-tetramers contribute to function in the heart, or what role hERG1b might play in disease are all questions to be answered. Structurally, the two isoforms differ only in the N-terminal region located in the cytoplasm: hERG1b is 340 residues shorter than hERG1a and the initial 36 residues of hERG1b are unique to this isoform. In this study, we combined electrophysiological measurements for HEK cells, kinetics and structural modeling to tease out the individual contributions of each isoform to Action Potential formation and then make predictions about the effects of having various mixture ratios of the two isoforms. By coupling electrophysiological data with computational kinetic modeling, two proposed mechanisms of hERG gating in two homo-tetramers were examined. Sets of data from various experimental stimulation protocols (HEK cells) were analyzed simultaneously and fitted to Markov-chain models (M-models). The minimization procedure presented here, allowed assessment of suitability of different Markov model topologies and the corresponding parameters that describe the channel kinetics. The kinetics modeling pointed to key differences in the gating kinetics that were linked to the full channel structure. Interactions between soluble domains and the transmembrane part of the channel appeared to be critical determinants of the gating kinetics. The structures of the full channel in the open and closed states were compared for the first time using the recent Cryo-EM resolved structure for full open hERG channel and an homology model for the closed state, based on the highly homolog EAG1 channel. Key potential interactions which emphasize the importance of electrostatic interactions between N-PAS cap, S4-S5, and C-linker are suggested based on the structural analysis. The derived kinetic parameters were later used in higher order models of cells and tissue to track down the effect of varying the ratios of hERG1a and hERG1b on cardiac action potentials and computed electrocardiograms. Simulations suggest that the recovery from inactivation of hERG1b may contribute to its physiologic role of this isoform in the action potential. Finally, the results presented here contribute to the growing body of evidence that hERG1b significantly affects the generation of the cardiac I_kr and plays an important role in cardiac electrophysiology. We highlight the importance of carefully revisiting the Markov models previously proposed in order to properly account for the relative abundance of the hERG1 a- and b- isoforms.

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.

Simultaneous Quantification of Spatially Discordant Alternans in Voltage and Intracellular Calcium in Langendorff-Perfused Rabbit Hearts and Inconsistencies with Models of Cardiac Action Potentials and Ca Transients

Rationale: Discordant alternans, a phenomenon in which the action potential duration (APDs) and/or intracellular calcium transient durations (CaDs) in different spatial regions of cardiac tissue are out of phase, present a dynamical instability for complex spatial dispersion that can be associated with long-QT syndrome (LQTS) and the initiation of reentrant arrhythmias. Because the use of numerical simulations to investigate arrhythmic effects, such as acquired LQTS by drugs is beginning to be studied by the FDA, it is crucial to validate mathematical models that may be used during this process. Objective: In this study, we characterized with high spatio-temporal resolution the development of discordant alternans patterns in transmembrane voltage (Vm) and intracellular calcium concentration ([Cai]+2) as a function of pacing period in rabbit hearts. Then we compared the dynamics to that of the latest state-of-the-art model for ventricular action potentials and calcium transients to better understand the underlying mechanisms of discordant alternans and compared the experimental data to the mathematical models representing Vm and [Cai]+2 dynamics. Methods and Results: We performed simultaneous dual optical mapping imaging of Vm and [Cai]+2 in Langendorff-perfused rabbit hearts with higher spatial resolutions compared with previous studies. The rabbit hearts developed discordant alternans through decreased pacing period protocols and we quantified the presence of multiple nodal points along the direction of wave propagation, both in APD and CaD, and compared these findings with results from theoretical models. In experiments, the nodal lines of CaD alternans have a steeper slope than those of APD alternans, but not as steep as predicted by numerical simulations in rabbit models. We further quantified several additional discrepancies between models and experiments. Conclusions: Alternans in CaD have nodal lines that are about an order of magnitude steeper compared to those of APD alternans. Current action potential models lack the necessary coupling between voltage and calcium compared to experiments and fail to reproduce some key dynamics such as, voltage amplitude alternans, smooth development of calcium alternans in time, conduction velocity and the steepness of the nodal lines of APD and CaD.

Differential calcium sensitivity in NaV 1.5 mixed syndrome mutants

KEY POINTS

SCN5a mutations may express gain-of-function (Long QT Syndrome-3), loss-of-function (Brugada Syndrome 1) or both (mixed syndromes), depending on the mutation and environmental triggers. One such trigger may be an increase in cytosolic calcium, accompanying exercise. Many mixed syndromes mutants, including ∆KPQ, E1784K, 1795insD and Q1909R, are found in calcium-sensitive regions. Elevated cytosolic calcium attenuates gain-of-function properties in ∆KPQ, 1795insD and Q1909R, but not in E1784K. By contrast, elevated cytosolic calcium further exacerbates gain-of-function in E1784K by destabilizing slow inactivation. Action potential modelling, using a modified O'Hara Rudy model, suggests that elevated heart rate rescues action potential duration in ∆KPQ, 1795insD and Q1909R, but not in E1784K. Action potential simulations suggest that E1784K carriers have an increased intracellular sodium-to-calcium ratio under bradycardia and tachycardia conditions. Elevated cytosolic calcium, which is common during high heart rates, ameliorates or exacerbates the mixed syndrome phenotype depending on the genetic signature.

ABSTRACT

Inherited arrhythmias may arise from mutations in the gene for SCN5a, which encodes the cardiac voltage-gated sodium channel, NaV 1.5. Mutants in NaV 1.5 result in Brugada Syndrome (BrS1), Long-QT Syndrome (LQT3) or mixed syndromes (an overlap of BrS1/LQT3). Exercise is a potential arrhythmogenic trigger in mixed syndromes. We aimed to determine the effects of elevated cytosolic calcium, which is common during exercise, in mixed syndrome NaV 1.5 mutants. We used whole-cell patch clamp to assess the biophysical properties of NaV 1.5 wild-type (WT), ∆KPQ, E1784K, 1795insD and Q1909R mutants in human embryonic kidney 293 cells transiently transfected with the NaV 1.5 α subunit (WT or mutants), β1 subunit and enhanced green fluorescent protein. Voltage-dependence and kinetics were measured at cytosolic calcium levels of approximately 0, 500 and 2500 nm. In silico, action potential (AP) model simulations were performed using a modified O'Hara Rudy model. Elevated cytosolic calcium attenuates the late sodium current in ∆KPQ, 1795insD and Q1909R, but not in E1784K. Elevated cytosolic calcium restores steady-state slow inactivation (SSSI) to the WT-form in Q1909R, but depolarized SSSI in E1784K. Our AP simulations showed a frequency-dependent reduction of AP duration in ∆KPQ, 1795insD and Q1909R carriers. In E1784K, AP duration is relatively prolonged at both low and high heart rates, resulting in a sodium overload. Cellular perturbations during exercise may affect BrS1/LQT3 patients differently depending on their individual genetic signature. Thus, exercise may be therapeutic or may be an arrhythmogenic trigger in some SCN5a patients.

Hysteretic Dynamics of Multi-Stable Early Afterdepolarisations with Repolarisation Reserve Attenuation: A Potential Dynamical Mechanism for Cardiac Arrhythmias

Some cardiovascular and non-cardiovascular drugs frequently cause excessive prolongation of the cardiac action potential (AP) and lead to the development of early afterdepolarisations (EADs), which trigger lethal ventricular arrhythmias. Combining computer simulations in APs with numerical calculations based on dynamical system theory, we investigated stability changes of APs observed in a paced human ventricular myocyte model by decreasing and/or increasing the rapid (I_Kr) and slow (I_Ks) components of delayed rectifying K⁺ current. Upon reducing I_Kr, the APs without EADs (no-EAD response) showed gradual prolongation of AP duration (APD), and were annihilated without AP configuration changes due to the occurrence of saddle-node bifurcations. This annihilation caused a transition to an AP with EADs as a new stable steady state. Furthermore, reducing repolarisation currents (repolarisation reserve attenuation) evoked multi-stable states consisting of APs with different APDs, and caused multiple hysteretic dynamics. Depending on initial ion circumstances within ventricular myocytes, these multi-stable AP states might increase the local/global heterogeneity of AP repolarisations in the ventricle. Thus, the EAD-induced arrhythmias with repolarisation reserve attenuation might be attributed to the APD variability caused by multi-stability in cardiac AP dynamics.

Slow [Na+]i dynamics impacts arrhythmogenesis and spiral wave reentry in cardiac myocyte ionic model

Accumulation of intracellular Na⁺ is gaining recognition as an important regulator of cardiac myocyte electrophysiology. The intracellular Na⁺ concentration can be an important determinant of the cardiac action potential duration, can modulate the tissue-level conduction of excitation waves, and can alter vulnerability to arrhythmias. Mathematical models of cardiac electrophysiology often incorporate a dynamic intracellular Na⁺ concentration, which changes much more slowly than the remaining variables. We investigated the dependence of several arrhythmogenesis-related factors on [Na⁺]_i in a mathematical model of the human atrial action potential. In cell simulations, we found that [Na⁺]_i accumulation stabilizes the action potential duration to variations in several conductances and that the slow dynamics of [Na⁺]_i impacts bifurcations to pro-arrhythmic afterdepolarizations, causing intermittency between different rhythms. In long-lasting tissue simulations of spiral wave reentry, [Na⁺]_i becomes spatially heterogeneous with a decreased area around the spiral wave rotation center. This heterogeneous region forms a functional anchor, resulting in diminished meandering of the spiral wave. Our findings suggest that slow, physiological, rate-dependent variations in [Na⁺]_i may play complex roles in cellular and tissue-level cardiac dynamics.

Efficient parameterization of cardiac action potential models using a genetic algorithm

Finding appropriate values for parameters in mathematical models of cardiac cells is a challenging task. Here, we show that it is possible to obtain good parameterizations in as little as 30-40 s when as many as 27 parameters are fit simultaneously using a genetic algorithm and two flexible phenomenological models of cardiac action potentials. We demonstrate how our implementation works by considering cases of "model recovery" in which we attempt to find parameter values that match model-derived action potential data from several cycle lengths. We assess performance by evaluating the parameter values obtained, action potentials at fit and non-fit cycle lengths, and bifurcation plots for fidelity to the truth as well as consistency across different runs of the algorithm. We also fit the models to action potentials recorded experimentally using microelectrodes and analyze performance. We find that our implementation can efficiently obtain model parameterizations that are in good agreement with the dynamics exhibited by the underlying systems that are included in the fitting process. However, the parameter values obtained in good parameterizations can exhibit a significant amount of variability, raising issues of parameter identifiability and sensitivity. Along similar lines, we also find that the two models differ in terms of the ease of obtaining parameterizations that reproduce model dynamics accurately, most likely reflecting different levels of parameter identifiability for the two models.

A multiscale computational modelling approach predicts mechanisms of female sex risk in the setting of arousal-induced arrhythmias

KEY POINTS

This study represents a first step toward predicting mechanisms of sex-based arrhythmias that may lead to important developments in risk stratification and may inform future drug design and screening. We undertook simulations to reveal the conditions (i.e. pacing, drugs, sympathetic stimulation) required for triggering and sustaining reentrant arrhythmias. Using the recently solved cryo-EM structure for the Eag-family channel as a template, we revealed potential interactions of oestrogen with the pore loop hERG mutation (G604S). Molecular models suggest that oestrogen and dofetilide blockade can concur simultaneously in the hERG channel pore.

ABSTRACT

Female sex is a risk factor for inherited and acquired long-QT associated torsade de pointes (TdP) arrhythmias, and sympathetic discharge is a major factor in triggering TdP in female long-QT syndrome patients. We used a combined experimental and computational approach to predict 'the perfect storm' of hormone concentration, I_Kr block and sympathetic stimulation that induces arrhythmia in females with inherited and acquired long-QT. More specifically, we developed mathematical models of acquired and inherited long-QT syndrome in male and female ventricular human myocytes by combining effects of a hormone and a hERG blocker, dofetilide, or hERG mutations. These 'male' and 'female' model myocytes and tissues then were used to predict how various sex-based differences underlie arrhythmia risk in the setting of acute sympathetic nervous system discharge. The model predicted increased risk for arrhythmia in females when acute sympathetic nervous system discharge was applied in the settings of both inherited and acquired long-QT syndrome. Females were predicted to have protection from arrhythmia induction when progesterone is high. Males were protected by the presence of testosterone. Structural modelling points towards two plausible and distinct mechanisms of oestrogen action enhancing torsadogenic effects: oestradiol interaction with hERG mutations in the pore loop containing G604 or with common TdP-related blockers in the intra-cavity binding site. Our study presents findings that constitute the first evidence linking structure to function mechanisms underlying female dominance of arousal-induced arrhythmias.

Sex and regional differences in rabbit right ventricular L-type calcium current levels and mathematical modelling of arrhythmia vulnerability

NEW FINDINGS

What is the central question of this study? Regional variations of ventricular L-type calcium current (I_Ca-L ) amplitude may underlie the increased arrhythmia risk in adult females. Current amplitude variations have been described for the left ventricle but not for the right ventricle. What is the main finding and its importance? Adult female rabbit right ventricular base myocytes exhibit elevated I_Ca-L compared with female apex or male myocytes. Oestrogen upregulated I_Ca-L in cultured female myocytes. Mathematical simulations modelling long QT syndrome type 2 demonstrated that elevated I_Ca-L prolonged action potentials and induced early after-depolarizations. Thus, ventricular arrhythmias in adult females may be associated with an oestrogen-induced upregulation of I_Ca-L . Previous studies have shown that adult rabbit left ventricular myocytes exhibit sex and regional differences in L-type calcium current (I_Ca-L ) levels that contribute to increased female susceptibility to arrhythmogenic early after-depolarizations (EADs). We used patch-clamp recordings from isolated adult male and female rabbit right ventricular myocytes to determine apex-base differences in I_Ca-L density and used mathematical modelling to examine the contribution of I_Ca-L to EAD formation. Current density measured at 0 mV in female base myocytes was 67% higher than in male base myocytes and 55% higher than in female apex myocytes. No differences were observed between male and female apex myocytes, between male apex and base myocytes, or in the voltage dependences of I_Ca-L activation or inactivation. The role of oestrogen was investigated using cultured adult female right ventricular base myocytes. After 2 days, 17β-estradiol (1 nm) produced a 65% increase in I_Ca-L density compared with untreated control myocytes, suggesting an oestrogen-induced upregulation of I_Ca-L . Action potential simulations using a modified Luo-Rudy cardiomyocyte model showed that increased I_Ca-L density, at the level observed in female base myocytes, resulted in longer duration action potentials, and when combined with a 50% reduction of the rapidly inactivating delayed rectifier potassium current conductance to model long QT syndrome type 2, the action potential was accompanied by one or more EADs. Thus, we found higher levels of I_Ca-L in adult female right ventricle base myocytes and the upregulation of this current by oestrogen. Simulations of long QT syndrome type 2 showed that elevated I_Ca-L contributed to genesis of EADs.

Developmental changes in the balance of glycolytic ATP production and oxidative phosphorylation in ventricular cells: A simulation study

The developmental program of the heart requires accurate regulation to ensure continuous circulation and simultaneous cardiac morphogenesis, because any functional abnormalities may progress to congenital heart malformation. Notably, energy metabolism in fetal ventricular cells is regulated in a manner that differs from adult ventricular cells: fetal cardiomyocytes generally have immature mitochondria and fetal ventricular cells show greater dependence on glycolytic ATP production. However, although various characteristics of energy metabolism in fetal ventricular cells have been reported, to our knowledge, a quantitative description of the contributions of these factors to fetal ventricular cell functions has not yet been established. Here, we constructed a mathematical model to integrate various characteristics of fetal ventricular cells and predicted the contribution of each characteristic to the maintenance of intracellular ATP concentration and sarcomere contraction under anoxic conditions. Our simulation results demonstrated that higher glycogen content, higher hexokinase activity, and lower creatine concentration helped prolong the time for which ventricular cell contraction was maintained under anoxic conditions. The integrated model also enabled us to quantitatively assess the contributions of factors related to energy metabolism in ventricular cells. Because fetal cardiomyocytes exhibit similar energy metabolic profiles to stem cell-derived cardiomyocytes and those in the failing heart, an improved understanding of these fetal ventricular cells will contribute to a better comprehension of the processes in stem cell-derived cardiomyocytes or under pathological conditions.

Impairment of Excitation-Contraction Coupling in Right Ventricular Hypertrophied Muscle with Fibrosis Induced by Pulmonary Artery Banding

Interstitial myocardial fibrosis is one of the factors responsible for dysfunction of the heart. However, how interstitial fibrosis affects cardiac function and excitation-contraction coupling (E-C coupling) has not yet been clarified. We developed an animal model of right ventricular (RV) hypertrophy with fibrosis by pulmonary artery (PA) banding in rats. Two, four, and six weeks after the PA-banding operation, the tension and intracellular Ca²⁺ concentration of RV papillary muscles were simultaneously measured (n = 33). The PA-banding rats were clearly divided into two groups by the presence or absence of apparent interstitial fibrosis in the papillary muscles: F+ or F- group, respectively. The papillary muscle diameter and size of myocytes were almost identical between F+ and F-, although the RV free wall weight was heavier in F+ than in F-. F+ papillary muscles exhibited higher stiffness, lower active tension, and lower Ca²⁺ responsiveness compared with Sham and F- papillary muscles. In addition, we found that the time to peak Ca²⁺ had the highest correlation coefficient to percent of fibrosis among other parameters, such as RV weight and active tension of papillary muscles. The phosphorylation level of troponin I in F+ was significantly higher than that in Sham and F-, which supports the idea of lower Ca²⁺ responsiveness in F+. We also found that connexin 43 in F+ was sparse and disorganized in the intercalated disk area where interstitial fibrosis strongly developed. In the present study, the RV papillary muscles obtained from the PA-banding rats enabled us to directly investigate the relationship between fibrosis and cardiac dysfunction, the impairment of E-C coupling in particular. Our results suggest that interstitial fibrosis worsens cardiac function due to 1) the decrease in Ca²⁺ responsiveness and 2) the asynchronous activation of each cardiac myocyte in the fibrotic preparation due to sparse cell-to-cell communication.

Molecular Pathophysiology of Congenital Long QT Syndrome

Ion channels represent the molecular entities that give rise to the cardiac action potential, the fundamental cellular electrical event in the heart. The concerted function of these channels leads to normal cyclical excitation and resultant contraction of cardiac muscle. Research into cardiac ion channel regulation and mutations that underlie disease pathogenesis has greatly enhanced our knowledge of the causes and clinical management of cardiac arrhythmia. Here we review the molecular determinants, pathogenesis, and pharmacology of congenital Long QT Syndrome. We examine mechanisms of dysfunction associated with three critical cardiac currents that comprise the majority of congenital Long QT Syndrome cases: 1) IKs, the slow delayed rectifier current; 2) IKr, the rapid delayed rectifier current; and 3) INa, the voltage-dependent sodium current. Less common subtypes of congenital Long QT Syndrome affect other cardiac ionic currents that contribute to the dynamic nature of cardiac electrophysiology. Through the study of mutations that cause congenital Long QT Syndrome, the scientific community has advanced understanding of ion channel structure-function relationships, physiology, and pharmacological response to clinically employed and experimental pharmacological agents. Our understanding of congenital Long QT Syndrome continues to evolve rapidly and with great benefits: genotype-driven clinical management of the disease has improved patient care as precision medicine becomes even more a reality.

Mathematical modeling of the female reproductive system: from oocyte to delivery

From ovulation to delivery, and through the menstrual cycle, the female reproductive system undergoes many dynamic changes to provide an optimal environment for the embryo to implant, and to develop successfully. It is difficult ethically and practically to observe the system over the timescales involved in growth and development (often hours to days). Even in carefully monitored conditions clinicians and biologists can only see snapshots of the development process. Mathematical models are emerging as a key means to supplement our knowledge of the reproductive process, and to tease apart complexity in the reproductive system. These models have been used successfully to test existing hypotheses regarding the mechanisms of female infertility and pathological fetal development, and also to provide new experimentally testable hypotheses regarding the process of development. This new knowledge has allowed for improvements in assisted reproductive technologies and is moving toward translation to clinical practice via multiscale assessments of the dynamics of ovulation, development in pregnancy, and the timing and mechanics of delivery. WIREs Syst Biol Med 2017, 9:e1353. doi: 10.1002/wsbm.1353 For further resources related to this article, please visit the WIREs website.

Sex hormonal regulation of cardiac ion channels in drug-induced QT syndromes

Female sex is an independent risk factor for development of torsade de pointes (TdP) arrhythmias not only in congenital long QT syndromes but also in acquired long QT syndromes. Clinical and experimental evidences suggest that the gender differences may be due to, at least in part, gender differences in regulation of rate-corrected QT (QT_C) interval between men and women. In adult women, both QT_C interval and arrhythmic risks in TdP alter cyclically during menstrual cycle, suggesting a critical role of female sex hormones in cardiac repolarization process. These gender differences in fundamental cardiac electrophysiology result from variable ion channel expression and diverse sex hormonal regulation via long term genomic and acute non-genomic actions, and sex differences in drug responses and metabolisms. In particular, non-genomic actions of testosterone and progesterone on cardiac ion channels are likely to contribute to the gender differences in cardiac repolarization processes. This review summarizes current knowledge on sex hormonal regulation of cardiac ion channels which contribute to cardiac repolarization processes and its implication for gender differences in drug-induced long QT syndromes.

Simulating the effects of growth and fiber dispersion on the electromechanical response of a cardiac ventricular wedge affected from concentric hypertrophy

In this paper, we analyze the epicardial electromechanical response of an in silico cardiac ventricular wedge under both healthy and concentric hypertrophic conditions. This is achieved by taking into account the growth of the wedge thickness and the fiber dispersion that may follow. The electromechanical response is described in terms of some macroscopic measures, i.e. the action potential duration, the conduction velocity, the contractility and the contraction force. Our results suggest that growth reduces the action potential duration and conduction velocity, whilst it increases the contractility and contraction force, yielding an overall negative effect. In presence of fiber dispersion, the action potential duration and conduction velocity are not affected further, whilst the effect on the contractility and contraction force is enhanced.

Precisely parameterized experimental and computational models of tissue organization

Patterns of cellular organization in diverse tissues frequently display a complex geometry and topology tightly related to the tissue function. Progressive disorganization of tissue morphology can lead to pathologic remodeling, necessitating the development of experimental and theoretical methods of analysis of the tolerance of normal tissue function to structural alterations. A systematic way to investigate the relationship of diverse cell organization to tissue function is to engineer two-dimensional cell monolayers replicating key aspects of the in vivo tissue architecture. However, it is still not clear how this can be accomplished on a tissue level scale in a parameterized fashion, allowing for a mathematically precise definition of the model tissue organization and properties down to a cellular scale with a parameter dependent gradual change in model tissue organization. Here, we describe and use a method of designing precisely parameterized, geometrically complex patterns that are then used to control cell alignment and communication of model tissues. We demonstrate direct application of this method to guiding the growth of cardiac cell cultures and developing mathematical models of cell function that correspond to the underlying experimental patterns. Several anisotropic patterned cultures spanning a broad range of multicellular organization, mimicking the cardiac tissue organization of different regions of the heart, were found to be similar to each other and to isotropic cell monolayers in terms of local cell-cell interactions, reflected in similar confluency, morphology and connexin-43 expression. However, in agreement with the model predictions, different anisotropic patterns of cell organization, paralleling in vivo alterations of cardiac tissue morphology, resulted in variable and novel functional responses with important implications for the initiation and maintenance of cardiac arrhythmias. We conclude that variations of tissue geometry and topology can dramatically affect cardiac tissue function even if the constituent cells are themselves similar, and that the proposed method can provide a general strategy to experimentally and computationally investigate when such variation can lead to impaired tissue function.