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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.)

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 (Ca(2+)) spark, which arises from a cluster of ryanodine receptors (RyR). Opening of these RyR clusters is triggered to produce a local, regenerative release of Ca(2+) from the sarcoplasmic reticulum (SR). The Ca(2+) leak out of the SR is an important process for cellular Ca(2+) management, and it is critically influenced by spark fidelity, i.e., the probability that a spontaneous RyR opening triggers a Ca(2+) spark. Here, we present a detailed, three-dimensional model of a cardiac Ca(2+) release unit that incorporates diffusion, intracellular buffering systems, and stochastically gated ion channels. The model exhibits realistic Ca(2+) sparks and robust Ca(2+) spark termination across a wide range of geometries and conditions. Furthermore, the model captures the details of Ca(2+) spark and nonspark-based SR Ca(2+) leak, and it produces normal excitation-contraction coupling gain. We show that SR luminal Ca(2+)-dependent regulation of the RyR is not critical for spark termination, but it can explain the exponential rise in the SR Ca(2+) leak-load relationship demonstrated in previous experimental work. Perturbations to subspace dimensions, which have been observed in experimental models of disease, strongly alter Ca(2+) spark dynamics. In addition, we find that the structure of RyR clusters also influences Ca(2+) release properties due to variations in inter-RyR coupling via local subspace Ca(2+) concentration ([Ca(2+)]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., (Copyright © 2014 The Authors. Published by Elsevier Inc. All rights reserved.)

Existing theory suggests that mitochondria act as significant, dynamic buffers of cytosolic calcium ([Ca(2+)]i) in heart. These buffers can remove up to one-third of the Ca(2+) that enters the cytosol during the [Ca(2+)]i transients that underlie contractions. However, few quantitative experiments have been presented to test this hypothesis. Here, we investigate the influence of Ca(2+) movement across the inner mitochondrial membrane during both subcellular and global cellular cytosolic Ca(2+) signals (i.e., Ca(2+) sparks and [Ca(2+)]i transients, respectively) in isolated rat cardiomyocytes. By rapidly turning off the mitochondria using depolarization of the inner mitochondrial membrane potential (ΔΨm), the role of the mitochondria in buffering cytosolic Ca(2+) signals was investigated. We show here that rapid loss of ΔΨm leads to no significant changes in cytosolic Ca(2+) signals. Second, we make direct measurements of mitochondrial [Ca(2+)] ([Ca(2+)]m) using a mitochondrially targeted Ca(2+) probe (MityCam) and these data suggest that [Ca(2+)]m is near the [Ca(2+)]i level (∼100 nM) under quiescent conditions. These two findings indicate that although the mitochondrial matrix is fully buffer-capable under quiescent conditions, it does not function as a significant dynamic buffer during physiological Ca(2+) signaling. Finally, quantitative analysis using a computational model of mitochondrial Ca(2+) cycling suggests that mitochondrial Ca(2+) uptake would need to be at least ∼100-fold greater than the current estimates of Ca(2+) influx for mitochondria to influence measurably cytosolic [Ca(2+)] signals under physiological conditions. Combined, these experiments and computational investigations show that mitochondrial Ca(2+) uptake does not significantly alter cytosolic Ca(2+) signals under normal conditions and indicates that mitochondria do not act as important dynamic buffers of [Ca(2+)]i under physiological conditions in heart., (Copyright © 2014 Biophysical Society. Published by Elsevier Inc. All rights reserved.)

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.)

Skeletal muscle stores Ca²(+) in the sarcoplasmic reticulum (SR) and releases it to initiate contraction, but the concentration of luminal Ca²(+) in the SR ([Ca²(+)](SR)) and the amount that is released by physiological or pharmacological stimulation has been difficult to measure. Here we present a novel, yet simple and direct, method that provides the first quantitative estimates of static content and dynamic changes in [Ca²(+)](SR) in mammalian skeletal muscle, to our knowledge. The method uses fluo-5N loaded into the SR of single, mammalian skeletal muscle cells (murine flexor digitorum brevis myofibers) and confocal imaging to detect and calibrate the signals. Using this method, we have determined that [Ca²(+)](SR, free) is 390 μM. 4-Chloro-m-cresol, an activator of the skeletal muscle ryanodine receptor, reduces [Ca²(+)](SR, free) to ∼8 μM, when values are corrected for background fluorescence from cytoplasmic pools of dye. Prolonged electrical stimulation (10 s) at 50 Hz releases 88% of the SR Ca²(+) content, whereas stimulation at 1 Hz (10 s) releases only 20%. Our results lay the foundation for molecular modeling of the dynamics of luminal SR Ca²(+) and for future studies of the role of SR Ca²(+) in healthy and diseased mammalian muscle., (Copyright © 2010 Biophysical Society. Published by 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.)

Diastolic Ca leak from the sarcoplasmic reticulum (SR) of ventricular myocytes reduces the SR Ca content, stabilizing the activity of the SR Ca release channel ryanodine receptor for the next beat. SR Ca leak has been visualized globally using whole-cell fluorescence, or locally using confocal microscopy, but never both ways. When using confocal microscopy, leak is imaged as "Ca sparks," which are fluorescent objects generated by the local reaction-diffusion of released Ca and cytosolic indicator. Here, we used confocal microscopy and simultaneously measured the global ryanodine-receptor-mediated leak rate (J(leak)) and Ca sparks in intact mouse ventricular myocytes. We found that spark frequency and J(leak) are correlated, as expected if both are manifestations of a common phenomenon. However, we also found that sparks explain approximately half of J(leak). Our strategy unmasks the presence of a subresolution (i.e., nonspark) release of potential physiological relevance., (Copyright 2010 Biophysical Society. Published by Elsevier Inc. All rights reserved.)

The outer mitochondrial membrane (OMM) is the last barrier between the mitochondrion and the cytoplasm. Breaches of OMM integrity result in the release of cytochrome c oxidase, triggering apoptosis. In this study, we used calibrated gold nanoparticles to probe the OMM in rat permeabilized ventricular cells and in isolated cardiac mitochondria under quasi-physiological ionic conditions and during permeability transition. Our experiments showed that under control conditions, the OMM is not permeable to 6-nm particles. However, 3-nm particles could enter the mitochondrial intermembrane space in mitochondria of permeabilized cells and isolated cardiac mitochondria. Known inhibitors of the voltage-dependent anion channel (VDAC), König polyanion, and 4,4'-diisothiocyanatostilbene-2,2'-disulfonic acid inhibited this entrance. Thus, 3-nm particles must have entered the mitochondrial intermembrane space through the VDAC. The permeation of the isolated cardiac mitochondria OMM for 3-nm particles was approximately 20 times that in permeabilized cells, suggesting low availability of VDAC pores within the cell. Experiments with expressed green fluorescent protein showed the existence of intracellular barriers restricting the VDAC pore availability in vivo. Thus, our data showed that 1), the physical diameter of VDAC pores in cardiac mitochondria is >or=3 nm but

The physical organization of the ventricular myocyte includes barriers for the movement of objects of varying dimensions ranging from ions to solid particles. There are two kinds of diffusion in the cell: lateral (in membranes) and aqueous. Here we examine the size constraints of aqueous diffusion pathways and discuss their impact on cellular physiology. Calibrated gold nanoparticles were used to probe the accessibility of the entire transverse-axial tubular system (TATS), the sarcoplasm, and intracellular structures. The TATS tubules, although up to 300 nm in diameter, permitted only particles 3 nm; 3), the mitochondrial voltage-dependent anion channel and the nuclear pore complex in ventricular cells could not be penetrated by particles >/=6 nm; and 4), there is a difference in size clearance between transversal and longitudinal sarcoplasmic diffusional pathways.

A Ca(2+) spark arises when a cluster of sarcoplasmic reticulum (SR) channels (ryanodine receptors or RyRs) opens to release calcium in a locally regenerative manner. Normally triggered by Ca(2+) influx across the sarcolemmal or transverse tubule membrane neighboring the cluster, the Ca(2+) spark has been shown to be the elementary Ca(2+) signaling event of excitation-contraction coupling in heart muscle. However, the question of how the Ca(2+) spark terminates remains a central, unresolved issue. Here we present a new model, "sticky cluster," of SR Ca(2+) release that simulates Ca(2+) spark behavior and enables robust Ca(2+) spark termination. Two newly documented features of RyR behavior have been incorporated in this otherwise simple model: "coupled gating" and an opening rate that depends on SR lumenal [Ca(2+)]. Using a Monte Carlo method, local Ca(2+)-induced Ca(2+) release from clusters containing between 10 and 100 RyRs is modeled. After release is triggered, Ca(2+) flux from RyRs diffuses into the cytosol and binds to intracellular buffers and the fluorescent Ca(2+) indicator fluo-3 to produce the model Ca(2+) spark. Ca(2+) sparks generated by the sticky cluster model resemble those observed experimentally, and Ca(2+) spark duration and amplitude are largely insensitive to the number of RyRs in a cluster. As expected from heart cell investigation, the spontaneous Ca(2+) spark rate in the model increases with elevated cytosolic or SR lumenal [Ca(2+)]. Furthermore, reduction of RyR coupling leads to prolonged model Ca(2+) sparks just as treatment with FK506 lengthens Ca(2+) sparks in heart cells. This new model of Ca(2+) spark behavior provides a "proof of principle" test of a new hypothesis for Ca(2+) spark termination and reproduces critical features of Ca(2+) sparks observed experimentally.

The elementary events of excitation-contraction coupling in heart muscle are Ca2+ sparks, which arise from one or more ryanodine receptors in the sarcoplasmic reticulum (SR). Here a simple numerical model is constructed to explore Ca2+ spark formation, detection, and interpretation in cardiac myocytes. This model includes Ca2+ release, cytosolic diffusion, resequestration by SR Ca2+-ATPases, and the association and dissociation of Ca2+ with endogenous Ca2+-binding sites and a diffusible indicator dye (fluo-3). Simulations in a homogeneous, isotropic cytosol reproduce the brightness and the time course of a typical cardiac Ca2+ spark, but underestimate its spatial size (approximately 1.1 micron vs. approximately 2.0 micron). Back-calculating [Ca2+]i by assuming equilibrium with indicator fails to provide a good estimate of the free Ca2+ concentration even when using blur-free fluorescence data. A parameter sensitivity study reveals that the mobility, kinetics, and concentration of the indicator are essential determinants of the shape of Ca2+ sparks, whereas the stationary buffers and pumps are less influential. Using a geometrically more complex version of the model, we show that the asymmetric shape of Ca2+ sparks is better explained by anisotropic diffusion of Ca2+ ions and indicator dye rather than by subsarcomeric inhomogeneities of the Ca2+ buffer and transport system. In addition, we examine the contribution of off-center confocal sampling to the variance of spark statistics.

The intracellular calcium ([Ca2+]i) transient in adult rat heart cells was examined using the fluorescent calcium indicator fluo-3 and a laser scanning confocal microscope. We find that the electrically evoked [Ca2+]i transient does not rise at a uniform rate at all points within the cell during the [Ca2+]i transient. These spatial non-uniformities in [Ca2+]i are observed immediately upon depolarization and largely disappear by the time the peak of the [Ca2+]i transient occurs. Importantly, some of the spatial non-uniformity in [Ca2+]i varies randomly in location from beat to beat. Analysis of the spatial character of the non-uniformities suggests that they arise from the stochastic nature of the activation of SR calcium-release channels. The non-uniformities in [Ca2+]i are markedly enhanced by low concentrations of Cd2+, suggesting that activation of L-type calcium channels is the primary source of activator calcium for the calcium transient. In addition, the pattern of calcium release in these conditions was very similar to the spontaneous calcium sparks that are observed under resting conditions and which are due to spontaneous calcium release from the SR. The spatial non-uniformity in the evoked [Ca2+]i transient under normal conditions can be explained by the temporal and spatial summation of a large number of calcium sparks whose activation is a stochastic process. The results are discussed with respect to a stochastic local control model for excitation-contraction (E-C) coupling, and it is proposed that the fundamental unit of E-C coupling consists of one dihydropyridine receptor activating a small group of ryanodine receptors (possibly four) in a square packing model.

Emission spectra of the photolabile Ca2+ chelators DM-nitrophen, nitr-5, and diazo-2 were studied alone, and in the presence of indo-1, to investigate potential interactions that would make the simultaneous manipulation and ratiometric measurement of the intracellular Ca2+ concentration difficult. Neither diazo-2 nor its photoproduct were found to be significantly fluorescent, and consequently concentrations of diazo-2 up to 20 times that of indo-1 did not distort the emission spectra of indo-1. DM-nitrophen was scarcely fluorescent, but its fluorescence did increase upon photolysis. In contrast to diazo-2 and DM-nitrophen, nitr-5 itself was found to be quite fluorescent, and this fluorescence was significantly increased upon photolysis. Thus, combined use of nitr-5 and indo-1 poses the most difficulty. The emission spectra of all the investigated compounds were used to define experimental conditions and calibration procedures that make possible simultaneous measurement and manipulation of the intracellular Ca2+ concentration.

Intracellular photorelease of Ca2+ from "caged calcium" (DM-nitrophen) was used to investigate the Ca(2+)-activated currents in ventricular myocytes isolated from guinea pig hearts. The patch-clamp technique was applied in the whole-cell configuration to measure membrane current and to dialyze the cytosol with a pipette solution containing the caged compound. In the presence of inhibitors for Ca2+, K+, and Na+ channels, concentration jumps of [Ca2+]i induced a rapidly activating inward Na-Ca exchange current which then decayed slowly (tau approximately 500 ms). The initial peak of the inward current and the time-course of current decay were voltage-dependent, and no reversal of the current direction was found between -100 and +100 mV. The observed shallow voltage dependence can be described in terms of the movement of an apparently fractional elementary charge (+0.44e-) across an energy barrier located symmetrically in the electrical field of the membrane. The currents were dependent on extracellular Na+ with a half-maximal activation at 73 mM and a Hill coefficient of 2.8. No change of membrane conductance was activated by the Ca2+ concentration jump when extracellular Na+ was completely replaced by Li+ or N-methyl-D-glucamine (NMG) or when the Na-Ca exchange was inhibited by extracellular Ni2+, La3+, or dichlorobenzamil (DCB). The velocity of relengthening after a twitch induced by photorelease of Ca2+ was only reduced drastically when both the sarcoplasmic reticulum and the Na-Ca exchange were inhibited suggesting that all other Ca2+ removing mechanisms have a low transport capacity under these conditions. In conclusion, we have used a novel approach to study Na-Ca exchange activity with photolysis of "caged" calcium. We found that in guinea pig heart muscle cells the Na-Ca exchange is a potent mechanism for Ca2+ extrusion, is weakly voltage-dependent (118 mV for e-fold change) and can be studied without contamination with other Ca(2+)-activated currents.

The dependence of KATP channel activity on [ATP] has been examined in isolated membrane patches from rat ventricular myocytes. The steady-state [ATP] dependence of channel open probability could be described by a sigmoidal relationship with the ki ([ATP] causing half-maximal inhibition of open probability) = 25 microM and Hill coefficient of 2. Description of channel open- and closed-time distributions required at least 2, and 3, time constants, respectively. Long open-channel lifetimes decreased with [ATP]; unconditional mean channel closed-times increased with [ATP]. Step decrease (jump) in bathing [ATP] resulted in a delay (of up to hundreds of milliseconds) followed by a pseudo-exponential rise of current (with a time constant of up to hundreds of milliseconds). The time course of channel current after changes of [ATP] (or the ATP-analogue AMP-PNP) was shown to be predominantly determined by the time course of diffusion into the tip of the electrode and to the membrane. This time course of diffusion of ATP into the pipette tip had to be taken into account when analyzing the current response to [ATP] steps. Several possible kinetic models of the ATP-dependent regulation of channel activity were considered. Adequate explanation of the data required a model with sequential ATP-binding sites. The model can account for the time course of channel opening after steps of [ATP], as well as for the steady-state dependence of P0 on [ATP]. The model predicts [ATP]-dependent closed and open lifetimes as were observed experimentally.

Concentration jumps of intracellular ATP were produced by photolysis of P3-1-(2-nitrophenyl)ethyl (NPE)-caged ATP and were used to investigate the passive relengthening properties in unloaded cardiac myocytes. Patch-clamp pipettes in the whole-cell mode were used to voltage-clamp the myocytes and to load the cells with caged ATP while optical methods were applied to record sarcomere length or cell length simultaneously. Cell length was varied using energy deprivation contractures while intracellular Ca2+ was controlled with EGTA. At sarcomere lengths between 1.8 and 1.4 microns cellular relengthening after photolysis of caged ATP was rapid (t1/2 approximately 100 ms) and could be well described by a simple mechanical model. However, ATP jumps made at sarcomere lengths approximately 1.1 microns led to slow relengthening (t1/2 approximately seconds), comparable to the slow reextensions observed in skinned myocytes after bulk solution changes. We attribute the slow and incomplete relengthening of intact and skinned myocytes after severe rigor shortening to deformation and alteration of structural elements inside the cell. Relengthening from intermediate sarcomere lengths in intact cells is elastic and provides information about the underlying relengthening forces inside the cell. The data do not support the presence of a significant discontinuity in elastic modulus at a sarcomere length of approximately 1.6 microns expected from ultrastructural features of the sarcomeres and from observations in skinned myocytes. Our results suggest that the cell length measurements usually performed in this preparation provide an adequate description of the force produced by the unloaded cell in the steady state. The results also provide a way to estimate the error arising from viscous forces during rapid shortening.