Modeling effects of L-type ca(2+) current and na(+)-ca(2+) exchanger on ca(2+) trigger flux in rabbit myocytes with realistic T-tubule geometries

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.

An Open-Source Mesh Generation Platform for Biophysical Modeling Using Realistic Cellular Geometries

Advances in imaging methods such as electron microscopy, tomography, and other modalities are enabling high-resolution reconstructions of cellular and organelle geometries. Such advances pave the way for using these geometries for biophysical and mathematical modeling once these data can be represented as a geometric mesh, which, when carefully conditioned, enables the discretization and solution of partial differential equations. In this work, we outline the steps for a naïve user to approach the Geometry-preserving Adaptive MeshER software version 2, a mesh generation code written in C++ designed to convert structural data sets to realistic geometric meshes while preserving the underlying shapes. We present two example cases: 1) mesh generation at the subcellular scale as informed by electron tomography and 2) meshing a protein with a structure from x-ray crystallography. We further demonstrate that the meshes generated by the Geometry-preserving Adaptive MeshER software are suitable for use with numerical methods. Together, this collection of libraries and tools simplifies the process of constructing realistic geometric meshes from structural biology data.

Modeling Depolarization Delay, Sodium Currents, and Electrical Potentials in Cardiac Transverse Tubules

T-tubules are invaginations of the lateral membrane of striated muscle cells that provide a large surface for ion channels and signaling proteins, thereby supporting excitation–contraction coupling. T-tubules are often remodeled in heart failure. To better understand the electrical behavior of T-tubules of cardiac cells in health and disease, this study addresses two largely unanswered questions regarding their electrical properties: (1) the delay of T-tubular membrane depolarization and (2) the effects of T-tubular sodium current on T-tubular potentials. Here, we present an elementary computational model to determine the delay in depolarization of deep T-tubular membrane segments as the narrow T-tubular lumen provides resistance against the extracellular current. We compare healthy tubules to tubules with constrictions and diseased tubules from mouse and human, and conclude that constrictions greatly delay T-tubular depolarization, while diseased T-tubules depolarize faster than healthy ones due to tubule widening. Increasing the tubule length non-linearly delays the depolarization. We moreover model the effect of T-tubular sodium current on intraluminal T-tubular potentials. We observe that extracellular potentials become negative during the sodium current transient (up to −40 mV in constricted T-tubules), which feedbacks on sodium channel function (self-attenuation) in a manner resembling ephaptic effects that have been described for intercalated discs where opposing membranes are very close together. The intraluminal potential and sodium current self-attenuation however greatly depend on sodium current conductance. These results show that (1) the changes in passive electrical properties of remodeled T-tubules cannot explain the excitation–contraction coupling defects in diseased cells; and (2) the sodium current may modulate intraluminal potentials. Such extracellular potentials might also affect excitation–contraction coupling and macroscopic conduction.

A fundamental evaluation of the electrical properties and function of cardiac transverse tubules

This work discusses active and passive electrical properties of transverse (T-)tubules in ventricular cardiomyocytes to understand the physiological roles of T-tubules. T-tubules are invaginations of the lateral membrane that provide a large surface for calcium-handling proteins to facilitate sarcomere shortening. Higher heart rates correlate with higher T-tubular densities in mammalian ventricular cardiomyocytes. We assess ion dynamics in T-tubules and the effects of sodium current in T-tubules on the extracellular potential, which leads to a partial reduction of the sodium current in deep segments of a T-tubule. We moreover reflect on the impact of T-tubules on macroscopic conduction velocity, integrating fundamental principles of action potential propagation and conduction. We also theoretically assess how the conduction velocity is affected by different T-tubular sodium current densities. Lastly, we critically assess literature on ion channel expression to determine whether action potentials can be initiated in T-tubules.

Impaired Activity of Ryanodine Receptors Contributes to Calcium Mishandling in Cardiomyocytes of Metabolic Syndrome Rats

Metabolic syndrome (MetS) has become a global epidemic. MetS is a serious health problem because of its related cardiovascular complications, which include hypertension and delayed heart rate recovery after exercise. The molecular bases of cardiac dysfunction in MetS are still under scrutiny and may be related to anomalies in the activity and expression of key proteins involved in the cardiac excitation-contraction coupling (ECC). The cardiac Ca²⁺ channel/ryanodine receptor (RyR2) participates in releasing Ca²⁺ from internal stores and plays a key role in the modulation of ECC. We examined alterations in expression, phosphorylation status, Ca²⁺ sensitivity, and in situ function (by measuring Ca²⁺ sparks and Ca²⁺ transients) of RyR2; alterations in these characteristics could help to explain the Ca²⁺ handling disturbances in MetS cardiomyocytes. MetS was induced in rats by adding commercially refined sugar (30% sucrose) to their drinking water for 24 weeks. Cardiomyocytes of MetS rats displayed decreased Ca²⁺ transient amplitude and cell contractility at all stimulation frequencies. Quiescent MetS cardiomyocytes showed a decrease in Ca²⁺ spark frequency, amplitude, and spark-mediated Ca²⁺ leak. The [³H]-ryanodine binding data showed that functionally active RyRs are significantly diminished in MetS heart microsomes; and exhibited rapid Ca²⁺-induced inactivation. The phosphorylation of corresponding Ser2814 (a preferential target for CaMKII) of the hRyR2 was significantly diminished. RyR2 protein expression and Ser2808 phosphorylation level were both unchanged. Further, we demonstrated that cardiomyocyte Ca²⁺ mishandling was associated with reduced SERCA pump activity due to decreased Thr17-PLN phosphorylation, suggesting a downregulation of CaMKII in MetS hearts, though the SR Ca²⁺ load remained unchanged. The reduction in the phosphorylation level of RyR2 at Ser2814 decreases RyR2 availability for activation during ECC. In conclusion, the impaired in situ activity of RyR2 may also account for the poor overall cardiac outcome reported in MetS patients; hence, the SERCA pump and RyR2 are both attractive potential targets for future therapies.

A Matched-Filter-Based Algorithm for Subcellular Classification of T-System in Cardiac Tissues

In mammalian ventricular cardiomyocytes, invaginations of the surface membrane form the transverse tubular system (T-system), which consists of transverse tubules (TTs) that align with sarcomeres and Z-lines as well as longitudinal tubules (LTs) that are present between Z-lines in some species. In many cardiac disease etiologies, the T-system is perturbed, which is believed to promote spatially heterogeneous, dyssynchronous Ca2+ release and inefficient contraction. In general, T-system characterization approaches have been directed primarily at isolated cells and do not detect subcellular T-system heterogeneity. Here, we present MatchedMyo, a matched-filter-based algorithm for subcellular T-system characterization in isolated cardiomyocytes and millimeter-scale myocardial sections. The algorithm utilizes "filters" representative of TTs, LTs, and T-system absence. Application of the algorithm to cardiomyocytes isolated from rat disease models of myocardial infarction (MI), dilated cardiomyopathy induced via aortic banding, and sham surgery confirmed and quantified heterogeneous T-system structure and remodeling. Cardiomyocytes from post-MI hearts exhibited increasing T-system disarray as proximity to the infarct increased. We found significant (p < 0.05, Welch's t-test) increases in LT density within cardiomyocytes proximal to the infarct (12 ± 3%, data reported as mean ± SD, n = 3) versus sham (4 ± 2%, n = 5), but not distal to the infarct (7 ± 1%, n = 3). The algorithm also detected decreases in TTs within 5° of the myocyte minor axis for isolated aortic banding (36 ± 9%, n = 3) and MI cardiomyocytes located intermediate (37 ± 4%, n = 3) and proximal (34 ± 4%, n = 3) to the infarct versus sham (57 ± 12%, n = 5). Application of bootstrapping to rabbit MI tissue revealed distal sections comprised 18.9 ± 1.0% TTs, whereas proximal sections comprised 10.1 ± 0.8% TTs (p < 0.05), a 46.6% decrease. The matched-filter approach therefore provides a robust and scalable technique for T-system characterization from isolated cells through millimeter-scale myocardial sections.

Simulation of P2X-mediated calcium signalling in microglia

KEY POINTS

A computational model of P2X channel activation in microglia was developed that includes downfield Ca²⁺ -dependent signalling pathways. This model provides quantitative insights into how diverse signalling pathways in microglia converge to control microglial function.

ABSTRACT

Microglia function is orchestrated through highly coupled signalling pathways that depend on calcium (Ca²⁺ ). In response to extracellular ATP, transient increases in intracellular Ca²⁺ driven through the activation of purinergic receptors, P2X and P2Y, are sufficient to promote cytokine synthesis. Although the steps comprising the pathways bridging purinergic receptor activation with transcriptional responses have been probed in great detail, a quantitative model for how these steps collectively control cytokine production has not been established. Here we developed a minimal computational model that quantitatively links extracellular stimulation of two prominent ionotropic purinergic receptors, P2X4 and P2X7, with the graded production of a gene product, namely the tumour necrosis factor α (TNFα) cytokine. In addition to Ca²⁺ handling mechanisms common to eukaryotic cells, our model includes microglia-specific processes including ATP-dependent P2X4 and P2X7 activation, activation of nuclear factor of activated T-cells (NFAT) transcription factors, and TNFα production. Parameters for this model were optimized to reproduce published data for these processes, where available. With this model, we determined the propensity for TNFα production in microglia, subject to a wide range of ATP exposure amplitudes, frequencies and durations that the cells could encounter in vivo. Furthermore, we have investigated the extent to which modulation of the signal transduction pathways influence TNFα production. Our results suggest that pulsatile stimulation of P2X4 via micromolar ATP may be sufficient to promote TNFα production, whereas high-amplitude ATP exposure is necessary for production via P2X7. Furthermore, under conditions that increase P2X4 expression, for instance, following activation by pathogen-associated molecular factors, P2X4-associated TNFα production is greatly enhanced. Given that Ca²⁺ homeostasis in microglia is profoundly important to its function, this computational model provides a quantitative framework to explore hypotheses pertaining to microglial physiology.

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).

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.

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.

Computational modeling of amylin-induced calcium dysregulation in rat ventricular cardiomyocytes

Hyperamylinemia is a condition that accompanies obesity and precedes type II diabetes, and it is characterized by above-normal blood levels of amylin, the pancreas-derived peptide. Human amylin oligomerizes easily and can deposit in the pancreas [1], brain [2], and heart [3], where they have been associated with calcium dysregulation. In the heart, accumulating evidence suggests that human amylin oligomers form moderately cation-selective [4,5] channels that embed in the cell sarcolemma (SL). The oligomers increase membrane conductance in a concentration-dependent manner [5], which is correlated with elevated cytosolic Ca²⁺. These findings motivate our core hypothesis that non-selective inward Ca²⁺ conduction afforded by human amylin oligomers increase cytosolic and sarcoplasmic reticulum (SR) Ca²⁺ load, which thereby magnifies intracellular Ca²⁺ transients. Questions remain however regarding the mechanism of amylin-induced Ca²⁺ dysregulation, including whether enhanced SL Ca²⁺ influx is sufficient to elevate cytosolic Ca²⁺ load [6], and if so, how might amplified Ca²⁺ transients perturb Ca²⁺-dependent cardiac pathways. To investigate these questions, we modified a computational model of cardiomyocytes Ca²⁺ signaling to reflect experimentally-measured changes in SL membrane permeation and decreased sarcoplasmic/endoplasmic reticulum calcium ATPase (SERCA) function stemming from acute and transgenic human amylin peptide exposure. With this model, we confirmed the hypothesis that increasing SL permeation alone was sufficient to enhance Ca²⁺ transient amplitudes. Our model indicated that amplified cytosolic transients are driven by increased Ca²⁺ loading of the SR and that greater fractional release may contribute to the Ca²⁺-dependent activation of calmodulin, which could prime the activation of myocyte remodeling pathways. Importantly, elevated Ca²⁺ in the SR and dyadic space collectively drive greater fractional SR Ca²⁺ release for human amylin expressing rats (HIP) and acute amylin-exposed rats (+Amylin) mice, which contributes to the inotropic rise in cytosolic Ca²⁺ transients. These findings suggest that increased membrane permeation induced by oligomeratization of amylin peptide in cell sarcolemma contributes to Ca²⁺ dysregulation in pre-diabetes.

Enzyme localization, crowding, and buffers collectively modulate diffusion-influenced signal transduction: Insights from continuum diffusion modeling

Biochemical reaction networks consisting of coupled enzymes connect substrate signaling events with biological function. Substrates involved in these reactions can be strongly influenced by diffusion "barriers" arising from impenetrable cellular structures and macromolecules, as well as interactions with biomolecules, especially within crowded environments. For diffusion-influenced reactions, the spatial organization of diffusion barriers arising from intracellular structures, non-specific crowders, and specific-binders (buffers) strongly controls the temporal and spatial reaction kinetics. In this study, we use two prototypical biochemical reactions, a Goodwin oscillator, and a reaction with a periodic source/sink term to examine how a diffusion barrier that partitions substrates controls reaction behavior. Namely, we examine how conditions representative of a densely packed cytosol, including reduced accessible volume fraction, non-specific interactions, and buffers, impede diffusion over nanometer length-scales. We find that diffusion barriers can modulate the frequencies and amplitudes of coupled diffusion-influenced reaction networks, as well as give rise to "compartments" of decoupled reactant populations. These effects appear to be intensified in the presence of buffers localized to the diffusion barrier. These findings have strong implications for the role of the cellular environment in tuning the dynamics of signaling pathways.

Superresolution modeling of calcium release in the heart

Stable calcium-induced calcium release (CICR) is critical for maintaining normal cellular contraction during cardiac excitation-contraction coupling. The fundamental element of CICR in the heart is the calcium (Ca²⁺) spark, which arises from a cluster of ryanodine receptors (RyR). Opening of these RyR clusters is triggered to produce a local, regenerative release of Ca²⁺ from the sarcoplasmic reticulum (SR). The Ca²⁺ leak out of the SR is an important process for cellular Ca²⁺ management, and it is critically influenced by spark fidelity, i.e., the probability that a spontaneous RyR opening triggers a Ca²⁺ spark. Here, we present a detailed, three-dimensional model of a cardiac Ca²⁺ release unit that incorporates diffusion, intracellular buffering systems, and stochastically gated ion channels. The model exhibits realistic Ca²⁺ sparks and robust Ca²⁺ spark termination across a wide range of geometries and conditions. Furthermore, the model captures the details of Ca²⁺ spark and nonspark-based SR Ca²⁺ leak, and it produces normal excitation-contraction coupling gain. We show that SR luminal Ca²⁺-dependent regulation of the RyR is not critical for spark termination, but it can explain the exponential rise in the SR Ca²⁺ leak-load relationship demonstrated in previous experimental work. Perturbations to subspace dimensions, which have been observed in experimental models of disease, strongly alter Ca²⁺ spark dynamics. In addition, we find that the structure of RyR clusters also influences Ca²⁺ release properties due to variations in inter-RyR coupling via local subspace Ca²⁺ concentration ([Ca²⁺]_ss). These results are illustrated for RyR clusters based on super-resolution stimulated emission depletion microscopy. Finally, we present a believed-novel approach by which the spark fidelity of a RyR cluster can be predicted from structural information of the cluster using the maximum eigenvalue of its adjacency matrix. These results provide critical insights into CICR dynamics in heart, under normal and pathological conditions.

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.

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

Spatio-temporal dynamics of intracellular calcium, [Ca²⁺]_i, regulate the contractile function of cardiac muscle cells. Measuring [Ca²⁺]_i flux is central to the study of mechanisms that underlie both normal cardiac function and calcium-dependent etiologies in heart disease. However, current imaging techniques are limited in the spatial resolution to which changes in [Ca²⁺]_i can be detected. Using spatial point process statistics techniques we developed a novel method to simulate the spatial distribution of RyR clusters, which act as the major mediators of contractile Ca²⁺ release, upon a physiologically-realistic cellular landscape composed of tightly-packed mitochondria and myofibrils. We applied this method to computationally combine confocal-scale (~ 200 nm) data of RyR clusters with 3D electron microscopy data (~ 30 nm) of myofibrils and mitochondria, both collected from adult rat left ventricular myocytes. Using this hybrid-scale spatial model, we simulated reaction-diffusion of [Ca²⁺]_i during the rising phase of the transient (first 30 ms after initiation). At 30 ms, the average peak of the simulated [Ca²⁺]_i transient and of the simulated fluorescence intensity signal, F/F₀, reached values similar to that found in the literature ([Ca²⁺]_i ≈1 μM; F/F₀≈5.5). However, our model predicted the variation in [Ca²⁺]_i to be between 0.3 and 12.7 μM (~3 to 100 fold from resting value of 0.1 μM) and the corresponding F/F₀ signal ranging from 3 to 9.5. We demonstrate in this study that: (i) heterogeneities in the [Ca²⁺]_i transient are due not only to heterogeneous distribution and clustering of mitochondria; (ii) but also to heterogeneous local densities of RyR clusters. Further, we show that: (iii) these structure-induced heterogeneities in [Ca²⁺]_i can appear in line scan data. Finally, using our unique method for generating RyR cluster distributions, we demonstrate the robustness in the [Ca²⁺]_i transient to differences in RyR cluster distributions measured between rat and human cardiomyocytes.

Calcium (Ca²⁺) acts as a signal for many functions in the heart cell, from its primary role in triggering contractions during the heartbeat to acting as a signal for cell growth. Cellular function is tightly coupled to its ultra-structural organization. Spatially-realistic and biophysics-based computational models can provide quantitative insights into structure-function relationships in Ca²⁺ signaling. We developed a novel computational model of a rat ventricular myocyte that integrates structural information from confocal and electron microscopy datasets that were independently acquired and includes: myofibrils (protein complexes that contract during the heartbeat), mitochondria (organelles that provide energy for contraction), and ryanodine receptors (RyR, ion channels that release the Ca²⁺ required to trigger myofibril contraction from intracellular stores). Using this model, we examined [Ca²⁺]_i dynamics throughout the cell cross-section at a much higher resolution than previously possible. We estimated the size of structural maladaptation that would cause disease-related alterations in [Ca²⁺]_i dynamics. Using our methods for data integration, we also tested whether reducing the density of RyRs in human cardiomyocytes (~40% relative to rat) would have a significant effect on [Ca²⁺]_i. We found that Ca²⁺ release patterns between the two species are similar, suggesting Ca²⁺ dynamics are robust to variations in cell ultrastructure.

Revealing T-Tubules in Striated Muscle with New Optical Super-Resolution Microscopy Techniquess

The t-tubular system plays a central role in the synchronisation of calcium signalling and excitation-contraction coupling in most striated muscle cells. Light microscopy has been used for imaging t-tubules for well over 100 years and together with electron microscopy (EM), has revealed the three-dimensional complexities of the t-system topology within cardiomyocytes and skeletal muscle fibres from a range of species. The emerging super-resolution single molecule localisation microscopy (SMLM) techniques are offering a near 10-fold improvement over the resolution of conventional fluorescence light microscopy methods, with the ability to spectrally resolve nanometre scale distributions of multiple molecular targets. In conjunction with the next generation of electron microscopy, SMLM has allowed the visualisation and quantification of intricate t-tubule morphologies within large areas of muscle cells at an unprecedented level of detail. In this paper, we review recent advancements in the t-tubule structural biology with the utility of various microscopy techniques. We outline the technical considerations in adapting SMLM to study t-tubules and its potential to further our understanding of the molecular processes that underlie the sub-micron scale structural alterations observed in a range of muscle pathologies.

Animal model of reversible, right ventricular failure

BACKGROUND

Heart failure is a leading cause of death but very little is known about right ventricular (RV) failure (RVF) and right ventricular recovery (RVR). A robust animal model of reversible, RVF does not exist, which currently limits research opportunities and clinical progress. We sought to develop an animal model of reversible, pressure-overload RVF to study RVF and RVR.

MATERIALS AND METHODS

Fifteen New Zealand rabbits underwent implantation of a fully implantable, adjustable, pulmonary artery band. Animals were assigned to the control, RVF, and RVR groups (n = 5 for each). For the RVF and RVR groups, the pulmonary artery bands were serially tightened to create RVF and released for RVR. Echocardiographic, cardiac magnetic resonance imaging, and histologic analysis were performed.

RESULTS

RV chamber size and wall thickness increased during RVF and regressed during RVR. RV volumes were 1023 μL ± 123 for control, 2381 μL ± 637 for RVF, and 635 μL ± 549 for RVR, and RV wall thicknesses were 0.98 mm ± 0.12 for controls (P = 0.05), 1.72 mm ± 0.60 for RVF, and 1.16 mm ± 0.03 for RVR animals (P = 0.04), respectively. Similarly, heart weight, liver weight, cardiomyocyte size, and the degree of cardiac and hepatic fibrosis increased with RVF and decreased during RVR.

CONCLUSIONS

We report an animal model of chronic, reversible, pressure-overload RVF to study RVF and RVR. This model will be used for preclinical studies that improve our understanding of the mechanisms of RVF and that develop and test RV protective and RVR strategies to be studied later in humans.

Molecular and subcellular-scale modeling of nucleotide diffusion in the cardiac myofilament lattice

Contractile function of cardiac cells is driven by the sliding displacement of myofilaments powered by the cycling myosin crossbridges. Critical to this process is the availability of ATP, which myosin hydrolyzes during the cross-bridge cycle. The diffusion of adenine nucleotides through the myofilament lattice has been shown to be anisotropic, with slower radial diffusion perpendicular to the filament axis relative to parallel, and is attributed to the periodic hexagonal arrangement of the thin (actin) and thick (myosin) filaments. We investigated whether atomistic-resolution details of myofilament proteins can refine coarse-grain estimates of diffusional anisotropy for adenine nucleotides in the cardiac myofibril, using homogenization theory and atomistic thin filament models from the Protein Data Bank. Our results demonstrate considerable anisotropy in ATP and ADP diffusion constants that is consistent with experimental measurements and dependent on lattice spacing and myofilament overlap. A reaction-diffusion model of the half-sarcomere further suggests that diffusional anisotropy may lead to modest adenine nucleotide gradients in the myoplasm under physiological conditions.

Computational modeling of subcellular transport and signaling

Numerous signaling processes in the cell are controlled in microdomains that are defined by cellular structures ranging from nm to μm in size. Recent improvements in microscopy enable the resolution and reconstruction of these micro domains, while new computational methods provide the means to elucidate their functional roles. Collectively these tools allow for a biophysical understanding of the cellular environment and its pathological progression in disease. Here we review recent advancements in microscopy, and subcellular modeling on the basis of reconstructed geometries, with a special focus on signaling microdomains that are important for the excitation contraction coupling in cardiac myocytes.

Sensitivity of rabbit ventricular action potential and Ca²⁺ dynamics to small variations in membrane currents and ion diffusion coefficients

Little is known about how small variations in ionic currents and Ca²⁺ and Na⁺ diffusion coefficients impact action potential and Ca²⁺ dynamics in rabbit ventricular myocytes. We applied sensitivity analysis to quantify the sensitivity of Shannon et al. model (Biophys. J., 2004) to 5%-10% changes in currents conductance, channels distribution, and ion diffusion in rabbit ventricular cells. We found that action potential duration and Ca²⁺ peaks are highly sensitive to 10% increase in L-type Ca²⁺ current; moderately influenced by 10% increase in Na⁺-Ca²⁺ exchanger, Na⁺-K⁺ pump, rapid delayed and slow transient outward K⁺ currents, and Cl⁻ background current; insensitive to 10% increases in all other ionic currents and sarcoplasmic reticulum Ca²⁺ fluxes. Cell electrical activity is strongly affected by 5% shift of L-type Ca²⁺ channels and Na⁺-Ca²⁺ exchanger in between junctional and submembrane spaces while Ca²⁺-activated Cl⁻-channel redistribution has the modest effect. Small changes in submembrane and cytosolic diffusion coefficients for Ca²⁺, but not in Na⁺ transfer, may alter notably myocyte contraction. Our studies highlight the need for more precise measurements and further extending and testing of the Shannon et al. model. Our results demonstrate usefulness of sensitivity analysis to identify specific knowledge gaps and controversies related to ventricular cell electrophysiology and Ca²⁺ signaling.

Alterations in T-tubule and dyad structure in heart disease: challenges and opportunities for computational analyses

Compelling recent experimental results make clear that sub-cellular structures are altered in ventricular myocytes during the development of heart failure, in both human samples and diverse experimental models. These alterations can include, but are not limited to, changes in the clusters of sarcoplasmic reticulum (SR) Ca(2+)-release channels, ryanodine receptors, and changes in the average distance between the cell membrane and ryanodine receptor clusters. In this review, we discuss the potential consequences of these structural alterations on the triggering of SR Ca(2+) release during excitation-contraction coupling. In particular, we describe how mathematical models of local SR Ca(2+) release can be used to predict functional changes resulting from diverse modifications that occur in disease states. We review recent studies that have used simulations to understand the consequences of sub-cellular structural changes, and we discuss modifications that will allow for future modelling studies to address unresolved questions. We conclude with a discussion of improvements in both experimental and mathematical modelling techniques that will be required to provide a stronger quantitative understanding of the functional consequences of changes in sub-cellular structure in heart disease.

Finite Element Estimation of Protein-Ligand Association Rates with Post-Encounter Effects: Applications to Calcium binding in Troponin C and SERCA

We introduce a computational pipeline and suite of software tools for the approximation of diffusion-limited binding based on a recently developed theoretical framework. Our approach handles molecular geometries generated from high-resolution structural data and can account for active sites buried within the protein or behind gating mechanisms. Using tools from the FEniCS library and the APBS solver, we implement a numerical code for our method and study two Ca(2+)-binding proteins: Troponin C and the Sarcoplasmic Reticulum Ca(2+) ATPase (SERCA). We find that a combination of diffusional encounter and internal 'buried channel' descriptions provide superior descriptions of association rates, improving estimates by orders of magnitude.