Role of coupled gating between cardiac ryanodine receptors in the genesis of triggered arrhythmias

Modeling Calcium Cycling in the Heart: Progress, Pitfalls, and Challenges

Intracellular calcium (Ca) cycling in the heart plays key roles in excitation-contraction coupling and arrhythmogenesis. In cardiac myocytes, the Ca release channels, i.e., the ryanodine receptors (RyRs), are clustered in the sarcoplasmic reticulum membrane, forming Ca release units (CRUs). The RyRs in a CRU act collectively to give rise to discrete Ca release events, called Ca sparks. A cell contains hundreds to thousands of CRUs, diffusively coupled via Ca to form a CRU network. A rich spectrum of spatiotemporal Ca dynamics is observed in cardiac myocytes, including Ca sparks, spark clusters, mini-waves, persistent whole-cell waves, and oscillations. Models of different temporal and spatial scales have been developed to investigate these dynamics. Due to the complexities of the CRU network and the spatiotemporal Ca dynamics, it is challenging to model the Ca cycling dynamics in the cardiac system, particularly at the tissue sales. In this article, we review the progress of modeling of Ca cycling in cardiac systems from single RyRs to the tissue scale, the pros and cons of the current models and different modeling approaches, and the challenges to be tackled in the future.

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.

Understanding How Phosphorylation and Redox Modifications Regulate Cardiac Ryanodine Receptor Type 2 Activity to Produce an Arrhythmogenic Phenotype in Advanced Heart Failure

Heart failure (HF) is a global pandemic with significant mortality and morbidity. Despite current medications, 50% of individuals die within 5 years of diagnosis. Of these deaths, 30-50% will be a result of sudden cardiac death from ventricular arrhythmias. This review discusses two stress-induced mechanisms, phosphorylation from chronic β-adrenoceptor (β-AR) stimulation and thiol modifications from oxidative stress, and how they modulate the cardiac ryanodine receptor type 2 (RyR2) and foster an arrhythmogenic phenotype. Calcium (Ca²⁺) is the ubiquitous secondary messenger of excitation-contraction coupling and provides a common pathway for contractile dysfunction and arrhythmia genesis. In a healthy heart, Ca²⁺ is released from the sarcoplasmic reticulum (SR) by RyR2. The open probability of RyR2 is under the dynamic influence of co-proteins, ions, and kinases that are in strict balance to ensure normal physiological functioning. In HF, chronic β-AR activity and production of reactive oxygen species and reactive nitrogen species provide two stress-induced mechanisms uncoupling RyR2 control, resulting in pathological diastolic SR Ca²⁺ leak. This increased cytosolic [Ca²⁺] promotes Ca²⁺ extrusion via the local Na⁺/Ca²⁺ exchanger, resulting in net sarcolemmal depolarization, delayed after depolarization and ventricular arrhythmia. Experimental models researching oxidative stress and phosphorylation have aimed to identify how post-translational modifications to the RyR2 macromolecular complex, and the associated Na⁺/Ca²⁺ cycling proteins, result in pathological Ca²⁺ handling and diastolic leak. However, the causative molecular changes remain controversial and undefined. Through understanding the molecular mechanisms that produce an arrhythmic phenotype, novel therapeutic targets to treat HF and prevent its malignant course can be identified.

Calcium-voltage coupling in the genesis of early and delayed afterdepolarizations in cardiac myocytes

Early afterdepolarizations (EADs) and delayed afterdepolarizations (DADs) are voltage oscillations known to cause cardiac arrhythmias. EADs are mainly driven by voltage oscillations in the repolarizing phase of the action potential (AP), while DADs are driven by spontaneous calcium (Ca) release during diastole. Because voltage and Ca are bidirectionally coupled, they modulate each other's behaviors, and new AP and Ca cycling dynamics can emerge from this coupling. In this study, we performed computer simulations using an AP model with detailed spatiotemporal Ca cycling incorporating stochastic openings of Ca channels and ryanodine receptors to investigate the effects of Ca-voltage coupling on EAD and DAD dynamics. Simulations were complemented by experiments in mouse ventricular myocytes. We show that: 1) alteration of the Ca transient due to increased ryanodine receptor leakiness and/or sarco/endoplasmic reticulum Ca ATPase activity can either promote or suppress EADs due to the complex effects of Ca on ionic current properties; 2) spontaneous Ca waves also exhibit complex effects on EADs, but cannot induce EADs of significant amplitude without the participation of ICa,L; 3) lengthening AP duration and the occurrence of EADs promote DADs by increasing intracellular Ca loading, and two mechanisms of DADs are identified, i.e., Ca-wave-dependent and Ca-wave-independent; and 4) Ca-voltage coupling promotes complex EAD patterns such as EAD alternans that are not observed for solely voltage-driven EADs. In conclusion, Ca-voltage coupling combined with the nonlinear dynamical behaviors of voltage and Ca cycling play a key role in generating complex EAD and DAD dynamics observed experimentally in cardiac myocytes, whose mechanisms are complex but analyzable.

The link between abnormal calcium handling and electrical instability in acquired long QT syndrome--Does calcium precipitate arrhythmic storms?

Release of Ca(2+) ions from sarcoplasmic reticulum (SR) into myocyte cytoplasm and their binding to troponin C is the final signal form myocardial contraction. Synchronous contraction of ventricular myocytes is necessary for efficient cardiac pumping function. This requires both shuttling of Ca(2+) between SR and cytoplasm in individual myocytes, and organ-level synchronization of this process by means of electrical coupling among ventricular myocytes. Abnormal Ca(2+) release from SR causes arrhythmias in the setting of CPVT (catecholaminergic polymorphic ventricular tachycardia) and digoxin toxicity. Recent optical mapping data indicate that abnormal Ca(2+) handling causes arrhythmias in models of both repolarization impairment and profound bradycardia. The mechanisms involve dynamic spatial heterogeneity of myocardial Ca(2+) handling preceding arrhythmia onset, cell-synchronous systolic secondary Ca(2+) elevation (SSCE), as well as more complex abnormalities of intracellular Ca(2+) handling detected by subcellular optical mapping in Langendorff-perfused hearts. The regional heterogeneities in Ca(2+) handling cause action potential (AP) heterogeneities through sodium-calcium exchange (NCX) activation and eventually overwhelm electrical coupling of the tissue. Divergent Ca(2+) dynamics among different myocardial regions leads to temporal instability of AP duration and - on the patient level - in T wave lability. Although T-wave alternans has been linked to cardiac arrhythmias, non-alternans lability is observed in pre-clinical models of the long QT syndrome (LQTS) and CPVT, and in LQTS patients. Analysis of T wave lability may provide a real-time window on the abnormal Ca(2+) dynamics causing specific arrhythmias such as Torsade de Pointes (TdP).

Ryanodine receptor cluster fragmentation and redistribution in persistent atrial fibrillation enhance calcium release

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.

Nonlinear and Stochastic Dynamics in the Heart

In a normal human life span, the heart beats about 2 to 3 billion times. Under diseased conditions, a heart may lose its normal rhythm and degenerate suddenly into much faster and irregular rhythms, called arrhythmias, which may lead to sudden death. The transition from a normal rhythm to an arrhythmia is a transition from regular electrical wave conduction to irregular or turbulent wave conduction in the heart, and thus this medical problem is also a problem of physics and mathematics. In the last century, clinical, experimental, and theoretical studies have shown that dynamical theories play fundamental roles in understanding the mechanisms of the genesis of the normal heart rhythm as well as lethal arrhythmias. In this article, we summarize in detail the nonlinear and stochastic dynamics occurring in the heart and their links to normal cardiac functions and arrhythmias, providing a holistic view through integrating dynamics from the molecular (microscopic) scale, to the organelle (mesoscopic) scale, to the cellular, tissue, and organ (macroscopic) scales. We discuss what existing problems and challenges are waiting to be solved and how multi-scale mathematical modeling and nonlinear dynamics may be helpful for solving these problems.

The emergence of subcellular pacemaker sites for calcium waves and oscillations

Calcium (Ca(2+)) waves generating oscillatory Ca(2+) signals are widely observed in biological cells. Experimental studies have shown that under certain conditions, initiation of Ca(2+) waves is random in space and time, while under other conditions, waves occur repetitively from preferred locations (pacemaker sites) from which they entrain the whole cell. In this study, we use computer simulations to investigate the self-organization of Ca(2+) sparks into pacemaker sites generating Ca(2+) oscillations. In both ventricular myocyte experiments and computer simulations of a heterogeneous Ca(2+) release unit (CRU) network model, we show that Ca(2+) waves occur randomly in space and time when the Ca(2+) level is low, but as the Ca(2+) level increases, waves occur repetitively from the same sites. Our analysis indicates that this transition to entrainment can be attributed to the fact that random Ca(2+) sparks self-organize into Ca(2+) oscillations differently at low and high Ca(2+) levels. At low Ca(2+), the whole cell Ca(2+) oscillation frequency of the coupled CRU system is much slower than that of an isolated single CRU. Compared to a single CRU, the distribution of interspike intervals (ISIs) of the coupled CRU network exhibits a greater variation, and its ISI distribution is asymmetric with respect to the peak, exhibiting a fat tail. At high Ca(2+), however, the coupled CRU network has a faster frequency and lesser ISI variation compared to an individual CRU. The ISI distribution of the coupled network no longer exhibits a fat tail and is well-approximated by a Gaussian distribution. This same Ca(2+) oscillation behaviour can also be achieved by varying the number of ryanodine receptors per CRU or the distance between CRUs. Using these results, we develop a theory for the entrainment of random oscillators which provides a unified explanation for the experimental observations underlying the emergence of pacemaker sites and Ca(2+) oscillations.

The timing statistics of spontaneous calcium release in cardiac myocytes

A variety of cardiac arrhythmias are initiated by a focal excitation that disrupts the regular beating of the heart. In some cases it is known that these excitations are due to calcium (Ca) release from the sarcoplasmic reticulum (SR) via propagating subcellular Ca waves. However, it is not understood what are the physiological factors that determine the timing of these excitations at both the subcellular and tissue level. In this paper we apply analytic and numerical approaches to determine the timing statistics of spontaneous Ca release (SCR) in a simplified model of a cardiac myocyte. In particular, we compute the mean first passage time (MFPT) to SCR, in the case where SCR is initiated by spontaneous Ca sparks, and demonstrate that this quantity exhibits either an algebraic or exponential dependence on system parameters. Based on this analysis we identify the necessary requirements so that SCR occurs on a time scale comparable to the cardiac cycle. Finally, we study how SCR is synchronized across many cells in cardiac tissue, and identify a quantitative measure that determines the relative timing of SCR in an ensemble of cells. Using this approach we identify the physiological conditions so that cell-to-cell variations in the timing of SCR is small compared to the typical duration of an SCR event. We argue further that under these conditions inward currents due to SCR can summate and generate arrhythmogenic triggered excitations in cardiac tissue.

FKBP12.6 overexpression does not protect against remodelling after myocardial infarction

Reducing the open probability of the ryanodine receptor (RyR) has been proposed to have beneficial effects in heart failure. We investigated whether conditional FKBP12.6 overexpression at the time of myocardial infarction (MI) could improve cardiac remodelling and cell Ca(2+) handling. Wild-type (WT) mice and mice overexpressing FKBP12.6 (Tg) were studied on average 7.5 ± 0.2 weeks after MI and compared with sham-operated mice for in vivo, myocyte function and remodelling. At baseline, unloaded cell shortening in Tg was not different from WT. The [Ca(2+)](i) transient amplitude was similar, but sarcoplasmic reticulum (SR) Ca(2+) content was larger in Tg, suggesting reduced fractional release. Spontaneous spark frequency was similar despite the increased SR Ca(2+) content, consistent with a reduced RyR channel open probability in Tg. After MI, left ventricular dilatation and myocyte hypertrophy were present in both groups, but more pronounced in Tg. Cell shortening amplitude was unchanged with MI in WT, but increased with MI in Tg. The amplitude of the [Ca(2+)](i) transient was not affected by MI in either genotype, but time to peak was increased; this was most pronounced in Tg. The SR Ca(2+) content and Na(+)- Ca(2+) exchanger function were not affected by MI. Spontaneous spark frequency was increased significantly after MI in Tg, and larger than in WT (at 4 Hz, 2.6 ± 0.4 sparks (100 μm)(-1) s(-1) in Tg MI versus 1.6 ± 0.2 sparks (100 μm)(-1) s(-1) in WT MI; P < 0.05). We conclude that FKPB12.6 overexpression can effectively reduce RyR open probability with maintained cardiomyocyte contraction. However, this approach appears insufficient to prevent and reduce post-MI remodelling, indicating that additional pathways may need to be targeted.

Criticality in intracellular calcium signaling in cardiac myocytes

Calcium (Ca) is a ubiquitous second messenger that regulates many biological functions. The elementary events of local Ca signaling are Ca sparks, which occur randomly in time and space, and integrate to produce global signaling events such as intra- and intercellular Ca waves and whole-cell Ca oscillations. Despite extensive experimental characterization in many systems, the transition from local random to global synchronous events is still poorly understood. Here we show that criticality, a ubiquitous dynamical phenomenon in nature, is responsible for the transition from local to global Ca signaling. We demonstrate this first in a computational model of Ca signaling in a cardiac myocyte and then experimentally in mouse ventricular myocytes, complemented by a theoretical agent-based model to delineate the underlying dynamics. We show that the interaction between the Ca release units via Ca-induced Ca release causes self-organization of Ca spark clusters. When the coupling between Ca release units is weak, the cluster-size distribution is exponential. As the interactions become strong, the cluster-size distribution changes to a power-law distribution, which is characteristic of criticality in thermodynamic and complex nonlinear systems, and facilitates the formation and propagation of Ca waves and whole-cell Ca oscillations. Our findings illustrate how criticality is harnessed by a biological cell to regulate Ca signaling via self-organization of random subcellular events into cellular-scale oscillations, and provide a general theoretical framework for the transition from local Ca signaling to global Ca signaling in biological cells.

Calcium alternans in a couplon network model of ventricular myocytes: role of sarcoplasmic reticulum load

Intracellular calcium (Ca) alternans in cardiac myocytes have been shown in many experimental studies, and the mechanisms remain incompletely understood. We recently developed a "3R theory" that links Ca sparks to whole cell Ca alternans through three critical properties: randomness of Ca sparks; recruitment of a Ca spark by neighboring Ca sparks; and refractoriness of Ca release units. In this study, we used computer simulation of a physiologically detailed mathematical model of a ventricular myocyte couplon network to study how sarcoplasmic reticulum (SR) Ca load and other physiological parameters, such as ryanodine receptor sensitivity, SR uptake rate, Na-Ca exchange strength, and Ca buffer levels affect Ca alternans in the context of 3R theory. We developed a method to calculate the parameters used in the 3R theory (i.e., the primary spark rate and the recruitment rate) from the physiologically detailed Ca cycling model and paced the model periodically to elicit Ca alternans. We show that alternans only occurs for an intermediate range of the SR Ca load, and the underlying mechanism can be explained via its effects on the 3Rs. Furthermore, we show that altering the physiological parameters not only directly changes the 3Rs but also alters the SR Ca load, having an indirect effect on the 3Rs as well. Therefore, our present study links the SR Ca load and other physiological parameters to whole cell Ca alternans through the framework of the 3R theory, providing a general mechanistic understanding of Ca alternans in ventricular myocytes.

Effects of taurine-magnesium coordination compound on ionic channels in rat ventricular myocytes of arrhythmia induced by ouabain

Taurine-magnesium coordination compound (TMCC) has anti-arrhythmic effects. The aim of the present study was to explore the targets of the anti-arrhythmic effect of TMCC and the electrophysiological effects of TMCC on ouabain-induced arrhythmias in rat ventricular myocytes. Sodium current (I(Na)), L-type calcium current (I(ca, L)), and transient outward potassium current (I(to)) were measured and analyzed using whole-cell patch-clamp recording technique in normal rat cardiac myocytes and rat ventricular myocytes of arrhythmia induced by ouabain. In isolated ventricular myocytes, I(Na) and I(to) were blocked by TMCC (100, 200, 400 μM) in a concentration-dependent manner, and the effects of TMCC (400 μM) were equal to that of amiodarone. However, I (ca, L) was moderately increased by TMCC (400 μM) while significantly decreased by amiodarone. Ouabain (5 μM) significantly decreased sodium, L-type calcium, and transient outward potassium currents. TMCC (100 μM) relieved abnormal sodium currents induced by ouabain through facilitation of steady-state inactivation. TMCC (200 and 400 μM) relieved abnormal L-type calcium currents induced by ouabain through facilitation of steady-state activation and retardation of steady-state inactivation. TMCC failed to further inhibit abnormal transient outward potassium currents induced by ouabain. However, amiodarone inhibited the decreasing sodium, L-type calcium, and transient outward potassium currents further. These data suggest that I(Na), I(ca, L), and I(to) may be the targets of the antiarrhythmic effect of TMCC, which can antagonize ouabain-induced changes of ionic currents in rat ventricular myocytes.

Computational modeling and numerical methods for spatiotemporal calcium cycling in ventricular myocytes

Intracellular calcium (Ca) cycling dynamics in cardiac myocytes is regulated by a complex network of spatially distributed organelles, such as sarcoplasmic reticulum (SR), mitochondria, and myofibrils. In this study, we present a mathematical model of intracellular Ca cycling and numerical and computational methods for computer simulations. The model consists of a coupled Ca release unit (CRU) network, which includes a SR domain and a myoplasm domain. Each CRU contains 10 L-type Ca channels and 100 ryanodine receptor channels, with individual channels simulated stochastically using a variant of Gillespie’s method, modified here to handle time-dependent transition rates. Both the SR domain and the myoplasm domain in each CRU are modeled by 5 × 5 × 5 voxels to maintain proper Ca diffusion. Advanced numerical algorithms implemented on graphical processing units were used for fast computational simulations. For a myocyte containing 100 × 20 × 10 CRUs, a 1-s heart time simulation takes about 10 min of machine time on a single NVIDIA Tesla C2050. Examples of simulated Ca cycling dynamics, such as Ca sparks, Ca waves, and Ca alternans, are shown.

The statistics of calcium-mediated focal excitations on a one-dimensional cable

It is well known that various cardiac arrhythmias are initiated by an ill-timed excitation that originates from a focal region of the heart. However, up to now, it is not known what governs the timing, location, and morphology of these focal excitations. Recent studies have shown that these excitations can be caused by abnormalities in the calcium (Ca) cycling system. However, the cause-and-effect relationships linking subcellular Ca dynamics and focal activity in cardiac tissue is not completely understood. In this article, we present a minimal model of Ca-mediated focal excitations in cardiac tissue. This model accounts for the stochastic nature of spontaneous Ca release on a one-dimensional cable of cardiac cells. Using this model, we show that the timing of focal excitations is equivalent to a first passage time problem in a spatially extended system. In particular, we find that for a short cable the mean first passage time increases exponentially with the number of cells in tissue, and is critically dependent on the ratio of inward to outward currents near the threshold for an action potential. For long cables excitations occurs due to ectopic foci that occur on a length scale determined by the minimum length of tissue that can induce an action potential. Furthermore, we find that for long cables the mean first passage time decreases as a power law in the number cells. These results provide precise criteria for the occurrence of focal excitations in cardiac tissue, and will serve as a guide to determine the propensity of Ca-mediated triggered arrhythmias in the heart.

Exploring the parameter space of a rabbit ventricular action potential model to investigate the effect of variation on action potential and calcium transients

Computational models for cardiomyocyte action potentials (AP) often make use of a large parameter set. This parameter set can contain some elements that are fitted to experimental data independently of any other element, some elements that are derived concurrently with other elements to match experimental data, and some elements that are derived purely from phenomenological fitting to produce the desired AP output. Furthermore, models can make use of several different data sets, not always derived for the same conditions or even the same species. It is consequently uncertain whether the parameter set for a given model is physiologically accurate. Furthermore, it is only recently that the possibility of degeneracy in parameter values in producing a given simulation output has started to be addressed. In this study, we examine the effects of varying two parameters (the L-type calcium current (I(CaL)) and the delayed rectifier potassium current (I(Ks))) in a computational model of a rabbit ventricular cardiomyocyte AP on both the membrane potential (V(m)) and calcium (Ca(2+)) transient. It will subsequently be determined if there is degeneracy in this model to these parameter values, which will have important implications on the stability of these models to cell-to-cell parameter variation, and also whether the current methodology for generating parameter values is flawed. The accuracy of AP duration (APD) as an indicator of AP shape will also be assessed.

A mathematical model of spontaneous calcium release in cardiac myocytes

In cardiac myocytes, calcium (Ca) can be released from the sarcoplasmic reticulum independently of Ca influx from voltage-dependent membrane channels. This efflux of Ca, referred to as spontaneous Ca release (SCR), is due to Ryanodine receptor fluctuations, which can induce spontaneous Ca sparks, which propagate to form Ca waves. This release of Ca can then induce delayed after-depolarizations (DADs), which can lead to arrhythmogenic-triggered activity in the heart. However, despite its importance, to date there is no mathematical model of SCR that accounts for experimentally observed features of subcellular Ca. In this article, we present an experimentally based model of SCR that reproduces the timing distribution of spontaneous Ca sparks and key features of the propagation of Ca waves emanating from these spontaneous sparks. We have coupled this model to an ionic model for the rabbit ventricular action potential to simulate SCR within several thousand cells in cardiac tissue. We implement this model to study the formation of an ectopic beat on a cable of cells that exhibit SCR-induced DADs.

Alternans and arrhythmias: from cell to heart

The goal of systems biology is to relate events at the molecular level to more integrated scales from organelle to cell, tissue, and living organism. Here, we review how normal and abnormal excitation-contraction coupling properties emerge from the protein scale, where behaviors are dominated by randomness, to the cell and tissue scales, where heart has to beat with reliable regularity for a lifetime. Beginning with the fundamental unit of excitation-contraction coupling, the couplon where L-type Ca channels in the sarcolemmal membrane adjoin ryanodine receptors in the sarcoplasmic reticulum membrane, we show how a network of couplons with 3 basic properties (random activation, refractoriness, and recruitment) produces the classic physiological properties of excitation-contraction coupling and, under pathophysiological conditions, leads to Ca alternans and Ca waves. Moving to the tissue scale, we discuss how cellular Ca alternans and Ca waves promote both reentrant and focal arrhythmias in the heart. Throughout, we emphasize the qualitatively novel properties that emerge at each new scale of integration.

Automaticity in acute ischemia: bifurcation analysis of a human ventricular model

Acute ischemia (restriction in blood supply to part of the heart as a result of myocardial infarction) induces major changes in the electrophysiological properties of the ventricular tissue. Extracellular potassium concentration ([K(o)(+)]) increases in the ischemic zone, leading to an elevation of the resting membrane potential that creates an "injury current" (I(S)) between the infarcted and the healthy zone. In addition, the lack of oxygen impairs the metabolic activity of the myocytes and decreases ATP production, thereby affecting ATP-sensitive potassium channels (I(Katp)). Frequent complications of myocardial infarction are tachycardia, fibrillation, and sudden cardiac death, but the mechanisms underlying their initiation are still debated. One hypothesis is that these arrhythmias may be triggered by abnormal automaticity. We investigated the effect of ischemia on myocyte automaticity by performing a comprehensive bifurcation analysis (fixed points, cycles, and their stability) of a human ventricular myocyte model [K. H. W. J. ten Tusscher and A. V. Panfilov, Am. J. Physiol. Heart Circ. Physiol. 291, H1088 (2006)] as a function of three ischemia-relevant parameters [K(o)(+)], I(S), and I(Katp). In this single-cell model, we found that automatic activity was possible only in the presence of an injury current. Changes in [K(o)(+)] and I(Katp) significantly altered the bifurcation structure of I(S), including the occurrence of early-after depolarization. The results provide a sound basis for studying higher-dimensional tissue structures representing an ischemic heart.

Variability in timing of spontaneous calcium release in the intact rat heart is determined by the time course of sarcoplasmic reticulum calcium load

BACKGROUND

Abnormalities in intracellular calcium (Ca) cycling during Ca overload can cause triggered activity because spontaneous calcium release (SCR) activates sufficient Ca-sensitive inward currents to induce delayed afterdepolarizations (DADs). However, little is known about the mechanisms relating SCR and triggered activity on the tissue scale.

METHODS AND RESULTS

Laser scanning confocal microscopy was used to measure the spatiotemporal properties of SCR within large myocyte populations in intact rat heart. Computer simulations were used to predict how these properties of SCR determine DAD magnitude. We measured the average and standard deviation of the latency distribution of SCR within a large population of myocytes in intact tissue. We found that as external [Ca] is increased, and with faster pacing rates, the average and SD of the latency distribution decreases substantially. This result demonstrates that the timing of SCR occurs with less variability as the sarcoplasmic reticulum (SR) Ca load is increased, causing more sites to release Ca within each cell. We then applied a mathematical model of subcellular Ca cycling to show that a decrease in SCR variability leads to a higher DAD amplitude and is dictated by the rate of SR Ca refilling following an action potential.

CONCLUSIONS

Our results demonstrate that the variability of the timing of SCR in a population of cells in tissue decreases with SR load and is dictated by the time course of the SR Ca content.

Simulation of the effect of rogue ryanodine receptors on a calcium wave in ventricular myocytes with heart failure

Calcium homeostasis is considered to be one of the most important factors for the contraction and relaxation of the heart muscle. However, under some pathological conditions, such as heart failure (HF), calcium homeostasis is disordered, and spontaneous waves may occur. In this study, we developed a mathematical model of formation and propagation of a calcium wave based upon a governing system of diffusion-reaction equations presented by Izu et al (2001 Biophys. J. 80 103-20) and integrated non-clustered or 'rogue' ryanodine receptors (rogue RyRs) into a two-dimensional (2D) model of ventricular myocytes isolated from failing hearts in which sarcoplasmic reticulum (SR) Ca(2+) pools are partially unloaded. The model was then used to simulate the effect of rogue RyRs on initiation and propagation of the calcium wave in ventricular myocytes with HF. Our simulation results show that rogue RyRs can amplify the diastolic SR Ca(2+) leak in the form of Ca(2+) quarks, increase the probability of occurrence of spontaneous Ca(2+) waves even with smaller SR Ca(2+) stores, accelerate Ca(2+) wave propagation, and hence lead to delayed afterdepolarizations (DADs) and cardiac arrhythmia in the diseased heart. This investigation suggests that incorporating rogue RyRs in the Ca(2+) wave model under HF conditions provides a new view of Ca(2+) dynamics that could not be mimicked by adjusting traditional parameters involved in Ca(2+) release units and other ion channels, and contributes to understanding the underlying mechanism of HF.

Ryanodine receptor mutations in arrhythmia: The continuing mystery of channel dysfunction

Mutations in RyR2 are causative of an inherited disorder which often results in sudden cardiac death. Dysfunctional channel behaviour has been the subject of many investigations varying from single channel analysis through to complex animal models. This review discusses recent advances in the field, describes the controversy surrounding the exact consequences of RyR2 mutation and how the disparate data may be reconciled. This heterogeneity of function with respect to the effects of polymorphisms, phosphorylation, cytosolic and luminal Ca(2+) as well as inter-domain interactions may have important implications for the recent pharmaceutical therapies which have been put forward. We surmise that a comprehensive characterisation of mutations on a case-by-case basis may be beneficial for the development of specifically targeted therapies.