Local control models of cardiac excitation-contraction coupling. A possible role for allosteric interactions between ryanodine receptors

Formation and regulation of calcium sparks on a nonlinear spatial network of ryanodine receptors

Accurate regulation of calcium release is essential for cellular signaling, with the spatial distribution of ryanodine receptors (RyRs) playing a critical role. In this study, we present a nonlinear spatial network model that simulates RyR spatial organization to investigate calcium release dynamics by integrating RyR behavior, calcium buffering, and calsequestrin (CSQ) regulation. The model successfully reproduces calcium sparks, shedding light on their initiation, duration, and termination mechanisms under clamped calcium conditions. Our simulations demonstrate that RyR clusters act as on-off switches for calcium release, producing short-lived calcium quarks and longer-lasting calcium sparks based on distinct activation patterns. Spark termination is governed by calcium gradients and stochastic RyR dynamics, with CSQ facilitating RyR closure and spark termination. We also uncover the dual role of CSQ as both a calcium buffer and a regulator of RyRs. Elevated CSQ levels prolong calcium release due to buffering effects, while CSQ-RyR interactions induce excessive refractoriness, a phenomenon linked to pathological conditions such as ventricular arrhythmias. Dysregulated CSQ function disrupts the on-off switching behavior of RyRs, impairing calcium release dynamics. These findings provide new insights into RyR-mediated calcium signaling, highlighting CSQ's pivotal role in maintaining calcium homeostasis and its implications for pathological conditions. This work advances the understanding of calcium spark regulation and underscores its significance for cardiomyocyte function.

Gain-of-Function and Loss-of-Function Mutations in the RyR2-Expressing Gene Are Responsible for the CPVT1-Related Arrhythmogenic Activities in the Heart

Mutations in the ryanodine receptor (RyR2) gene have been linked to arrhythmia and possibly sudden cardiac death (SCD) during acute emotional stress, physical activities, or catecholamine perfusion. The most prevalent disorder is catecholaminergic polymorphic ventricular tachycardia (CPVT1). Four primary mechanisms have been proposed to describe CPVT1 with a RyR2 mutation: (a) gain-of-function, (b) destabilization of binding proteins, (c) store-overload-induced Ca2+ release (SOICR), and (d) loss of function. The goal of this study was to use computational models to understand these four mechanisms and how they might contribute to arrhythmia. To this end, we have developed a local control stochastic model of a ventricular cardiac myocyte and used it to investigate how the Ca2+ dynamics in the mutant RyR2 are responsible for the development of an arrhythmogenic episode under the condition of β-adrenergic (β-AR) stimulation or pauses afterward. Into the model, we have incorporated 20,000 distinct cardiac dyads consisting of stochastically gated L-type Ca2+ channels (LCCs) and ryanodine receptors (RyR2s) and the intervening dyadic cleft to analyze the alterations in Ca2+ dynamics. Recent experimental findings were incorporated into the model parameters to test these proposed mechanisms and their role in triggering arrhythmias. The model could not find any connection between SOICR and the destabilization of binding proteins as the arrhythmic mechanisms in the mutant myocyte. On the other hand, the model was able to observe loss-of-function and gain-of-function mutations resulting in EADs (Early Afterdepolarizations) and variations in action potential amplitudes and durations as the precursors to generate arrhythmia, respectively. These computational studies demonstrate how GOF and LOF mutations can lead to arrhythmia and cast doubt on the feasibility of SOICR as a mechanism of arrhythmia.

Electrophysical cardiac remodeling at the molecular level: Insights into ryanodine receptor activation and calcium-induced calcium release from a stochastic explicit-particle model

We present the first-ever, fully discrete, stochastic model of triggered cardiac Ca2+ dynamics. Using anatomically accurate subcellular cardiac myocyte geometries, we simulate the molecular players involved in Ca2+ handling using high-resolution stochastic and explicit-particle methods at the level of an individual cardiac dyadic junction. Integrating data from multiple experimental sources, the model not only replicates the findings of traditional in silico studies and complements in vitro experimental data but also reveals new insights into the molecular mechanisms driving cardiac dysfunction under stress and disease conditions. We improve upon older, nondiscrete models using the same realistic geometry by incorporating molecular mechanisms for spontaneous, as well as triggered calcium-induced calcium release (CICR). Action potentials are used to activate L-type calcium channels (LTCC), triggering CICR through ryanodine receptors (RyRs) on the surface of the sarcoplasmic reticulum. These improvements allow for the specific focus on the couplon: the structure-function relationship between LTCC and RyR. We investigate the electrophysical effects of normal and diseased action potentials on CICR and interrogate the effects of dyadic junction deformation through detubulation and orphaning of RyR. Our work demonstrates the importance of the electrophysical integrity of the calcium release unit on CICR fidelity, giving insights into the molecular basis of heart disease. Finally, we provide a unique, detailed, molecular view of the CICR process using advanced rendering techniques. This easy-to-use model comes complete with tutorials and the necessary software for use and analysis to maximize usability and reproducibility. Our work focuses on quantifying, qualifying, and visualizing the behavior of the molecular species that underlie the function and dysfunction of subcellular cardiomyocyte systems.

Loss-of-function W4645R mutation in the RyR2-caffeine binding site: implications for synchrony and arrhythmogenesis

AIMS

Previous studies have identified RyR2 W4645R mutation, located in the caffeine-binding site, to associate with CPVT1 pathology. Caffeine binding to its site is thought to displace the carboxyl-terminal domain to Ca2+-binding, allowing the tryptophan residue (W4645) to regulate Ca2+ sensitivity of RyR2. To gain insights into regulation of RyR2 Ca2+-binding and its interaction with caffeine-binding site, we introduced W4645R-RyR2 point mutation via CRISPR/Cas9 gene-editing in human induced pluripotent stem cell-derived cardiomyocytes (hiPSCCMs) and characterized their Ca2+-signaling phenotype compared to WT hiPSCCMs.

METHODS AND RESULTS

W4645R-RyR2 cardiomyocytes had: (1) no significant change in ICa magnitude or voltage-dependence; (2) slightly reduced CICR; (3) altered relaxation kinetics of Ca2+-transients with no change in isoproterenol sensitivity; (4) complete loss of caffeine-triggered Ca2+ release; (5) larger SR Ca2+ leak resulting in 40 % lower SR Ca2+ content, as determined by myocytes' response to 4-CmC; (6) lower incidence of calcium sparks and asynchronous spontaneous SR Ca2+ releases.

CONCLUSIONS

W4645R-RyR2 mutation induces loss of caffeine-triggered SR Ca2+ release and enhances SR Ca2+ leak that underlie asynchronous spontaneous Ca2+ releases, triggering arrhythmia and impairing cardiac function.

A detailed mathematical model of the human atrial cardiomyocyte: integration of electrophysiology and cardiomechanics

Mechano-electric regulations (MER) play an important role in the maintenance of cardiac performance. Mechano-calcium and mechano-electric feedback (MCF and MEF) pathways adjust the cardiomyocyte contractile force according to mechanical perturbations and affects electro-mechanical coupling. MER integrates all these regulations in one unit resulting in a complex phenomenon. Computational modelling is a useful tool to accelerate the mechanistic understanding of complex experimental phenomena. We have developed a novel model that integrates the MER loop for human atrial cardiomyocytes with proper consideration of feedforward and feedback pathways. The model couples a modified version of the action potential (AP) Koivumäki model with the contraction model by Quarteroni group. The model simulates iso-sarcometric and isometric twitches and the feedback effects on AP and Ca2+-handling. The model showed a biphasic response of Ca2+ transient (CaT) peak to increasing pacing rates and highlights the possible mechanisms involved. The model has shown a shift of the threshold for AP and CaT alternans from 4.6 to 4 Hz under post-operative atrial fibrillation, induced by depressed SERCA activity. The alternans incidence was dependent on a chain of mechanisms including RyRs availability time, MCF coupling, CaMKII phosphorylation, and the stretch levels. As a result, the model predicted a 10% slowdown of conduction velocity for a 20% stretch, suggesting a role of stretch in creation of substrate formation for atrial fibrillation. Overall, we conclude that the developed model provides a physiological CaT followed by a physiological twitch. This model can open pathways for the future studies of human atrial electromechanics. KEY POINTS: With the availability of human atrial cellular data, interest in atrial-specific model integration has been enhanced. We have developed a detailed mathematical model of human atrial cardiomyocytes including the mechano-electric regulatory loop. The model has gone through calibration and evaluation phases against a wide collection of available human in-vitro data. The usefulness of the model for analysing clinical problems has been preliminaryly tested by simulating the increased incidence of Ca2+ transient and action potential alternans at high rates in post-operative atrial fibrillation condition. The model determines the possible role of mechano-electric feedback in alternans incidence, which can increase vulnerability to atrial arrhythmias by varying stretch levels. We found that our physiologically accurate description of Ca2+ handling can reproduce many experimental phenomena and can help to gain insights into the underlying pathophysiological mechanisms.

Ptpn23 Controls Cardiac T-Tubule Patterning by Promoting the Assembly of Dystrophin-Glycoprotein Complex

BACKGROUND

Cardiac transverse tubules (T-tubules) are anchored to sarcomeric Z-discs by costameres to establish a regular spaced pattern. One of the major components of costameres is the dystrophin-glycoprotein complex (DGC). Nevertheless, how the assembly of the DGC coordinates with the formation and maintenance of T-tubules under physiological and pathological conditions remains unclear.

METHODS

Given the known role of Ptpn23 (protein tyrosine phosphatase, nonreceptor type 23) in regulating membrane deformation, its expression in patients with dilated cardiomyopathy was determined. Taking advantage of Cre/Loxp, CRISPR/Cas9, and adeno-associated virus 9 (AAV9)-mediated in vivo gene editing, we generated cardiomyocyte-specific Ptpn23 and Actn2 (α-actinin-2, a major component of Z-discs) knockout mice. We also perturbed the DGC by using dystrophin global knockout mice (DmdE4*). MM 4-64 and Di-8-ANEPPS staining, Cav3 immunofluorescence, and transmission electron microscopy were performed to determine T-tubule structure in isolated cells and intact hearts. In addition, the assembly of the DGC with Ptpn23 and dystrophin loss of function was determined by glycerol-gradient fractionation and SDS-PAGE analysis.

RESULTS

The expression level of Ptpn23 was reduced in failing hearts from dilated cardiomyopathy patients and mice. Genetic deletion of Ptpn23 resulted in disorganized T-tubules with enlarged diameters and progressive dilated cardiomyopathy without affecting sarcomere organization. AAV9-mediated mosaic somatic mutagenesis further indicated a cell-autonomous role of Ptpn23 in regulating T-tubule formation. Genetic and biochemical analyses showed that Ptpn23 was essential for the integrity of costameres, which anchor the T-tubule membrane to Z-discs, through interactions with α-actinin and dystrophin. Deletion of α-actinin altered the subcellular localization of Ptpn23 and DGCs. In addition, genetic inactivation of dystrophin caused similar T-tubule defects to Ptpn23 loss-of-function without affecting Ptpn23 localization at Z-discs. Last, inducible Ptpn23 knockout at 1 month of age showed Ptpn23 is also required for the maintenance of T-tubules in adult cardiomyocytes.

CONCLUSIONS

Ptpn23 is essential for cardiac T-tubule formation and maintenance along Z-discs. During postnatal heart development, Ptpn23 interacts with sarcomeric α-actinin and coordinates the assembly of the DGC at costameres to sculpt T-tubule spatial patterning and morphology.

Mathematical modeling of cardio-oncology: Modeling the systemic effects of cancer therapeutics on the cardiovascular system

Cardiotoxicity is a common side-effect of many cancer therapeutics; however, to-date there has been very little push to understand the mechanisms underlying this group of pathologies. This has led to the emergence of cardio-oncology, a field of medicine focused on understanding the effects of cancer and its treatment on the human heart. Here, we describe how mechanistic modeling approaches have been applied to study open questions in the cardiovascular system and how these approaches are being increasingly applied to advance knowledge of the underlying effects of cancer treatments on the human heart. A variety of mechanistic, mathematical modeling techniques have been applied to explore the link between common cancer treatments, such as chemotherapy, radiation, targeted therapy, and immunotherapy, and cardiotoxicity, nevertheless there is limited coverage in the different types of cardiac dysfunction that may be associated with these treatments. Moreover, cardiac modeling has a rich heritage of mathematical modeling and is well suited for the further development of novel approaches for understanding the cardiotoxicities associated with cancer therapeutics. There are many opportunities to combine mechanistic, bottom-up approaches with data-driven, top-down approaches to improve personalized, precision oncology to better understand, and ultimately mitigate, cardiac dysfunction in cancer patients.

Clustering properties of the cardiac ryanodine receptor in health and heart failure

The cardiac ryanodine receptor (RyR2) is an intracellular Ca2+ release channel vital for the function of the heart. Physiologically, RyR2 is triggered to release Ca2+ from the sarcoplasmic reticulum (SR) which enables cardiac contraction; however, spontaneous Ca2+ leak from RyR2 has been implicated in the pathophysiology of heart failure (HF). RyR2 channels have been well documented to assemble into clusters within the SR membrane, with the organisation of RyR2 clusters recently gaining interest as a mechanism by which the occurrence of pathological Ca2+ leak is regulated, including in HF. In this review, we explain the terminology relating to key nanoscale RyR2 clustering properties as both single clusters and functionally grouped Ca2+ release units, with a focus on the advancements in super-resolution imaging approaches which have enabled the detailed study of cluster organisation. Further, we discuss proposed mechanisms for modulating RyR2 channel organisation and the debate regarding the potential impact of cluster organisation on Ca2+ leak activity. Finally, recent experimental evidence investigating the nanoscale remodelling and functional alterations of RyR2 clusters in HF is discussed with consideration of the clinical implications.

Spine apparatus modulates Ca 2+ in spines through spatial localization of sources and sinks

Dendritic spines are small protrusions on dendrites in neurons and serve as sites of postsynaptic activity. Some of these spines contain smooth endoplasmic reticulum (SER), and sometimes an even further specialized SER known as the spine apparatus (SA). In this work, we developed a stochastic spatial model to investigate the role of the SER and the SA in modulating Ca 2+ dynamics. Using this model, we investigated how ryanodine receptor (RyR) localization, spine membrane geometry, and SER geometry can impact Ca 2+ transients in the spine and in the dendrite. Our simulations found that RyR opening is dependent on where it is localized in the SER and on the SER geometry. In order to maximize Ca 2+ in the dendrites (for activating clusters of spines and spine-spine communication), a laminar SA was favorable with RyRs localized in the neck region, closer to the dendrite. We also found that the presence of the SER without the laminar structure, coupled with RyR localization at the head, leads to higher Ca 2+ presence in the spine. These predictions serve as design principles for understanding how spines with an ER can regulate Ca 2+ dynamics differently from spines without ER through a combination of geometry and receptor localization.

Highlights

1RyR opening in dendritic spine ER is location dependent and spine geometry dependent. Ca 2+ buffers and SERCA can buffer against runaway potentiation of spines even when CICR is activated. RyRs located towards the ER neck allow for more Ca 2+ to reach the dendrites. RyRs located towards the spine head are favorable for increased Ca 2+ in spines.

The role of subunit cooperativity on ryanodine receptor 2 calcium signaling

The ryanodine receptor type 2 (RyR2) is composed of four subunits that control calcium (Ca) release in cardiac cells. RyR2 serves primarily as a Ca sensor and can respond to rapid sub-millisecond pulses of Ca while remaining shut at resting concentrations. However, it is not known how the four subunits interact for the RyR2 to function as an effective Ca sensor. To address this question, and to understand the role of subunit cooperativity in Ca-mediated signal transduction, we have developed a computational model of the RyR2 composed of four interacting subunits. We first analyze the statistical properties of a single RyR2 tetramer, where each subunit can exist in a closed or open conformation. Our findings indicate that the number of subunits in the open state is a crucial parameter that dictates RyR2 kinetics. We find that three or four open subunits are required for the RyR2 to harness cooperative interactions to respond to sub-millisecond changes in Ca, while at the same time remaining shut at the resting Ca levels in the cardiac cell. If the required number of open subunits is lowered to one or two, the RyR2 cannot serve as a robust Ca sensor, as the large cooperativity required to stabilize the closed state prevents channel activation. Using this four-subunit model, we analyze the kinetics of Ca release from a RyR2 cluster. We show that the closure of a cluster of RyR2 channels is highly sensitive to the balance of cooperative interactions between closed and open subunits. Based on this result, we analyze how specific interactions between RyR2 subunits can induce persistent Ca leak from the sarcoplasmic reticulum (SR), which is believed to be arrhythmogenic. Thus, these results provide a framework to analyze how a pharmacologic or genetic modification of RyR2 subunit cooperativity can induce abnormal Ca cycling that can potentially lead to life-threatening arrhythmias.

The 'Reverse FDUF' Mechanism of Atrial Excitation-Contraction Coupling Sustains Calcium Alternans-A Hypothesis

Cardiac calcium alternans is defined as beat-to-beat alternations of Ca transient (CaT) amplitude and has been linked to cardiac arrhythmia, including atrial fibrillation. We investigated the mechanism of atrial alternans in isolated rabbit atrial myocytes using high-resolution line scan confocal Ca imaging. Alternans was induced by increasing the pacing frequency until stable alternans was observed (1.6-2.5 Hz at room temperature). In atrial myocytes, action potential-induced Ca release is initiated in the cell periphery and subsequently propagates towards the cell center by Ca-induced Ca release (CICR) in a Ca wave-like fashion, driven by the newly identified 'fire-diffuse-uptake-fire' (FDUF) mechanism. The development of CaT alternans was accompanied by characteristic changes of the spatio-temporal organization of the CaT. During the later phase of the CaT, central [Ca]_i exceeded peripheral [Ca]_i that was indicative of a reversal of the subcellular [Ca]_i gradient from centripetal to centrifugal. This gradient reversal resulted in a reversal of CICR propagation, causing a secondary Ca release during the large-amplitude alternans CaT, thereby prolonging the CaT, enhancing Ca-release refractoriness and reducing Ca release on the subsequent beat, thus enhancing the degree of CaT alternans. Here, we propose the 'reverse FDUF' mechanism as a novel cellular mechanism of atrial CaT alternans, which explains how the uncoupling of central from peripheral Ca release leads to the reversal of propagating CICR and to alternans.

The spatio-temporal properties of calcium transients in hippocampal pyramidal neurons in vitro

The spatio-temporal properties of calcium signals were studied in cultured pyramidal neurons of the hippocampus using two-dimensional fluorescence microscopy and ratiometric dye Fura-2. Depolarization-induced Ca²⁺ transients revealed an asynchronous delayed increase in free Ca²⁺ concentration. We found that the level of free resting calcium in the cell nucleus is significantly lower compared to the soma, sub-membrane, and dendritic tree regions. Calcium release from the endoplasmic reticulum under the action of several stimuli (field stimulation, high K⁺ levels, and caffeine) occurs in all areas studied. Under depolarization, calcium signals developed faster in the dendrites than in other areas, while their amplitude was significantly lower since larger and slower responses inside the soma. The peak value of the calcium response to the application of 10 mM caffeine, ryanodine receptors (RyRs) agonist, does not differ in the sub-membrane zone, central region, and nucleus but significantly decreases in the dendrites. In the presence of caffeine, the delay of Ca²⁺ signals between various areas under depolarization significantly declined. Thirty percentage of the peak amplitude of Ca²⁺ transients at prolonged electric field stimulation corresponded to calcium release from the ER store by RyRs, while short-term stimulation did not depend on them. 20 μM dantrolene, RyRs inhibitor, significantly reduces Ca²⁺ transient under high K⁺ levels depolarization of the neuron. RyRs-mediated enhancement of the Ca²⁺ signal is more pronounced in the central part and nucleus compared to the sub-membrane or dendrites regions of the neuron. In summary, using the ratiometric imaging allowed us to obtain additional information about the involvement of RyRs in the intracellular dynamics of Ca²⁺ signals induced by depolarization or electrical stimulation train, with an underlying change in Ca²⁺ concentration in various regions of interest in hippocampal pyramidal neurons.

Adenosine reduces sinoatrial node cell action potential firing rate by uncoupling its membrane and calcium clocks

The spontaneous action potential (AP) firing rate of sinoatrial nodal cells (SANC) is regulated by a system of intracellular Ca²⁺ and membrane ion current clocks driven by Ca²⁺-calmodulin-activated adenylyl cyclase-protein kinase-A signaling. The mean AP-cycle length (APCL) and APCL variability inform on the effectiveness of clock coupling. Endogenous ATP metabolite adenosine binds to adenosine receptors (A₁, A₃) that couple to G_i protein-coupled receptors, reducing spontaneous AP firing rate via G_βγ signaling that activates I_KAch,Ado. Adenosine also inhibits adenylyl cyclase activity via G_αi signaling, impacting cAMP-mediated protein kinase-A-dependent protein phosphorylation. We hypothesize that in addition to I_KAch,Ado activation, adenosine impacts also Ca²⁺ via G_αi signaling and that both effects reduce AP firing rate by reducing the effectiveness of the Ca²⁺ and membrane clock coupling. To this end, we measured Ca²⁺ and membrane potential characteristics in enzymatically isolated single rabbit SANC. 10 µM adenosine substantially increased both the mean APCL (on average by 43%, n = 10) and AP beat-to-beat variability from 5.1 ± 1.7% to 7.2 ± 2.0% (n = 10) measured via membrane potential and 5.0 ± 2.2% to 10.6 ± 5.9% (n = 40) measured via Ca²⁺ (assessed as the coefficient of variability = SD/mean). These effects were mediated by hyperpolarization of the maximum diastolic membrane potential (membrane clock effect) and suppression of diastolic local Ca²⁺releases (LCRs) (Ca²⁺-clock effect): as LCR size distributions shifted to smaller values, the time of LCR occurrence during diastolic depolarization (LCR period) became prolonged, and the ensemble LCR signal became reduced. The tight linear relationship of coupling between LCR period to the APCL in the presence of adenosine "drifted" upward and leftward, i.e. for a given LCR period, APCL was prolonged, becoming non-linear indicating clock uncoupling. An extreme case of uncoupling occurred at higher adenosine concentrations (>100 µM): small stochastic LCRs failed to self-organize and synchronize to the membrane clock, thus creating a failed attempt to generate an AP resulting in arrhythmia and cessation of AP firing. Thus, the effects of adenosine to activate G_βγ and I_KACh,Ado and to activate G_αi, suppressing adenylyl cyclase activity, both contribute to the adenosine-induced increase in the mean APCL and APCL variability by reducing the fidelity of clock coupling and AP firing rate.

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.

How does flecainide impact RyR2 channel function?

Flecainide, a cardiac class 1C blocker of the surface membrane sodium channel (NaV1.5), has also been reported to reduce cardiac ryanodine receptor (RyR2)-mediated sarcoplasmic reticulum (SR) Ca2+ release. It has been introduced as a clinical antiarrhythmic agent for catecholaminergic polymorphic ventricular tachycardia (CPVT), a condition most commonly associated with gain-of-function RyR2 mutations. Current debate concerns both cellular mechanisms of its antiarrhythmic action and molecular mechanisms of its RyR2 actions. At the cellular level, it targets NaV1.5, RyR2, Na+/Ca2+ exchange (NCX), and additional proteins involved in excitation-contraction (EC) coupling and potentially contribute to the CPVT phenotype. This Viewpoint primarily addresses the various direct molecular actions of flecainide on isolated RyR2 channels in artificial lipid bilayers. Such studies demonstrate different, multifarious, flecainide binding sites on RyR2, with voltage-dependent binding in the channel pore or voltage-independent binding at distant peripheral sites. In contrast to its single NaV1.5 pore binding site, flecainide may bind to at least four separate inhibitory sites on RyR2 and one activation site. None of these binding sites have been specifically located in the linear RyR2 sequence or high-resolution structure. Furthermore, it is not clear which of the inhibitory sites contribute to flecainide's reduction of spontaneous Ca2+ release in cellular studies. A confounding observation is that flecainide binding to voltage-dependent inhibition sites reduces cation fluxes in a direction opposite to physiological Ca2+ flow from SR lumen to cytosol. This may suggest that, rather than directly blocking Ca2+ efflux, flecainide can reduce Ca2+ efflux by blocking counter currents through the pore which otherwise limit SR membrane potential change during systolic Ca2+ efflux. In summary, the antiarrhythmic effects of flecainide in CPVT seem to involve multiple components of EC coupling and multiple actions on RyR2. Their clarification may identify novel specific drug targets and facilitate flecainide's clinical utilization in CPVT.

Critical Requirements for the Initiation of a Cardiac Arrhythmia in Rat Ventricle: How Many Myocytes?

Cardiovascular disease is the leading cause of death worldwide due in a large part to arrhythmia. In order to understand how calcium dynamics play a role in arrhythmogenesis, normal and dysfunctional Ca²⁺ signaling in a subcellular, cellular, and tissued level is examined using cardiac ventricular myocytes at a high temporal and spatial resolution using multiscale computational modeling. Ca²⁺ sparks underlie normal excitation-contraction coupling. However, under pathological conditions, Ca²⁺ sparks can combine to form Ca²⁺ waves. These propagating elevations of (Ca²⁺)_i can activate an inward Na⁺-Ca²⁺ exchanger current (I_NCX) that contributes to early after-depolarization (EADs) and delayed after-depolarizations (DADs). However, how cellular currents lead to full depolarization of the myocardium and how they initiate extra systoles is still not fully understood. This study explores how many myocytes must be entrained to initiate arrhythmogenic depolarizations in biophysically detailed computational models. The model presented here suggests that only a small number of myocytes must activate in order to trigger an arrhythmogenic propagating action potential. These conditions were examined in 1-D, 2-D, and 3-D considering heart geometry. The depolarization of only a few hundred ventricular myocytes is required to trigger an ectopic depolarization. The number decreases under disease conditions such as heart failure. Furthermore, in geometrically restricted parts of the heart such as the thin muscle strands found in the trabeculae and papillary muscle, the number of cells needed to trigger a propagating depolarization falls even further to less than ten myocytes.

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.

Ion Channel Partnerships: Odd and Not-So-Odd Couples Controlling Neuronal Ion Channel Function

The concerted function of the large number of ion channels expressed in excitable cells, including brain neurons, shapes diverse signaling events by controlling the electrical properties of membranes. It has long been recognized that specific groups of ion channels are functionally coupled in mediating ionic fluxes that impact membrane potential, and that these changes in membrane potential impact ion channel gating. Recent studies have identified distinct sets of ion channels that can also physically and functionally associate to regulate the function of either ion channel partner beyond that afforded by changes in membrane potential alone. Here, we review canonical examples of such ion channel partnerships, in which a Ca²⁺ channel is partnered with a Ca²⁺-activated K⁺ channel to provide a dedicated route for efficient coupling of Ca²⁺ influx to K⁺ channel activation. We also highlight examples of non-canonical ion channel partnerships between Ca²⁺ channels and voltage-gated K⁺ channels that are not intrinsically Ca²⁺ sensitive, but whose partnership nonetheless yields enhanced regulation of one or the other ion channel partner. We also discuss how these ion channel partnerships can be shaped by the subcellular compartments in which they are found and provide perspectives on how recent advances in techniques to identify proteins in close proximity to one another in native cells may lead to an expanded knowledge of other ion channel partnerships.

Mutation in RyR2-FKBP Binding site alters Ca2+ signaling modestly but increases "arrhythmogenesis" in human stem cells derived cardiomyocytes

AIMS

To gain insights into FKBP regulation of cardiac ryanodine receptor (RyR2) and Ca²⁺ signaling, we introduced the point mutation (N771D-RyR2) corresponding to skeletal muscle mutation (N760D-RyR1) associated with central core disease (CCD) via CRISPR/Cas9 gene-editing in the RyR2 FKBP binding site expressed in human induced pluripotent stem cell-derived cardiomyocytes (hiPSCCMs). Patients inflicted with CCD and other hereditary skeletal muscle diseases often show higher incidence of atrial or ventricular arrhythmias.

METHODS AND RESULTS

Ca²⁺ imaging of voltage-clamped N771D-RyR2 mutant compared to WT hiPSCCMs showed: (1) ∼30% suppressed I_Ca with no significant changes in the gating kinetics of I_Ca; (2) 29% lower SR Ca²⁺ content and 33% lower RyR2 Ca²⁺ leak; (3) higher CICR gain and 30-35% increased efficiency of I_Ca-triggered Ca^2±release; (4) higher incidence of aberrant SR Ca²⁺ releases, DADs, and Ca²⁺ sparks; (5) no change in fractional Ca²⁺-release, action potential morphology, sensitivity to isoproterenol, and sarcomeric FKBP-binding pattern.

CONCLUSIONS

The more frequent spontaneous Ca²⁺ releases and longer Ca²⁺ sparks underlie the increased incidence of DADs and cellular arrhythmogenesis of N771D-RyR2 mutant. The smaller RyR2 Ca^2±leak and SR content result from suppressed I_Cathat is compensated by higher CICR gain.

Calpain-2 specifically cleaves Junctophilin-2 at the same site as Calpain-1 but with less efficacy

Calpain proteolysis contributes to the pathogenesis of heart failure but the calpain isoforms responsible and their substrate specificities have not been rigorously defined. One substrate, Junctophilin-2 (JP2), is essential for maintaining junctional cardiac dyads and excitation-contraction coupling. We previously demonstrated that mouse JP2 is cleaved by calpain-1 (CAPN1) between Arginine 565 (R⁵⁶⁵) and Threonine 566 (T⁵⁶⁶). Recently, calpain-2 (CAPN2) was reported to cleave JP2 at a novel site between Glycine 482 (G⁴⁸²) and Threonine 483 (T⁴⁸³). We aimed to directly compare the contributions of each calpain isoform, their Ca²⁺ sensitivity, and their cleavage site selection for JP2. We find CAPN1, CAPN2 and their requisite CAPNS1 regulatory subunit are induced by pressure overload stress that is concurrent with JP2 cleavage. Using in vitro calpain cleavage assays, we demonstrate that CAPN1 and CAPN2 cleave JP2 into similar 75 kD N-terminal (JP2NT) and 25 kD C-terminal fragments (JP2CT) with CAPNS1 co-expression enhancing proteolysis. Deletion mutagenesis shows both CAPN1 and CAPN2 require R⁵⁶⁵/T⁵⁶⁶ but not G⁴⁸²/T⁴⁸³. When heterologously expressed, the JP2CT peptide corresponding to R⁵⁶⁵/T⁵⁶⁶ cleavage approximates the 25 kD species found during cardiac stress while the C-terminal peptide from potential cleavage at G⁴⁸²/T⁴⁸³ produces a 35 kD product. Similar results were obtained for human JP2. Finally, we show that CAPN1 has higher Ca²⁺ sensitivity and cleavage efficacy than CAPN2 on JP2 and other cardiac substrates including cTnT, cTnI and β2-spectrin. We conclude that CAPN2 cleaves JP2 at the same functionally conserved R⁵⁶⁵/T⁵⁶⁶ site as CAPN1 but with less efficacy and suggest heart failure may be targeted through specific inhibition of CAPN1.

Sensitivity Analysis of Ion Channel Conductance on Myocardial Electromechanical Delay: Computational Study

It is well known that cardiac electromechanical delay (EMD) can cause dyssynchronous heart failure (DHF), a prominent cardiovascular disease (CVD). This work computationally assesses the conductance variation of every ion channel on the cardiac cell to give rise to EMD prolongation. The electrical and mechanical models of human ventricular tissue were simulated, using a population approach with four conductance reductions for each ion channel. Then, EMD was calculated by determining the difference between the onset of action potential and the start of cell shortening. Finally, EMD data were put into the optimized conductance dimensional stacking to show which ion channel has the most influence in elongating the EMD. We found that major ion channels, such as L-type calcium (CaL), slow-delayed rectifier potassium (Ks), rapid-delayed rectifier potassium (Kr), and inward rectifier potassium (K1), can significantly extend the action potential duration (APD) up to 580 ms. Additionally, the maximum intracellular calcium (Cai) concentration is greatly affected by the reduction in channel CaL, Ks, background calcium, and Kr. However, among the aforementioned major ion channels, only the CaL channel can play a superior role in prolonging the EMD up to 83 ms. Furthermore, ventricular cells with long EMD have been shown to inherit insignificant mechanical response (in terms of how strong the tension can grow and how far length shortening can go) compared with that in normal cells. In conclusion, despite all variations in every ion channel conductance, only the CaL channel can play a significant role in extending EMD. In addition, cardiac cells with long EMD tend to have inferior mechanical responses due to a lack of Cai compared with normal conditions, which are highly likely to result in a compromised pump function of the heart.

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.

Excitation-contraction coupling and calcium release in atrial muscle

In cardiac muscle, the process of excitation-contraction coupling (ECC) describes the chain of events that links action potential induced myocyte membrane depolarization, surface membrane ion channel activation, triggering of Ca2+ induced Ca2+ release from the sarcoplasmic reticulum (SR) Ca2+ store to activation of the contractile machinery that is ultimately responsible for the pump function of the heart. Here we review similarities and differences of structural and functional attributes of ECC between atrial and ventricular tissue. We explore a novel "fire-diffuse-uptake-fire" paradigm of atrial ECC and Ca2+ release that assigns a novel role to the SR SERCA pump and involves a concerted "tandem" activation of the ryanodine receptor Ca2+ release channel by cytosolic and luminal Ca2+. We discuss the contribution of the inositol 1,4,5-trisphosphate (IP3) receptor Ca2+ release channel as an auxiliary pathway to Ca2+ signaling, and we review IP3 receptor-induced Ca2+ release involvement in beat-to-beat ECC, nuclear Ca2+ signaling, and arrhythmogenesis. Finally, we explore the topic of electromechanical and Ca2+ alternans and its ramifications for atrial arrhythmia.

In Silico Assessment of Class I Antiarrhythmic Drug Effects on Pitx2-Induced Atrial Fibrillation: Insights from Populations of Electrophysiological Models of Human Atrial Cells and Tissues

Electrical remodelling as a result of homeodomain transcription factor 2 (Pitx2)-dependent gene regulation was linked to atrial fibrillation (AF) and AF patients with single nucleotide polymorphisms at chromosome 4q25 responded favorably to class I antiarrhythmic drugs (AADs). The possible reasons behind this remain elusive. The purpose of this study was to assess the efficacy of the AADs disopyramide, quinidine, and propafenone on human atrial arrhythmias mediated by Pitx2-induced remodelling, from a single cell to the tissue level, using drug binding models with multi-channel pharmacology. Experimentally calibrated populations of human atrial action po-tential (AP) models in both sinus rhythm (SR) and Pitx2-induced AF conditions were constructed by using two distinct models to represent morphological subtypes of AP. Multi-channel pharmaco-logical effects of disopyramide, quinidine, and propafenone on ionic currents were considered. Simulated results showed that Pitx2-induced remodelling increased maximum upstroke velocity (dVdtmax), and decreased AP duration (APD), conduction velocity (CV), and wavelength (WL). At the concentrations tested in this study, these AADs decreased dVdtmax and CV and prolonged APD in the setting of Pitx2-induced AF. Our findings of alterations in WL indicated that disopyramide may be more effective against Pitx2-induced AF than propafenone and quinidine by prolonging WL.

Ca2+-CaM Dependent Inactivation of RyR2 Underlies Ca2+ Alternans in Intact Heart

RATIONALE

Ca²⁺ alternans plays an essential role in cardiac alternans that can lead to ventricular fibrillation, but the mechanism underlying Ca²⁺ alternans remains undefined. Increasing evidence suggests that Ca²⁺ alternans results from alternations in the inactivation of cardiac RyR2 (ryanodine receptor 2). However, what inactivates RyR2 and how RyR2 inactivation leads to Ca²⁺ alternans are unknown.

OBJECTIVE

To determine the role of CaM (calmodulin) on Ca²⁺ alternans in intact working mouse hearts.

METHODS AND RESULTS

We used an in vivo local gene delivery approach to alter CaM function by directly injecting adenoviruses expressing CaM-wild type, a loss-of-function CaM mutation, CaM (1-4), and a gain-of-function mutation, CaM-M37Q, into the anterior wall of the left ventricle of RyR2 wild type or mutant mouse hearts. We monitored Ca²⁺ transients in ventricular myocytes near the adenovirus-injection sites in Langendorff-perfused intact working hearts using confocal Ca²⁺ imaging. We found that CaM-wild type and CaM-M37Q promoted Ca²⁺ alternans and prolonged Ca²⁺ transient recovery in intact RyR2 wild type and mutant hearts, whereas CaM (1-4) exerted opposite effects. Altered CaM function also affected the recovery from inactivation of the L-type Ca²⁺ current but had no significant impact on sarcoplasmic reticulum Ca²⁺ content. Furthermore, we developed a novel numerical myocyte model of Ca²⁺ alternans that incorporates Ca²⁺-CaM-dependent regulation of RyR2 and the L-type Ca²⁺ channel. Remarkably, the new model recapitulates the impact on Ca²⁺ alternans of altered CaM and RyR2 functions under 9 different experimental conditions. Our simulations reveal that diastolic cytosolic Ca²⁺ elevation as a result of rapid pacing triggers Ca²⁺-CaM dependent inactivation of RyR2. The resultant RyR2 inactivation diminishes sarcoplasmic reticulum Ca²⁺ release, which, in turn, reduces diastolic cytosolic Ca²⁺, leading to alternations in diastolic cytosolic Ca²⁺, RyR2 inactivation, and sarcoplasmic reticulum Ca²⁺ release (ie, Ca²⁺ alternans).

CONCLUSIONS

Our results demonstrate that inactivation of RyR2 by Ca²⁺-CaM is a major determinant of Ca²⁺ alternans, making Ca²⁺-CaM dependent regulation of RyR2 an important therapeutic target for cardiac alternans.

The central domain of cardiac ryanodine receptor governs channel activation, regulation, and stability

Structural analyses identified the central domain of ryanodine receptor (RyR) as a transducer converting conformational changes in the cytoplasmic platform to the RyR gate. The central domain is also a regulatory hub encompassing the Ca²⁺-, ATP-, and caffeine-binding sites. However, the role of the central domain in RyR activation and regulation has yet to be defined. Here, we mutated five residues that form the Ca²⁺ activation site and 10 residues with negatively charged or oxygen-containing side chains near the Ca²⁺ activation site. We also generated eight disease-associated mutations within the central domain of RyR2. We determined the effect of these mutations on Ca²⁺, ATP, and caffeine activation and Mg²⁺ inhibition of RyR2. Mutating the Ca²⁺ activation site markedly reduced the sensitivity of RyR2 to Ca²⁺ and caffeine activation. Unexpectedly, Ca²⁺ activation site mutation E3848A substantially enhanced the Ca²⁺-independent basal activity of RyR2, suggesting that E3848A may also affect the stability of the closed state of RyR2. Mutations in the Ca²⁺ activation site also abolished the effect of ATP/caffeine on the Ca²⁺-independent basal activity, suggesting that the Ca²⁺ activation site is also a critical determinant of ATP/caffeine action. Mutating residues with negatively charged or oxygen-containing side chains near the Ca²⁺ activation site significantly altered Ca²⁺ and caffeine activation and reduced Mg²⁺ inhibition. Furthermore, disease-associated RyR2 mutations within the central domain significantly enhanced Ca²⁺ and caffeine activation and reduced Mg²⁺ inhibition. Our data demonstrate that the central domain plays an important role in channel activation, channel regulation, and closed state stability.

The architecture and function of cardiac dyads

Cardiac excitation-contraction (EC) coupling, which links plasma membrane depolarization to activation of cardiomyocyte contraction, occurs at dyads, the nanoscopic microdomains formed by apposition of transverse (T)-tubules and junctional sarcoplasmic reticulum (jSR). In a dyadic junction, EC coupling occurs through Ca2+-induced Ca2+ release. Membrane depolarization opens voltage-gated L-type Ca2+ channels (LTCCs) in the T-tubule. The resulting influx of extracellular Ca2+ into the dyadic cleft opens Ca2+ release channels known as ryanodine receptors (RYRs) in the jSR, leading to the rapid increase in cytosolic Ca2+ that triggers sarcomere contraction. The efficacy of LTCC-RYR communication greatly affects a myriad of downstream intracellular signaling events, and it is controlled by many factors, including T-tubule and jSR structure, spatial distribution of ion channels, and regulatory proteins that closely regulate the activities of channels within dyads. Alterations in dyad architecture and/or channel activity are seen in many types of heart disease. This review will focus on the current knowledge regarding cardiac dyad structure and function, their alterations in heart failure, and new approaches to study the composition and function of dyads.

Two-variable nullcline analysis of ionic general equilibrium predicts calcium homeostasis in ventricular myocytes

Ventricular contraction is roughly proportional to the amount of calcium released from the Sarcoplasmic Reticulum (SR) during systole. While it is rather straightforward to measure calcium levels and contractibility under different physiological conditions, the complexity of calcium handling during systole and diastole has made the prediction of its release at steady state impossible. Here we approach the problem analyzing the evolution of intracellular and extracellular calcium fluxes during a single beat which is away from homeostatic balance. Using an in-silico subcellular model of rabbit ventricular myocyte, we show that the high dimensional nonlinear problem of finding the steady state can be reduced to a two-variable general equilibrium condition where pre-systolic calcium level in the cytosol and in the SR must fulfill simultaneously two different equalities. This renders calcium homeostasis as a problem that can be studied in terms of its equilibrium structure, leading to precise predictions of steady state from single-beat measurements. We show how changes in ion channels modify the general equilibrium, as shocks would do in general equilibrium macroeconomic models. This allows us to predict when an enhanced entrance of calcium in the cell reduces its contractibility and explain why SERCA gene therapy, a change in calcium handling to treat heart failure, might fail to improve contraction even when it successfully increases SERCA expression.

Cardiomyocytes, upon voltage excitation, release calcium, which leads to cell contraction. However, under some pathological conditions, calcium handling is impaired. Recently, SERCA gene therapy, whose aim is to improve Ca²⁺ sequestration by the Sarcoplasmic Reticulum (SR), has failed to improve the prognosis of patients with Heart Failure. This, together with recent counterintuitive results in calcium handling, has highlighted the need for a framework to understand calcium homeostasis across species and pathologies. We show here that the proper framework is a general equilibrium approach of two independent variables. The development of this framework allows us to find a possible mechanism for the failure of SERCA gene therapy even when it manages to increase Ca SERCA expression.

Distinct mechanisms mediate pacemaker dysfunction associated with catecholaminergic polymorphic ventricular tachycardia mutations: Insights from computational modeling

Catecholaminergic polymorphic ventricular tachycardia (CPVT) is a stress-induced ventricular arrhythmia associated with rhythm disturbance and impaired sinoatrial node cell (SANC) automaticity (pauses). Mutations associated with dysfunction of Ca²⁺-related mechanisms have been shown to be present in CPVT. These dysfunctions include impaired Ca²⁺ release from the ryanodine receptor (i.e., RyR2^R4496C mutation) or binding to calsequestrin 2 (CASQ2). In SANC, Ca²⁺ signaling directly and indirectly mediates pacemaker function. We address here the following research questions: (i) what coupled-clock mechanisms and pathways mediate pacemaker mutations associated with CPVT in basal and in response to β-adrenergic stimulation? (ii) Can different mechanisms lead to the same CPVT-related pacemaker pauses? (iii) Can the mutation-induced deteriorations in SANC function be reversed by drug intervention or gene manipulation? We used a numerical model of mice SANC that includes membrane and intracellular mechanisms and their interconnected signaling pathways. In the basal state of RyR2^R4496C SANC, the model predicted that the Na⁺-Ca²⁺ exchanger current (I_NCX) and T-type Ca²⁺ current (I_CaT) mediate between changes in Ca²⁺ signaling and SANC dysfunction. Under β-adrenergic stimulation, changes in cAMP-PKA signaling and the sodium currents (I_Na), in addition to I_NCX and I_CaT, mediate between changes in Ca²⁺ signaling and SANC automaticity pauses. Under basal conditions in Casq2^-/-, the same mechanisms drove changes in Ca²⁺ signaling and subsequent pacemaker dysfunction. However, SANC automaticity pauses in response to β-AR stimulation were mediated by I_CaT and I_Na. Taken together, distinct mechanisms can lead to CPVT-associated SANC automaticity pauses. In addition, we predict that specifically increasing SANC cAMP-PKA activity by either a pharmacological agent (IBMX, a phosphodiesterase (PDE) inhibitor), gene manipulation (overexpression of adenylyl cyclase 1/8) or direct manipulation of the SERCA phosphorylation target through changes in gene expression, compensate for the impairment in SANC automaticity. These findings suggest new insights for understanding CPVT and its therapeutic approach.

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.

Ca2+ Channels Mediate Bidirectional Signaling between Sarcolemma and Sarcoplasmic Reticulum in Muscle Cells

The skeletal muscle and myocardial cells present highly specialized structures; for example, the close interaction between the sarcoplasmic reticulum (SR) and mitochondria—responsible for excitation-metabolism coupling—and the junction that connects the SR with T-tubules, critical for excitation-contraction (EC) coupling. The mechanisms that underlie EC coupling in these two cell types, however, are fundamentally distinct. They involve the differential expression of Ca²⁺ channel subtypes: Ca_V1.1 and RyR1 (skeletal), vs. Ca_V1.2 and RyR2 (cardiac). The Ca_V channels transform action potentials into elevations of cytosolic Ca²⁺, by activating RyRs and thus promoting SR Ca²⁺ release. The high levels of Ca²⁺, in turn, stimulate not only the contractile machinery but also the generation of mitochondrial reactive oxygen species (ROS). This forward signaling is reciprocally regulated by the following feedback mechanisms: Ca²⁺-dependent inactivation (of Ca²⁺ channels), the recruitment of Na⁺/Ca²⁺ exchanger activity, and oxidative changes in ion channels and transporters. Here, we summarize both well-established concepts and recent advances that have contributed to a better understanding of the molecular mechanisms involved in this bidirectional signaling.

Recruiting RyRs to Open in a Ca2+ Release Unit: Single-RyR Gating Properties Make RyR Group Dynamics

In cardiac myocytes, clusters of type-2 ryanodine receptors (RyR2s) release Ca²⁺ from the sarcoplasmic reticulum (SR) via a positive feedback mechanism in which fluxed Ca²⁺ activates nearby RyRs. Although the general principles of this are understood, less is known about how single-RyR gating properties define the RyR group dynamics in an array of many channels. Here, we examine this using simulations with three models of RyR gating that have identical open probabilities: the commonly used two-state Markov gating model, one that utilizes multiple exponentials to fit single-channel open time (OT) and closed time (CT) distributions, and an extension of this multiexponential model that also includes experimentally measured correlations between single-channel OTs and CTs. The simulations of RyR clusters that utilize the multiexponential gating model produce infrequent Ca²⁺ release events with relatively few open RyRs. Ca²⁺ release events become even smaller when OT/CT correlations are included. This occurs because the correlations produce a small but consistent bias against recruiting more RyRs to open during the middle of a Ca²⁺ release event, between the initiation and termination phases (which are unaltered compared to the uncorrelated simulations). In comparison, the two-state model produces frequent, large, and long Ca²⁺ release events because it had a recruitment bias in favor of opening more RyRs. This difference stems from the two-state model's single-RyR OT and CT distributions being qualitatively different from the experimental ones. Thus, the details of single-RyR gating can profoundly affect SR Ca²⁺ release even if open probability and mean OTs and CTs are identical. We also show that Ca²⁺ release events can terminate spontaneously without any reduction in SR [Ca²⁺], luminal regulation, Ca²⁺-dependent inactivation, or physical coupling between RyRs when Ca²⁺ flux is below a threshold value. This supports and extends the pernicious attrition/induction decay hypothesis that SR Ca²⁺ release events terminate below a threshold Ca²⁺ flux.

Interplay between Triadin and Calsequestrin in the Pathogenesis of CPVT in the Mouse

Recessive forms of catecholaminergic polymorphic ventricular tachycardia (CPVT) are induced by mutations in genes encoding triadin or calsequestrin, two proteins that belong to the Ca²⁺ release complex, responsible for intracellular Ca²⁺ release triggering cardiac contractions. To better understand the mechanisms of triadin-induced CPVT and to assay multiple therapeutic interventions, we used a triadin knockout mouse model presenting a CPVT-like phenotype associated with a decrease in calsequestrin protein level. We assessed different approaches to rescue protein expression and to correct intracellular Ca²⁺ release and cardiac function: pharmacological treatment with kifunensine or a viral gene transfer-based approach, using adeno-associated virus serotype 2/9 (AAV2/9) encoding the triadin or calsequestrin. We observed that the levels of triadin and calsequestrin are intimately linked, and that reduction of both proteins contributes to the CPVT phenotype. Different combinations of triadin and calsequestrin expression level were obtained using these therapeutic approaches. A full expression of each is not necessary to correct the phenotype; a fine-tuning of the relative re-expression of both triadin and calsequestrin is required to correct the CPVT phenotype and rescue the cardiac function. AAV-mediated gene delivery of calsequestrin or triadin and treatment with kifunensine are potential treatments for recessive forms of CPVT due to triadin mutations.

Computational Model of Calcium Signaling in Cardiac Atrial Cells at the Submicron Scale

In cardiac cells, calcium is the mediator of excitation-contraction coupling. Dysfunctions in calcium handling have been identified as the origin of some cardiac arrhythmias. In the particular case of atrial myocytes, recent available experimental data has found links between these dysfunctions and structural changes in the calcium handling machinery (ryanodine cluster size and distribution, t-tubular network, etc). To address this issue, we have developed a computational model of an atrial myocyte that takes into account the detailed intracellular structure. The homogenized macroscopic behavior is described with a two-concentration field model, using effective diffusion coefficients of calcium in the sarcoplasmic reticulum (SR) and in the cytoplasm. The model reproduces the right calcium transients and dependence with pacing frequency. Under basal conditions, the calcium rise is mostly restricted to the periphery of the cell, with a large concentration ratio between the periphery and the interior. We have then studied the dependence of the speed of the calcium wave on cytosolic and SR diffusion coefficients, finding an almost linear relation with the former, in agreement with a diffusive and fire mechanism of propagation, and little dependence on the latter. Finally, we have studied the effect of a change in RyR cluster microstructure. We find that, under resting conditions, the spark frequency decreases slightly with RyR cluster spatial dispersion, but markedly increases when the RyRs are distributed in clusters of larger size, stressing the importance of RyR cluster organization to understand atrial arrhythmias, as recent experimental results suggest (Macquaide et al., 2015).

Calcium-induced release of calcium in muscle: 50 years of work and the emerging consensus

Ryanodine-sensitive intracellular Ca2+ channels (RyRs) open upon binding Ca2+ at cytosolic-facing sites. This results in concerted, self-reinforcing opening of RyRs clustered in specialized regions on the membranes of Ca2+ storage organelles (endoplasmic reticulum and sarcoplasmic reticulum), a process that produces Ca2+-induced Ca2+ release (CICR). The process is optimized to achieve large but brief and localized increases in cytosolic Ca2+ concentration, a feature now believed to be critical for encoding the multiplicity of signals conveyed by this ion. In this paper, I trace the path of research that led to a consensus on the physiological significance of CICR in skeletal muscle, beginning with its discovery. I focus on the approaches that were developed to quantify the contribution of CICR to the Ca2+ increase that results in contraction, as opposed to the flux activated directly by membrane depolarization (depolarization-induced Ca2+ release [DICR]). Although the emerging consensus is that CICR plays an important role alongside DICR in most taxa, its contribution in most mammalian muscles appears to be limited to embryogenesis. Finally, I survey the relevance of CICR, confirmed or plausible, to pathogenesis as well as the multiple questions about activation of release channels that remain unanswered after 50 years.

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

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

Role of FK506-binding protein in Ca2+ spark regulation

The elementary Ca²⁺ release events, Ca²⁺ sparks, has been found for a quarter of century. However, the molecular regulation of the spark generator, the ryanodine receptor (RyR) on the sarcoplasmic reticulum, remains obscure. Although each subunit of the RyR homotetramer has a site for FK506-binding protein (FKBP), the role of FKBPs in modifying RyR Ca²⁺ sparks has been debated for long. One of the reasons behind the controversy is that most previous studies detect spontaneous sparks, where the mixture with out-of-focus events and local wavelets prevents an accurate characterization of Ca²⁺ sparks. In the present study, we detected Ca²⁺ sparks triggered by single L-type Ca²⁺ channels (LCCs) under loose-seal patch clamp conditions in FK506-treated or FKBP12.6 knockout cardiomyocytes. We found that FKBP dissociation both by FK506 and by rapamycin decreased the Ca²⁺ spark amplitude in ventricular cardiomyocytes. This change was neither due to decreased releasable Ca²⁺ in the sarcoplasmic reticulum, nor explained by changed RyR sensitivity. Actually FK506 increased the LCC-RyR coupling probability and curtailed the latency for an LCC to trigger a RyR Ca²⁺ spark. FKBP12.6 knockout had similar effects as FK506/rapamycin treatment, indicating that the decreased spark amplitude was attributable to the dissociation of FKBP12.6 rather than FKBP12. We also explained how decreased amplitude of spontaneous sparks after FKBP dissociation sometimes appears to be increased or unchanged due to inappropriate data processing. Our results provided firm evidence that without the inter-RyR coordination by functional FKBP12.6, the RyR recruitment during a Ca²⁺ spark would be compromised despite the sensitization of individual RyRs.

Minimal model for calcium alternans due to SR release refractoriness

In the heart, rapid pacing rates may induce alternations in the strength of cardiac contraction, termed pulsus alternans. Often, this is due to an instability in the dynamics of the intracellular calcium concentration, whose transients become larger and smaller at consecutive beats. This alternation has been linked experimentally and theoretically to two different mechanisms: an instability due to (1) a strong dependence of calcium release on sarcoplasmic reticulum (SR) load, together with a slow calcium reuptake into the SR or (2) to SR release refractoriness, due to a slow recovery of the ryanodine receptors (RyR2) from inactivation. The relationship between calcium alternans and refractoriness of the RyR2 has been more elusive than the corresponding SR Ca load mechanism. To study the former, we reduce a general calcium model, which mimics the deterministic evolution of a calcium release unit, to its most basic elements. We show that calcium alternans can be understood using a simple nonlinear equation for calcium concentration at the dyadic space, coupled to a relaxation equation for the number of recovered RyR2s. Depending on the number of RyR2s that are recovered at the beginning of a stimulation, the increase in calcium concentration may pass, or not, over an excitability threshold that limits the occurrence of a large calcium transient. When the recovery of the RyR2 is slow, this produces naturally a period doubling bifurcation, resulting in calcium alternans. We then study the effects of inactivation, calcium diffusion, and release conductance for the onset of alternans. We find that the development of alternans requires a well-defined value of diffusion while it is less sensitive to the values of inactivation or release conductance.

The intricacies of atrial calcium cycling during excitation-contraction coupling

Blatter discusses the initiation and spread of Ca release, Ca store depletion, and release termination in atrial myocytes.

Perspectives on "Control of Ca release from within the cardiac sarcoplasmic reticulum"

Five groups of experts unravel the complex modulation of a function crucial for the beating heart.

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.

Ultrastructural Analysis of Self-Associated RyR2s

In heart, type-2 ryanodine receptor (RyR2) forms discrete supramolecular clusters in the sarcoplasmic reticulum known as calcium release units (CRUs), which are responsible for most of the Ca(2+) released for muscle contraction. To learn about the substructure of the CRU, we sought to determine whether RyR2s have the ability to self-associate in the absence of other factors and if so, whether they do it in a specific manner. Purified RyR2 was negatively stained and imaged on the transmission electron microscope, and RyR2 particles closely associated were further analyzed using bias-free multivariate statistical analysis and classification. The resulting two-dimensional averages show that RyR2s can interact in two rigid, reproducible configurations: "adjoining", with two RyR2s alongside each other, and "oblique", with two partially overlapped RyR2s forming an angle of 12°. The two configurations are nearly identical under two extreme physiological Ca(2+) concentrations. Pseudo-atomic models for these two interactions indicate that the adjoining interaction involves contacts between the P1, SPRY1 and the helical domains. The oblique interaction is mediated by extensive contacts between the SPRY1 domains (domains 9) and P1 domains (domains 10) of both RyR2s and not through domain 6 as previously thought; in addition its asymmetric interface imposes steric constrains that inhibit the growth of RyR2 as a checkerboard, which is the configuration usually assumed, and generates new configurations, i.e., "branched" and "interlocked". This first, to our knowledge, structural detailed analysis of the inter-RyR2 interactions helps to understand important morphological and functional aspects of the CRU in the context of cardiac EC coupling.

Mechanisms of the cyclic nucleotide cross-talk signaling network in cardiac L-type calcium channel regulation

Regulation of L-type Calcium (Ca2+) Channel (LCC) gating is critical to shaping the cardiac action potential (AP) and triggering the initiation of excitation-contraction (EC) coupling in cardiac myocytes. The cyclic nucleotide (cN) cross-talk signaling network, which encompasses the β-adrenergic and the Nitric Oxide (NO)/cGMP/Protein Kinase G (PKG) pathways and their interaction (cross-talk) through distinctively-regulated phosphodiesterase isoenzymes (PDEs), regulates LCC current via Protein Kinase A- (PKA) and PKG-mediated phosphorylation. Due to the tightly-coupled and intertwined biochemical reactions involved, it remains to be clarified how LCC gating is regulated by the signaling network from receptor to end target. In addition, the large number of EC coupling-related phosphorylation targets of PKA and PKG makes it difficult to quantify and isolate changes in L-type Ca2+ current (ICaL) responses regulated by the signaling network. We have developed a multi-scale, biophysically-detailed computational model of LCC regulation by the cN signaling network that is supported by experimental data. LCCs are modeled with functionally distinct PKA- and PKG-phosphorylation dependent gating modes. The model exhibits experimentally observed single channel characteristics, as well as whole-cell LCC currents upon activation of the cross-talk signaling network. Simulations show 1) redistribution of LCC gating modes explains changes in whole-cell current under various stimulation scenarios of the cN cross-talk network; 2) NO regulation occurs via potentiation of a gating mode characterized by prolonged closed times; and 3) due to compensatory actions of cross-talk and antagonizing functions of PKA- and PKG-mediated phosphorylation of LCCs, the effects of individual inhibitions of PDEs 2, 3, and 4 on ICaL are most pronounced at low levels of β-adrenergic stimulation. Simulations also delineate the contribution of the following two mechanisms to overall LCC regulation, which have otherwise been challenging to distinguish: 1) regulation of PKA and PKG activation via cN cross-talk (Mechanism 1); and 2) LCC interaction with activated PKA and PKG (Mechanism 2). These results provide insights into how cN signals transduced via the cN cross-talk signaling network are integrated via LCC regulation in the heart.

A novel mechanism of tandem activation of ryanodine receptors by cytosolic and SR luminal Ca2+ during excitation-contraction coupling in atrial myocytes

KEY POINTS

In atrial myocytes excitation-contraction coupling is strikingly different from ventricle because atrial myocytes lack a transverse tubule membrane system: Ca²⁺ release starts in the cell periphery and propagates towards the cell centre by Ca²⁺ -induced Ca²⁺ release from the sarcoplasmic reticulum (SR) Ca²⁺ store. The cytosolic Ca²⁺ sensitivity of the ryanodine receptor (RyRs) Ca²⁺ release channel is low and it is unclear how Ca²⁺ release can be activated in the interior of atrial cells. Simultaneous confocal imaging of cytosolic and intra-SR calcium revealed a transient elevation of store Ca²⁺ that we termed 'Ca²⁺ sensitization signal'. We propose a novel paradigm of atrial ECC that is based on tandem activation of the RyRs by cytosolic and luminal Ca²⁺ through a 'fire-diffuse-uptake-fire' (or FDUF) mechanism: Ca²⁺ uptake by SR Ca²⁺ pumps at the propagation front elevates Ca²⁺ inside the SR locally, leading to luminal RyR sensitization and lowering of the cytosolic Ca²⁺ activation threshold.

ABSTRACT

In atrial myocytes Ca²⁺ release during excitation-contraction coupling (ECC) is strikingly different from ventricular myocytes. In many species atrial myocytes lack a transverse tubule system, dividing the sarcoplasmic reticulum (SR) Ca²⁺ store into the peripheral subsarcolemmnal junctional (j-SR) and the much more abundant central non-junctional (nj-SR) SR. Action potential (AP)-induced Ca²⁺ entry activates Ca²⁺ -induced Ca²⁺ release (CICR) from j-SR ryanodine receptor (RyR) Ca²⁺ release channels. Peripheral elevation of [Ca²⁺ ]_i initiates CICR from nj-SR and sustains propagation of CICR to the cell centre. Simultaneous confocal measurements of cytosolic ([Ca²⁺ ]_i ; with the fluorescent Ca²⁺ indicator rhod-2) and intra-SR ([Ca²⁺ ]_SR ; fluo-5N) Ca²⁺ in rabbit atrial myocytes revealed that Ca²⁺ release from j-SR resulted in a cytosolic Ca²⁺ transient of higher amplitude compared to release from nj-SR; however, the degree of depletion of j-SR [Ca²⁺ ]_SR was smaller than nj-SR [Ca²⁺ ]_SR . Similarly, Ca²⁺ signals from individual release sites of the j-SR showed a larger cytosolic amplitude (Ca²⁺ sparks) but smaller depletion (Ca²⁺ blinks) than release from nj-SR. During AP-induced Ca²⁺ release the rise of [Ca²⁺ ]_i detected at individual release sites of the nj-SR preceded the depletion of [Ca²⁺ ]_SR , and during this latency period a transient elevation of [Ca²⁺ ]_SR occurred. We propose that Ca²⁺ release from nj-SR is activated by cytosolic and luminal Ca²⁺ (tandem RyR activation) via a novel 'fire-diffuse-uptake-fire' (FDUF) mechanism. This novel paradigm of atrial ECC predicts that Ca²⁺ uptake by sarco-endoplasmic reticulum Ca²⁺ -ATPase (SERCA) at the propagation front elevates local [Ca²⁺ ]_SR , leading to luminal RyR sensitization and lowering of the activation threshold for cytosolic CICR.

Extensive Ca2+ leak through K4750Q cardiac ryanodine receptors caused by cytosolic and luminal Ca2+ hypersensitivity

The K4750Q mutation in ryanodine receptor 2 causes severe catecholaminergic polymorphic ventricular tachycardia. Uehara et al. reveal extensive Ca²⁺ leak through this mutant receptor and show it is caused by altered gating kinetics, increased Ca²⁺ sensitivity, and the absence of Ca²⁺-dependent inactivation.

Various ryanodine receptor 2 (RyR2) point mutations cause catecholamine-induced polymorphic ventricular tachycardia (CPVT), a life-threatening arrhythmia evoked by diastolic intracellular Ca²⁺ release dysfunction. These mutations occur in essential regions of RyR2 that regulate Ca²⁺ release. The molecular dysfunction caused by CPVT-associated RyR2 mutations as well as the functional consequences remain unresolved. Here, we study the most severe CPVT-associated RyR2 mutation (K4750Q) known to date. We define the molecular and cellular dysfunction generated by this mutation and detail how it alters RyR2 function, using Ca²⁺ imaging, ryanodine binding, and single-channel recordings. HEK293 cells and cardiac HL-1 cells expressing RyR2-K4750Q show greatly enhanced spontaneous Ca²⁺ oscillations. An endoplasmic reticulum–targeted Ca²⁺ sensor, R-CEPIA1er, revealed that RyR2-K4750Q mediates excessive diastolic Ca²⁺ leak, which dramatically reduces luminal [Ca²⁺]. We further show that the K4750Q mutation causes three RyR2 defects: hypersensitization to activation by cytosolic Ca²⁺, loss of cytosolic Ca²⁺/Mg²⁺-mediated inactivation, and hypersensitization to luminal Ca²⁺ activation. These defects combine to kinetically stabilize RyR2-K4750Q openings, thus explaining the extensive diastolic Ca²⁺ leak from the sarcoplasmic reticulum, frequent Ca²⁺ waves, and severe CPVT phenotype. As the multiple concurrent defects are induced by a single point mutation, the K4750 residue likely resides at a critical structural point at which cytosolic and luminal RyR2 control input converge.

Sarcoplasmic Reticulum Structure and Functional Properties that Promote Long-Lasting Calcium Sparks

Calcium (Ca) sparks are the fundamental sarcoplasmic reticulum (SR) Ca release events in cardiac myocytes, and they have a typical duration of 20-40 ms. However, when a fraction of ryanodine receptors (RyRs) are blocked by tetracaine or ruthenium red, Ca sparks lasting hundreds of milliseconds have been observed experimentally. The fundamental mechanism underlying these extremely prolonged Ca sparks is not understood. In this study, we use a physiologically detailed mathematical model of subcellular Ca cycling to examine how Ca spark duration is influenced by the number of functional RyRs in a junctional cluster (which is reduced by tetracaine or ruthenium red) and other SR Ca handling properties. One RyR cluster contains a few to several hundred RyRs, and we use a four-state Markov RyR gating model. Each RyR opens stochastically and is regulated by cytosolic and luminal Ca. We varied the number of functional RyRs in the single cluster, diffusion within the SR network, diffusion between network and junctional SR, cytosolic Ca diffusion, SERCA uptake activity, and RyR open probability. For long-lasting Ca release events, opening events within the cluster must occur continuously because the typical open time of the RyR is only a few milliseconds. We found the following: 1) if the number of RyRs is too small, it is difficult to maintain consecutive openings and stochastic attrition terminates the release; 2) if the number of RyRs is too large, the depletion of Ca from the junctional SR terminates the release; and 3) very long release events require relatively small-sized RyR clusters (reducing flux as seen experimentally with tetracaine) and sufficiently rapid intra-SR Ca diffusion, such that local junctional intra-SR [Ca] can be maintained by intra-SR diffusion and overall SR Ca reuptake.

The calcium-frequency response in the rat ventricular myocyte: an experimental and modelling study

KEY POINTS

In the majority of species, including humans, increased heart rate increases cardiac contractility. This change is known as the force-frequency response (FFR). The majority of mammals have a positive force-frequency relationship (FFR). In rat the FFR is controversial. We derive a species- and temperature-specific data-driven model of the rat ventricular myocyte. As a measure of the FFR, we test the effects of changes in frequency and extracellular calcium on the calcium-frequency response (CFR) in our model and three altered models. The results show a biphasic peak calcium-frequency response, due to biphasic behaviour of the ryanodine receptor and the combined effect of the rapid calmodulin buffer and the frequency-dependent increase in diastolic calcium. Alterations to the model reveal that inclusion of Ca(2+) /calmodulin-dependent protein kinase II (CAMKII)-mediated L-type channel and transient outward K(+) current activity enhances the positive magnitude calcium-frequency response, and the absence of CAMKII-mediated increase in activity of the sarco/endoplasmic reticulum Ca(2+) -ATPase induces a negative magnitude calcium-frequency response.

ABSTRACT

An increase in heart rate affects the strength of cardiac contraction by altering the Ca(2+) transient as a response to physiological demands. This is described by the force-frequency response (FFR), a change in developed force with pacing frequency. The majority of mammals, including humans, have a positive FFR, and cardiac contraction strength increases with heart rate. However, the rat and mouse are exceptions, with the majority of studies reporting a negative FFR, while others report either a biphasic or a positive FFR. Understanding the differences in the FFR between humans and rats is fundamental to interpreting rat-based experimental findings in the context of human physiology. We have developed a novel model of rat ventricular electrophysiology and calcium dynamics, derived predominantly from experimental data recorded under physiological conditions. As a measure of FFR, we tested the effects of changes in stimulation frequency and extracellular calcium concentration on the simulated Ca(2+) transient characteristics and showed a biphasic peak calcium-frequency relationship, consistent with recent observations of a shift from negative to positive FFR when approaching the rat physiological frequency range. We tested the hypotheses that (1) inhibition of Ca(2+) /calmodulin-dependent protein kinase II (CAMKII)-mediated increase in sarco/endoplasmic reticulum Ca(2+) -ATPase (SERCA) activity, (2) CAMKII modulation of SERCA, L-type channel and transient outward K(+) current activity and (3) Na(+) /K(+) pump dynamics play a significant role in the rat FFR. The results reveal a major role for CAMKII modulation of SERCA in the peak Ca(2+) -frequency response, driven most significantly by the cytosolic calcium buffering system and changes in diastolic Ca(2+) .

Superresolution modeling of calcium release in the heart

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