Regulation of excitation-contraction coupling in mouse cardiac myocytes: integrative analysis with mathematical modelling

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.

Vascular Endothelial Growth Factor-B Induces a Distinct Electrophysiological Phenotype in Mouse Heart

Vascular endothelial growth factor B (VEGF-B) is a potent mediator of vascular, metabolic, growth, and stress responses in the heart, but the effects on cardiac muscle and cardiomyocyte function are not known. The purpose of this study was to assess the effects of VEGF-B on the energy metabolism, contractile, and electrophysiological properties of mouse cardiac muscle and cardiac muscle cells. In vivo and ex vivo analysis of cardiac-specific VEGF-B TG mice indicated that the contractile function of the TG hearts was normal. Neither the oxidative metabolism of isolated TG cardiomyocytes nor their energy substrate preference showed any difference to WT cardiomyocytes. Similarly, myocyte Ca²⁺ signaling showed only minor changes compared to WT myocytes. However, VEGF-B overexpression induced a distinct electrophysiological phenotype characterized by ECG changes such as an increase in QRSp time and decreases in S and R amplitudes. At the level of isolated TG cardiomyocytes, these changes were accompanied with decreased action potential upstroke velocity and increased duration (APD_60–70). These changes were partly caused by downregulation of sodium current (I_Na) due to reduced expression of Na_v1.5. Furthermore, TG myocytes had alterations in voltage-gated K⁺ currents, namely decreased density of transient outward current (I_to) and total K⁺ current (I_peak). At the level of transcription, these were accompanied by downregulation of K_v channel-interacting protein 2 (Kcnip2), a known modulatory subunit for K_v4.2/3 channel. Cardiac VEGF-B overexpression induces a distinct electrophysiological phenotype including remodeling of cardiomyocyte ion currents, which in turn induce changes in action potential waveform and ECG.

Nuclear calcium in cardiac myocytes

Calcium (Ca) is a universal second messenger involved in the regulation of various cellular processes, including electrical signaling, contraction, secretion, memory, gene transcription, and cell death. In heart, Ca governs cardiomyocyte contraction, is central in electrophysiological properties, and controls major signaling pathway implicated in gene transcription. How cardiomyocytes decode Ca signal to regulate gene expression without interfering with, or being controlled by, "contractile" Ca that floods the entire cytosol during each heartbeat is still elusive. In this review, we summarize recent findings on nuclear Ca regulation and its downstream signaling in cardiomyocytes. We will address difficulties in reliable quantification of nuclear Ca fluxes and discuss its role in the development and progression of cardiac hypertrophy and heart failure. We also point out key open questions to stimulate future work.

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.

Myokit: A simple interface to cardiac cellular electrophysiology

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

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

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

Role of CaMKII in cardiac arrhythmias

Protein phosphorylation is a central mechanism in vertebrates for the regulation of signaling. With regard to the cardiovascular system, phosphorylation of myocyte targets is critical for the regulation of excitation contraction coupling, metabolism, intracellular calcium regulation, mitochondrial activity, transcriptional regulation, and cytoskeletal dynamics. In fact, pathways that tune protein kinase signaling have been a mainstay for cardiovascular therapies for the past 60 years. The calcium/calmodulin-dependent protein kinase II (CaMKII) is a multifunctional serine/threonine kinase with numerous roles in human physiology. Dysfunction in CaMKII-based signaling has been linked with a host of cardiovascular phenotypes including heart failure and arrhythmia, and CaMKII levels are elevated in human and animal disease models of heart disease. While nearly a decade has been invested in targeting CaMKII for the treatment of heart failure and arrhythmia phenotypes, to date, approaches to target the molecule for antiarrhythmic benefit have been unsuccessful for reasons that are still not entirely clear, although (1) lack of compound specificity and (2) the multitude of downstream targets are likely contributing factors. This review will provide an update on current pathways regulated by CaMKII with the goal of illustrating potential upstream regulatory mechanisms and downstream targets that may be modulated for the prevention of cardiac electrical defects. While the review will cover multiple aspects of CaMKII dysfunction in cardiovascular disease, we have given special attention to the potential of CaMKII-associated late Na(+) current as a novel therapeutic target for cardiac arrhythmia.

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

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

Modeling CaMKII in cardiac physiology: from molecule to tissue

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

A novel computational model of mouse myocyte electrophysiology to assess the synergy between Na+ loading and CaMKII

Ca(2+)-calmodulin-dependent protein kinase II (CaMKII) hyperactivity in heart failure causes intracellular Na(+) ([Na(+)]i) loading (at least in part by enhancing the late Na(+) current). This [Na(+)]i gain promotes intracellular Ca(2+) ([Ca(2+)]i) overload by altering the equilibrium of the Na(+)-Ca(2+) exchanger to impair forward-mode (Ca(2+) extrusion), and favour reverse-mode (Ca(2+) influx) exchange. In turn, this Ca(2+) overload would be expected to further activate CaMKII and thereby form a pathological positive feedback loop of ever-increasing CaMKII activity, [Na(+)]i, and [Ca(2+)]i. We developed an ionic model of the mouse ventricular myocyte to interrogate this potentially arrhythmogenic positive feedback in both control conditions and when CaMKIIδC is overexpressed as in genetically engineered mice. In control conditions, simulation of increased [Na(+)]i causes the expected increases in [Ca(2+)]i, CaMKII activity, and target phosphorylation, which degenerate into unstable Ca(2+) handling and electrophysiology at high [Na(+)]i gain. Notably, clamping CaMKII activity to basal levels ameliorates but does not completely offset this outcome, suggesting that the increase in [Ca(2+)]i per se plays an important role. The effect of this CaMKII-Na(+)-Ca(2+)-CaMKII feedback is more striking in CaMKIIδC overexpression, where high [Na(+)]i causes delayed afterdepolarizations, which can be prevented by imposing low [Na(+)]i, or clamping CaMKII phosphorylation of L-type Ca(2+) channels, ryanodine receptors and phospholamban to basal levels. In this setting, Na(+) loading fuels a vicious loop whereby increased CaMKII activation perturbs Ca(2+) and membrane potential homeostasis. High [Na(+)]i is also required to produce instability when CaMKII is further activated by increased Ca(2+) loading due to β-adrenergic activation. Our results support recent experimental findings of a synergistic interaction between perturbed Na(+) fluxes and CaMKII, and suggest that pharmacological inhibition of intracellular Na(+) loading can contribute to normalizing Ca(2+) and membrane potential dynamics in heart failure.

Interpreting genetic effects through models of cardiac electromechanics

Multiscale models of cardiac electromechanics are being increasingly focused on understanding how genetic variation and environment underpin multiple disease states. In this paper we review the current state of the art in both the development of specific models and the physiological insights they have produced. This growing research body includes the development of models for capturing the effects of changes in function in both single and multiple proteins in both specific expression systems and in vivo contexts. Finally, the potential for using this approach for ultimately predicting phenotypes from genetic sequence information is discussed.

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.

How the Hodgkin-Huxley equations inspired the Cardiac Physiome Project

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

The role of in vivo Ca²⁺ signals acting on Ca²⁺-calmodulin-dependent proteins for skeletal muscle plasticity

Skeletal muscle fibres are highly heterogeneous regarding size, metabolism and contractile function. They also show a large capacity for adaptations in response to alterations in the activation pattern. A major part of this activity-dependent plasticity relies on transcriptional alterations controlled by intracellular Ca(2+) signals. In this review we discuss how intracellular Ca(2+) fluctuations induced by activation patterns likely to occur in vivo control muscle properties via effects on Ca(2+)-calmodulin-dependent proteins. We focus on two such Ca(2+) decoders: calcineurin and Ca(2+)-calmodulin-dependent protein kinase II. Inherent Ca(2+) transients during contractions differ rather little between slow- and fast-twitch muscle fibres and this difference is unlikely to have any significant impact on the activity of Ca(2+) decoders. The major exception to this is fatigue-induced changes in Ca(2+) transients that occur in fast-twitch fibres exposed to high-intensity activation typical of slow-twitch motor units. In conclusion, the cascade from neural stimulation pattern to Ca(2+)-dependent transcription is likely to be central in maintaining the fibre phenotypes in both fast- and slow-twitch fibres. Moreover, changes in Ca(2+) signalling (e.g. induced by endurance training) can result in altered muscle properties (e.g. increased mitochondrial biogenesis) and this plasticity involves other signalling pathways.

Ca2+-calmodulin-dependent protein kinase II represses cardiac transcription of the L-type calcium channel alpha(1C)-subunit gene (Cacna1c) by DREAM translocation

Recent studies have demonstrated that changes in the activity of calcium-calmodulin-dependent protein kinase II (CaMKII) induce a unique cardiomyocyte phenotype through the regulation of specific genes involved in excitation-contraction (E-C)-coupling. To explain the transcriptional effects of CaMKII we identified a novel CaMKII-dependent pathway for controlling the expression of the pore-forming α-subunit (Cav1.2) of the L-type calcium channel (LTCC) in cardiac myocytes. We show that overexpression of either cytosolic (δC) or nuclear (δB) CaMKII isoforms selectively downregulate the expression of the Cav1.2. Pharmacological inhibition of CaMKII activity induced measurable changes in LTCC current density and subsequent changes in cardiomyocyte calcium signalling in less than 24 h. The effect of CaMKII on the α1C-subunit gene (Cacna1c) promoter was abolished by deletion of the downstream regulatory element (DRE), which binds transcriptional repressor DREAM/calsenilin/KChIP3. Imaging DREAM-GFP (green fluorescent protein)-expressing cardiomyocytes showed that CaMKII potentiates the calcium-induced nuclear translocation of DREAM. Thereby CaMKII increases DREAM binding to the DRE consensus sequence of the endogenous Cacna1c gene. By mathematical modelling we demonstrate that the LTCC downregulation through the Ca2+-CaMKII-DREAM cascade constitutes a physiological feedback mechanism enabling cardiomyocytes to adjust the calcium intrusion through LTCCs to the amount of intracellular calcium detected by CaMKII.

Synergy between CaMKII substrates and β-adrenergic signaling in regulation of cardiac myocyte Ca(2+) handling

Cardiac excitation-contraction coupling is a highly coordinated process that is controlled by protein kinase signaling pathways, including Ca(2+)/calmodulin-dependent protein kinase II (CaMKII) and protein kinase A (PKA). Increased CaMKII expression and activity (as occurs during heart failure) destabilizes EC coupling and may lead to sudden cardiac death. To better understand mechanisms of cardiac CaMKII function, we integrated dynamic CaMKII-dependent regulation of key Ca(2+) handling targets with previously validated models of cardiac EC coupling, Ca(2+)/calmodulin-dependent activation of CaMKII, and β-adrenergic activation of PKA. Model predictions are validated against CaMKII-overexpression data from rabbit ventricular myocytes. The model demonstrates how overall changes to Ca(2+) handling during CaMKII overexpression are explained by interactions between individual CaMKII substrates. CaMKII and PKA activities during β-adrenergic stimulation may synergistically facilitate inotropic responses and contribute to a CaMKII-Ca(2+)-CaMKII feedback loop. CaMKII regulated early frequency-dependent acceleration of relaxation and EC coupling gain (which was highly sarcoplasmic reticulum Ca(2+) load-dependent). Additionally, the model identifies CaMKII-dependent ryanodine receptor hyperphosphorylation as a proarrhythmogenic trigger. In summary, we developed a detailed computational model of CaMKII and PKA signaling in cardiac myocytes that provides unique insights into their regulation of normal and pathological Ca(2+) handling.

Integrative modeling of the cardiac ventricular myocyte

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