Ryanodine Receptor Open Times Are Determined in the Closed State

Ca2+ spark latency and control of intrinsic Ca2+ release dyssynchrony in rat cardiac ventricular muscle cells

Cardiac excitation-contraction coupling (ECC) depends on Ca2+ release from intracellular stores via ryanodine receptors (RyRs) triggered by L-type Ca2+ channels (LCCs). Uncertain numbers of RyRs and LCCs form 'couplons' whose activation produces Ca2+ sparks, which summate to form a cell-wide Ca2+ transient that switches on contraction. Voltage (Vm) changes during the action potential (AP) and stochasticity in channel gating should create variability in Ca2+ spark timing, but Ca2+ transient wavefronts have remarkable uniformity. To examine how this is achieved, we measured the Vm-dependence of evoked Ca2+ spark probability (Pspark) and latency over a wide voltage range in rat ventricular cells. With depolarising steps, Ca2+ spark latency showed a U-shaped Vm-dependence, while repolarising steps from 50 mV produced Ca2+ spark latencies that increased monotonically with Vm. A computer model based on reported channel gating and geometry reproduced our experimental data and revealed a likely RyR:LCC stoichiometry of ∼ 5:1 for the Ca2+ spark initiating complex (IC). Using the experimental AP waveform, the model revealed a high coupling fidelity (Pcpl ∼ 0.5) between each LCC opening and IC activation. The presence of ∼ 4 ICs per couplon reduced Ca2+ spark latency and increased Pspark to match experimental data. Variability in AP release timing is less than that seen with voltage steps because the AP overshoot and later repolarization decrease Pspark due to effects on LCC flux and LCC deactivation respectively. This work provides a framework for explaining the Vm- and time-dependence of Pspark, and indicates how ion channel dispersion in disease can contribute to dyssynchrony in Ca2+ release.

Mechanisms of spontaneous Ca2+ release-mediated arrhythmia in a novel 3D human atrial myocyte model: I. Transverse-axial tubule variation

Intracellular calcium (Ca2+ ) cycling is tightly regulated in the healthy heart ensuring effective contraction. This is achieved by transverse (t)-tubule membrane invaginations that facilitate close coupling of key Ca2+ -handling proteins such as the L-type Ca2+ channel and Na+ -Ca2+ exchanger (NCX) on the cell surface with ryanodine receptors (RyRs) on the intracellular Ca2+ store. Although less abundant and regular than in the ventricle, t-tubules also exist in atrial myocytes as a network of transverse invaginations with axial extensions known as the transverse-axial tubule system (TATS). In heart failure and atrial fibrillation, there is TATS remodelling that is associated with aberrant Ca2+ -handling and Ca2+ -induced arrhythmic activity; however, the mechanism underlying this is not fully understood. To address this, we developed a novel 3D human atrial myocyte model that couples electrophysiology and Ca2+ -handling with variable TATS organization and density. We extensively parameterized and validated our model against experimental data to build a robust tool examining TATS regulation of subcellular Ca2+ release. We found that varying TATS density and thus the localization of key Ca2+ -handling proteins has profound effects on Ca2+ handling. Following TATS loss, there is reduced NCX that results in increased cleft Ca2+ concentration through decreased Ca2+ extrusion. This elevated Ca2+ increases RyR open probability causing spontaneous Ca2+ releases and the promotion of arrhythmogenic waves (especially in the cell interior) leading to voltage instabilities through delayed afterdepolarizations. In summary, the present study demonstrates a mechanistic link between TATS remodelling and Ca2+ -driven proarrhythmic behaviour that probably reflects the arrhythmogenic state observed in disease. KEY POINTS: Transverse-axial tubule systems (TATS) modulate Ca2+ handling and excitation-contraction coupling in atrial myocytes, with TATS remodelling in heart failure and atrial fibrillation being associated with altered Ca2+ cycling and subsequent arrhythmogenesis. To investigate the poorly understood mechanisms linking TATS variation and spontaneous Ca2+ release, we built, parameterized and validated a 3D human atrial myocyte model coupling electrophysiology and spatially-detailed subcellular Ca2+ handling governed by the TATS. Simulated TATS loss causes diastolic Ca2+ and voltage instabilities through reduced Na+ -Ca2+ exchanger-mediated Ca2+ removal, cleft Ca2+ accumulation and increased ryanodine receptor open probability, resulting in spontaneous Ca2+ release and promotion of arrhythmogenic waves and delayed afterdepolarizations. At fast electrical rates typical of atrial tachycardia/fibrillation, spontaneous Ca2+ releases are larger and more frequent in the cell interior than at the periphery. Our work provides mechanistic insight into how atrial TATS remodelling can lead to Ca2+ -driven instabilities that may ultimately contribute to the arrhythmogenic state in disease.

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 Role of Ca2+ Sparks in Force Frequency Relationships in Guinea Pig Ventricular Myocytes

Calcium sparks are the elementary Ca2+ release events in excitation-contraction coupling that underlie the Ca2+ transient. The frequency-dependent contractile force generated by cardiac myocytes depends upon the characteristics of the Ca2+ transients. A stochastic computational local control model of a guinea pig ventricular cardiomyocyte was developed, to gain insight into mechanisms of force-frequency relationship (FFR). This required the creation of a new three-state RyR2 model that reproduced the adaptive behavior of RyR2, in which the RyR2 channels transition into a different state when exposed to prolonged elevated subspace [Ca2+]. The model simulations agree with previous experimental and modeling studies on interval-force relations. Unlike previous common pool models, this local control model displayed stable action potential trains at 7 Hz. The duration and the amplitude of the [Ca2+]myo transients increase in pacing rates consistent with the experiments. The [Ca2+]myo transient reaches its peak value at 4 Hz and decreases afterward, consistent with experimental force-frequency curves. The model predicts, in agreement with previous modeling studies of Jafri and co-workers, diastolic sarcoplasmic reticulum, [Ca2+]sr, and RyR2 adaptation increase with the increased stimulation frequency, producing rising, rather than falling, amplitude of the myoplasmic [Ca2+] transients. However, the local control model also suggests that the reduction of the L-type Ca2+ current, with an increase in pacing frequency due to Ca2+-dependent inactivation, also plays a role in the negative slope of the FFR. In the simulations, the peak Ca2+ transient in the FFR correlated with the highest numbers of SR Ca2+ sparks: the larger average amplitudes of those sparks, and the longer duration of the Ca2+ sparks.

Image-Driven Modeling of Nanoscopic Cardiac Function: Where Have We Come From, and Where Are We Going?

Complementary developments in microscopy and mathematical modeling have been critical to our understanding of cardiac excitation-contraction coupling. Historically, limitations imposed by the spatial or temporal resolution of imaging methods have been addressed through careful mathematical interrogation. Similarly, limitations imposed by computational power have been addressed by imaging macroscopic function in large subcellular domains or in whole myocytes. As both imaging resolution and computational tractability have improved, the two approaches have nearly merged in terms of the scales that they can each be used to interrogate. With this review we will provide an overview of these advances and their contribution to understanding ventricular myocyte function, including exciting developments over the last decade. We specifically focus on experimental methods that have pushed back limits of either spatial or temporal resolution of nanoscale imaging (e.g., DNA-PAINT), or have permitted high resolution imaging on large cellular volumes (e.g., serial scanning electron microscopy). We also review the progression of computational approaches used to integrate and interrogate these new experimental data sources, and comment on near-term advances that may unify understanding of the underlying biology. Finally, we comment on several outstanding questions in cardiac physiology that stand to benefit from a concerted and complementary application of these new experimental and computational methods.

Flecainide Paradoxically Activates Cardiac Ryanodine Receptor Channels under Low Activity Conditions: A Potential Pro-Arrhythmic Action

Cardiac ryanodine receptor (RyR2) mutations are implicated in the potentially fatal catecholaminergic polymorphic ventricular tachycardia (CPVT) and in atrial fibrillation. CPVT has been successfully treated with flecainide monotherapy, with occasional notable exceptions. Reported actions of flecainide on cardiac sodium currents from mice carrying the pro-arrhythmic homozygotic RyR2-P2328S mutation prompted our explorations of the effects of flecainide on their RyR2 channels. Lipid bilayer electrophysiology techniques demonstrated a novel, paradoxical increase in RyR2 activity. Preceding flecainide exposure, channels were mildly activated by 1 mM luminal Ca²⁺ and 1 µM cytoplasmic Ca²⁺, with open probabilities (P_o) of 0.03 ± 0.01 (wild type, WT) or 0.096 ± 0.024 (P2328S). Open probability (P_o) increased within 0.5 to 3 min of exposure to 0.5 to 5.0 µM cytoplasmic flecainide, then declined with higher concentrations of flecainide. There were no such increases in a subset of high P_o channels with P_o ≥ 0.08, although P_o then declined with ≥5 µM (WT) or ≥50 µM flecainide (P2328S). On average, channels with P_o < 0.08 were significantly activated by 0.5 to 10 µM of flecainide (WT) or 0.5 to 50 µM of flecainide (P2328S). These results suggest that flecainide can bind to separate activation and inhibition sites on RyR2, with activation dominating in lower activity channels and inhibition dominating in more active channels.

Simulating cardiac Ca2+ release units: effects of RyR cluster size and Ca2+ buffers on diastolic Ca2+ leak

Leak of Ca²⁺ out of the cardiac sarcoplasmic reticulum (SR) via ryanodine receptors (RyRs) during diastole is vital to regulate SR Ca²⁺ levels. This leak can become deleterious when large spontaneous RyR-mediated Ca²⁺ release events evoke proarrhythmic Ca²⁺ waves that can lead to delayed after-depolarizations. Here, we model diastolic SR Ca²⁺ leak at individual SR Ca²⁺ release sites using computer simulations of RyR arrays like those in the dyadic cleft. The results show that RyR arrays size has a significant effect on SR Ca²⁺ leak, with bigger arrays producing larger and more frequent Ca²⁺ release events. Moreover, big RyR arrays are more susceptible to small changes in the levels of dyadic Ca²⁺ buffers. Such changes in buffering shift Ca²⁺ leak from small Ca²⁺ release events (involving few open RyRs) to larger events (with many open RyRs). Moreover, by analyzing a large parameter space of possible buffering and SR Ca²⁺ loads, we find further evidence for the hypothesis that SR Ca²⁺ leak by RyR arrays can undergo a sudden phase transition.

Cardiomyocyte Calcium Ion Oscillations-Lessons From Physics

We review a theoretical, coarse-grained description for cardiomyocytes calcium dynamics that is motivated by experiments on RyR channel dynamics and provides an analogy to other spontaneously oscillating systems. We show how a minimal model, that focuses on calcium channel and pump dynamics and kinetics, results in a single, easily understood equation for spontaneous calcium oscillations (the Van-der-Pol equation). We analyze experiments on isolated RyR channels to quantify how the channel dynamics depends both on the local calcium concentration, as well as its temporal behavior (“adaptation”). Our oscillator model analytically predicts the conditions for spontaneous oscillations, their frequency and amplitude, and how each of those scale with the small number of relevant parameters related to calcium channel and pump activity. The minimal model is easily extended to include the effects of noise and external pacing (electrical or mechanical). We show how our simple oscillator predicts and explains the experimental observations of synchronization, “bursting” and reduction of apparent noise in the beating dynamics of paced cells. Thus, our analogy and theoretical approach provides robust predictions for the beating dynamics, and their biochemical and mechanical modulation.

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.

Physics of Spontaneous Calcium Oscillations in Cardiac Cells and Their Entrainment

Mechanical contraction in muscle cells requires Ca to allow myosin binding to actin. Beating cardiomyocytes contain internal Ca stores whose cytoplasmic concentration oscillates. Our theory explains observed single channel dynamics as well as cellular oscillations in spontaneously beating cardiomyocytes. The Ca dependence of channel activity responsible for Ca release includes positive feedback with a delayed response. We use this to predict a dynamical equation for global calcium oscillations with only a few physically relevant parameters. The theory accounts for the observed entrainment of beating to an oscillatory electric or mechanical field.