A structure-based computational model of IP3R1 incorporating Ca and IP3 regulation.

The inositol 1,4,5-triphosphate receptor (IP3R) mediates Ca release in many cell types and is pivotal to a wide range of cellular processes. High-resolution cryoelectron microscopy studies have provided new structural details of IP3R type 1 (IP3R1), showing that channel function is determined by the movement of various domains within and between each of its four subunits. Channel properties are regulated by ligands, such as Ca and IP3, which bind at specific sites and control the interactions between these domains. However, it is not known how the various ligand-binding sites on IP3R1 interact to control the opening of the channel. In this study, we present a coarse-grained model of IP3R1 that accounts for the channel architecture and the location of specific Ca- and IP3-binding sites. This computational model accounts for the domain-domain interactions within and between the four subunits that form IP3R1, and it also describes how ligand binding regulates these interactions. Using a kinetic model, we explore how two Ca-binding sites on the cytosolic side of the channel interact with the IP3-binding site to regulate the channel open probability. Our primary finding is that the bell-shaped open probability of IP3R1 provides constraints on the relative strength of these regulatory binding sites. In particular, we argue that a specific Ca-binding site, whose function has not yet been established, is very likely a channel antagonist. Additionally, we apply our model to show that domain-domain interactions between neighboring subunits exert control over channel cooperativity and dictate the nonlinear response of the channel to Ca concentration. This suggests that specific domain-domain interactions play a pivotal role in maintaining the channel's stability, and a disruption of these interactions may underlie disease states associated with Ca dysregulation.

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.

Voltage-mediated mechanism for calcium wave synchronization and arrhythmogenesis in atrial tissue.

A wide range of atrial arrythmias are caused by molecular defects in proteins that regulate calcium (Ca) cycling. In many cases, these defects promote the propagation of subcellular Ca waves in the cell, which can perturb the voltage time course and induce dangerous perturbations of the action potential (AP). However, subcellular Ca waves occur randomly in cells and, therefore, electrical coupling between cells substantially decreases their effect on the AP. In this study, we present evidence that Ca waves in atrial tissue can synchronize in-phase owing to an order-disorder phase transition. In particular, we show that, below a critical pacing rate, Ca waves are desynchronized and therefore do not induce substantial AP fluctuations in tissue. However, above this critical pacing rate, Ca waves gradually synchronize over millions of cells, which leads to a dramatic amplification of AP fluctuations. We exploit an underlying Ising symmetry of paced cardiac tissue to show that this transition exhibits universal properties common to a wide range of physical systems in nature. Finally, we show that in the heart, phase synchronization induces spatially out-of-phase AP duration alternans which drives wave break and reentry. These results suggest that cardiac tissue exhibits a phase transition that is required for subcellular Ca cycling defects to induce a life-threatening arrhythmia.

Mechanistic link between CaM-RyR2 interactions and the genesis of cardiac arrhythmia.

In this study, we develop a computational model of the interaction between ryanodine receptor type 2 (RyR2) and calmodulin (CaM) to explore the mechanistic link between CaM-RyR2 interactions and cardiac arrhythmia. Our starting point is a biophysically based computational model of CaM binding to a single RyR2 subunit, which reproduces single-channel RyR2 measurements in lipid bilayers. We then integrate this CaM-RyR2 model into a spatially distributed whole-cell model of Ca cycling, which is used to investigate the relationship between CaM and Ca cycling homeostasis. We show that a reduction in CaM concentration leads to a substantial increase in the rate of spontaneous Ca sparks, and this induces a marked reduction in sarcoplasmic reticulum Ca load during steady-state pacing. Also, we show that a reduction in CaM modifies the RyR2 open probability, which makes the cell more prone to Ca wave propagation. These results indicate that aberrant Ca cycling activity during pacing is determined by the interplay between sarcoplasmic reticulum load reduction and the threshold for Ca wave propagation. Based on these results, we show that when CaM is reduced, Ca waves can occur in a cell and induce action potential perturbations that are arrhythmogenic. Thus, this study outlines a novel, to our knowledge, mechanistic link between CaM-RyR2 binding kinetics and the induction of arrhythmias in the heart.

Role of t-tubule remodeling on mechanisms of abnormal calcium release during heart failure development in canine ventricle.

The goal of this work was to investigate the role of t-tubule (TT) remodeling in abnormal Ca2+ cycling in ventricular myocytes of failing dog hearts. Heart failure (HF) was induced using rapid right ventricular pacing. Extensive changes in echocardiographic parameters, including left and right ventricular dilation and systolic dysfunction, diastolic dysfunction, elevated left ventricular filling pressures, and abnormal cardiac mechanics, indicated that severe HF developed. TT loss was extensive when measured as the density of total cell volume, derived from three-dimensional confocal image analysis, and significantly increased the distances in the cell interior to closest cell membrane. Changes in Ca2+ transients indicated increases in heterogeneity of Ca2+ release along the cell length. When critical properties of Ca2+ release variability were plotted as a function of TT organization, there was a complex, nonlinear relationship between impaired calcium release and decreasing TT organization below a certain threshold of TT organization leading to increased sensitivity in Ca2+ release below a TT density threshold of 1.5%. The loss of TTs was also associated with a greater incidence of triggered Ca2+ waves during rapid pacing. Finally, virtually all of these observations were replicated by acute detubulation by formamide treatment, indicating an important role of TT remodeling in impaired Ca2+ cycling. We conclude that TT remodeling itself is a major contributor to abnormal Ca2+ cycling in HF, reducing myocardial performance. The loss of TTs is also responsible for a greater incidence of triggered Ca2+ waves that may play a role in ventricular arrhythmias arising in HF.NEW & NOTEWORTHY Three-dimensional analysis of t-tubule density showed t-tubule disruption throughout the whole myocyte in failing dog ventricle. A double-linear relationship between Ca2+ release and t-tubule density displays a steeper slope at t-tubule densities below a threshold value (∼1.5%) above which there is little effect on Ca2+ release (T-tubule reserve). T-tubule loss increases incidence of triggered Ca2+ waves. Chemically induced t-tubule disruption suggests that t-tubule loss alone is a critical component of abnormal Ca2+ cycling in heart failure.

Buffering and total calcium levels determine the presence of oscillatory regimes in cardiac cells.

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.

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.

Factors Associated with Attitude towards Wife-Beating among Married Women of the Reproductive Ages in Arba Minch Town, Southern Ethiopia: A Community-Based Cross-Sectional Study.

Evidence from demographic and health surveys in various countries and Ethiopia too showed that more women are generally believed to justify intimate partner violence (IPV) than men do. An attitude that justifies IPV is one of the factors affecting victimization and perpetration from IPV. However, women's justification about the violence and factors affecting the justification are not well documented, particularly by addressing household factors such as household food conditions. Therefore, the present study aims to fill this gap among married women of childbearing age so that evidence can be drawn for holistic interventions. A community-based cross-sectional study was conducted among 696 currently married women of childbearing age (15-49) by using a multistage cluster sampling technique to obtain the women from 11 kebeles (the smallest administrative unit in the government structure of Ethiopia) of Arba Minch town, Southern Ethiopia. Data were collected using a pretested and structured questionnaire. Logistic regression was performed using IBM SPSS version 20. The odds ratio with its 95% confidence interval was used to show the degree of association between the outcome variable and explanatory variables. Nearly two-thirds (59.5%) of the study women justified wife-beating in at least one of the five conditions. A higher odds of justification of wife-beating was observed among women whose marriage was arranged by any other person than the couples themselves, from food-insecure households, with a family size of 5 and above, in the age group of 30-39 years, and whose partner was in the age range of 31-39 years. In contrast, lower odds of justification of wife-beating was observed among women having an age difference of 10 or more years with their partner and those in a household wealth index of middle and higher category. Despite great efforts in realizing gender equality in the country, a higher proportion of women were having the attitude that justifies wife-beating in the five conditions specified to them. Interventions targeting the improvement of women's attitude towards wife-beating should target against the traditional norms of arranged marriage, improve household food conditions, and decrease family size.

Remodeling Promotes Proarrhythmic Disruption of Calcium Homeostasis in Failing Atrial Myocytes.

It is well known that heart failure (HF) typically coexists with atrial fibrillation (AF). However, until now, no clear mechanism has been established that relates HF to AF. In this study, we apply a multiscale computational framework to establish a mechanistic link between atrial myocyte structural remodeling in HF and AF. Using a spatially distributed model of calcium (Ca) signaling, we show that disruption of the spatial relationship between L-type Ca channels (LCCs) and ryanodine receptors results in markedly increased Ca content of the sarcoplasmic reticulum (SR). This increase in SR load is due to changes in the balance between Ca entry via LCCs and Ca extrusion due to the sodium-calcium exchanger after an altered spatial relationship between these signaling proteins. Next, we show that the increased SR load in atrial myocytes predisposes these cells to subcellular Ca waves that occur during the action potential (AP) and are triggered by LCC openings. These waves are common in atrial cells because of the absence of a well-developed t-tubule system in most of these cells. This distinct spatial architecture allows for the presence of a large pool of orphaned ryanodine receptors, which can fire and sustain Ca waves during the AP. Finally, we incorporate our atrial cell model in two-dimensional tissue simulations and demonstrate that triggered wave generation in cells leads to electrical waves in tissue that tend to fractionate to form wavelets of excitation. This fractionation is driven by the underlying stochasticity of subcellular Ca waves, which perturbs AP repolarization and consequently induces localized conduction block in tissue. We outline the mechanism for this effect and argue that it may explain the propensity for atrial arrhythmias in HF.

Feedback control of calcium driven alternans in cardiac myocytes.

Cardiac alternans is a beat-to-beat alternation of the action potential duration (APD), which has been implicated as a possible cause of ventricular fibrillation. Previous studies have shown that alternans can originate via a period doubling bifurcation caused by the nonlinear dependence of the APD on the previous diastolic interval. In this case, it has been demonstrated that alternans can be eliminated by applying feedback control on the pacing cycle length. However, studies have shown that alternans can also originate due to unstable calcium (Ca) cycling in cardiac myocytes. In this study, we explore the effectiveness of APD feedback control to suppress alternans when the underlying instability is due to unstable Ca cycling. In particular, we explore the role of the bi-directional coupling between Ca and voltage and determine the effectiveness of feedback control under a wide range of conditions. We also analyze the applicability of feedback control on a coupled two cell system and show that APD control induces spatially out-of-phase alternans. We analyze the onset and the necessary conditions for the emergence of these out-of-phase patterns and assess the effectiveness of feedback control to suppress Ca driven alternans in a multi-cellular system.

Stochastic coupled map model of subcellular calcium cycling in cardiac cells.

In this study, we analyze a nonlinear map model of intracellular calcium (Ca) and voltage in cardiac cells. In this model, Ca release from the sarcoplasmic reticulum (SR) occurs at spatially distributed dyadic junctions that are diffusively coupled. At these junctions, release occurs with a probability that depends on key variables such as the SR load and the diastolic interval. Using this model, we explore how nonlinearity and stochasticity determine the spatial distribution of Ca release events within a cardiac cell. In particular, we identify a novel synchronization transition, which occurs at rapid pacing rates, in which the global Ca transient transitions from a period 2 response to a period 1 response. In the global period 2 response dyadic junctions fire in unison, on average, on alternate beats, while in the period 1 regime, Ca release at individual dyads is highly irregular. A close examination of the spatial distribution of Ca reveals that in the period 1 regime, the system coarsens into spatially out-of-phase regions with a length scale much smaller than the system size, but larger than the spacing between dyads. We have also explored in detail the coupling to membrane voltage. We study first the case of positive coupling, where a large Ca transient promotes a long action potential duration (APD). Here, the coupling to voltage synchronizes Ca release so that the system exhibits a robust period 2 response that is independent of initial conditions. On the other hand, in the case of negative coupling, where a large Ca transient tends to shorten the APD, we find a multitude of metastable states which consist of complex spatially discordant alternans patterns. Using an analogy to equilibrium statistical mechanics, we show that the spatial patterns observed can be explained by a mapping to the Potts model, with an additional term that accounts for a global coupling of spin states. Using this analogy, we argue that Ca cycling in cardiac cells exhibits complex spatiotemporal patterns that emerge via first or second order phase transitions. These results show that voltage and Ca can interact in order to induce complex subcellular responses, which can potentially lead to heart rhythm disorders.

Synchronization of Triggered Waves in Atrial Tissue.

When an atrial cell is paced rapidly, calcium (Ca) waves can form on the cell boundary and propagate to the cell interior. These waves are referred to as "triggered waves" because they are initiated by Ca influx from the L-type Ca channel and occur during the action potential. However, the consequences of triggered waves in atrial tissue are not known. Here, we develop a phenomenological model of Ca cycling in atrial myocytes that accounts for the formation of triggered waves. Using this model, we show that a fundamental requirement for triggered waves to induce abnormal electrical activity in tissue is that these waves must be synchronized over large populations of cells. This is partly because triggered waves induce a long action potential duration (APD) followed by a short APD. Thus, if these events are not synchronized between cells, then they will on average cancel and have minimal effects on the APD in tissue. Using our computational model, we identify two distinct mechanisms for triggered wave synchronization. The first relies on cycle length (CL) variability, which can prolong the CL at a given beat. In cardiac tissue, we show that CL prolongation leads to a substantial amplification of APD because of the synchronization of triggered waves. A second synchronization mechanism applies in a parameter regime in which the cell exhibits stochastic alternans in which a triggered wave fires, on average, only every other beat. In this scenario, we identify a slow synchronization mechanism that relies on the bidirectional feedback between the APD in tissue and triggered wave initiation. On large cables, this synchronization mechanism leads to spatially discordant APD alternans with spatial variations on a scale of hundreds of cells. We argue that these spatial patterns can potentially serve as an arrhythmogenic substrate for the initiation of atrial fibrillation.

Mechanism for Triggered Waves in Atrial Myocytes.

Excitation-contraction coupling in atrial cells is mediated by calcium (Ca) signaling between L-type Ca channels and Ryanodine receptors that occurs mainly at the cell boundary. This unique architecture dictates essential aspects of Ca signaling under both normal and diseased conditions. In this study we apply laser scanning confocal microscopy, along with an experimentally based computational model, to understand the Ca cycling dynamics of an atrial cell subjected to rapid pacing. Our main finding is that when an atrial cell is paced under Ca overload conditions, Ca waves can then nucleate on the cell boundary and propagate to the cell interior. These propagating Ca waves are referred to as "triggered waves" because they are initiated by L-type Ca channel openings during the action potential. These excitations are distinct from spontaneous Ca waves originating from random fluctuations of Ryanodine receptor channels, and which occur after much longer waiting times. Furthermore, we argue that the onset of these triggered waves is a highly nonlinear function of the sarcoplasmic reticulum Ca load. This strong nonlinearity leads to aperiodic response of Ca at rapid pacing rates that is caused by the complex interplay between paced Ca release and triggered waves. We argue further that this feature of atrial cells leads to dynamic instabilities that may underlie atrial arrhythmias. These studies will serve as a starting point to explore the nonlinear dynamics of atrial cells and will yield insights into the trigger and maintenance of atrial fibrillation.

Stochastic spontaneous calcium release events and sodium channelopathies promote ventricular arrhythmias.

Premature ventricular complexes (PVCs), the first initiating beats of a variety of cardiac arrhythmias, have been associated with spontaneous calcium release (SCR) events at the cell level. However, the mechanisms underlying the degeneration of such PVCs into arrhythmias are not fully understood. The objective of this study was to investigate the conditions under which SCR-mediated PVCs can lead to ventricular arrhythmias. In particular, we sought to determine whether sodium (Na+) current loss-of-function in the structurally normal ventricles provides a substrate for unidirectional conduction block and reentry initiated by SCR-mediated PVCs. To achieve this goal, a stochastic model of SCR was incorporated into an anatomically accurate compute model of the rabbit ventricles with the His-Purkinje system (HPS). Simulations with reduced Na+ current due to a negative-shift in the steady-state channel inactivation showed that SCR-mediated delayed afterdepolarizations led to PVC formation in the HPS, where the electrotonic load was lower, conduction block, and reentry in the 3D myocardium. Moreover, arrhythmia initiation was only possible when intrinsic electrophysiological heterogeneity in action potential within the ventricles was present. In conclusion, while benign in healthy individuals SCR-mediated PVCs can lead to life-threatening ventricular arrhythmias when combined with Na+ channelopathies.

Calcium alternans is due to an order-disorder phase transition in cardiac cells.

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.

Identifying Key Binding Interactions Between the Cardiac L-Type Calcium Channel and Calmodulin Using Molecular Dynamics Simulations.

Defects in the binding of the calcium sensing protein calmodulin (CaM) to the L-type calcium channel (CaV1.2) or to the ryanodine receptor type 2 (RyR2) can lead to dangerous cardiac arrhythmias with distinct phenotypes, such as long-QT syndrome (LQTS) and catecholaminergic ventricular tachycardia (CPVT). Certain CaM mutations lead to LQTS while other mutations lead to CPVT, but the mechanisms by which a specific mutation can lead to each disease phenotype are not well-understood. In this study, we use long, 2 µs molecular dynamics simulations and a multitrajectory approach to identify the key binding interactions between the IQ domain of CaV1.2 and CaM. Five key interactions are found between CaV1.2 and CaM in the C-lobe, 1 in the central linker, and 2 in the N-lobe. In addition, while 5 key interactions appear between residues 120-149 in the C-lobe of CaM when it interacts with CaV1.2, only 1 key interaction is found within this region of CaM when it interacts with the RyR2. We show that this difference in the distribution of key interactions correlates with the known distribution of CaM mutations that lead to LQTS or CPVT. This correlation suggests that a disruption of key binding interactions is a plausible mechanism that can lead to these two different disease phenotypes.

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

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

Cardiac cellular coupling and the spread of early instabilities in intracellular Ca2+.

Recent experimental and modeling studies demonstrate the fine spatial scale, complex nature, and independent contribution of Ca(2+) dynamics as a proarrhythmic factor in the heart. The mechanism of progression of cell-level Ca(2+) instabilities, known as alternans, to tissue-level arrhythmias is not well understood. Because gap junction coupling dictates cardiac syncytial properties, we set out to elucidate its role in the spatiotemporal evolution of Ca(2+) instabilities. We experimentally perturbed cellular coupling in cardiac syncytium in vitro. Coupling was quantified by fluorescence recovery after photobleaching, and related to function, including subtle fine-scale Ca(2+) alternans, captured by optical mapping. Conduction velocity and threshold for alternans monotonically increased with coupling. Lower coupling enhanced Ca(2+) alternans amplitude, but the spatial spread of early (<2 Hz) alternation was the greatest under intermediate (not low) coupling. This nonmonotonic relationship was closely matched by the percent of samples exhibiting large-scale alternans at higher pacing rates. Computer modeling corroborated these experimental findings for strong but not weak electromechanical (voltage-Ca(2+)) coupling, and offered mechanistic insight. In conclusion, using experimental and modeling approaches, we reveal a general mechanism for the spatial spread of subtle cellular Ca(2+) alternans that relies on a combination of gap-junctional and voltage-Ca(2+) coupling.

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

BACKGROUND: Abnormalities in intracellular calcium (Ca) cycling during Ca overload can cause triggered activity because spontaneous calcium release (SCR) activates sufficient Ca-sensitive inward currents to induce delayed afterdepolarizations (DADs). However, little is known about the mechanisms relating SCR and triggered activity on the tissue scale. METHODS AND RESULTS: Laser scanning confocal microscopy was used to measure the spatiotemporal properties of SCR within large myocyte populations in intact rat heart. Computer simulations were used to predict how these properties of SCR determine DAD magnitude. We measured the average and standard deviation of the latency distribution of SCR within a large population of myocytes in intact tissue. We found that as external [Ca] is increased, and with faster pacing rates, the average and SD of the latency distribution decreases substantially. This result demonstrates that the timing of SCR occurs with less variability as the sarcoplasmic reticulum (SR) Ca load is increased, causing more sites to release Ca within each cell. We then applied a mathematical model of subcellular Ca cycling to show that a decrease in SCR variability leads to a higher DAD amplitude and is dictated by the rate of SR Ca refilling following an action potential. CONCLUSIONS: Our results demonstrate that the variability of the timing of SCR in a population of cells in tissue decreases with SR load and is dictated by the time course of the SR Ca content.

Exploring the dynamics of dimer crossing over a Kramers type potential.

We explore the escape rate of a dimer crossing a potential barrier using both analytical and numerical approaches. We find that for small coupling strength k, the barrier hopping can be well approximated by a two step reaction scheme where one monomer hops over the barrier and is then followed by the other. In this regime the escape rate increases with k showing that the cooperativity between monomers enhances the crossing rate. However, in the limit of large coupling strength, applying the method of adiabatic elimination, we find that the escape rate is a decreasing function of k. Thus, we find that the escape rate is a non-monotonic function of the spring constant which is peaked at an optimal coupling strength. Furthermore, in the presence of a weak periodic signal, we show that the system response to the periodic signal is pronounced at a particular spring constant showing the dimer can be transported rapidly across the reaction coordinate in a half period.