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

Engineering the maturation of stem cell-derived cardiomyocytes

The maturation of human stem cell-derived cardiomyocytes (hSC-CMs) has been a major challenge to further expand the scope of their application. Over the past years, several strategies have been proven to facilitate the structural and functional maturation of hSC-CMs, which include but are not limited to engineering the geometry or stiffness of substrates, providing favorable extracellular matrices, applying mechanical stretch, fluidic or electrical stimulation, co-culturing with niche cells, regulating biochemical cues such as hormones and transcription factors, engineering and redirecting metabolic patterns, developing 3D cardiac constructs such as cardiac organoid or engineered heart tissue, or culturing under in vivo implantation. In this review, we summarize these maturation strategies, especially the recent advancements, and discussed their advantages as well as the pressing problems that need to be addressed in future studies.

Close agreement between deterministic versus stochastic modeling of first-passage time to vesicle fusion

Ca2+-dependent cell processes, such as neurotransmitter or endocrine vesicle fusion, are inherently stochastic due to large fluctuations in Ca2+ channel gating, Ca2+ diffusion, and Ca2+ binding to buffers and target sensors. However, previous studies revealed closer-than-expected agreement between deterministic and stochastic simulations of Ca2+ diffusion, buffering, and sensing if Ca2+ channel gating is not Ca2+ dependent. To understand this result more fully, we present a comparative study complementing previous work, focusing on Ca2+ dynamics downstream of Ca2+ channel gating. Specifically, we compare deterministic (mean-field/mass-action) and stochastic simulations of vesicle exocytosis latency, quantified by the probability density of the first-passage time (FPT) to the Ca2+-bound state of a vesicle fusion sensor, following a brief Ca2+ current pulse. We show that under physiological constraints, the discrepancy between FPT densities obtained using the two approaches remains small even if as few as ∼50 Ca2+ ions enter per single channel-vesicle release unit. Using a reduced two-compartment model for ease of analysis, we illustrate how this close agreement arises from the smallness of correlations between fluctuations of the reactant molecule numbers, despite the large magnitude of fluctuation amplitudes. This holds if all relevant reactions are heteroreaction between molecules of different species, as is the case for bimolecular Ca2+ binding to buffers and downstream sensor targets. In this case, diffusion and buffering effectively decorrelate the state of the Ca2+ sensor from local Ca2+ fluctuations. Thus, fluctuations in the Ca2+ sensor's state underlying the FPT distribution are only weakly affected by the fluctuations in the local Ca2+ concentration around its average, deterministically computable value.

Electron microscopy of cardiac 3D nanodynamics: form, function, future

The 3D nanostructure of the heart, its dynamic deformation during cycles of contraction and relaxation, and the effects of this deformation on cell function remain largely uncharted territory. Over the past decade, the first inroads have been made towards 3D reconstruction of heart cells, with a native resolution of around 1 nm³, and of individual molecules relevant to heart function at a near-atomic scale. These advances have provided access to a new generation of data and have driven the development of increasingly smart, artificial intelligence-based, deep-learning image-analysis algorithms. By high-pressure freezing of cardiomyocytes with millisecond accuracy after initiation of an action potential, pseudodynamic snapshots of contraction-induced deformation of intracellular organelles can now be captured. In combination with functional studies, such as fluorescence imaging, exciting insights into cardiac autoregulatory processes at nano-to-micro scales are starting to emerge. In this Review, we discuss the progress in this fascinating new field to highlight the fundamental scientific insight that has emerged, based on technological breakthroughs in biological sample preparation, 3D imaging and data analysis; to illustrate the potential clinical relevance of understanding 3D cardiac nanodynamics; and to predict further progress that we can reasonably expect to see over the next 10 years.

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.

Characteristics of Bisphenol Cardiotoxicity: Impaired Excitability, Contractility, and Relaxation

Bisphenol a (BPA) is a high production volume chemical that is frequently used to manufacture epoxy resins and polycarbonate plastics. BPA-containing products are now pervasive, and as a result, biomonitoring studies report widespread exposure in > 90% of adults, adolescents, and children. Both epidemiological and experimental studies have reported associations between BPA exposure and adverse cardiovascular health outcomes. With increasing concerns regarding BPA exposure, a few structurally similar bisphenol chemicals have been introduced as replacements, including bisphenol s (BPS) and bisphenol f (BPF). In accordance with the recently established "Key characteristics of cardiovascular toxicants", we reviewed the literature to highlight the immediate effects of bisphenol chemicals on (1) cardiac excitability, and (2) contractility and relaxation. BPA inhibits key cardiac ion channels, impairs cardiac excitability, and acts as a more potent inhibitor as compared to BPF and BPS. Through the inhibition of calcium current, some studies report that bisphenol chemicals can act as negative inotropic agents. Yet, others suggest that low dose exposures may increase contractility and precipitate triggered arrhythmias via the phosphorylation of key calcium handling proteins. Accordingly, we propose additional considerations for future work to comprehensively address the cardiac safety profile of BPA, as compared to replacement chemicals.

Computationally efficient model of myocardial electromechanics for multiscale simulations

A model of myocardial electromechanics is suggested. It combines modified and simplified versions of previously published models of cardiac electrophysiology, excitation-contraction coupling, and mechanics. The mechano-calcium and mechano-electrical feedbacks, including the strain-dependence of the propagation velocity of the action potential, are also accounted for. The model reproduces changes in the twitch amplitude and Ca2+-transients upon changes in muscle strain including the slow response. The model also reproduces the Bowditch effect and changes in the twitch amplitude and duration upon changes in the interstimulus interval, including accelerated relaxation at high stimulation frequency. Special efforts were taken to reduce the stiffness of the differential equations of the model. As a result, the equations can be integrated numerically with a relatively high time step making the model suitable for multiscale simulation of the human heart and allowing one to study the impact of myocardial mechanics on arrhythmias.

Primary cilium: a paradigm for integrating mathematical modeling with experiments and numerical simulations in mechanobiology

Primary cilia are non-motile, solitary (one per cell) microtubule-based organelles that emerge from the mother centriole after cells have exited the mitotic cycle. Identified as a mechanosensing organelle that responds to both mechanical and chemical stimuli, the primary cilium provides a fertile ground for integrative investigations of mathematical modeling, numerical simulations, and experiments. Recent experimental findings revealed considerable complexity to the underlying mechanosensory mechanisms that transmit extracellular stimuli to intracellular signaling many of which include primary cilia. In this invited review, we provide a brief survey of experimental findings on primary cilia and how these results lead to various mathematical models of the mechanics of the primary cilium bent under an external forcing such as a fluid flow or a trap. Mathematical modeling of the primary cilium as a fluid-structure interaction problem highlights the importance of basal anchorage and the anisotropic moduli of the microtubules. As theoretical modeling and numerical simulations progress, along with improved state-of-the-art experiments on primary cilia, we hope that details of ciliary regulated mechano-chemical signaling dynamics in cellular physiology will be understood in the near future.

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.

Calcium Dynamics and Cardiac Arrhythmia

This Special Collection will gather all studies highlighting recent advances in theoretical and experimental studies of arrhythmia, with a specific focus on research seeking to elucidate links between calcium homeostasis in cardiac cells and organ-scale disruption of heart rhythm.