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Aims: In atrial fibrillation (AF), abnormalities in Ca(2+) release contribute to arrhythmia generation and contractile dysfunction. We explore whether ryanodine receptor (RyR) cluster ultrastructure is altered and is associated with functional abnormalities in AF., Methods and Results: Using high-resolution confocal microscopy (STED), we examined RyR cluster morphology in fixed atrial myocytes from sheep with persistent AF (N = 6) and control (Ctrl; N = 6) animals. RyR clusters on average contained 15 contiguous RyRs; this did not differ between AF and Ctrl. However, the distance between clusters was significantly reduced in AF (288 ± 12 vs. 376 ± 17 nm). When RyR clusters were grouped into Ca(2+) release units (CRUs), i.e. clusters separated by <150 nm, CRUs in AF had more clusters (3.43 ± 0.10 vs. 2.95 ± 0.02 in Ctrl), which were more dispersed. Furthermore, in AF cells, more RyR clusters were found between Z lines. In parallel experiments, Ca(2+) sparks were monitored in live permeabilized myocytes. In AF, myocytes had >50% higher spark frequency with increased spark time to peak (TTP) and duration, and a higher incidence of macrosparks. A computational model of the CRU was used to simulate the morphological alterations observed in AF cells. Increasing cluster fragmentation to the level observed in AF cells caused the observed changes, i.e. higher spark frequency, increased TTP and duration; RyR clusters dispersed between Z-lines increased the occurrence of macrosparks., Conclusion: In persistent AF, ultrastructural reorganization of RyR clusters within CRUs is associated with overactive Ca(2+) release, increasing the likelihood of propagating Ca(2+) release., (© The Author 2015. Published by Oxford University Press on behalf of the European Society of Cardiology.)

Stretching single ventricular cardiac myocytes has been shown experimentally to activate transmembrane nicotinamide adenine dinucleotide phosphate oxidase type 2 to produce reactive oxygen species (ROS) and increase the Ca2+ spark rate in a process called X-ROS signaling. The increase in Ca2+ spark rate is thought to be due to an increase in ryanodine receptor type 2 (RyR2) open probability by direct oxidation of the RyR2 protein complex. In this article, a computational model is used to examine the regulation of ROS and calcium homeostasis by local, subcellular X-ROS signaling and its role in cardiac excitation-contraction coupling. To this end, a four-state RyR2 model was developed that includes an X-ROS-dependent RyR2 mode switch. When activated, [Ca2+]i-sensitive RyR2 open probability increases, and the Ca2+ spark rate changes in a manner consistent with experimental observations. This, to our knowledge, new model is used to study the transient effects of diastolic stretching and subsequent ROS production on RyR2 open probability, Ca2+ sparks, and the myoplasmic calcium concentration ([Ca2+]i) during excitation-contraction coupling. The model yields several predictions: 1) [ROS] is produced locally near the RyR2 complex during X-ROS signaling and increases by an order of magnitude more than the global ROS signal during myocyte stretching; 2) X-ROS activation just before the action potential, corresponding to ventricular filling during diastole, increases the magnitude of the Ca2+ transient; 3) during prolonged stretching, the X-ROS-induced increase in Ca2+ spark rate is transient, so that long-sustained stretching does not significantly increase sarcoplasmic reticulum Ca2+ leak; and 4) when the chemical reducing capacity of the cell is decreased, activation of X-ROS signaling increases sarcoplasmic reticulum Ca2+ leak and contributes to global oxidative stress, thereby increases the possibility of arrhythmia. The model provides quantitative information not currently obtainable through experimental means and thus provides a framework for future X-ROS signaling experiments., (Copyright © 2015 Biophysical Society. Published by Elsevier Inc. All rights reserved.)

Rationale: Transverse tubules (TTs) couple electric surface signals to remote intracellular Ca(2+) release units (CRUs). Diffraction-limited imaging studies have proposed loss of TT components as disease mechanism in heart failure (HF)., Objectives: Objectives were to develop quantitative super-resolution strategies for live-cell imaging of TT membranes in intact cardiomyocytes and to show that TT structures are progressively remodeled during HF development, causing early CRU dysfunction., Methods and Results: Using stimulated emission depletion (STED) microscopy, we characterized individual TTs with nanometric resolution as direct readout of local membrane morphology 4 and 8 weeks after myocardial infarction (4pMI and 8pMI). Both individual and network TT properties were investigated by quantitative image analysis. The mean area of TT cross sections increased progressively from 4pMI to 8pMI. Unexpectedly, intact TT networks showed differential changes. Longitudinal and oblique TTs were significantly increased at 4pMI, whereas transversal components appeared decreased. Expression of TT-associated proteins junctophilin-2 and caveolin-3 was significantly changed, correlating with network component remodeling. Computational modeling of spatial changes in HF through heterogeneous TT reorganization and RyR2 orphaning (5000 of 20 000 CRUs) uncovered a local mechanism of delayed subcellular Ca(2+) release and action potential prolongation., Conclusions: This study introduces STED nanoscopy for live mapping of TT membrane structures. During early HF development, the local TT morphology and associated proteins were significantly altered, leading to differential network remodeling and Ca(2+) release dyssynchrony. Our data suggest that TT remodeling during HF development involves proliferative membrane changes, early excitation-contraction uncoupling, and network fracturing.

Excitation-contraction coupling describes the processes relating to electrical excitation through force generation and contraction in the heart. It occurs at multiple levels from the whole heart, to single myocytes and down to the sarcomere. A central process that links electrical excitation to contraction is calcium mobilization. Computational models that are well grounded in experimental data have been an effective tool to understand the complex dynamics of the processes involved in excitation-contraction coupling. Presented here is a summary of some computational models that have added to the understanding of the cellular and subcellular mechanisms that control ventricular myocyte calcium dynamics. Models of cardiac ventricular myocytes that have given insight into termination of calcium release and interval-force relations are discussed in this manuscript. Computational modeling of calcium sparks, the elementary events in cardiac excitation-contraction coupling, has given insight into mechanism governing their dynamics and termination as well as their role in excitation-contraction coupling and is described herein.

We present what we believe to be a new mathematical model of Ca(2+) leak from the sarcoplasmic reticulum (SR) in the heart. To our knowledge, it is the first to incorporate a realistic number of Ca(2+)-release units, each containing a cluster of stochastically gating Ca(2+) channels (RyRs), whose biophysical properties (e.g., Ca(2+) sensitivity and allosteric interactions) are informed by the latest molecular investigations. This realistic model allows for the detailed characterization of RyR Ca(2+)-release properties, and shows how this balances reuptake by the SR Ca(2+) pump. Simulations reveal that SR Ca(2+) leak consists of brief but frequent single RyR openings (~3000 cell(-1) s(-1)) that are likely to be experimentally undetectable, and are, therefore, "invisible". We also observe that these single RyR openings can recruit additional RyRs to open, due to elevated local (Ca(2+)), and occasionally lead to the generation of Ca(2+) sparks (~130 cell(-1) s(-1)). Furthermore, this physiological formulation of "invisible" leak allows for the removal of the ad hoc, non-RyR mediated Ca(2+) leak terms present in prior models. Finally, our model shows how Ca(2+) sparks can be robustly triggered and terminated under both normal and pathological conditions. Together, these discoveries profoundly influence how we interpret and understand diverse experimental and clinical results from both normal and diseased hearts., (Copyright © 2011 Biophysical Society. Published by Elsevier Inc. All rights reserved.)

Mathematical and computational modeling of cardiac excitation-contraction coupling has produced considerable insights into how the heart muscle contracts. With the increase in biophysical and physiological data available, the modeling has become more sophisticated with investigations spanning in scale from molecular components to whole cells. These modeling efforts have provided insight into cardiac excitation-contraction coupling that advanced and complemented experimental studies. One goal is to extend these detailed cellular models to model the whole heart. While this has been done with mechanical and electrophysiological models, the complexity and fast time course of calcium dynamics have made inclusion of detailed calcium dynamics in whole heart models impractical. Novel methods such as the probability density approach and moment closure technique which increase computational efficiency might make this tractable., ((c) 2010 Elsevier Inc. All rights reserved.)

Of the many ongoing controversies regarding the workings of the sarcoplasmic reticulum (SR) in cardiac myocytes, two unresolved and interconnected topics are 1), mechanisms of calcium (Ca(2+)) wave propagation, and 2), speed of Ca(2+) diffusion within the SR. Ca(2+) waves are initiated when a spontaneous local SR Ca(2+) release event triggers additional release from neighboring clusters of SR release channels (ryanodine receptors (RyRs)). A lack of consensus regarding the effective Ca(2+) diffusion constant in the SR (D(Ca,SR)) severely complicates our understanding of whether dynamic local changes in SR [Ca(2+)] can influence wave propagation. To address this problem, we have implemented a computational model of cytosolic and SR [Ca(2+)] during Ca(2+) waves. Simulations have investigated how dynamic local changes in SR [Ca(2+)] are influenced by 1), D(Ca,SR); 2), the distance between RyR clusters; 3), partial inhibition or stimulation of SR Ca(2+) pumps; 4), SR Ca(2+) pump dependence on cytosolic [Ca(2+)]; and 5), the rate of transfer between network and junctional SR. Of these factors, D(Ca,SR) is the primary determinant of how release from one RyR cluster alters SR [Ca(2+)] in nearby regions. Specifically, our results show that local increases in SR [Ca(2+)] ahead of the wave can potentially facilitate Ca(2+) wave propagation, but only if SR diffusion is relatively slow. These simulations help to delineate what changes in [Ca(2+)] are possible during SR Ca(2+)release, and they broaden our understanding of the regulatory role played by dynamic changes in [Ca(2+)](SR)., (Copyright (c) 2010 Biophysical Society. Published by Elsevier Inc. All rights reserved.)

In prior work, we introduced a probability density approach to modeling local control of Ca2+-induced Ca2+ release in cardiac myocytes, where we derived coupled advection-reaction equations for the time-dependent bivariate probability density of subsarcolemmal subspace and junctional sarcoplasmic reticulum (SR) [Ca2+] conditioned on Ca2+ release unit (CaRU) state. When coupled to ordinary differential equations (ODEs) for the bulk myoplasmic and network SR [Ca2+], a realistic but minimal model of cardiac excitation-contraction coupling was produced that avoids the computationally demanding task of resolving spatial aspects of global Ca2+ signaling, while accurately representing heterogeneous local Ca2+ signals in a population of diadic subspaces and junctional SR depletion domains. Here we introduce a computationally efficient method for simulating such whole cell models when the dynamics of subspace [Ca2+] are much faster than those of junctional SR [Ca2+]. The method begins with the derivation of a system of ODEs describing the time-evolution of the moments of the univariate probability density functions for junctional SR [Ca2+] jointly distributed with CaRU state. This open system of ODEs is then closed using an algebraic relationship that expresses the third moment of junctional SR [Ca2+] in terms of the first and second moments. In simulated voltage-clamp protocols using 12-state CaRUs that respond to the dynamics of both subspace and junctional SR [Ca2+], this moment-closure approach to simulating local control of excitation-contraction coupling produces high-gain Ca2+ release that is graded with changes in membrane potential, a phenomenon not exhibited by common pool models. Benchmark simulations indicate that the moment-closure approach is nearly 10,000-times more computationally efficient than corresponding Monte Carlo simulations while leading to nearly identical results. We conclude by applying the moment-closure approach to study the restitution of Ca2+-induced Ca2+ release during simulated two-pulse voltage-clamp protocols.

We present a probability density approach to modeling localized Ca2+ influx via L-type Ca2+ channels and Ca2+-induced Ca2+ release mediated by clusters of ryanodine receptors during excitation-contraction coupling in cardiac myocytes. Coupled advection-reaction equations are derived relating the time-dependent probability density of subsarcolemmal subspace and junctional sarcoplasmic reticulum [Ca2+] conditioned on "Ca2+ release unit" state. When these equations are solved numerically using a high-resolution finite difference scheme and the resulting probability densities are coupled to ordinary differential equations for the bulk myoplasmic and sarcoplasmic reticulum [Ca2+], a realistic but minimal model of cardiac excitation-contraction coupling is produced. Modeling Ca2+ release unit activity using this probability density approach avoids the computationally demanding task of resolving spatial aspects of global Ca2+ signaling, while accurately representing heterogeneous local Ca2+ signals in a population of diadic subspaces and junctional sarcoplasmic reticulum depletion domains. The probability density approach is validated for a physiologically realistic number of Ca2+ release units and benchmarked for computational efficiency by comparison to traditional Monte Carlo simulations. In simulated voltage-clamp protocols, both the probability density and Monte Carlo approaches to modeling local control of excitation-contraction coupling produce high-gain Ca2+ release that is graded with changes in membrane potential, a phenomenon not exhibited by so-called "common pool" models. However, a probability density calculation can be significantly faster than the corresponding Monte Carlo simulation, especially when cellular parameters are such that diadic subspace [Ca2+] is in quasistatic equilibrium with junctional sarcoplasmic reticulum [Ca2+] and, consequently, univariate rather than multivariate probability densities may be employed.

Oscillations in energy metabolism have been observed in a variety of cells under metabolically deprived conditions such as ischemia. In cardiac ventricular myocytes these metabolic oscillations may cause oscillations in the action potential duration, creating the potential for cardiac arrhythmias during ischemia (O'Rourke, 2000). A mathematical model of the mechanism behind metabolic oscillations is developed here. The model consists of descriptions of the mitochondrial components that regulate mitochondrial membrane potential (Psi), mitochondrial inorganic phosphate concentration, mitochondrial magnesium concentration, and cellular NADH and NAD(+) concentrations. Using parameters from the experimental literature, the model produces physiological values for these both under normoxic (steady state) and ischemic (oscillatory) conditions. The model includes the mitochondrial inner membrane anion channel (IMAC), the centum picosiemen channel (mCS), the phosphate carrier (PIC), and the respiration driven proton pumps. The model suggests that these are the essential components for producing oscillations with mCS essential for the rapid depolarization, PIC for the recovery from depolarization, and IMAC for the slow depolarization between depolarization peaks. A decrease of the inner membrane potential due to ischemia or experimental conditions seems to be a triggering factor for the oscillations. The model simulates the experimental observations that high levels of mitochondrial ADP and ATP abolish the oscillations, as does inhibition of electron transport. The model makes predictions on the influence of pH and magnesium levels on metabolic oscillations.

A computational model of energy metabolism in the mammalian ventricular myocyte is developed to study the effect of cytosolic calcium (Ca(2+)) transients on adenosine triphosphate (ATP) production. The model couples the Jafri-Dudycha model for tricarboxylic acid cycle regulation to a modified version of the Magnus-Keizer model for the mitochondria. The fluxes associated with Ca(2+) uptake and efflux (i.e., the Ca(2+) uniporter and Na(+)-Ca(2+) exchanger) and the F(1)F(0)-ATPase were modified to better model heart mitochondria. Simulations were performed at steady state and with Ca(2+) transients at various pacing frequencies generated by the Rice-Jafri-Winslow model for the guinea pig ventricular myocyte. The effects of the Ca(2+) transients for mitochondria both adjacent to the dyadic space and in the bulk myoplasm were studied. The model shows that Ca(2+) activation of both the tricarboxylic acid cycle and the F(1)F(0)-ATPase are necessary to produce increases in ATP production. The model also shows that in mitochondria located near the subspace, the large Ca(2+) transients can depolarize the mitochondrial membrane potential sufficiently to cause a transient decline in ATP production. However, this transient is of short duration, minimizing its impact on overall ATP production.

The elementary event of Ca(2+) release in heart is the Ca(2+) spark. It occurs at a low rate during diastole, activated only by the low cytosolic [Ca(2+)](i). Synchronized activation of many sparks is due to the high local [Ca(2+)](i) in the region surrounding the sarcoplasmic reticulum (SR) Ca(2+) release channels and is responsible for the systolic [Ca(2+)](i) transient. The biophysical basis of this calcium signaling is discussed. Attention is placed on the local organization of the ryanodine receptors (SR Ca(2+) release channels, RyRs) and the other proteins that underlie and modulate excitation-contraction (EC) coupling. A brief review of specific elements that regulate SR Ca(2+) release (including SR lumenal Ca(2+) and coupled gating of RyRs) is presented. Finally integrative calcium signaling in heart is presented in the context of normal heart function and heart failure.