A mathematical model of action potential heterogeneity in adult rat left ventricular myocytes

Electrophysiological effects of stretch-activated ion channels: a systematic computational characterization

Cardiac electrophysiology and mechanics are strongly interconnected. Their interaction is, among others, mediated by mechano-electric feedback through stretch-activated ion channels (SACs). The electrophysiological changes induced by SACs may contribute to arrhythmogenesis, but the precise SAC-induced electrophysiological changes remain incompletely understood. Here, we provide a systematic characterization of stretch effects through three distinguished SACs on cardiac electrophysiology using computational modelling. We implemented potassium-selective, calcium-selective and non-selective SACs in the Tomek-Rodriguez-O'Hara-Rudy model of human ventricular electrophysiology. The model was calibrated to experimental data from isolated cardiomyocytes undergoing stretch, considering inter-species differences, and disease-related remodelling of SACs. SAC-mediated effects on the action potential (AP) were analysed by varying stretch amplitude, application timing and/or duration. Afterdepolarizations of different amplitudes were observed with transient 10-ms stretch stimuli of 15-18% applied during phase 4, while stretch ≥18% during phase 4 elicited triggered APs. Longer stimuli shifted the threshold of AP trigger during phase 4 to lower amplitudes, while shorter stimuli increased it. Continuous stretch provoked electrophysiological remodelling. Furthermore, stretch shortened duration or changed morphology of a subsequent electrically evoked AP, and, if applied during a vulnerable time window with sufficient amplitude, prevented its occurrence because of stretch-induced modulation of sodium and L-type calcium channel gating. These effects were more pronounced with disease-related SAC remodelling due to increased stretch sensitivity of diseased hearts. We showed that SACs may induce afterdepolarizations and triggered activities, and prevent subsequent AP generation or change its morphology. These effects depend on cardiomyocyte stretch characteristics and disease-related SACs remodelling and may contribute to cardiac arrhythmogenesis. KEY POINTS: The interplay between cardiac electrophysiology and mechanics is mediated by mechano-electric feedback through stretch-activated ion channels (SACs). These channels may be pro-arrhythmic, but their precise effect on electrophysiology remains unclear. Here we present a systematic in silico characterization of stretch effects through three SACs by implementing inter-species differences as well as disease-related remodelling of SACs in a novel computational model of human ventricular cardiomyocyte electrophysiology. Our simulations showed that, at the cellular level, SACs may provoke electrophysiological remodelling, afterdepolarizations, triggered activities, change the morphology or shorten subsequent electrically evoked action potentials. The model further suggests that a vulnerable window exists in which stretch prevents the following electrically triggered beat occurrence. The pro-arrhythmic effects of stretch strongly depend on disease-related SAC remodelling as well as on stretch characteristics, such as amplitude, time of application and duration. Our study helps in understanding the role of stretch in cardiac arrhythmogenesis and revealing the underlying cellular mechanisms.

Ionic current changes underlying action potential repolarization responses to physiological pacing and adrenergic stimulation in adult rat ventricular myocytes

This study aimed to simulate ventricular responses to elevations in myocyte pacing and adrenergic stimulation using a novel electrophysiological rat model and investigate ion channel responses underlying action potential (AP) modulations. Peak ion currents and AP repolarization to 50% and 90% of full repolarization (APD_50-90 ) were recorded during simulations at 1-10 Hz pacing under control and adrenergic stimulation conditions. Further simulations were performed with incremental ion current block (L-type calcium current, I_Ca ; transient outward current, I_to ; slow delayed rectifier potassium current, I_Ks ; rapid delayed rectifier potassium current, I_Kr ; inward rectifier potassium current, I_K1 ) to identify current influence on AP response to exercise. Simulated APD_50-90 closely resembled experimental findings. Rate-dependent increases in I_Ks (6%-101%), I_Kr (141%-1339%), and I_Ca (0%-15%) and reductions in I_to (11%-57%) and I_K1 (1%-9%) were observed. Meanwhile, adrenergic stimulation triggered moderate increases in all currents (23%-67%) except I_K1 . Further analyses suggest AP plateau is most sensitive to modulations in I_to and I_Ca while late repolarization is most sensitive to I_K1 , I_Ca , and I_Ks , with alterations in I_Ks predominantly stimulating the greatest magnitude of influence on late repolarization (35%-846% APD₉₀ prolongation). The modified Leeds rat model (mLR) is capable of accurately modeling APs during physiological stress. This study highlights the importance of I_Ca , I_to , I_K1, and I_Ks in controlling electrophysiological responses to exercise. This work will benefit the study of cardiac dysfunction, arrythmia, and disease, though future physiologically relevant experimental studies and model development are required.

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.

In silico assessment of pharmacotherapy for carbon monoxide induced arrhythmias in healthy and failing human hearts

Background: Carbon monoxide (CO) is gaining increased attention in air pollution-induced arrhythmias. The severe cardiotoxic consequences of CO urgently require effective pharmacotherapy to treat it. However, existing evidence demonstrates that CO can induce arrhythmias by directly affecting multiple ion channels, which is a pathway distinct from heart ischemia and has received less concern in clinical treatment.

Objective: To evaluate the efficacy of some common clinical antiarrhythmic drugs for CO-induced arrhythmias, and to propose a potential pharmacotherapy for CO-induced arrhythmias through the virtual pathological cell and tissue models.

Methods: Two pathological models describing CO effects on healthy and failing hearts were constructed as control baseline models. After this, we first assessed the efficacy of some common antiarrhythmic drugs like ranolazine, amiodarone, nifedipine, etc., by incorporating their ion channel-level effects into the cell model. Cellular biomarkers like action potential duration and tissue-level biomarkers such as the QT interval from pseudo-ECGs were obtained to assess the drug efficacy. In addition, we also evaluated multiple specific IKr activators in a similar way to multi-channel blocking drugs, as the IKr activator showed great potency in dealing with CO-induced pathological changes.

Results: Simulation results showed that the tested seven antiarrhythmic drugs failed to rescue the heart from CO-induced arrhythmias in terms of the action potential and the ECG manifestation. Some of them even worsened the condition of arrhythmogenesis. In contrast, IKr activators like HW-0168 effectively alleviated the proarrhythmic effects of CO.

Conclusion: Current antiarrhythmic drugs including the ranolazine suggested in previous studies did not achieve therapeutic effects for the cardiotoxicity of CO, and we showed that the specific IKr activator is a promising pharmacotherapy for the treatment of CO-induced arrhythmias.

A novel modular modeling approach for understanding different electromechanics between left and right heart in rat

While ion channels and transporters involved in excitation-contraction coupling have been linked and constructed as comprehensive computational models, validation of whether each individual component of a model can be reused has not been previously attempted. Here we address this issue while using a novel modular modeling approach to investigate the underlying mechanism for the differences between left ventricle (LV) and right ventricle (RV). Our model was developed from modules constructed using the module assembly principles of the CellML model markup language. The components of three existing separate models of cardiac function were disassembled as to create smaller modules, validated individually, and then the component parts were combined into a new integrative model of a rat ventricular myocyte. The model was implemented in OpenCOR using the CellML standard in order to ensure reproducibility. Simulated action potential (AP), Ca²⁺ transient, and tension were in close agreement with our experimental measurements: LV AP showed a prolonged duration and a more prominent plateau compared with RV AP; Ca²⁺ transient showed prolonged duration and slow decay in LV compared to RV; the peak value and relaxation of tension were larger and slower, respectively, in LV compared to RV. Our novel approach of module-based mathematical modeling has established that the ionic mechanisms underlying the APs and Ca²⁺ handling play a role in the variation in force production between ventricles. This simulation process also provides a useful way to reuse and elaborate upon existing models in order to develop a new model.

Addressing barriers in comprehensiveness, accessibility, reusability, interoperability and reproducibility of computational models in systems biology

Computational models are often employed in systems biology to study the dynamic behaviours of complex systems. With the rise in the number of computational models, finding ways to improve the reusability of these models and their ability to reproduce virtual experiments becomes critical. Correct and effective model annotation in community-supported and standardised formats is necessary for this improvement. Here, we present recent efforts toward a common framework for annotated, accessible, reproducible and interoperable computational models in biology, and discuss key challenges of the field.

Increased atrial effectiveness of flecainide conferred by altered biophysical properties of sodium channels

Atrial fibrillation (AF) affects over 1% of the population and is a leading cause of stroke and heart failure in the elderly. A feared side effect of sodium channel blocker therapy, ventricular pro-arrhythmia, appears to be relatively rare in patients with AF. The biophysical reasons for this relative safety of sodium blockers are not known. Our data demonstrates intrinsic differences between atrial and ventricular cardiac voltage-gated sodium currents (INa), leading to reduced maximum upstroke velocity of action potential and slower conduction, in left atria compared to ventricle. Reduced atrial INa is only detected at physiological membrane potentials and is driven by alterations in sodium channel biophysical properties and not by NaV1.5 protein expression. Flecainide displayed greater inhibition of atrial INa, greater reduction of maximum upstroke velocity of action potential, and slowed conduction in atrial cells and tissue. Our work highlights differences in biophysical properties of sodium channels in left atria and ventricles and their response to flecainide. These differences can explain the relative safety of sodium channel blocker therapy in patients with atrial fibrillation.

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.

Lower troponin expression in the right ventricle of rats explains interventricular differences in E-C coupling

Despite distinctive functional and anatomic differences, a precise understanding of the cardiac interventricular differences in excitation–contraction (E–C) coupling mechanisms is still lacking. Here, we directly compared rat right and left cardiomyocytes (RVCM and LVCM). Whole-cell patch clamp, the IonOptix system, and fura-2 fluorimetry were used to measure electrical properties (action potential and ionic currents), single-cell contractility, and cytosolic Ca²⁺ ([Ca²⁺]_i), respectively. Myofilament proteins were analyzed by immunoblotting. RVCM showed significantly shorter action potential duration (APD) and higher density of transient outward K⁺ current (I_to). However, the triggered [Ca²⁺]_i change (Ca²⁺ transient) was not different, while the decay rate of the Ca²⁺ transient was slower in RVCM. Although the relaxation speed was also slower, the sarcomere shortening amplitude (ΔSL) was smaller in RVCM. SERCA activity was ∼60% lower in RVCM, which is partly responsible for the slower decay of the Ca²⁺ transient. Immunoblot analysis revealed lower expression of the cardiac troponin complex (cTn) in RVCM, implying a smaller Ca²⁺ buffering capacity (κ_S), which was proved by in situ analysis. The introduction of these new levels of cTn, I_to, and SERCA into a mathematical model of rat LVCM reproduced the similar Ca²⁺ transient, slower Ca²⁺ decay, shorter APD, and smaller ΔSL of RVCM. Taken together, these data show reduced expression of cTn proteins in the RVCM, which provides an explanation for the interventricular difference in the E–C coupling kinetics.

Troponin levels make a difference

JGP study reveals that lower troponin expression in the right ventricle underlies interventricular differences in excitation-contraction coupling.

Heart-on-Chip for Combined Cellular Dynamics Measurements and Computational Modeling Towards Clinical Applications

Organ-on-chip or micro-engineered three-dimensional cellular or tissue models are increasingly implemented in the study of cardiovascular pathophysiology as alternatives to traditional in vitro cell culture. Drug induced cardiotoxicity is a key issue in drug development pipelines, but the current in vitro and in vivo studies suffer from inter-species differences, high costs, and lack of reliability and accuracy in predicting cardiotoxicity. Microfluidic heart-on-chip devices can impose a paradigm shift to the current tools. They can not only recapitulate cardiac tissue level functionality and the communication between cells and extracellular matrices but also allow higher throughput studies conducive to drug screening especially with their added functionalities or sensors that extract disease-specific phenotypic, genotypic, and electrophysiological information in real-time. Such electrical and mechanical components can tailor the electrophysiology and mechanobiology of the experiment to better mimic the in vivo condition as well. Recent advancements and challenges are reviewed in the fabrication, functionalization and sensor assisted mechanical and electrophysiological measurements, numerical and computational modeling of cardiomyocytes' behavior, and the clinical applications in drug screening and disease modeling. This review concludes with the current challenges and perspectives on the future of such organ-on-chip platforms.

Proarrhythmic effects of carbon monoxide in human ventricular tissue: insights from computational modeling

Epidemiological studies have demonstrated that ambient air pollution has been closely associated with cardiovascular diseases. Carbon monoxide (CO) is a common ambient air pollutant that can cause adverse effects on the heart. CO is known to cause tissue ischemia, resulting in ventricular arrhythmias. However, accumulating biological studies showed that CO could exert effects on multiple cardiac ionic channels under normoxic conditions, which might indicate new proarrhythmic mechanisms other than ischemia-mediated electrophysiology changes. In this work, we evaluated the functional impacts of CO on human ventricles using a multi-scale model of human ventricular tissue. Experimental data regarding the effects of CO on different ion channels were incorporated into the cell model to explore the alterations of ventricular electrophysiology. Simulation results suggested that CO significantly prolonged the duration of ventricular action potentials, enhanced the transmural dispersion of repolarization, and reduced the adaptability of ventricular tissue to fast heart rates. In addition, simulated pseudo-ECGs showed consistent manifestations with the clinical observation that CO caused an apparent QT interval prolongation and T-wave widening, indicating that CO affected the heart's abnormal ventricular repolarization.

A Stochastic Spatiotemporal Model of Rat Ventricular Myocyte Calcium Dynamics Demonstrated Necessary Features for Calcium Wave Propagation

Calcium (Ca2+) plays a central role in the excitation and contraction of cardiac myocytes. Experiments have indicated that calcium release is stochastic and regulated locally suggesting the possibility of spatially heterogeneous calcium levels in the cells. This spatial heterogeneity might be important in mediating different signaling pathways. During more than 50 years of computational cell biology, the computational models have been advanced to incorporate more ionic currents, going from deterministic models to stochastic models. While periodic increases in cytoplasmic Ca2+ concentration drive cardiac contraction, aberrant Ca2+ release can underly cardiac arrhythmia. However, the study of the spatial role of calcium ions has been limited due to the computational expense of using a three-dimensional stochastic computational model. In this paper, we introduce a three-dimensional stochastic computational model for rat ventricular myocytes at the whole-cell level that incorporate detailed calcium dynamics, with (1) non-uniform release site placement, (2) non-uniform membrane ionic currents and membrane buffers, (3) stochastic calcium-leak dynamics and (4) non-junctional or rogue ryanodine receptors. The model simulates spark-induced spark activation and spark-induced Ca2+ wave initiation and propagation that occur under conditions of calcium overload at the closed-cell condition, but not when Ca2+ levels are normal. This is considered important since the presence of Ca2+ waves contribute to the activation of arrhythmogenic currents.

Quantitative cross-species translators of cardiac myocyte electrophysiology: Model training, experimental validation, and applications

Animal experimentation is key in the evaluation of cardiac efficacy and safety of novel therapeutic compounds. However, interspecies differences in the mechanisms regulating excitation-contraction coupling can limit the translation of experimental findings from animal models to human physiology and undermine the assessment of drugs’ efficacy and safety. Here, we built a suite of translators for quantitatively mapping electrophysiological responses in ventricular myocytes across species. We trained these statistical operators using a broad dataset obtained by simulating populations of our biophysically detailed computational models of action potential and Ca2+ transient in mouse, rabbit, and human. We then tested our translators against experimental data describing the response to stimuli, such as ion channel block, change in beating rate, and β-adrenergic challenge. We demonstrate that this approach is well suited to predicting the effects of perturbations across different species or experimental conditions and suggest its integration into mechanistic studies and drug development pipelines.

Modelling the action potential propagation in a heart with structural heterogeneities: From high-resolution MRI to numerical simulations

Mathematical modelling and numerical simulation in cardiac electrophysiology have already been studied extensively. However, there is a clear lack of techniques and methodologies for studying the propagation of action potential in a heart with structural defects. In this article, we present a modified version of the bidomain model, derived using homogenisation techniques with the assumption of existence of diffusive inclusions in the cardiac tissue. The diffusive inclusions represent regions without electrically active myocytes, for example, fat, fibrosis, and so forth. We present an application of this model to a rat heart. Starting from high-resolution MRI, the geometry of the heart is built and meshed using image processing techniques. We perform a study of the effects of tissue heterogeneities induced by diffusive inclusions on the velocity and shape of the depolarisation wavefront. We present several test cases with different geometries of diffusive inclusions. We reach the conclusion that the conduction velocity is not affected in the best cases, while it is affected by up to 76% in the worst case scenario. Additionally, the shape of the wavefront was affected in some cases.

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.

A Multi-Scale Computational Model for the Rat Ventricle: Construction, Parallelization, and Applications

BACKGROUND

Cardiovascular diseases are the top killer of human beings. The ventricular arrhythmia, as a type of malignant cardiac arrhythmias, typically leads to death if not treated within minutes. The multi-scale virtual heart provides an idealized tool for exploring the underlying mechanisms, by means of incorporating abundant experimental data at the level of ion channels and analyzing the subsequent pathological changes at organ levels. However, there are few studies on building a virtual heart model for rats-a species most widely used in experiments.

OBJECTIVE

To build a multi-scale computational model for rats, with detailed methodology for the model construction, computational optimization, and its applications.

METHODS

First, approaches for building multi-scale models ranging from cellular to 3-D organ levels are introduced, with detailed descriptions of handling the ventricular myocardium heterogeneity, geometry processing, and boundary conditions, etc. Next, for dealing with the expensive computational costs of 3-D models, optimization approaches including an optimized representation and a GPU-based parallelization method are introduced. Finally, methods for reproducing of some key phenomenon (e.g., electrocardiograph, spiral/scroll waves) are demonstrated.

RESULTS

Three types of heterogeneity, including the transmural heterogeneity, the interventricular heterogeneity, and the base-apex heterogeneity are incorporated into the model. The normal and reentrant excitation waves, as well as the corresponding pseudo-ECGs are reproduced by the constructed ventricle model. In addition, the temporal and spatial vulnerability to reentry arrhythmias are quantified based on the evaluation experiments of vulnerable window and the critical length.

CONCLUSIONS

The constructed multi-scale rat ventricle model is able to reproduce both the physiological and the pathological phenomenon in different scales. Evaluation experiments suggest that the apex is the most susceptible area to arrhythmias. The model can be a promising tool for the investigation of arrhythmogenesis and the screening of anti-arrhythmic drugs.

A new model of myofibroblast-cardiomyocyte interactions and their differences across species

Although coupling between cardiomyocytes and myofibroblasts is well known to affect the physiology and pathophysiology of cardiac tissues across species, relating these observations to humans is challenging because the effect of this coupling varies across species and because the sources of these effects are not known. To identify the sources of cross-species variation, we built upon previous mathematical models of myofibroblast electrophysiology and developed a mechanoelectrical model of cardiomyocyte-myofibroblast interactions as mediated by electrotonic coupling and transforming growth factor-β1. The model, as verified by experimental data from the literature, predicted that both electrotonic coupling and transforming growth factor-β1 interaction between myocytes and myofibroblast prolonged action potential in rat myocytes but shortened action potential in human myocytes. This variance could be explained by differences in the transient outward K⁺ current associated with differential Kv4.2 gene expression across species. Results are useful for efforts to extrapolate the results of animal models to the predicted effects in humans and point to potential therapeutic targets for fibrotic cardiomyopathy.

Quantitative roles of ion channel dynamics on ventricular action potential

Mathematical models for the action potential (AP) generation of the electrically excitable cells including the heart are involved different mechanisms including the voltage-dependent currents with nonlinear time- and voltage-gating properties. From the shape of the AP waveforms to the duration of the refractory periods or heart rhythms are greatly affected by the functions describing the features or the quantities of these ion channels. In this work, a mathematical measure to analyze the regional contributions of voltage-gated channels is defined by dividing the AP into phases, epochs, and intervals of interest. The contribution of each time-dependent current for the newly defined cardiomyocyte model is successfully calculated and it is found that the contribution of dominant ion channels changes substantially not only for each phase but also for different regions of the cardiac AP. Besides, the defined method can also be applied in all Hodgkin–Huxley types of electrically excitable cell models to be able to understand the underlying dynamics better.

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.

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

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

Prolonged ursodeoxycholic acid administration reduces acute ischaemia-induced arrhythmias in adult rat hearts

Acute myocardial ischaemia and reperfusion (I-R) are major causes of ventricular arrhythmias in patients with a history of coronary artery disease. Ursodeoxycholic acid (UDCA) has previously been shown to be antiarrhythmic in fetal hearts. This study was performed to investigate if UDCA protects against ischaemia-induced and reperfusion-induced arrhythmias in the adult myocardium, and compares the effect of acute (perfusion only) versus prolonged (2 weeks pre-treatment plus perfusion) UDCA administration. Langendorff-perfused adult Sprague-Dawley rat hearts were subjected to acute regional ischaemia by ligation of the left anterior descending artery (10 min), followed by reperfusion (2 min), and arrhythmia incidence quantified. Prolonged UDCA administration reduced the incidence of acute ischaemia-induced arrhythmias (p = 0.028), with a reduction in number of ventricular ectopic beats during the ischaemic phase compared with acute treatment (10 ± 3 vs 58 ± 15, p = 0.036). No antiarrhythmic effect was observed in the acute UDCA administration group. Neither acute nor prolonged UDCA treatment altered the incidence of reperfusion arrhythmias. The antiarrhythmic effect of UDCA may be partially mediated by an increase in cardiac wavelength, due to the attenuation of conduction velocity slowing (p = 0.03), and the preservation of Connexin43 phosphorylation during acute ischaemia (p = 0.0027). The potential antiarrhythmic effects of prolonged UDCA administration merit further investigation.

Impact of ISK Voltage and Ca2+/Mg2+-Dependent Rectification on Cardiac Repolarization

Cardiac small conductance Ca²⁺-activated K⁺ (SK) channels are activated solely by Ca²⁺, but the SK current (I_SK) is inwardly rectified. However, the impact of inward rectification in shaping action potentials (APs) in ventricular cardiomyocytes under β-adrenergic stimulation or in disease states remains undefined. Two processes underlie this inward rectification: an intrinsic rectification caused by an electrostatic energy barrier from positively charged amino acids at the inner pore and a voltage-dependent Ca²⁺/Mg²⁺ block. Thus, Ca²⁺ has a biphasic effect on I_SK, activating at low [Ca²⁺] yet inhibiting I_SK at high [Ca²⁺]. We examined the effect of I_SK rectification on APs in rat cardiomyocytes by simultaneously recording whole-cell apamin-sensitive currents and Ca²⁺ transients during an AP waveform and developed a computer model of SK channels with rectification features. The typical profile of I_SK during AP clamp included an initial peak (mean 1.6 pA/pF) followed by decay to the point that submembrane [Ca²⁺] reached ∼10 μM. During the rest of the AP stimulus, I_SK either plateaued or gradually increased as the cell repolarized and submembrane [Ca²⁺] decreased further. We used a six-state gating model combined with intrinsic and Ca²⁺/Mg²⁺-dependent rectification to simulate I_SK and investigated the relative contributions of each type of rectification to AP shape. This SK channel model replicates key features of I_SK recording during AP clamp showing that intrinsic rectification limits I_SK at high V_m during the early and plateau phase of APs. Furthermore, the initial rise of Ca²⁺ transients activates, but higher [Ca²⁺] blocks SK channels, yielding a transient outward-like I_SK trajectory. During the decay phase of Ca²⁺, the Ca²⁺-dependent block is released, causing I_SK to rise again and contribute to repolarization. Therefore, I_SK is an important repolarizing current, and the rectification characteristics of an SK channel determine its impact on early, plateau, and repolarization phases of APs.

Observability analysis and state observer design for a cardiac ionic cell model

To gain insights into cardiac arrhythmias, researchers have developed and employed various measurement techniques, such as electrocardiography, optical mapping, and patch clamping. However, there are no measurement methods that allow simultaneous recording of all cellular quantities, including intracellular ionic concentrations and gating states, that may play an important role in arrhythmia formation. To help address this shortcoming, we applied observability analysis, a method from control theory, to the Luo-Rudy dynamic (LRd) model of a cardiac ventricular myocyte. After linearizing the time-integrated LRd model about selected periodic orbits, we computed the observability properties of the model to determine whether past system states could be reconstructed from different hypothetical sets of measurements. Under the simplifying assumption that only one dynamical variable could be measured periodically, we found that intracellular potassium concentration generally yielded the largest observability values and thus contained the most information about the dominant modes of the system. The impacts on observability of measurement timings, inter-stimulus interval length, and an alternans-promoting parameter shift were also studied. Pole-placement state observer algorithms were designed and tested in simulations for several scenarios, and we found that it is possible to infer unmeasured variables from potassium-concentration measurements, and to an extent from membrane-potential measurements, both for longer periods that represent normal rhythms and shorter periods associated with tachyarrhythmias. Our results could lead to improved data assimilation algorithms that combine model predictions with measurements to estimate quantities that are difficult or impossible to measure during in vitro experiments.

Mathematical model of the ventricular action potential and effects of isoproterenol-induced cardiac hypertrophy in rats

Mathematical action potential (AP) modeling is a well-established but still-developing area of research to better understand physiological and pathological processes. In particular, changes in AP mechanisms in the isoproterenol (ISO) -induced hypertrophic heart model are incompletely understood. Here we present a mathematical model of the rat AP based on recordings from rat ventricular myocytes. In our model, for the first time, all channel kinetics are defined with a single type of function that is simple and easy to apply. The model AP and channels dynamics are consistent with the APs recorded from rats for both Control (absence of ISO) and ISO-treated cases. Our mathematical model helps us to understand the reason for the prolongation in AP duration after ISO application while ISO treatment helps us to validate our mathematical model. We reveal that the smaller density and the slower gating kinetics of the transient K⁺ current help explain the prolonged AP duration after ISO treatment and the increasing amplitude of the rapid and the slow inward rectifier currents also contribute to this prolongation alongside the flux in Ca²⁺ currents. ISO induced an increase in the density of the Na⁺ current that can explain the faster upstroke. We believe that AP dynamics from rat ventricular myocytes can be reproduced very well with this mathematical model and that it provides a powerful tool for improved insights into the underlying dynamics of clinically important AP properties such as ISO application.

Statistical Approaches for the Analysis of Dependency Among Neurons Under Noise

Neuronal noise is a major factor affecting the communication between coupled neurons. In this work, we propose a statistical toolset to infer the coupling between two neurons under noise. We estimate these statistical dependencies from data which are generated by a coupled Hodgkin-Huxley (HH) model with additive noise. To infer the coupling using observation data, we employ copulas and information-theoretic quantities, such as the mutual information (MI) and the transfer entropy (TE). Copulas and MI between two variables are symmetric quantities, whereas TE is asymmetric. We demonstrate the performances of copulas and MI as functions of different noise levels and show that they are effective in the identification of the interactions due to coupling and noise. Moreover, we analyze the inference of TE values between neurons as a function of noise and conclude that TE is an effective tool for finding out the direction of coupling between neurons under the effects of noise.

The Effects of Mechanical Preload on Transmural Differences in Mechano-Calcium-Electric Feedback in Single Cardiomyocytes: Experiments and Mathematical Models

Transmural differences in ventricular myocardium are maintained by electromechanical coupling and mechano-calcium/mechano-electric feedback. In the present study, we experimentally investigated the influence of preload on the force characteristics of subendocardial (Endo) and subepicardial (Epi) single ventricular cardiomyocytes stretched by up to 20% from slack sarcomere length (SL) and analyzed the results with the help of mathematical modeling. Mathematical models of Endo and Epi cells, which accounted for regional heterogeneity in ionic currents, Ca²⁺ handling, and myofilament contractile mechanisms, showed that a greater slope of the active tension–length relationship observed experimentally in Endo cardiomyocytes could be explained by greater length-dependent Ca²⁺ activation in Endo cells compared with Epi ones. The models also predicted that greater length dependence of Ca²⁺ activation in Endo cells compared to Epi ones underlies, via mechano-calcium-electric feedback, the reduction in the transmural gradient in action potential duration (APD) at a higher preload. However, the models were unable to reproduce the experimental data on a decrease of the transmural gradient in the time to peak contraction between Endo and Epi cells at longer end-diastolic SL. We hypothesize that preload-dependent changes in viscosity should be involved alongside the Frank–Starling effects to regulate the transmural gradient in length-dependent changes in the time course of contraction of Endo and Epi cardiomyocytes. Our experimental data and their analysis based on mathematical modeling give reason to believe that mechano-calcium-electric feedback plays a critical role in the modulation of electrophysiological and contractile properties of myocytes across the ventricular wall.

Pro-arrhythmic Effects of Hydrogen Sulfide in Healthy and Ischemic Cardiac Tissues: Insight From a Simulation Study

Hydrogen sulfide (H₂S), an ambient air pollutant, has been reported to increase cardiac events in patients with cardiovascular diseases, but the underlying mechanisms remain not elucidated. This study investigated the pro-arrhythmic effects of H₂S in healthy and ischemic conditions. Experimental data of H₂S effects on ionic channels (including the L-type Ca²⁺ channel and ATP-sensitive K⁺ channel) were incorporated into a virtual heart model to evaluate their integral action on cardiac arrhythmogenesis. It was shown that H₂S depressed cellular excitability, abbreviated action potential duration, and augmented tissue’s transmural dispersion of repolarization, resulting in an increase in tissue susceptibility to initiation and maintenance of reentry. The observed effects of H₂S on cardiac excitation are more remarkable in the ischemic condition than in the healthy condition. This study provides mechanistic insights into the pro-arrhythmic effects of air pollution (H₂S), especially in the case with extant ischemic conditions.

Investigation of the Role of Myocyte Orientations in Cardiac Arrhythmia Using Image-Based Models

Cardiac electrical excitation-propagation is influenced by myocyte orientations (cellular organization). Quantitatively understanding this relationship presents a significant research challenge, especially during arrhythmias in which excitation patterns become complex. Tissue-scale simulations of cardiac electrophysiology, incorporating both dynamic action potential behavior and image-based myocardial architecture, provide an approach to investigate three-dimensional (3D) propagation of excitation waves in the heart. In this study, we aimed to assess the importance of natural variation in myocyte orientations on cardiac arrhythmogenesis using 3D tissue electrophysiology simulations. Three anatomical models (i.e., describing myocyte orientations) of healthy rat ventricles—obtained using diffusion tensor imaging at 100 μm resolution—were registered to a single biventricular geometry (i.e., a single cardiac shape), in which the myocyte orientations could be represented by each of the diffusion tensor imaging data sets or by an idealized rule-based description. The Fenton-Karma cellular excitation model was modified to reproduce rat ventricular action potential duration restitution to create reaction-diffusion cardiac electrophysiology models. Over 250 3D simulations were performed to investigate the effects of myocyte orientations on the following: 1) ventricular activation, 2) location-dependent arrhythmia induction via rapid pacing, and 3) dynamics of re-entry averaged over multiple episodes. It was shown that 1) myocyte orientation differences manifested themselves in local activation times, but the influence on total activation time was small; 2) differences in myocyte orientations could critically affect the inducibility and persistence of arrhythmias for specific stimulus-location/cycle-length combinations; and 3) myocyte orientations alone could be an important determinant of scroll wave break, although no significant differences were observed in averaged arrhythmia dynamics between the four myocyte orientation scenarios considered. Our results show that myocyte orientations are an important determinant of arrhythmia inducibility, persistence, and scroll wave break. These findings suggest that where specificity is desired (for example, when predicting location-dependent, patient-specific arrhythmia inducibility), subject-specific myocyte orientations may be important.

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.

The Use of iPSC-Derived Cardiomyocytes and Optical Mapping for Erythromycin Arrhythmogenicity Testing

Erythromycin is an antibiotic that prolongs the QT-interval and causes Torsade de Pointes (TdP) by blocking the rapid delayed rectifying potassium current (I_Kr) without affecting either the slow delayed rectifying potassium current (I_Ks) or inward rectifying potassium current (I_K1). Erythromycin exerts this effect in the range of 1.5-100 μM. However, the mechanism of action underlying its cardiotoxic effect and its role in the induction of arrhythmias, especially in multicellular cardiac experimental models, remain unclear. In this study, the re-entry formation, conduction velocity, and maximum capture rate were investigated in a monolayer of human-induced pluripotent stem cell (iPSC)-derived cardiomyocytes from a healthy donor and in a neonatal rat ventricular myocyte (NRVM) monolayer using the optical mapping method under erythromycin concentrations of 15, 30, and 45 μM. In the monolayer of human iPSC-derived cardiomyocytes, the conduction velocity (CV) varied up to 12 ± 9% at concentrations of 15-45 μM as compared with that of the control, whereas the maximum capture rate (MCR) declined substantially up to 28 ± 12% (p < 0.01). In contrast, the tests on the NRVM monolayer showed no significant effect on the MCR. The results of the arrhythmogenicity test provided evidence for a "window" of concentrations of the drug (15-30 μM) at which the probability of re-entry increased.

SCN5A variant R222Q generated abnormal changes in cardiac sodium current and action potentials in murine myocytes and Purkinje cells

BACKGROUND

The cardiac sodium channel (SCN5A) mutation R222Q neutralizes a positive charge in the domain I voltage sensor. Mutation carriers display very frequent ectopy and dilated cardiomyopathy.

OBJECTIVES

To describe the effect of SCN5A R222Q on murine myocyte and Purkinje fiber electrophysiology, and identify underlying mechanisms.

METHODS

We generated mice carrying humanized wild-type (H) and mutant (RQ) SCN5A channels. We characterized whole-heart and isolated ventricular and Purkinje myocyte properties.

RESULTS

RQ/RQ mice were not viable. I_Na from RQ/H ventricular myocytes displayed increased "window current" and hyperpolarizing shifts in both inactivation and activation compared to H/H, as previously reported in heterologous expression systems. Surprisingly, action potentials were markedly abbreviated in RQ/H myocytes (action potential durations at 90% repolarization: 12.6 ± 1.3 ms vs 29.1 ± 1.0 ms in H/H, P < .01, n = 10 each). We identified a large [K⁺]_o-dependent outward gating pore current in RQ/H but not H/H myocytes, and decreasing [K⁺]_o elicited early afterdepolarizations (EADs) and triggered activity in isolated myocytes and ectopic beats in whole hearts. Further, RQ/H Purkinje cells displayed striking, consistent low-voltage EADs. In vivo, however, RQ/H mice displayed little ectopy and contractile function was normal.

CONCLUSION

While SCN5A R222Q increases plateau inward sodium current, action potentials were unexpectedly shortened, likely reflecting an outward gating-pore current. Low extracellular potassium increased this pore current, and was arrhythmogenic in vitro and ex vivo.

Mathematical modeling of circadian rhythms

Circadian rhythms are endogenous ~24-hr oscillations usually entrained to daily environmental cycles of light/dark. Many biological processes and physiological functions including mammalian body temperature, the cell cycle, sleep/wake cycles, neurobehavioral performance, and a wide range of diseases including metabolic, cardiovascular, and psychiatric disorders are impacted by these rhythms. Circadian clocks are present within individual cells and at tissue and organismal levels as emergent properties from the interaction of cellular oscillators. Mathematical models of circadian rhythms have been proposed to provide a better understanding of and to predict aspects of this complex physiological system. These models can be used to: (a) manipulate the system in silico with specificity that cannot be easily achieved using in vivo and in vitro experimental methods and at lower cost, (b) resolve apparently contradictory empirical results, (c) generate hypotheses, (d) design new experiments, and (e) to design interventions for altering circadian rhythms. Mathematical models differ in structure, the underlying assumptions, the number of parameters and variables, and constraints on variables. Models representing circadian rhythms at different physiologic scales and in different species are reviewed to promote understanding of these models and facilitate their use. This article is categorized under: Physiology > Mammalian Physiology in Health and Disease Models of Systems Properties and Processes > Organ, Tissue, and Physiological Models.

Rethinking multiscale cardiac electrophysiology with machine learning and predictive modelling

We review some of the latest approaches to analysing cardiac electrophysiology data using machine learning and predictive modelling. Cardiac arrhythmias, particularly atrial fibrillation, are a major global healthcare challenge. Treatment is often through catheter ablation, which involves the targeted localised destruction of regions of the myocardium responsible for initiating or perpetuating the arrhythmia. Ablation targets are either anatomically defined, or identified based on their functional properties as determined through the analysis of contact intracardiac electrograms acquired with increasing spatial density by modern electroanatomic mapping systems. While numerous quantitative approaches have been investigated over the past decades for identifying these critical curative sites, few have provided a reliable and reproducible advance in success rates. Machine learning techniques, including recent deep-learning approaches, offer a potential route to gaining new insight from this wealth of highly complex spatio-temporal information that existing methods struggle to analyse. Coupled with predictive modelling, these techniques offer exciting opportunities to advance the field and produce more accurate diagnoses and robust personalised treatment. We outline some of these methods and illustrate their use in making predictions from the contact electrogram and augmenting predictive modelling tools, both by more rapidly predicting future states of the system and by inferring the parameters of these models from experimental observations.

K2p 3.1 protein is expressed as a transmural gradient across the rat left ventricular free wall

Introduction

K_2p3.1, also known as TASK‐1, is a twin‐pore acid‐sensitive repolarizing K⁺ channel, responsible for a background potassium current that significantly contributes to setting the resting membrane potential of cardiac myocytes. Inhibition of I_K2p3.1 alters cardiac repolarization and is proarrhythmogenic. In this study, we have examined the expression of K_2p3.1 and function of this channel in tissue and myocytes from across the left ventricular free wall.

Methods and Results

Using fluorescence immunocytochemistry, the expression of K_2p3.1 protein in myocytes from the subendocardial region was found to be twice (205% ± 13.5%) that found in myocytes from the subepicardial region of the left ventricle (100% ± 5.3%). The left ventricular free wall exhibited a marked transmural gradient of K_2p3.1 protein expression. Western blot analysis confirmed significantly higher K_2p3.1 protein expression in subendocardial tissue (156% ± 2.5%) than subepicardial tissue (100% ± 5.0%). However, there was no difference in K_2p3.1 messenger RNA expression. Whole‐cell patch clamp identified I_K2p3.1 current density to be significantly greater in myocytes isolated from the subendocardium (7.66 ± 0.53 pA/pF) compared with those from the subepicardium (3.47 ± 0.74 pA/pF).

Conclusions

This is the first study to identify a transmural gradient of K_2p3.1 in the left ventricle. This gradient has implications for understanding ventricular arrhythmogenesis under conditions of ischemia but also in response to other modulatory factors, such as adrenergic stimulation and the presence of anesthetics that inhibits or activates this channel.

A Heart for Diversity: Simulating Variability in Cardiac Arrhythmia Research

In cardiac electrophysiology, there exist many sources of inter- and intra-personal variability. These include variability in conditions and environment, and genotypic and molecular diversity, including differences in expression and behavior of ion channels and transporters, which lead to phenotypic diversity (e.g., variable integrated responses at the cell, tissue, and organ levels). These variabilities play an important role in progression of heart disease and arrhythmia syndromes and outcomes of therapeutic interventions. Yet, the traditional in silico framework for investigating cardiac arrhythmias is built upon a parameter/property-averaging approach that typically overlooks the physiological diversity. Inspired by work done in genetics and neuroscience, new modeling frameworks of cardiac electrophysiology have been recently developed that take advantage of modern computational capabilities and approaches, and account for the variance in the biological data they are intended to illuminate. In this review, we outline the recent advances in statistical and computational techniques that take into account physiological variability, and move beyond the traditional cardiac model-building scheme that involves averaging over samples from many individuals in the construction of a highly tuned composite model. We discuss how these advanced methods have harnessed the power of big (simulated) data to study the mechanisms of cardiac arrhythmias, with a special emphasis on atrial fibrillation, and improve the assessment of proarrhythmic risk and drug response. The challenges of using in silico approaches with variability are also addressed and future directions are proposed.

Transmural cellular heterogeneity in myocardial electromechanics

Myocardial heterogeneity is an attribute of the normal heart. We have developed integrative models of cardiomyocytes from the subendocardial (ENDO) and subepicardial (EPI) ventricular regions that take into account experimental data on specific regional features of intracellular electromechanical coupling in the guinea pig heart. The models adequately simulate experimental data on the differences in the action potential and contraction between the ENDO and EPI cells. The modeling results predict that heterogeneity in the parameters of calcium handling and myofilament mechanics in isolated ENDO and EPI cardiomyocytes are essential to produce the differences in Ca2+ transients and contraction profiles via cooperative mechanisms of mechano-calcium-electric feedback and may further slightly modulate transmural differences in the electrical properties between the cells. Simulation results predict that ENDO cells have greater sensitivity to changes in the mechanical load than EPI cells. These data are important for understanding the behavior of cardiomyocytes in the intact heart.

Cell shortening and calcium dynamics in epicardial and endocardial myocytes from the left ventricle of Goto-Kakizaki type 2 diabetic rats

NEW FINDINGS

What is the central question of this study? To investigate haemodynamic dysfunction in the type 2 diabetic Goto-Kakizaki (GK) rat, we measured shortening and Ca²⁺ transport in ventricular myocytes from epicardial (EPI) and endocardial (ENDO) regions. What is the main finding and its importance? EPI and ENDO GK myocytes displayed similar hypertrophy. Time to peak (TPK) and time to half (THALF) relaxation were prolonged in EPI GK myocytes. TPK Ca²⁺ transient was prolonged and THALF decay of the Ca²⁺ transient was shortened in EPI GK myocytes. Amplitude of shortening, Ca²⁺ transient and sarcoplasmic reticulum Ca²⁺ were unaltered in EPI and ENDO myocytes from Goto-Kakizaki compared with control rats. We demostrated regional differences in shortening and Ca²⁺ transport in Goto-Kakizaki rats.

ABSTRACT

Diabetic cardiomyopathy is considered to be one of the major diabetes-associated complications, and the pathogenesis of cardiac dysfunction is not well understood. The electromechanical properties of cardiac myocytes vary across the walls of the chambers. The aim of this study was to investigate shortening and Ca²⁺ transport in epicardial (EPI) and endocardial (ENDO) left ventricular myocytes in the Goto-Kakizaki (GK) type 2 diabetic rat heart. Shortening and intracellular Ca²⁺ transients were measured by video edge detection and fluorescence photometry. Myocyte surface area was increased in EPI-GK and ENDO-GK compared with control EPI-CON and ENDO-CON myocytes. Time to peak shortening was prolonged in EPI-GK compared with EPI-CON and in ENDO-CON compared with EPI-CON myocytes. Time to half-relaxation of shortening and time to peak Ca²⁺ transient were prolonged in EPI-GK compared with EPI-CON myocytes. Time to half-decay of the Ca²⁺ transient was prolonged in EPI-CON compared with EPI-GK and in EPI-CON compared with ENDO-CON myocytes. The amplitude of shortening and the Ca²⁺ transient were unaltered in EPI-GK and ENDO-GK compared with their respective controls. Sarcoplasmic reticulum Ca²⁺ and myofilament sensitivity to Ca²⁺ were unaltered in EPI-GK and ENDO-GK compared with their respective controls. Regional differences in Ca²⁺ signalling in healthy and diabetic myocytes might account for variation in the dynamics of myocyte shortening. Further studies will be required to clarify the mechanisms underlying regional differences in the time course of shortening and the Ca²⁺ transient in EPI and ENDO myocytes from diabetic and control hearts.

Computational modeling of amylin-induced calcium dysregulation in rat ventricular cardiomyocytes

Hyperamylinemia is a condition that accompanies obesity and precedes type II diabetes, and it is characterized by above-normal blood levels of amylin, the pancreas-derived peptide. Human amylin oligomerizes easily and can deposit in the pancreas [1], brain [2], and heart [3], where they have been associated with calcium dysregulation. In the heart, accumulating evidence suggests that human amylin oligomers form moderately cation-selective [4,5] channels that embed in the cell sarcolemma (SL). The oligomers increase membrane conductance in a concentration-dependent manner [5], which is correlated with elevated cytosolic Ca²⁺. These findings motivate our core hypothesis that non-selective inward Ca²⁺ conduction afforded by human amylin oligomers increase cytosolic and sarcoplasmic reticulum (SR) Ca²⁺ load, which thereby magnifies intracellular Ca²⁺ transients. Questions remain however regarding the mechanism of amylin-induced Ca²⁺ dysregulation, including whether enhanced SL Ca²⁺ influx is sufficient to elevate cytosolic Ca²⁺ load [6], and if so, how might amplified Ca²⁺ transients perturb Ca²⁺-dependent cardiac pathways. To investigate these questions, we modified a computational model of cardiomyocytes Ca²⁺ signaling to reflect experimentally-measured changes in SL membrane permeation and decreased sarcoplasmic/endoplasmic reticulum calcium ATPase (SERCA) function stemming from acute and transgenic human amylin peptide exposure. With this model, we confirmed the hypothesis that increasing SL permeation alone was sufficient to enhance Ca²⁺ transient amplitudes. Our model indicated that amplified cytosolic transients are driven by increased Ca²⁺ loading of the SR and that greater fractional release may contribute to the Ca²⁺-dependent activation of calmodulin, which could prime the activation of myocyte remodeling pathways. Importantly, elevated Ca²⁺ in the SR and dyadic space collectively drive greater fractional SR Ca²⁺ release for human amylin expressing rats (HIP) and acute amylin-exposed rats (+Amylin) mice, which contributes to the inotropic rise in cytosolic Ca²⁺ transients. These findings suggest that increased membrane permeation induced by oligomeratization of amylin peptide in cell sarcolemma contributes to Ca²⁺ dysregulation in pre-diabetes.

Regional effects of streptozotocin-induced diabetes on shortening and calcium transport in epicardial and endocardial myocytes from rat left ventricle

In the heart, the left ventricle pumps blood at higher pressure than the right ventricle. Within the left ventricle, the electromechanical properties of ventricular cardiac myocytes vary transmurally and this may be related to the gradients of stress and strain experienced in vivo across the ventricular wall. Diabetes is also associated with alterations in hemodynamic function. The aim of this study was to investigate shortening and Ca²⁺ transport in epicardial (EPI) and endocardial (ENDO) left ventricular myocytes in the streptozotocin (STZ)‐induced diabetic rat. Shortening, intracellular Ca²⁺ and L‐type Ca²⁺ current (I_Ca,L) were measured by video detection, fura‐2 microfluorimetry, and whole‐cell patch clamp techniques, respectively. Time to peak (TPK) shortening was prolonged to similar extents in ENDO and EPI myocytes from STZ‐treated rats compared to ENDO and EPI myocytes from controls. Time to half (THALF) relaxation of shortening was prolonged in ENDO myocytes from STZ‐treated rats compared to ENDO controls. TPK Ca²⁺ transient was prolonged in ENDO myocytes from STZ‐treated rats compared to ENDO controls. THALF decay of the Ca²⁺ transient was prolonged in ENDO myocytes from STZ‐treated rats compared to ENDO controls. Sarcoplasmic reticulum (SR) fractional release of Ca²⁺ was reduced in EPI myocytes from STZ‐treated rats compared to EPI controls. I_Ca,L activation, inactivation, and recovery from inactivation were not significantly altered in EPI and ENDO myocytes from STZ‐treated rats or controls. Regional differences in Ca²⁺ transport may partly underlie differences in ventricular myocyte shortening across the wall of the healthy and the STZ‐treated rat left ventricle.

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.

Efficient parameterization of cardiac action potential models using a genetic algorithm

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

Arrhythmia Vulnerability in Diabetic Cardiac Tissue is Species-Dependent: Effects of I KATP, Uncoupling, and Connexin Lateralization

Amongst the complications of diabetes is arrhythmia, the risk of which depends on multiple factors. This study was designed to investigate several factors, including the effects of ATP-sensitive potassium current, lateralized connexins, and gap junction uncoupling. ATP-sensitive potassium channel (I _KATP) opening is caused by ischemia, which can occur in diabetic or non-diabetic hearts. I _KATP opening was simulated in this work to determine if the risk of ischemia-induced arrhythmias is affected by diabetes. Simulations were performed using healthy and diabetic models of rat and rabbit ventricle. Results showed that the diabetic rat model is less vulnerable to reentrant arrhythmia than the healthy rat model. The diabetic rabbit model was more vulnerable to reentrant arrhythmia than the healthy rabbit model. In both rabbit models, the vulnerability increased as the gap junctional coupling decreased. Opening of I _KATP resulted in larger window of vulnerability. Conduction reserve was simulated based on 1D simulations for both rat and rabbit models. There was no difference between rat and rabbit conduction reserve. Our results showed that the simulation results are model-dependent, i.e., results from the rabbit model are similar to human clinical data, while the results from the rat model contradict human clinical observations, suggesting a significant species-dependence in arrhythmia vulnerability in the diabetic heart.

An approach to expand description of the pump and co-transporter steady-state current

The membrane transporters (pumps and co-transporters) are the main players in maintaining the cell homeostasis. Models of various types, each with their own drawbacks, describe transporter behavior. The aim of this study is to find the link between the biophysically based and empirical models to face and solve their specific problems. Instead of decreasing the number of states and using few complex rate constants as is usually done, we use the number of states as great as possible. Then, each transition in the cycle can represent an elementary process and we can apply the mass action law, according to which if rate constants depend on concentrations the dependence is linear. Thus, the expression for the steady state transporter current can be transformed from a function of rate constants into a function of concentrations. When transporter states form a single cycle, it can be characterized by two modes of action - forward and backward ones. Specific mode is realized depending on the available free energy. Each mode of action is characterized by a set of transporter affinities together with a parameter that describes the maximal turning rate. Except standard affinities corresponding to the substances that are binding to the transporter, affinities for the substances that are released are also defined. Such scheme provides great possibilities to construct approximations as each individual affinity could be estimated from experiments as precisely as possible. The approximations may be used for not only description and study of the transporter current but also in cellular models that attempt to describe wide variety of processes in excitable cells.

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

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

Cardiac inotropy, lusitropy, and Ca2+ handling with major metabolic substrates in rat heart

Fatty acid (FA)-dependent oxidation is the predominant process for energy supply in normal heart. Impaired FA metabolism and metabolic insufficiency underlie the failing of the myocardium. So far, FA metabolism in normal cardiac physiology and heart failure remains undetermined. Here, we evaluate the mechanisms of FA and major metabolic substrates (termed NF) on the contraction, relaxation, and Ca²⁺ handling in rat left ventricular (LV) myocytes. Our results showed that NF significantly increased myocyte contraction and facilitated relaxation. Moreover, NF increased the amplitudes of diastolic and systolic Ca²⁺ transients ([Ca²⁺]_i), abbreviated time constant of [Ca²⁺]_i decay (tau), and prolonged the peak duration of [Ca²⁺]_i. Whole-cell patch-clamp experiments revealed that NF increased Ca²⁺ influx via L-type Ca²⁺ channels (LTCC, I_Ca-integral) and prolonged the action potential duration (APD). Further analysis revealed that NF shifted the relaxation phase of sarcomere lengthening vs. [Ca²⁺]_i trajectory to the right and increased [Ca²⁺]_i for 50 % of sarcomere relengthening (EC₅₀), suggesting myofilament Ca²⁺ desensitization. Butanedione monoxime (BDM), a myosin ATPase inhibitor that reduces myofilament Ca²⁺ sensitivity, abolished the NF-induced enhancement of [Ca²⁺]_i amplitude and the tau of [Ca²⁺]_i decay, indicating the association of myofilament Ca²⁺ desensitization with the changes in [Ca²⁺]_i profile in NF. NF reduced intracellular pH ([pH_i]). Increasing [pH]_i buffer capacity with HCO₃/CO₂ attenuated Δ [pH]_i and reversed myofilament Ca²⁺ desensitization and Ca²⁺ handling in NF. Collectively, greater Ca²⁺ influx through LTCCs and myofilament Ca²⁺ desensitization, via reducing [pH]_i, are likely responsible for the positive inotropic and lusitropic effects of NF. Computer simulation recapitulated the effects of NF.

Current-Voltage Relationship for Late Na(+) Current in Adult Rat Ventricular Myocytes

It is now well established that the slowly inactivating component of the Na(+) current (INa-L) in the mammalian heart is a significant regulator of the action potential waveform. This insight has led to detailed studies of the role of INa-L in a number of important and challenging pathophysiological settings. These include genetically based ventricular arrhythmias (LQT 1, 2, and 3), ventricular arrhythmias arising from progressive cardiomyopathies (including diabetic), and proarrhythmic abnormalities that develop during local or global ventricular ischemia. Inhibition of INa-L may also be a useful strategy for management of atrial flutter and fibrillation. Many important biophysical parameters that characterize INa-L have been identified; and INa-L as an antiarrhythmia drug target has been studied extensively. However, relatively little information is available regarding (1) the ion transfer or current-voltage relationship for INa-L or (2) the time course of its reactivation at membrane potentials similar to the resting or diastolic membrane potential in mammalian ventricle. This chapter is based on our preliminary findings concerning these two very important physiological/biophysical descriptors for INa-L. Our results were obtained using whole-cell voltage clamp methods applied to enzymatically isolated rat ventricular myocytes. A chemical agent, BDF 9148, which was once considered to be a drug candidate in the Na(+)-dependent inotropic agent category has been used to markedly enhance INa-L current. BDF acts in a potent, selective, and reversible fashion. These BDF 9148 effects are compared and contrasted with the prototypical activator of INa-L, a sea anemone toxin, ATX II.

There and back again: Iterating between population-based modeling and experiments reveals surprising regulation of calcium transients in rat cardiac myocytes

While many ion channels and transporters involved in cardiac cellular physiology have been identified and described, the relative importance of each in determining emergent cellular behaviors remains unclear. Here we address this issue with a novel approach that combines population-based mathematical modeling with experimental tests to systematically quantify the relative contributions of different ion channels and transporters to the amplitude of the cellular Ca(2+) transient. Sensitivity analysis of a mathematical model of the rat ventricular cardiomyocyte quantified the response of cell behaviors to changes in the level of each ion channel and transporter, and experimental tests of these predictions were performed to validate or invalidate the predictions. The model analysis found that partial inhibition of the transient outward current in rat ventricular epicardial myocytes was predicted to have a greater impact on Ca(2+) transient amplitude than either: (1) inhibition of the same current in endocardial myocytes, or (2) comparable inhibition of the sarco/endoplasmic reticulum Ca(2+) ATPase (SERCA). Experimental tests confirmed the model predictions qualitatively but showed some quantitative disagreement. This guided us to recalibrate the model by adjusting the relative importance of several Ca(2+) fluxes, thereby improving the consistency with experimental data and producing a more predictive model. Analysis of human cardiomyocyte models suggests that the relative importance of outward currents to Ca(2+) transporters is generalizable to human atrial cardiomyocytes, but not ventricular cardiomyocytes. Overall, our novel approach of combining population-based mathematical modeling with experimental tests has yielded new insight into the relative importance of different determinants of cell behavior.

The calcium-frequency response in the rat ventricular myocyte: an experimental and modelling study

KEY POINTS

In the majority of species, including humans, increased heart rate increases cardiac contractility. This change is known as the force-frequency response (FFR). The majority of mammals have a positive force-frequency relationship (FFR). In rat the FFR is controversial. We derive a species- and temperature-specific data-driven model of the rat ventricular myocyte. As a measure of the FFR, we test the effects of changes in frequency and extracellular calcium on the calcium-frequency response (CFR) in our model and three altered models. The results show a biphasic peak calcium-frequency response, due to biphasic behaviour of the ryanodine receptor and the combined effect of the rapid calmodulin buffer and the frequency-dependent increase in diastolic calcium. Alterations to the model reveal that inclusion of Ca(2+) /calmodulin-dependent protein kinase II (CAMKII)-mediated L-type channel and transient outward K(+) current activity enhances the positive magnitude calcium-frequency response, and the absence of CAMKII-mediated increase in activity of the sarco/endoplasmic reticulum Ca(2+) -ATPase induces a negative magnitude calcium-frequency response.

ABSTRACT

An increase in heart rate affects the strength of cardiac contraction by altering the Ca(2+) transient as a response to physiological demands. This is described by the force-frequency response (FFR), a change in developed force with pacing frequency. The majority of mammals, including humans, have a positive FFR, and cardiac contraction strength increases with heart rate. However, the rat and mouse are exceptions, with the majority of studies reporting a negative FFR, while others report either a biphasic or a positive FFR. Understanding the differences in the FFR between humans and rats is fundamental to interpreting rat-based experimental findings in the context of human physiology. We have developed a novel model of rat ventricular electrophysiology and calcium dynamics, derived predominantly from experimental data recorded under physiological conditions. As a measure of FFR, we tested the effects of changes in stimulation frequency and extracellular calcium concentration on the simulated Ca(2+) transient characteristics and showed a biphasic peak calcium-frequency relationship, consistent with recent observations of a shift from negative to positive FFR when approaching the rat physiological frequency range. We tested the hypotheses that (1) inhibition of Ca(2+) /calmodulin-dependent protein kinase II (CAMKII)-mediated increase in sarco/endoplasmic reticulum Ca(2+) -ATPase (SERCA) activity, (2) CAMKII modulation of SERCA, L-type channel and transient outward K(+) current activity and (3) Na(+) /K(+) pump dynamics play a significant role in the rat FFR. The results reveal a major role for CAMKII modulation of SERCA in the peak Ca(2+) -frequency response, driven most significantly by the cytosolic calcium buffering system and changes in diastolic Ca(2+) .

A Mathematical Model of Neonatal Rat Atrial Monolayers with Constitutively Active Acetylcholine-Mediated K+ Current

Atrial fibrillation (AF) is the most frequent form of arrhythmia occurring in the industrialized world. Because of its complex nature, each identified form of AF requires specialized treatment. Thus, an in-depth understanding of the bases of these arrhythmias is essential for therapeutic development. A variety of experimental studies aimed at understanding the mechanisms of AF are performed using primary cultures of neonatal rat atrial cardiomyocytes (NRAMs). Previously, we have shown that the distinct advantage of NRAM cultures is that they allow standardized, systematic, robust re-entry induction in the presence of a constitutively-active acetylcholine-mediated K⁺ current (I_KACh-c). Experimental studies dedicated to mechanistic explorations of AF, using these cultures, often use computer models for detailed electrophysiological investigations. However, currently, no mathematical model for NRAMs is available. Therefore, in the present study we propose the first model for the action potential (AP) of a NRAM with constitutively-active acetylcholine-mediated K⁺ current (I_KACh-c). The descriptions of the ionic currents were based on patch-clamp data obtained from neonatal rats. Our monolayer model closely mimics the action potential duration (APD) restitution and conduction velocity (CV) restitution curves presented in our previous in vitro studies. In addition, the model reproduces the experimentally observed dynamics of spiral wave rotation, in the absence and in the presence of drug interventions, and in the presence of localized myofibroblast heterogeneities.

A fundamentally important element in cardiac in silico research is a model for the cardiac cell. It provides a link between measurable characteristics at the subcellular level and biological processes at the whole cell level, thereby allowing the researcher to study mechanisms of cardiac arrhythmias from a molecular cell biological perspective. Such studies are of vast importance for the advancement of understanding of living systems from cells to patient populations. This paper is a joint in silico-experimental study in which we propose the first model for the action potential of an NRAM. To develop this model, we fitted patch-clamp data from recent literature, while additionally performing specific measurements of I_KACh-c in NRAMs. I_KACh-c is an important factor in atrial arrhythmogenesis and a promising target for pharmacological AF-management. The model reproduces in vitro results such as standard characteristics of AP morphology, restitution, and spiral wave dynamics in monolayers, with effects of a subsequent drug-intervention and in the presence of localized myofibroblast heterogeneities. Thus it can be used as a tool to provide computational support to a variety of systematic experimental studies that investigate the mechanisms underlying atrial fibrillation (AF) in NRAM cultures.