Mechanisms of excitation-contraction coupling in an integrative model of the cardiac ventricular myocyte

Electroanatomical adaptations in the guinea pig heart from neonatal to adulthood

AIMS

Electroanatomical adaptations during the neonatal to adult phase have not been comprehensively studied in preclinical animal models. To explore the impact of age as a biological variable on cardiac electrophysiology, we employed neonatal and adult guinea pigs, which are a recognized animal model for developmental research.

METHODS AND RESULTS

Electrocardiogram recordings were collected in vivo from anaesthetized animals. A Langendorff-perfusion system was employed for the optical assessment of action potentials and calcium transients. Optical data sets were analysed using Kairosight 3.0 software. The allometric relationship between heart weight and body weight diminishes with age, it is strongest at the neonatal stage (R2 = 0.84) and abolished in older adults (R2 = 1E-06). Neonatal hearts exhibit circular activation, while adults show prototypical elliptical shapes. Neonatal conduction velocity (40.6 ± 4.0 cm/s) is slower than adults (younger: 61.6 ± 9.3 cm/s; older: 53.6 ± 9.2 cm/s). Neonatal hearts have a longer action potential duration (APD) and exhibit regional heterogeneity (left apex; APD30: 68.6 ± 5.6 ms, left basal; APD30: 62.8 ± 3.6), which was absent in adults. With dynamic pacing, neonatal hearts exhibit a flatter APD restitution slope (APD70: 0.29 ± 0.04) compared with older adults (0.49 ± 0.04). Similar restitution characteristics are observed with extrasystolic pacing, with a flatter slope in neonates (APD70: 0.54 ± 0.1) compared with adults (younger: 0.85 ± 0.4; older: 0.95 ± 0.7). Neonatal hearts display unidirectional excitation-contraction coupling, while adults exhibit bidirectionality.

CONCLUSION

Postnatal development is characterized by transient changes in electroanatomical properties. Age-specific patterns can influence cardiac physiology, pathology, and therapies for cardiovascular diseases. Understanding heart development is crucial to evaluating therapeutic eligibility, safety, and efficacy.

Electroanatomical Adaptations in the Guinea Pig Heart from Neonatal to Adulthood

Background

Electroanatomical adaptations during the neonatal to adult phase have not been comprehensively studied in preclinical animal models. To explore the impact of age as a biological variable on cardiac electrophysiology, we employed neonatal and adult guinea pigs, which are a recognized animal model for developmental research.

Methods

Healthy guinea pigs were categorized into three age groups (neonates, n=10; younger adults, n=13; and older adults, n=26). Electrocardiogram (ECG) recordings were collected in vivo from anesthetized animals (2-3% isoflurane). A Langendorff-perfusion system was employed for optical assessment of epicardial action potentials and calcium transients, using intact excised heart preparations. Optical data sets were analyzed and metric maps were constructed using Kairosight 3.0.

Results

The allometric relationship between heart weight and body weight diminishes with age, as it is strongest at the neonatal stage (R 2 = 0.84) and completely abolished in older adults (R 2 = 1E-06). Neonatal hearts exhibit circular activation waveforms, while adults show prototypical elliptical shapes. Neonatal conduction velocity (40.6±4.0 cm/s) is slower than adults (younger adults: 61.6±9.3 cm/s; older adults: 53.6±9.2 cm/s). Neonatal hearts have a longer action potential duration (APD) and exhibit regional heterogeneity (left apex; APD30: 68.6±5.6 ms, left basal; APD30: 62.8±3.6), which was absent in adult epicardium. With dynamic pacing, neonatal hearts exhibit a flatter APD restitution slope (APD70: 0.29±0.04) compared to older adults (0.49±0.04). Similar restitution characteristics are observed with extrasystolic pacing, with a flatter slope in neonatal hearts (APD70: 0.54±0.1) compared to adults (Younger adults: 0.85±0.4; Older adults: 0.95±0.7). Finally, neonatal hearts display unidirectional excitation-contraction coupling, while adults exhibit bidirectionality.

Conclusion

The transition from neonatal to adulthood in guinea pig hearts is characterized by transient changes in electroanatomic properties. Age-specific patterns can influence cardiac physiology, pathology, and therapies for cardiovascular diseases. Understanding postnatal heart development is crucial to evaluating therapeutic eligibility, safety, and efficacy.

What is Known

Age-specific cardiac electroanatomical characteristics have been documented in humans and some preclinical animal models. These age-specific patterns can influence cardiac physiology, pathology, and therapies for cardiovascular diseases.

What the Study Adds

Cardiac electroanatomical characteristics are age-specific in guinea pigs, a well-known preclinical model for developmental studies. Age-dependent adaptations in cardiac electrophysiology are readily observed in the electrocardiogram recordings and via optical mapping of epicardial action potentials and calcium transients. Our findings reveal unique activation and repolarization characteristics between neonatal and adult animals.

T cell Ca2+ microdomains through the lens of computational modeling

Cellular Ca2+ signaling is highly organized in time and space. Locally restricted and short-lived regions of Ca2+ increase, called Ca2+ microdomains, constitute building blocks that are differentially arranged to create cellular Ca2+ signatures controlling physiological responses. Here, we focus on Ca2+ microdomains occurring in restricted cytosolic spaces between the plasma membrane and the endoplasmic reticulum, called endoplasmic reticulum-plasma membrane junctions. In T cells, these microdomains have been finely characterized. Enough quantitative data are thus available to develop detailed computational models of junctional Ca2+ dynamics. Simulations are able to predict the characteristics of Ca2+ increases at the level of single channels and in junctions of different spatial configurations, in response to various signaling molecules. Thanks to the synergy between experimental observations and computational modeling, a unified description of the molecular mechanisms that create Ca2+ microdomains in the first seconds of T cell stimulation is emerging.

Membrane remodelling triggers maturation of excitation-contraction coupling in 3D-shaped human-induced pluripotent stem cell-derived cardiomyocytes

The prospective use of human-induced pluripotent stem cell-derived cardiomyocytes (hiPSC-CM) for cardiac regenerative medicine strongly depends on the electro-mechanical properties of these cells, especially regarding the Ca2+-dependent excitation-contraction (EC) coupling mechanism. Currently, the immature structural and functional features of hiPSC-CM limit the progression towards clinical applications. Here, we show that a specific microarchitecture is essential for functional maturation of hiPSC-CM. Structural remodelling towards a cuboid cell shape and induction of BIN1, a facilitator of membrane invaginations, lead to transverse (t)-tubule-like structures. This transformation brings two Ca2+ channels critical for EC coupling in close proximity, the L-type Ca2+ channel at the sarcolemma and the ryanodine receptor at the sarcoplasmic reticulum. Consequently, the Ca2+-dependent functional interaction of these channels becomes more efficient, leading to improved spatio-temporal synchronisation of Ca2+ transients and higher EC coupling gain. Thus, functional maturation of hiPSC-cardiomyocytes by optimised cell microarchitecture needs to be considered for future cardiac regenerative approaches.

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.

Gradient-based parameter optimization method to determine membrane ionic current composition in human induced pluripotent stem cell-derived cardiomyocytes

Premature cardiac myocytes derived from human induced pluripotent stem cells (hiPSC-CMs) show heterogeneous action potentials (APs), probably due to different expression patterns of membrane ionic currents. We developed a method for determining expression patterns of functional channels in terms of whole-cell ionic conductance (G_x) using individual spontaneous AP configurations. It has been suggested that apparently identical AP configurations can be obtained using different sets of ionic currents in mathematical models of cardiac membrane excitation. If so, the inverse problem of G_x estimation might not be solved. We computationally tested the feasibility of the gradient-based optimization method. For a realistic examination, conventional 'cell-specific models' were prepared by superimposing the model output of AP on each experimental AP recorded by conventional manual adjustment of G_xs of the baseline model. G_xs of 4-6 major ionic currents of the 'cell-specific models' were randomized within a range of ± 5-15% and used as an initial parameter set for the gradient-based automatic G_xs recovery by decreasing the mean square error (MSE) between the target and model output. Plotting all data points of the MSE-G_x relationship during optimization revealed progressive convergence of the randomized population of G_xs to the original value of the cell-specific model with decreasing MSE. The absence of any other local minimum in the global search space was confirmed by mapping the MSE by randomizing G_xs over a range of 0.1-10 times the control. No additional local minimum MSE was obvious in the whole parameter space, in addition to the global minimum of MSE at the default model parameter.

Live-Cell Imaging of the Contractile Velocity and Transient Intracellular Ca2+ Fluctuations in Human Stem Cell-Derived Cardiomyocytes

Live-cell imaging techniques are essential for acquiring vital physiological and pathophysiological knowledge to understand and treat heart disease. For live-cell imaging of transient alterations of [Ca2+]i in human cardiomyocytes, we engineered human-induced pluripotent stem cells carrying a genetically-encoded Ca2+-indicator (GECI). To monitor sarcomere shortening and relaxation in cardiomyocytes in real-time, we generated a α-cardiac actinin (ACTN2)-copepod (cop) green fluorescent protein (GFP+)-human-induced pluripotent stem cell line by using the CRISPR-Cas9 and a homology directed recombination approach. The engineered human-induced pluripotent stem cells were differentiated in transgenic GECI-enhanced GFP+-cardiomyocytes and ACTN2-copGFP+-cardiomyocytes, allowing real-time imaging of [Ca2+]i transients and live recordings of the sarcomere shortening velocity of ACTN2-copGFP+-cardiomyocytes. We developed a video analysis software tool to quantify various parameters of sarcoplasmic Ca2+ fluctuations recorded during contraction of cardiomyocytes and to calculate the contraction velocity of cardiomyocytes in the presence and absence of different drugs affecting cardiac function. Our cellular and software tool not only proved the positive and negative inotropic and lusitropic effects of the tested cardioactive drugs but also quantified the expected effects precisely. Our platform will offer a human-relevant in vitro alternative for high-throughput drug screenings, as well as a model to explore the underlying mechanisms of cardiac diseases.

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.

Mechanisms Underlying the Cardioprotection of YangXinDingJi Capsule against Myocardial Ischemia in Rats

Background

YangXinDingJi (YXDJ) capsule is one of traditional Chinese medicines (TCMs) derived from Zhigancao decoction, which is usually used for the treatment of cardiovascular disease in China. Aim of the Study. Cardiovascular events are one of the leading causes of death worldwide. Myocardial ischemia (MI) severely reduces myocyte longevity and function. The YangXinDingJi (YXDJ) capsule has been used in the treatment of clinical cardiac disease in China. Nevertheless, the underlying cellular mechanisms for the benefits to heart function resulting from the use of this capsule are still unclear. The aim of this study was to evaluate the protective effects of the YXDJ on isoprenaline-induced MI in rats and to clarify its underlying myocardial protective mechanisms based on L-type calcium channels and myocardial contractility.

Materials and Methods

Rats were randomly divided into five groups with ten rats in each group: (1) control; (2) ISO-induced model; (3) high-dose YXDJ (2.8 g/kg/day intraperitoneally for five days), (4) low-dose YXDJ (1.4 g/kg/day for five days); and (5) verapamil (n = 10 in each group). Isoproterenol (ISO) was injected subcutaneously for two consecutive days to induce the rat model of MI. Heart and biochemical parameters were obtained. The patch-clamp technique was used to observe the regulatory effects of YXDJ on the L-type calcium current (I_Ca-L) in isolated cardiomyocytes. An IonOptix MyoCam detection system was used to observe the contractility of YXDJ on isolated cardiomyocytes.

Results

YXDJ caused a significant improvement in pathological heart morphology and alleviated oxidative stress and inflammatory responses. Exposure to YXDJ caused a decrease in blockade of I_Ca-L in a concentration-dependent manner.

Conclusions

The results indicate that YXDJ significantly inhibited inflammatory cytokine expressions, oxidative stress, and L-type Ca²⁺ channels, and decreased contractility in isolated rat cardiomyocytes. These findings may be relevant to the cardioprotective efficacy of YXDJ.

Using cardiac ionic cell models to interpret clinical data

For over 100 years cardiac electrophysiology has been measured in the clinic. The electrical signals that can be measured span from noninvasive ECG and body surface potentials measurements through to detailed invasive measurements of local tissue electrophysiology. These electrophysiological measurements form a crucial component of patient diagnosis and monitoring; however, it remains challenging to quantitatively link changes in clinical electrophysiology measurements to biophysical cellular function. Multi-scale biophysical computational models represent one solution to this problem. These models provide a formal framework for linking cellular function through to emergent whole organ function and routine clinical diagnostic signals. In this review, we describe recent work on the use of computational models to interpret clinical electrophysiology signals. We review the simulation of human cardiac myocyte electrophysiology in the atria and the ventricles and how these models are being used to link organ scale function to patient disease mechanisms and therapy response in patients receiving implanted defibrillators, \cardiac resynchronisation therapy or suffering from atrial fibrillation and ventricular tachycardia. There is a growing use of multi-scale biophysical models to interpret clinical data. This allows cardiologists to link clinical observations with cellular mechanisms to better understand cardiopathophysiology and identify novel treatment strategies. This article is categorized under: Cardiovascular Diseases > Computational Models Cardiovascular Diseases > Biomedical Engineering Cardiovascular Diseases > Molecular and Cellular Physiology.

Integration of mechanical conditioning into a high throughput contractility assay for cardiac safety assessment

INDUCTION

Despite increasing acceptance of human induced pluripotent stem cell-derived cardiomyocytes (hiPSC-CMs) in safety pharmacology, controversy remains about the physiological relevance of existing in vitro models for their mechanical testing. We hypothesize that existing signs of immaturity of the cell models result from an improper mechanical environment. With the presented study, we aimed at validating the newly developed FLEXcyte96 technology with respect to physiological responses of hiPSC-CMs to pharmacological compounds with known inotropic and/or cardiotoxic effects.

METHODS

hiPSC-CMs were cultured in a 96-well format on hyperelastic silicone membranes imitating their native mechanical environment. Cardiomyocyte contractility was measured contact-free by application of capacitive displacement sensing of the cell-membrane biohybrids. Acute effects of positive inotropic compounds with distinct mechanisms of action were examined. Additionally, cardiotoxic effects of tyrosine kinase inhibitors and anthracyclines were repetitively examined during repeated exposure to drug concentrations for up to 5 days.

RESULTS

hiPSC-CMs grown on biomimetic membranes displayed increased contractility responses to isoproterenol, S-Bay K8644 and omecamtiv mecarbil without the need for additional stimulation. Tyrosine kinase inhibitor erlotinib, vandetanib, nilotinib, gefitinib, A-674563 as well as anthracycline idarubicin showed the expected cardiotoxic effects, including negative inotropy and induction of proarrhythmic events.

DISCUSSION

We conclude that the FLEXcyte 96 system is a reliable high throughput tool for invitro cardiac contractility research, providing the user with data obtained under physiological conditions which resemble the native environment of human heart tissue. We showed that the results obtained for both acute and sub-chronic compound administration are consistent with the respective physiological responses in humans.

A bilobal model of Ca2+-dependent inactivation to probe the physiology of L-type Ca2+ channels

L-type calcium channels undergo Ca²⁺-dependent inactivation (CDI) in order to precisely control the entry of Ca²⁺ into cells such as cardiomyocytes. Limpitikul et al. develop a bilobal model of CDI and use it to understand the pathogenesis of arrhythmias associated with mutations in CaM.

L-type calcium channels (LTCCs) are critical elements of normal cardiac function, playing a major role in orchestrating cardiac electrical activity and initiating downstream signaling processes. LTCCs thus use feedback mechanisms to precisely control calcium (Ca²⁺) entry into cells. Of these, Ca²⁺-dependent inactivation (CDI) is significant because it shapes cardiac action potential duration and is essential for normal cardiac rhythm. This important form of regulation is mediated by a resident Ca²⁺ sensor, calmodulin (CaM), which is comprised of two lobes that are each capable of responding to spatially distinct Ca²⁺ sources. Disruption of CaM-mediated CDI leads to severe forms of long-QT syndrome (LQTS) and life-threatening arrhythmias. Thus, a model capable of capturing the nuances of CaM-mediated CDI would facilitate increased understanding of cardiac (patho)physiology. However, one critical barrier to achieving a detailed kinetic model of CDI has been the lack of quantitative data characterizing CDI as a function of Ca²⁺. This data deficit stems from the experimental challenge of uncoupling the effect of channel gating on Ca²⁺ entry. To overcome this obstacle, we use photo-uncaging of Ca²⁺ to deliver a measurable Ca²⁺ input to CaM/LTCCs, while simultaneously recording CDI. Moreover, we use engineered CaMs with Ca²⁺ binding restricted to a single lobe, to isolate the kinetic response of each lobe. These high-resolution measurements enable us to build mathematical models for each lobe of CaM, which we use as building blocks for a full-scale bilobal model of CDI. Finally, we use this model to probe the pathogenesis of LQTS associated with mutations in CaM (calmodulinopathies). Each of these models accurately recapitulates the kinetics and steady-state properties of CDI in both physiological and pathological states, thus offering powerful new insights into the mechanistic alterations underlying cardiac arrhythmias.

Quantitative systems models illuminate arrhythmia mechanisms in heart failure: Role of the Na+ -Ca2+ -Ca2+ /calmodulin-dependent protein kinase II-reactive oxygen species feedback

Quantitative systems modeling aims to integrate knowledge in different research areas with models describing biological mechanisms and dynamics to gain a better understanding of complex clinical syndromes. Heart failure (HF) is a chronic complex cardiac disease that results from structural or functional disorders impairing the ability of the ventricle to fill with or eject blood. Highly interactive and dynamic changes in mechanical, structural, neurohumoral, metabolic, and electrophysiological properties collectively predispose the failing heart to cardiac arrhythmias, which are responsible for about a half of HF deaths. Multiscale cardiac modeling and simulation integrate structural and functional data from HF experimental models and patients to improve our mechanistic understanding of this complex arrhythmia syndrome. In particular, they allow investigating how disease-induced remodeling alters the coupling of electrophysiology, Ca²⁺ and Na⁺ handling, contraction, and energetics that lead to rhythm derangements. The Ca²⁺ /calmodulin-dependent protein kinase II, which expression and activity are enhanced in HF, emerges as a critical hub that modulates the feedbacks between these various subsystems and promotes arrhythmogenesis. This article is categorized under: Physiology > Mammalian Physiology in Health and Disease Models of Systems Properties and Processes > Mechanistic Models Models of Systems Properties and Processes > Cellular Models Models of Systems Properties and Processes > Organ, Tissue, and Physiological Models.

Concise Whole-Cell Modeling of BKCa-CaV Activity Controlled by Local Coupling and Stoichiometry

Large-conductance Ca²⁺-dependent K⁺ (BK_Ca) channels are important regulators of electrical activity. These channels colocalize and form ion channel complexes with voltage-dependent Ca²⁺ (CaV) channels. Recent stochastic simulations of the BK_Ca-CaV complex with 1:1 stoichiometry have given important insight into the local control of BK_Ca channels by fluctuating nanodomains of Ca²⁺. However, such Monte Carlo simulations are computationally expensive, and are therefore not suitable for large-scale simulations of cellular electrical activity. In this work we extend the stochastic model to more realistic BK_Ca-CaV complexes with 1:n stoichiometry, and analyze the single-complex model with Markov chain theory. From the description of a single BK_Ca-CaV complex, using arguments based on timescale analysis, we derive a concise model of whole-cell BK_Ca currents, which can readily be analyzed and inserted into models of cellular electrical activity. We illustrate the usefulness of our results by inserting our BK_Ca description into previously published whole-cell models, and perform simulations of electrical activity in various cell types, which show that BK_Ca-CaV stoichiometry can affect whole-cell behavior substantially. Our work provides a simple formulation for the whole-cell BK_Ca current that respects local interactions in BK_Ca-CaV complexes, and indicates how local-global coupling of ion channels may affect cell behavior.

Mechanisms of the cyclic nucleotide cross-talk signaling network in cardiac L-type calcium channel regulation

Regulation of L-type Calcium (Ca2+) Channel (LCC) gating is critical to shaping the cardiac action potential (AP) and triggering the initiation of excitation-contraction (EC) coupling in cardiac myocytes. The cyclic nucleotide (cN) cross-talk signaling network, which encompasses the β-adrenergic and the Nitric Oxide (NO)/cGMP/Protein Kinase G (PKG) pathways and their interaction (cross-talk) through distinctively-regulated phosphodiesterase isoenzymes (PDEs), regulates LCC current via Protein Kinase A- (PKA) and PKG-mediated phosphorylation. Due to the tightly-coupled and intertwined biochemical reactions involved, it remains to be clarified how LCC gating is regulated by the signaling network from receptor to end target. In addition, the large number of EC coupling-related phosphorylation targets of PKA and PKG makes it difficult to quantify and isolate changes in L-type Ca2+ current (ICaL) responses regulated by the signaling network. We have developed a multi-scale, biophysically-detailed computational model of LCC regulation by the cN signaling network that is supported by experimental data. LCCs are modeled with functionally distinct PKA- and PKG-phosphorylation dependent gating modes. The model exhibits experimentally observed single channel characteristics, as well as whole-cell LCC currents upon activation of the cross-talk signaling network. Simulations show 1) redistribution of LCC gating modes explains changes in whole-cell current under various stimulation scenarios of the cN cross-talk network; 2) NO regulation occurs via potentiation of a gating mode characterized by prolonged closed times; and 3) due to compensatory actions of cross-talk and antagonizing functions of PKA- and PKG-mediated phosphorylation of LCCs, the effects of individual inhibitions of PDEs 2, 3, and 4 on ICaL are most pronounced at low levels of β-adrenergic stimulation. Simulations also delineate the contribution of the following two mechanisms to overall LCC regulation, which have otherwise been challenging to distinguish: 1) regulation of PKA and PKG activation via cN cross-talk (Mechanism 1); and 2) LCC interaction with activated PKA and PKG (Mechanism 2). These results provide insights into how cN signals transduced via the cN cross-talk signaling network are integrated via LCC regulation in the heart.

Studying dyadic structure-function relationships: a review of current modeling approaches and new insights into Ca2+ (mis)handling

Excitation–contraction coupling in cardiac myocytes requires calcium influx through L-type calcium channels in the sarcolemma, which gates calcium release through sarcoplasmic reticulum ryanodine receptors in a process known as calcium-induced calcium release, producing a myoplasmic calcium transient and enabling cardiomyocyte contraction. The spatio-temporal dynamics of calcium release, buffering, and reuptake into the sarcoplasmic reticulum play a central role in excitation–contraction coupling in both normal and diseased cardiac myocytes. However, further quantitative understanding of these cells’ calcium machinery and the study of mechanisms that underlie both normal cardiac function and calcium-dependent etiologies in heart disease requires accurate knowledge of cardiac ultrastructure, protein distribution and subcellular function. As current imaging techniques are limited in spatial resolution, limiting insight into changes in calcium handling, computational models of excitation–contraction coupling have been increasingly employed to probe these structure–function relationships. This review will focus on the development of structural models of cardiac calcium dynamics at the subcellular level, orienting the reader broadly towards the development of models of subcellular calcium handling in cardiomyocytes. Specific focus will be given to progress in recent years in terms of multi-scale modeling employing resolved spatial models of subcellular calcium machinery. A review of the state-of-the-art will be followed by a review of emergent insights into calcium-dependent etiologies in heart disease and, finally, we will offer a perspective on future directions for related computational modeling and simulation efforts.

Neuronal sodium channels: emerging components of the nano-machinery of cardiac calcium cycling

Excitation-contraction coupling is the bridge between cardiac electrical activation and mechanical contraction. It is driven by the influx of Ca²⁺ across the sarcolemma triggering Ca²⁺ release from the sarcoplasmic reticulum (SR) - a process termed Ca²⁺ -induced Ca²⁺ release (CICR) - followed by re-sequestration of Ca²⁺ into the SR. The Na⁺ /Ca²⁺ exchanger inextricably couples the cycling of Ca²⁺ and Na⁺ in cardiac myocytes. Thus, influx of Na⁺ via voltage-gated Na⁺ channels (Na_V ) has emerged as an important regulator of CICR both in health and in disease. Recent insights into the subcellular distribution of cardiac and neuronal Na_V isoforms and their ultrastructural milieu have important implications for the roles of these channels in mediating Ca²⁺ -driven arrhythmias. This review will discuss functional insights into the role of neuronal Na_V isoforms vis-à-vis cardiac Na_V s in triggering such arrhythmias and their potential as therapeutic targets in the context of the aforementioned structural observations.

The relative contributions of store-operated and voltage-gated Ca2+ channels to the control of Ca2+ oscillations in airway smooth muscle

KEY POINTS

Agonist-dependent oscillations in the concentration of free cytosolic calcium are a vital mechanism for the control of airway smooth muscle contraction and thus are a critical factor in airway hyper-responsiveness. Using a mathematical model, closely tied to experimental work, we show that the oscillations in membrane potential accompanying the calcium oscillations have no significant effect on the properties of the calcium oscillations. In addition, the model shows that calcium entry through store-operated calcium channels is critical for calcium oscillations, but calcium entry through voltage-gated channels has much less effect. The model predicts that voltage-gated channels are less important than store-operated channels in the control of airway smooth muscle tone.

ABSTRACT

Airway smooth muscle contraction is typically the key mechanism underlying airway hyper-responsiveness, and the strength of muscle contraction is determined by the frequency of oscillations of intracellular calcium (Ca²⁺ ) concentration. In airway smooth muscle cells, these Ca²⁺ oscillations are caused by cyclic Ca²⁺ release from the sarcoplasmic reticulum, although Ca²⁺ influx via plasma membrane channels is also necessary to sustain the oscillations over longer times. To assess the relative contributions of store-operated and voltage-gated Ca²⁺ channels to this Ca²⁺ influx, we generated a comprehensive mathematical model, based on experimental Ca²⁺ measurements in mouse precision-cut lung slices, to simulate Ca²⁺ oscillations and changes in membrane potential. Agonist-induced Ca²⁺ oscillations are accompanied by oscillations in membrane potential, although the membrane potential oscillations are too small to generate large Ca²⁺ currents through voltage-gated Ca²⁺ channels, and thus have little effect on the Ca²⁺ oscillations. Ca²⁺ entry through voltage-gated channels only becomes important when the cell is depolarized (e.g. by a high external K⁺ concentration). As a result, agonist-induced Ca²⁺ oscillations are critically dependent on Ca²⁺ entry through store-operated channels but do not depend strongly on Ca²⁺ entry though voltage-gated channels.

A human ventricular myocyte model with a refined representation of excitation-contraction coupling

Cardiac Ca(2+)-induced Ca(2+) release (CICR) occurs by a regenerative activation of ryanodine receptors (RyRs) within each Ca(2+)-releasing unit, triggered by the activation of L-type Ca(2+) channels (LCCs). CICR is then terminated, most probably by depletion of Ca(2+) in the junctional sarcoplasmic reticulum (SR). Hinch et al. previously developed a tightly coupled LCC-RyR mathematical model, known as the Hinch model, that enables simulations to deal with a variety of functional states of whole-cell populations of a Ca(2+)-releasing unit using a personal computer. In this study, we developed a membrane excitation-contraction model of the human ventricular myocyte, which we call the human ventricular cell (HuVEC) model. This model is a hybrid of the most recent HuVEC models and the Hinch model. We modified the Hinch model to reproduce the regenerative activation and termination of CICR. In particular, we removed the inactivated RyR state and separated the single step of RyR activation by LCCs into triggering and regenerative steps. More importantly, we included the experimental measurement of a transient rise in Ca(2+) concentrations ([Ca(2+)], 10-15 μM) during CICR in the vicinity of Ca(2+)-releasing sites, and thereby calculated the effects of the local Ca(2+) gradient on CICR as well as membrane excitation. This HuVEC model successfully reconstructed both membrane excitation and key properties of CICR. The time course of CICR evoked by an action potential was accounted for by autonomous changes in an instantaneous equilibrium open probability of couplons. This autonomous time course was driven by a core feedback loop including the pivotal local [Ca(2+)], influenced by a time-dependent decay in the SR Ca(2+) content during CICR.

Ryanodine receptor sensitivity governs the stability and synchrony of local calcium release during cardiac excitation-contraction coupling

Calcium-induced calcium release is the principal mechanism that triggers the cell-wide [Ca(2+)]i transient that activates muscle contraction during cardiac excitation-contraction coupling (ECC). Here, we characterize this process in mouse cardiac myocytes with a novel mathematical action potential (AP) model that incorporates realistic stochastic gating of voltage-dependent L-type calcium (Ca(2+)) channels (LCCs) and sarcoplasmic reticulum (SR) Ca(2+) release channels (the ryanodine receptors, RyR2s). Depolarization of the sarcolemma during an AP stochastically activates the LCCs elevating subspace [Ca(2+)] within each of the cell's 20,000 independent calcium release units (CRUs) to trigger local RyR2 opening and initiate Ca(2+) sparks, the fundamental unit of triggered Ca(2+) release. Synchronization of Ca(2+) sparks during systole depends on the nearly uniform cellular activation of LCCs and the likelihood of local LCC openings triggering local Ca(2+) sparks (ECC fidelity). The detailed design and true SR Ca(2+) pump/leak balance displayed by our model permits investigation of ECC fidelity and Ca(2+) spark fidelity, the balance between visible (Ca(2+) spark) and invisible (Ca(2+) quark/sub-spark) SR Ca(2+) release events. Excess SR Ca(2+) leak is examined as a disease mechanism in the context of "catecholaminergic polymorphic ventricular tachycardia (CPVT)", a Ca(2+)-dependent arrhythmia. We find that that RyR2s (and therefore Ca(2+) sparks) are relatively insensitive to LCC openings across a wide range of membrane potentials; and that key differences exist between Ca(2+) sparks evoked during quiescence, diastole, and systole. The enhanced RyR2 [Ca(2+)]i sensitivity during CPVT leads to increased Ca(2+) spark fidelity resulting in asynchronous systolic Ca(2+) spark activity. It also produces increased diastolic SR Ca(2+) leak with some prolonged Ca(2+) sparks that at times become "metastable" and fail to efficiently terminate. There is a huge margin of safety for stable Ca(2+) handling within the cell and this novel mechanistic model provides insight into the molecular signaling characteristics that help maintain overall Ca(2+) stability even under the conditions of high SR Ca(2+) leak during CPVT. Finally, this model should provide tools for investigators to examine normal and pathological Ca(2+) signaling characteristics in the heart.

Roles of phosphodiesterases in the regulation of the cardiac cyclic nucleotide cross-talk signaling network

The balanced signaling between the two cyclic nucleotides (cNs) cAMP and cGMP plays a critical role in regulating cardiac contractility. Their degradation is controlled by distinctly regulated phosphodiesterase isoenzymes (PDEs), which in turn are also regulated by these cNs. As a result, PDEs facilitate communication between the β-adrenergic and Nitric Oxide (NO)/cGMP/Protein Kinase G (PKG) signaling pathways, which regulate the synthesis of cAMP and cGMP respectively. The phenomena in which the cAMP and cGMP pathways influence the dynamics of each other are collectively referred to as cN cross-talk. However, the cross-talk response and the individual roles of each PDE isoenzyme in shaping this response remain to be fully characterized. We have developed a computational model of the cN cross-talk network that mechanistically integrates the β-adrenergic and NO/cGMP/PKG pathways via regulation of PDEs by both cNs. The individual model components and the integrated network model replicate experimentally observed activation-response relationships and temporal dynamics. The model predicts that, due to compensatory interactions between PDEs, NO stimulation in the presence of sub-maximal β-adrenergic stimulation results in an increase in cytosolic cAMP accumulation and corresponding increases in PKA-I and PKA-II activation; however, the potentiation is small in magnitude compared to that of NO activation of the NO/cGMP/PKG pathway. In a reciprocal manner, β-adrenergic stimulation in the presence of sub-maximal NO stimulation results in modest cGMP elevation and corresponding increase in PKG activation. In addition, we demonstrate that PDE2 hydrolyzes increasing amounts of cAMP with increasing levels of β-adrenergic stimulation, and hydrolyzes increasing amounts of cGMP with decreasing levels of NO stimulation. Finally, we show that PDE2 compensates for inhibition of PDE5 both in terms of cGMP and cAMP dynamics, leading to cGMP elevation and increased PKG activation, while maintaining whole-cell β-adrenergic responses similar to that prior to PDE5 inhibition. By defining and quantifying reactions comprising cN cross-talk, the model characterizes the cross-talk response and reveals the underlying mechanisms of PDEs in this non-linear, tightly-coupled reaction system.

Averaging for a Fully Coupled Piecewise-Deterministic Markov Process in Infinite Dimensions

In this paper we consider the generalized Hodgkin-Huxley model introduced in Austin (2008). This model describes the propagation of an action potential along the axon of a neuron at the scale of ion channels. Mathematically, this model is a fully coupled piecewise-deterministic Markov process (PDMP) in infinite dimensions. We introduce two time scales in this model in considering that some ion channels open and close at faster jump rates than others. We perform a slow-fast analysis of this model and prove that, asymptotically, this ‘two-time-scale’ model reduces to the so-called averaged model, which is still a PDMP in infinite dimensions, for which we provide effective evolution equations and jump rates.

Averaging for a Fully Coupled Piecewise-Deterministic Markov Process in Infinite Dimensions

In this paper we consider the generalized Hodgkin-Huxley model introduced in Austin (2008). This model describes the propagation of an action potential along the axon of a neuron at the scale of ion channels. Mathematically, this model is a fully coupled piecewise-deterministic Markov process (PDMP) in infinite dimensions. We introduce two time scales in this model in considering that some ion channels open and close at faster jump rates than others. We perform a slow-fast analysis of this model and prove that, asymptotically, this ‘two-time-scale’ model reduces to the so-called averaged model, which is still a PDMP in infinite dimensions, for which we provide effective evolution equations and jump rates.

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.

Selective Na(+) /Ca(2+) exchanger inhibition prevents Ca(2+) overload-induced triggered arrhythmias

BACKGROUND AND PURPOSE

Augmented Na(+) /Ca(2+) exchanger (NCX) activity may play a crucial role in cardiac arrhythmogenesis; however, data regarding the anti-arrhythmic efficacy of NCX inhibition are debatable. Feasible explanations could be the unsatisfactory selectivity of NCX inhibitors and/or the dependence of the experimental model on the degree of Ca(2+) i overload. Hence, we used NCX inhibitors SEA0400 and the more selective ORM10103 to evaluate the efficacy of NCX inhibition against arrhythmogenic Ca(2+) i rise in conditions when [Ca(2+) ]i was augmented via activation of the late sodium current (INaL ) or inhibition of the Na(+) /K(+) pump.

EXPERIMENTAL APPROACH

Action potentials (APs) were recorded from canine papillary muscles and Purkinje fibres by microelectrodes. NCX current (INCX ) was determined in ventricular cardiomyocytes utilizing the whole-cell patch clamp technique. Ca(2+) i transients (CaTs) were monitored with a Ca(2+) -sensitive fluorescent dye, Fluo-4.

KEY RESULTS

Enhanced INaL increased the Ca(2+) load and AP duration (APD). SEA0400 and ORM10103 suppressed INCX and prevented/reversed the anemone toxin II (ATX-II)-induced [Ca(2+) ]i rise without influencing APD, CaT or cell shortening, or affecting the ATX-II-induced increased APD. ORM10103 significantly decreased the number of strophanthidin-induced spontaneous diastolic Ca(2+) release events; however, SEA0400 failed to restrict the veratridine-induced augmentation in Purkinje-ventricle APD dispersion.

CONCLUSIONS AND IMPLICATIONS

Selective NCX inhibition - presumably by blocking rev INCX (reverse mode NCX current) - is effective against arrhythmogenesis caused by [Na(+) ]i -induced [Ca(2+) ]i elevation, without influencing the AP waveform. Therefore, selective INCX inhibition, by significantly reducing the arrhythmogenic trigger activity caused by the perturbed Ca(2+) i handling, should be considered as a promising anti-arrhythmic therapeutic strategy.

Calcium homeostasis in a local/global whole cell model of permeabilized ventricular myocytes with a Langevin description of stochastic calcium release

Population density approaches to modeling local control of Ca2+-induced Ca2+ release in cardiac myocytes can be used to construct minimal whole cell models that accurately represent heterogeneous local Ca2+ signals. Unfortunately, the computational complexity of such “local/global” whole cell models scales with the number of Ca2+ release unit (CaRU) states, which is a rapidly increasing function of the number of ryanodine receptors (RyRs) per CaRU. Here we present an alternative approach based on a Langevin description of the collective gating of RyRs coupled by local Ca2+ concentration ([Ca2+]). The computational efficiency of this approach no longer depends on the number of RyRs per CaRU. When the RyR model is minimal, Langevin equations may be replaced by a single Fokker-Planck equation, yielding an extremely compact and efficient local/global whole cell model that reproduces and helps interpret recent experiments that investigate Ca2+ homeostasis in permeabilized ventricular myocytes. Our calculations show that elevated myoplasmic [Ca2+] promotes elevated network sarcoplasmic reticulum (SR) [Ca2+] via SR Ca2+-ATPase-mediated Ca2+ uptake. However, elevated myoplasmic [Ca2+] may also activate RyRs and promote stochastic SR Ca2+ release, which can in turn decrease SR [Ca2+]. Increasing myoplasmic [Ca2+] results in an exponential increase in spark-mediated release and a linear increase in nonspark-mediated release, consistent with recent experiments. The model exhibits two steady-state release fluxes for the same network SR [Ca2+] depending on whether myoplasmic [Ca2+] is low or high. In the later case, spontaneous release decreases SR [Ca2+] in a manner that maintains robust Ca2+ sparks.

EAD and DAD mechanisms analyzed by developing a new human ventricular cell model

It has long been suggested that the Ca(2+)-mechanisms are largely involved in generating the early afterdepolarization (EAD) as well as the delayed afterdepolarization (DAD). This view was examined in a quantitative manner by applying the lead potential analysis to a new human ventricular cell model. In this ventricular cell model, the tight coupled LCC-RyR model (CaRU) based on local control theory (Hinch et al. 2004) and ion channel models mostly based on human electrophysiological data were included to reproduce realistic Ca(2+) dynamics as well as the membrane excitation. Simultaneously, the Ca(2+) accumulation near the Ca(2+) releasing site was incorporated as observed in real cardiac myocytes. The maximum rate of ventricular repolarization (-1.02 mV/ms) is due to IK1 (-0.55 mV/ms) and the rest is provided nearly equally by INCX (-0.20 mV/ms), INaL (-0.16 mV/ms) and INaT (-0.13 mV/ms). These INaL and INaT components are due to closure of the voltage gate, which remains partially open during the plateau potential. DADs could be evoked by applying high-frequency stimulations supplemented by a partial Na(+)/K(+) pump inhibition, or by a microinjection of Ca(2+). EADs was evoked by retarding the inactivation of INaL. The lead potential (VL) analysis revealed that IK1 and IKr played the primary role to reverse the AP repolarization to depolarizing limb of EAD. ICaL and INCX amplified EAD, while the remaining currents partially antagonized dVL/dt. The maximum rate of rise of EAD was attributable to the rapid activation of both ICaL (45.5%) and INCX (54.5%).

Mitochondrial calcium handling within the interstitial cells of Cajal

The interstitial cells of Cajal (ICC) drive rhythmic pacemaking contractions in the gastrointestinal system. The ICC generate pacemaking signals by membrane depolarizations associated with the release of intracellular calcium (Ca(2+)) in the endoplasmic reticulum (ER) through inositol-trisphosphate (IP3) receptors (IP3R) and uptake by mitochondria (MT). This Ca(2+) dynamic is hypothesized to generate pacemaking signals by calibrating ER Ca(2+) store depletions and membrane depolarization with ER store-operated Ca(2+) entry mechanisms. Using a biophysically based spatio-temporal model of integrated Ca(2+) transport in the ICC, we determined the feasibility of ER depletion timescale correspondence with experimentally observed pacemaking frequencies while considering the impact of IP3R Ca(2+) release and MT uptake on bulk cytosolic Ca(2+) levels because persistent elevations of free intracellular Ca(2+) are toxic to the cell. MT densities and distributions are varied in the model geometry to observe MT influence on free cytosolic Ca(2+) and the resulting frequencies of ER Ca(2+) store depletions, as well as the sarco-endoplasmic reticulum Ca(2+) ATP-ase (SERCA) and IP3 agonist concentrations. Our simulations show that high MT densities observed in the ICC are more relevant to ER establishing Ca(2+) depletion frequencies than protection of the cytosol from elevated free Ca(2+), whereas the SERCA pump is more relevant to containing cytosolic Ca(2+) elevations. Our results further suggest that the level of IP3 agonist stimulating ER Ca(2+) release, subsequent MT uptake, and eventual activation of ER store-operated Ca(2+) entry may determine frequencies of rhythmic pacemaking exhibited by the ICC across species and tissue types.

Inhibiting Na+/K+ ATPase can impair mitochondrial energetics and induce abnormal Ca2+ cycling and automaticity in guinea pig cardiomyocytes

Cardiac glycosides have been used for the treatment of heart failure because of their capabilities of inhibiting Na⁺/K⁺ ATPase (NKA), which raises [Na⁺]_i and attenuates Ca²⁺ extrusion via the Na⁺/Ca²⁺ exchanger (NCX), causing [Ca²⁺]_i elevation. The resulting [Ca²⁺]_i accumulation further enhances Ca²⁺-induced Ca²⁺ release, generating the positive inotropic effect. However, cardiac glycosides have some toxic and side effects such as arrhythmogenesis, confining their extensive clinical applications. The mechanisms underlying the proarrhythmic effect of glycosides are not fully understood. Here we investigated the mechanisms by which glycosides could cause cardiac arrhythmias via impairing mitochondrial energetics using an integrative computational cardiomyocyte model. In the simulations, the effect of glycosides was mimicked by blocking NKA activity. Results showed that inhibiting NKA not only impaired mitochondrial Ca²⁺ retention (thus suppressed reactive oxygen species (ROS) scavenging) but also enhanced oxidative phosphorylation (thus increased ROS production) during the transition of increasing workload, causing oxidative stress. Moreover, concurrent blocking of mitochondrial Na⁺/Ca²⁺ exchanger, but not enhancing of Ca²⁺ uniporter, alleviated the adverse effects of NKA inhibition. Intriguingly, NKA inhibition elicited Ca²⁺ transient and action potential alternans under more stressed conditions such as severe ATP depletion, augmenting its proarrhythmic effect. This computational study provides new insights into the mechanisms underlying cardiac glycoside-induced arrhythmogenesis. The findings suggest that targeting both ion handling and mitochondria could be a very promising strategy to develop new glycoside-based therapies in the treatment of heart failure.

A computational model of lysosome-ER Ca2+ microdomains

Acidic organelles form an important intracellular Ca(2+) pool that can drive global Ca(2+) signals through coupling with endoplasmic reticulum (ER) Ca(2+) stores. Recently identified lysosome-ER membrane contact sites might allow formation of Ca(2+) microdomains, although their size renders observation of Ca(2+) dynamics impractical. Here, we generated a computational model of lysosome-ER coupling that incorporated a previous model of the inositol trisphosphate (IP3) receptor as the ER Ca(2+) 'amplifier' and lysosomal leaks as the Ca(2+) 'trigger'. The model qualitatively described global Ca(2+) responses to the lysosomotropic agent GPN, which caused a controlled but substantial depletion of small solutes from the lysosome. Adapting this model to physiological lysosomal leaks induced by the Ca(2+) mobilising messenger NAADP demonstrated that lysosome-ER microdomains are capable of driving global Ca(2+) oscillations. Interestingly, our simulations suggest that the microdomain [Ca(2+)] need not be higher than that in the cytosol for responses to occur, thus matching the relatively high affinity of IP3 receptors for Ca(2+). The relative distribution and overall density of the lysosomal leaks dictated whether microdomains triggered or modulated global signals. Our data provide a computational framework for probing lysosome-ER Ca(2+) dynamics.

Cardiac resynchronization therapy improves altered Na channel gating in canine model of dyssynchronous heart failure

BACKGROUND

Slowed Na⁺ current (INa) decay and enhanced late INa (INa-L) prolong the action potential duration (APD) and contribute to early afterdepolarizations. Cardiac resynchronization therapy (CRT) shortens APD compared with dyssynchronous heart failure (DHF); however, the role of altered Na⁺ channel gating in CRT remains unexplored.

METHODS AND RESULTS

Adult dogs underwent left-bundle branch ablation and right atrial pacing (200 beats/min) for 6 weeks (DHF) or 3 weeks followed by 3 weeks of biventricular pacing at the same rate (CRT). INa and INa-L were measured in left ventricular myocytes from nonfailing, DHF, and CRT dogs. DHF shifted voltage-dependence of INa availability by -3 mV compared with nonfailing, enhanced intermediate inactivation, and slowed recovery from inactivation. CRT reversed the DHF-induced voltage shift of availability, partially reversed enhanced intermediate inactivation but did not affect DHF-induced slowed recovery. DHF markedly increased INa-L compared with nonfailing. CRT dramatically reduced DHF-induced enhanced INa-L, abbreviated the APD, and suppressed early afterdepolarizations. CRT was associated with a global reduction in phosphorylated Ca²⁺/Calmodulin protein kinase II, which has distinct effects on inactivation of cardiac Na⁺ channels. In a canine AP model, alterations of INa-L are sufficient to reproduce the effects on APD observed in DHF and CRT myocytes.

CONCLUSIONS

CRT improves DHF-induced alterations of Na⁺ channel function, especially suppression of INa-L, thus, abbreviating the APD and reducing the frequency of early afterdepolarizations. Changes in the levels of phosphorylated Ca²⁺/Calmodulin protein kinase II suggest a molecular pathway for regulation of INa by biventricular pacing of the failing heart.

Specification, construction, and exact reduction of state transition system models of biochemical processes

Biochemical reaction systems may be viewed as discrete event processes characterized by a number of states and state transitions. These systems may be modeled as state transition systems with transitions representing individual reaction events. Since they often involve a large number of interactions, it can be difficult to construct such a model for a system, and since the resulting state-level model can involve a huge number of states, model analysis can be difficult or impossible. Here, we describe methods for the high-level specification of a system using hypergraphs, for the automated generation of a state-level model from a high-level model, and for the exact reduction of a state-level model using information from the high-level model. Exact reduction is achieved through the automated application to the high-level model of the symmetry reduction technique and reduction by decomposition by independent subsystems, allowing potentially significant reductions without the need to generate a full model. The application of the method to biochemical reaction systems is illustrated by models describing a hypothetical ion-channel at several levels of complexity. The method allows for the reduction of the otherwise intractable example models to a manageable size.

Decoding myocardial Ca²⁺ signals across multiple spatial scales: a role for sensitivity analysis

Numerous studies have employed mathematical modeling to quantitatively understand release of Ca(2+) from the sarcoplasmic reticulum (SR) in the heart. Models have been used to investigate physiologically important phenomena such as triggering of SR Ca(2+) release by Ca(2+) entry across the cell membrane and spontaneous leak of Ca(2+) from the SR in quiescent heart cells. In this review we summarize studies that have modeled myocardial Ca(2+) at different spatial scales: the sub-cellular level, the cellular level, and the multicellular level. We discuss each category of models from the standpoint of parameter sensitivity analysis, a common simulation procedure that can generate quantitative, comprehensive predictions about how changes in conditions influence model output. We propose that this is a useful perspective for conceptualizing models, in part because a sensitivity analysis requires the investigator to define the relevant parameters and model outputs. This procedure therefore helps to illustrate the capabilities and limitations of each model. We further suggest that in future studies, sensitivity analyses will aid in simplifying complex models and in suggesting experiments to differentiate between competing models built with different assumptions. We conclude with a discussion of unresolved questions that are likely to be addressed over the next several years.

A computational approach to understanding the cardiac electromechanical activation sequence in the normal and failing heart, with translation to the clinical practice of CRT

Cardiac resynchronization therapy (CRT) is an established clinical treatment modality that aims to recoordinate contraction of the heart in dyssynchrous heart failure (DHF) patients. Although CRT reduces morbidity and mortality, a significant percentage of CRT patients fail to respond to the therapy, reflecting an insufficient understanding of the electromechanical activity of the DHF heart. Computational models of ventricular electromechanics are now poised to fill this knowledge gap and provide a comprehensive characterization of the spatiotemporal electromechanical interactions in the normal and DHF heart. The objective of this paper is to demonstrate the powerful utility of computational models of ventricular electromechanics in characterizing the relationship between the electrical and mechanical activation in the DHF heart, and how this understanding can be utilized to devise better CRT strategies. The computational research presented here exploits knowledge regarding the three dimensional distribution of the electromechanical delay, defined as the time interval between myocyte depolarization and onset of myofiber shortening, in determining the optimal location of the LV pacing electrode for CRT. The simulation results shown here also suggest utilizing myocardial efficiency and regional energy consumption as a guide to optimize CRT.

Toward an integrative computational model of the Guinea pig cardiac myocyte

The local control theory of excitation-contraction (EC) coupling asserts that regulation of calcium (Ca²⁺) release occurs at the nanodomain level, where openings of single L-type Ca²⁺ channels (LCCs) trigger openings of small clusters of ryanodine receptors (RyRs) co-localized within the dyad. A consequence of local control is that the whole-cell Ca²⁺ transient is a smooth continuous function of influx of Ca²⁺ through LCCs. While this so-called graded release property has been known for some time, its functional importance to the integrated behavior of the cardiac ventricular myocyte has not been fully appreciated. We previously formulated a biophysically based model, in which LCCs and RyRs interact via a coarse-grained representation of the dyadic space. The model captures key features of local control using a low-dimensional system of ordinary differential equations. Voltage-dependent gain and graded Ca²⁺ release are emergent properties of this model by virtue of the fact that model formulation is closely based on the sub-cellular basis of local control. In this current work, we have incorporated this graded release model into a prior model of guinea pig ventricular myocyte electrophysiology, metabolism, and isometric force production. The resulting integrative model predicts the experimentally observed causal relationship between action potential (AP) shape and timing of Ca²⁺ and force transients, a relationship that is not explained by models lacking the graded release property. Model results suggest that even relatively subtle changes in AP morphology that may result, for example, from remodeling of membrane transporter expression in disease or spatial variation in cell properties, may have major impact on the temporal waveform of Ca²⁺ transients, thus influencing tissue level electromechanical function.

Phospholemman is a negative feed-forward regulator of Ca2+ in β-adrenergic signaling, accelerating β-adrenergic inotropy

Sympathetic stimulation enhances cardiac contractility by stimulating β-adrenergic signaling and protein kinase A (PKA). Recently, phospholemman (PLM) has emerged as an important PKA substrate capable of regulating cytosolic Ca(2+) transients. However, it remains unclear how PLM contributes to β-adrenergic inotropy. Here we developed a computational model to clarify PLM's role in the β-adrenergic signaling response. Simulating Na(+) and sarcoplasmic reticulum (SR) Ca(2+) clamps, we identify an effect of PLM phosphorylation on SR unloading as the key mechanism by which PLM confers cytosolic Ca(2+) adaptation to long-term β-adrenergic receptor (β-AR) stimulation. Moreover, we show that phospholamban (PLB) opposes and overtakes these actions on SR load, forming a negative feed-forward loop in the β-adrenergic signaling cascade. This network motif dominates the negative feedback conferred by β-AR desensitization and accelerates β-AR-induced inotropy. Model analysis therefore unmasks key actions of PLM phosphorylation during β-adrenergic signaling, indicating that PLM is a critical component of the fight-or-flight response.

Data-based theoretical identification of subcellular calcium compartments and estimation of calcium dynamics in cardiac myocytes

In cardiac cells, Ca(2+) release flux (J(rel)) via ryanodine receptors (RyRs) from the sarcoplasmic reticulum (SR) has a complex effect on the action potential (AP). Coupling between J(rel) and the AP occurs via L-type Ca(2+) channels (I(Ca)) and the Na(+)/Ca(2+) exchanger (I(NCX)). We used a combined experimental and modelling approach to study interactions between J(rel), I(Ca) and I(NCX) in porcine ventricular myocytes.We tested the hypothesis that during normal uniform J(rel), the interaction between these fluxes can be represented as occurring in two myoplasmic subcompartments for Ca(2+) distribution, one (T-space) associated with RyR and enclosed by the junctional portion of the SR membrane and corresponding T-tubular portion of the sarcolemma, the other (M-space) encompassing the rest of the myoplasm. I(Ca) and I(NCX) were partitioned into subpopulations in the T-space and M-space sarcolemma. We denoted free Ca(2+) concentrations in T-space and M-space Ca(t) and Ca(m), respectively. Experiments were designed to allow separate measurements of I(Ca) and I(NCX) as a function of J(rel). Inclusion of T-space in themodel allowed us to reproduce in silico the following important experimental results: (1) hysteresis of I(NCX) dependence on Ca(m); (2) delay between peak I(NCX) and peak Ca(m) during caffeine application protocol; (3) delay between I(NCX) and Ca(m) during Ca(2+)-induced-Ca(2+)-release; (4) rapid I(Ca) inactivation (within 2 ms) due to J(rel), with magnitude graded as a function of the SR Ca(2+) content; (5) time delay between I(Ca) inactivation due to J(rel) and Ca(m). Partition of 25% NCX in T-space and 75% in M-space provided the best fit to the experimental data. Measured Ca(m) and I(Ca) or I(NCX) were used as input to the model for estimating Ca(t). The actual model-computed Ca(t), obtained by simulating specific experimental protocols, was used as a gold standard for comparison. The model predicted peak Ca(t) in the range of 6–25 μM, with time to equilibrium of Ca(t) with Ca(m) of ~350 ms. These Ca(t) values are in the range of LCC and RyR sensitivity to Ca(2+). An increase of the SR Ca(2+) load increased the time to equilibrium. The I(Ca)-based estimation method was most accurate during the ascending phase of Ca(t). The I(NCX)-based method provided a good estimate for the descending phase of Ca(t). Thus, application of both methods in combination provides the best estimate of the entire Ca(t) time course.

How the Hodgkin-Huxley equations inspired the Cardiac Physiome Project

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

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

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

Dynamic local changes in sarcoplasmic reticulum calcium: physiological and pathophysiological roles

Evidence obtained in recent years indicates that, in cardiac myocytes, release of Ca(2+) from the sarcoplasmic reticulum (SR) is regulated by changes in the concentration of Ca(2+) within the SR. In this review, we summarize recent advances in our understanding of this regulatory role, with a particular emphasis on dynamic and local changes in SR [Ca(2+)]. We focus on five important questions that are to some extent unresolved and controversial. These questions concern: (1) the importance of SR [Ca(2+)] depletion in the termination of Ca(2+) release; (2) the quantitative extent of depletion during local release events such as Ca(2+) sparks; (3) the influence of SR [Ca(2+)] refilling on release refractoriness and the propensity for pathological Ca(2+) release; (4) dynamic changes in SR [Ca(2+)] during propagating Ca(2+) waves; and (5) the speed of Ca(2+) diffusion within the SR. With each issue, we discuss data supporting alternative viewpoints, and we identify fundamental questions that are being actively investigated. We conclude with a discussion of experimental and computational advances that will help to resolve controversies. This article is part of a special issue entitled "Local Signaling in Myocytes."

Critical role of cardiac t-tubule system for the maintenance of contractile function revealed by a 3D integrated model of cardiomyocytes

T-tubules in mammalian ventricular myocytes constitute an elaborate system for coupling membrane depolarization with intracellular Ca(2+) signaling to control cardiac contraction. Deletion of t-tubules (detubulation) has been reported in heart diseases, although the complex nature of the cardiac excitation-contraction (E-C) coupling process makes it difficult to experimentally establish causal relationships between detubulation and cardiac dysfunction. Alternatively, numerical simulations incorporating the t-tubule system have been proposed to elucidate its functional role. However, the majority of models treat the subcellular spaces as lumped compartments, and are thus unable to dissect the impact of morphological changes in t-tubules. We developed a 3D finite element model of cardiomyocytes in which subcellular components including t-tubules, myofibrils, sarcoplasmic reticulum, and mitochondria were modeled and realistically arranged. Based on this framework, physiological E-C coupling was simulated by simultaneously solving the reaction-diffusion equation and the mechanical equilibrium for the mathematical models of electrophysiology and contraction distributed among these subcellular components. We then examined the effect of detubulation in this model by comparing with and without the t-tubule system. This model reproduced the Ca(2+) transients and contraction observed in experimental studies, including the response to beta-adrenergic stimulation, and provided detailed information beyond the limits of experimental approaches. In particular, the analysis of sarcomere dynamics revealed that the asynchronous contraction caused by a large detubulated region can lead to impairment of myocyte contractile efficiency. These data clearly demonstrate the importance of the t-tubule system for the maintenance of contractile function.

Multi-scale computational models of familial hypertrophic cardiomyopathy: genotype to phenotype

Familial hypertrophic cardiomyopathy (FHC) is an inherited disorder affecting roughly one in 500 people. Its hallmark is abnormal thickening of the ventricular wall, leading to serious complications that include heart failure and sudden cardiac death. Treatment is complicated by variation in the severity, symptoms and risks for sudden death within the patient population. Nearly all of the genetic lesions associated with FHC occur in genes encoding sarcomeric proteins, indicating that defects in cardiac muscle contraction underlie the condition. Detailed biophysical data are increasingly available for computational analyses that could be used to predict heart phenotypes based on genotype. These models must integrate the dynamic processes occurring in cardiac cells with properties of myocardial tissue, heart geometry and haemodynamic load in order to predict strain and stress in the ventricular walls and overall pump function. Recent advances have increased the biophysical detail in these models at the myofilament level, which will allow properties of FHC-linked mutant proteins to be accurately represented in simulations of whole heart function. The short-term impact of these models will be detailed descriptions of contractile dysfunction and altered myocardial strain patterns at the earliest stages of the disease-predictions that could be validated in genetically modified animals. Long term, these multi-scale models have the potential to improve clinical management of FHC through genotype-based risk stratification and personalized therapy.

Cardiac myocytes and local signaling in nano-domains

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

Models of cardiac electromechanics based on individual hearts imaging data: image-based electromechanical models of the heart

Current multi-scale computational models of ventricular electromechanics describe the full process of cardiac contraction on both the micro- and macro- scales including: the depolarization of cardiac cells, the release of calcium from intracellular stores, tension generation by cardiac myofilaments, and mechanical contraction of the whole heart. Such models are used to reveal basic mechanisms of cardiac contraction as well as the mechanisms of cardiac dysfunction in disease conditions. In this paper, we present a methodology to construct finite element electromechanical models of ventricular contraction with anatomically accurate ventricular geometry based on magnetic resonance and diffusion tensor magnetic resonance imaging of the heart. The electromechanical model couples detailed representations of the cardiac cell membrane, cardiac myofilament dynamics, electrical impulse propagation, ventricular contraction, and circulation to simulate the electrical and mechanical activity of the ventricles. The utility of the model is demonstrated in an example simulation of contraction during sinus rhythm using a model of the normal canine ventricles.

Imaging the electromechanical activity of the heart in vivo

Cardiac conduction abnormalities remain a major cause of death and disability worldwide. However, as of today, there is no standard clinical imaging modality that can noninvasively provide maps of the electrical activation. In this paper, electromechanical wave imaging (EWI), a novel ultrasound-based imaging method, is shown to be capable of mapping the electromechanics of all four cardiac chambers at high temporal and spatial resolutions and a precision previously unobtainable in a full cardiac view in both animals and humans. The transient deformations resulting from the electrical activation of the myocardium were mapped in 2D and combined in 3D biplane ventricular views. EWI maps were acquired during five distinct conduction configurations and were found to be closely correlated to the electrical activation sequences. EWI in humans was shown to be feasible and capable of depicting the normal electromechanical activation sequence of both atria and ventricles. This validation of EWI as a direct, noninvasive, and highly translational approach underlines its potential to serve as a unique imaging tool for the early detection, diagnosis, and treatment monitoring of arrhythmias through ultrasound-based mapping of the transmural electromechanical activation sequence reliably at the point of care, and in real time.

Stochastic hybrid modeling of intracellular calcium dynamics

Deterministic models of biochemical processes at the subcellular level might become inadequate when a cascade of chemical reactions is induced by a few molecules. Inherent randomness of such phenomena calls for the use of stochastic simulations. However, being computationally intensive, such simulations become infeasible for large and complex reaction networks. To improve their computational efficiency in handling these networks, we present a hybrid approach, in which slow reactions and fluxes are handled through exact stochastic simulation and their fast counterparts are treated partially deterministically through chemical Langevin equation. The classification of reactions as fast or slow is accompanied by the assumption that in the time-scale of fast reactions, slow reactions do not occur and hence do not affect the probability of the state. Our new approach also handles reactions with complex rate expressions such as Michaelis-Menten kinetics. Fluxes which cannot be modeled explicitly through reactions, such as flux of Ca(2+) from endoplasmic reticulum to the cytosol through inositol 1,4,5-trisphosphate receptor channels, are handled deterministically. The proposed hybrid algorithm is used to model the regulation of the dynamics of cytosolic calcium ions in mouse macrophage RAW 264.7 cells. At relatively large number of molecules, the response characteristics obtained with the stochastic and deterministic simulations coincide, which validates our approach in the limit of large numbers. At low doses, the response characteristics of some key chemical species, such as levels of cytosolic calcium, predicted with stochastic simulations, differ quantitatively from their deterministic counterparts. These observations are ubiquitous throughout dose response, sensitivity, and gene-knockdown response analyses. While the relative differences between the peak-heights of the cytosolic [Ca(2+)] time-courses obtained from stochastic (mean of 16 realizations) and deterministic simulations are merely 1%-4% for most perturbations, it is specially sensitive to levels of G(βγ) (relative difference as large as 90% at very low G(βγ)).

Alternans and arrhythmias: from cell to heart

The goal of systems biology is to relate events at the molecular level to more integrated scales from organelle to cell, tissue, and living organism. Here, we review how normal and abnormal excitation-contraction coupling properties emerge from the protein scale, where behaviors are dominated by randomness, to the cell and tissue scales, where heart has to beat with reliable regularity for a lifetime. Beginning with the fundamental unit of excitation-contraction coupling, the couplon where L-type Ca channels in the sarcolemmal membrane adjoin ryanodine receptors in the sarcoplasmic reticulum membrane, we show how a network of couplons with 3 basic properties (random activation, refractoriness, and recruitment) produces the classic physiological properties of excitation-contraction coupling and, under pathophysiological conditions, leads to Ca alternans and Ca waves. Moving to the tissue scale, we discuss how cellular Ca alternans and Ca waves promote both reentrant and focal arrhythmias in the heart. Throughout, we emphasize the qualitatively novel properties that emerge at each new scale of integration.

Integrative systems models of cardiac excitation-contraction coupling

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