Analysing cardiac excitation–contraction coupling with mathematical models of local control

The ryanodine receptor microdomain in cardiomyocytes

The ryanodine receptor type 2 (RyR) is a key player in Ca2+ handling during excitation-contraction coupling. During each heartbeat, RyR channels are responsible for linking the action potential with the contractile machinery of the cardiomyocyte by releasing Ca2+ from the sarcoplasmic reticulum. RyR function is fine-tuned by associated signalling molecules, arrangement in clusters and subcellular localization. These parameters together define RyR function within microdomains and are subject to disease remodelling. This review describes the latest findings on RyR microdomain organization, the alterations with disease which result in increased subcellular heterogeneity and emergence of microdomains with enhanced arrhythmogenic potential, and presents novel technologies that guide future research to study and target RyR channels within specific microdomains.

In silico simulations reveal that RYR distribution affects the dynamics of calcium release in cardiac myocytes

The dyads of cardiac myocytes contain ryanodine receptors (RYRs) that generate calcium sparks upon activation. To test how geometric factors of RYR distribution contribute to the formation of calcium sparks, which cannot be addressed experimentally, we performed in silico simulations on a large set of models of calcium release sites (CRSs). Our models covered the observed range of RYR number, density, and spatial arrangement. The calcium release function of CRSs was modeled by RYR openings, with an open probability dependent on concentrations of free Ca2+ and Mg2+ ions, in a rapidly buffered system, with a constant open RYR calcium current. We found that simulations of spontaneous sparks by repeatedly opening one of the RYRs in a CRS produced three different types of calcium release events (CREs) in any of the models. Transformation of simulated CREs into fluorescence signals yielded calcium sparks with characteristics close to the observed ones. CRE occurrence varied broadly with the spatial distribution of RYRs in the CRS but did not consistently correlate with RYR number, surface density, or calcium current. However, it correlated with RYR coupling strength, defined as the weighted product of RYR vicinity and calcium current, so that CRE characteristics of all models followed the same state-response function. This finding revealed the synergy between structure and function of CRSs in shaping dyad function. Lastly, rearrangements of RYRs simulating hypothetical experiments on splitting and compaction of a dyad revealed an increased propensity to generate spontaneous sparks and an overall increase in calcium release in smaller and more compact dyads, thus underlying the importance and physiological role of RYR arrangement in cardiac myocytes.

Multi-scale approaches for the simulation of cardiac electrophysiology: II - Tissue-level structure and function

Computational models of the heart, from cell-level models, through one-, two- and three-dimensional tissue-level simplifications, to biophysically-detailed three-dimensional models of the ventricles, atria or whole heart, allow the simulation of excitation and propagation of this excitation, and have provided remarkable insight into the normal and pathological functioning of the heart. In this article we present equations for modelling cellular excitation (i.e. the cell action potential) from both a phenomenological and a biophysical perspective. Hodgkin-Huxley formalism is discussed, along with the current generation of biophysically-detailed cardiac cell models. Alternative Markovian formulations for modelling ionic currents are also presented. Equations describing propagation of this cellular excitation, through one-, two- and three-dimensional idealised or realistic tissues, are then presented. For all types of model, from cell to tissue, methods for discretisation and integration of the underlying equations are discussed. The article finishes with a discussion of two tissue-level experimental imaging techniques - diffusion tensor magnetic resonance imaging and optical imaging - that can be used to provide data for parameterisation and validation of cell- and tissue-level cardiac models.

Quenching the spark: Termination of CICR in the submicroscopic space of the dyad

Cannell and Kong discuss the different termination mechanisms proposed for CICR in cardiac myocytes.

Transverse tubule remodelling: a cellular pathology driven by both sides of the plasmalemma?

Transverse (t)-tubules are invaginations of the plasma membrane that form a complex network of ducts, 200-400 nm in diameter depending on the animal species, that penetrates deep within the cardiac myocyte, where they facilitate a fast and synchronous contraction across the entire cell volume. There is now a large body of evidence in animal models and humans demonstrating that pathological distortion of the t-tubule structure has a causative role in the loss of myocyte contractility that underpins many forms of heart failure. Investigations into the molecular mechanisms of pathological t-tubule remodelling to date have focused on proteins residing in the intracellular aspect of t-tubule membrane that form linkages between the membrane and myocyte cytoskeleton. In this review, we shed light on the mechanisms of t-tubule remodelling which are not limited to the intracellular side. Our recent data have demonstrated that collagen is an integral part of the t-tubule network and that it increases within the tubules in heart failure, suggesting that a fibrotic mechanism could drive cardiac junctional remodelling. We examine the evidence that the linkages between the extracellular matrix, t-tubule membrane and cellular cytoskeleton should be considered as a whole when investigating the mechanisms of t-tubule pathology in the failing heart.

A deterministic model predicts the properties of stochastic calcium oscillations in airway smooth muscle cells

The inositol trisphosphate receptor () is one of the most important cellular components responsible for oscillations in the cytoplasmic calcium concentration. Over the past decade, two major questions about the have arisen. Firstly, how best should the be modeled? In other words, what fundamental properties of the allow it to perform its function, and what are their quantitative properties? Secondly, although calcium oscillations are caused by the stochastic opening and closing of small numbers of , is it possible for a deterministic model to be a reliable predictor of calcium behavior? Here, we answer these two questions, using airway smooth muscle cells (ASMC) as a specific example. Firstly, we show that periodic calcium waves in ASMC, as well as the statistics of calcium puffs in other cell types, can be quantitatively reproduced by a two-state model of the , and thus the behavior of the is essentially determined by its modal structure. The structure within each mode is irrelevant for function. Secondly, we show that, although calcium waves in ASMC are generated by a stochastic mechanism, stochasticity is not essential for a qualitative prediction of how oscillation frequency depends on model parameters, and thus deterministic models demonstrate the same level of predictive capability as do stochastic models. We conclude that, firstly, calcium dynamics can be accurately modeled using simplified models, and, secondly, to obtain qualitative predictions of how oscillation frequency depends on parameters it is sufficient to use a deterministic model.

The inositol trisphosphate receptor () is one of the most important cellular components responsible for calcium oscillations. Over the past decade, two major questions about the have arisen. Firstly, what fundamental properties of the allow it to perform its function? Secondly, although calcium oscillations are caused by the stochastic properties of small numbers of is it possible for a deterministic model to be a reliable predictor of calcium dynamics? Using airway smooth muscle cells as an example, we show that calcium dynamics can be accurately modeled using simplified models, and, secondly, that deterministic models are qualitatively accurate predictors of calcium dynamics. These results are important for the study of calcium dynamics in many cell types.

Translating intracellular calcium signaling into models

The rich experimental data on intracellular calcium has put theoreticians in an ideal position to derive models of intracellular calcium signaling. Over the last 25 years, a large number of modeling frameworks have been suggested. Here, I will review some of the milestones of intracellular calcium modeling with a special emphasis on calcium-induced calcium release (CICR) through inositol-1,4,5-trisphosphate and ryanodine receptors. I will highlight key features of CICR and how they are represented in models as well as the challenges that theoreticians face when translating our current understanding of calcium signals into equations. The selected examples demonstrate that a successful model provides mechanistic insights into the molecular machinery of the Ca²⁺ signaling toolbox and determines the contribution of local Ca²⁺ release to global Ca²⁺ patterns, which at the moment cannot be resolved experimentally.

Modeling CaMKII-mediated regulation of L-type Ca(2+) channels and ryanodine receptors in the heart

Excitation-contraction coupling (ECC) in the cardiac myocyte is mediated by a number of highly integrated mechanisms of intracellular Ca²⁺ transport. Voltage- and Ca²⁺-dependent L-type Ca²⁺ channels (LCCs) allow for Ca²⁺ entry into the myocyte, which then binds to nearby ryanodine receptors (RyRs) and triggers Ca²⁺ release from the sarcoplasmic reticulum in a process known as Ca²⁺-induced Ca²⁺ release. The highly coordinated Ca²⁺-mediated interaction between LCCs and RyRs is further regulated by the cardiac isoform of the Ca²⁺/calmodulin-dependent protein kinase (CaMKII). Because CaMKII targets and modulates the function of many ECC proteins, elucidation of its role in ECC and integrative cellular function is challenging and much insight has been gained through the use of detailed computational models. Multiscale models that can both reconstruct the detailed nature of local signaling events within the cardiac dyad and predict their functional consequences at the level of the whole cell have played an important role in advancing our understanding of CaMKII function in ECC. Here, we review experimentally based models of CaMKII function with a focus on LCC and RyR regulation, and the mechanistic insights that have been gained through their application.

Molecular determinants of allosteric regulation in NCX proteins

Allosteric activation of NCX involves the binding of cytosolic Ca(2+) to regulatory domains CBD1 and CBD2. Previous studies with isolated CBD12 and full-size NCX identified synergistic interactions between the two CBD domains that modify the affinity and kinetic properties of Ca(2+) sensing, although it remains unclear how the Ca(2+)-binding signal is decoded and propagates to transmembrane domains. Biophysical analyses (X-ray, SAXS, and stopped-flow techniques) of isolated preparations of CBD1, CBD2, and CBD12 have shown that Ca(2+) binding to Ca3-Ca4 sites of CBD1 results in interdomain tethering of CBDs through specific amino acids on CBD1 (Asp499 and Asp500) and CBD2 (Arg532 and Asp565). Mutant analyses of isolated CBDs suggest that the two-domain interface governs Ca(2+)-driven conformational alignment of CBDs, resulting in slow dissociation of Ca(2+) from CBD12, and thus, it mediates Ca(2+)-induced conformational transitions associated with allosteric signal transmission. Specifically, occupation of Ca3-Ca4 sites by Ca(2+) induces disorder-to-order transition owing to charge neutralization and coordination, thereby constraining CBD conformational freedom, rigidifying the NCX1 f-loop, and triggering allosteric signal transmission to the membrane domain. The newly found interdomain switch is highly conserved among NCX isoform/splice variants, although some additional structural motifs may shape the regulatory specificity of NCX variants.

Genetically Encoded Calcium Indicators and Astrocyte Calcium Microdomains

The discovery of intracellular Ca2+ signals within astrocytes has changed our view of how these ubiquitous cells contribute to brain function. Classically thought merely to serve supportive functions, astrocytes are increasingly thought to respond to, and regulate, neurons. The use of organic Ca2+ indicator dyes such as Fluo-4 and Fura-2 has proved instrumental in the study of astrocyte physiology. However, progress has recently been accelerated by the use of cytosolic and membrane targeted genetically encoded calcium indicators (GECIs). Herein, we review these recent findings, discuss why studying astrocyte Ca2+ signals is important to understand brain function, and summarize work that led to the discovery of TRPA1 channel-mediated near-membrane Ca2+ signals in astrocytes and their indirect neuromodulatory roles at inhibitory synapses in the CA1 stratum radiatum region of the hippocampus. We suggest that the use of membrane-targeted and cytosolic GECIs holds great promise to explore the diversity of Ca2+ signals within single astrocytes and also to study diversity of function for astrocytes in different parts of the brain.

Properties of Ca2+ sparks revealed by four-dimensional confocal imaging of cardiac muscle

Parameters (amplitude, width, kinetics) of Ca²⁺ sparks imaged confocally are affected by errors when the spark source is not in focus. To identify sparks that were in focus, we used fast scanning (LSM 5 LIVE; Carl Zeiss) combined with fast piezoelectric focusing to acquire x–y images in three planes at 1-µm separation (x-y-z-t mode). In 3,000 x–y scans in each of 34 membrane-permeabilized cat atrial cardiomyocytes, 6,906 sparks were detected. 767 sparks were in focus. They had greater amplitude, but their spatial width and rise time were similar compared with all sparks recorded. Their distribution of amplitudes had a mode at ΔF/F₀ = 0.7. The Ca²⁺ release current underlying in-focus sparks was 11 pA, requiring 20 to 30 open channels, a number at the high end of earlier estimates. Spark frequency was greater than in earlier imaging studies of permeabilized ventricular cells, suggesting a greater susceptibility to excitation, which could have functional relevance for atrial cells. Ca²⁺ release flux peaked earlier than the time of peak fluorescence and then decayed, consistent with significant sarcoplasmic reticulum (SR) depletion. The evolution of fluorescence and release flux were strikingly similar for in-focus sparks of different rise time (T). Spark termination involves both depletion of Ca²⁺ in the SR and channel closure, which may be synchronized by depletion. The observation of similar flux in sparks of different T requires either that channel closure and other termination processes be independent of the determinants of flux (including [Ca²⁺]_SR) or that different channel clusters respond to [Ca²⁺]_SR with different sensitivity.

TRPA1 channels regulate astrocyte resting calcium and inhibitory synapse efficacy through GAT-3

Astrocytes contribute to the formation and function of synapses and are found throughout the brain, where they show intracellular store-mediated Ca(2+) signals. Here, using a membrane-tethered, genetically encoded calcium indicator (Lck-GCaMP3), we report the serendipitous discovery of a new type of Ca(2+) signal in rat hippocampal astrocyte-neuron cocultures. We found that Ca(2+) fluxes mediated by transient receptor potential A1 (TRPA1) channels gave rise to frequent and highly localized 'spotty' Ca(2+) microdomains near the membrane that contributed appreciably to resting Ca(2+) in astrocytes. Mechanistic evaluations in brain slices showed that decreases in astrocyte resting Ca(2+) concentrations mediated by TRPA1 channels decreased interneuron inhibitory synapse efficacy by reducing GABA transport by GAT-3, thus elevating extracellular GABA. Our data show how a transmembrane Ca(2+) source (TRPA1) targets a transporter (GAT-3) in astrocytes to regulate inhibitory synapses.

Cardiac myocytes and local signaling in nano-domains

It is well known that calcium-induced calcium-release in cardiac myocytes takes place in spatially restricted regions known as dyads, where discrete patches of junctional sarcoplasmic reticulum tightly associate with the t-tubule membrane. The dimensions of a dyad are so small that it contains only a few Ca²⁺ ions at any given time. Ca²⁺ signaling in the dyad is therefore noisy, and dominated by the Brownian motion of Ca²⁺ ions in a potential field. Remarkably, from this complexity emerges the integrated behavior of the myocyte in which, under normal conditions, precise control of Ca²⁺ release and muscle contraction is maintained over the life of the cell. This is but one example of how signal processing within the cardiac myocyte and other cells often occurs in small "nano-domains" where proteins and protein complexes interact at spatial dimensions on the order of ∼1-10 nm and at time-scales on the order of nanoseconds to perform the functions of the cell. In this article, we will review several examples of local signaling in nano-domains, how it contributes to the integrative behavior of the cardiac myocyte, and present computational methods for modeling signal processing within these domains across differing spatio-temporal scales.

Local control in cardiac E-C coupling

The development of local control theories in cardiac excitation-contraction coupling solved a major problem in the calcium-induced calcium release (CICR) hypothesis. Local control explained how regeneration, inherent in the CICR mechanism, might be limited spatially to enable graded Ca release (and force production). The key lies in the stochastic recruitment of individual calcium release units (couplons or CRUs) where adjacent CRUs are partially uncoupled by the distance between them. In the CRU, individual groups of sarcoplasmic reticulum calcium release channels (RyRs) are very close to the surface membrane where calcium influx, controlled by membrane depolarization, leads to high local Ca levels that enable a high speed response from RyRs that have a very low probability to opening at resting Ca levels. However, calcium diffusion from an activated CRU results in adjacent CRUs being exposed to much lower levels of Ca and probability of activation. This effectively uncouples the CRUs and limits overall regenerative gain to enable stability without compromising sensitivity. Nevertheless, it is still unclear how the CRU terminates its release of calcium on the physiological timescale, and possible mechanisms (and problems) are briefly reviewed. We suggest that modulation in RyR gating may serve to control average SR Ca levels to regulate other metabolic functions of the sarco(endo)plasmic reticulum beyond regulating contractility. This article is part of a special issue entitled "Local Signaling in Myocytes."

Integrative systems models of cardiac excitation-contraction coupling

Excitation-contraction coupling in the cardiac myocyte is mediated by a number of highly integrated mechanisms of intracellular Ca²(+) transport. The complexity and integrative nature of heart cell electrophysiology and Ca²(+) cycling has led to an evolution of computational models that have played a crucial role in shaping our understanding of heart function. An important emerging theme in systems biology is that the detailed nature of local signaling events, such as those that occur in the cardiac dyad, have important consequences at higher biological scales. Multiscale modeling techniques have revealed many mechanistic links between microscale events, such as Ca²(+) binding to a channel protein, and macroscale phenomena, such as excitation-contraction coupling gain. Here, we review experimentally based multiscale computational models of excitation-contraction coupling and the insights that have been gained through their application.

Physiologic gating properties of unitary cardiac L-type Ca2+ channels

The contraction of adult mammalian ventricular cardiomyocytes is triggered by the influx of Ca(2+) ions through sarcolemmal L-type Ca(2+) channels (LCCs). However, the gating properties of unitary LCCs under physiologic conditions have remained elusive. Towards this end, we investigated the voltage-dependence of the gating kinetics of unitary LCCs, with a physiologic concentration of Ca(2+) ions permeating the channel. Unitary LCC currents were recorded with 2mM external Ca(2+) ions (in the absence of LCC agonists), using cell-attached patches on K-depolarized adult rat ventricular myocytes. The voltage-dependence of the peak probability of channel opening (Po vs. Vm) displayed a maximum value of 0.3, a midpoint of -12 mV, and a slope factor of 8.5. The maximum value for Po of the unitary LCC was significantly higher than previously assumed, under physiologic conditions. We also found that the mean open dwell time of the unitary LCC increased twofold with depolarization, ranging from 0.53+/-0.02 ms at -30 mV to 1.08+/-0.03 ms at 0 mV. The increase in mean LCC open time with depolarization counterbalanced the decrease in the single LCC current amplitude; the latter due to the decrease in driving force for Ca(2+) ion entry. Thus, the average amount of Ca(2+) ions entering through an individual LCC opening ( approximately 300-400 ions) remained relatively constant over this range of potentials. These novel results establish the voltage-dependence of unitary LCC gating kinetics using a physiologic Ca(2+) ion concentration. Moreover, they provide insight into local Ca(2+)-induced Ca(2+) release and a more accurate basis for mathematical modeling of excitation-contraction coupling in cardiac myocytes.

Ca(2+)-dependent components of inactivation of unitary cardiac L-type Ca(2+) channels

A Ca(2+) ion-dependent inactivation (CDI) of L-type Ca(2+) channels (LCC) is vital in limiting and shaping local Ca(2+) ion signalling in a variety of excitable cell types. However, under physiological conditions the unitary LCC properties that underlie macroscopic inactivation are unclear. Towards this end, we have probed the gating kinetics of individual cardiac LCCs recorded with a physiological Ca(2+) ion concentration (2 mM) permeating the channel, and in the absence of channel agonists. Upon depolarization the ensemble-averaged LCC current decayed with a fast and a slow exponential component. We analysed the unitary behaviour responsible for this biphasic decay by means of a novel kinetic dissection of LCC gating parameters. We found that inactivation was caused by a rapid decrease in the frequency of LCC reopening, and a slower decline in mean open time of the LCC. In contrast, with barium ions permeating the channel ensemble-averaged currents displayed only a single, slow exponential decay and little time dependence of the LCC open time. Our results demonstrate that the fast and slow phases of macroscopic inactivation reflect the distinct time courses for the decline in the frequency of LCC reopening and the open dwell time, both of which are modulated by Ca(2+) influx. Analysis of the evolution of CDI in individual LCC episodes was employed to examine the stochastic nature of the underlying molecular switch, and revealed that influx on the order of a thousand Ca(2+) ions may be sufficient to trigger CDI. This is the first study to characterize both the unitary kinetics and the stoichiometry of CDI of LCCs with a physiological Ca(2+) concentration. These novel findings may provide a basis for understanding the mechanisms regulating unitary LCC gating, which is a pivotal element in the local control of Ca(2+)-dependent signalling processes.

Mitochondria in cardiomyocyte Ca2+ signaling

Ca(2+) signaling is of vital importance to cardiac cell function and plays an important role in heart failure. It is based on sarcolemmal, sarcoplasmic reticulum and mitochondrial Ca(2+) cycling. While the first two are well characterized, the latter remains unclear, controversial and technically challenging. In mammalian cardiac myocytes, Ca(2+) influx through L-type calcium channels in the sarcolemmal membrane triggers Ca(2+) release from the nearby junctional sarcoplasmic reticulum to produce Ca(2+) sparks. When this triggering is synchronized by the cardiac action potential, a global [Ca(2+)](i) transient arises from coordinated Ca(2+) release events. The ends of intermyofibrillar mitochondria are located within 20 nm of the junctional sarcoplasmic reticulum and thereby experience a high local [Ca(2+)] during the Ca(2+) release process. Both local and global Ca(2+) signals may thus influence calcium signaling in mitochondria and, reciprocally, mitochondria may contribute to the local control of calcium signaling. In addition to the intermyofibrillar mitochondria, morphologically distinct mitochondria are also located in the perinuclear and subsarcolemmal regions of the cardiomyocyte and thus experience a different local [Ca(2+)]. Here we review the literature in regard to several issues of broad interest: (1) the ultrastructural basis for mitochondrion - sarcoplasmic reticulum cross-signaling; (2) mechanisms of sarcoplasmic reticulum signaling; (3) mitochondrial calcium signaling; and (4) the possible interplay of calcium signaling between the sarcoplasmic reticulum and adjacent mitochondria. Finally, this review discusses experimental findings and mathematical models of cardiac calcium signaling between the sarcoplasmic reticulum and mitochondria, identifies weaknesses in these models, and suggests strategies and approaches for future investigations.

Three-dimensional electron microscopy reveals new details of membrane systems for Ca2+ signaling in the heart

In the current study, the three-dimensional (3D) topologies of dyadic clefts and associated membrane organelles were mapped in mouse ventricular myocardium using electron tomography. The morphological details and the distribution of membrane systems, including transverse tubules (T-tubules), junctional sarcoplasmic reticulum (SR) and vicinal mitochondria, were determined and presumed to be crucial for controlling cardiac Ca(2+) dynamics. The geometric complexity of T-tubules that varied in diameter with frequent branching was clarified. Dyadic clefts were intricately shaped and remarkably small (average 4.39x10(5) nm(3), median 2.81x10(5) nm(3)). Although a dyadic cleft of average size could hold maximum 43 ryanodine receptor (RyR) tetramers, more than one-third of clefts were smaller than the size that is able to package as many as 15 RyR tetramers. The dyadic clefts were also adjacent to one another (average end-to-end distance to the nearest dyadic cleft, 19.9 nm) and were distributed irregularly along T-tubule branches. Electron-dense structures that linked membrane organelles were frequently observed between mitochondrial outer membranes and SR or T-tubules. We, thus, propose that the topology of dyadic clefts and the neighboring cellular micro-architecture are the major determinants of the local control of Ca(2+) in the heart, including the establishment of the quantal nature of SR Ca(2+) releases (e.g. Ca(2+) sparks).

Ryanodine receptor-mediated arrhythmias and sudden cardiac death

The cardiac ryanodine receptor-Ca²⁺ release channel (RyR2) is an essential sarcoplasmic reticulum (SR) transmembrane protein that plays a central role in excitation–contraction coupling (ECC) in cardiomyocytes. Aberrant spontaneous, diastolic Ca²⁺ leak from the SR due to dysfunctional RyR2 contributes to the formation of delayed after-depolarisations, which are thought to underlie the fatal arrhythmia that occurs in both heart failure (HF) and in catecholaminergic polymorphic ventricular tachycardia (CPVT). CPVT is an inherited disorder associated with mutations in either the RyR2 or a SR luminal protein, calsequestrin. RyR2 shows normal function at rest in CPVT but the RyR2 dysfunction is unmasked by physical exercise or emotional stress, suggesting abnormal RyR2 activation as an underlying mechanism. Several potential mechanisms have been advanced to explain the dysfunctional RyR2 observed in HF and CPVT, including enhanced RyR2 phosphorylation status, altered RyR2 regulation at luminal/cytoplasmic sites and perturbed RyR2 intra/inter-molecular interactions. This review considers RyR2 dysfunction in the context of the structural and functional modulation of the channel, and potential therapeutic strategies to stabilise RyR2 function in cardiac pathology.

Ontogeny of Ca2+-induced Ca2+ release in rabbit ventricular myocytes

It is commonly accepted that L-type Ca(2+) channel-mediated Ca(2+)-induced Ca(2+) release (CICR) is the dominant mode of excitation-contraction (E-C) coupling in the adult mammalian heart and that there is no appreciable CICR in neonates. However, we have observed that cell contraction in the neonatal heart was significantly decreased after sarcoplasmic reticulum (SR) Ca(2+) depletion with caffeine. Therefore, the present study investigated the developmental changes of CICR in rabbit ventricular myocytes at 3, 10, 20, and 56 days of age. We found that the inhibitory effect of the L-type Ca(2+) current (I(Ca)) inhibitor nifedipine (Nif; 15 microM) caused an increasingly larger reduction of Ca(2+) transients on depolarization in older age groups [from approximately 15% in 3-day-old (3d) myocytes to approximately 90% in 56-day-old (56d) myocytes]. The remaining Ca(2+) transient in the presence of Nif in younger age groups was eliminated by the inhibition of Na(+)/Ca(2+) exchanger (NCX) with the subsequent addition of 10 microM KB-R7943 (KB-R). Furthermore, Ca(2+) transients were significantly reduced in magnitude after the depletion of SR Ca(2+) with caffeine in all age groups, although the effect was significantly greater in the older age groups (from approximately 40% in 3d myocytes up to approximately 70% in 56d myocytes). This SR Ca(2+)-sensitive Ca(2+) transient in the earliest developmental stage was insensitive to Nif but was sensitive to the subsequent addition of KB-R, indicating the presence of NCX-mediated CICR that decreased significantly with age (from approximately 37% in 3d myocytes to approximately 0.5% in 56d myocytes). In contrast, the I(Ca)-mediated CICR increased significantly with age (from approximately 10% in 3d myocytes to approximately 70% in 56d myocytes). The CICR gain as estimated by the integral of the CICR Ca(2+) transient divided by the integral of its Ca(2+) transient trigger was smaller when mediated by NCX ( approximately 1.0 for 3d myocytes) than when mediated by I(Ca) ( approximately 3.0 for 56d myocytes). We conclude that the lower-efficiency NCX-mediated CICR is a predominant mode of CICR in the earliest developmental stages that gradually decreases as the more efficient L-type Ca(2+) channel-mediated CICR increases in prominence with ontogeny.

Macroscopic consequences of calcium signaling in microdomains: a first-passage-time approach

Calcium (Ca) plays an important role in regulating various cellular processes. In a variety of cell types, Ca signaling occurs within microdomains where channels deliver localized pulses of Ca activating a nearby collection of Ca-sensitive receptors. The small number of channels involved ensures that the signaling process is stochastic. The aggregate response of several thousand of these microdomains yields a whole-cell response which dictates the cell behavior. Here, we study the statistical properties of a population of these microdomains in response to a trigger signal. We use a first-passage-time approach to show analytically how Ca release in the whole cell depends on properties of Ca channels within microdomains. Using these results we explain for the first time the underlying mechanism for the graded relationship between Ca influx and Ca release in cardiac cells.

A guide to modelling cardiac electrical activity in anatomically detailed ventricles

One of the most recent trends in cardiac electrophysiology is the development of integrative anatomically accurate models of the heart, which include description of cardiac activity from sub-cellular and cellular level to the level of the whole organ. In order to construct this type of model, a researcher needs to collect a wide range of information from books and journal articles on various aspects of biology, physiology, electrophysiology, numerical mathematics and computer programming. The aim of this methodological article is to survey recent developments in integrative modelling of electrical activity in the ventricles of the heart, and to provide a practical guide to the resources and tools that are available for work in this exciting and challenging area.

Sub-plasmalemmal [Ca2+]i upstroke in myocytes of the guinea-pig small intestine evoked by muscarinic stimulation: IP3R-mediated Ca2+ release induced by voltage-gated Ca2+ entry

Membrane depolarization triggers Ca²⁺ release from the sarcoplasmic reticulum (SR) in skeletal muscles via direct interaction between the voltage-gated L-type Ca²⁺ channels (the dihydropyridine receptors; VGCCs) and ryanodine receptors (RyRs), while in cardiac muscles Ca²⁺ entry through VGCCs triggers RyR-mediated Ca²⁺ release via a Ca²⁺-induced Ca²⁺ release (CICR) mechanism. Here we demonstrate that in phasic smooth muscle of the guinea-pig small intestine, excitation evoked by muscarinic receptor activation triggers an abrupt Ca²⁺ release from sub-plasmalemmal (sub-PM) SR elements enriched with inositol 1,4,5-trisphosphate receptors (IP₃Rs) and poor in RyRs. This was followed by a lesser rise, or oscillations in [Ca²⁺]_i. The initial abrupt sub-PM [Ca²⁺]_i upstroke was all but abolished by block of VGCCs (by 5 μM nicardipine), depletion of intracellular Ca²⁺ stores (with 10 μM cyclopiazonic acid) or inhibition of IP₃Rs (by 2 μM xestospongin C or 30 μM 2-APB), but was not affected by block of RyRs (by 50–100 μM tetracaine or 100 μM ryanodine). Inhibition of either IP₃Rs or RyRs attenuated phasic muscarinic contraction by 73%. Thus, in contrast to cardiac muscles, excitation–contraction coupling in this phasic visceral smooth muscle occurs by Ca²⁺ entry through VGCCs which evokes an initial IP₃R-mediated Ca²⁺ release activated via a CICR mechanism.

Modelling calcium microdomains using homogenisation

Microdomains of calcium (i.e., areas on the nanometer scale that have qualitatively different calcium concentrations from that in the bulk cytosol) are known to be important in many situations. In cardiac cells, for instance, a calcium microdomain between the L-type channels and the ryanodine receptors, the so-called diadic cleft, is where the majority of the control of calcium release occurs. In other cell types that exhibit calcium oscillations and waves, the importance of microdomains in the vicinity of clusters of inositol trisphosphate receptors, or between the endoplasmic reticulum (ER) and other internal organelles or the plasma membrane, is clear. Given the limits of computational power, it is not currently realistic to model an entire cellular cytoplasm by incorporating detailed structural information about the ER throughout the entire cytoplasm. Hence, most models use a homogenised approach, assuming that both cytoplasm and ER coexist at each point of the domain. Conversely, microdomain models can be constructed, in which detailed structural information can be incorporated, but, until now, methods have not been developed for linking such a microdomain model to a model at the level of the entire cell. Using the homogenisation approach we developed in an earlier paper [Goel, P., Friedman, A., Sneyd, J., 2006. Homogenization of the cell cytoplasm: the calcium bidomain equations. SIAM J. Multiscale Modeling Simulation, in press] we show how a multiscale model of a calcium microdomain can be constructed. In this model a detailed model of the microdomain (in which the ER and the cytoplasm are separate compartments) is coupled to a homogenised model of the entire cell in a rigorous way. Our method is illustrated by a simple model of the diadic cleft of a cardiac half-sarcomere.

Temporal dissociation of frequency-dependent acceleration of relaxation and protein phosphorylation by CaMKII

Frequency-dependent acceleration of relaxation (FDAR) is an important intrinsic mechanism that allows for diastolic filling of the ventricle at higher heart rates, yet its molecular mechanism is still not understood. Previous studies showed that FDAR is dependent on functional sarcoplasmic reticulum (SR) and can be abolished by phosphatase or by Ca/CaM kinase (CaMKII) inhibition. Additionally, CaMKII activity/autophosphorylation has been shown to be frequency-dependent. Thus, we tested the hypothesis that CaMKII phosphorylation of SR Ca(2+)-handling proteins (Phospholamban (PLB), Ca(2+) release channel (RyR)) mediates FDAR. Here we show that FDAR occurs abruptly in fluo-4 loaded isolated rat ventricular myocytes when frequency is raised from 0.1 to 2 Hz. The effect is essentially complete within four beats (2 s) with the tau of [Ca(2+)](i) decline decreasing by 42+/-3%. While there is a detectable increase in PLB Thr-17 and RyR Ser-2814 phosphorylation, the increase is quantitatively small (PLB<5%, RyR approximately 8%) and the time-course is clearly delayed with regard to FDAR. The low substrate phosphorylation indicates that pacing of myocytes only mildly activates CaMKII and consistent with this CaMKIIdelta autophosphorylation did not increase with pacing alone. However, in the presence of phosphatase 1 inhibition pacing triggered a net-increase in autophosphorylated CaMKII and also greatly enhanced PLB and RyR phosphorylation. We conclude that FDAR does not rely on phosphorylation of PLB or RyR. Even though CaMKII does become activated when myocytes are paced, phosphatases immediately antagonize CaMKII action, limit substrate phosphorylation and also prevent sustained CaMKII autophosphorylation (thereby suppressing global CaMKII effects).

Dynamic interreceptor coupling: a novel working mechanism of two-dimensional ryanodine receptor array

Ryanodine receptors (RyRs) usually form two-dimensional regular array in sarcoplasmic reticulum membranes in muscle cells. The inter-RyRs coupling may be essential for the maintenance of quiescent Ca2+ release in resting state, as well as for the coordinated activation and rapid termination of RyR-mediated Ca2+ release during excitation-contraction coupling. In our previous work, we have reported that the inter-RyRs interaction is modulated by RyR channel's functional state, which inspired us to propose a novel working mechanism of RyR array: "dynamic inter-RyR coupling". In this work, we built a simple model based on cellular automata and the Monte-Carlo method to quantitatively investigate the roles of intermolecular coupling and its modulation in regulating the signaling capabilities of RyR array. Our simulation results showed that with a suitable inter-RyR coupling strength, the combination of rest stability and high response efficiency, namely optimal signal/noise ratio, of Ca2+ signaling could be achieved. Moreover, we also found the continued coupling between open RyRs would delay the system termination rate. The coacquisition of robust termination of array opening relied on the proper decrease of coupling strength between activated RyRs. Obviously, such temporally asymmetric coupling would simultaneously endow the system with physiologically relevant resting stability and fast termination.

Role of Cellular Compartmentation in the Metabolic Response to Stress: Mechanistic Insights from Computational Models

The mechanisms controlling ATP generation in the transition from normal resting conditions to either high work states or ischemia are poorly understood. ATP generation depends upon compartmentation between the mitochondria and cytosol of metabolic pathways and key energy transfer species that cannot be easily assessed experimentally. We developed a multicompartment mathematical model of cardiac metabolism to simulate the metabolic responses to ischemia and increased workload. The model is based on mass balances, transport, and metabolic processes in cardiac tissue, and has three distinct compartments (blood, cytosol, and mitochondria). In addition to distinguishing between cytosol and mitochondria, the model includes a cytosolic subcompartment for glycolytic metabolic channeling. The model simulations predict the rapid activation of glycogenolysis and lactate production at the onset of ischemia, and support the concept of localization of glycolysis to a cytosolic subcompartment. In addition, simulations show that mitochondrial NADH/NAD(+) is primarily determined by oxygen consumption during ischemia, while cytosolic NADH/NAD(+) and lactate production are largely a function of glycolytic flux during the initial phase, and is controlled by mitochondrial NADH/NAD(+) and the malate-aspartate shuttle during the steady state. Finally, the model predicts that metabolic activation with an abrupt increase in workload requires parallel activation of ATP hydrolysis, glycolysis, mitochondrial dehydrogenases, the electron transport chain, and ADP phosphorylation. Taken together, these studies demonstrate the importance of metabolic compartmentation in the regulation of cardiac energetics in response to acute stress, and they highlight the usefulness of computational models in this line of investigation.

Spatial and temporal Ca2+, Mg2+, and ATP2- dynamics in cardiac dyads during calcium release

We have constructed a three-dimensional reaction-diffusion model of the mammalian cardiac calcium release unit. We analyzed effects of diffusion coefficients, single channel current amplitude, density of RyR channels, and reaction kinetics of ATP(2-) with Ca(2+) and Mg(2+) ions on spatiotemporal concentration profiles of Ca(2+), Mg(2+), and ATP(2-) in the dyadic cleft during Ca(2+) release. The model revealed that Ca(2+) concentration gradients persist near RyRs in the steady state. Even with low number of open RyRs, peak [Ca(2+)] in the dyadic space reached values similar to estimates of luminal [Ca(2+)] in approximately 1 ms, suggesting that during calcium release the Ca(2+) gradient moves from the cisternal membrane towards the boundary of the dyadic space with the cytosol. The released Ca(2+) bound to ATP(2-), and thus substantially decreased ATP(2-) concentration in the dyadic space. The released Ca(2+) could also replace Mg(2+) in its complex with ATP(2-) during first milliseconds of release if dissociation of MgATP was fast. The results suggest that concentration changes of Ca(2+), Mg(2+), and ATP(2-) might be large and fast enough to reduce dyadic RyR activity. Thus, under physiological conditions, termination of calcium release may be facilitated by the synergic effect of the construction and chemistry of mammalian cardiac dyads.

The functional role of cardiac T-tubules explored in a model of rat ventricular myocytes

The morphology of the cardiac transverse-axial tubular system (TATS) has been known for decades, but its function has received little attention. To explore the possible role of this system in the physiological modulation of electrical and contractile activity, we have developed a mathematical model of rat ventricular cardiomyocytes in which the TATS is described as a single compartment. The geometrical characteristics of the TATS, the biophysical characteristics of ion transporters and their distribution between surface and tubular membranes were based on available experimental data. Biophysically realistic values of mean access resistance to the tubular lumen and time constants for ion exchange with the bulk extracellular solution were included. The fraction of membrane in the TATS was set to 56%. The action potentials initiated in current-clamp mode are accompanied by transient K+ accumulation and transient Ca2+ depletion in the TATS lumen. The amplitude of these changes relative to external ion concentrations was studied at steady-state stimulation frequencies of 1-5 Hz. Ca2+ depletion increased from 7 to 13.1% with stimulation frequency, while K+ accumulation decreased from 4.1 to 2.7%. These ionic changes (particularly Ca2+ depletion) implicated significant decrease of intracellular Ca2+ load at frequencies natural for rat heart.