Computer model of action potential of mouse ventricular myocytes

Preclinical Models of Cardiac Disease: A Comprehensive Overview for Clinical Scientists

For recent decades, cardiac diseases have been the leading cause of death and morbidity worldwide. Despite significant achievements in their management, profound understanding of disease progression is limited. The lack of biologically relevant and robust preclinical disease models that truly grasp the molecular underpinnings of cardiac disease and its pathophysiology attributes to this stagnation, as well as the insufficiency of platforms that effectively explore novel therapeutic avenues. The area of fundamental and translational cardiac research has therefore gained wide interest of scientists in the clinical field, while the landscape has rapidly evolved towards an elaborate array of research modalities, characterized by diverse and distinctive traits. As a consequence, current literature lacks an intelligible and complete overview aimed at clinical scientists that focuses on selecting the optimal platform for translational research questions. In this review, we present an elaborate overview of current in vitro, ex vivo, in vivo and in silico platforms that model cardiac health and disease, delineating their main benefits and drawbacks, innovative prospects, and foremost fields of application in the scope of clinical research incentives.

Efficient termination of cardiac arrhythmias using optogenetic resonant feedback pacing

Malignant cardiac tachyarrhythmias are associated with complex spatiotemporal excitation of the heart. The termination of these life-threatening arrhythmias requires high-energy electrical shocks that have significant side effects, including tissue damage, excruciating pain, and worsening prognosis. This significant medical need has motivated the search for alternative approaches that mitigate the side effects, based on a comprehensive understanding of the nonlinear dynamics of the heart. Cardiac optogenetics enables the manipulation of cellular function using light, enhancing our understanding of nonlinear cardiac function and control. Here, we investigate the efficacy of optically resonant feedback pacing (ORFP) to terminate ventricular tachyarrhythmias using numerical simulations and experiments in transgenic Langendorff-perfused mouse hearts. We show that ORFP outperforms the termination efficacy of the optical single-pulse (OSP) approach. When using ORFP, the total energy required for arrhythmia termination, i.e., the energy summed over all pulses in the sequence, is 1 mJ. With a success rate of 50%, the energy per pulse is 40 times lower than with OSP with a pulse duration of 10 ms. We demonstrate that even at light intensities below the excitation threshold, ORFP enables the termination of arrhythmias by spatiotemporal modulation of excitability inducing spiral wave drift.

Optogenetic confirmation of transverse-tubular membrane excitability in intact cardiac myocytes

T-tubules (TT) form a complex network of sarcolemmal membrane invaginations, essential for well-co-ordinated excitation-contraction coupling (ECC) and thus homogeneous mechanical activation of cardiomyocytes. ECC is initiated by rapid depolarization of the sarcolemmal membrane. Whether TT membrane depolarization is active (local generation of action potentials; AP) or passive (following depolarization of the outer cell surface sarcolemma; SS) has not been experimentally validated in cardiomyocytes. Based on the assessment of ion flux pathways needed for AP generation, we hypothesize that TT are excitable. We therefore explored TT excitability experimentally, using an all-optical approach to stimulate and record trans-membrane potential changes in TT that were structurally disconnected, and hence electrically insulated, from the SS membrane by transient osmotic shock. Our results establish that cardiomyocyte TT can generate AP. These AP show electrical features that differ substantially from those observed in SS, consistent with differences in the density of ion channels and transporters in the two different membrane domains. We propose that TT-generated AP represent a safety mechanism for TT AP propagation and ECC, which may be particularly relevant in pathophysiological settings where morpho-functional changes reduce the electrical connectivity between SS and TT membranes. KEY POINTS: Cardiomyocytes are characterized by a complex network of membrane invaginations (the T-tubular system) that propagate action potentials to the core of the cell, causing uniform excitation-contraction coupling across the cell. In the present study, we investigated whether the T-tubular system is able to generate action potentials autonomously, rather than following depolarization of the outer cell surface sarcolemma. For this purpose, we developed a fully optical platform to probe and manipulate the electrical dynamics of subcellular membrane domains. Our findings demonstrate that T-tubules are intrinsically excitable, revealing distinct characteristics of self-generated T-tubular action potentials. This active electrical capability would protect cells from voltage drops potentially occurring within the T-tubular network.

Dissolution of spiral wave's core using cardiac optogenetics

Rotating spiral waves in the heart are associated with life-threatening cardiac arrhythmias such as ventricular tachycardia and fibrillation. These arrhythmias are treated by a process called defibrillation, which forces electrical resynchronization of the heart tissue by delivering a single global high-voltage shock directly to the heart. This method leads to immediate termination of spiral waves. However, this may not be the only mechanism underlying successful defibrillation, as certain scenarios have also been reported, where the arrhythmia terminated slowly, over a finite period of time. Here, we investigate the slow termination dynamics of an arrhythmia in optogenetically modified murine cardiac tissue both in silico and ex vivo during global illumination at low light intensities. Optical imaging of an intact mouse heart during a ventricular arrhythmia shows slow termination of the arrhythmia, which is due to action potential prolongation observed during the last rotation of the wave. Our numerical studies show that when the core of a spiral is illuminated, it begins to expand, pushing the spiral arm towards the inexcitable boundary of the domain, leading to termination of the spiral wave. We believe that these fundamental findings lead to a better understanding of arrhythmia dynamics during slow termination, which in turn has implications for the improvement and development of new cardiac defibrillation techniques.

In silico optical modulation of spiral wave trajectories in cardiac tissue

Life-threatening cardiac arrhythmias such as ventricular tachycardia and fibrillation are common precursors to sudden cardiac death. They are associated with the occurrence of abnormal electrical spiral waves in the heart that rotate at a high frequency. In severe cases, arrhythmias are combated with a clinical method called defibrillation, which involves administering a single global high-voltage shock to the heart to reset all its activity and restore sinus rhythm. Despite its high efficiency in controlling arrhythmias, defibrillation is associated with several negative side effects that render the method suboptimal. The best approach to optimize this therapeutic technique is to deepen our understanding of the dynamics of spiral waves. Here, we use computational cardiac optogenetics to study and control the dynamics of a single spiral wave in a two-dimensional, electrophysiologically detailed, light-sensitive model of a mouse ventricle. First, we illuminate the domain globally by applying a sequence of periodic optical pulses with different frequencies in the sub-threshold regime where no excitation wave is induced. In doing so, we obtain epicycloidal, hypocycloidal, and resonant drift trajectories of the spiral wave core. Then, to effectively control the wave dynamics, we use a method called resonant feedback pacing. In this approach, each global optical pulse is applied when the measuring electrode positioned on the domain registers a predefined value of the membrane voltage. This enables us to steer the spiral wave in a desired direction determined by the position of the electrode. Our study thus provides valuable mechanistic insights into the success or failure of global optical stimulation in executing efficient arrhythmia control.

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

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

Sodium channel subpopulations with distinct biophysical properties and subcellular localization enhance cardiac conduction

Sodium (Na+) current is responsible for the rapid depolarization of cardiac myocytes that triggers the cardiac action potential upstroke. Recent studies have illustrated the presence of multiple pools of Na+ channels with distinct biophysical properties and subcellular localization, including clustering of channels at the intercalated disk and along the lateral membrane. Computational studies predict that Na+ channel clusters at the intercalated disk can regulate cardiac conduction via modulation of the narrow intercellular cleft between electrically coupled myocytes. However, these studies have primarily focused on the redistribution of Na+ channels between intercalated disk and lateral membranes and have not considered the distinct biophysical properties of the Na+ channel subpopulations. In this study, we use computational modeling to simulate computational models of single cardiac cells and one-dimensional cardiac tissues and predict the function of distinct Na+ channel subpopulations. Single-cell simulations predict that a subpopulation of Na+ channels with shifted steady-state activation and inactivation voltage dependency promotes an earlier action potential upstroke. In cardiac tissues that account for distinct subcellular spatial localization, simulations predict that shifted Na+ channels contribute to faster and more robust conduction in response to changes in tissue structure (i.e., cleft width), gap junctional coupling, and rapid pacing rates. Simulations predict that the intercalated disk-localized shifted Na+ channels contribute proportionally more to total Na+ charge than lateral membrane-localized Na+ channels. Importantly, our work supports the hypothesis that Na+ channel redistribution may be a critical mechanism by which cells can respond to perturbations to support fast and robust conduction.

A compartmentalized mathematical model of the β1- and β2-adrenergic signaling systems in ventricular myocytes from mouse in heart failure

Mouse models of heart failure are extensively used to research human cardiovascular diseases. In particular, one of the most common is the mouse model of heart failure resulting from transverse aortic constriction (TAC). Despite this, there are no comprehensive compartmentalized mathematical models that describe the complex behavior of the action potential, [Ca²⁺]_i transients, and their regulation by β₁- and β₂-adrenergic signaling systems in failing mouse myocytes. In this paper, we develop a novel compartmentalized mathematical model of failing mouse ventricular myocytes after TAC procedure. The model describes well the cell geometry, action potentials, [Ca²⁺]_i transients, and β₁- and β₂-adrenergic signaling in the failing cells. Simulation results obtained with the failing cell model are compared with those from the normal ventricular myocytes. Exploration of the model reveals the sarcoplasmic reticulum Ca²⁺ load mechanisms in failing ventricular myocytes. We also show a larger susceptibility of the failing myocytes to early and delayed afterdepolarizations and to a proarrhythmic behavior of Ca²⁺ dynamics upon stimulation with isoproterenol. The mechanisms of the proarrhythmic behavior suppression are investigated and sensitivity analysis is performed. The developed model can explain the existing experimental data on failing mouse ventricular myocytes and make experimentally testable predictions of a failing myocyte's behavior.

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

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

Estimation of the firing behaviour of a complete motoneuron pool by combining electromyography signal decomposition and realistic motoneuron modelling

Our understanding of the firing behaviour of motoneuron (MN) pools during human voluntary muscle contractions is currently limited to electrophysiological findings from animal experiments extrapolated to humans, mathematical models of MN pools not validated for human data, and experimental results obtained from decomposition of electromyographical (EMG) signals. These approaches are limited in accuracy or provide information on only small partitions of the MN population. Here, we propose a method based on the combination of high-density EMG (HDEMG) data and realistic modelling for predicting the behaviour of entire pools of motoneurons in humans. The method builds on a physiologically realistic model of a MN pool which predicts, from the experimental spike trains of a smaller number of individual MNs identified from decomposed HDEMG signals, the unknown recruitment and firing activity of the remaining unidentified MNs in the complete MN pool. The MN pool model is described as a cohort of single-compartment leaky fire-and-integrate (LIF) models of MNs scaled by a physiologically realistic distribution of MN electrophysiological properties and driven by a spinal synaptic input, both derived from decomposed HDEMG data. The MN spike trains and effective neural drive to muscle, predicted with this method, have been successfully validated experimentally. A representative application of the method in MN-driven neuromuscular modelling is also presented. The proposed approach provides a validated tool for neuroscientists, experimentalists, and modelers to infer the firing activity of MNs that cannot be observed experimentally, investigate the neuromechanics of human MN pools, support future experimental investigations, and advance neuromuscular modelling for investigating the neural strategies controlling human voluntary contractions.

Our experimental understanding of the firing behaviour of motoneuron (MN) pools during human voluntary muscle contractions is currently limited to the observation of small samples of active MNs obtained from EMG decomposition. EMG decomposition therefore provides an important but incomplete description of the role of individual MNs in the firing activity of the complete MN pool, which limits our understanding of the neural strategies of the whole MN pool and of how the firing activity of each MN contributes to the neural drive to muscle. Here, we combine decomposed high-density EMG (HDEMG) data and a physiologically realistic model of MN population to predict the unknown recruitment and firing activity of the remaining unidentified MNs in the complete MN pool. In brief, an experimental estimation of the synaptic current is input to a cohort of MN models, which are calibrated using the available decomposed HDEMG data, and predict the MN spike trains fired by the entire MN population. This novel approach is experimentally validated and applied to muscle force prediction from neuromuscular modelling.

Critical Requirements for the Initiation of a Cardiac Arrhythmia in Rat Ventricle: How Many Myocytes?

Cardiovascular disease is the leading cause of death worldwide due in a large part to arrhythmia. In order to understand how calcium dynamics play a role in arrhythmogenesis, normal and dysfunctional Ca²⁺ signaling in a subcellular, cellular, and tissued level is examined using cardiac ventricular myocytes at a high temporal and spatial resolution using multiscale computational modeling. Ca²⁺ sparks underlie normal excitation-contraction coupling. However, under pathological conditions, Ca²⁺ sparks can combine to form Ca²⁺ waves. These propagating elevations of (Ca²⁺)_i can activate an inward Na⁺-Ca²⁺ exchanger current (I_NCX) that contributes to early after-depolarization (EADs) and delayed after-depolarizations (DADs). However, how cellular currents lead to full depolarization of the myocardium and how they initiate extra systoles is still not fully understood. This study explores how many myocytes must be entrained to initiate arrhythmogenic depolarizations in biophysically detailed computational models. The model presented here suggests that only a small number of myocytes must activate in order to trigger an arrhythmogenic propagating action potential. These conditions were examined in 1-D, 2-D, and 3-D considering heart geometry. The depolarization of only a few hundred ventricular myocytes is required to trigger an ectopic depolarization. The number decreases under disease conditions such as heart failure. Furthermore, in geometrically restricted parts of the heart such as the thin muscle strands found in the trabeculae and papillary muscle, the number of cells needed to trigger a propagating depolarization falls even further to less than ten myocytes.

Integrative Computational Modeling of Cardiomyocyte Calcium Handling and Cardiac Arrhythmias: Current Status and Future Challenges

Cardiomyocyte calcium-handling is the key mediator of cardiac excitation-contraction coupling. In the healthy heart, calcium controls both electrical impulse propagation and myofilament cross-bridge cycling, providing synchronous and adequate contraction of cardiac muscles. However, calcium-handling abnormalities are increasingly implicated as a cause of cardiac arrhythmias. Due to the complex, dynamic and localized interactions between calcium and other molecules within a cardiomyocyte, it remains experimentally challenging to study the exact contributions of calcium-handling abnormalities to arrhythmogenesis. Therefore, multiscale computational modeling is increasingly being used together with laboratory experiments to unravel the exact mechanisms of calcium-mediated arrhythmogenesis. This article describes various examples of how integrative computational modeling makes it possible to unravel the arrhythmogenic consequences of alterations to cardiac calcium handling at subcellular, cellular and tissue levels, and discusses the future challenges on the integration and interpretation of such computational data.

Bifurcations and Proarrhythmic Behaviors in Cardiac Electrical Excitations

The heart is a hierarchical dynamic system consisting of molecules, cells, and tissues, and acts as a pump for blood circulation. The pumping function depends critically on the preceding electrical activity, and disturbances in the pattern of excitation propagation lead to cardiac arrhythmia and pump failure. Excitation phenomena in cardiomyocytes have been modeled as a nonlinear dynamical system. Because of the nonlinearity of excitation phenomena, the system dynamics could be complex, and various analyses have been performed to understand the complex dynamics. Understanding the mechanisms underlying proarrhythmic responses in the heart is crucial for developing new ways to prevent and control cardiac arrhythmias and resulting contractile dysfunction. When the heart changes to a pathological state over time, the action potential (AP) in cardiomyocytes may also change to a different state in shape and duration, often undergoing a qualitative change in behavior. Such a dynamic change is called bifurcation. In this review, we first summarize the contribution of ion channels and transporters to AP formation and our knowledge of ion-transport molecules, then briefly describe bifurcation theory for nonlinear dynamical systems, and finally detail its recent progress, focusing on the research that attempts to understand the developing mechanisms of abnormal excitations in cardiomyocytes from the perspective of bifurcation phenomena.

Exploring the Coordination of Cardiac Ion Channels With Action Potential Clamp Technique

The patch clamp technique underwent continual advancement and developed numerous variants in cardiac electrophysiology since its introduction in the late 1970s. In the beginning, the capability of the technique was limited to recording one single current from one cell stimulated with a rectangular command pulse. Since that time, the technique has been extended to record multiple currents under various command pulses including action potential. The current review summarizes the development of the patch clamp technique in cardiac electrophysiology with special focus on the potential applications in integrative physiology.

A Mathematical Model for Electrical Activity in Pig Atrial Tissue

State of the art mathematical models are currently used to bridge the gap between basic research conducted in the laboratory and preclinical research conducted on large animals, which ultimately paves the way for clinical translation. In this regard, there is a great need for models that can be used alongside experiments for in-depth investigation and validation. One such experimental model is the porcine atrium, which is commonly used to study the mechanisms of onset and control of atrial fibrillation in the context of its surgical management. However, a mathematical model of pig atria is lacking. In this paper, we present the first ionically detailed mathematical model of porcine atrial electrophysiology, at body temperature. The model includes 12 ionic currents, 4 of which were designed based on experimental patch-clamp data directly obtained from literature. The formulations for the other currents are adopted from the human atrial model, and modified for porcine specificity based on our measured restitution data for different action potential characteristics: resting membrane potential, action potential amplitude, maximum upstroke velocity and action potential duration and different levels of membrane voltage repolarization. The intracellular Ca²⁺ dynamics follows the Luo-Rudy formulation for guinea pig ventricular cardiomyocytes. The resulting model represents “normal” cells which are formulated as a system of ordinary differential equations. We extend our model to two dimensions to obtain plane wave propagation in tissue with a velocity of 0.58 m/s and a wavelength of 8 cm. The wavelength reduces to 5 cm when the tissue is paced at 200 ms. Using S1-S2 cross-field protocol, we demonstrate in an 11.26 cm square simulation domain, the ability to initiate single spiral waves (rotation period ≃ 180 ms) that remain stable for more than 40 s. The spiral tip exhibits hypermeander. In agreement with previous experimental results using pig atria, our model shows that early repolarization is primarily driven by a calcium-mediated chloride current, I_ClCa, which is completely inactivated at high pacing frequencies. This is a condition that occurs only in porcine atria. Furthermore, the model shows spatiotemporal chaos with reduced repolarization.

Simulation Modeling of Reduced Glycosylation Effects on Potassium Channels of Mouse Cardiomyocytes

Dilated cardiomyopathy (DCM) is the third most common cause of heart failure and the primary reason for heart transplantation; upward of 70% of DCM cases are considered idiopathic. Our in-vitro experiments showed that reduced hybrid/complex N-glycosylation in mouse cardiomyocytes is linked with DCM. Further, we observed direct effects of reduced N-glycosylation on Kv gating. However, it is difficult to rigorously determine the effects of glycosylation on Kv activity, because there are multiple Kv isoforms in cardiomyocytes contributing to the cardiac excitation. Due to complex functions of Kv isoforms, only the sum of K+ currents (IKsum) can be recorded experimentally and decomposed later using exponential fitting to estimate component currents, such as IKto, IKslow, and IKss. However, such estimation cannot adequately describe glycosylation effects and Kv mechanisms. Here, we propose a framework of simulation modeling of Kv kinetics in mouse ventricular myocytes and model calibration using the in-vitro data under normal and reduced glycosylation conditions through ablation of the Mgat1 gene (i.e., Mgat1KO). Calibrated models facilitate the prediction of Kv characteristics at different voltages that are not directly observed in the in-vitro experiments. A model calibration procedure is developed based on the genetic algorithm. Experimental results show that, in the Mgat1KO group, both IKto and IKslow densities are shown to be significantly reduced and the rate of IKslow inactivation is much slower. The proposed approach has strong potential to couple simulation models with experimental data for gaining a better understanding of glycosylation effects on Kv kinetics.

In silico Cell Therapy Model Restores Failing Human Myocyte Electrophysiology and Calcium Cycling in Fibrotic Myocardium

Myocardial delivery of human c-kit+ cardiac interstitial cells (hCICs) and human mesenchymal stem cells (hMSCs), an emerging approach for treating the failing heart, has been limited by an incomplete understanding of the effects on host myocardium. This computational study aims to model hCIC and hMSC effects on electrophysiology and calcium cycling of healthy and diseased human cardiomyocytes (hCM), and reveals a possible cardiotherapeutic benefit independent of putative regeneration processes. First, we developed an original hCIC mathematical model with an electrical profile comprised of distinct experimentally identified ion currents. Next, we verified the model by confirming it is representative of published experiments on hCIC whole-cell electrophysiology and on hCIC co-cultures with rodent cardiomyocytes. We then used our model to compare electrophysiological effects of hCICs to other non-excitable cells, as well as clinically relevant hCIC-hMSC combination therapies and fused hCIC-hMSC CardioChimeras. Simulation of direct coupling of hCICs to healthy or failing hCMs through gap junctions led to greater increases in calcium cycling with lesser reductions in action potential duration (APD) compared with hMSCs. Combined coupling of hCICs and hMSCs to healthy or diseased hCMs led to intermediate effects on electrophysiology and calcium cycling compared to individually coupled hCICs or hMSCs. Fused hCIC-hMSC CardioChimeras decreased healthy and diseased hCM APD and calcium transient amplitude compared to individual or combined cell treatments. Finally, to provide a theoretical basis for optimizing cell-based therapies, we randomized populations of 2,500 models incorporating variable hMSC and hCIC interventions and simulated their effects on restoring diseased cardiomyocyte electrophysiology and calcium handling. The permutation simulation predicted the ability to correct abnormal properties of heart failure hCMs in fibrotic, but not non-fibrotic, myocardium. This permutation experiment also predicted paracrine signaling to be a necessary and sufficient mechanism for this correction, counteracting the fibrotic effects while also restoring arrhythmia-related metrics such as upstroke velocity and resting membrane potential. Altogether, our in silico findings suggest anti-fibrotic effects of paracrine signaling are critical to abrogating pathological cardiomyocyte electrophysiology and calcium cycling in fibrotic heart failure, and support further investigation of delivering an optimized cellular secretome as a potential strategy for improving heart failure therapy.

Optogenetic manipulation of cardiac electrical dynamics using sub-threshold illumination: dissecting the role of cardiac alternans in terminating rapid rhythms

Cardiac action potential (AP) shape and propagation are regulated by several key dynamic factors such as ion channel recovery and intracellular Ca²⁺ cycling. Experimental methods for manipulating AP electrical dynamics commonly use ion channel inhibitors that lack spatial and temporal specificity. In this work, we propose an approach based on optogenetics to manipulate cardiac electrical activity employing a light-modulated depolarizing current with intensities that are too low to elicit APs (sub-threshold illumination), but are sufficient to fine-tune AP electrical dynamics. We investigated the effects of sub-threshold illumination in isolated cardiomyocytes and whole hearts by using transgenic mice constitutively expressing a light-gated ion channel (channelrhodopsin-2, ChR2). We find that ChR2-mediated depolarizing current prolongs APs and reduces conduction velocity (CV) in a space-selective and reversible manner. Sub-threshold manipulation also affects the dynamics of cardiac electrical activity, increasing the magnitude of cardiac alternans. We used an optical system that uses real-time feedback control to generate re-entrant circuits with user-defined cycle lengths to explore the role of cardiac alternans in spontaneous termination of ventricular tachycardias (VTs). We demonstrate that VT stability significantly decreases during sub-threshold illumination primarily due to an increase in the amplitude of electrical oscillations, which implies that cardiac alternans may be beneficial in the context of self-termination of VT.

Cardiac Alternans Occurs through the Synergy of Voltage- and Calcium-Dependent Mechanisms

Cardiac alternans is characterized by alternating weak and strong beats of the heart. This signaling at the cellular level may appear as alternating long and short action potentials (APs) that occur in synchrony with alternating large and small calcium transients, respectively. Previous studies have suggested that alternans manifests itself through either a voltage dependent mechanism based upon action potential restitution or as a calcium dependent mechanism based on refractoriness of calcium release. We use a novel model of cardiac excitation-contraction (EC) coupling in the rat ventricular myocyte that includes 20,000 calcium release units (CRU) each with 49 ryanodine receptors (RyR2s) and 7 L-type calcium channels that are all stochastically gated. The model suggests that at the cellular level in the case of alternans produced by rapid pacing, the mechanism requires a synergy of voltage- and calcium-dependent mechanisms. The rapid pacing reduces AP duration and magnitude reducing the number of L-type calcium channels activating individual CRUs during each AP and thus increases the population of CRUs that can be recruited stochastically. Elevated myoplasmic and sarcoplasmic reticulum (SR) calcium, [Ca2+]myo and [Ca2+]SR respectively, increases ryanodine receptor open probability (Po) according to our model used in this simulation and this increased the probability of activating additional CRUs. A CRU that opens in one beat is less likely to open the subsequent beat due to refractoriness caused by incomplete refilling of the junctional sarcoplasmic reticulum (jSR). Furthermore, the model includes estimates of changes in Na+ fluxes and [Na+]i and thus provides insight into how changes in electrical activity, [Na+]i and sodium-calcium exchanger activity can modulate alternans. The model thus tracks critical elements that can account for rate-dependent changes in [Na+]i and [Ca2+]myo and how they contribute to the generation of Ca2+ signaling alternans in the heart.

Acute Genetic Ablation of Cardiac Sodium/Calcium Exchange in Adult Mice: Implications for Cardiomyocyte Calcium Regulation, Cardioprotection, and Arrhythmia

Background

Sodium‐calcium (Ca²⁺) exchanger isoform 1 (NCX1) is the dominant Ca²⁺ efflux mechanism in cardiomyocytes and is critical to maintaining Ca²⁺ homeostasis during excitation‐contraction coupling. NCX1 activity has been implicated in the pathogenesis of cardiovascular diseases, but a lack of specific NCX1 blockers complicates experimental interpretation. Our aim was to develop a tamoxifen‐inducible NCX1 knockout (KO) mouse to investigate compensatory adaptations of acute ablation of NCX1 on excitation‐contraction coupling and intracellular Ca²⁺ regulation, and to examine whether acute KO of NCX1 confers resistance to triggered arrhythmia and ischemia/reperfusion injury.

Methods and Results

We used the α‐myosin heavy chain promoter (Myh6)‐MerCreMer promoter to create a tamoxifen‐inducible cardiac‐specific NCX1 KO mouse. Within 1 week of tamoxifen injection, NCX1 protein expression and current were dramatically reduced. Diastolic Ca²⁺ increased despite adaptive reductions in Ca²⁺ current and action potential duration and compensatory increases in excitation‐contraction coupling gain, sarcoplasmic reticulum Ca²⁺ ATPase 2 and plasma membrane Ca2+ ATPase. As these adaptations progressed over 4 weeks, diastolic Ca²⁺ normalized and SR Ca²⁺ load increased. Left ventricular function remained normal, but mild fibrosis and hypertrophy developed. Transcriptomics revealed modification of cardiovascular‐related gene networks including cell growth and fibrosis. NCX1 KO reduced spontaneous action potentials triggered by delayed afterdepolarizations and reduced scar size in response to ischemia/reperfusion.

Conclusions

Tamoxifen‐inducible NCX1 KO mice adapt to acute genetic ablation of NCX1 by reducing Ca²⁺ influx, increasing alternative Ca²⁺ efflux pathways, and increasing excitation‐contraction coupling gain to maintain contractility at the cost of mild Ca²⁺‐activated hypertrophy and fibrosis and decreased survival. Nevertheless, KO myocytes are protected against spontaneous action potentials and ischemia/reperfusion injury.

Constructing Adult Zebrafish Einthoven's Triangle to Define Electrical Heart Axes

Zebrafish is a popular high-throughput vertebrate model to study human cardiac electrophysiology, arrhythmias, and myopathies. One reason for this popularity is the purported striking similarities between zebrafish and human electrocardiograms (ECGs). However, zebrafish electrical heart axes were unknown. It is impossible to define heart axis based on single-lead ECG because determination of an electrical heart axis in the frontal plane requires the use of the hexaxial reference system (or Cabrera system) derived from Einthoven’s triangle. Construction of Einthoven’s triangle requires simultaneous ECG recording from at least two Einthoven bipolar leads. Therefore, we systematically constructed the first zebrafish Einthoven’s triangle by simultaneous bipolar dual-lead ECG recording to determine for the first time the three frontal electrical heart axes using the Cabrera system. Comparing zebrafish with human Einthoven’s triangle reveals that their normal frontal electrical axes were reflections of each other across 0° in the Cabrera system. The responsible mechanisms involve zebrafish vs. human cardiac activation propagating in the same direction along the heart horizontal axis but in opposite directions along the heart longitudinal axis. The same observations are true for zebrafish vs. human cardiac repolarization. This study marks a technical breakthrough in the first bipolar dual-lead ECG recording in live adult zebrafish to construct for the first time zebrafish Einthoven’s triangle. This first systematic analysis of the actual differences and similarities between normal adult zebrafish and human Einthoven’s triangles unmasked differences and similarities in the underlying cardiac axis mechanisms. Insights of the live adult zebrafish main heart axis and its three frontal electrical heart axes provide critical contextual framework to interpret the clinical relevance of the adult zebrafish heart as model for human cardiac electrophysiology.

Bootstrapping and Pinning down the Root Meristem; the Auxin-PLT-ARR Network Unites Robustness and Sensitivity in Meristem Growth Control

After germination, the meristem of the embryonic plant root becomes activated, expands in size and subsequently stabilizes to support post-embryonic root growth. The plant hormones auxin and cytokinin, together with master transcription factors of the PLETHORA (PLT) family have been shown to form a regulatory network that governs the patterning of this root meristem. Still, which functional constraints contributed to shaping the dynamics and architecture of this network, has largely remained unanswered. Using a combination of modeling approaches we reveal how the interplay between auxin and PLTs enables meristem activation in response to above-threshold stimulation, while its embedding in a PIN-mediated auxin reflux loop ensures localized PLT transcription and thereby, a finite meristem size. We furthermore demonstrate how this constrained PLT transcriptional domain enables independent control of meristem size and division rates, further supporting a division of labor between auxin and PLT. We subsequently reveal how the weaker auxin antagonism of the earlier active Arabidopsis response regulator 12 (ARR12) may arise from the absence of a DELLA protein interaction domain. Our model indicates that this reduced strength is essential to prevent collapse in the early stages of meristem expansion while at later stages the enhanced strength of Arabidopsis response regulator 1 (ARR1) is required for sufficient meristem size control. Summarizing, our work indicates that functional constraints significantly contribute to shaping the auxin-cytokinin-PLT regulatory network.

Giant ankyrin-G regulates cardiac function

Cardiovascular disease (CVD) remains the most common cause of adult morbidity and mortality in developed nations. As a result, predisposition for CVD is increasingly important to understand. Ankyrins are intracellular proteins required for the maintenance of membrane domains. Canonical ankyrin-G (AnkG) has been shown to be vital for normal cardiac function, specifically cardiac excitability, via targeting and regulation of the cardiac voltage-gated sodium channel. Noncanonical (giant) AnkG isoforms play a key role in neuronal membrane biogenesis and excitability, with evidence for human neurologic disease when aberrant. However, the role of giant AnkG in cardiovascular tissue has yet to be explored. Here, we identify giant AnkG in the myocardium and identify that it is enriched in 1-week-old mice. Using a new mouse model lacking giant AnkG expression in myocytes, we identify that young mice displayed a dilated cardiomyopathy phenotype with aberrant electrical conduction and enhanced arrhythmogenicity. Structural and electrical dysfunction occurred at 1 week of age, when giant AnkG was highly expressed and did not appreciably change in adulthood until advanced age. At a cellular level, loss of giant AnkG results in delayed and early afterdepolarizations. However, surprisingly, giant AnkG cKO myocytes display normal I_Na, but abnormal myocyte contractility, suggesting unique roles of the large isoform in the heart. Finally, transcript analysis provided evidence for unique pathways that may contribute to the structural and electrical findings shown in giant AnkG cKO animals. In summary, we identify a critical role for giant AnkG that adds to the diversity of ankyrin function in the heart.

Transient receptor potential vanilloid 4 channel participates in mouse ventricular electrical activity

The TRPV4 channel is a calcium-permeable channel (PCa/PNa ∼ 10). Its expression has been reported in ventricular myocytes, where it is involved in several cardiac pathological mechanisms. In this study, we investigated the implication of TRPV4 in ventricular electrical activity. Left ventricular myocytes were isolated from trpv4+/+ and trpv4-/- mice. TRPV4 membrane expression and its colocalization with L-type calcium channels (Cav1.2) was confirmed using Western blot biotinylation, immunoprecipitation, and immunostaining experiments. Then, electrocardiograms (ECGs) and patch-clamp recordings showed shortened QTc and action potential (AP) duration in trpv4-/- compared with trpv4+/+ mice. Thus, TRPV4 activator GSK1016790A produced a transient and dose-dependent increase in AP duration at 90% of repolarization (APD90) in trpv4+/+ but not in trpv4-/- myocytes or when combined with TRPV4 inhibitor GSK2193874 (100 nM). Hence, GSK1016790A increased calcium transient (CaT) amplitude in trpv4+/+ but not in trpv4-/- myocytes, suggesting that TRPV4 carries an inward Ca2+ current in myocytes. Conversely, TRPV4 inhibitor GSK2193874 (100 nM) alone reduced APD90 in trpv4+/+ but not in trpv4-/- myocytes, suggesting that TRPV4 prolongs AP duration in basal condition. Finally, introducing TRPV4 parameters in a mathematical model predicted the development of an inward TRPV4 current during repolarization that increases AP duration and CaT amplitude, in accord with what was found experimentally. This study shows for the first time that TRPV4 modulates AP and QTc durations. It would be interesting to evaluate whether TRPV4 could be involved in long QT-mediated ventricular arrhythmias.NEW & NOTEWORTHY Transient receptor potential vanilloid 4 (TRPV4) is expressed at the membrane of mouse ventricular myocytes and colocalizes with non-T-tubular L-type calcium channels. Deletion of trpv4 gene in mice results in shortened QT interval on electrocardiogram and reduced action potential duration of ventricular myocytes. Pharmacological activation of TRPV4 channel leads to increased action potential duration and increased calcium transient amplitude in trpv4-/- but not in trpv4-/- ventricular myocytes. To the contrary, TRPV4 channel pharmacological inhibition reduces action potential duration in trpv4+/+ but not in trpv4-/- myocytes. Integration of TRPV4 channel in a computational model of mouse action potential shows that the channel carries an inward current contributing to slowing down action potential repolarization and to increase calcium transient amplitude, similarly to what is observed experimentally. This study highlights for the first time the involvement of TRPV4 channel in ventricular electrical activity.

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.

Altered calcium handling in cardiomyocytes from arginine-glycine amidinotransferase-knockout mice is rescued by creatine

The creatine kinase system facilitates energy transfer between mitochondria and the major ATPases in the heart. Creatine-deficient mice, which lack arginine-glycine amidinotransferase (AGAT) to synthesize creatine and homoarginine, exhibit reduced cardiac contractility. We studied how the absence of a functional CK system influences calcium handling in isolated cardiomyocytes from AGAT-knockouts and wild-type littermates as well as in AGAT-knockout mice receiving lifelong creatine supplementation via the food. Using a combination of whole cell patch clamp and fluorescence microscopy, we demonstrate that the L-type calcium channel (LTCC) current amplitude and voltage range of activation were significantly lower in AGAT-knockout compared with wild-type littermates. Additionally, the inactivation of LTCC and the calcium transient decay were significantly slower. According to our modeling results, these changes can be reproduced by reducing three parameters in knockout mice when compared with wild-type: LTCC conductance, the exchange constant of Ca2+ transfer between subspace and cytosol, and SERCA activity. Because tissue expression of LTCC and SERCA protein were not significantly different between genotypes, this suggests the involvement of posttranslational regulatory mechanisms or structural reorganization. The AGAT-knockout phenotype of calcium handling was fully reversed by dietary creatine supplementation throughout life. Our results indicate reduced calcium cycling in cardiomyocytes from AGAT-knockouts and suggest that the creatine kinase system is important for the development of calcium handling in the heart.NEW & NOTEWORTHY Creatine-deficient mice lacking arginine-glycine amidinotransferase exhibit compromised cardiac function. Here, we show that this is at least partially due to an overall slowing of calcium dynamics. Calcium influx into the cytosol via the L-type calcium current (LTCC) is diminished, and the rate of the sarcoendoplasmic reticulum calcium ATPase (SERCA) pumping calcium back into the sarcoplasmic reticulum is slower. The expression of LTCC and SERCA did not change, suggesting that the changes are regulatory.

Drift and termination of spiral waves in optogenetically modified cardiac tissue at sub-threshold illumination

The development of new approaches to control cardiac arrhythmias requires a deep understanding of spiral wave dynamics. Optogenetics offers new possibilities for this. Preliminary experiments show that sub-threshold illumination affects electrical wave propagation in the mouse heart. However, a systematic exploration of these effects is technically challenging. Here, we use state-of-the-art computer models to study the dynamic control of spiral waves in a two-dimensional model of the adult mouse ventricle, using stationary and non-stationary patterns of sub-threshold illumination. Our results indicate a light-intensity-dependent increase in cellular resting membrane potentials, which together with diffusive cell-cell coupling leads to the development of spatial voltage gradients over differently illuminated areas. A spiral wave drifts along the positive gradient. These gradients can be strategically applied to ensure drift-induced termination of a spiral wave, both in optogenetics and in conventional methods of electrical defibrillation.

The ForceLAB simulator: Application to the comparison of current models of cardiomyocyte contraction

Mathematical models are useful tools in the study of physiological phenomena. However, due to differences in assumptions and formulations, discrepancy in simulations may occur. Among the models for cardiomyocyte contraction based on Huxley's cross-bridge cycling, those proposed by Negroni and Lascano (NL) and Rice et al. (RWH) are the most frequently used. This study was aimed at developing a computational tool, ForceLAB, which allows implementing different contraction models and modifying several functional parameters. As an application, electrically-stimulated twitches triggered by an equal Ca²⁺ input and steady-state force x pCa relationship (pCa = -log of the molar free Ca²⁺ concentration) simulated with the NL and RWH models were compared. The equilibrium Ca²⁺-troponin C (TnC) dissociation constant (K_d) was modified by changing either the association (k_on) or the dissociation (k_off) rate constant. With the NL model, raising K_d by either maneuver decreased monotonically twitch amplitude and duration, as expected. With the RWH model, in contrast, the same K_d variation caused increase or decrease of peak force depending on which rate constant was modified. Additionally, force x pCa curves simulated using Ca²⁺ binding constants estimated in cardiomyocytes bearing wild-type and mutated TnC were compared to curves previously determined in permeabilized fibers. Mutations increased k_on and k_off, and decreased K_d. Both models produced curves fairly comparable to the experimental ones, although sensitivity to Ca²⁺ was greater, especially with RWH model. The NL model reproduced slightly better the qualitative changes associated with the mutations. It is expected that this tool can be useful for teaching and investigation.

Ca2+-CaM Dependent Inactivation of RyR2 Underlies Ca2+ Alternans in Intact Heart

RATIONALE

Ca²⁺ alternans plays an essential role in cardiac alternans that can lead to ventricular fibrillation, but the mechanism underlying Ca²⁺ alternans remains undefined. Increasing evidence suggests that Ca²⁺ alternans results from alternations in the inactivation of cardiac RyR2 (ryanodine receptor 2). However, what inactivates RyR2 and how RyR2 inactivation leads to Ca²⁺ alternans are unknown.

OBJECTIVE

To determine the role of CaM (calmodulin) on Ca²⁺ alternans in intact working mouse hearts.

METHODS AND RESULTS

We used an in vivo local gene delivery approach to alter CaM function by directly injecting adenoviruses expressing CaM-wild type, a loss-of-function CaM mutation, CaM (1-4), and a gain-of-function mutation, CaM-M37Q, into the anterior wall of the left ventricle of RyR2 wild type or mutant mouse hearts. We monitored Ca²⁺ transients in ventricular myocytes near the adenovirus-injection sites in Langendorff-perfused intact working hearts using confocal Ca²⁺ imaging. We found that CaM-wild type and CaM-M37Q promoted Ca²⁺ alternans and prolonged Ca²⁺ transient recovery in intact RyR2 wild type and mutant hearts, whereas CaM (1-4) exerted opposite effects. Altered CaM function also affected the recovery from inactivation of the L-type Ca²⁺ current but had no significant impact on sarcoplasmic reticulum Ca²⁺ content. Furthermore, we developed a novel numerical myocyte model of Ca²⁺ alternans that incorporates Ca²⁺-CaM-dependent regulation of RyR2 and the L-type Ca²⁺ channel. Remarkably, the new model recapitulates the impact on Ca²⁺ alternans of altered CaM and RyR2 functions under 9 different experimental conditions. Our simulations reveal that diastolic cytosolic Ca²⁺ elevation as a result of rapid pacing triggers Ca²⁺-CaM dependent inactivation of RyR2. The resultant RyR2 inactivation diminishes sarcoplasmic reticulum Ca²⁺ release, which, in turn, reduces diastolic cytosolic Ca²⁺, leading to alternations in diastolic cytosolic Ca²⁺, RyR2 inactivation, and sarcoplasmic reticulum Ca²⁺ release (ie, Ca²⁺ alternans).

CONCLUSIONS

Our results demonstrate that inactivation of RyR2 by Ca²⁺-CaM is a major determinant of Ca²⁺ alternans, making Ca²⁺-CaM dependent regulation of RyR2 an important therapeutic target for cardiac alternans.

Universal mechanisms for self-termination of rapid cardiac rhythm

Excitable media sustain circulating waves. In the heart, sustained circulating waves can lead to serious impairment or even death. To investigate factors affecting the stability of such waves, we have used optogenetic techniques to stimulate a region at the apex of a mouse heart at a fixed delay after the detection of excitation at the base of the heart. For long delays, rapid circulating rhythms can be sustained, whereas for shorter delays, there are paroxysmal bursts of activity that start and stop spontaneously. By considering the dependence of the action potential and conduction velocity on the preceding recovery time using restitution curves, as well as the reduced excitability (fatigue) due to the rapid excitation, we model prominent features of the dynamics including alternation of the duration of the excited phases and conduction times, as well as termination of the bursts for short delays. We propose that this illustrates universal mechanisms that exist in biological systems for the self-termination of such activities.

Modeling the Interactions Between Sodium Channels Provides Insight Into the Negative Dominance of Certain Channel Mutations

BACKGROUND

Nav1.5 cardiac Na+ channel mutations can cause arrhythmogenic syndromes. Some of these mutations exert a dominant negative effect on wild-type channels. Recent studies showed that Na+ channels can dimerize, allowing coupled gating. This leads to the hypothesis that allosteric interactions between Na+ channels modulate their function and that these interactions may contribute to the negative dominance of certain mutations.

METHODS

To investigate how allosteric interactions affect microscopic and macroscopic channel function, we developed a modeling paradigm in which Markovian models of two channels are combined. Allosteric interactions are incorporated by modifying the free energies of the composite states and/or barriers between states.

RESULTS

Simulations using two generic 2-state models (C-O, closed-open) revealed that increasing the free energy of the composite states CO/OC leads to coupled gating. Simulations using two 3-state models (closed-open-inactivated) revealed that coupled closings must also involve interactions between further composite states. Using two 6-state cardiac Na+ channel models, we replicated previous experimental results mainly by increasing the energies of the CO/OC states and lowering the energy barriers between the CO/OC and the CO/OO states. The channel model was then modified to simulate a negative dominant mutation (Nav1.5 p.L325R). Simulations of homodimers and heterodimers in the presence and absence of interactions showed that the interactions with the variant channel impair the opening of the wild-type channel and thus contribute to negative dominance.

CONCLUSION

Our new modeling framework recapitulates qualitatively previous experimental observations and helps identifying possible interaction mechanisms between ion channels.

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

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

Ionic Mechanisms of Impulse Propagation Failure in the FHF2-Deficient Heart

RATIONALE

FHFs (fibroblast growth factor homologous factors) are key regulators of sodium channel (Na_V) inactivation. Mutations in these critical proteins have been implicated in human diseases including Brugada syndrome, idiopathic ventricular arrhythmias, and epileptic encephalopathy. The underlying ionic mechanisms by which reduced Na_v availability in Fhf2 knockout (Fhf2^KO) mice predisposes to abnormal excitability at the tissue level are not well defined.

OBJECTIVE

Using animal models and theoretical multicellular linear strands, we examined how FHF2 orchestrates the interdependency of sodium, calcium, and gap junctional conductances to safeguard cardiac conduction.

METHODS AND RESULTS

Fhf2^KO mice were challenged by reducing calcium conductance (gCa_V) using verapamil or by reducing gap junctional conductance (Gj) using carbenoxolone or by backcrossing into a cardiomyocyte-specific Cx43 (connexin 43) heterozygous background. All conditions produced conduction block in Fhf2^KO mice, with Fhf2 wild-type (Fhf2^WT) mice showing normal impulse propagation. To explore the ionic mechanisms of block in Fhf2^KO hearts, multicellular linear strand models incorporating FHF2-deficient Na_v inactivation properties were constructed and faithfully recapitulated conduction abnormalities seen in mutant hearts. The mechanisms of conduction block in mutant strands with reduced gCa_V or diminished Gj are very different. Enhanced Na_v inactivation due to FHF2 deficiency shifts dependence onto calcium current (I_Ca) to sustain electrotonic driving force, axial current flow, and action potential (AP) generation from cell-to-cell. In the setting of diminished Gj, slower charging time from upstream cells conspires with accelerated Na_v inactivation in mutant strands to prevent sufficient downstream cell charging for AP propagation.

CONCLUSIONS

FHF2-dependent effects on Na_v inactivation ensure adequate sodium current (I_Na) reserve to safeguard against numerous threats to reliable cardiac impulse propagation.

A Mathematical Model of the Mouse Atrial Myocyte With Inter-Atrial Electrophysiological Heterogeneity

Biophysically detailed mathematical models of cardiac electrophysiology provide an alternative to experimental approaches for investigating possible ionic mechanisms underlying the genesis of electrical action potentials and their propagation through the heart. The aim of this study was to develop a biophysically detailed mathematical model of the action potentials of mouse atrial myocytes, a popular experimental model for elucidating molecular and cellular mechanisms of arrhythmogenesis. Based on experimental data from isolated mouse atrial cardiomyocytes, a set of mathematical equations for describing the biophysical properties of membrane ion channel currents, intracellular Ca²⁺ handling, and Ca²⁺-calmodulin activated protein kinase II and β-adrenergic signaling pathways were developed. Wherever possible, membrane ion channel currents were modeled using Markov chain formalisms, allowing detailed representation of channel kinetics. The model also considered heterogeneous electrophysiological properties between the left and the right atrial cardiomyocytes. The developed model was validated by its ability to reproduce the characteristics of action potentials and Ca²⁺ transients, matching quantitatively to experimental data. Using the model, the functional roles of four K⁺ channel currents in atrial action potential were evaluated by channel block simulations, results of which were quantitatively in agreement with existent experimental data. To conclude, this newly developed model of mouse atrial cardiomyocytes provides a powerful tool for investigating possible ion channel mechanisms of atrial electrical activity at the cellular level and can be further used to investigate mechanisms underlying atrial arrhythmogenesis.

The Amplitude-Normalized Area of a Bipolar Electrogram as a Measure of Local Conduction Delay in the Heart

BACKGROUND

Re-entrant ventricular tachycardia may be non-inducible or haemodynamically compromising, requiring assessment of the electrophysiological properties of the myocardium during sinus rhythm (i.e., substrate mapping). Areas of heart tissue with slow conduction can act as a critical isthmus for re-entrant electrical excitation and are a potential target for ablation therapy.

AIM

To develop and validate a novel metric of local conduction delay in the heart, the amplitude-normalized electrogram area (norm_EA).

METHODS

A computational model of a propagating mouse action potential was used to establish the impact of altering sodium channel conductance, intracellular conductivity, fibrosis density, and electrode size/orientation on bipolar electrogram morphology. Findings were then validated in experimental studies in mouse and guinea pig hearts instrumented for the recording of bipolar electrograms from a multipolar linear mapping catheter. norm_EA was calculated by integrating the absolute area of a bipolar electrogram divided by the electrogram amplitude. Electrogram metrics were correlated with the local conduction delay during sodium channel block, gap junction inhibition, and acute ischemia.

RESULTS

In computational simulations, reducing sodium channel conductance and intracellular conductivity resulted in a decrease in signal amplitude and increase in norm_EA (reflecting a broadening of electrogram morphology). For larger electrodes (3 mm diameter/7.1 mm2 area), the change in norm_EA was essentially linear with the change in local conduction delay. Experimental studies supported this finding, showing that the magnitude of change in norm_EA induced by flecainide (1-4 μM), carbenoxolone (10-50 μM), and low-flow ischemia (25% of initial flow rate) was linearly correlated with the local conduction delay in each condition (r 2 = 0.92). Qualitatively similar effects were observed in guinea pig hearts perfused with flecainide. Increasing fibrosis density in the computational model also resulted in a decrease in signal amplitude and increase in norm_EA. However, this remains to be validated using experimental/clinical data of chronic infarct.

CONCLUSION

norm_EA is a quantitative measure of local conduction delay between the electrode pair that generates a bipolar electrogram, which may have utility in electrophysiological substrate mapping of non-inducible or haemodynamically compromising tachyarrhythmia.

A distinct molecular mechanism by which phenytoin rescues a novel long QT 3 variant

BACKGROUND

Genetic variants in SCN5A can result in channelopathies such as the long QT syndrome type 3 (LQT3), but the therapeutic response to Na⁺ channel blockers can vary. We previously reported a case of an infant with malignant LQT3 and a missense Q1475P SCN5A variant, who was effectively treated with phenytoin, but only partially with mexiletine. Here, we functionally characterized this variant and investigated possible mechanisms for the differential drug actions.

METHODS

Wild-type or mutant Na_v1.5 cDNAs were examined in transfected HEK293 cells with patch clamping and biochemical assays. We used computational modeling to provide insights into altered channel kinetics and to predict effects on the action potential.

RESULTS

The Q1475P variant in Na_v1.5 reduced the current density and channel surface expression, characteristic of a trafficking defect. The variant also led to positive shifts in the voltage dependence of steady-state activation and inactivation, faster inactivation and recovery from inactivation, and increased the "late" Na⁺ current. Simulations of Na_v1.5 gating with a 9-state Markov model suggested that transitions from inactivated to closed states were accelerated in Q1475P channels, leading to accumulation of channels in non-inactivated closed states. Simulations with a human ventricular myocyte model predicted action potential prolongation with Q1475P, compared with wild type, channels. Patch clamp data showed that mexiletine and phenytoin similarly rescued some of the gating defects. Chronic incubation with mexiletine, but not phenytoin, rescued the Na_v1.5-Q1475P trafficking defect, thus increasing mutant channel expression.

CONCLUSIONS

The gain-of-function effects of Na_v1.5-Q1475P predominate to cause a malignant long QT phenotype. Phenytoin partially corrects the gating defect without restoring surface expression of the mutant channel, whereas mexiletine restores surface expression of the mutant channel, which may explain the lack of efficacy of mexiletine when compared to phenytoin. Our data makes a case for experimental studies before embarking on a one-for-all therapy of arrhythmias.

Mathematical model for β1-adrenergic regulation of the mouse ventricular myocyte contraction

The β1-adrenergic regulation of cardiac myocyte contraction plays an important role in regulating heart function. Activation of this system leads to an increased heart rate and stronger myocyte contraction. However, chronic stimulation of the β1-adrenergic signaling system can lead to cardiac hypertrophy and heart failure. To understand the mechanisms of action of β1-adrenoceptors, a mathematical model of cardiac myocyte contraction that includes the β1-adrenergic system was developed and studied. The model was able to simulate major experimental protocols for measurements of steady-state force-calcium relationships, cross-bridge release rate and force development rate, force-velocity relationship, and force redevelopment rate. It also reproduced quite well frequency and isoproterenol dependencies for intracellular Ca2+ concentration ([Ca2+]i) transients, total contraction force, and sarcomere shortening. The mathematical model suggested the mechanisms of increased contraction force and myocyte shortening on stimulation of β1-adrenergic receptors is due to phosphorylation of troponin I and myosin-binding protein C and increased [Ca2+]i transient resulting from activation of the β1-adrenergic signaling system. The model was used to simulate work-loop contractions and estimate the power during the cardiac cycle as well as the effects of 4-aminopyridine and tedisamil on the myocyte contraction. The developed mathematical model can be used further for simulations of contraction of ventricular myocytes from genetically modified mice and myocytes from mice with chronic cardiac diseases.

NEW & NOTEWORTHY A new mathematical model of mouse ventricular myocyte contraction that includes the β1-adrenergic system was developed. The model simulated major experimental protocols for myocyte contraction and predicted the effects of 4-aminopyridine and tedisamil on the myocyte contraction. The model also allowed for simulations of work-loop contractions and estimation of the power during the cardiac cycle.

A compartmentalized mathematical model of mouse atrial myocytes

Various experimental mouse models are extensively used to research human diseases, including atrial fibrillation, the most common cardiac rhythm disorder. Despite this, there are no comprehensive mathematical models that describe the complex behavior of the action potential and [Ca²⁺]_i transients in mouse atrial myocytes. Here, we develop a novel compartmentalized mathematical model of mouse atrial myocytes that combines the action potential, [Ca²⁺]_i dynamics, and β-adrenergic signaling cascade for a subpopulation of right atrial myocytes with developed transverse-axial tubule system. The model consists of three compartments related to β-adrenergic signaling (caveolae, extracaveolae, and cytosol) and employs local control of Ca²⁺ release. It also simulates ionic mechanisms of action potential generation and describes atrial-specific Ca²⁺ handling as well as frequency dependences of the action potential and [Ca²⁺]_i transients. The model showed that the T-type Ca²⁺ current significantly affects the later stage of the action potential, with little effect on [Ca²⁺]_i transients. The block of the small-conductance Ca²⁺-activated K⁺ current leads to a prolongation of the action potential at high intracellular Ca²⁺. Simulation results obtained from the atrial model cells were compared with those from ventricular myocytes. The developed model represents a useful tool to study complex electrical properties in the mouse atria and could be applied to enhance the understanding of atrial physiology and arrhythmogenesis.NEW & NOTEWORTHY A new compartmentalized mathematical model of mouse right atrial myocytes was developed. The model simulated action potential and Ca²⁺ dynamics at baseline and after stimulation of the β-adrenergic signaling system. Simulations showed that the T-type Ca²⁺ current markedly prolonged the later stage of atrial action potential repolarization, with a minor effect on [Ca²⁺]_i transients. The small-conductance Ca²⁺-activated K⁺ current block resulted in prolongation of the action potential only at the relatively high intracellular Ca²⁺.

Temporal irregularity quantification and mapping of optical action potentials using wave morphology similarity

Background

Cardiac optical mapping enables direct and high spatio-temporal resolution recording of action potential (AP) morphology. Temporal alterations in AP morphology are both predictive and consequent of arrhythmia. Here we sought to test if methods that quantify regularity of recorded waveforms could be applied to detect and quantify periods of temporal instability in optical mapping datasets in a semi-automated, user-unbiased manner.

Methods and results

We developed, tested and applied algorithms to quantify optical wave similarity (OWS) to study morphological temporal similarity of optically recorded APs. Unlike other measures (e.g. alternans ratio, beat-to-beat variability, arrhythmia scoring), the quantification of OWS is achieved without a restrictive definition of specific signal points/features and is instead derived by analysing the complete morphology from the entire AP waveform.

Using model datasets, we validated the ability of OWS to measure changes in AP morphology, and tested OWS mapping in guinea pig hearts and mouse atria. OWS successfully detected and measured alterations in temporal regularity in response to several proarrhythmic stimuli, including alterations in pacing frequency, premature contractions, alternans and ventricular fibrillation.

Conclusion

OWS mapping provides an effective measure of temporal regularity that can be applied to optical datasets to detect and quantify temporal alterations in action potential morphology. This methodology provides a new metric for arrhythmia inducibility and scoring in optical mapping datasets.

Metabolic regulation of Kv channels and cardiac repolarization by Kvβ2 subunits

Voltage-gated potassium (Kv) channels control myocardial repolarization. Pore-forming Kvα proteins associate with intracellular Kvβ subunits, which bind pyridine nucleotides with high affinity and differentially regulate channel trafficking, plasmalemmal localization and gating properties. Nevertheless, it is unclear how Kvβ subunits regulate myocardial K⁺ currents and repolarization. Here, we tested the hypothesis that Kvβ2 subunits regulate the expression of myocardial Kv channels and confer redox sensitivity to Kv current and cardiac repolarization. Co-immunoprecipitation and in situ proximity ligation showed that in cardiac myocytes, Kvβ2 interacts with Kv1.4, Kv1.5, Kv4.2, and Kv4.3. Cardiac myocytes from mice lacking Kcnab2 (Kvβ2^-/-) had smaller cross sectional areas, reduced sarcolemmal abundance of Kvα binding partners, reduced I_to, I_K,slow1, and I_K,slow2 densities, and prolonged action potential duration compared with myocytes from wild type mice. These differences in Kvβ2^-/- mice were associated with greater P wave duration and QT interval in electrocardiograms, and lower ejection fraction, fractional shortening, and left ventricular mass in echocardiographic and morphological assessments. Direct intracellular dialysis with a high NAD(P)H:NAD(P)⁺ accelerated Kv inactivation in wild type, but not Kvβ2^-/- myocytes. Furthermore, elevated extracellular levels of lactate increased [NADH]_i and prolonged action potential duration in wild type cardiac myocytes and perfused wild type, but not Kvβ2^-/-, hearts. Taken together, these results suggest that Kvβ2 regulates myocardial electrical activity by supporting the functional expression of proteins that generate I_to and I_K,slow, and imparting redox and metabolic sensitivity to Kv channels, thereby coupling cardiac repolarization to myocyte metabolism.

Four Ways to Fit an Ion Channel Model

Mathematical models of ionic currents are used to study the electrophysiology of the heart, brain, gut, and several other organs. Increasingly, these models are being used predictively in the clinic, for example, to predict the risks and results of genetic mutations, pharmacological treatments, or surgical procedures. These safety-critical applications depend on accurate characterization of the underlying ionic currents. Four different methods can be found in the literature to fit voltage-sensitive ion channel models to whole-cell current measurements: method 1, fitting model equations directly to time-constant, steady-state, and I-V summary curves; method 2, fitting by comparing simulated versions of these summary curves to their experimental counterparts; method 3, fitting to the current traces themselves from a range of protocols; and method 4, fitting to a single current trace from a short and rapidly fluctuating voltage-clamp protocol. We compare these methods using a set of experiments in which hERG1a current was measured in nine Chinese hamster ovary cells. In each cell, the same sequence of fitting protocols was applied, as well as an independent validation protocol. We show that methods 3 and 4 provide the best predictions on the independent validation set and that short, rapidly fluctuating protocols like that used in method 4 can replace much longer conventional protocols without loss of predictive ability. Although data for method 2 are most readily available from the literature, we find it performs poorly compared to methods 3 and 4 both in accuracy of predictions and computational efficiency. Our results demonstrate how novel experimental and computational approaches can improve the quality of model predictions in safety-critical applications.

Normal interventricular differences in tissue architecture underlie right ventricular susceptibility to conduction abnormalities in a mouse model of Brugada syndrome

Aims

Loss-of-function of the cardiac sodium channel Na_V1.5 is a common feature of Brugada syndrome. Arrhythmias arise preferentially from the right ventricle (RV) despite equivalent Na_V1.5 downregulation in the left ventricle (LV). The reasons for increased RV sensitivity to Na_V1.5 loss-of-function mutations remain unclear. Because ventricular electrical activation occurs predominantly in the transmural axis, we compare RV and LV transmural electrophysiology to determine the underlying cause of the asymmetrical conduction abnormalities in Scn5a haploinsufficient mice (Scn5a^+/−).

Methods and results

Optical mapping and two-photon microscopy in isolated-perfused mouse hearts demonstrated equivalent depression of transmural conduction velocity (CV) in the LV and RV of Scn5a^+/− vs. wild-type littermates. Only RV transmural conduction was further impaired when challenged with increased pacing frequencies. Epicardial dispersion of activation and beat-to-beat variation in activation time were increased only in the RV of Scn5a^+/− hearts. Analysis of confocal and histological images revealed larger intramural clefts between cardiomyocyte layers in the RV vs. LV, independent of genotype. Acute sodium current inhibition in wild type hearts using tetrodotoxin reproduced beat-to-beat activation variability and frequency-dependent CV slowing in the RV only, with the LV unaffected. The influence of clefts on conduction was examined using a two-dimensional monodomain computational model. When peak sodium channel conductance was reduced to 50% of normal the presence of clefts between cardiomyocyte layers reproduced the activation variability and conduction phenotype observed experimentally.

Conclusions

Normal structural heterogeneities present in the RV are responsible for increased vulnerability to conduction slowing in the presence of reduced sodium channel function. Heterogeneous conduction slowing seen in the RV will predispose to functional block and the initiation of re-entrant ventricular arrhythmias.

Mechanisms Underlying Spontaneous Action Potential Generation Induced by Catecholamine in Pulmonary Vein Cardiomyocytes: A Simulation Study

Cardiomyocytes and myocardial sleeves dissociated from pulmonary veins (PVs) potentially generate ectopic automaticity in response to noradrenaline (NA), and thereby trigger atrial fibrillation. We developed a mathematical model of rat PV cardiomyocytes (PVC) based on experimental data that incorporates the microscopic framework of the local control theory of Ca²⁺ release from the sarcoplasmic reticulum (SR), which can generate rhythmic Ca²⁺ release (limit cycle revealed by the bifurcation analysis) when total Ca²⁺ within the cell increased. Ca²⁺ overload in SR increased resting Ca²⁺ efflux through the type II inositol 1,4,5-trisphosphate (IP₃) receptors (InsP₃R) as well as ryanodine receptors (RyRs), which finally triggered massive Ca²⁺ release through activation of RyRs via local Ca²⁺ accumulation in the vicinity of RyRs. The new PVC model exhibited a resting potential of −68 mV. Under NA effects, repetitive Ca²⁺ release from SR triggered spontaneous action potentials (APs) by evoking transient depolarizations (TDs) through Na⁺/Ca²⁺ exchanger (AP_TDs). Marked and variable latencies initiating AP_TDs could be explained by the time courses of the α1- and β1-adrenergic influence on the regulation of intracellular Ca²⁺ content and random occurrences of spontaneous TD activating the first AP_TD. Positive and negative feedback relations were clarified under AP_TD generation.

Properties of cardiac conduction in a cell-based computational model

The conduction of electrical signals through cardiac tissue is essential for maintaining the function of the heart, and conduction abnormalities are known to potentially lead to life-threatening arrhythmias. The properties of cardiac conduction have therefore been the topic of intense study for decades, but a number of questions related to the mechanisms of conduction still remain unresolved. In this paper, we demonstrate how the so-called EMI model may be used to study some of these open questions. In the EMI model, the extracellular space, the cell membrane, the intracellular space and the cell connections are all represented as separate parts of the computational domain, and the model therefore allows for study of local properties that are hard to represent in the classical homogenized bidomain or monodomain models commonly used to study cardiac conduction. We conclude that a non-uniform sodium channel distribution increases the conduction velocity and decreases the time delays over gap junctions of reduced coupling in the EMI model simulations. We also present a theoretical optimal cell length with respect to conduction velocity and consider the possibility of ephaptic coupling (i.e. cell-to-cell coupling through the extracellular potential) acting as an alternative or supporting mechanism to gap junction coupling. We conclude that for a non-uniform distribution of sodium channels and a sufficiently small intercellular distance, ephaptic coupling can influence the dynamics of the sodium channels and potentially provide cell-to-cell coupling when the gap junction connection is absent.

The electrochemical wave traversing the heart during every beat is essential for cardiac pumping function and supply of blood to the body. Understanding the stability of this wave is crucial to understanding how lethal arrhythmias are generated. Despite this importance, our knowledge of the physical determinants of wave propagation are still evolving. One particular challenge has been the lack of accurate mathematical models of conduction at the cellular level. Because cardiac muscle is an electrical syncytium, in which direct charge transfer between cells drives wave propagation, classical bidomain and monodomain tissue models employ a homogenized approximation of this process. This approximation is not valid at the length scale of single cells, and prevents any analysis of how cellular structures impact cardiac conduction. Instead, so-called microdomain models must be used for these questions. Here we utilize a recently developed modelling framework that is well suited to represent small collections of cells. By applying this framework, we show that concentration of sodium channels at the longitudinal borders of myocytes accelerates cardiac conduction. We also demonstrate that when juxtaposed cells are sufficiently close, this non-uniform distribution induces large ephaptic currents, which contribute to intercellular coupling.

Calcium-dependent inactivation controls cardiac L-type Ca2+ currents under β-adrenergic stimulation

During a cardiac action potential, the activity of L-type Ca²⁺ channels (LTCCs) is modulated by voltage- and calcium-dependent inactivation processes. Morales et al. show that, in the context of β-adrenergic stimulation, calcium-dependent inactivation directs the regulation of LTCC activity, limiting calcium influx during the action potential.

The activity of L-type calcium channels is associated with the duration of the plateau phase of the cardiac action potential (AP) and it is controlled by voltage- and calcium-dependent inactivation (VDI and CDI, respectively). During β-adrenergic stimulation, an increase in the L-type current and parallel changes in VDI and CDI are observed during square pulses stimulation; however, how these modifications impact calcium currents during an AP remains controversial. Here, we examined the role of both inactivation processes on the L-type calcium current activity in newborn rat cardiomyocytes in control conditions and after stimulation with the β-adrenergic agonist isoproterenol. Our approach combines a self-AP clamp (sAP-Clamp) with the independent inhibition of VDI or CDI (by overexpressing Ca_Vβ_2a or calmodulin mutants, respectively) to directly record the L-type calcium current during the cardiac AP. We find that at room temperature (20–23°C) and in the absence of β-adrenergic stimulation, the L-type current recapitulates the AP kinetics. Furthermore, under our experimental setting, the activity of the sodium–calcium exchanger (NCX) does not affect the shape of the AP. We find that hindering either VDI or CDI prolongs the L-type current and the AP in parallel, suggesting that both inactivation processes modulate the L-type current during the AP. In the presence of isoproterenol, wild-type and VDI-inhibited cardiomyocytes display mismatched L-type calcium current with respect to their AP. In contrast, CDI-impaired cells maintain L-type current with kinetics similar to its AP, demonstrating that calcium-dependent inactivation governs L-type current kinetics during β-adrenergic stimulation.

A Mathematical Model of the Human Cardiac Na+ Channel

Sodium ion channel is a membrane protein that plays an important role in excitable cells, as it is responsible for the initiation of action potentials. Understanding the electrical characteristics of sodium channels is essential in predicting their behavior under different physiological conditions. We investigated several Markov models for the human cardiac sodium channel Na_V1.5 to derive a minimal mathematical model that describes the reported experimental data obtained using major voltage clamp protocols. We obtained simulation results for peak current-voltage relationships, the voltage dependence of normalized ion channel conductance, steady-state inactivation, activation and deactivation kinetics, fast and slow inactivation kinetics, and recovery from inactivation kinetics. Good agreement with the experimental data provides us with the mechanisms of the fast and slow inactivation of the human sodium channel and the coupling of its inactivation states to the closed and open states in the activation pathway.

The Ca2+ transient as a feedback sensor controlling cardiomyocyte ionic conductances in mouse populations

Conductances of ion channels and transporters controlling cardiac excitation may vary in a population of subjects with different cardiac gene expression patterns. However, the amount of variability and its origin are not quantitatively known. We propose a new conceptual approach to predict this variability that consists of finding combinations of conductances generating a normal intracellular Ca²⁺ transient without any constraint on the action potential. Furthermore, we validate experimentally its predictions using the Hybrid Mouse Diversity Panel, a model system of genetically diverse mouse strains that allows us to quantify inter-subject versus intra-subject variability. The method predicts that conductances of inward Ca²⁺ and outward K⁺ currents compensate each other to generate a normal Ca²⁺ transient in good quantitative agreement with current measurements in ventricular myocytes from hearts of different isogenic strains. Our results suggest that a feedback mechanism sensing the aggregate Ca²⁺ transient of the heart suffices to regulate ionic conductances.