Regulation of Ca2+ and electrical alternans in cardiac myocytes: role of CAMKII and repolarizing currents

Computational modeling of cardiac electrophysiology and arrhythmogenesis: toward clinical translation

The complexity of cardiac electrophysiology, involving dynamic changes in numerous components across multiple spatial (from ion channel to organ) and temporal (from milliseconds to days) scales, makes an intuitive or empirical analysis of cardiac arrhythmogenesis challenging. Multiscale mechanistic computational models of cardiac electrophysiology provide precise control over individual parameters, and their reproducibility enables a thorough assessment of arrhythmia mechanisms. This review provides a comprehensive analysis of models of cardiac electrophysiology and arrhythmias, from the single cell to the organ level, and how they can be leveraged to better understand rhythm disorders in cardiac disease and to improve heart patient care. Key issues related to model development based on experimental data are discussed, and major families of human cardiomyocyte models and their applications are highlighted. An overview of organ-level computational modeling of cardiac electrophysiology and its clinical applications in personalized arrhythmia risk assessment and patient-specific therapy of atrial and ventricular arrhythmias is provided. The advancements presented here highlight how patient-specific computational models of the heart reconstructed from patient data have achieved success in predicting risk of sudden cardiac death and guiding optimal treatments of heart rhythm disorders. Finally, an outlook toward potential future advances, including the combination of mechanistic modeling and machine learning/artificial intelligence, is provided. As the field of cardiology is embarking on a journey toward precision medicine, personalized modeling of the heart is expected to become a key technology to guide pharmaceutical therapy, deployment of devices, and surgical interventions.

Increased Risk for Atrial Alternans in Rabbit Heart Failure: The Role of Ca2+/Calmodulin-Dependent Kinase II and Inositol-1,4,5-trisphosphate Signaling

Heart failure (HF) increases the probability of cardiac arrhythmias, including atrial fibrillation (AF), but the mechanisms linking HF to AF are poorly understood. We investigated disturbances in Ca2+ signaling and electrophysiology in rabbit atrial myocytes from normal and failing hearts and identified mechanisms that contribute to the higher risk of atrial arrhythmias in HF. Ca2+ transient (CaT) alternans-beat-to-beat alternations in CaT amplitude-served as indicator of increased arrhythmogenicity. We demonstrate that HF atrial myocytes were more prone to alternans despite no change in action potentials duration and only moderate decrease of L-type Ca2+ current. Ca2+/calmodulin-dependent kinase II (CaMKII) inhibition suppressed CaT alternans. Activation of IP3 signaling by endothelin-1 (ET-1) and angiotensin II (Ang II) resulted in acute, but transient reduction of CaT amplitude and sarcoplasmic reticulum (SR) Ca2+ load, and lowered the alternans risk. However, prolonged exposure to ET-1 and Ang II enhanced SR Ca2+ release and increased the degree of alternans. Inhibition of IP3 receptors prevented the transient ET-1 and Ang II effects and by itself increased the degree of CaT alternans. Our data suggest that activation of CaMKII and IP3 signaling contribute to atrial arrhythmogenesis in HF.

Prokaryotic voltage-gated sodium channels are more effective than endogenous Nav1.5 channels in rescuing cardiac action potential conduction: an in silico study

Methods to augment Na+ current in cardiomyocytes hold potential for the treatment of various cardiac arrhythmias involving conduction slowing. Because the gene coding cardiac Na+ channel (Nav1.5) is too large to fit in a single adeno-associated virus (AAV) vector, new gene therapies are being developed to enhance endogenous Nav1.5 current (by overexpression of chaperon molecules or use of multiple AAV vectors) or to exogenously introduce prokaryotic voltage-gated Na+ channels (BacNav) whose gene size is significantly smaller than that of the Nav1.5. In this study, based on experimental measurements in heterologous expression systems, we developed an improved computational model of the BacNav channel, NavSheP D60A. We then compared in silico how NavSheP D60A expression vs. Nav1.5 augmentation affects the electrophysiology of cardiac tissue. We found that the incorporation of BacNav channels in both adult guinea pig and human cardiomyocyte models increased their excitability and reduced action potential duration. When compared with equivalent augmentation of Nav1.5 current in simulated settings of reduced tissue excitability, the addition of the BacNav current was superior in improving the safety of conduction under conditions of current source-load mismatch, reducing the vulnerability to unidirectional conduction block during premature pacing, preventing the instability and breakup of spiral waves, and normalizing the conduction and ECG in Brugada syndrome tissues with mutated Nav1.5. Overall, our studies show that compared with a potential enhancement of the endogenous Nav1.5 current, expression of the BacNav channels with their slower inactivation kinetics can provide greater anti-arrhythmic benefits in hearts with compromised action potential conduction.NEW & NOTEWORTHY Slow action potential conduction is a common cause of various cardiac arrhythmias; yet, current pharmacotherapies cannot augment cardiac conduction. This in silico study compared the efficacy of recently proposed antiarrhythmic gene therapy approaches that increase peak sodium current in cardiomyocytes. When compared with the augmentation of endogenous sodium current, expression of slower-inactivating bacterial sodium channels was superior in preventing conduction block and arrhythmia induction. These results further the promise of antiarrhythmic gene therapies targeting sodium channels.

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.

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.

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

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

Dapagliflozin reduces the vulnerability of rats with pulmonary arterial hypertension-induced right heart failure to ventricular arrhythmia by restoring calcium handling

Background

Malignant ventricular arrhythmia (VA) is a major contributor to sudden cardiac death (SCD) in patients with pulmonary arterial hypertension (PAH)-induced right heart failure (RHF). Recently, dapagliflozin (DAPA), a sodium/glucose cotransporter-2 inhibitor (SGLT2i), has been found to exhibit cardioprotective effects in patients with left ventricular systolic dysfunction. In this study, we examined the effects of DAPA on VA vulnerability in a rat model of PAH-induced RHF.

Methods

Rats randomly received monocrotaline (MCT, 60 mg/kg) or vehicle via a single intraperitoneal injection. A day later, MCT-injected rats were randomly treated with placebo, low-dose DAPA (1 mg/kg/day), or high-dose (3 mg/kg/day) DAPA orally for 35 days. Echocardiographic analysis, haemodynamic experiments, and histological assessments were subsequently performed to confirm the presence of PAH-induced RHF. Right ventricle (RV) expression of calcium (Ca²⁺) handling proteins were detected via Western blotting. RV expression of connexin 43 (Cx43) was determined via immunohistochemical staining. An optical mapping study was performed to assess the electrophysiological characteristics in isolated hearts. Cellular Ca²⁺ imaging from RV cardiomyocytes (RVCMs) was recorded using Fura-2 AM or Fluo-4 AM.

Results

High-dose DAPA treatment attenuated RV structural remodelling, improved RV function, alleviated Cx43 remodelling, increased the conduction velocity, restored the expression of key Ca²⁺ handling proteins, increased the threshold for Ca²⁺ and action potential duration (APD) alternans, decreased susceptibility to spatially discordant APD alternans and spontaneous Ca²⁺ events, promoted cellular Ca²⁺ handling, and reduced VA vulnerability in PAH-induced RHF rats. Low-dose DAPA treatment also showed antiarrhythmic effects in hearts with PAH-induced RHF, although with a lower level of efficacy.

Conclusion

DAPA administration reduced VA vulnerability in rats with PAH-induced RHF by improving RVCM Ca²⁺ handling.

Supplementary Information

The online version contains supplementary material available at 10.1186/s12933-022-01614-5.

Mechanisms of arrhythmia termination during acute myocardial ischemia: Role of ephaptic coupling and complex geometry of border zone

Myocardial ischemia occurs when blood flow to the heart is reduced, preventing the heart muscle from receiving enough oxygen required for survival. Several anatomical and electrophysiological changes occur at the ischemic core (IC) and border zone (BZ) during myocardial ischemia, for example, gap junctional remodeling, changes in ionic channel kinetics and electrophysiologic changes in cell excitability, which promote the development of cardiac arrhythmia. Ephaptic coupling (EpC), which is an electrical field effect developed in the shared cleft space between adjacent cells, has been suggested to rescue the conduction when gap junctions are impaired, such as myocardial ischemia. In this manuscript, we explored the impact of EpC, electrophysiological and anatomical components of myocardial ischemia on reentry termination during non-ischemic and ischemic condition. Our results indicated that EpC and BZ with complex geometry have opposite effects on the reentry termination. In particular, the presence of homogeneous EpC terminates reentry, whereas BZ with complex geometry alone facilitates reentry by producing wave break-up and alternating conduction block. The reentry is terminated in the presence of homogeneous or heterogeneous EpC despite the presence of complex geometry of the BZ, independent of the location of BZ. The inhibition of reentry can be attributed to a current-to-load mismatch. Our results points to an antiarrhythmic role of EpC and a pro-arrhythmic role of BZ with complex geometry.

Automaticity in ventricular myocyte cell pairs with ephaptic and gap junction coupling

Spontaneous electrical activity, or automaticity, in the heart is required for normal physiological function. However, irregular automaticity, in particular, originating from the ventricles, can trigger life-threatening cardiac arrhythmias. Thus, understanding mechanisms of automaticity and synchronization is critical. Recent work has proposed that excitable cells coupled via a shared narrow extracellular cleft can mediate coupling, i.e., ephaptic coupling, that promotes automaticity in cell pairs. However, the dynamics of these coupled cells incorporating both ephaptic and gap junction coupling has not been explored. Here, we show that automaticity and synchronization robustly emerges via a Hopf bifurcation from either (i) increasing the fraction of inward rectifying potassium channels (carrying the I_K1 current) at the junctional membrane or (ii) by decreasing the cleft volume. Furthermore, we explore how heterogeneity in the fraction of potassium channels between coupled cells can produce automaticity of both cells or neither cell, or more rarely in only one cell (i.e., automaticity without synchronization). Interestingly, gap junction coupling generally has minor effects, with only slight changes in regions of parameter space of automaticity. This work provides insight into potentially new mechanisms that promote spontaneous activity and, thus, triggers for arrhythmias in ventricular tissue.

Engineered bacterial voltage-gated sodium channel platform for cardiac gene therapy

Therapies for cardiac arrhythmias could greatly benefit from approaches to enhance electrical excitability and action potential conduction in the heart by stably overexpressing mammalian voltage-gated sodium channels. However, the large size of these channels precludes their incorporation into therapeutic viral vectors. Here, we report a platform utilizing small-size, codon-optimized engineered prokaryotic sodium channels (BacNav) driven by muscle-specific promoters that significantly enhance excitability and conduction in rat and human cardiomyocytes in vitro and adult cardiac tissues from multiple species in silico. We also show that the expression of BacNav significantly reduces occurrence of conduction block and reentrant arrhythmias in fibrotic cardiac cultures. Moreover, functional BacNav channels are stably expressed in healthy mouse hearts six weeks following intravenous injection of self-complementary adeno-associated virus (scAAV) without causing any adverse effects on cardiac electrophysiology. The large diversity of prokaryotic sodium channels and experimental-computational platform reported in this study should facilitate the development and evaluation of BacNav-based gene therapies for cardiac conduction disorders.

Hypernatremia and intercalated disc edema synergistically exacerbate long-QT syndrome type 3 phenotype

Cardiac voltage-gated sodium channel gain-of-function prolongs repolarization in the long-QT syndrome type 3 (LQT3). Previous studies suggest that narrowing the perinexus within the intercalated disc, leading to rapid sodium depletion, attenuates LQT3-associated action potential duration (APD) prolongation. However, it remains unknown whether extracellular sodium concentration modulates APD prolongation during sodium channel gain-of-function. We hypothesized that elevated extracellular sodium concentration and widened perinexus synergistically prolong APD in LQT3. LQT3 was induced with sea anemone toxin (ATXII) in Langendorff-perfused guinea pig hearts (n = 34). Sodium concentration was increased from 145 to 160 mM. Perinexal expansion was induced with mannitol or the sodium channel β1-subunit adhesion domain antagonist (βadp1). Epicardial ventricular action potentials were optically mapped. Individual and combined effects of varying clefts and sodium concentrations were simulated in a computational model. With ATXII, both mannitol and βadp1 significantly widened the perinexus and prolonged APD, respectively. The elevated sodium concentration alone significantly prolonged APD as well. Importantly, the combination of elevated sodium concentration and perinexal widening synergistically prolonged APD. Computational modeling results were consistent with animal experiments. Concurrently elevating extracellular sodium and increasing intercalated disc edema prolongs repolarization more than the individual interventions alone in LQT3. This synergistic effect suggests an important clinical implication that hypernatremia in the presence of cardiac edema can markedly increase LQT3-associated APD prolongation. Therefore, to our knowledge, this is the first study to provide evidence of a tractable and effective strategy to mitigate LQT3 phenotype by means of managing sodium levels and preventing cardiac edema in patients.NEW & NOTEWORTHY This is the first study to demonstrate that the long-QT syndrome type 3 (LQT3) phenotype can be exacerbated or concealed by regulating extracellular sodium concentrations and/or the intercalated disc separation. The animal experiments and computational modeling in the current study reveal a critically important clinical implication: sodium dysregulation in the presence of edema within the intercalated disc can markedly increase the risk of arrhythmia in LQT3. These findings strongly suggest that maintaining extracellular sodium within normal physiological limits may be an effective and inexpensive therapeutic option for patients with congenital or acquired sodium channel gain-of-function diseases.

Cellular Size, Gap Junctions, and Sodium Channel Properties Govern Developmental Changes in Cardiac Conduction

Electrical conduction in cardiac ventricular tissue is regulated via sodium (Na⁺) channels and gap junctions (GJs). We and others have recently shown that Na⁺channels preferentially localize at the site of cell-cell junctions, the intercalated disc (ID), in adult cardiac tissue, facilitating coupling via the formation of intercellular Na⁺nanodomains, also termed ephaptic coupling (EpC). Several properties governing EpC vary with age, including Na⁺channel and GJ expression and distribution and cell size. Prior work has shown that neonatal cardiomyocytes have immature IDs with Na⁺channels and GJs diffusively distributed throughout the sarcolemma, while adult cells have mature IDs with preferentially localized Na⁺channels and GJs. In this study, we perform an in silico investigation of key age-dependent properties to determine developmental regulation of cardiac conduction. Simulations predict that conduction velocity (CV) biphasically depends on cell size, depending on the strength of GJ coupling. Total cell Na⁺channel conductance is predictive of CV in cardiac tissue with high GJ coupling, but not correlated with CV for low GJ coupling. We find that ephaptic effects are greatest for larger cells with low GJ coupling typically associated with intermediate developmental stages. Finally, simulations illustrate how variability in cellular properties during different developmental stages can result in a range of possible CV values, with a narrow range for both neonatal and adult myocardium but a much wider range for an intermediate developmental stage. Thus, we find that developmental changes predict associated changes in cardiac conduction.

Initiation and entrainment of multicellular automaticity via diffusion limited extracellular domains

Electrically excitable cells often spontaneously and synchronously depolarize in vitro and in vivo preparations. It remains unclear how cells entrain and autorhythmically activate above the intrinsic mean activation frequency of isolated cells with or without pacemaking mechanisms. Recent studies suggest that cyclic ion accumulation and depletion in diffusion-limited extracellular volumes modulate electrophysiology by ephaptic mechanisms (nongap junction or synaptic coupling). This report explores how potassium accumulation and depletion in a restricted extracellular domain induces spontaneous action potentials in two different computational models of excitable cells without gap junctional coupling: Hodgkin-Huxley and Luo-Rudy. Importantly, neither model will spontaneously activate on its own without external stimuli. Simulations demonstrate that cells sharing a diffusion-limited extracellular compartment can become autorhythmic and entrained despite intercellular electrical heterogeneity. Autorhythmic frequency is modulated by the cleft volume and potassium fluxes through the cleft. Additionally, inexcitable cells can suppress or induce autorhythmic activity in an excitable cell via a shared cleft. Diffusion-limited shared clefts can also entrain repolarization. Critically, this model predicts a mechanism by which diffusion-limited shared clefts can initiate, entrain, and modulate multicellular automaticity in the absence of gap junctions.

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

Background

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

Objective

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

Methods

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

Results

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

Conclusions

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

The development of L-type Ca2+ current mediated alternans does not depend on the restitution slope in canine ventricular myocardium

Cardiac alternans have crucial importance in the onset of ventricular fibrillation. The early explanation for alternans development was the voltage-driven mechanism, where the action potential (AP) restitution steepness was considered as crucial determining factor. Recent results suggest that restitution slope is an inadequate predictor for alternans development, but several studies still claim the role of membrane potential as underlying mechanism of alternans. These controversial data indicate that the relationship of restitution and alternans development is not completely understood. APs were measured by conventional microelectrode technique from canine right ventricular papillary muscles. Ionic currents combined with fluorescent measurements were recorded by patch-clamp technique. APs combined with fluorescent measurements were monitored by sharp microelectrodes. Rapid pacing evoked restitution-independent AP duration (APD) alternans. When non-alternating AP voltage command was used, Ca²⁺_i-transient (CaT) alternans were not observed. When alternating rectangular voltage pulses were applied, CaT alternans were proportional to I_CaL amplitude alternans. Selective I_CaL inhibition did not influence the fast phase of APD restitution. In this study we found that I_CaL has minor contribution in shaping the fast phase of restitution curve suggesting that I_CaL—if it plays important role in the alternans mechanism—could be an additional factor that attenuates the reliability of APD restitution slope to predict alternans.

Mechanoelectric coupling and arrhythmogenesis in cardiomyocytes contracting under mechanical afterload in a 3D viscoelastic hydrogel

The heart pumps blood against the mechanical afterload from arterial resistance, and increased afterload may alter cardiac electrophysiology and contribute to life-threatening arrhythmias. However, the cellular and molecular mechanisms underlying mechanoelectric coupling in cardiomyocytes remain unclear. We developed an innovative patch-clamp-in-gel technology to embed cardiomyocytes in a three-dimensional (3D) viscoelastic hydrogel that imposes an afterload during regular myocyte contraction. Here, we investigated how afterload affects action potentials, ionic currents, intracellular Ca2+ transients, and cell contraction of adult rabbit ventricular cardiomyocytes. We found that afterload prolonged action potential duration (APD), increased transient outward K+ current, decreased inward rectifier K+ current, and increased L-type Ca2+ current. Increased Ca2+ entry caused enhanced Ca2+ transients and contractility. Moreover, elevated afterload led to discordant alternans in APD and Ca2+ transient. Ca2+ alternans persisted under action potential clamp, indicating that the alternans was Ca2+ dependent. Furthermore, all these afterload effects were significantly attenuated by inhibiting nitric oxide synthase 1 (NOS1). Taken together, our data reveal a mechano-chemo-electrotransduction (MCET) mechanism that acutely transduces afterload through NOS1-nitric oxide signaling to modulate the action potential, Ca2+ transient, and contractility. The MCET pathway provides a feedback loop in excitation-Ca2+ signaling-contraction coupling, enabling autoregulation of contractility in cardiomyocytes in response to afterload. This MCET mechanism is integral to the individual cardiomyocyte (and thus the heart) to intrinsically enhance its contractility in response to the load against which it has to do work. While this MCET is largely compensatory for physiological load changes, it may also increase susceptibility to arrhythmias under excessive pathological loading.

Inhibition of Ca2+-dependent protein kinase C rescues high calcium-induced pro-arrhythmogenic cardiac alternans in rabbit hearts

Cardiac alternans closely linked to calcium dysregulation is a crucial risk factor for fatal arrhythmia causing especially sudden death. Calcium overload is well-known to activate Ca²⁺-dependent protein kinase C (PKC); however, the effects of PKC on arrhythmogenic cardiac alternans have not yet been investigated. This study aimed to determine the contributions of PKC activities in cardiac alternans associated with calcium cycling disturbances. In the present study, action potential duration alternans (APD-ALT) induced by high free intracellular calcium ([Ca²⁺]_i) exerted not only in a calcium concentration-dependent manner but also in a frequency-dependent manner. High [Ca²⁺]_i-induced APD-ALT was suppressed by not only BAPTA-AM but also nifedipine. On the other hand, PKC inhibitors BIM and Gö 6976 eliminated high [Ca²⁺]_i-induced APD-ALT, and PKC activator PMA was found to induce APD-ALT at normal [Ca²⁺]_i condition. Furthermore, BIM effectively prevented calcium transient alternans (CaT-ALT) and even CaT disorders caused by calcium overload. Moreover, BIM not only eliminated electrocardiographic T-wave alternans (TWA) caused by calcium dysregulation, but also lowered the incidence of ventricular arrhythmias in isolated hearts. What's more, BIM prevented the expression of PKC α upregulated by calcium overload in high calcium-perfused hearts. We firstly found that pharmacologically inhibiting Ca²⁺-dependent PKC over-activation suppressed high [Ca²⁺]_i-induced cardiac alternans. This recognition indicates that inhibition of PKC activities may become a therapeutic target for the prevention of pro-arrhythmogenic cardiac alternans associated with calcium dysregulation.

Mechanisms underlying age-associated manifestation of cardiac sodium channel gain-of-function

Cardiac action potentials are initiated by sodium ion (Na+) influx through voltage-gated Na+ channels. Na+ channel gain-of-function (GOF) can arise in inherited conditions due to mutations in the gene encoding the cardiac Na+ channel, such as Long QT syndrome type 3 (LQT3). LQT3 can be a "concealed" disease, as patients with LQT3-associated mutations can remain asymptomatic until later in life; however, arrhythmias can also arise early in life in LQT3 patients, demonstrating a complex age-associated manifestation. We and others recently demonstrated that cardiac Na+ channels preferentially localize at the intercalated disc (ID) in adult cardiac tissue, which facilitates ephaptic coupling and formation of intercellular Na+ nanodomains that regulate pro-arrhythmic early afterdepolarization (EAD) formation in tissue with Na+ channel GOF. Several properties related to ephaptic coupling vary with age, such as cell size and Na+ channel and gap junction (GJ) expression and distribution: neonatal cells have immature IDs, with Na+ channels and GJs primarily diffusively distributed, while adult myocytes have mature IDs with preferentially localized Na+ channels and GJs. Here, we perform an in silico study varying critical age-dependent parameters to investigate mechanisms underlying age-associated manifestation of Na+ channel GOF in a model of guinea pig cardiac tissue. Simulations predict that total Na+ current conductance is a critical factor in action potential duration (APD) prolongation. We find a complex cell size/ Na+ channel expression relationship: increases in cell size (without concurrent increases in Na+ channel expression) suppress EAD formation, while increases in Na+ channel expression (without concurrent increases in cell size) promotes EAD formation. Finally, simulations with neonatal and early age-associated parameters predict normal APD with minimal dependence on intercellular cleft width; however, variability in cellular properties can lead to EADs presenting in early developmental stages. In contrast, for adult-associated parameters, EAD formation is highly dependent on cleft width, consistent with a mechanism underlying the age-associated manifestation of the Na+ channel GOF.

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.

Intercellular Sodium Regulates Repolarization in Cardiac Tissue with Sodium Channel Gain of Function

In cardiac myocytes, action potentials are initiated by an influx of sodium (Na⁺) ions via voltage-gated Na⁺ channels. Na⁺ channel gain of function (GOF), arising in both inherited conditions associated with mutation in the gene encoding the Na⁺ channel and acquired conditions associated with heart failure, ischemia, and atrial fibrillation, enhance Na⁺ influx, generating a late Na⁺ current that prolongs action potential duration (APD) and triggering proarrhythmic early afterdepolarizations (EADs). Recent studies have shown that Na⁺ channels are highly clustered at the myocyte intercalated disk, facilitating formation of Na⁺ nanodomains in the intercellular cleft between cells. Simulations from our group have recently predicted that narrowing the width of the intercellular cleft can suppress APD prolongation and EADs in the presence of Na⁺ channel mutations because of increased intercellular cleft Na⁺ ion depletion. In this study, we investigate the effects of modulating multiple extracellular spaces, specifically the intercellular cleft and bulk interstitial space, in a novel computational model and experimentally via osmotic agents albumin, dextran 70, and mannitol. We perform optical mapping and transmission electron microscopy in a drug-induced (sea anemone toxin, ATXII) Na⁺ channel GOF isolated heart model and modulate extracellular spaces via osmotic agents. Single-cell patch-clamp experiments confirmed that the osmotic agents individually do not enhance late Na⁺ current. Both experiments and simulations are consistent with the conclusion that intercellular cleft narrowing or expansion regulates APD prolongation; in contrast, modulating the bulk interstitial space has negligible effects on repolarization. Thus, we predict that intercellular cleft Na⁺ nanodomain formation and collapse critically regulates cardiac repolarization in the setting of Na⁺ channel GOF.

Interplay between ephaptic coupling and complex geometry of border zone during acute myocardial ischemia: Effect on arrhythmogeneity

Acute myocardial ischemia is an imbalance between myocardial blood supply and demand, which is caused by the cessation of blood flow within the heart resulting from an obstruction in one of the major coronary arteries. A severe blockage may result in a region of nonperfused tissue known as ischemic core (IC). As a result, a border zone (BZ) between perfused and nonperfused regions is created due to differences in blood and oxygen supplies. Recent experimental findings reveal a complex "finger-like" geometry in BZ; however, its effect on arrhythmogenicity is not clear. Ephaptic coupling, which relies on the intercalated disk between cell ends, has been suggested to play an active role in mediating intercellular electrical communication when gap junctions are impaired. In this paper, we explored the interplay between ephaptic coupling and the geometry of BZ on action potential propagation across the ischemic region. Our study shows that ephaptic coupling can greatly suppress the occurrence of a conduction block, which points to its beneficial effect. The beneficial effect of ephaptic coupling is more evident in BZ with the "finger-like" geometry. In addition, the complex geometry of BZ, i.e., more frequent, deeper, and wider "fingers," promotes the conduction through the ischemic region. In contrast, the larger size of IC impedes the cardiac conduction across the ischemic region. Our results also show that ephaptic coupling promotes the impact of the complex geometry of BZ on signal propagation; however, it inhibits the impact of IC size.

Mechanistic investigation of Ca2+ alternans in human heart failure and its modulation by fibroblasts

Background

Heart failure (HF) is characterized, among other factors, by a progressive loss of contractile function and by the formation of an arrhythmogenic substrate, both aspects partially related to intracellular Ca²⁺ cycling disorders. In failing hearts both electrophysiological and structural remodeling, including fibroblast proliferation, contribute to changes in Ca²⁺ handling which promote the appearance of Ca²⁺ alternans (Ca-alt). Ca-alt in turn give rise to repolarization alternans, which promote dispersion of repolarization and contribute to reentrant activity. The computational analysis of the incidence of Ca²⁺ and/or repolarization alternans under HF conditions in the presence of fibroblasts could provide a better understanding of the mechanisms leading to HF arrhythmias and contractile function disorders.

Methods and findings

The goal of the present study was to investigate in silico the mechanisms leading to the formation of Ca-alt in failing human ventricular myocytes and tissues with disperse fibroblast distributions. The contribution of ionic currents variability to alternans formation at the cellular level was analyzed and the results show that in normal ventricular tissue, altered Ca²⁺ dynamics lead to Ca-alt, which precede APD alternans and can be aggravated by the presence of fibroblasts. Electrophysiological remodeling of failing tissue alone is sufficient to develop alternans. The incidence of alternans is reduced when fibroblasts are present in failing tissue due to significantly depressed Ca²⁺ transients. The analysis of the underlying ionic mechanisms suggests that Ca-alt are driven by Ca²⁺-handling protein and Ca²⁺ cycling dysfunctions in the junctional sarcoplasmic reticulum and that their contribution to alternans occurrence depends on the cardiac remodeling conditions and on myocyte-fibroblast interactions.

Conclusion

It can thus be concluded that fibroblasts modulate the formation of Ca-alt in human ventricular tissue subjected to heart failure-related electrophysiological remodeling. Pharmacological therapies should thus consider the extent of both the electrophysiological and structural remodeling present in the failing heart.

Abnormal synchronization patterns in the electrical stimulation-contractile response coupling decrease with noise

Synchronization theory predicts that if an oscillator interacts with a rhythmical external force, then it should react to a rhythmical force by adjusting its frequency. Furthermore, noise is present in nature, and it affects the nervous and cardiovascular systems. In this paper, we analyze the heart as an oscillator, where noisy periodic electrical stimulation can be regarded as an external forcing. This study aimed to investigate, from an experimental point of view, whether noise can induce synchronization of higher order in the mechanical heart response. A Langendorff heart preparation was used to obtain two variables of the mechanical response, intensity of contractile force and heart rate. The experiments show frequency locking in the electrical stimulation-contractile response coupling with and without noise induced. The role of noise in the response of effector organs invites further investigation.

Computing Optimal Properties of Drugs Using Mathematical Models of Single Channel Dynamics

Single channel dynamics can be modeled using stochastic differential equations, and the dynamics of the state of the channel (e.g. open, closed, inactivated) can be represented using Markov models. Such models can also be used to represent the effect of mutations as well as the effect of drugs used to alleviate deleterious effects of mutations. Based on the Markov model and the stochastic models of the single channel, it is possible to derive deterministic partial differential equations (PDEs) giving the probability density functions (PDFs) of the states of the Markov model. In this study, we have analyzed PDEs modeling wild type (WT) channels, mutant channels (MT) and mutant channels for which a drug has been applied (MTD). Our aim is to show that it is possible to optimize the parameters of a given drug such that the solution of theMTD model is very close to that of the WT: the mutation’s effect is, theoretically, reduced significantly.We will present the mathematical framework underpinning this methodology and apply it to several examples. In particular, we will show that it is possible to use the method to, theoretically, improve the properties of some well-known existing drugs.

Modulation of Cardiac Alternans by Altered Sarcoplasmic Reticulum Calcium Release: A Simulation Study

Background: Cardiac alternans is an important precursor to arrhythmia, facilitating formation of conduction block, and re-entry. Diseased hearts were observed to be particularly vulnerable to alternans, mainly in heart failure or after myocardial infarction. Alternans is typically linked to oscillation of calcium cycling, particularly in the sarcoplasmic reticulum (SR). While the role of SR calcium reuptake in alternans is well established, the role of altered calcium release by ryanodine receptors has not yet been studied extensively. At the same time, there is strong evidence that calcium release is abnormal in heart failure and other heart diseases, suggesting that these changes might play a pro-alternans role.

Aims: To demonstrate how changes to intracellular calcium release dynamics and magnitude affect alternans vulnerability.

Methods: We used the state-of-the-art Heijman–Rudy and O’Hara–Rudy computer models of ventricular myocyte, given their detailed representation of calcium handling and their previous utility in alternans research. We modified the models to obtain precise control over SR release dynamics and magnitude, allowing for the evaluation of these properties in alternans formation and suppression.

Results: Shorter time to peak SR release and shorter release duration decrease alternans vulnerability by improved refilling of releasable calcium within junctional SR; conversely, slow release promotes alternans. Modulating the total amount of calcium released, we show that sufficiently increased calcium release may surprisingly prevent alternans via a mechanism linked to the functional depletion of junctional SR during release. We show that this mechanism underlies differences between “eye-type” and “fork-type” alternans, which were observed in human in vivo and in silico. We also provide a detailed explanation of alternans formation in the given computer models, termed “sarcoplasmic reticulum calcium cycling refractoriness.” The mechanism relies on the steep SR load–release relationship, combined with relatively limited rate of junctional SR refilling.

Conclusion: Both altered dynamics and magnitude of SR calcium release modulate alternans vulnerability. In particular, slow dynamics of SR release, such as those observed in heart failure, promote alternans. Therefore, acceleration of intracellular calcium release, e.g., via synchronization of calcium sparks, may inhibit alternans in failing hearts and reduce arrhythmia occurrence.

A Comprehensive In Silico Method to Study the QSTR of the Aconitine Alkaloids for Designing Novel Drugs

A combined in silico method was developed to predict potential protein targets that are involved in cardiotoxicity induced by aconitine alkaloids and to study the quantitative structure⁻toxicity relationship (QSTR) of these compounds. For the prediction research, a Protein-Protein Interaction (PPI) network was built from the extraction of useful information about protein interactions connected with aconitine cardiotoxicity, based on nearly a decade of literature and the STRING database. The software Cytoscape and the PharmMapper server were utilized to screen for essential proteins in the constructed network. The Calcium-Calmodulin-Dependent Protein Kinase II alpha (CAMK2A) and gamma (CAMK2G) were identified as potential targets. To obtain a deeper insight on the relationship between the toxicity and the structure of aconitine alkaloids, the present study utilized QSAR models built in Sybyl software that possess internal robustness and external high predictions. The molecular dynamics simulation carried out here have demonstrated that aconitine alkaloids possess binding stability for the receptor CAMK2G. In conclusion, this comprehensive method will serve as a tool for following a structural modification of the aconitine alkaloids and lead to a better insight into the cardiotoxicity induced by the compounds that have similar structures to its derivatives.

Complex restitution behavior and reentry in a cardiac tissue model for neonatal mice

Spatiotemporal dynamics in cardiac tissue emerging from the coupling of individual cardiomyocytes underlie the heart's normal rhythm as well as undesired and possibly life-threatening arrhythmias. While single cells and their transmembrane currents have been studied extensively, systematically investigating spatiotemporal dynamics is complicated by the nontrivial relationship between single-cell and emergent tissue properties. Mathematical models have been employed to bridge this gap and contribute to a deepened understanding of the onset, development, and termination of arrhythmias. However, no such tissue-level model currently exists for neonatal mice. Here, we build on a recent single-cell model of neonatal mouse cardiomyocytes by Wang and Sobie (Am. J. Physiol. Heart Circ. Physiol 294:H2565) to predict properties that are commonly used to gauge arrhythmogenicity of cardiac substrates. We modify the model to yield well-defined behavior for common experimental protocols and construct a spatially extended version to study emergent tissue dynamics. We find a complex action potential duration (APD) restitution behavior characterized by a nonmonotonic dependence on pacing frequency. Electrotonic coupling in tissue leads not only to changes in action potential morphology but can also induce spatially concordant and discordant alternans not observed in the single-cell model. In two-dimensional tissue, our results show that the model supports stable functional reentry, whose frequency is in good agreement with that observed in adult mice. Our results can be used to further constrain and validate the mathematical model of neonatal mouse cardiomyocytes with future experiments.

Illuminating Myocyte-Fibroblast Homotypic and Heterotypic Gap Junction Dynamics Using Dynamic Clamp

Fibroblasts play a significant role in the development of electrical and mechanical dysfunction of the heart; however, the underlying mechanisms are only partially understood. One widely studied mechanism suggests that fibroblasts produce excess extracellular matrix, resulting in collagenous septa that slow propagation, cause zig-zag conduction paths, and decouple cardiomyocytes, resulting in a substrate for cardiac arrhythmia. An emerging mechanism suggests that fibroblasts promote arrhythmogenesis through direct electrical interactions with cardiomyocytes via gap junction (GJ) channels. In the heart, three major connexin (Cx) isoforms, Cx40, Cx43, and Cx45, form GJ channels in cell-type-specific combinations. Because each Cx is characterized by a unique time- and transjunctional voltage-dependent profile, we investigated whether the electrophysiological contributions of fibroblasts would vary with the specific composition of the myocyte-fibroblast (M-F) GJ channel. Due to the challenges of systematically modifying Cxs in vitro, we coupled native cardiomyocytes with in silico fibroblast and GJ channel electrophysiology models using the dynamic-clamp technique. We found that there is a reduction in the early peak of the junctional current during the upstroke of the action potential (AP) due to GJ channel gating. However, effects on the cardiomyocyte AP morphology were similar regardless of the specific type of GJ channel (homotypic Cx43 and Cx45, and heterotypic Cx43/Cx45 and Cx45/Cx43). To illuminate effects at the tissue level, we performed multiscale simulations of M-F coupling. First, we developed a cell-specific model of our dynamic-clamp experiments and investigated changes in the underlying membrane currents during M-F coupling. Second, we performed two-dimensional tissue sheet simulations of cardiac fibrosis and incorporated GJ channels in a cell type-specific manner. We determined that although GJ channel gating reduces junctional current, it does not significantly alter conduction velocity during cardiac fibrosis relative to static GJ coupling. These findings shed more light on the complex electrophysiological interplay between cardiac fibroblasts and myocytes.

Revealing the Concealed Nature of Long-QT Type 3 Syndrome

BACKGROUND

Gain-of-function mutations in the voltage-gated sodium channel (Nav1.5) are associated with the long-QT-3 (LQT3) syndrome. Nav1.5 is densely expressed at the intercalated disk, and narrow intercellular separation can modulate cell-to-cell coupling via extracellular electric fields and depletion of local sodium ion nanodomains. Models predict that significantly decreasing intercellular cleft widths slows conduction because of reduced sodium current driving force, termed "self-attenuation." We tested the novel hypothesis that self-attenuation can "mask" the LQT3 phenotype by reducing the driving force and late sodium current that produces early afterdepolarizations (EADs).

METHODS AND RESULTS

Acute interstitial edema was used to increase intercellular cleft width in isolated guinea pig heart experiments. In a drug-induced LQT3 model, acute interstitial edema exacerbated action potential duration prolongation and produced EADs, in particular, at slow pacing rates. In a computational cardiac tissue model incorporating extracellular electric field coupling, intercellular cleft sodium nanodomains, and LQT3-associated mutant channels, myocytes produced EADs for wide intercellular clefts, whereas for narrow clefts, EADs were suppressed. For both wide and narrow clefts, mutant channels were incompletely inactivated. However, for narrow clefts, late sodium current was reduced via self-attenuation, a protective negative feedback mechanism, masking EADs.

CONCLUSIONS

We demonstrated a novel mechanism leading to the concealing and revealing of EADs in LQT3 models. Simulations predict that this mechanism may operate independent of the specific mutation, suggesting that future therapies could target intercellular cleft separation as a compliment or alternative to sodium channels.

Alternans in atria: Mechanisms and clinical relevance

Atrial fibrillation is the most common sustained arrhythmia and its prevalence is rapidly rising with the aging of the population. Cardiac alternans, defined as cyclic beat-to-beat alternations in contraction force, action potential (AP) duration and intracellular Ca²⁺ release at constant stimulation rate, has been associated with the development of ventricular arrhythmias. Recent clinical data also provide strong evidence that alternans plays a central role in arrhythmogenesis in atria. The aim of this article is to review the mechanisms that are responsible for repolarization alternans and contribute to the transition from spatially concordant alternans to the more arrhythmogenic spatially discordant alternans in atria.

β-Adrenergic receptor stimulation inhibits proarrhythmic alternans in postinfarction border zone cardiomyocytes: a computational analysis

We integrated, for the first time, postmyocardial infarction electrical and autonomic remodeling in a detailed, validated computer model of β-adrenergic stimulation in ventricular cardiomyocytes. Here, we show that β-adrenergic stimulation inhibits alternans and provide novel insights into underlying mechanisms, adding to a recent controversy about pro-/antiarrhythmic effects of postmyocardial infarction hyperinnervation.

The border zone (BZ) of the viable myocardium adjacent to an infarct undergoes extensive autonomic and electrical remodeling and is prone to repolarization alternans-induced cardiac arrhythmias. BZ remodeling processes may promote or inhibit Ca²⁺ and/or repolarization alternans and may differentially affect ventricular arrhythmogenesis. Here, we used a detailed computational model of the canine ventricular cardiomyocyte to study the determinants of alternans in the BZ and their regulation by β-adrenergic receptor (β-AR) stimulation. The BZ model developed Ca²⁺ transient alternans at slower pacing cycle lengths than the control model, suggesting that the BZ may promote spatially heterogeneous alternans formation in an infarcted heart. β-AR stimulation abolished alternans. By evaluating all combinations of downstream β-AR stimulation targets, we identified both direct (via ryanodine receptor channels) and indirect [via sarcoplasmic reticulum (SR) Ca²⁺ load] modulation of SR Ca²⁺ release as critical determinants of Ca²⁺ transient alternans. These findings were confirmed in a human ventricular cardiomyocyte model. Cell-to-cell coupling indirectly modulated the likelihood of alternans by affecting the action potential upstroke, reducing the trigger for SR Ca²⁺ release in one-dimensional strand simulations. However, β-AR stimulation inhibited alternans in both single and multicellular simulations. Taken together, these data highlight a potential antiarrhythmic role of sympathetic hyperinnervation in the BZ by reducing the likelihood of alternans and provide new insights into the underlying mechanisms controlling Ca²⁺ transient and repolarization alternans.

NEW & NOTEWORTHY We integrated, for the first time, postmyocardial infarction electrical and autonomic remodeling in a detailed, validated computer model of β-adrenergic stimulation in ventricular cardiomyocytes. Here, we show that β-adrenergic stimulation inhibits alternans and provide novel insights into underlying mechanisms, adding to a recent controversy about pro-/antiarrhythmic effects of postmyocardial infarction hyperinnervation.

Listen to this article’s corresponding podcast at http://ajpheart.podbean.com/e/%CE%B2-ar-stimulation-and-alternans-in-border-zone-cardiomyocytes/.

A Precision Medicine Approach to the Rescue of Function on Malignant Calmodulinopathic Long-QT Syndrome

RATIONALE

Calmodulinopathies comprise a new category of potentially life-threatening genetic arrhythmia syndromes capable of producing severe long-QT syndrome (LQTS) with mutations involving CALM1, CALM2, or CALM3. The underlying basis of this form of LQTS is a disruption of Ca²⁺/calmodulin (CaM)-dependent inactivation of L-type Ca²⁺ channels.

OBJECTIVE

To gain insight into the mechanistic underpinnings of calmodulinopathies and devise new therapeutic strategies for the treatment of this form of LQTS.

METHODS AND RESULTS

We generated and characterized the functional properties of induced pluripotent stem cell-derived cardiomyocytes from a patient with D130G-CALM2-mediated LQTS, thus creating a platform with which to devise and test novel therapeutic strategies. The patient-derived induced pluripotent stem cell-derived cardiomyocytes display (1) significantly prolonged action potentials, (2) disrupted Ca²⁺ cycling properties, and (3) diminished Ca²⁺/CaM-dependent inactivation of L-type Ca²⁺ channels. Next, taking advantage of the fact that calmodulinopathy patients harbor a mutation in only 1 of 6 redundant CaM-encoding alleles, we devised a strategy using CRISPR interference to selectively suppress the mutant gene while sparing the wild-type counterparts. Indeed, suppression of CALM2 expression produced a functional rescue in induced pluripotent stem cell-derived cardiomyocytes with D130G-CALM2, as shown by the normalization of action potential duration and Ca²⁺/CaM-dependent inactivation after treatment. Moreover, CRISPR interference can be designed to achieve selective knockdown of any of the 3 CALM genes, making it a generalizable therapeutic strategy for any calmodulinopathy.

CONCLUSIONS

Overall, this therapeutic strategy holds great promise for calmodulinopathy patients as it represents a generalizable intervention capable of specifically altering CaM expression and potentially attenuating LQTS-triggered cardiac events, thus initiating a path toward precision medicine.

The dual effect of ephaptic coupling on cardiac conduction with heterogeneous expression of connexin 43

Decreased and heterogeneous expression of connexin 43 (Cx43) are common features in animal heart failure models. Ephpatic coupling, which relies on the presence of junctional cleft space between the ends of adjacent cells, has been suggested to play a more active role in mediating intercellular electrical communication when gap junctions are reduced. To better understand the interplay of Cx43 expression and ephaptic coupling on cardiac conduction during heart failure, we performed numerical simulations on our model when Cx43 expression is reduced and heterogeneous. Under severely reduced Cx43 expression, we identified three new phenomena in the presence of ephaptic coupling: alternating conduction, in which ephaptic and gap junction-mediated mechanisms alternate; instability of planar fronts; and small amplitude action potential (SAP), which has a smaller potential amplitude than the normal action potential. In the presence of heterogeneous Cx43 expression, ephaptic coupling can either prevent or promote conduction block (CB) depending on the Cx43 knockout (Cx43KO) content. When Cx43KO content is relatively high, ephaptic coupling reduces the probabilities of CB. However, ephaptic coupling promotes CB when Cx43KO and wild type cells are mixed in roughly equal proportion, which can be attributed to an increase in current-to-load mismatch.

Arrhythmogenesis in Timothy Syndrome is associated with defects in Ca(2+)-dependent inactivation

Timothy Syndrome (TS) is a multisystem disorder, prominently featuring cardiac action potential prolongation with paroxysms of life-threatening arrhythmias. The underlying defect is a single de novo missense mutation in Ca_V1.2 channels, either G406R or G402S. Notably, these mutations are often viewed as equivalent, as they produce comparable defects in voltage-dependent inactivation and cause similar manifestations in patients. Yet, their effects on calcium-dependent inactivation (CDI) have remained uncertain. Here, we find a significant defect in CDI in TS channels, and uncover a remarkable divergence in the underlying mechanism for G406R versus G402S variants. Moreover, expression of these TS channels in cultured adult guinea pig myocytes, combined with a quantitative ventricular myocyte model, reveals a threshold behaviour in the induction of arrhythmias due to TS channel expression, suggesting an important therapeutic principle: a small shift in the complement of mutant versus wild-type channels may confer significant clinical improvement.

Timothy Syndrome (TS) is a multisystem disorder caused by two mutations leading to dysfunction of the Ca_V1.2 channel. Here, Dick et al. uncover a major and mechanistically divergent effect of both mutations on Ca²⁺/calmodulin-dependent inactivation of Ca_V1.2 channels, suggesting genetic variant-tailored therapy for TS treatment.

Myokit: A simple interface to cardiac cellular electrophysiology

Myokit is a new powerful and versatile software tool for modeling and simulation of cardiac cellular electrophysiology. Myokit consists of an easy-to-read modeling language, a graphical user interface, single and multi-cell simulation engines and a library of advanced analysis tools accessible through a Python interface. Models can be loaded from Myokit's native file format or imported from CellML. Model export is provided to C, MATLAB, CellML, CUDA and OpenCL. Patch-clamp data can be imported and used to estimate model parameters. In this paper, we review existing tools to simulate the cardiac cellular action potential to find that current tools do not cater specifically to model development and that there is a gap between easy-to-use but limited software and powerful tools that require strong programming skills from their users. We then describe Myokit's capabilities, focusing on its model description language, simulation engines and import/export facilities in detail. Using three examples, we show how Myokit can be used for clinically relevant investigations, multi-model testing and parameter estimation in Markov models, all with minimal programming effort from the user. This way, Myokit bridges a gap between performance, versatility and user-friendliness.

Modeling calcium regulation of contraction, energetics, signaling, and transcription in the cardiac myocyte

Calcium (Ca(2+)) plays many important regulatory roles in cardiac muscle cells. In the initial phase of the action potential, influx of Ca(2+) through sarcolemmal voltage-gated L-type Ca(2+) channels (LCCs) acts as a feed-forward signal that triggers a large release of Ca(2+) from the junctional sarcoplasmic reticulum (SR). This Ca(2+) drives heart muscle contraction and pumping of blood in a process known as excitation-contraction coupling (ECC). Triggered and released Ca(2+) also feed back to inactivate LCCs, attenuating the triggered Ca(2+) signal once release has been achieved. The process of ECC consumes large amounts of ATP. It is now clear that in a process known as excitation-energetics coupling, Ca(2+) signals exert beat-to-beat regulation of mitochondrial ATP production that closely couples energy production with demand. This occurs through transport of Ca(2+) into mitochondria, where it regulates enzymes of the tricarboxylic acid cycle. In excitation-signaling coupling, Ca(2+) activates a number of signaling pathways in a feed-forward manner. Through effects on their target proteins, these interconnected pathways regulate Ca(2+) signals in complex ways to control electrical excitability and contractility of heart muscle. In a process known as excitation-transcription coupling, Ca(2+) acting primarily through signal transduction pathways also regulates the process of gene transcription. Because of these diverse and complex roles, experimentally based mechanistic computational models are proving to be very useful for understanding Ca(2+) signaling in the cardiac myocyte.

Implementation of Contraction to Electrophysiological Ventricular Myocyte Models, and Their Quantitative Characterization via Post-Extrasystolic Potentiation

Heart failure (HF) affects over 5 million Americans and is characterized by impairment of cellular cardiac contractile function resulting in reduced ejection fraction in patients. Electrical stimulation such as cardiac resynchronization therapy (CRT) and cardiac contractility modulation (CCM) have shown some success in treating patients with HF. Computer simulations have the potential to help improve such therapy (e.g. suggest optimal lead placement) as well as provide insight into the underlying mechanisms which could be beneficial. However, these myocyte models require a quantitatively accurate excitation-contraction coupling such that the electrical and contraction predictions are correct. While currently there are close to a hundred models describing the detailed electrophysiology of cardiac cells, the majority of cell models do not include the equations to reproduce contractile force or they have been added ad hoc. Here we present a systematic methodology to couple first generation contraction models into electrophysiological models via intracellular calcium and then compare the resulting model predictions to experimental data. This is done by using a post-extrasystolic pacing protocol, which captures essential dynamics of contractile forces. We found that modeling the dynamic intracellular calcium buffers is necessary in order to reproduce the experimental data. Furthermore, we demonstrate that in models the mechanism of the post-extrasystolic potentiation is highly dependent on the calcium released from the Sarcoplasmic Reticulum. Overall this study provides new insights into both specific and general determinants of cellular contractile force and provides a framework for incorporating contraction into electrophysiological models, both of which will be necessary to develop reliable simulations to optimize electrical therapies for HF.

ELECTRICAL INSTABILITY DUE TO REGIONAL INCREASE IN EXTRACELLULAR POTASSIUM ION CONCENTRATION

INTRODUCTION

Ventricular tachycardia and ventricular fibrillation are the two most dangerous arrhythmias. Both are related to reentrant electrical activity in the ventricles. Many studies of arrhythmias consider a homogeneous sheet of cardiac tissue. Since normal ventricular myocardium is inhomogeneous and inhomogeneities play an important role in the induction of reentry, we investigate the effect of a localized inhomogeniety developed at the border between normal and ischemic region.

METHODS

We used the bidomain model to represent the electrical properties of cardiac tissue and a modified version of the dynamic Luo-Rudy (LRd) model to represent the active properties of the membrane. To investigate the effect of a localized inhomogeneity, the extracellular potassium [K]e concentration is raised to 10 mM from normal [K]e (4 mM) on the right half of the tissue.

RESULTS AND DISCUSSION

A train of cathodal stimuli are applied from the lower left corner of the tissue with different basic cycle lengths (BCL). At certain BCL, the spatial heterogeneity created with regional elevation of [K]e can lead to action potential instability (alternans) in the normal and border regions, and 2:1 conduction block in the ischemic region. We observed the reentry when local heterogeneity in [K]e is changed from 10 to 12 mM on the right half of the virtual ventricular myocardium sheet.

CONCLUSION

Electrical alternans occur during high heart rates and are observed in patients suffering from ventricular tachycardia. It is an early indication of left ventricular systolic impairment. This study will help to evaluate alternans as a predictor and guide for antiarrhythmic therapy.

Cellular cardiac electrophysiology modeling with Chaste and CellML

Chaste is an open-source C++ library for computational biology that has well-developed cardiac electrophysiology tissue simulation support. In this paper, we introduce the features available for performing cardiac electrophysiology action potential simulations using a wide range of models from the Physiome repository. The mathematics of the models are described in CellML, with units for all quantities. The primary idea is that the model is defined in one place (the CellML file), and all model code is auto-generated at compile or run time; it never has to be manually edited. We use ontological annotation to identify model variables describing certain biological quantities (membrane voltage, capacitance, etc.) to allow us to import any relevant CellML models into the Chaste framework in consistent units and to interact with them via consistent interfaces. This approach provides a great deal of flexibility for analysing different models of the same system. Chaste provides a wide choice of numerical methods for solving the ordinary differential equations that describe the models. Fixed-timestep explicit and implicit solvers are provided, as discussed in previous work. Here we introduce the Rush–Larsen and Generalized Rush–Larsen integration techniques, made available via symbolic manipulation of the model equations, which are automatically rearranged into the forms required by these approaches. We have also integrated the CVODE solvers, a ‘gold standard’ for stiff systems, and we have developed support for symbolic computation of the Jacobian matrix, yielding further increases in the performance and accuracy of CVODE. We discuss some of the technical details of this work and compare the performance of the available numerical methods. Finally, we discuss how this is generalized in our functional curation framework, which uses a domain-specific language for defining complex experiments as a basis for comparison of model behavior.

Disrupted calcium release as a mechanism for atrial alternans associated with human atrial fibrillation

Atrial fibrillation (AF) is the most common cardiac arrhythmia, but our knowledge of the arrhythmogenic substrate is incomplete. Alternans, the beat-to-beat alternation in the shape of cardiac electrical signals, typically occurs at fast heart rates and leads to arrhythmia. However, atrial alternans have been observed at slower pacing rates in AF patients than in controls, suggesting that increased vulnerability to arrhythmia in AF patients may be due to the proarrythmic influence of alternans at these slower rates. As such, alternans may present a useful therapeutic target for the treatment and prevention of AF, but the mechanism underlying alternans occurrence in AF patients at heart rates near rest is unknown. The goal of this study was to determine how cellular changes that occur in human AF affect the appearance of alternans at heart rates near rest. To achieve this, we developed a computational model of human atrial tissue incorporating electrophysiological remodeling associated with chronic AF (cAF) and performed parameter sensitivity analysis of ionic model parameters to determine which cellular changes led to alternans. Of the 20 parameters tested, only decreasing the ryanodine receptor (RyR) inactivation rate constant (ki_Ca) produced action potential duration (APD) alternans seen clinically at slower pacing rates. Using single-cell clamps of voltage, fluxes, and state variables, we determined that alternans onset was Ca²⁺-driven rather than voltage-driven and occurred as a result of decreased RyR inactivation which led to increased steepness of the sarcoplasmic reticulum (SR) Ca²⁺ release slope. Iterated map analysis revealed that because SR Ca²⁺ uptake efficiency was much higher in control atrial cells than in cAF cells, drastic reductions in ki_Ca were required to produce alternans at comparable pacing rates in control atrial cells. These findings suggest that RyR kinetics may play a critical role in altered Ca²⁺ homeostasis which drives proarrhythmic APD alternans in patients with AF.

Atrial fibrillation is an irregular heart rhythm affecting millions of people worldwide. Effective treatment of this cardiac disorder relies upon our detailed knowledge and understanding of the mechanisms that lead to arrhythmia. Recent clinical observations have suggested that alternans, a phenomenon where the shape of the electrical signal in the heart alternates from beat to beat, may play an important role in this process, but the underlying mechanisms remain unknown. In this study, we use computational models to conduct a detailed examination of the causes and contributors to alternans associated with human atrial fibrillation. We find that in atria remodeled by atrial fibrillation, alternans appears near resting heart rates because several aspects of calcium cycling are disrupted in the atrial cells. In particular, the release and uptake of calcium from the cellular storage compartment, the sarcoplasmic reticulum, becomes imbalanced, leading to alternation in calcium signals from beat to beat. These findings provide important insights into the mechanisms of proarrhythmic alternans in human atrial fibrillation which may be used to develop novel therapeutic targets and treatment strategies in the future.

Targeted antioxidant treatment decreases cardiac alternans associated with chronic myocardial infarction

BACKGROUND

In myocardial infarction (MI), repolarization alternans is a potent arrhythmia substrate that has been linked to Ca2+ cycling proteins, such as sarcoplasmic reticulum Ca2+ ATPase (SERCA2a), located in the sarcoplasmic reticulum. MI is also associated with oxidative stress and increased xanthine oxidase (XO) activity, an important source of reactive oxygen species (ROS) in the sarcoplasmic reticulum that may reduce SERCA2a function. We hypothesize that in chronic MI, XO-mediated oxidation of SERCA2a is a mechanism of cardiac alternans.

METHODS AND RESULTS

Male Lewis rats underwent ligation of the left anterior descending coronary artery (n=54) or sham procedure (n=24). At 4 weeks, optical mapping of intracellular Ca2+ and ROS was performed. ECG T-wave alternans (ECG ALT) and Ca2+ transient alternans (Ca2+ALT) were induced by rapid pacing (300-120 ms) before and after the XO inhibitor allopurinol (ALLO, 50 µmol/L). In MI, ECG ALT (2.32±0.41%) and Ca2+ ALT (22.3±4.5%) were significantly greater compared with sham (0.18±0.08%, P<0.001; 0.79±0.32%, P<0.01). Additionally, ROS was increased by 137% (P<0.01) and oxidation of SERCA2a by 30% (P<0.05) in MI compared with sham. Treatment with ALLO significantly decreased ECG ALT (-77±9%, P<0.05) and Ca2+ ALT (-56±7%, P<0.05) and, importantly, reduced ROS (-65%, P<0.01) and oxidation of SERCA2a (-38%, P<0.05). CaMKII inhibition and general antioxidant treatment had no effect on ECG ALT and Ca2+ ALT.

CONCLUSIONS

These results demonstrate, for the first time, that in MI, increased ROS from XO is a significant cause of repolarization alternans. This suggests that targeting XO ROS production may be effective at preventing arrhythmia substrates in chronic MI.

Cellular mechanism of cardiac alternans: an unresolved chicken or egg problem

T-wave alternans, a specific form of cardiac alternans, has been associated with the increased susceptibility to cardiac arrhythmias and sudden cardiac death (SCD). Plenty of evidence has related cardiac alternans at the tissue level to the instability of voltage kinetics or Ca(2+) handling dynamics at the cellular level. However, to date, none of the existing experiments could identify the exact cellular mechanism of cardiac alternans due to the bi-directional coupling between voltage kinetics and Ca(2+) handling dynamics. Either of these systems could be the origin of alternans and the other follows as a secondary change, therefore making the cellular mechanism of alternans a difficult chicken or egg problem. In this context, theoretical analysis combined with experimental techniques provides a possibility to explore this problem. In this review, we will summarize the experimental and theoretical advances in understanding the cellular mechanism of alternans. We focus on the roles of action potential duration (APD) restitution and Ca(2+) handling dynamics in the genesis of alternans and show how the theoretical analysis combined with experimental techniques has provided us a new insight into the cellular mechanism of alternans. We also discuss the possible reasons of increased propensity for alternans in heart failure (HF) and the new possible therapeutic targets. Finally, according to the level of electrophysiological recording techniques and theoretical strategies, we list some critical experimental or theoretical challenges which may help to determine the origin of alternans and to find more effective therapeutic targets in the future.

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

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

Mathematical modeling of physiological systems: an essential tool for discovery

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

Ca2+/calmodulin-dependent protein kinase II increases the susceptibility to the arrhythmogenic action potential alternans in spontaneously hypertensive rats

Action potential duration alternans (APD-ALT), defined as long-short-long repetitive pattern of APD, potentially leads to lethal ventricular arrhythmia. However, the mechanisms of APD-ALT in the arrhythmogenesis of cardiac hypertrophy remain undetermined. Ca2+/calmodulin-dependent protein kinase II (CaMKII) is known to modulate the function of cardiac sarcoplasmic reticulum and play an important role in Ca2+ cycling. We thus aimed to determine the role of CaMKII in the increased susceptibility to APD-ALT and arrhythmogenesis in the hypertrophied heart. APD was measured by high-resolution optical mapping in left ventricular (LV) anterior wall from normotensive Wistar-Kyoto (WKY; n = 10) and spontaneously hypertensive rats (SHR; n = 10) during rapid ventricular pacing. APD-ALT was evoked at significantly lower pacing rate in SHR compared with WKY (382 ± 43 vs. 465 ± 45 beats/min, P < 0.01). These changes in APD-ALT in SHR were completely reversed by KN-93 (1 μmol/l; n = 5), an inhibitor of CaMKII, but not its inactive analog, KN-92 (1 μmol/l; n = 5). The magnitude of APD-ALT was also significantly greater in SHR than WKY and was completely normalized by KN-93. Ventricular fibrillation (VF) was induced by rapid pacing more frequently in SHR than in WKY (60 vs. 10%; P < 0.05), which was also abolished by KN-93 (0%, P < 0.05). Western blot analyses indicated that the CaMKII autophosphorylation at Thr287 was significantly increased in SHR compared with WKY. The increased susceptibility to APD-ALT and VF during rapid pacing in hypertrophied heart was prevented by KN-93. CaMKII could be an important mechanism of arrhythmogenesis in cardiac hypertrophy.

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

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

Modeling CaMKII in cardiac physiology: from molecule to tissue

Post-translational modification of membrane proteins (e.g., ion channels, receptors) by protein kinases is an essential mechanism for control of excitable cell function. Importantly, loss of temporal and/or spatial control of ion channel post-translational modification is common in congenital and acquired forms of cardiac disease and arrhythmia. The multifunctional Ca²⁺/calmodulin-dependent protein kinase II (CaMKII) regulates a number of diverse cellular functions in heart, including excitation-contraction coupling, gene transcription, and apoptosis. Dysregulation of CaMKII signaling has been implicated in human and animal models of disease. Understanding of CaMKII function has been advanced by mathematical modeling approaches well-suited to the study of complex biological systems. Early kinetic models of CaMKII function in the brain characterized this holoenzyme as a bistable molecular switch capable of storing information over a long period of time. Models of CaMKII activity have been incorporated into models of the cell and tissue (particularly in the heart) to predict the role of CaMKII in regulating organ function. Disease models that incorporate CaMKII overexpression clearly demonstrate a link between its excessive activity and arrhythmias associated with congenital and acquired heart disease. This review aims at discussing systems biology approaches that have been applied to analyze CaMKII signaling from the single molecule to intact cardiac tissue. In particular, efforts to use computational biology to provide new insight into cardiac disease mechanisms are emphasized.

Computational optogenetics: empirically-derived voltage- and light-sensitive channelrhodopsin-2 model

Channelrhodospin-2 (ChR2), a light-sensitive ion channel, and its variants have emerged as new excitatory optogenetic tools not only in neuroscience, but also in other areas, including cardiac electrophysiology. An accurate quantitative model of ChR2 is necessary for in silico prediction of the response to optical stimulation in realistic tissue/organ settings. Such a model can guide the rational design of new ion channel functionality tailored to different cell types/tissues. Focusing on one of the most widely used ChR2 mutants (H134R) with enhanced current, we collected a comprehensive experimental data set of the response of this ion channel to different irradiances and voltages, and used these data to develop a model of ChR2 with empirically-derived voltage- and irradiance- dependence, where parameters were fine-tuned via simulated annealing optimization. This ChR2 model offers: 1) accurate inward rectification in the current-voltage response across irradiances; 2) empirically-derived voltage- and light-dependent kinetics (activation, deactivation and recovery from inactivation); and 3) accurate amplitude and morphology of the response across voltage and irradiance settings. Temperature-scaling factors (Q₁₀) were derived and model kinetics was adjusted to physiological temperatures. Using optical action potential clamp, we experimentally validated model-predicted ChR2 behavior in guinea pig ventricular myocytes. The model was then incorporated in a variety of cardiac myocytes, including human ventricular, atrial and Purkinje cell models. We demonstrate the ability of ChR2 to trigger action potentials in human cardiomyocytes at relatively low light levels, as well as the differential response of these cells to light, with the Purkinje cells being most easily excitable and ventricular cells requiring the highest irradiance at all pulse durations. This new experimentally-validated ChR2 model will facilitate virtual experimentation in neural and cardiac optogenetics at the cell and organ level and provide guidance for the development of in vivo tools.

Optogenetics, the use of light-sensitive ion channels for stimulation of mammalian cells and tissues, offers specificity and superior precision of control compared to traditional chemical or electrical means of stimulation. In particular, Channelrhodospin-2 (ChR2), a light-sensitive ion channel, originally derived from algae, has found wide-spread application in neuroscience for controlled stimulation of different brain regions. More recently, this work was extended to other organs, including the heart, where it opens the possibility for a new generation of optical pacemakers. The development of new optogenetic tools that allow for more efficient optical stimulation can be guided by computational prediction of the response of different cells and tissues to light. In this report, we provide a new computational model of ChR2 that was empirically validated and can be inserted into different cell types – neurons or heart cells – for virtual optical stimulation and prediction of optimal light-delivery arrangements, minimum energy needs etc. Overall, virtual optogenetics can accelerate the development of new optical stimulation tools for better understanding and control of brain and heart function.