Properties and ionic mechanisms of action potential adaptation, restitution, and accommodation in canine epicardium

His bundle activates faster than ventricular myocardium during prolonged ventricular fibrillation

Background

The Purkinje fiber system has recently been implicated as an important driver of the rapid activation rate during long duration ventricular fibrillation (VF>2 minutes). The goal of this study is to determine whether this activity propagates to or occurs in the proximal specialized conduction system during VF as well.

Methods and Results

An 8×8 array with 300 µm spaced electrodes was placed over the His bundles of isolated, perfused rabbit hearts (n = 12). Ventricular myocardial (VM) and His activations were differentiated by calculating Laplacian recordings from unipolar signals. Activation rates of the VM and His bundle were compared and the His bundle conduction velocity was measured during perfused VF followed by 8 minutes of unperfused VF. During perfused VF the average VM activation rate of 11.04 activations/sec was significantly higher than the His bundle activation rate of 6.88 activations/sec (p<0.05). However from 3–8 minutes of unperfused VF the His system activation rate (6.16, 5.53, 5.14, 5.22, 6.00, and 4.62 activations/sec significantly faster than the rate of the VM (4.67, 3.63, 2.94, 2.24, 3.45, and 2.31 activations/sec) (p<0.05). The conduction velocity of the His system immediately decreased to 94% of the sinus rate during perfused VF then gradually decreased to 67% of sinus rhythm conduction at 8 minutes of unperfused VF.

Conclusion

During prolonged VF the activation rate of the His bundle is faster than that of the VM. This suggests that the proximal conduction system, like the distal Purkinje system, may be an important driver during long duration VF and may be a target for interventional therapy.

Modeling CaMKII-mediated regulation of L-type Ca(2+) channels and ryanodine receptors in the heart

Excitation-contraction coupling (ECC) in the cardiac myocyte is mediated by a number of highly integrated mechanisms of intracellular Ca²⁺ transport. Voltage- and Ca²⁺-dependent L-type Ca²⁺ channels (LCCs) allow for Ca²⁺ entry into the myocyte, which then binds to nearby ryanodine receptors (RyRs) and triggers Ca²⁺ release from the sarcoplasmic reticulum in a process known as Ca²⁺-induced Ca²⁺ release. The highly coordinated Ca²⁺-mediated interaction between LCCs and RyRs is further regulated by the cardiac isoform of the Ca²⁺/calmodulin-dependent protein kinase (CaMKII). Because CaMKII targets and modulates the function of many ECC proteins, elucidation of its role in ECC and integrative cellular function is challenging and much insight has been gained through the use of detailed computational models. Multiscale models that can both reconstruct the detailed nature of local signaling events within the cardiac dyad and predict their functional consequences at the level of the whole cell have played an important role in advancing our understanding of CaMKII function in ECC. Here, we review experimentally based models of CaMKII function with a focus on LCC and RyR regulation, and the mechanistic insights that have been gained through their application.

hERG inhibitors with similar potency but different binding kinetics do not pose the same proarrhythmic risk: implications for drug safety assessment

INTRODUCTION

Since the discovery of the link that exists between drug-induced hERG inhibition and Torsade de Pointes (TdP), extreme attention has been given to avoid new drugs inhibiting this channel. hERG inhibition is routinely screened for in new drugs and, typically, IC50 values are compared to projected plasma concentrations to define a safety margin.

METHODS AND RESULTS

We aimed to show that drugs with similar hERG potency are not uniformly pro-arrhythmic-this depends on the drug binding kinetics and mode of action (trapped or not) rather than the IC50 value only. We used a mathematical model of hERG and its related encoded current IKr to simulate drug binding in different configurations. Expression systems mimicking the screening process were first investigated. hERG model was then incorporated into a canine action potential (AP) and tissue model to study the impact of drug binding configurations on AP and pseudo-ECG (QT interval prolongation). Our data show that: (1) trapped and not trapped configurations and different binding kinetics could be identified during hERG screening; (2) slow binding, not trapped drugs, induced less AP prolongation and minimal QT interval prolongation (4.7%) at a concentration equal to the IC50 whereas maximal pro-arrhythmic risk was observed for trapped drugs at the same concentration (QT interval prolongation, 23.1%).

CONCLUSION

Our study demonstrates the need for screening for hERG binding configurations rather than potency alone. It also demonstrates the potential link between hERG, drug mode of action and TdP, and the need to question the current regulatory guidance.

Determinants of beat-to-beat variability of repolarization duration in the canine ventricular myocyte: a computational analysis

Beat-to-beat variability of repolarization duration (BVR) is an intrinsic characteristic of cardiac function and a better marker of proarrhythmia than repolarization prolongation alone. The ionic mechanisms underlying baseline BVR in physiological conditions, its rate dependence, and the factors contributing to increased BVR in pathologies remain incompletely understood. Here, we employed computer modeling to provide novel insights into the subcellular mechanisms of BVR under physiological conditions and during simulated drug-induced repolarization prolongation, mimicking long-QT syndromes type 1, 2, and 3. We developed stochastic implementations of 13 major ionic currents and fluxes in a model of canine ventricular-myocyte electrophysiology. Combined stochastic gating of these components resulted in short- and long-term variability, consistent with experimental data from isolated canine ventricular myocytes. The model indicated that the magnitude of stochastic fluctuations is rate dependent due to the rate dependence of action-potential (AP) duration (APD). This process (the “active” component) and the intrinsic nonlinear relationship between membrane current and APD (“intrinsic component”) contribute to the rate dependence of BVR. We identified a major role in physiological BVR for stochastic gating of the persistent Na⁺ current (I_Na) and rapidly activating delayed-rectifier K⁺ current (I_Kr). Inhibition of I_Kr or augmentation of I_Na significantly increased BVR, whereas subsequent β-adrenergic receptor stimulation reduced it, similar to experimental findings in isolated myocytes. In contrast, β-adrenergic stimulation increased BVR in simulated long-QT syndrome type 1. In addition to stochastic channel gating, AP morphology, APD, and beat-to-beat variations in Ca²⁺ were found to modulate single-cell BVR. Cell-to-cell coupling decreased BVR and this was more pronounced when a model cell with increased BVR was coupled to a model cell with normal BVR. In conclusion, our results provide new insights into the ionic mechanisms underlying BVR and suggest that BVR reflects multiple potentially proarrhythmic parameters, including increased ion-channel stochasticity, prolonged APD, and abnormal Ca²⁺ handling.

Every heartbeat has an electrical recovery (repolarization) interval that varies in duration from beat to beat. Excessive beat-to-beat variability of repolarization duration has been shown to be a risk marker of potentially fatal heart-rhythm disorders, but the contributing subcellular mechanisms remain incompletely understood. Computational models have greatly enhanced our understanding of several basic electrophysiological mechanisms. We developed a detailed computer model of the ventricular myocyte that can simulate beat-to-beat changes in repolarization duration by taking into account stochastic changes in the opening and closing of individual ion channels responsible for all main ion currents. The model accurately reproduced experimental data from isolated myocytes under both physiological and pathological conditions. Using the model, we identified several mechanisms contributing to repolarization variability, including stochastic gating of ion channels, duration and morphology of the repolarization phase, and intracellular calcium handling, thereby providing insights into its basis as a proarrhythmic marker. Our computer model provides a detailed framework to study the dynamics of cardiac electrophysiology and arrhythmias.

Heterogeneity and function of K(ATP) channels in canine hearts

BACKGROUND

The concept that pore-forming Kir6.2 and regulatory SUR2A subunits form cardiac ATP-sensitive potassium (K(ATP)) channels is challenged by recent reports that SUR1 is predominant in mouse atrial K(ATP) channels.

OBJECTIVE

To assess SUR subunit composition of K(ATP) channels and consequence of K(ATP) activation for action potential duration (APD) in dog hearts.

METHODS

Patch-clamp techniques were used on isolated dog cardiomyocytes to investigate K(ATP) channel properties. Dynamic current clamp, by injection of a linear K(+) conductance to simulate activation of the native current, was used to study the consequences of K(ATP) activation on APD.

RESULTS

Metabolic inhibitor (MI)-activated current was not significantly different from pinacidil (SUR2A-specific)-activated current, and both currents were larger than diazoxide (SUR1-specific)-activated current in both the atrium and the ventricle. Mean K(ATP) conductance (activated by MI) did not differ significantly between chambers, although, within the ventricle, both MI-induced and pinacidil-induced currents tended to decrease from the epicardium to the endocardium. Dynamic current-clamp results indicate that myocytes with longer baseline APDs are more susceptible to injected K(ATP) current, a result reproduced in silico by using a canine action potential model (Hund-Rudy) to simulate epicardial and endocardial myocytes.

CONCLUSIONS

Even a small fraction of K(ATP) activation significantly shortens APD in a manner that depends on existing heterogeneity in K(ATP) current and APD.

Ionic bases for electrical remodeling of the canine cardiac ventricle

Emerging evidence suggests that ventricular electrical remodeling (VER) is triggered by regional myocardial strain via mechanoelectrical feedback mechanisms; however, the ionic mechanisms underlying strain-induced VER are poorly understood. To determine its ionic basis, VER induced by altered electrical activation in dogs undergoing left ventricular pacing (n = 6) were compared with unpaced controls (n = 4). Action potential (AP) durations (APDs), ionic currents, and Ca(2+) transients were measured from canine epicardial myocytes isolated from early-activated (low strain) and late-activated (high strain) left ventricular regions. VER in the early-activated region was characterized by minimal APD prolongation, but marked attenuation of the AP phase 1 notch attributed to reduced transient outward K(+) current. In contrast, VER in the late-activated region was characterized by significant APD prolongation. Despite marked APD prolongation, there was surprisingly minimal change in ion channel densities but a twofold increase in diastolic Ca(2+). Computer simulations demonstrated that changes in sarcolemmal ion channel density could only account for attenuation of the AP notch observed in the early-activated region but failed to account for APD remodeling in the late-activated region. Furthermore, these simulations identified that cytosolic Ca(2+) accounted for APD prolongation in the late-activated region by enhancing forward-mode Na(+)/Ca(2+) exchanger activity, corroborated by increased Na(+)/Ca(2+) exchanger protein expression. Finally, assessment of skinned fibers after VER identified altered myofilament Ca(2+) sensitivity in late-activated regions to be associated with increased diastolic levels of Ca(2+). In conclusion, we identified two distinct ionic mechanisms that underlie VER: 1) strain-independent changes in early-activated regions due to remodeling of sarcolemmal ion channels with no changes in Ca(2+) handling and 2) a novel and unexpected mechanism for strain-induced VER in late-activated regions in the canine arising from remodeling of sarcomeric Ca(2+) handling rather than sarcolemmal ion channels.

Na/K pump regulation of cardiac repolarization: insights from a systems biology approach

The sodium-potassium pump is widely recognized as the principal mechanism for active ion transport across the cellular membrane of cardiac tissue, being responsible for the creation and maintenance of the transarcolemmal sodium and potassium gradients, crucial for cardiac cell electrophysiology. Importantly, sodium-potassium pump activity is impaired in a number of major diseased conditions, including ischemia and heart failure. However, its subtle ways of action on cardiac electrophysiology, both directly through its electrogenic nature and indirectly via the regulation of cell homeostasis, make it hard to predict the electrophysiological consequences of reduced sodium-potassium pump activity in cardiac repolarization. In this review, we discuss how recent studies adopting the systems biology approach, through the integration of experimental and modeling methodologies, have identified the sodium-potassium pump as one of the most important ionic mechanisms in regulating key properties of cardiac repolarization and its rate dependence, from subcellular to whole organ levels. These include the role of the pump in the biphasic modulation of cellular repolarization and refractoriness, the rate control of intracellular sodium and calcium dynamics and therefore of the adaptation of repolarization to changes in heart rate, as well as its importance in regulating pro-arrhythmic substrates through modulation of dispersion of repolarization and restitution. Theoretical findings are consistent across a variety of cell types and species including human, and widely in agreement with experimental findings. The novel insights and hypotheses on the role of the pump in cardiac electrophysiology obtained through this integrative approach could eventually lead to novel therapeutic and diagnostic strategies.

Role of temperature on nonlinear cardiac dynamics

Thermal effects affecting spatiotemporal behavior of cardiac tissue are discussed by relating temperature variations to proarrhythmic dynamics in the heart. By introducing a thermoelectric coupling in a minimal model of cardiac tissue, we are able to reproduce experimentally measured dynamics obtained simultaneously from epicardial and endocardial canine right ventricles at different temperatures. A quantitative description of emergent proarrhythmic properties of restitution, conduction velocity, and alternans regimes as a function of temperature is presented. Complex discordant alternans patterns that enhance tissue dispersion consisting of one wave front and three wave backs are described in both simulations and experiments. Possible implications for model generalization are finally discussed.

Human atrial fibrillation: insights from computational electrophysiological models

Computational electrophysiology has proven useful to investigate the mechanisms of cardiac arrhythmias at various spatial scales, from isolated myocytes to the whole heart. This article reviews how mathematical modeling has aided our understanding of human atrial myocyte electrophysiology to study the contribution of structural and electrical remodeling to human atrial fibrillation. Potential new avenues of investigation and model development are suggested.

Bridging experiments, models and simulations: an integrative approach to validation in computational cardiac electrophysiology

Computational models in physiology often integrate functional and structural information from a large range of spatiotemporal scales from the ionic to the whole organ level. Their sophistication raises both expectations and skepticism concerning how computational methods can improve our understanding of living organisms and also how they can reduce, replace, and refine animal experiments. A fundamental requirement to fulfill these expectations and achieve the full potential of computational physiology is a clear understanding of what models represent and how they can be validated. The present study aims at informing strategies for validation by elucidating the complex interrelations among experiments, models, and simulations in cardiac electrophysiology. We describe the processes, data, and knowledge involved in the construction of whole ventricular multiscale models of cardiac electrophysiology. Our analysis reveals that models, simulations, and experiments are intertwined, in an assemblage that is a system itself, namely the model-simulation-experiment (MSE) system. We argue that validation is part of the whole MSE system and is contingent upon 1) understanding and coping with sources of biovariability; 2) testing and developing robust techniques and tools as a prerequisite to conducting physiological investigations; 3) defining and adopting standards to facilitate the interoperability of experiments, models, and simulations; 4) and understanding physiological validation as an iterative process that contributes to defining the specific aspects of cardiac electrophysiology the MSE system targets, rather than being only an external test, and that this is driven by advances in experimental and computational methods and the combination of both.

How the Hodgkin-Huxley equations inspired the Cardiac Physiome Project

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

An in silico canine cardiac midmyocardial action potential duration model as a tool for early drug safety assessment

Cell lines expressing ion channels (IC) and the advent of plate-based electrophysiology device have enabled a molecular understanding of the action potential (AP) as a means of early QT assessment. We sought to develop an in silico AP (isAP) model that provides an assessment of the effect of a compound on the myocyte AP duration (APD) using concentration-effect curve data from a panel of five ICs (hNav1.5, hCav1.2, hKv4.3/hKChIP2.2, hKv7.1/hminK, hKv11.1). A test set of 53 compounds was selected to cover a range of selective and mixed IC modulators that were tested for their effects on optically measured APD. A threshold of >10% change in APD at 90% repolarization (APD90) was used to signify an effect at the top test concentration. To capture the variations observed in left ventricular midmyocardial myocyte APD data from 19 different dogs, the isAP model was calibrated to produce an ensemble of 19 model variants that could capture the shape and form of the APs and also quantitatively replicate dofetilide- and diltiazem-induced APD90 changes. Provided with IC panel data only, the isAP model was then used, blinded, to predict APD90 changes greater than 10%. At a simulated concentration of 30 μM and based on a criterion that six of the variants had to agree, isAP prediction was scored as showing greater than 80% predictivity of compound activity. Thus, early in drug discovery, the isAP model allows integrating separate IC data and is amenable to the throughput required for use as a virtual screen.

Analysis of the contribution of I(to) to repolarization in canine ventricular myocardium

BACKGROUND AND PURPOSE

The contribution of the transient outward potassium current (I(to)) to ventricular repolarization is controversial as it depends on the experimental conditions, the region of myocardium and the species studied. The aim of the present study was therefore to characterize I(to) and estimate its contribution to repolarization reserve in canine ventricular myocardium.

EXPERIMENTAL APPROACH

Ion currents were recorded using conventional whole-cell voltage clamp and action potential voltage clamp techniques in canine isolated ventricular cells. Action potentials were recorded from canine ventricular preparations using microelectrodes. The contribution of I(to) to repolarization was studied using 100 µM chromanol 293B in the presence of 0.5 µM HMR 1556, which fully blocks I(Ks).

KEY RESULTS

The high concentration of chromanol 293B used effectively suppressed I(to) without affecting other repolarizing K(+) currents (I(K1), I(Kr), I(p)). Action potential clamp experiments revealed a slowly inactivating and a 'late' chromanol-sensitive current component occurring during the action potential plateau. Action potentials were significantly lengthened by chromanol 293B in the presence of HMR 1556. This lengthening effect induced by I(to) inhibition was found to be reverse rate-dependent. It was significantly augmented after additional attenuation of repolarization reserve by 0.1 µM dofetilide and this caused the occurrence of early afterdepolarizations. The results were confirmed by computer simulation.

CONCLUSIONS AND IMPLICATIONS

The results indicate that I(to) is involved in regulating repolarization in canine ventricular myocardium and that it contributes significantly to the repolarization reserve. Therefore, blockade of I(to) may enhance pro-arrhythmic risk.

Delayed endosome-dependent CamKII and p38 kinase signaling in cardiomyocytes destabilizes Kv4.3 mRNA

The Kv4.3 transient outward current (I(to)) channel, which produces early repolarization in human cardiomyocytes, is downregulated with cardiac pathology. This is evident in cultured neonatal rat cardiomyocytes in which Angiotensin II (Ang II) acts via p38 mitogen-activated protein kinase (p38K) to increase apoptosis and induce Kv4.3 mRNA destabilization to downregulate the channel protein. However, it is not understood how p38K activation, which is activated transiently for minutes, induces downstream effects hours later. Here we show that there is a second phase of p38K activation. Inhibiting this delayed p38K activation eliminated Kv4.3 mRNA destabilization. Furthermore, inhibiting endosome generation left the transient activation of p38K intact, but blocked delayed p38K activation and the Kv4.3 effect. CamKII was also found to be required for delayed p38K activation and Kv4.3 mRNA destabilization. Finally, CamKII methionine oxidation and activation are biphasic, with the delayed phase requiring endosomes. Hence, in addition to participating in channel traffic, cardiomyocyte endosomes control channel mRNA expression by mediating delayed oxidative CamKII-p38K signaling.

Models of excitation-contraction coupling in cardiac ventricular myocytes

Excitation-contraction coupling describes the processes relating to electrical excitation through force generation and contraction in the heart. It occurs at multiple levels from the whole heart, to single myocytes and down to the sarcomere. A central process that links electrical excitation to contraction is calcium mobilization. Computational models that are well grounded in experimental data have been an effective tool to understand the complex dynamics of the processes involved in excitation-contraction coupling. Presented here is a summary of some computational models that have added to the understanding of the cellular and subcellular mechanisms that control ventricular myocyte calcium dynamics. Models of cardiac ventricular myocytes that have given insight into termination of calcium release and interval-force relations are discussed in this manuscript. Computational modeling of calcium sparks, the elementary events in cardiac excitation-contraction coupling, has given insight into mechanism governing their dynamics and termination as well as their role in excitation-contraction coupling and is described herein.

Quantitative comparison of cardiac ventricular myocyte electrophysiology and response to drugs in human and nonhuman species

Explanations for arrhythmia mechanisms at the cellular level are usually based on experiments in nonhuman myocytes. However, subtle electrophysiological differences between species may lead to different rhythmic or arrhythmic cellular behaviors and drug response given the nonlinear and highly interactive cellular system. Using detailed and quantitatively accurate mathematical models for human, dog, and guinea pig ventricular action potentials (APs), we simulated and compared cell electrophysiology mechanisms and response to drugs. Under basal conditions (absence of β-adrenergic stimulation), Na(+)/K(+)-ATPase changes secondary to Na(+) accumulation determined AP rate dependence for human and dog but not for guinea pig where slow delayed rectifier current (I(Ks)) was the major rate-dependent current. AP prolongation with reduction of rapid delayed rectifier current (I(Kr)) and I(Ks) (due to mutations or drugs) showed strong species dependence in simulations, as in experiments. For humans, AP prolongation was 80% following I(Kr) block. It was 30% for dog and 20% for guinea pig. Under basal conditions, I(Ks) block was of no consequence for human and dog, but for guinea pig, AP prolongation after I(Ks) block was severe. However, with β-adrenergic stimulation, I(Ks) played an important role in all species, particularly in AP shortening at fast rate. Quantitative comparison of AP repolarization, rate-dependence mechanisms, and drug response in human, dog, and guinea pig revealed major species differences (e.g., susceptibility to arrhythmogenic early afterdepolarizations). Extrapolation from animal to human electrophysiology and drug response requires great caution.

Efficacy of synaptic inhibition depends on multiple, dynamically interacting mechanisms implicated in chloride homeostasis

Chloride homeostasis is a critical determinant of the strength and robustness of inhibition mediated by GABA(A) receptors (GABA(A)Rs). The impact of changes in steady state Cl(-) gradient is relatively straightforward to understand, but how dynamic interplay between Cl(-) influx, diffusion, extrusion and interaction with other ion species affects synaptic signaling remains uncertain. Here we used electrodiffusion modeling to investigate the nonlinear interactions between these processes. Results demonstrate that diffusion is crucial for redistributing intracellular Cl(-) load on a fast time scale, whereas Cl(-)extrusion controls steady state levels. Interaction between diffusion and extrusion can result in a somato-dendritic Cl(-) gradient even when KCC2 is distributed uniformly across the cell. Reducing KCC2 activity led to decreased efficacy of GABA(A)R-mediated inhibition, but increasing GABA(A)R input failed to fully compensate for this form of disinhibition because of activity-dependent accumulation of Cl(-). Furthermore, if spiking persisted despite the presence of GABA(A)R input, Cl(-) accumulation became accelerated because of the large Cl(-) driving force that occurs during spikes. The resulting positive feedback loop caused catastrophic failure of inhibition. Simulations also revealed other feedback loops, such as competition between Cl(-) and pH regulation. Several model predictions were tested and confirmed by [Cl(-)](i) imaging experiments. Our study has thus uncovered how Cl(-) regulation depends on a multiplicity of dynamically interacting mechanisms. Furthermore, the model revealed that enhancing KCC2 activity beyond normal levels did not negatively impact firing frequency or cause overt extracellular K(-) accumulation, demonstrating that enhancing KCC2 activity is a valid strategy for therapeutic intervention.

High-throughput functional curation of cellular electrophysiology models

Effective reuse of a quantitative mathematical model requires not just access to curated versions of the model equations, but also an understanding of the functional capabilities of the model, and the advisable scope of its application. To enable this "functional curation" we have developed a simulation environment that provides high-throughput evaluation of a mathematical model's functional response to an arbitrary user-defined protocol, and optionally compares the results against experimental data. In this study we demonstrate the efficacy of this simulation environment on 31 cardiac electrophysiology cell models using two test cases. The S1-S2 response is evaluated to characterise the models' restitution curves, and their L-type calcium channel current-voltage curves are evaluated. The significant variation in the response of these models, even when the models represent the same species and temperature, demonstrates the importance of knowing the functional characteristics of a model prior to its reuse. We also discuss the wider implications for this approach, in improving the selection of models for reuse, enabling the identification of models that exhibit particular experimentally observed phenomena, and making the incremental development of models more robust.

Ca²⁺-induced delayed afterdepolarizations are triggered by dyadic subspace Ca2²⁺ affirming that increasing SERCA reduces aftercontractions

Ca(2+)-induced delayed afterdepolarizations (DADs) are depolarizations that occur after full repolarization. They have been observed across multiple species and cell types. Experimental results have indicated that the main cause of DADs is Ca(2+) overload. The main hypothesis as to their initiation has been Ca(2+) overflow from the overloaded sarcoplasmic reticulum (SR). Our results using 37 previously published mathematical models provide evidence that Ca(2+)-induced DADs are initiated by the same mechanism as Ca(2+)-induced Ca(2+) release, i.e., the modulation of the opening of ryanodine receptors (RyR) by Ca(2+) in the dyadic subspace; an SR overflow mechanism was not necessary for the induction of DADs in any of the models. The SR Ca(2+) level is better viewed as a modulator of the appearance of DADs and the magnitude of Ca(2+) release. The threshold for the total Ca(2+) level within the cell (not only the SR) at which Ca(2+) oscillations arise in the models is close to their baseline level (∼1- to 3-fold). It is most sensitive to changes in the maximum sarco(endo)plasmic reticulum Ca(2+)-ATPase (SERCA) pump rate (directly proportional), the opening probability of RyRs, and the Ca(2+) diffusion rate from the dyadic subspace into the cytosol (both indirectly proportional), indicating that the appearance of DADs is multifactorial. This shift in emphasis away from SR overload as the trigger for DADs toward a multifactorial analysis could explain why SERCA overexpression has been shown to suppress DADs (while increasing contractility) and why DADs appear during heart failure (at low SR Ca(2+) levels).

Simulation of the undiseased human cardiac ventricular action potential: model formulation and experimental validation

Cellular electrophysiology experiments, important for understanding cardiac arrhythmia mechanisms, are usually performed with channels expressed in non myocytes, or with non-human myocytes. Differences between cell types and species affect results. Thus, an accurate model for the undiseased human ventricular action potential (AP) which reproduces a broad range of physiological behaviors is needed. Such a model requires extensive experimental data, but essential elements have been unavailable. Here, we develop a human ventricular AP model using new undiseased human ventricular data: Ca(2+) versus voltage dependent inactivation of L-type Ca(2+) current (I(CaL)); kinetics for the transient outward, rapid delayed rectifier (I(Kr)), Na(+)/Ca(2+) exchange (I(NaCa)), and inward rectifier currents; AP recordings at all physiological cycle lengths; and rate dependence and restitution of AP duration (APD) with and without a variety of specific channel blockers. Simulated APs reproduced the experimental AP morphology, APD rate dependence, and restitution. Using undiseased human mRNA and protein data, models for different transmural cell types were developed. Experiments for rate dependence of Ca(2+) (including peak and decay) and intracellular sodium ([Na(+)](i)) in undiseased human myocytes were quantitatively reproduced by the model. Early afterdepolarizations were induced by I(Kr) block during slow pacing, and AP and Ca(2+) alternans appeared at rates >200 bpm, as observed in the nonfailing human ventricle. Ca(2+)/calmodulin-dependent protein kinase II (CaMK) modulated rate dependence of Ca(2+) cycling. I(NaCa) linked Ca(2+) alternation to AP alternans. CaMK suppression or SERCA upregulation eliminated alternans. Steady state APD rate dependence was caused primarily by changes in [Na(+)](i), via its modulation of the electrogenic Na(+)/K(+) ATPase current. At fast pacing rates, late Na(+) current and I(CaL) were also contributors. APD shortening during restitution was primarily dependent on reduced late Na(+) and I(CaL) currents due to inactivation at short diastolic intervals, with additional contribution from elevated I(Kr) due to incomplete deactivation.

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

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

Transient outward current (I(to)) gain-of-function mutations in the KCND3-encoded Kv4.3 potassium channel and Brugada syndrome

BACKGROUND

Brugada syndrome (BrS) is a sudden death-predisposing genetic condition characterized electrocardiographically by ST segment elevation in the leads V(1)-V(3). Given the prominent role of the transient outward current (I(to)) in BrS pathogenesis, we hypothesized that rare gain-of-function mutations in KCND3 may serve as a pathogenic substrate for BrS.

METHODS

Comprehensive mutational analysis of KCND3-encoded Kv4.3 (I(to)) was conducted using polymerase chain reaction, denaturing high performance liquid chromatography, and direct sequencing of DNA derived from 86 unrelated BrS1-8 genotype-negative BrS patients. DNA from 780 healthy individuals was examined to assess allelic frequency for nonsynonymous variants. Putative BrS-associated Kv4.3 mutations were engineered and coexpressed with wild-type KChIP2 in HEK293 cells. Wild-type and mutant I(to) ion currents were recorded using whole-cell patch clamp.

RESULTS

Two BrS1-8 genotype-negative cases possessed novel Kv4.3 missense mutations. Both Kv4.3-L450F and Kv4.3-G600R were absent in 1,560 reference alleles and involved residues highly conserved across species. Both Kv4.3-L450F and Kv4.3-G600R demonstrated a gain-of-function phenotype, increasing peak I(to) current density by 146.2% (n = 15, P <.05) and 50.4% (n = 15, P <.05), respectively. Simulations using a Luo-Rudy II action potential (AP) model demonstrated the stable loss of the AP dome as a result of the increased I(to) maximal conductance associated with the heterozygous expression of either L450F or G600R.

CONCLUSIONS

These findings provide the first molecular and functional evidence implicating novel KCND3 gain-of-function mutations in the pathogenesis and phenotypic expression of BrS, with the potential for a lethal arrhythmia being precipitated by a genetically enhanced I(to) current gradient within the right ventricle where KCND3 expression is the highest.

Local control of β-adrenergic stimulation: Effects on ventricular myocyte electrophysiology and Ca(2+)-transient

Local signaling domains and numerous interacting molecular pathways and substrates contribute to the whole-cell response of myocytes during β-adrenergic stimulation (βARS). We aimed to elucidate the quantitative contribution of substrates and their local signaling environments during βARS to the canine epicardial ventricular myocyte electrophysiology and calcium transient (CaT). We present a computational compartmental model of βARS and its electrophysiological effects. Novel aspects of the model include localized signaling domains, incorporation of β1 and β2 receptor isoforms, a detailed population-based approach to integrate the βAR and Ca(2+)/Calmodulin kinase (CaMKII) signaling pathways and their effects on a wide range of substrates that affect whole-cell electrophysiology and CaT. The model identifies major roles for phosphodiesterases, adenylyl cyclases, PKA and restricted diffusion in the control of local cAMP levels and shows that activation of specific cAMP domains by different receptor isoforms allows for specific control of action potential and CaT properties. In addition, the model predicts increased CaMKII activity during βARS due to rate-dependent accumulation and increased Ca(2+) cycling. CaMKII inhibition, reduced compartmentation, and selective blockade of β1AR is predicted to reduce the occurrence of delayed afterdepolarizations during βARS. Finally, the relative contribution of each PKA substrate to whole-cell electrophysiology is quantified by comparing simulations with and without phosphorylation of each target. In conclusion, this model enhances our understanding of localized βAR signaling and its whole-cell effects in ventricular myocytes by incorporating receptor isoforms, multiple pathways and a detailed representation of multiple-target phosphorylation; it provides a basis for further studies of βARS under pathological conditions.

Ionic mechanisms of cellular electrical and mechanical abnormalities in Brugada syndrome

The Brugada syndrome (BrS) is a right ventricular (RV) arrhythmia that is responsible for up to 12% of sudden cardiac deaths. The aims of our study were to determine the cellular mechanisms of the electrical abnormality in BrS and the potential basis of the RV contractile abnormality observed in the syndrome. Tetrodotoxin was used to reduce cardiac Na(+) current (I(Na)) to mimic a BrS-like setting in canine ventricular myocytes. Moderate reduction (<50%) of I(Na) with tetrodotoxin resulted in all-or-none repolarization in a fraction of RV epicardial myocytes. Dynamic clamp and modeling show that reduction of I(Na) shifts the action potential (AP) duration-transient outward current (I(to)) density curve to the left and has a biphasic effect on AP duration. In the presence of a large I(to), I(Na) reduction either prolongs or collapses the AP, depending on the exact density of I(to). These repolarization changes reduce Ca(2+) influx and sarcoplasmic reticulum load, resulting in marked attenuation of myocyte contraction and Ca(2+) transient in RV epicardial myocytes. We conclude that I(Na) reduction alters repolarization by reducing the threshold for I(to)-induced all-or-none repolarization. These cellular electrical changes suppress myocyte excitation-contraction coupling and contraction and may be a contributing factor to the contractile abnormality of the RV wall in BrS.

Ionic mechanisms of electrophysiological heterogeneity and conduction block in the infarct border zone

The increased incidence of arrhythmia in the healing phase after infarction has been linked to remodeling in the epicardial border zone (EBZ). Ionic models of normal zone (NZ) and EBZ myocytes were incorporated into one-dimensional models of propagation to gain mechanistic insights into how ion channel remodeling affects action potential (AP) duration (APD) and refractoriness, vulnerability to conduction block, and conduction safety postinfarction. We found that EBZ tissue exhibited abnormal APD restitution. The remodeled Na(+) current (I(Na)) and L-type Ca(2+) current (I(Ca,L)) promoted increased effective refractory period and prolonged APD at a short diastolic interval. While postrepolarization refractoriness due to remodeled EBZ I(Na) was the primary determinant of the vulnerable window for conduction block at the NZ-to-EBZ transition in response to premature S2 stimuli, altered EBZ restitution also promoted APD dispersion and increased the vulnerable window at fast S1 pacing rates. Abnormal EBZ APD restitution and refractoriness also led to abnormal periodic conduction block patterns for a range of fast S1 pacing rates. In addition, we found that I(Na) remodeling decreased conduction safety in the EBZ but that inward rectifier K(+) current remodeling partially offset this decrease. EBZ conduction was characterized by a weakened AP upstroke and short intercellular delays, which prevented I(Ca,L) and transient outward K(+) current remodeling from playing a role in EBZ conduction in uncoupled tissue. Simulations of a skeletal muscle Na(+) channel SkM1-I(Na) injection into the EBZ suggested that this recently proposed antiarrhythmic therapy has several desirable effects, including normalization of EBZ effective refractory period and APD restitution, elimination of vulnerability to conduction block, and normalization of conduction in tissue with reduced intercellular coupling.

Models of cardiac excitation-contraction coupling in ventricular myocytes

Mathematical and computational modeling of cardiac excitation-contraction coupling has produced considerable insights into how the heart muscle contracts. With the increase in biophysical and physiological data available, the modeling has become more sophisticated with investigations spanning in scale from molecular components to whole cells. These modeling efforts have provided insight into cardiac excitation-contraction coupling that advanced and complemented experimental studies. One goal is to extend these detailed cellular models to model the whole heart. While this has been done with mechanical and electrophysiological models, the complexity and fast time course of calcium dynamics have made inclusion of detailed calcium dynamics in whole heart models impractical. Novel methods such as the probability density approach and moment closure technique which increase computational efficiency might make this tractable.

Mechanisms of ventricular rate adaptation as a predictor of arrhythmic risk

Protracted QT interval (QTI) adaptation to abrupt heart rate (HR) changes has been identified as a clinical arrhythmic risk marker. This study investigates the ionic mechanisms of QTI rate adaptation and its relationship to arrhythmic risk. Computer simulations and experimental recordings in human and canine ventricular tissue were used to investigate the ionic basis of QTI and action potential duration (APD) to abrupt changes in HR with a protocol commonly used in clinical studies. The time for 90% QTI adaptation is 3.5 min in simulations, in agreement with experimental and clinical data in humans. APD adaptation follows similar dynamics, being faster in midmyocardial cells (2.5 min) than in endocardial and epicardial cells (3.5 min). Both QTI and APD adapt in two phases following an abrupt HR change: a fast initial phase with time constant < 30 s, mainly related to L-type calcium and slow-delayed rectifier potassium current, and a second slow phase of >2 min driven by intracellular sodium concentration ([Na+]i) dynamics. Alterations in [Na+]i dynamics due to Na+/K+ pump current inhibition result in protracted rate adaptation and are associated with increased proarrhythmic risk, as indicated by action potential triangulation and faster L-type calcium current recovery from inactivation, leading to the formation of early afterdepolarizations. In conclusion, this study suggests that protracted QTI adaptation could be an indicator of altered [Na+]i dynamics following Na+/K+ pump inhibition as it occurs in patients with ischemia or heart failure. An increased risk of cardiac arrhythmias in patients with protracted rate adaptation may be due to an increased risk of early afterdepolarization formation.

Role of the transient outward current in regulating mechanical properties of canine ventricular myocytes

INTRODUCTION

The transient outward current (I(to)) is a major repolarizing current in the heart. Reduction of I(to) density is consistently observed in human heart failure (HF) and animal HF models. It has been proposed that I(to), via its influence on phase-1 repolarization of the action potential, facilitates L-type Ca(2+) current (I(Ca-L)) activation and sarcoplasmic reticulum Ca(2+) release, and that its down-regulation may contribute to the impaired contractility in failing heart.

METHODS AND RESULTS

We used the dynamic clamp to quantitatively examine the influence of I(to) on the mechanical properties of canine left ventricular myocytes at 34 degrees C. In endocardial myocytes, where the native I(to) is small, simulation of an epicardial-level artificial I(to) accentuated the phase-1 repolarization and significantly suppressed cell shortening. The peak amplitude of Ca(2+) transient was also reduced in the presence of simulated I(to), although the rate of rise of the Ca(2+) transient was increased. Conversely, subtraction, or "blockade" of the native I(to) enhanced contractility in epicardial cells. These results agree with the inverse correlation between I(to) levels and myocyte contractility and Ca(2+) transient amplitude in epicardial and endocardial myocytes. Action potential clamp studies showed that the phase-1 repolarization/I(to) versus I(Ca-L) relationship had an inverted-J shape; small I(to) enhanced peak I(Ca-L) while moderate-to-large I(to) decreased peak I(Ca-L) and markedly reduced early Ca(2+) influx.

CONCLUSION

Our results show that epicardial-level of I(to) acts as a negative, rather than positive regulator of myocyte mechanical properties in canine ventricular myocytes.

Uniqueness and stability of action potential models during rest, pacing, and conduction using problem-solving environment

Development and application of physiologically detailed dynamic models of the action potential (AP) and Ca2+ cycling in cardiac cells is a rapidly growing aspect of computational cardiac electrophysiology. Given the large scale of the nonlinear system involved, questions were recently raised regarding reproducibility, numerical stability, and uniqueness of model solutions, as well as ability of the model to simulate AP propagation in multicellular configurations. To address these issues, we reexamined ventricular models of myocyte AP developed in our laboratory with the following results. 1), Recognizing that the model involves a system of differential-algebraic equations, a procedure is developed for estimating consistent initial conditions that insure uniqueness and stability of the solution. 2), Model parameters that can be used to modify these initial conditions according to experimental values are identified. 3), A convergence criterion for steady-state solution is defined based on tracking the incremental contribution of each ion species to the membrane voltage. 4), Singularities in state variable formulations are removed analytically. 5), A biphasic current stimulus is implemented to completely eliminate stimulus artifact during long-term pacing over a broad range of frequencies. 6), Using the AP computed based on 1-5 above, an efficient scheme is developed for computing propagation in multicellular models.

A multiscale model linking ion-channel molecular dynamics and electrostatics to the cardiac action potential

Ion-channel function is determined by its gating movement. Yet, molecular dynamics and electrophysiological simulations were never combined to link molecular structure to function. We performed multiscale molecular dynamics and continuum electrostatics calculations to simulate a cardiac K(+) channel (I(Ks)) gating and its alteration by mutations that cause arrhythmias and sudden death. An all-atom model of the I(Ks) alpha-subunit KCNQ1, based on the recent Kv1.2 structure, is used to calculate electrostatic energies during gating. Simulations are compared with experiments where varying degrees of positive charge-added via point mutation-progressively reduce current. Whole-cell simulations show that mutations cause action potential and ECG QT interval prolongation, consistent with clinical phenotypes. This framework allows integration of multiscale observations to study the molecular basis of excitation and its alteration by disease.