Examination of the Effects of Heterogeneous Organization of RyR Clusters, Myofibrils and Mitochondria on Ca2+ Release Patterns in Cardiomyocytes

Ca2+ dynamics in interstitial cells: foundational mechanisms for the motor patterns in the gastrointestinal tract

The gastrointestinal (GI) tract displays multiple motor patterns that move nutrients and wastes through the body. Smooth muscle cells (SMCs) provide the forces necessary for GI motility, but interstitial cells, electrically coupled to SMCs, tune SMC excitability, transduce inputs from enteric motor neurons, and generate pacemaker activity that underlies major motor patterns, such as peristalsis and segmentation. The interstitial cells regulating SMCs are interstitial cells of Cajal (ICC) and PDGF receptor (PDGFR)α+ cells. Together these cells form the SIP syncytium. ICC and PDGFRα+ cells express signature Ca2+-dependent conductances: ICC express Ca2+-activated Cl- channels, encoded by Ano1, that generate inward current, and PDGFRα+ cells express Ca2+-activated K+ channels, encoded by Kcnn3, that generate outward current. The open probabilities of interstitial cell conductances are controlled by Ca2+ release from the endoplasmic reticulum. The resulting Ca2+ transients occur spontaneously in a stochastic manner. Ca2+ transients in ICC induce spontaneous transient inward currents and spontaneous transient depolarizations (STDs). Neurotransmission increases or decreases Ca2+ transients, and the resulting depolarizing or hyperpolarizing responses conduct to other cells in the SIP syncytium. In pacemaker ICC, STDs activate voltage-dependent Ca2+ influx, which initiates a cluster of Ca2+ transients and sustains activation of ANO1 channels and depolarization during slow waves. Regulation of GI motility has traditionally been described as neurogenic and myogenic. Recent advances in understanding Ca2+ handling mechanisms in interstitial cells and how these mechanisms influence motor patterns of the GI tract suggest that the term "myogenic" should be replaced by the term "SIPgenic," as this review discusses.

Live-cell photo-activated localization microscopy correlates nanoscale ryanodine receptor configuration to calcium sparks in cardiomyocytes

Ca2+ sparks constitute the fundamental units of Ca2+ release in cardiomyocytes. Here we investigate how ryanodine receptors (RyRs) collectively generate these events by employing a transgenic mouse with a photo-activated label on RyR2. This allowed correlative imaging of RyR localization, by super-resolution Photo-Activated Localization Microscopy, and Ca2+ sparks, by high-speed imaging. Two populations of Ca2+ sparks were observed: stationary events and "travelling" events that spread between neighbouring RyR clusters. Travelling sparks exhibited up to 8 distinct releases, sourced from local or distal junctional sarcoplasmic reticulum. Quantitative analyses showed that sparks may be triggered by any number of RyRs within a cluster, and that acute β-adrenergic stimulation augments intra-cluster RyR recruitment to generate larger events. In contrast, RyR "dispersion" during heart failure facilitates the generation of travelling sparks. Thus, RyRs cooperatively generate Ca2+ sparks in a complex, malleable fashion, and channel organization regulates the propensity for local propagation of Ca2+ release.

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'.

The Cell Physiome: What Do We Need in a Computational Physiology Framework for Predicting Single-Cell Biology?

Modern biology and biomedicine are undergoing a big data explosion, needing advanced computational algorithms to extract mechanistic insights on the physiological state of living cells. We present the motivation for the Cell Physiome project: a framework and approach for creating, sharing, and using biophysics-based computational models of single-cell physiology. Using examples in calcium signaling, bioenergetics, and endosomal trafficking, we highlight the need for spatially detailed, biophysics-based computational models to uncover new mechanisms underlying cell biology. We review progress and challenges to date toward creating cell physiome models. We then introduce bond graphs as an efficient way to create cell physiome models that integrate chemical, mechanical, electromagnetic, and thermal processes while maintaining mass and energy balance. Bond graphs enhance modularization and reusability of computational models of cells at scale. We conclude with a look forward at steps that will help fully realize this exciting new field of mechanistic biomedical data science. Expected final online publication date for the Annual Review of Biomedical Data Science, Volume 5 is August 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

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.

A correlative super-resolution protocol to visualise structural underpinnings of fast second-messenger signalling in primary cell types

Nanometre-scale cellular information obtained through super-resolution microscopies are often unaccompanied by functional information, particularly transient and diffusible signals through which life is orchestrated in the nano-micrometre spatial scale. We describe a correlative imaging protocol which allows the ubiquitous intracellular second messenger, calcium (Ca2+), to be directly visualised against nanoscale patterns of the ryanodine receptor (RyR) Ca2+ channels which give rise to these Ca2+ signals in wildtype primary cells. This was achieved by combining total internal reflection fluorescence (TIRF) imaging of the elementary Ca2+ signals, with the subsequent DNA-PAINT imaging of the RyRs. We report a straightforward image analysis protocol of feature extraction and image alignment between correlative datasets and demonstrate how such data can be used to visually identify the ensembles of Ca2+ channels that are locally activated during the genesis of cytoplasmic Ca2+ signals.

A Novel Computational Model of the Rabbit Atrial Cardiomyocyte With Spatial Calcium Dynamics

Models of cardiac electrophysiology are widely used to supplement experimental results and to provide insight into mechanisms of cardiac function and pathology. The rabbit has been a particularly important animal model for studying mechanisms of atrial pathophysiology and atrial fibrillation, which has motivated the development of models for the rabbit atrial cardiomyocyte electrophysiology. Previously developed models include detailed representations of membrane currents and intracellular ionic concentrations, but these so-called “common-pool” models lack a spatially distributed description of the calcium handling system, which reflects the detailed ultrastructure likely found in cells in vivo. Because of the less well-developed T-tubular system in atrial compared to ventricular cardiomyocytes, spatial gradients in intracellular calcium concentrations may play a more significant role in atrial cardiomyocyte pathophysiology, rendering common-pool models less suitable for investigating underlying electrophysiological mechanisms. In this study, we developed a novel computational model of the rabbit atrial cardiomyocyte incorporating detailed compartmentalization of intracellular calcium dynamics, in addition to a description of membrane currents and intracellular processes. The spatial representation of calcium was based on dividing the intracellular space into eighteen different compartments in the transversal direction, each with separate systems for internal calcium storage and release, and tracking ionic fluxes between compartments in addition to the dynamics driven by membrane currents and calcium release. The model was parameterized employing a population-of-models approach using experimental data from different sources. The parameterization of this novel model resulted in a reduced population of models with inherent variability in calcium dynamics and electrophysiological properties, all of which fall within the range of observed experimental values. As such, the population of models may represent natural variability in cardiomyocyte electrophysiology or inherent uncertainty in the underlying experimental data. The ionic model population was also able to reproduce the U-shaped waveform observed in line-scans of triggered calcium waves in atrial cardiomyocytes, characteristic of the absence of T-tubules, resulting in a centripetal calcium wave due to subcellular calcium diffusion. This novel spatial model of the rabbit atrial cardiomyocyte can be used to integrate experimental findings, offering the potential to enhance our understanding of the pathophysiological role of calcium-handling abnormalities under diseased conditions, such as atrial fibrillation.

Structure and Function of the Human Ryanodine Receptors and Their Association with Myopathies-Present State, Challenges, and Perspectives

Cardiac arrhythmias are serious, life-threatening diseases associated with the dysregulation of Ca2+ influx into the cytoplasm of cardiomyocytes. This dysregulation often arises from dysfunction of ryanodine receptor 2 (RyR2), the principal Ca2+ release channel. Dysfunction of RyR1, the skeletal muscle isoform, also results in less severe, but also potentially life-threatening syndromes. The RYR2 and RYR1 genes have been found to harbor three main mutation “hot spots”, where mutations change the channel structure, its interdomain interface properties, its interactions with its binding partners, or its dynamics. In all cases, the result is a defective release of Ca2+ ions from the sarcoplasmic reticulum into the myocyte cytoplasm. Here, we provide an overview of the most frequent diseases resulting from mutations to RyR1 and RyR2, briefly review some of the recent experimental structural work on these two molecules, detail some of the computational work describing their dynamics, and summarize the known changes to the structure and function of these receptors with particular emphasis on their N-terminal, central, and channel domains.

Ca2+ Release via IP3 Receptors Shapes the Cardiac Ca2+ Transient for Hypertrophic Signaling

Calcium (Ca²⁺) plays a central role in mediating both contractile function and hypertrophic signaling in ventricular cardiomyocytes. L-type Ca²⁺ channels trigger release of Ca²⁺ from ryanodine receptors for cellular contraction, whereas signaling downstream of G-protein-coupled receptors stimulates Ca²⁺ release via inositol 1,4,5-trisphosphate receptors (IP₃Rs), engaging hypertrophic signaling pathways. Modulation of the amplitude, duration, and duty cycle of the cytosolic Ca²⁺ contraction signal and spatial localization have all been proposed to encode this hypertrophic signal. Given current knowledge of IP₃Rs, we develop a model describing the effect of functional interaction (cross talk) between ryanodine receptor and IP₃R channels on the Ca²⁺ transient and examine the sensitivity of the Ca²⁺ transient shape to properties of IP₃R activation. A key result of our study is that IP₃R activation increases Ca²⁺ transient duration for a broad range of IP₃R properties, but the effect of IP₃R activation on Ca²⁺ transient amplitude is dependent on IP₃ concentration. Furthermore we demonstrate that IP₃-mediated Ca²⁺ release in the cytosol increases the duty cycle of the Ca²⁺ transient, the fraction of the cycle for which [Ca²⁺] is elevated, across a broad range of parameter values and IP₃ concentrations. When coupled to a model of downstream transcription factor (NFAT) activation, we demonstrate that there is a high correspondence between the Ca²⁺ transient duty cycle and the proportion of activated NFAT in the nucleus. These findings suggest increased cytosolic Ca²⁺ duty cycle as a plausible mechanism for IP₃-dependent hypertrophic signaling via Ca²⁺-sensitive transcription factors such as NFAT in ventricular cardiomyocytes.

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.

Automated segmentation of cardiomyocyte Z-disks from high-throughput scanning electron microscopy data

Background

With the advent of new high-throughput electron microscopy techniques such as serial block-face scanning electron microscopy (SBF-SEM) and focused ion-beam scanning electron microscopy (FIB-SEM) biomedical scientists can study sub-cellular structural mechanisms of heart disease at high resolution and high volume. Among several key components that determine healthy contractile function in cardiomyocytes are Z-disks or Z-lines, which are located at the lateral borders of the sarcomere, the fundamental unit of striated muscle. Z-disks play the important role of anchoring contractile proteins within the cell that make the heartbeat. Changes to their organization can affect the force with which the cardiomyocyte contracts and may also affect signaling pathways that regulate cardiomyocyte health and function. Compared to other components in the cell, such as mitochondria, Z-disks appear as very thin linear structures in microscopy data with limited difference in contrast to the remaining components of the cell.

Methods

In this paper, we propose to generate a 3D model of Z-disks within single adult cardiac cells from an automated segmentation of a large serial-block-face scanning electron microscopy (SBF-SEM) dataset. The proposed fully automated segmentation scheme is comprised of three main modules including “pre-processing”, “segmentation” and “refinement”. We represent a simple, yet effective model to perform segmentation and refinement steps. Contrast stretching, and Gaussian kernels are used to pre-process the dataset, and well-known “Sobel operators” are used in the segmentation module.

Results

We have validated our model by comparing segmentation results with ground-truth annotated Z-disks in terms of pixel-wise accuracy. The results show that our model correctly detects Z-disks with 90.56% accuracy. We also compare and contrast the accuracy of the proposed algorithm in segmenting a FIB-SEM dataset against the accuracy of segmentations from a machine learning program called Ilastik and discuss the advantages and disadvantages that these two approaches have.

Conclusions

Our validation results demonstrate the robustness and reliability of our algorithm and model both in terms of validation metrics and in terms of a comparison with a 3D visualisation of Z-disks obtained using immunofluorescence based confocal imaging.

Assessing Cardiomyocyte Excitation-Contraction Coupling Site Detection From Live Cell Imaging Using a Structurally-Realistic Computational Model of Calcium Release

Calcium signaling plays a pivotal role in cardiomyocytes, coupling electrical excitation to mechanical contraction of the heart. Determining locations of active calcium release sites, and how their recruitment changes in response to stimuli and in disease states is therefore of central interest in cardiac physiology. Current algorithms for detecting release sites from live cell imaging data are however not easily validated against a known “ground truth,” which makes interpretation of the output of such algorithms, in particular the degree of confidence in site detection, a challenging task. Computational models are capable of integrating findings from multiple sources into a consistent, predictive framework. In cellular physiology, such models have the potential to reveal structure and function beyond the temporal and spatial resolution limitations of individual experimental measurements. Here, we create a spatially detailed computational model of calcium release in an eight sarcomere section of a ventricular cardiomyocyte, using electron tomography reconstruction of cardiac ultrastructure and confocal imaging of protein localization. This provides a high-resolution model of calcium diffusion from intracellular stores, which can be used as a platform to simulate confocal fluorescence imaging in the context of known ground truth structures from the higher resolution model. We use this capability to evaluate the performance of a recently proposed method for detecting the functional response of calcium release sites in live cells. Model permutations reveal how calcium release site density and mitochondria acting as diffusion barriers impact the detection performance of the algorithm. We demonstrate that site density has the greatest impact on detection precision and recall, in particular affecting the effective detectable depth of sites in confocal data. Our findings provide guidance on how such detection algorithms may best be applied to experimental data and give insights into limitations when using two-dimensional microscopy images to analyse three-dimensional cellular structures.

Multiscale Modeling of Dyadic Structure-Function Relation in Ventricular Cardiac Myocytes

Cardiovascular disease is often related to defects of subcellular components in cardiac myocytes, specifically in the dyadic cleft, which include changes in cleft geometry and channel placement. Modeling of these pathological changes requires both spatially resolved cleft as well as whole cell level descriptions. We use a multiscale model to create dyadic structure-function relationships to explore the impact of molecular changes on whole cell electrophysiology and calcium cycling. This multiscale model incorporates stochastic simulation of individual L-type calcium channels and ryanodine receptor channels, spatially detailed concentration dynamics in dyadic clefts, rabbit membrane potential dynamics, and a system of partial differential equations for myoplasmic and lumenal free Ca²⁺ and Ca²⁺-binding molecules in the bulk of the cell. We found action potential duration, systolic, and diastolic [Ca²⁺] to respond most sensitively to changes in L-type calcium channel current. The ryanodine receptor channel cluster structure inside dyadic clefts was found to affect all biomarkers investigated. The shape of clusters observed in experiments by Jayasinghe et al. and channel density within the cluster (characterized by mean occupancy) showed the strongest correlation to the effects on biomarkers.

Computational Model of Calcium Signaling in Cardiac Atrial Cells at the Submicron Scale

In cardiac cells, calcium is the mediator of excitation-contraction coupling. Dysfunctions in calcium handling have been identified as the origin of some cardiac arrhythmias. In the particular case of atrial myocytes, recent available experimental data has found links between these dysfunctions and structural changes in the calcium handling machinery (ryanodine cluster size and distribution, t-tubular network, etc). To address this issue, we have developed a computational model of an atrial myocyte that takes into account the detailed intracellular structure. The homogenized macroscopic behavior is described with a two-concentration field model, using effective diffusion coefficients of calcium in the sarcoplasmic reticulum (SR) and in the cytoplasm. The model reproduces the right calcium transients and dependence with pacing frequency. Under basal conditions, the calcium rise is mostly restricted to the periphery of the cell, with a large concentration ratio between the periphery and the interior. We have then studied the dependence of the speed of the calcium wave on cytosolic and SR diffusion coefficients, finding an almost linear relation with the former, in agreement with a diffusive and fire mechanism of propagation, and little dependence on the latter. Finally, we have studied the effect of a change in RyR cluster microstructure. We find that, under resting conditions, the spark frequency decreases slightly with RyR cluster spatial dispersion, but markedly increases when the RyRs are distributed in clusters of larger size, stressing the importance of RyR cluster organization to understand atrial arrhythmias, as recent experimental results suggest (Macquaide et al., 2015).

Insights on the impact of mitochondrial organisation on bioenergetics in high-resolution computational models of cardiac cell architecture

Recent electron microscopy data have revealed that cardiac mitochondria are not arranged in crystalline columns but are organised with several mitochondria aggregated into columns of varying sizes spanning the cell cross-section. This raises the question—how does the mitochondrial arrangement affect the metabolite distributions within cardiomyocytes and what is its impact on force dynamics? Here, we address this question by employing finite element modeling of cardiac bioenergetics on computational meshes derived from electron microscope images. Our results indicate that heterogeneous mitochondrial distributions can lead to significant spatial variation across the cell in concentrations of inorganic phosphate, creatine (Cr) and creatine phosphate (PCr). However, our model predicts that sufficient activity of the creatine kinase (CK) system, coupled with rapid diffusion of Cr and PCr, maintains near uniform ATP and ADP ratios across the cell cross sections. This homogenous distribution of ATP and ADP should also evenly distribute force production and twitch duration with contraction. These results suggest that the PCr shuttle and associated enzymatic reactions act to maintain uniform force dynamics in the cell despite the heterogeneous mitochondrial organization. However, our model also predicts that under hypoxia activity of mitochondrial CK enzymes and diffusion of high-energy phosphate compounds may be insufficient to sustain uniform ATP/ADP distribution and hence force generation.

Mammalian cardiomyocytes contain a high volume of mitochondria, which maintains the continuous and bulk supply of ATP to sustain normal heart function. Previously, cardiac mitochondria were understood to be distributed in a regular, crystalline pattern, which facilitated a steady supply of ATP at different workloads. Using electron microscopy images of cell cross sections, we recently found that they are not regularly distributed inside cardiomyocytes. We created new spatially accurate computational models of cardiac cell bioenergetics and tested whether this heterogeneous distribution of mitochondria causes non-uniform energy supply and contractile force production in the cardiomyocyte. We found that ATP and ADP concentrations remain uniform throughout the cell because of the activity of creatine kinase (CK) enzymes that convert ATP produced in the mitochondria into creatine phosphate. Creatine phosphate rapidly diffuses to the myofibril region where it can be converted back to ATP for the contraction cycle in a timely manner. This mechanism is called the phosphocreatine shuttle (PCr shuttle). The PCr shuttle ensures that different areas of the cell produce the same amount of force regardless of the mitochondrial distribution. However, our model also shows that when the cellular oxygen supply is limited—as can be the case in conditions such as heart failure—the PCr shuttle cannot maintain uniform ATP and ADP concentrations across the cell. This causes a non-uniform acto-myosin force distribution and non-uniform twitch duration across the cell cross section. Our study suggests that mechanisms other than the PCr shuttle may be necessary to maintain uniform supply of ATP in a hypoxic environment.

Shining New Light on the Structural Determinants of Cardiac Couplon Function: Insights From Ten Years of Nanoscale Microscopy

Remodelling of the membranes and protein clustering patterns during the pathogenesis of cardiomyopathies has renewed the interest in spatial visualisation of these structures in cardiomyocytes. Coincidental emergence of single molecule (super-resolution) imaging and tomographic electron microscopy tools in the last decade have led to a number of new observations on the structural features of the couplons, the primary sites of excitation-contraction coupling in the heart. In particular, super-resolution and tomographic electron micrographs have revised and refined the classical views of the nanoscale geometries of couplons, t-tubules and the organisation of the principal calcium handling proteins in both healthy and failing hearts. These methods have also allowed the visualisation of some features which were too small to be detected with conventional microscopy tools. With new analytical capabilities such as single-protein mapping, in situ protein quantification, correlative and live cell imaging we are now observing an unprecedented interest in adapting these research tools across the cardiac biophysical research discipline. In this article, we review the depth of the new insights that have been enabled by these tools toward understanding the structure and function of the cardiac couplon. We outline the major challenges that remain in these experiments and emerging avenues of research which will be enabled by these technologies.

Calcium in the Pathophysiology of Atrial Fibrillation and Heart Failure

Atrial fibrillation (AF) is commonly associated with heart failure. A bidirectional relationship exists between the two-AF exacerbates heart failure causing a significant increase in heart failure symptoms, admissions to hospital and cardiovascular death, while pathological remodeling of the atria as a result of heart failure increases the risk of AF. A comprehensive understanding of the pathophysiology of AF is essential if we are to break this vicious circle. In this review, the latest evidence will be presented showing a fundamental role for calcium in both the induction and maintenance of AF. After outlining atrial electrophysiology and calcium handling, the role of calcium-dependent afterdepolarizations and atrial repolarization alternans in triggering AF will be considered. The atrial response to rapid stimulation will be discussed, including the short-term protection from calcium overload in the form of calcium signaling silencing and the eventual progression to diastolic calcium leak causing afterdepolarizations and the development of an electrical substrate that perpetuates AF. The role of calcium in the bidirectional relationship between heart failure and AF will then be covered. The effects of heart failure on atrial calcium handling that promote AF will be reviewed, including effects on both atrial myocytes and the pulmonary veins, before the aspects of AF which exacerbate heart failure are discussed. Finally, the limitations of human and animal studies will be explored allowing contextualization of what are sometimes discordant results.

Nanoscale remodeling of ryanodine receptor cluster size underlies cerebral microvascular dysfunction in Duchenne muscular dystrophy

Duchenne muscular dystrophy (DMD) is a hereditary neuromuscular disease that results from mutations in the gene encoding dystrophin. The effects of the disease on cardiac and skeletal muscle have been intensely investigated, but much less is known about how DMD impacts vascular smooth muscle cells (SMCs). Using superresolution nanoscopy, we demonstrate that clusters of ryanodine receptors (RyR2s) on the sarcoplasmic reticulum (SR) of cerebral artery SMCs from the mdx mouse model of DMD are larger compared with controls. Increased RyR2 cluster size is associated with augmented SR Ca²⁺ release and Ca²⁺-activated K⁺ channel activity, resulting in impaired vasoconstriction of cerebral microvessels. Our findings demonstrate that remodeling of RyR2 clusters at the molecular level results in cerebral microvascular dysfunction during DMD.

Duchenne muscular dystrophy (DMD) results from mutations in the gene encoding dystrophin which lead to impaired function of skeletal and cardiac muscle, but little is known about the effects of the disease on vascular smooth muscle cells (SMCs). Here we used the mdx mouse model to study the effects of mutant dystrophin on the regulation of cerebral artery and arteriole SMC contractility, focusing on an important Ca²⁺-signaling pathway composed of type 2 ryanodine receptors (RyR2s) on the sarcoplasmic reticulum (SR) and large-conductance Ca²⁺-activated K⁺ (BK) channels on the plasma membrane. Nanoscale superresolution image analysis revealed that RyR2 and BKα were organized into discrete clusters, and that the mean size of RyR2 clusters that colocalized with BKα was larger in SMCs from mdx mice (∼62 RyR2 monomers) than in controls (∼40 RyR2 monomers). We further found that the frequency and signal mass of spontaneous, transient Ca²⁺-release events through SR RyR2s (“Ca²⁺ sparks”) were greater in SMCs from mdx mice. Patch-clamp electrophysiological recordings indicated a corresponding increase in Ca²⁺-dependent BK channel activity. Using pressure myography, we found that cerebral pial arteries and parenchymal arterioles from mdx mice failed to develop appreciable spontaneous myogenic tone. Inhibition of RyRs with tetracaine and blocking of BK channels with paxilline restored myogenic tone to control levels, demonstrating that enhanced RyR and BK channel activity is responsible for the diminished pressure-induced constriction of arteries and arterioles from mdx mice. We conclude that increased size of RyR2 protein clusters in SMCs from mdx mice increases Ca²⁺ spark and BK channel activity, resulting in cerebral microvascular dysfunction.

Size Matters: Ryanodine Receptor Cluster Size Affects Arrhythmogenic Sarcoplasmic Reticulum Calcium Release

BACKGROUND

Ryanodine receptors (RyR) mediate sarcoplasmic reticulum calcium (Ca2+) release and influence myocyte Ca2+ homeostasis and arrhythmias. In cardiac myocytes, RyRs are found in clusters of various sizes and shapes, and RyR cluster size may critically influence normal and arrhythmogenic Ca2+ spark and wave formation. However, the actual RyR cluster sizes at specific Ca2+ spark sites have never been measured in the physiological setting.

METHODS AND RESULTS

Here we measured RyR cluster size and Ca2+ sparks simultaneously to assess how RyR cluster size influences Ca2+ sparks and sarcoplasmic reticulum Ca2+ leak. For small RyR cluster sizes (<50), Ca2+ spark frequency is very low but then increases dramatically at larger cluster sizes. In contrast, Ca2+ spark amplitude is nearly maximal even at relatively small RyR cluster size (≈10) and changes little at larger cluster size. These properties agreed with computational simulations of RyR gating within clusters.

CONCLUSIONS

Our study explains how this combination of properties may limit arrhythmogenic Ca2+ sparks and wave propagation (at many junctions) while preserving the efficacy and spatial synchronization of Ca2+-induced Ca2+-release during normal excitation-contraction coupling. However, variations in RyR cluster size among individual junctions and RyR sensitivity could exacerbate heterogeneity of local sarcoplasmic reticulum Ca2+ release and arrhythmogenesis under pathological conditions.

Creating a Structurally Realistic Finite Element Geometric Model of a Cardiomyocyte to Study the Role of Cellular Architecture in Cardiomyocyte Systems Biology

With the advent of three-dimensional (3D) imaging technologies such as electron tomography, serial-block-face scanning electron microscopy and confocal microscopy, the scientific community has unprecedented access to large datasets at sub-micrometer resolution that characterize the architectural remodeling that accompanies changes in cardiomyocyte function in health and disease. However, these datasets have been under-utilized for investigating the role of cellular architecture remodeling in cardiomyocyte function. The purpose of this protocol is to outline how to create an accurate finite element model of a cardiomyocyte using high resolution electron microscopy and confocal microscopy images. A detailed and accurate model of cellular architecture has significant potential to provide new insights into cardiomyocyte biology, more than experiments alone can garner. The power of this method lies in its ability to computationally fuse information from two disparate imaging modalities of cardiomyocyte ultrastructure to develop one unified and detailed model of the cardiomyocyte. This protocol outlines steps to integrate electron tomography and confocal microscopy images of adult male Wistar (name for a specific breed of albino rat) rat cardiomyocytes to develop a half-sarcomere finite element model of the cardiomyocyte. The procedure generates a 3D finite element model that contains an accurate, high-resolution depiction (on the order of ~35 nm) of the distribution of mitochondria, myofibrils and ryanodine receptor clusters that release the necessary calcium for cardiomyocyte contraction from the sarcoplasmic reticular network (SR) into the myofibril and cytosolic compartment. The model generated here as an illustration does not incorporate details of the transverse-tubule architecture or the sarcoplasmic reticular network and is therefore a minimal model of the cardiomyocyte. Nevertheless, the model can already be applied in simulation-based investigations into the role of cell structure in calcium signaling and mitochondrial bioenergetics, which is illustrated and discussed using two case studies that are presented following the detailed protocol.

Computational modeling of single-cell mechanics and cytoskeletal mechanobiology

Cellular cytoskeletal mechanics plays a major role in many aspects of human health from organ development to wound healing, tissue homeostasis and cancer metastasis. We summarize the state-of-the-art techniques for mathematically modeling cellular stiffness and mechanics and the cytoskeletal components and factors that regulate them. We highlight key experiments that have assisted model parameterization and compare the advantages of different models that have been used to recapitulate these experiments. An overview of feed-forward mechanisms from signaling to cytoskeleton remodeling is provided, followed by a discussion of the rapidly growing niche of encapsulating feedback mechanisms from cytoskeletal and cell mechanics to signaling. We discuss broad areas of advancement that could accelerate research and understanding of cellular mechanobiology. A precise understanding of the molecular mechanisms that affect cell and tissue mechanics and function will underpin innovations in medical device technologies of the future. WIREs Syst Biol Med 2018, 10:e1407. doi: 10.1002/wsbm.1407 This article is categorized under: Models of Systems Properties and Processes > Mechanistic Models Physiology > Mammalian Physiology in Health and Disease Models of Systems Properties and Processes > Cellular Models.

An automated workflow for segmenting single adult cardiac cells from large-volume serial block-face scanning electron microscopy data

This paper presents a new algorithm to automatically segment the myofibrils, mitochondria and nuclei within single adult cardiac cells that are part of a large serial-block-face scanning electron microscopy (SBF-SEM) dataset. The algorithm only requires a set of manually drawn contours that roughly demarcate the cell boundary at routine slice intervals (every 50th, for example). The algorithm correctly classified pixels within the single cell with 97% accuracy when compared to manual segmentations. One entire cell and the partial volumes of two cells were segmented. Analysis of segmentations within these cells showed that myofibrils and mitochondria occupied 47.5% and 51.6% on average respectively, while the nuclei occupy 0.7% of the cell for which the entire volume was captured in the SBF-SEM dataset. Mitochondria clustering increased at the periphery of the nucleus region and branching points of the cardiac cell. The segmentations also showed high area fraction of mitochondria (up to 70% of the 2D image slice) in the sub-sarcolemmal region, whilst it was closer to 50% in the intermyofibrillar space. We finally demonstrate that our segmentations can be turned into 3D finite element meshes for cardiac cell computational physiology studies. We offer our large dataset and MATLAB implementation of the algorithm for research use at www.github.com/CellSMB/sbfsem-cardiac-cell-segmenter/. We anticipate that this timely tool will be of use to cardiac computational and experimental physiologists alike who study cardiac ultrastructure and its role in heart function.

Transverse tubular network structures in the genesis of intracellular calcium alternans and triggered activity in cardiac cells

RATIONALE

The major role of a transverse-tubular (TT) network in a cardiac cell is to facilitate effective excitation-contraction coupling and signaling. The TT network structures are heterogeneous within a single cell, and vary between different types of cells and species. They are also remodeled in cardiac diseases. However, how different TT network structures predispose cardiac cells to arrhythmogenesis remains to be revealed.

OBJECTIVE

To systematically investigate the roles of TT network structure and the underlying mechanisms in the genesis of intracellular calcium (Ca2+) alternans and triggered activity (TA).

METHODS AND RESULTS

Based on recent experimental observations, different TT network structures, including uniformly and non-uniformly random TT distributions, were modeled in a cardiac cell model consisting of a three-dimensional network of Ca2+ release units (CRUs). Our simulations showed that both Ca2+ alternans and Ca2+ wave-mediated TA were promoted when the fraction of orphaned CRUs was in an intermediate range, but suppressed in cells exhibiting either well-organized TT networks or low TT densities. Ca2+ alternans and TA could be promoted by low TT densities when the cells were small or the CRU coupling was strong. Both alternans and TA occurred more easily in uniformly random TT networks than in non-uniformly random TT networks. Subcellular spatially discordant Ca2+ alternans was promoted by non-uniformly random TT networks but suppressed by increasing CRU coupling strength. These mechanistic insights provide a holistic understanding of the effects of TT network structure on the susceptibility to arrhythmogenesis.

CONCLUSIONS

The TT network plays important roles in promoting Ca2+ alternans and TA, and different TT network structures may predispose cardiac cells differently to arrhythmogenesis.

A computational model of spatio-temporal cardiac intracellular calcium handling with realistic structure and spatial flux distribution from sarcoplasmic reticulum and t-tubule reconstructions

Intracellular calcium cycling is a vital component of cardiac excitation-contraction coupling. The key structures responsible for controlling calcium dynamics are the cell membrane (comprising the surface sarcolemma and transverse-tubules), the intracellular calcium store (the sarcoplasmic reticulum), and the co-localisation of these two structures to form dyads within which calcium-induced-calcium-release occurs. The organisation of these structures tightly controls intracellular calcium dynamics. In this study, we present a computational model of intracellular calcium cycling in three-dimensions (3-D), which incorporates high resolution reconstructions of these key regulatory structures, attained through imaging of tissue taken from the sheep left ventricle using serial block face scanning electron microscopy. An approach was developed to model the sarcoplasmic reticulum structure at the whole-cell scale, by reducing its full 3-D structure to a 3-D network of one-dimensional strands. The model reproduces intracellular calcium dynamics during control pacing and reveals the high-resolution 3-D spatial structure of calcium gradients and intracellular fluxes in both the cytoplasm and sarcoplasmic reticulum. We also demonstrated the capability of the model to reproduce potentially pro-arrhythmic dynamics under perturbed conditions, pertaining to calcium-transient alternans and spontaneous release events. Comparison with idealised cell models emphasised the importance of structure in determining calcium gradients and controlling the spatial dynamics associated with calcium-transient alternans, wherein the probabilistic nature of dyad activation and recruitment was constrained. The model was further used to highlight the criticality in calcium spark propagation in relation to inter-dyad distances. The model presented provides a powerful tool for future investigation of structure-function relationships underlying physiological and pathophysiological intracellular calcium handling phenomena at the whole-cell. The approach allows for the first time direct integration of high-resolution images of 3-D intracellular structures with models of calcium cycling, presenting the possibility to directly assess the functional impact of structural remodelling at the cellular scale.

The organisation of the membrane and sub-cellular structures of cells in the heart closely controls the coupling between its electrical and mechanical function. Computational models of the cellular calcium handling system, which is responsible for this electro-mechanical coupling, have been developed in recent years to study underlying structure-function relationships. Previous models have been largely idealised in structure; we present a new model which incorporates experimental data describing the high-resolution organisation of the primary structures involved in calcium dynamics. Significantly, the structure of the intracellular calcium store is modelled for the first time. The model is shown to reproduce calcium dynamics in control cells in both normal and abnormal conditions, demonstrating its suitability for future investigation of structure-function relationships. Thus, the model presented provides a powerful tool for the direct integration of experimentally acquired structural data in healthy and diseased cells and assessment of the role of structure in regulating normal and abnormal calcium dynamics.

Calcium and Excitation-Contraction Coupling in the Heart

Cardiac contractility is regulated by changes in intracellular Ca concentration ([Ca²⁺]_i). Normal function requires that [Ca²⁺]_i be sufficiently high in systole and low in diastole. Much of the Ca needed for contraction comes from the sarcoplasmic reticulum and is released by the process of calcium-induced calcium release. The factors that regulate and fine-tune the initiation and termination of release are reviewed. The precise control of intracellular Ca cycling depends on the relationships between the various channels and pumps that are involved. We consider 2 aspects: (1) structural coupling: the transporters are organized within the dyad, linking the transverse tubule and sarcoplasmic reticulum and ensuring close proximity of Ca entry to sites of release. (2) Functional coupling: where the fluxes across all membranes must be balanced such that, in the steady state, Ca influx equals Ca efflux on every beat. The remainder of the review considers specific aspects of Ca signaling, including the role of Ca buffers, mitochondria, Ca leak, and regulation of diastolic [Ca²⁺]_i.

A computational study of the role of mitochondrial organization on cardiac bioenergetics

All cells in the body have a specific shape and internal organization which is specific to that cell's function. Heart cells are rod-shaped, and contain arrays of contractile protines (myofibrils) and mitochondria (organelles that produce energy) that are aligned along the length of the rod. This arrangement is presumed to allow the cell to generate maximal contractile force for each heartbeat and for energy metabolites to be readily available to generate this force. Heart disease phenotypes, such as diabetic cardiomyopathy and heart failure, exhibit altered organization of mitochondria. However, physiological and computational studies have predominantly investigated the effect of the biochemical changes that accompany the disease alone, such as reduced rates of ATP production by mitochondria. We present a modeling study that examines the effect of mitochondrial organization on energy metabolite distribution during the heartbeat. A 2D micrograph of the cell cross-section was selected from a 3D image stack of structural data of a cardiac cell. The image was used to generate a 2D finite element model, on which mitochondrial oxidative phosphorylation and energy metabolite diffusion was modelled. Results illustrate that mitochondrial density can induce heterogeneity in the distribution of metabolites across the cell area. We discuss the implications of these findings and avenues for future, more indepth studies.

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.

Electron tomography of rabbit cardiomyocyte three-dimensional ultrastructure

The field of cardiovascular research has benefitted from rapid developments in imaging technology over the last few decades. Accordingly, an ever growing number of large, multidimensional data sets have begun to appear, often challenging existing pre-conceptions about structure and function of biological systems. For tissue and cell structure imaging, the move from 2D section-based microscopy to true 3D data collection has been a major driver of new insight. In the sub-cellular domain, electron tomography is a powerful technique for exploration of cellular structures in 3D with unparalleled fidelity at nanometer resolution.

Electron tomography is particularly advantageous for studying highly compartmentalised cells such as cardiomyocytes, where elaborate sub-cellular structures play crucial roles in electrophysiology and mechanics. Although the anatomy of specific ultra-structures, such as dyadic couplons, has been extensively explored using 2D electron microscopy of thin sections, we still lack accurate, quantitative knowledge of true individual shape, volume and surface area of sub-cellular domains, as well as their 3D spatial interrelations; let alone of how these are reshaped during the cycle of contraction and relaxation. Here we discuss and illustrate the utility of ET for identification, visualisation, and analysis of 3D cardiomyocyte ultrastructures such as the T-tubular system, sarcoplasmic reticulum, mitochondria and microtubules.

Multiphysics and multiscale modelling, data-model fusion and integration of organ physiology in the clinic: ventricular cardiac mechanics

With heart and cardiovascular diseases continually challenging healthcare systems worldwide, translating basic research on cardiac (patho)physiology into clinical care is essential. Exacerbating this already extensive challenge is the complexity of the heart, relying on its hierarchical structure and function to maintain cardiovascular flow. Computational modelling has been proposed and actively pursued as a tool for accelerating research and translation. Allowing exploration of the relationships between physics, multiscale mechanisms and function, computational modelling provides a platform for improving our understanding of the heart. Further integration of experimental and clinical data through data assimilation and parameter estimation techniques is bringing computational models closer to use in routine clinical practice. This article reviews developments in computational cardiac modelling and how their integration with medical imaging data is providing new pathways for translational cardiac modelling.