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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., This work was supported by research grants from the Heart and Stroke Foundation of Canada (G-19-0026444), the Heart and Stroke Foundation Chair in Cardiovascular Research (END611955), the Canadian Institutes of Health Research to S.R.W. Chen (PJT-155940), the Spanish Ministry of Science Innovation and Universities SAF2017-88019-C3-1R, 2R, and 3R (to L. Hove-Madsen, R. Benitez, and B. Echebarria), Marato-TV3 20152030 (to L. Hove-Madsen) and 20151110 (to B. Echebarria), and Generalitat de Catalunya SGR2017-1769 (to L. Hove-Madsen).

Calcium oscillations and waves induce depolarization in cardiac cells which are believed to cause life-threathening arrhythimas. In this work, we study the conditions for the appearance of calcium oscillations in both a detailed subcellular model of calcium dynamics and a minimal model that takes into account just the minimal ingredients of the calcium toolkit. To avoid the effects of homeostatic changes and the interaction with the action potential we consider the somewhat artificial condition of a cell without pacing and with no calcium exchange with the extracellular medium. Both the full subcellular model and the minimal model present the same scenarios depending on the calcium load: two stationary states, one with closed ryanodine receptors (RyR) and most calcium in the cell stored in the sarcoplasmic reticulum (SR), and another, with open RyRs and a depleted SR. In between, calcium oscillations may appear. The robustness of these oscillations is determined by the amount of calsequestrin (CSQ). The lack of this buffer in the SR enhances the appearance of oscillations. The minimal model allows us to relate the stability of the oscillating state to the nullcline structure of the system, and find that its range of existence is bounded by a homoclinic and a Hopf bifurcation, resulting in a sudden transition to the oscillatory regime as the cell calcium load is increased. Adding a small amount of noise to the RyR behavior increases the parameter region where oscillations appear and provides a gradual transition from the resting state to the oscillatory regime, as observed in the subcellular model and experimentally., Author summary In cardiac cells, calcium plays a very important role. An increase in calcium levels is the trigger used by the cell to initiate contraction. Besides, calcium modulates several transmembrane currents, affecting the cell transmembrane potential. Thus, dysregulations in calcium handling have been associated with the appearance of arrhythmias. Often, this dysregulation results in the appearance of periodic calcium waves or global oscillations, providing a pro-arrhythmic substrate. In this paper, we study the onset of calcium oscillations in cardiac cells using both a detailed subcellular model of calcium dynamics and a minimal model that takes into account the essential ingredients of the calcium toolkit. Both reproduce the main experimental results and link this behavior with the presence of different steady-state solutions and bifurcations that depend on the total amount of calcium in the cell and in the level of buffering present. We expect that this work will help to clarify the conditions under which calcium oscillations appear in cardiac myocytes and, therefore, will represent a step further in the understanding of the origin of cardiac arrhythmias.

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., Author summary 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.

Atrial fibrillation (AF), a cardiac arrhythmia characterized by an abnormal heart rythm originated in the atria, is one of the most prevalent cardiac diseases. Although it may have diverse causes, genetic screening has shown that a percentage of pacients suffering of AF present a genetic variant related to disregulation of calcium-activated potassium (SK) channels. In this paper we review the main characteristics of these channels and use several mathematical models of human atrial cardiomyocytes to study their influence in the form of the atrial action potential. We show that an overexpression of SK channels results in decreased action potential duration and, under some circumstances, it may give rise to alternans, suggesting a pro-arrhythmic role of this current. This effect becomes more important at higher pacing rates. Nevertheless, we also find it to protect against spontaneous calcium release induced afterdepolarizations, acting in this case as an antiarrhythmic factor.

Among the different potassium channels present in cardiac myocytes, the small conductance Ca2+ activated potassium channels (SK channels) are particular because they are affected by changes in intracellular calcium. The functional role of these channels in cardiac electrophysiology is still under intense debate. While they do not seem to play an important role in healthy hearts – their associated current, IKCa, is smaller than other potassium currents -, there is increasing evidence that they may become relevant under pathological conditions. In fact, both pro- and anti-arrhythmic effects have been assigned to these channels, depending on the clinical situation. In this work, we have incorporated the current through SK channels, IKCa, into an electrophysiological ionic model of human atria myocyte. This allows us to evaluate changes in the action potential under different parameters affecting the kinetics of these channels. We observe a large dependence of the action potential duration with the conductance and gate dynamics of the channel. The dependence of SK channels with changes in intracellular calcium dynamics helps decreasing the proarrhythmic effect of spontaneous calcium release events

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.

Calcium release from the sarcoplasmic reticulum (SR) plays a central role in the regulation of cardiac contraction and rhythm in mammals and humans but its role is controversial in teleosts. Since the zebrafish is an emerging model for studies of cardiovascular function and regeneration we here sought to determine if basic features of SR calcium release are phylogenetically conserved. Confocal calcium imaging was used to detect spontaneous calcium release (calcium sparks and waves) from the SR. Calcium sparks were detected in 16 of 38 trout atrial myocytes and 6 of 15 ventricular cells. The spark amplitude was 1.45±0.03 times the baseline fluorescence and the time to half maximal decay of sparks was 27±3 ms. Spark frequency was 0.88 sparks µm−1 min−1 while calcium waves were 8.5 times less frequent. Inhibition of SR calcium uptake reduced the calcium transient (F/F0) from 1.77±0.17 to 1.12±0.18 (p = 0.002) and abolished calcium sparks and waves. Moreover, elevation of extracellular calcium from 2 to 10 mM promoted early and delayed afterdepolarizations (from 0.6±0.3 min−1 to 8.1±2.0 min−1, p = 0.001), demonstrating the ability of SR calcium release to induce afterdepolarizations in the trout heart. Calcium sparks of similar width and duration were also observed in zebrafish ventricular myocytes. In conclusion, this is the first study to consistently report calcium sparks in teleosts and demonstrate that the basic features of calcium release through the ryanodine receptor are conserved, suggesting that teleost cardiac myocytes is a relevant model to study the functional impact of abnormal SR function., This work was funded by grants from the Spanish Ministry of Science and Technology (SAF2007-60174 and CNIC2007-12) and a Network grant from Instituto de Salud Carlos III (REDINSCOR RD06-0003). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript

We have developed an automatic method for the analysis and identification of dynamical regimes in intracellular calcium patterns from confocal calcium images. The method allows the identification of different dynamical patterns such as spatially concordant and discordant alternans, irregular behavior or phase-locking regimes such as period doubling or halving. The method can be applied to the analysis of different cardiac pathologies related to anomalies at the cellular level such as ventricular reentrant arrhythmias.

Electromechanical alternans is a beat-to-beat alterna- tion in the strength of contraction of a cardiac cell which appears often due to an instability of calcium cycling. The global calcium signal in cardiomyocytes is the result of the combined effect of several thousand micron scale domains called Calcium Release Units (CaRU), coupled through diffusion, where the flow of calcium among different cell compartments is regulated by stochastic signaling involv- ing the ryanodine receptor (RyR). Recently, numerical sim- ulations have suggested that the transition from regular Ca cycling to alternans is an order-disorder phase transition consistent with the Ising universality class. Inside the cell, groups of CaRU form transient areas within the cell where alternans appear. However, global alternans appears only as a result of the synchronization of the oscillation phase among different subunits. We show here that this transi- tion is indeed robust and universal upon changes in the behavior of the RyR. Using three different set of parame- ters for the transition rates among open, closed and inacti- vated states in the RyR, we show that different RyR behav- ior leads to the same type of order-disorder transition.

Electromechanical alternans is a beat-to-beat alternation in the strength of contraction of a cardiac cell, which can be caused by an instability of calcium cycling. Using a distributed model of subcellular calcium we show that alternans occurs via an order-disorder phase transition which exhibits critical slowing down and a diverging correlation length. We apply finite size scaling along with a mapping to a stochastic coupled map model, to show that this transition in two dimensions is characterized by critical exponents consistent with the Ising universality class. These findings highlight the important role of cooperativity in biological cells, and suggest novel approaches to investigate the onset of the alternans instability in the heart.