LabHEART: an interactive computer model of rabbit ventricular myocyte ion channels and Ca transport

Nernst-Planck-Gaussian modelling of electrodiffusional recovery from ephaptic excitation between mammalian cardiomyocytes

Introduction: In addition to gap junction conduction, recent reports implicate possible ephaptic coupling contributions to action potential (AP) propagation between successive adjacent cardiomyocytes. Here, AP generation in an active cell, withdraws Na+ from, creating a negative potential within, ephaptic spaces between the participating membranes, activating the initially quiescent neighbouring cardiomyocyte. However, sustainable ephaptic transmission requires subsequent complete recovery of the ephaptic charge difference. We explore physical contributions of passive electrodiffusive ion exchange with the remaining extracellular space to this recovery for the first time. Materials and Methods: Computational, finite element, analysis examined limiting, temporal and spatial, ephaptic [Na+], [Cl-], and the consequent Gaussian charge differences and membrane potential recovery patterns following a ΔV∼130 mV AP upstroke at physiological (37°C) temperatures. This incorporated Nernst-Planck formalisms into equations for the time-dependent spatial concentration gradient profiles. Results: Mammalian atrial, ventricular and purkinje cardiomyocyte ephaptic junctions were modelled by closely apposed circularly symmetric membranes, specific capacitance 1 μF cm-2, experimentally reported radii a = 8,000, 12,000 and 40,000 nm respectively and ephaptic axial distance w = 20 nm. This enclosed an ephaptic space containing principal ions initially at normal extracellular [Na+] = 153.1 mM and [Cl-] = 145.8 mM, respective diffusion coefficients D Na = 1.3 × 109 and D Cl = 2 × 109 nm2s-1. Stable, concordant computational solutions were confirmed exploring ≤1,600 nm mesh sizes and Δt≤0.08 ms stepsize intervals. The corresponding membrane voltage profile changes across the initially quiescent membrane were obtainable from computed, graphically represented a and w-dependent ionic concentration differences adapting Gauss's flux theorem. Further simulations explored biological variations in ephaptic dimensions, membrane anatomy, and diffusion restrictions within the ephaptic space. Atrial, ventricular and Purkinje cardiomyocytes gave 40, 180 and 2000 ms 99.9% recovery times, with 720 or 360 ms high limits from doubling ventricular radius or halving diffusion coefficient. Varying a, and D Na and D Cl markedly affected recovery time-courses with logarithmic and double-logarithmic relationships, Varying w exerted minimal effects. Conclusion: We thereby characterise the properties of, and through comparing atrial, ventricular and purkinje recovery times with interspecies in vivo background cardiac cycle duration data, (blue whale ∼2000, human∼90, Etruscan shrew, ∼40 ms) can determine physical limits to, electrodiffusive contributions to ephaptic recovery.

Bacterial toxins and heart function: heat-labile Escherichia coli enterotoxin B promotes changes in cardiac function with possible relevance for sudden cardiac death

Bacterial toxins can cause cardiomyopathy, though it is not its most common cause. Some bacterial toxins can form pores in the membrane of cardiomyocytes, while others can bind to membrane receptors. Enterotoxigenic E. coli can secrete enterotoxins, including heat-resistant (ST) or labile (LT) enterotoxins. LT is an AB5-type toxin that can bind to specific cell receptors and disrupt essential host functions, causing several common conditions, such as certain diarrhea. The pentameric B subunit of LT, without A subunit (LTB), binds specifically to certain plasma membrane ganglioside receptors, found in lipid rafts of cardiomyocytes. Isolated guinea pig hearts and cardiomyocytes were exposed to different concentrations of purified LTB. In isolated hearts, mechanical and electrical alternans and an increment of heart rate variability, with an IC50 of ~0.2 μg/ml LTB, were observed. In isolated cardiomyocytes, LTB promoted significant decreases in the amplitude and the duration of action potentials. Na+ currents were inhibited whereas L-type Ca2+ currents were augmented at their peak and their fast inactivation was promoted. Delayed rectifier K+ currents decreased. Measurements of basal Ca2+ or Ca2+ release events in cells exposed to LTB suggest that LTB impairs Ca2+ homeostasis. Impaired calcium homeostasis is linked to sudden cardiac death. The results are consistent with the recent view that the B subunit is not merely a carrier of the A subunit, having a role explaining sudden cardiac death in children (SIDS) infected with enterotoxigenic E. coli, explaining several epidemiological findings that establish a strong relationship between SIDS and ETEC E. coli.

Supplementary Information

The online version contains supplementary material available at 10.1007/s12551-023-01100-6.

Alterations of sarcoplasmic reticulum-mediated Ca2+ uptake in a model of premature ventricular contraction (PVC)-induced cardiomyopathy

Premature ventricular contractions (PVCs) are the most frequent ventricular arrhythmias in the overall population. PVCs are known to acutely enhance contractility by the post-extrasystolic potentiation phenomenon, but over time persistent PVCs promote PVC-induced cardiomyopathy (PVC-CM), characterized by a reduction of the left ventricular (LV) ejection fraction. Ca2+ cycling in myocytes commands muscle contraction and in this process, SERCA2 leads the Ca2+ reuptake into the sarcoplasmic reticulum (SR) shaping cytosolic Ca2+ signal decay and muscle relaxation. Altered Ca2+ reuptake can contribute to the contractile dysfunction observed in PVC-CM. To better understand Ca2+ handling using our PVC-CM model (canines with 50% PVC burden for 12 weeks), SR-Ca2+ reuptake was investigated by measuring Ca2+ dynamics and analyzing protein expression. Kinetic analysis of Ca2+ reuptake in electrically paced myocytes showed a ~ 21 ms delay in PVC-CM compared to Sham in intact isolated myocytes, along with a ~ 13% reduction in SERCA2 activity assessed in permeabilized myocytes. Although these trends were not statistically significant between groups using hierarchical statistics, relaxation of myocytes following contraction was significantly slower in PVC-CM vs Sham myocytes. Western blot analyses indicate a 22% reduction in SERCA2 expression, a 23% increase in phospholamban (PLN) expression, and a 50% reduction in PLN phosphorylation in PVC-CM samples vs Sham. Computational analysis simulating a 20% decrease in SR-Ca2+ reuptake resulted in a ~ 22 ms delay in Ca2+ signal decay, consistent with the experimental result described above. In conclusion, SERCA2 and PLB alterations described above have a modest contribution to functional adaptations observed in PVC-CM.

Capsaicin Inhibits Multiple Voltage-Gated Ion Channels in Rabbit Ventricular Cardiomyocytes in TRPV1-Independent Manner

Capsaicin is a naturally occurring alkaloid derived from chili pepper which is responsible for its hot, pungent taste. It exerts multiple pharmacological actions, including pain-relieving, anti-cancer, anti-inflammatory, anti-obesity, and antioxidant effects. Previous studies have shown that capsaicin significantly affects the contractility and automaticity of the heart and alters cardiovascular functions. In this study, the effects of capsaicin were investigated on voltage-gated ion currents in rabbit ventricular myocytes. Capsaicin inhibited rapidly activated (I_Kr) and slowly activated (I_Ks) K⁺ currents and transient outward (I_to) K⁺ current with IC₅₀ values of 3.4 µM,14.7 µM, and 9.6 µM, respectively. In addition, capsaicin, at higher concentrations, suppressed voltage-gated Na⁺ and Ca²⁺ currents and inward rectifier I_K1 current with IC₅₀ values of 42.7 µM, 34.9 µM, and 38.8 µM, respectively. Capsaicin inhibitions of I_Na, I_L-Ca, I_Kr, I_Ks, I_to, and I_K1 were not reversed in the presence of capsazepine (3 µM), a TRPV1 antagonist. The inhibitory effects of capsaicin on these currents developed gradually, reaching steady-state levels within 3 to 6 min, and the recoveries were usually incomplete during washout. In concentration-inhibition curves, apparent Hill coefficients higher than unity suggested multiple interaction sites of capsaicin on these channels. Collectively, these findings indicate that capsaicin affects cardiac electrophysiology by acting on a diverse range of ion channels and suggest that caution should be exercised when capsaicin is administered to carriers of cardiac channelopathies or to individuals with arrhythmia-prone conditions, such as ischemic heart diseases.

Cannabidiol Inhibits Multiple Ion Channels in Rabbit Ventricular Cardiomyocytes

Cannabidiol (CBD), a major non-psychotropic cannabinoid found in the Cannabis plant, has been shown to exert anti-nociceptive, anti-psychotic, and anti-convulsant effects and to also influence the cardiovascular system. In this study, the effects of CBD on major ion currents were investigated using the patch-clamp technique in rabbit ventricular myocytes. CBD inhibited voltage-gated Na⁺ and Ca²⁺ channels with IC₅₀ values of 5.4 and 4.8 µM, respectively. In addition, CBD, at lower concentrations, suppressed ion currents mediated by rapidly and slowly activated delayed rectifier K⁺ channels with IC₅₀ of 2.4 and 2.1 µM, respectively. CBD, up to 10 μM, did not have any significant effect on inward rectifier I_K1 and transient outward I_to currents. The effects of CBD on these currents developed gradually, reaching steady-state levels within 5–8 min, and recoveries were usually slow and partial. Hill coefficients higher than unity in concentration-inhibition curves suggested multiple CBD binding sites on these channels. These findings indicate that CBD affects cardiac electrophysiology by acting on a diverse range of ion channels and suggest that caution should be exercised when CBD is administered to carriers of cardiac channelopathies or to individuals using drugs known to affect the rhythm or the contractility of the heart.

Computer-based virtual laboratory simulations: LabHEART cardiac physiology practical

Practical demonstration of cardiomyocyte function requires substantial preparation, a source of freshly isolated animal hearts, and specialized equipment. Even where such resources are available, it is not conducive for demonstration to any more than a few students at a time. These approaches are also not consistent with the 3R principle (replacement, reduction, and refinement) of ethical use of animals. We present an implementation of the LabHEART software, developed by Donald Bers and Jose Puglisi, for medical students. Prior to the activity, students had lectures covering the physiological and pharmacological aspects of cardiac excitation-contraction (EC) coupling. We used this problem-based activity to help students consolidate their knowledge and to allow a hands-on approach to explore the key features of EC coupling. Students simulate and measure action potentials, intracellular calcium changes, and cardiomyocyte contraction. They also apply drugs that target ion channels (e.g., nifedipine or tetrodotoxin) or sympathetic input (using isoproterenol) and explore changes to EC coupling. Furthermore, by modifying the biophysical parameters of key ion channels involved in the electrical activity of the heart, students also explore the effect of channelopathies such as long QT syndromes. We describe approaches to implement this activity in a flipped classroom format, with recorded lecture materials provided ahead of the practical to facilitate active learning. We also describe our experiences implementing this activity online. The content and difficulty of the activity can be altered to suit individual courses and is also amenable to promote peer-driven learning.

Real-Time Interactive Simulations of Complex Ionic Cardiac Cell Models in 2D and 3D Heart Structures with GPUs on Personal Computers

AIMS

Cardiac modeling in heart structures for the study of arrhythmia mechanisms requires the use of software that runs on supercomputers. Therefore, computational studies are limited to groups with access to computer clusters and personnel with high-performance computing experience. We present how to use and implement WebGL programs via a custom-written library to run and visualize simulations of the most complex ionic models in 2D and 3D, in real time, interactively using the multi-core GPU of a single computer.

METHODS

We use Abubu.js, a library we developed for solving partial differential equations such as those describing crystal growth and fluid flow, along with a newly implemented visualization algorithm, to simulate complex ionic cell models. By combining this library with JavaScript, we allow direct real-time interactions with simulations. We implemented: 1) modification of any model parameters and equations at any time, with direct access to the code while it runs, 2) electrode stimulation anywhere in the 2D/3D tissue with a mouse click, 3) saving the solution of the system at any time to re-initiate the dynamics from saved initial conditions, and 4) rotation/visualization of 3D structures at any angle.

RESULTS

As examples of this modeling platform, we implemented a phenomenological cell model and the human ventricular OVVR model (41 variables). In 2D we illustrate the dynamics in an annulus, disk, and square tissue; in 2D and 3D porcine ventricles, we show the initiation of functional/anatomical reentry, spiral wave dynamics in different regimes, initiation of early afterdepolarizations (EADs), and the effects of model parameter variations in real time.

CONCLUSIONS

We present the first simulations of complex models in anatomical structures with enhanced visualization and extended interactivity that run on a single PC, without software downloads, and as fast as in real-time even for 3D full ventricles.

Mechanisms of phase-3 early afterdepolarizations and triggered activities in ventricular myocyte models

Early afterdepolarizations (EADs) are abnormal depolarizations during the repolarizing phase of the action potential, which are associated with cardiac arrhythmogenesis. EADs are classified into phase-2 and phase-3 EADs. Phase-2 EADs occur during phase 2 of the action potential, with takeoff potentials typically above -40 mV. Phase-3 EADs occur during phase 3 of the action potential, with takeoff potential between -70 and -50 mV. Since the amplitude of phase-3 EADs can be as large as that of a regular action potential, they are also called triggered activities (TAs). This also makes phase-3 EADs and TAs much more arrhythmogenic than phase-2 EADs since they can propagate easily in tissue. Although phase-2 EADs have been widely observed, phase-3 EADs and TAs have been rarely demonstrated in isolated ventricular myocytes. Here we carry out computer simulations of three widely used ventricular action potential models to investigate the mechanisms of phase-3 EADs and TAs. We show that when the T-type Ca2+ current (ICa,T ) is absent (e.g., in normal ventricular myocytes), besides the requirement of increasing inward currents and reducing outward currents as for phase-2 EADs, the occurrence of phase-3 EADs and TAs requires a substantially large increase of the L-type Ca2+ current and the slow component of the delayed rectifier K+ current. The presence of ICa,T (e.g., in neonatal and failing ventricular myocytes) can greatly reduce the thresholds of these two currents for phase-3 EADs and TAs. This implies that ICa,T may play an important role in arrhythmogenesis in cardiac diseases.

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.

Simulating Notch-Dome Morphology of Action Potential of Ventricular Cell: How the Speeds of Positive and Negative Feedbacks on Transmembrane Voltage Can Influence the Health of a Cell?

Ventricular action potential is well-known because of its plateau phase with a spike-notch-dome morphology. As such, the morphology of action potential is necessary for ensuring a correct heart functioning. Any distraction from normal notch-dome morphology may trigger a circus movement reentry in the form of lethal ventricular fibrillation. When the epicardial action potential dome propagates from a site where it is maintained to regions where it has been lost, it gives rise to the proposed mechanism for the Brugada syndrome. Despite the impact of notch-dome dynamics on the heart function, no independent and explicit research has been performed on the simulation of notch-dome dynamics and morphology. In this paper, using a novel mathematical approach, a three-state variable model is proposed; we show that our proposed model not only can simulate morphology of action potential of ventricular cells but also can propose a biological reasonable tool for controlling of the morphology of action potential spike-notch-dome. We show that the processes of activation and inactivation of ionic gating variables (as positive or negative feedbacks on the voltage of cell membrane) and the ratio of their speeds (time constants) can be treated as a reasonable biological tool for simulating ventricular cell notch-dome. This finding may led to a new insight to the quantification of the health of a ventricular cell and may also propose a new drug therapy strategy for cardiac diseases.

Afterdepolarizations and abnormal calcium handling in atrial myocytes with modulated SERCA uptake: a sensitivity analysis of calcium handling channels

Delayed afterdepolarizations (DADs) and spontaneous depolarizations (SDs) are typically triggered by spontaneous diastolic Ca²⁺ release from the sarcoplasmic reticulum (SR) which is caused by an elevated SR Ca²⁺-ATPase (SERCA) uptake and dysfunctional ryanodine receptors. However, recent studies on the T-box transcription factor gene (TBX5) demonstrated that abnormal depolarizations could occur despite a reduced SERCA uptake. Similar findings have also been reported in experimental or clinical studies of diabetes and heart failure. To investigate the sensitivity of SERCA in the genesis of DADs/SDs as well as its dependence on other Ca²⁺ handling channels, we performed systematic analyses using the Maleckar et al. model. Results showed that the modulation of SERCA alone cannot trigger abnormal depolarizations, but can instead affect the interdependency of other Ca²⁺ handling channels in triggering DADs/SDs. Furthermore, we discovered the existence of a threshold value for the intracellular concentration of Ca²⁺ ([Ca²⁺]_i) for abnormal depolarizations, which is modulated by the maximum SERCA uptake and the concentration of Ca²⁺ in the uptake and release compartments in the SR ([Ca²⁺]_up and [Ca²⁺]_rel). For the first time, our modelling study reconciles different mechanisms of abnormal depolarizations in the setting of 'lone' AF, reduced TBX5, diabetes and heart failure, and may lead to more targeted treatment for these patients. This article is part of the theme issue 'Uncertainty quantification in cardiac and cardiovascular modelling and simulation'.

Experimental assessment of a myocyte-based multiscale model of cardiac contractile dysfunction

Cardiac contractile dysfunction (CD) is a multifactorial syndrome caused by different acute or progressive diseases which hamper assessing the role of the underlying mechanisms characterizing a defined pathological condition. Mathematical modeling can help to understand the processes involved in CD and analyze their relative impact in the overall response. The aim of this study was thus to use a myocyte-based multiscale model of the circulatory system to simulate the effects of halothane, a volatile anesthetic which at high doses elicits significant acute CD both in isolated myocytes and intact animals. Ventricular chambers built using a human myocyte model were incorporated into a whole circulatory system represented by resistances and capacitances. Halothane-induced decreased sarco(endo)plasmic reticulum Ca²⁺ (SERCA2a) reuptake pump, transient outward K⁺ (I_to), Na⁺-Ca²⁺ exchanger (I_NCX) and L-type Ca²⁺ channel (I_CaL) currents, together with ryanodine receptor (RyR2) increased open probability (P_o) and reduced myofilament Ca²⁺ sensitivity, reproduced equivalent decreased action potential duration at 90% repolarization and intracellular Ca²⁺ concentration at the myocyte level reported in the literature. In the whole circulatory system, model reduction in mean arterial pressure, cardiac output and regional wall thickening fraction was similar to experimental results in open-chest sheep subjected to acute halothane overdose. Effective model performance indicates that the model structure could be used to study other changes in myocyte targets eliciting CD.

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.

MarkoLAB: A simulator to study ionic channel's stochastic behavior

Mathematical models of the cardiac cell have started to include markovian representations of the ionic channels instead of the traditional Hodgkin & Huxley formulations. There are many reasons for this: Markov models are not restricted to the idea of independent gates defining the channel, they allow more complex description with specific transitions between open, closed or inactivated states, and more importantly those states can be closely related to the underlying channel structure and conformational changes.

METHODS

We used the LabVIEW^® and MATLAB^® programs to implement the simulator MarkoLAB that allow a dynamical 3D representation of the markovian model of the channel. The Monte Carlo simulation was used to implement the stochastic transitions among states. The user can specify the voltage protocol by setting the holding potential, the step-to voltage and the duration of the stimuli.

RESULTS

The most studied feature of a channel is the current flowing through it. This happens when the channel stays in the open state, but most of the time, as revealed by the low open probability values, the channel remains on the inactive or closed states. By focusing only when the channel enters or leaves the open state we are missing most of its activity. MarkoLAB proved to be quite useful to visualize the whole behavior of the channel and not only when the channel produces a current. Such dynamic representation provides more complete information about channel kinetics and will be a powerful tool to demonstrate the effect of gene mutations or drugs on the channel function.

CONCLUSIONS

MarkoLAB provides an original way of visualizing the stochastic behavior of a channel. It clarifies concepts, such as recovery from inactivation, calcium- versus voltage-dependent inactivation, and tail currents. It is not restricted to ionic channels only but it can be extended to other transporters, such as exchangers and pumps. This program is intended as a didactical tool to illustrate the dynamical behavior of a channel. It has been implemented in two platforms MATLAB^® and LabVIEW^® to enhance the target users of this new didactical tool. The computational cost of implementing a stochastic simulation is within the range of a personal computer performance; making MarkoLAB suitable to be run during a lecture or presentation.

Study of the union method of microelectrode array and AFM for the recording of electromechanical activities in living cardiomyocytes

Electrophysiology and mechanics are two essential components in the functions of cardiomyocytes and skeletal muscle cells. The simultaneous recording of electrophysiological and mechanical activities is important for the understanding of mechanisms underlying cell functions. For example, on the one hand, mechanisms under cardiovascular drug effects will be investigated in a comprehensive way by the simultaneous recording of electrophysiological and mechanical activities. On the other hand, computational models of electromechanics provide a powerful tool for the research of cardiomyocytes. The electrical and mechanical activities are important in cardiomyocyte models. The simultaneous recording of electrophysiological and mechanical activities can provide much experimental data for the models. Therefore, an efficient method for the simultaneous recording of the electrical and mechanical data from cardiomyocytes is required for the improvement of cardiac modeling. However, as far as we know, most of the previous methods were not easy to be implemented in the electromechanical recording. For this reason, in this study, a union method of microelectrode array and atomic force microscope was proposed. With this method, the extracellular field potential and beating force of cardiomyocytes were recorded simultaneously with a low root-mean-square noise level of 11.67 μV and 60 pN. Drug tests were conducted to verify the feasibility of the experimental platform. The experimental results suggested the method would be useful for the cardiovascular drug screening and refinement of the computational cardiomyocyte models. It may be valuable for exploring the functional mechanisms of cardiomyocytes and skeletal muscle cells under physiological or pathological conditions.

Tetrodotoxin-sensitive Ca2+ Currents, but No T-type Currents in Normal, Hypertrophied, and Failing Mouse Cardiomyocytes

AIMS

To obtain functional evidence that ICa,T is involved in the pathogenesis of cardiac hypertrophy and heart failure. We unexpectedly identified ICa(TTX) rather than ICa,T, therefore, we adjusted our aim to encompass these findings.

METHODS AND RESULTS

We investigated (1) Cav3.1 (α1G) transgenic (Tg) mice compared with nontransgenic (tTA-Ntg); (2) Cav3.1-deficient mice (Cav3.1) compared with wild type (Wt) after chemically and surgically induced cardiac remodeling; and (3) spontaneous hypertensive rats and thoracic aortic constriction (TAC) rats. Whole-cell patch-clamp technique was used to measure ICa in ventricular myocytes. Cav3.1-Tg expressed ICa,T (-18.35 ± 1.02 pA/pF at -40 mV) without signs of compromised cardiac function. While we failed to detect ICa,T after hypertrophic stimuli, instead we demonstrated that both Wt and Cav3.1 mouse exhibit ICa(TTX). Using TAC rats, only 2 of 24 VMs showed ICa,T under our experimental conditions. Without TTX, ICa(TTX) occurred in VMs from Wt, spontaneous hypertensive rats, and TAC rats also.

CONCLUSIONS

These findings demonstrate for the first time that mouse VMs express ICa(TTX). We suggest that future studies should take into consideration the measuring conditions when interpreting ICa,T reappearance in ventricular myocytes in response to hypertrophic stress. Contamination with ICa(TTX) could possibly confuse the relevance of the data.

A Parsimonious Model of the Rabbit Action Potential Elucidates the Minimal Physiological Requirements for Alternans and Spiral Wave Breakup

Elucidating the underlying mechanisms of fatal cardiac arrhythmias requires a tight integration of electrophysiological experiments, models, and theory. Existing models of transmembrane action potential (AP) are complex (resulting in over parameterization) and varied (leading to dissimilar predictions). Thus, simpler models are needed to elucidate the "minimal physiological requirements" to reproduce significant observable phenomena using as few parameters as possible. Moreover, models have been derived from experimental studies from a variety of species under a range of environmental conditions (for example, all existing rabbit AP models incorporate a formulation of the rapid sodium current, INa, based on 30 year old data from chick embryo cell aggregates). Here we develop a simple "parsimonious" rabbit AP model that is mathematically identifiable (i.e., not over parameterized) by combining a novel Hodgkin-Huxley formulation of INa with a phenomenological model of repolarization similar to the voltage dependent, time-independent rectifying outward potassium current (IK). The model was calibrated using the following experimental data sets measured from the same species (rabbit) under physiological conditions: dynamic current-voltage (I-V) relationships during the AP upstroke; rapid recovery of AP excitability during the relative refractory period; and steady-state INa inactivation via voltage clamp. Simulations reproduced several important "emergent" phenomena including cellular alternans at rates > 250 bpm as observed in rabbit myocytes, reentrant spiral waves as observed on the surface of the rabbit heart, and spiral wave breakup. Model variants were studied which elucidated the minimal requirements for alternans and spiral wave break up, namely the kinetics of INa inactivation and the non-linear rectification of IK.The simplicity of the model, and the fact that its parameters have physiological meaning, make it ideal for engendering generalizable mechanistic insight and should provide a solid "building-block" to generate more detailed ionic models to represent complex rabbit electrophysiology.

Computational rabbit models to investigate the initiation, perpetuation, and termination of ventricular arrhythmia

Current understanding of cardiac electrophysiology has been greatly aided by computational work performed using rabbit ventricular models. This article reviews the contributions of multiscale models of rabbit ventricles in understanding cardiac arrhythmia mechanisms. This review will provide an overview of multiscale modeling of the rabbit ventricles. It will then highlight works that provide insights into the role of the conduction system, complex geometric structures, and heterogeneous cellular electrophysiology in diseased and healthy rabbit hearts to the initiation and maintenance of ventricular arrhythmia. Finally, it will provide an overview on the contributions of rabbit ventricular modeling on understanding the mechanisms underlying shock-induced defibrillation.

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

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

MioLab, a rat cardiac contractile force simulator: Applications to teaching cardiac cell physiology and biophysics

INTRODUCTION

Understanding the basic concepts of physiology and biophysics of cardiac cells can be improved by virtual experiments that illustrate the complex excitation-contraction coupling process in cardiac cells. The aim of this study is to propose a rat cardiac myocyte simulator, with which calcium dynamics in excitation-contraction coupling of an isolated cell can be observed. This model has been used in the course "Mathematical Modeling and Simulation of Biological Systems". In this paper we present the didactic utility of the simulator MioLab(®).

METHODS

The simulator enables virtual experiments that can help studying inhibitors and activators in the sarcoplasmic reticulum sodium-calcium exchanger, thus corroborating a better understanding of the effects of medications, which are used to treat arrhythmias, on these compartments. The graphical interfaces were developed not only to facilitate the use of the simulator, but also to promote a constructive learning on the subject, since there are animations and videos for each stage of the simulation. The effectiveness of the simulator was tested by a group of graduate students.

RESULTS

Some examples of simulations were presented in order to describe the overall structure of the simulator. Part of these virtual experiments became an activity for Biomedical Engineering graduate students, who evaluated the simulator based on its didactic quality. As a result, students answered a questionnaire on the usability and functionality of the simulator as a teaching tool. All students performed the proposed activities and classified the simulator as an optimal or good learning tool. In their written questions, students indicated as negative characteristics some problems with visualizing graphs; as positive characteristics, they indicated the simulator's didactic function, especially tutorials and videos on the topic of this study.

CONCLUSIONS

The results show that the simulator complements the study of the physiology and biophysics of the cardiac cell.

Lessons learned from multi-scale modeling of the failing heart

Heart failure constitutes a major public health problem worldwide. Affected patients experience a number of changes in the electrical function of the heart that predispose to potentially lethal cardiac arrhythmias. Due to the multitude of electrophysiological changes that may occur during heart failure, the scientific literature is complex and sometimes ambiguous, perhaps because these findings are highly dependent on the etiology, the stage of heart failure, and the experimental model used to study these changes. Nevertheless, a number of common features of failing hearts have been documented. Prolongation of the action potential (AP) involving ion channel remodeling and alterations in calcium handling have been established as the hallmark characteristics of myocytes isolated from failing hearts. Intercellular uncoupling and fibrosis are identified as major arrhythmogenic factors. Multi-scale computational simulations are a powerful tool that complements experimental and clinical research. The development of biophysically detailed computer models of single myocytes and cardiac tissues has contributed greatly to our understanding of processes underlying excitation and repolarization in the heart. The electrical, structural, and metabolic remodeling that arises in cardiac tissues during heart failure has been addressed from different computational perspectives to further understand the arrhythmogenic substrate. This review summarizes the contributions from computational modeling and simulation to predict the underlying mechanisms of heart failure phenotypes and their implications for arrhythmogenesis, ranging from the cellular level to whole-heart simulations. The main aspects of heart failure are presented in several related sections. An overview of the main electrophysiological and structural changes that have been observed experimentally in failing hearts is followed by the description and discussion of the simulation work in this field at the cellular level, and then in 2D and 3D cardiac structures. The implications for arrhythmogenesis in heart failure are also discussed including therapeutic measures, such as drug effects and cardiac resynchronization therapy. Finally, the future challenges in heart failure modeling and simulation will be discussed.

Representing variability and transmural differences in a model of human heart failure

During heart failure (HF) at the cellular level, the electrophysiological properties of single myocytes get remodeled, which can trigger the occurrence of ventricular arrhythmias that could be manifested in many forms such as early afterdepolarizations (EADs) and alternans (ALTs). In this paper, based on experimentally observed human HF data, specific ionic and exchanger current strengths are modified from a recently developed human ventricular cell model: the O'Hara-Virág-Varró-Rudy (OVVR) model. A new transmural HF-OVVR model is developed that incorporates HF changes and variability of the observed remodeling. This new heterogeneous HF-OVVR model is able to replicate many of the failing action potential (AP) properties and the dynamics of both [Ca(2+)]i and [Na(+)]i in accordance with experimental data. Moreover, it is able to generate EADs for different cell types and exhibits ALTs at modest pacing rate for transmural cell types. We have assessed the HF-OVVR model through the examination of the AP duration and the major ionic currents' rate dependence in single myocytes. The evaluation of the model comes from utilizing the steady-state (S-S) and S1-S2 restitution curves and from probing the accommodation of the HF-OVVR model to an abrupt change in cycle length. In addition, we have investigated the effect of chosen currents on the AP properties, such as blocking the slow sodium current to shorten the AP duration and suppress the EADs, and have found good agreement with experimental observations. This study should help elucidate arrhythmogenic mechanisms at the cellular level and predict unseen properties under HF conditions. In addition, this AP cell model might be useful for modeling and simulating HF at the tissue and organ levels.

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

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

Nonlinear and Stochastic Dynamics in the Heart

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

Decreased inward rectifying K+ current and increased ryanodine receptor sensitivity synergistically contribute to sustained focal arrhythmia in the intact rabbit heart

KEY POINTS

Heart failure leads to dramatic electrophysiological remodelling as a result of numerous cellular and tissue-level changes. Important cellular changes include increased sensitivity of ryanodine receptors (RyRs) to Ca(2+) release and down-regulation of the inward rectifying K(+) current (IK1), both of which contribute to triggered action potentials in isolated cells. We studied the role of increased RyR sensitivity and decreased IK1 in contributing to focal arrhythmia in the intact non-failing rabbit heart using optical mapping and pharmacological manipulation of RyRs and IK1. Neither increased RyR sensitivity or decreased IK1 alone led to significant increases in arrhythmia following local sympathetic stimulation; however, in combination, these two factors led to a significant increase in premature ventricular complexes and focal ventricular tachycardia. These results suggest synergism between increased RyR sensitivity and decreased IK1 in contributing to focal arrhythmia in the intact heart and may provide important insights into novel anti-arrhythmic treatments in heart failure.

ABSTRACT

Heart failure (HF) results in dramatic electrophysiological remodelling, including increased sensitivity of ryanodine receptors (RyRs) and decreased inward rectifying K(+) current (IK1), which predisposes HF myocytes to delayed afterdepolarizations and triggered activity. Therefore, we sought to determine the role of increased RyR sensitivity and decreased IK1 in contributing to focal arrhythmia in the intact non-failing heart. Optical mapping of transmembrane potential and intracellular Ca(2+) was performed in Langendorff-perfused rabbit hearts (n = 15). Local β-adrenergic receptor stimulation with noradrenaline (norepinephrine; NA, 50 μl, 250 μM) was applied to elicit focal activity (premature ventricular complexes (PVCs) or ventricular tachycardia (VT ≥ 3 beats)). NA was administered under control conditions (CTL) and following pretreatment with 50 μM BaCl2 to reduce IK1, or 200 μM caffeine (Caff) to sensitize RyRs, both alone and in combination. Local NA injection resulted in Ca(2+)-driven PVCs arising from the injection site in all hearts studied. No increase in NA-mediated PVCs was observed following pretreatment with either BaCl2 or Caff alone (CTL: 1.1 ± 0.7, BaCl2: 1.0 ± 0.7, Caff: 1.3 ± 0.8 PVCs/injection, P not significant). However, pretreatment with the combination of BaCl2 + Caff resulted in a significant increase in PVCs (2.3 ± 2.8 PVCs/injection, P < 0.05 vs. CTL, BaCl2, Caff). Additionally, pretreatment with BaCl2 + Caff led to sustained monomorphic VT arising from the NA application site in all hearts studied, which lasted up to 6 min following a single NA injection. VT was never observed under any other condition suggesting synergism between increased RyR sensitivity and decreased IK1 in contributing to focal activity. These findings may have important implications for the understanding and prevention of focal arrhythmia in HF.

Sensor spacing affects the tissue impedance spectra of rabbit ventricular epicardium

This study was designed to test the hypothesis that a complex composite impedance spectra develops when stimulation and recording of cardiac muscle with sufficiently fine spatial resolution in a four-electrode configuration is used. With traditional (millimeter scale) separations, the ratio between the recorded interstitial central potential difference and total supplied interstitial current is constant at all frequencies. This occurs because the fraction of supplied current that redistributes to the intracellular compartment depends on effective membrane resistance between electrodes, which is low, to a much greater extent than effective membrane capacitance. The spectra should therefore change with finer separations at which effective membrane resistance increases, as supplied current will remain primarily interstitial at lower frequencies and redistribute between compartments at higher frequencies. To test this hypothesis, we built arrays with sensors separated (d) by 804 μm, 452 μm, and 252 μm; positioned those arrays across myocyte axes on rabbit ventricular epicardium; and resolved spectra in terms of resistivity (ρt) and reactivity (χt) over the 10 Hz to 4,000 Hz range. With all separations, we measured comparable spectra with predictions from passive membrane simulations that used a three-dimensional structural framework in which intracellular, interstitial, and membrane properties were prescribed based on the limited data available from the literature. At the finest separation, we found mean ρt at 100 Hz and 4,000 Hz that lowered from 395 Ω-cm to 236 Ω-cm, respectively, with maximal mean χt of 160 Ω-cm. This experimental confirmation of spectra development in whole heart experiments is important because such development is central to achieve measurements of intracellular and interstitial passive electrical properties in cardiac electrophysiological experiments using only interstitial access.

Effects of deltamethrin on excitability and contractility of the rainbow trout (Oncorhynchus mykiss) heart

Pyrethroids are extensively used for the control of pest insects and disease vectors. Pyrethroid use is regarded safe due to their selective toxicity: they are effective against insects but relatively harmless to mammals and birds. Unfortunately, pyrethroids are very toxic to fishes. The high toxicity of pyrethroids to fishes is only partly explained by slow elimination rate of toxins, suggesting that high affinity binding to their molecular targets, the Na(+) channels, is involved. This study tests the hypothesis that Na(+) channels of the fish heart are targets to a type II pyrethroid, deltamethrin (DM), and therefore pyrethroids are cardiotoxic to fishes. In ventricular myocytes of the rainbow trout (Oncorhynchus mykiss) heart DM (10(-7)-3·10(-5) M) modified Na(+) current by slowing inactivation and shifting the reversal potential of the current to the left. Maximally 31±2% of the cardiac Na(+) channels were modified by DM and the half-maximal effect occurred at the concentration of 2.1 μM. The effect of DM on trout cardiac Na(+) channels is stronger and occurs about an order of magnitude lower in concentration in comparison to the orthologous mammalian Na(+) channels. In sinoatrial preparations of the trout heart DM (10 μM) caused irregularities in rate, rhythm and force of the heartbeat indicating that DM can be arrhythmogenic for the trout heart. Consistent with this, DM (>0.1 μM) induced spontaneous action potentials in otherwise quiescent ventricular myocytes. DM (10 μM) did not affect calcium current or inward rectifier and delayed rectifier potassium currents. Collectively, these findings indicate that DM exerts cardiotoxic effects in trout, and suggest that the high sensitivity of fishes to pyrethroid toxicity might be partially due to the high affinity of fish Na(+) channels to pyrethroids.

Sensitivity of rabbit ventricular action potential and Ca²⁺ dynamics to small variations in membrane currents and ion diffusion coefficients

Little is known about how small variations in ionic currents and Ca²⁺ and Na⁺ diffusion coefficients impact action potential and Ca²⁺ dynamics in rabbit ventricular myocytes. We applied sensitivity analysis to quantify the sensitivity of Shannon et al. model (Biophys. J., 2004) to 5%-10% changes in currents conductance, channels distribution, and ion diffusion in rabbit ventricular cells. We found that action potential duration and Ca²⁺ peaks are highly sensitive to 10% increase in L-type Ca²⁺ current; moderately influenced by 10% increase in Na⁺-Ca²⁺ exchanger, Na⁺-K⁺ pump, rapid delayed and slow transient outward K⁺ currents, and Cl⁻ background current; insensitive to 10% increases in all other ionic currents and sarcoplasmic reticulum Ca²⁺ fluxes. Cell electrical activity is strongly affected by 5% shift of L-type Ca²⁺ channels and Na⁺-Ca²⁺ exchanger in between junctional and submembrane spaces while Ca²⁺-activated Cl⁻-channel redistribution has the modest effect. Small changes in submembrane and cytosolic diffusion coefficients for Ca²⁺, but not in Na⁺ transfer, may alter notably myocyte contraction. Our studies highlight the need for more precise measurements and further extending and testing of the Shannon et al. model. Our results demonstrate usefulness of sensitivity analysis to identify specific knowledge gaps and controversies related to ventricular cell electrophysiology and Ca²⁺ signaling.

The force-frequency relationship: insights from mathematical modeling

The force-frequency relationship has intrigued researchers since its discovery by Bowditch in 1871. Many attempts have been made to construct mathematical descriptions of this phenomenon, beginning with the simple formulation of Koch-Wesser and Blinks in 1963 to the most sophisticated ones of today. This property of cardiac muscle is amplified by β-adrenergic stimulation, and, in a coordinated way, the neurohumoral state alters both frequency (acting on the sinoatrial node) as well as force generation (modifying ventricular myocytes). This synchronized tuning is needed to meet new metabolic demands. Cardiac modelers have already linked mechanical and electrical activity in their formulations and showed how those activities feedback on each other. However, now it is necessary to include neurological control to have a complete description of heart performance, especially when changes in frequency are involved. Study of arrhythmias (or antiarrhythmic drugs) based on mathematical models should incorporate this effect to make useful predictions or point out potential pharmaceutical targets.

Cardiac dynamics: a simplified model for action potential propagation

This paper analyzes a new semiphysiological ionic model, used recently to study reexitations and reentry in cardiac tissue [I.R. Cantalapiedra et al, PRE 82 011907 (2010)]. The aim of the model is to reproduce action potencial morphologies and restitution curves obtained, either from experimental data, or from more complex electrophysiological models. The model divides all ion currents into four groups according to their function, thus resulting into fast-slow and inward-outward currents. We show that this simplified model is flexible enough as to accurately capture the electrical properties of cardiac myocytes, having the advantage of being less computational demanding than detailed electrophysiological models. Under some conditions, it has been shown to be amenable to mathematical analysis. The model reproduces the action potential (AP) change with stimulation rate observed both experimentally and in realistic models of healthy human and guinea pig myocytes (TNNP and LRd models, respectively). When simulated in a cable it also gives the right dependence of the conduction velocity (CV) with stimulation rate. Besides reproducing correctly these restitution properties, it also gives a good fit for the morphology of the AP, including the notch typical of phase 1. Finally, we perform simulations in a realistic geometric model of the rabbit's ventricles, finding a good qualitative agreement in AP propagation and the ECG. Thus, this simplified model represents an alternative to more complex models when studying instabilities in wave propagation.

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.

The effect of adrenaline on the temperature dependency of cardiac action potentials in pink salmon Oncorhynchus gorbuscha

Using sharp electrode impalement, action potentials recorded from atrial and ventricular tissue of pink salmon Oncorhynchus gorbuscha generally decreased in duration with increasing test temperature (6, 10, 16 and 20° C). Stimulation of the tissue using 500 nM adrenaline had no significant effect on the duration of the atrial action potential at any test temperature but lengthened the ventricular action potential by ~17%.

Mathematical modeling and simulation of ventricular activation sequences: implications for cardiac resynchronization therapy

Next to clinical and experimental research, mathematical modeling plays a crucial role in medicine. Biomedical research takes place on many different levels, from molecules to the whole organism. Due to the complexity of biological systems, the interactions between components are often difficult or impossible to understand without the help of mathematical models. Mathematical models of cardiac electrophysiology have made a tremendous progress since the first numerical ECG simulations in the 1960s. This paper briefly reviews the development of this field and discusses some example cases where models have helped us forward, emphasizing applications that are relevant for the study of heart failure and cardiac resynchronization therapy.

Ranolazine stabilizes cardiac ryanodine receptors: a novel mechanism for the suppression of early afterdepolarization and torsades de pointes in long QT type 2

BACKGROUND

Ranolazine (Ran) is known to inhibit multiple targets, including the late Na(+)current, the rapid delayed rectifying K(+)current, the L-type Ca(2+)current, and fatty acid metabolism. Functionally, Ran suppresses early afterdepolarization (EADs) and torsades de pointes (TdP) in drug-induced long QT type 2 (LQT2) presumably by decreasing intracellular [Na(+)](i) and Ca(2+)overload. However, simulations of EADs in LQT2 failed to predict their suppression by Ran.

OBJECTIVE

To elucidate the mechanism(s) whereby Ran alters cardiac action potentials (APs) and cytosolic Ca(2+)transients and suppresses EADs and TdP in LQT2.

METHODS

The known effects of Ran were included in simulations (Shannon and Mahajan models) of rabbit ventricular APs and Ca(2+)transients in control and LQT2 models and compared with experimental optical mapping data from Langendorff rabbit hearts treated with E4031 (0.5 μM) to block the rapid delayed rectifying K(+)current. Direct effects of Ran on cardiac ryanodine receptors (RyR2) were investigated in single channels and changes in Ca(2+)-dependent high-affinity ryanodine binding.

RESULTS

Ran (10 μM) alone prolonged action potential durations (206 ± 4.6 to 240 ± 7.8 ms; P <0.05); E4031 prolonged action potential durations (204 ± 6 to 546 ± 35 ms; P <0.05) and elicited EADs and TdP that were suppressed by Ran (10 μM; n = 7 of 7 hearts). Simulations (Shannon but not Mahajan model) closely reproduced experimental data except for EAD suppression by Ran. Ran reduced open probability (P(o)) of RyR2 (half maximal inhibitory concentration = 10 ± 3 μM; n = 7) in bilayers and shifted half maximal effective concentration for Ca(2+)-dependent ryanodine binding from 0.42 ± 0.02 to 0.64 ± 0.02 μM with 30 μM Ran.

CONCLUSIONS

Ran reduces P(o) of RyR2, desensitizes Ca(2+)-dependent RyR2 activation, and inhibits Ca(i) oscillations, which represents a novel mechanism for its suppression of EADs and TdP.

Models of HERG gating

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

Systematic characterization of the ionic basis of rabbit cellular electrophysiology using two ventricular models

Several mathematical models of rabbit ventricular action potential (AP) have been proposed to investigate mechanisms of arrhythmias and excitation-contraction coupling. Our study aims at systematically characterizing how ionic current properties modulate the main cellular biomarkers of arrhythmic risk using two widely-used rabbit ventricular models, and comparing simulation results using the two models with experimental data available for rabbit. A sensitivity analysis of AP properties, Ca²⁺ and Na⁺ dynamics, and their rate dependence to variations (±15% and ±30%) in the main transmembrane current conductances and kinetics was performed using the Shannon et al. (2004) and the Mahajan et al. (2008a,b) AP rabbit models. The effects of severe transmembrane current blocks (up to 100%) on steady-state AP and calcium transients, and AP duration (APD) restitution curves were also simulated using both models. Our simulations show that, in both virtual rabbit cardiomyocytes, APD is significantly modified by most repolarization currents, AP triangulation is regulated mostly by the inward rectifier K⁺ current (I(K1)) whereas APD rate adaptation as well as [Na⁺](i) rate dependence is influenced by the Na⁺/K⁺ pump current (I(NaK)). In addition, steady-state [Ca²⁺](i) levels, APD restitution properties and [Ca²⁺](i) rate dependence are strongly dependent on I(NaK), the L-Type Ca²⁺ current (I(CaL)) and the Na⁺/Ca²⁺ exchanger current (I(NaCa)), although the relative role of these currents is markedly model dependent. Furthermore, our results show that simulations using both models agree with many experimentally-reported electrophysiological characteristics. However, our study shows that the Shannon et al. model mimics rabbit electrophysiology more accurately at normal pacing rates, whereas Mahajan et al. model behaves more appropriately at faster rates. Our results reinforce the usefulness of sensitivity analysis for further understanding of cellular electrophysiology and validation of cardiac AP models.

Cardiac myocytes and local signaling in nano-domains

It is well known that calcium-induced calcium-release in cardiac myocytes takes place in spatially restricted regions known as dyads, where discrete patches of junctional sarcoplasmic reticulum tightly associate with the t-tubule membrane. The dimensions of a dyad are so small that it contains only a few Ca²⁺ ions at any given time. Ca²⁺ signaling in the dyad is therefore noisy, and dominated by the Brownian motion of Ca²⁺ ions in a potential field. Remarkably, from this complexity emerges the integrated behavior of the myocyte in which, under normal conditions, precise control of Ca²⁺ release and muscle contraction is maintained over the life of the cell. This is but one example of how signal processing within the cardiac myocyte and other cells often occurs in small "nano-domains" where proteins and protein complexes interact at spatial dimensions on the order of ∼1-10 nm and at time-scales on the order of nanoseconds to perform the functions of the cell. In this article, we will review several examples of local signaling in nano-domains, how it contributes to the integrative behavior of the cardiac myocyte, and present computational methods for modeling signal processing within these domains across differing spatio-temporal scales.

Exploring the parameter space of a rabbit ventricular action potential model to investigate the effect of variation on action potential and calcium transients

Computational models for cardiomyocyte action potentials (AP) often make use of a large parameter set. This parameter set can contain some elements that are fitted to experimental data independently of any other element, some elements that are derived concurrently with other elements to match experimental data, and some elements that are derived purely from phenomenological fitting to produce the desired AP output. Furthermore, models can make use of several different data sets, not always derived for the same conditions or even the same species. It is consequently uncertain whether the parameter set for a given model is physiologically accurate. Furthermore, it is only recently that the possibility of degeneracy in parameter values in producing a given simulation output has started to be addressed. In this study, we examine the effects of varying two parameters (the L-type calcium current (I(CaL)) and the delayed rectifier potassium current (I(Ks))) in a computational model of a rabbit ventricular cardiomyocyte AP on both the membrane potential (V(m)) and calcium (Ca(2+)) transient. It will subsequently be determined if there is degeneracy in this model to these parameter values, which will have important implications on the stability of these models to cell-to-cell parameter variation, and also whether the current methodology for generating parameter values is flawed. The accuracy of AP duration (APD) as an indicator of AP shape will also be assessed.

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

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

Integrative systems models of cardiac excitation-contraction coupling

Excitation-contraction coupling in the cardiac myocyte is mediated by a number of highly integrated mechanisms of intracellular Ca²(+) transport. The complexity and integrative nature of heart cell electrophysiology and Ca²(+) cycling has led to an evolution of computational models that have played a crucial role in shaping our understanding of heart function. An important emerging theme in systems biology is that the detailed nature of local signaling events, such as those that occur in the cardiac dyad, have important consequences at higher biological scales. Multiscale modeling techniques have revealed many mechanistic links between microscale events, such as Ca²(+) binding to a channel protein, and macroscale phenomena, such as excitation-contraction coupling gain. Here, we review experimentally based multiscale computational models of excitation-contraction coupling and the insights that have been gained through their application.

Phorbol ester and endothelin-1 alter functional expression of Na+/Ca2+ exchange, K+, and Ca2+ currents in cultured neonatal rat myocytes

Endothelin-1 (ET-1) and activation of protein kinase C (PKC) have been implicated in alterations of myocyte function in cardiac hypertrophy and heart failure. Changes in cellular Ca2+ handling and electrophysiological properties also occur in these states and may contribute to mechanical dysfunction and arrhythmias. While ET-1 or PKC stimulation induces cellular hypertrophy in cultured neonatal rat ventricular myocytes (NRVMs), a system widely used in studies of hypertrophic signaling, there is little data about electrophysiological changes. Here we studied the effects of ET-1 (100 nM) or the PKC activator phorbol 12-myristate 13-acetate (PMA, 1 μM) on ionic currents in NRVMs. The acute effects of PMA or ET-1 (≤30 min) were small or insignificant. However, PMA or ET-1 exposure for 48-72 h increased cell capacitance by 100 or 25%, respectively, indicating cellular hypertrophy. ET-1 also slightly increased Ca2+ current density (T and L type). Na+/Ca2+ exchange current was increased by chronic pretreatment with either PMA or ET-1. In contrast, transient outward and delayed rectifier K+ currents were strongly downregulated by PMA or ET-1 pretreatment. Inward rectifier K+ current tended toward a decrease at larger negative potential, but time-independent outward K+ current was unaltered by either treatment. The enhanced inward and reduced outward currents also result in action potential prolongation after PMA or ET-1 pretreatment. We conclude that chronic PMA or ET-1 exposure in cultured NRVMs causes altered functional expression of cardiac ion currents, which mimic electrophysiological changes seen in whole animal and human hypertrophy and heart failure.

Integrative modeling of the cardiac ventricular myocyte

Cardiac electrophysiology is a discipline with a rich 50-year history of experimental research coupled with integrative modeling which has enabled us to achieve a quantitative understanding of the relationships between molecular function and the integrated behavior of the cardiac myocyte in health and disease. In this paper, we review the development of integrative computational models of the cardiac myocyte. We begin with a historical overview of key cardiac cell models that helped shape the field. We then narrow our focus to models of the cardiac ventricular myocyte and describe these models in the context of their subcellular functional systems including dynamic models of voltage-gated ion channels, mitochondrial energy production, ATP-dependent and electrogenic membrane transporters, intracellular Ca dynamics, mechanical contraction, and regulatory signal transduction pathways. We describe key advances and limitations of the models as well as point to new directions for future modeling research. WIREs Syst Biol Med 2011 3 392-413 DOI: 10.1002/wsbm.122

Ionic mechanisms for electrical heterogeneity between rabbit Purkinje fiber and ventricular cells

The intrinsic heterogeneity of electrical action potential (AP) properties between Purkinje fibers (PFs) and the ventricular wall, as well as within the wall, plays an important role in ensuring successful excitation of the ventricles. It can also be proarrhythmic due to nonuniform repolarization across the Purkinje-ventricular junction. However, the ionic mechanisms that underlie the marked AP differences between PFs and ventricular cells are not fully characterized. We studied such mechanisms by developing a new family of biophysically detailed AP models for rabbit PF cells and three transmural ventricular cell types. The models were based on and validated against experimental data recorded from rabbit at ionic channel, single cell, and tissue levels. They were then used to determine the functional roles of each individual ionic channel current in modulating the AP heterogeneity at the rabbit Purkinje-ventricular junction, and to identify specific currents responsible for the differential response of PFs and ventricular cells to pharmacological interventions.

Stiffness analysis of cardiac electrophysiological models

The electrophysiology in a cardiac cell can be modeled as a system of ordinary differential equations (ODEs). The efficient solution of these systems is important because they must be solved many times as sub-problems of tissue- or organ-level simulations of cardiac electrophysiology. The wide variety of existing cardiac cell models encompasses many different properties, including the complexity of the model and the degree of stiffness. Accordingly, no single numerical method can be expected to be the most efficient for every model. In this article, we study the stiffness properties of a range of cardiac cell models and discuss the implications for their numerical solution. This analysis allows us to select or design numerical methods that are highly effective for a given model and hence outperform commonly used methods.

Increased myofilament Ca2+-sensitivity and arrhythmia susceptibility

Increased myofilament Ca(2+) sensitivity is a common attribute of many inherited and acquired cardiomyopathies that are associated with cardiac arrhythmias. Accumulating evidence supports the concept that increased myofilament Ca(2+) sensitivity is an independent risk factor for arrhythmias. This review describes and discusses potential underlying molecular and cellular mechanisms how myofilament Ca(2+) sensitivity affects cardiac excitation and leads to the generation of arrhythmias. Emphasized are downstream effects of increased myofilament Ca(2+) sensitivity: altered Ca(2+) buffering/handling, impaired energy metabolism and increased mechanical stretch, and how they may contribute to arrhythmogenesis.

Luminal Ca(2+) content regulates intracellular Ca(2+) release in subepicardial myocytes of intact beating mouse hearts: effect of exogenous buffers

Ca(+)-induced Ca(2+) release tightly controls the function of ventricular cardiac myocytes under normal and pathological conditions. Two major factors contributing to the regulation of Ca(2+) release are the cytosolic free Ca(2+) concentration and sarcoplasmic reticulum (SR) Ca(2+) content. We hypothesized that the amount of Ca(2+) released from the SR during each heart beat strongly defines the refractoriness of Ca(2+) release. To test this hypothesis, EGTA AM, a high-affinity, slow-association rate Ca(2+) chelator, was used as a tool to modify luminal SR Ca(2+) content. An analysis of the cytosolic and luminal SR Ca(2+) dynamics recorded from the epicardial layer of intact mouse hearts indicated that the presence of EGTA reduced the diastolic SR free Ca(2+) concentration and fraction of SR Ca(2+) depletion during each beat. In addition, this maneuver shortened the refractory period and accelerated the restitution of Ca(2+) release. As a consequence of the accelerated restitution, the frequency dependence of Ca(2+) alternans was significantly shifted toward higher heart rates, suggesting a role of luminal SR Ca(2+) in the genesis of this highly arrhythmogenic phenomenon. Thus, intra-SR Ca(2+) dynamics set the refractoriness and frequency dependence of Ca(2+) transients in subepicardial ventricular myocytes.