A Spatiotemporal Ventricular Myocyte Model Incorporating Mitochondrial Calcium Cycling

Computational modeling of cardiac electrophysiology and arrhythmogenesis: toward clinical translation

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

Computational insight into energy control balance by Ca2+ and cAMP-PKA signaling in pacemaker cells

Cyclic adenosine monophosphate (cAMP)-protein kinase A (PKA) signaling controls sinoatrial node cell (SANC) function by affecting the degree of coupling between Ca2+ and membrane clocks. PKA is known to phosphorylate ionic channels, Ca2+ pump and release from the sarcoplasmic reticulum, and enzymes controlling ATP production in the mitochondria. While the PKA cytosolic targets in SANC have been extensively explored, its mitochondrial targets and its ability to maintain SANC energetic balance remain to be elucidated. To investigate the role of PKA in SANC energetics, we tested three hypotheses: (i) PKA is an important regulator of the ATP supply-to-demand balance, (ii) Ca2+ regulation of energetics is important for maintenance of NADH level and (iii) abrupt reduction in ATP demand first reduces the AP firing rate and, after dropping below a certain threshold, leads to a reduction in ATP. To gain mechanistic insights into the ATP supply-to-demand matching regulators, a modified model of mitochondrial energy metabolism was integrated into our coupled-clock model that describes ATP demand. Experimentally, increased ATP demand was accompanied by maintained ATP and NADH levels. Ca2+ regulation of energetics was found by the model to be important in the maintenance of NADH and PKA regulation was found to be important in the maintenance of intracellular ATP and the increase in oxygen consumption. PKA inhibition led to a biphasic reduction in AP firing rate, with the first phase being rapid and ATP-independent, while the second phase was slow and ATP-dependent. Thus, SANC energy balance is maintained by both Ca2+ and PKA signaling.

Increased SERCA2a sub-cellular heterogeneity in right-ventricular heart failure inhibits excitation-contraction coupling and modulates arrhythmogenic dynamics

The intracellular calcium handling system of cardiomyocytes is responsible for controlling excitation-contraction coupling (ECC) and has been linked to pro-arrhythmogenic cellular phenomena in conditions such as heart failure (HF). SERCA2a, responsible for intracellular uptake, is a primary regulator of calcium homeostasis, and remodelling of its function has been proposed as a causal factor underlying cellular and tissue dysfunction in disease. Whereas adaptations to the global (i.e. whole-cell) expression of SERCA2a have been previously investigated in the context of multiple diseases, the role of its spatial profile in the sub-cellular volume has yet to be elucidated. We present an approach to characterize the sub-cellular heterogeneity of SERCA2a and apply this approach to quantify adaptations to the length-scale of heterogeneity (the distance over which expression is correlated) associated with right-ventricular (RV)-HF. These characterizations informed simulations to predict the functional implications of this heterogeneity, and its remodelling in disease, on ECC, the dynamics of calcium-transient alternans and the emergence of spontaneous triggered activity. Image analysis reveals that RV-HF is associated with an increase in length-scale and its inter-cellular variability; simulations predict that this increase in length-scale can reduce ECC and critically modulate the vulnerability to both alternans and triggered activity. This article is part of the theme issue 'The cardiomyocyte: new revelations on the interplay between architecture and function in growth, health, and disease'.

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

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

Multi-Scale Computational Modeling of Spatial Calcium Handling From Nanodomain to Whole-Heart: Overview and Perspectives

Regulation of intracellular calcium is a critical component of cardiac electrophysiology and excitation-contraction coupling. The calcium spark, the fundamental element of the intracellular calcium transient, is initiated in specialized nanodomains which co-locate the ryanodine receptors and L-type calcium channels. However, calcium homeostasis is ultimately regulated at the cellular scale, by the interaction of spatially separated but diffusively coupled nanodomains with other sub-cellular and surface-membrane calcium transport channels with strong non-linear interactions; and cardiac electrophysiology and arrhythmia mechanisms are ultimately tissue-scale phenomena, regulated by the interaction of a heterogeneous population of coupled myocytes. Recent advances in imaging modalities and image-analysis are enabling the super-resolution reconstruction of the structures responsible for regulating calcium homeostasis, including the internal structure of nanodomains themselves. Extrapolating functional and imaging data from the nanodomain to the whole-heart is non-trivial, yet essential for translational insight into disease mechanisms. Computational modeling has important roles to play in relating structural and functional data at the sub-cellular scale and translating data across the scales. This review covers recent methodological advances that enable image-based modeling of the single nanodomain and whole cardiomyocyte, as well as the development of multi-scale simulation approaches to integrate data from nanometer to whole-heart. Firstly, methods to overcome the computational challenges of simulating spatial calcium dynamics in the nanodomain are discussed, including image-based modeling at this scale. Then, recent whole-cell models, capable of capturing a range of different structures (such as the T-system and mitochondria) and cellular heterogeneity/variability are discussed at two different levels of discretization. Novel methods to integrate the models and data across the scales and simulate stochastic dynamics in tissue-scale models are then discussed, enabling elucidation of the mechanisms by which nanodomain remodeling underlies arrhythmia and contractile dysfunction. Perspectives on model differences and future directions are provided throughout.

Mitochondrial Contributions in the Genesis of Delayed Afterdepolarizations in Ventricular Myocytes

Mitochondria fulfill the cell's energy demand and affect the intracellular calcium (Ca2+) dynamics via direct Ca2+ exchange, the redox effect of reactive oxygen species (ROS) on Ca2+ handling proteins, and other signaling pathways. Recent experimental evidence indicates that mitochondrial depolarization promotes arrhythmogenic delayed afterdepolarizations (DADs) in cardiac myocytes. However, the nonlinear interactions among the Ca2+ signaling pathways, ROS, and oxidized Ca2+/calmodulin-dependent protein kinase II (CaMKII) pathways make it difficult to reveal the mechanisms. Here, we use a recently developed spatiotemporal ventricular myocyte computer model, which consists of a 3-dimensional network of Ca2+ release units (CRUs) intertwined with mitochondria and integrates mitochondrial Ca2+ signaling and other complex signaling pathways, to study the mitochondrial regulation of DADs. With a systematic investigation of the synergistic or competing factors that affect the occurrence of Ca2+ waves and DADs during mitochondrial depolarization, we find that the direct redox effect of ROS on ryanodine receptors (RyRs) plays a critical role in promoting Ca2+ waves and DADs under the acute effect of mitochondrial depolarization. Furthermore, the upregulation of mitochondrial Ca2+ uniporter can promote DADs through Ca2+-dependent opening of mitochondrial permeability transition pores (mPTPs). Also, due to much slower dynamics than Ca2+ cycling and ROS, oxidized CaMKII activation and the cytosolic ATP do not appear to significantly impact the genesis of DADs during the acute phase of mitochondrial depolarization. However, under chronic conditions, ATP depletion suppresses and enhanced CaMKII activation promotes Ca2+ waves and DADs.

Roles of four feedback loops in mitochondrial permeability transition pore opening induced by Ca^{2+} and reactive oxygen species

Transient or sustained permeability transition pore (PTP) opening is important in normal physiology or cell death, respectively. These are closely linked to Ca^{2+} and reactive oxygen species (ROS). The entry of Ca^{2+} into mitochondria regulates ROS production, and both Ca^{2+} and ROS trigger PTP opening. In addition to this feedforward loop, there exist four feedback loops in the Ca^{2+}-ROS-PTP system. ROS promotes Ca^{2+} entering (F1) and induces further ROS generation (F2), forming two positive feedback loops. PTP opening results in the efflux of Ca^{2+} (F3) and ROS (F4) from the mitochondria, forming two negative feedback loops. Owing to these complexities, we construct a mathematical model to dissect the roles of these feedback loops in the dynamics of PTP opening. The qualitative agreement between simulation results and recent experimental observations supports our hypothesis that under physiological conditions the PTP opens in an oscillatory state, while under pathological conditions it opens in a high steady state. We clarify that the negative feedback loops are responsible for producing oscillations, wherein F3 plays a more prominent role than F4; whereas the positive feedback loops are beneficial for maintaining oscillation robustness, wherein F1 has a more dominant role than F2. Furthermore, we manifest that the proper increase in negative feedback strength or decrease in positive feedback strength not only facilitates the occurrence of oscillations and thus protects the system against a high steady state, but also assists in lowering the oscillation peak. This study may provide potential therapeutic strategies in treating neurodegenerative diseases due to PTP dysfunction.

Mitochondrial depolarization promotes calcium alternans: Mechanistic insights from a ventricular myocyte model

Mitochondria are vital organelles inside the cell and contribute to intracellular calcium (Ca2+) dynamics directly and indirectly via calcium exchange, ATP generation, and production of reactive oxygen species (ROS). Arrhythmogenic Ca2+ alternans in cardiac myocytes has been observed in experiments under abnormal mitochondrial depolarization. However, complex signaling pathways and Ca2+ cycling between mitochondria and cytosol make it difficult in experiments to reveal the underlying mechanisms of Ca2+ alternans under abnormal mitochondrial depolarization. In this study, we use a newly developed spatiotemporal ventricular myocyte computer model that integrates mitochondrial Ca2+ cycling and complex signaling pathways to investigate the mechanisms of Ca2+ alternans during mitochondrial depolarization. We find that elevation of ROS in response to mitochondrial depolarization plays a critical role in promoting Ca2+ alternans. Further examination reveals that the redox effect of ROS on ryanodine receptors and sarco/endoplasmic reticulum Ca2+-ATPase synergistically promote alternans. Upregulation of mitochondrial Ca2+ uniporter promotes Ca2+ alternans via Ca2+-dependent mitochondrial permeability transition pore opening. Due to their relatively slow kinetics, oxidized Ca2+/calmodulin-dependent protein kinase II activation and ATP do not play significant roles acutely in the genesis of Ca2+ alternans after mitochondrial depolarization, but their roles can be significant in the long term, mainly through their effects on sarco/endoplasmic reticulum Ca2+-ATPase activity. In conclusion, mitochondrial depolarization promotes Ca2+ alternans acutely via the redox effect of ROS and chronically by ATP reduction. It suppresses Ca2+ alternans chronically through oxidized Ca2+/calmodulin-dependent protein kinase II activation.

Cardiomyocyte calcium handling in health and disease: Insights from in vitro and in silico studies

Calcium (Ca²⁺) plays a central role in cardiomyocyte excitation-contraction coupling. To ensure an optimal electrical impulse propagation and cardiac contraction, Ca²⁺ levels are regulated by a variety of Ca²⁺-handling proteins. In turn, Ca²⁺ modulates numerous electrophysiological processes. Accordingly, Ca²⁺-handling abnormalities can promote cardiac arrhythmias via various mechanisms, including the promotion of afterdepolarizations, ion-channel modulation and structural remodeling. In the last 30 years, significant improvements have been made in the computational modeling of cardiomyocyte Ca²⁺ handling under physiological and pathological conditions. However, numerous questions involving the Ca²⁺-dependent regulation of different macromolecular complexes, cross-talk between Ca²⁺-dependent regulatory pathways operating over a wide range of time scales, and bidirectional interactions between electrophysiology and mechanics remain to be addressed by in vitro and in silico studies. A better understanding of disease-specific Ca²⁺-dependent proarrhythmic mechanisms may facilitate the development of improved therapeutic strategies. In this review, we describe the fundamental mechanisms of cardiomyocyte Ca²⁺ handling in health and disease, and provide an overview of currently available computational models for cardiomyocyte Ca²⁺ handling. Finally, we discuss important uncertainties and open questions about cardiomyocyte Ca²⁺ handling and highlight how synergy between in vitro and in silico studies may help to answer several of these issues.