Does the Goldilocks Principle apply to calcium release restitution in heart cells?

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.

Biological optimization, the Goldilocks principle, and how much is lagom in the preimplantation embryo

The quiet embryo hypothesis postulates that early embryo viability is associated with a relatively low metabolism (Leese, 2002 BioEssays 24: 845-849). This proposal is re-visited here using retrospective and prospective data on the metabolic activity and kinetics of preimplantation development alongside the concept that an optimal range of such indices and of energetic efficiency influences embryogenesis. It is concluded that these considerations may be rationalized by proposing the existence of a "Goldilocks zone," or as it is known in Sweden, of lagom-meaning "just the right amount"-within which embryos with maximum developmental potential can be categorized. Mol. Reprod. Dev. 83: 748-754, 2016 © 2016 Wiley Periodicals, Inc.

Oncogene Overdose: Too Much of a Bad Thing for Oncogene-Addicted Cancer Cells

Acquired resistance to targeted inhibitors remains a major, and inevitable, obstacle in the treatment of oncogene-addicted cancers. Newer-generation inhibitors may help overcome resistance mutations, and inhibitor combinations can target parallel pathways, but durable benefit to patients remains elusive in most clinical scenarios. Now, recent studies suggest a third approach may be available in some cases—exploitation of oncogene overexpression that may arise to promote resistance. Here, we discuss the importance of maintaining oncogenic signaling at “just-right” levels in cells, with too much signaling, or oncogene overdose, being potentially as detrimental as too little. This is highlighted in particular by recent studies of mutant-BRAF in melanoma and the fusion kinase nucleophosmin–anaplastic lymphoma kinase (NPM–ALK) in anaplastic large cell lymphoma. Oncogene overdose may be exploitable to prolong tumor control through intermittent dosing in some cases, and studies of acute lymphoid leukemias suggest that it may be specifically pharmacologically inducible.

Impaired calcium-calmodulin-dependent inactivation of Cav1.2 contributes to loss of sarcoplasmic reticulum calcium release refractoriness in mice lacking calsequestrin 2

AIMS

In cardiac muscle, Ca(2+) release from sarcoplasmic reticulum (SR) is reduced with successively shorter coupling intervals of premature stimuli, a phenomenon known as SR Ca(2+) release refractoriness. We recently reported that the SR luminal Ca(2+) binding protein calsequestrin 2 (Casq2) contributes to release refractoriness in intact mouse hearts, but the underlying mechanisms remain unclear. Here, we further investigate the mechanisms responsible for physiological release refractoriness.

METHODS AND RESULTS

Gene-targeted ablation of Casq2 (Casq2 KO) abolished SR Ca(2+) release refractoriness in isolated mouse ventricular myocytes. Surprisingly, impaired Ca(2+)-dependent inactivation of L-type Ca(2+) current (ICa), which is responsible for triggering SR Ca(2+) release, significantly contributed to loss of Ca(2+) release refractoriness in Casq2 KO myocytes. Recovery from Ca(2+)-dependent inactivation of ICa was significantly accelerated in Casq2 KO compared to wild-type (WT) myocytes. In contrast, voltage-dependent inactivation measured by using Ba(2+) as charge carrier was not significantly different between WT and Casq2 KO myocytes. Ca(2+)-dependent inactivation of ICa was normalized by intracellular dialysis of excess apo-CaM (20 μM), which also partially restored physiological Ca(2+) release refractoriness in Casq2 KO myocytes.

CONCLUSIONS

Our findings reveal that the intra-SR protein Casq2 is largely responsible for the phenomenon of SR Ca(2+) release refractoriness in murine ventricular myocytes. We also report a novel mechanism of impaired Ca(2+)-CaM-dependent inactivation of Cav1.2, which contributes to the loss of SR Ca(2+) release refractoriness in the Casq2 KO mouse model and, therefore, may further increase risk for ventricular arrhythmia in vivo.

Nonlinear and Stochastic Dynamics in the Heart

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

Maximal acceleration of Ca2+ release refractoriness by β-adrenergic stimulation requires dual activation of kinases PKA and CaMKII in mouse ventricular myocytes

KEY POINTS

Refractoriness of calcium release in heart cells is altered in several disease states, but the physiological mechanisms that regulate this process are incompletely understood. We examined refractoriness of calcium release in mouse ventricular myocytes and investigated how activation of different intracellular signalling pathways influenced this process. We found that refractoriness of calcium release is abbreviated by stimulation of the 'fight-or-flight' response, and that simultaneous activation of multiple intracellular signalling pathways contributes to this response. Data obtained under several conditions at the subcellular, microscopic level were consistent with results obtained at the cellular level. The results provide insight into regulation of cardiac calcium release and how alterations to this process may increase arrhythmia risk under different conditions.

ABSTRACT

Time-dependent refractoriness of calcium (Ca(2+)) release in cardiac myocytes is an important factor in determining whether pro-arrhythmic release patterns develop. At the subcellular level of the Ca(2+) spark, recent studies have suggested that recovery of spark amplitude is controlled by local sarcoplasmic reticulum (SR) refilling whereas refractoriness of spark triggering depends on both refilling and the sensitivity of the ryanodine receptor (RyR) release channels that produce sparks. Here we studied regulation of Ca(2+) spark refractoriness in mouse ventricular myocytes by examining how β-adrenergic stimulation influenced sequences of Ca(2+) sparks originating from individual RyR clusters. Our protocol allowed us to separately measure recovery of spark amplitude and delays between successive sparks, and data were interpreted quantitatively through simulations with a stochastic mathematical model. We found that, compared with spark sequences measured under control conditions: (1) β-adrenergic stimulation with isoproterenol (isoprenaline) accelerated spark amplitude recovery and decreased spark-to-spark delays; (2) activating protein kinase A (PKA) with forskolin accelerated amplitude recovery but did not affect spark-to-spark delays; (3) inhibiting PKA with H89 retarded amplitude recovery and increased spark-to-spark delays; (4) preventing phosphorylation of the RyR at serine 2808 with a knock-in mouse prevented the decrease in spark-to-spark delays seen with β-adrenergic stimulation; (5) inhibiting either PKA or Ca(2+)/calmodulin-dependent protein kinase II (CaMKII) during β-adrenergic stimulation prevented the decrease in spark-to-spark delays seen without inhibition. The results suggest that activation of either PKA or CaMKII is sufficient to speed SR refilling, but activation of both kinases appears necessary to observe increased RyR sensitivity. The data provide novel insight into β-adrenergic regulation of Ca(2+) release refractoriness in mouse myocytes.

Parameter sensitivity analysis of stochastic models provides insights into cardiac calcium sparks

We present a parameter sensitivity analysis method that is appropriate for stochastic models, and we demonstrate how this analysis generates experimentally testable predictions about the factors that influence local Ca(2+) release in heart cells. The method involves randomly varying all parameters, running a single simulation with each set of parameters, running simulations with hundreds of model variants, then statistically relating the parameters to the simulation results using regression methods. We tested this method on a stochastic model, containing 18 parameters, of the cardiac Ca(2+) spark. Results show that multivariable linear regression can successfully relate parameters to continuous model outputs such as Ca(2+) spark amplitude and duration, and multivariable logistic regression can provide insight into how parameters affect Ca(2+) spark triggering (a probabilistic process that is all-or-none in a single simulation). Benchmark studies demonstrate that this method is less computationally intensive than standard methods by a factor of 16. Importantly, predictions were tested experimentally by measuring Ca(2+) sparks in mice with knockout of the sarcoplasmic reticulum protein triadin. These mice exhibit multiple changes in Ca(2+) release unit structures, and the regression model both accurately predicts changes in Ca(2+) spark amplitude (30% decrease in model, 29% decrease in experiments) and provides an intuitive and quantitative understanding of how much each alteration contributes to the result. This approach is therefore an effective, efficient, and predictive method for analyzing stochastic mathematical models to gain biological insight.

Calcium alternans in cardiac myocytes: order from disorder

Calcium alternans is associated with T-wave alternans and pulsus alternans, harbingers of increased mortality in the setting of heart disease. Recent experimental, computational, and theoretical studies have led to new insights into the mechanisms of Ca alternans, specifically how disordered behaviors dominated by stochastic processes at the subcellular level become organized into ordered periodic behaviors. In this article, we summarize the recent progress in this area, outlining a holistic theoretical framework in which the complex effects of Ca cycling proteins on Ca alternans are linked to three key properties of the cardiac Ca cycling network: randomness, refractoriness, and recruitment. We also illustrate how this '3R theory' can reconcile many seemingly contradictory experimental observations.

Store-dependent deactivation: cooling the chain-reaction of myocardial calcium signaling

In heart cells, Ca(2+) released from the internal storage unit, the sarcoplasmic reticulum (SR) through ryanodine receptor (RyR2) channels is the predominant determinant of cardiac contractility. Evidence obtained in recent years suggests that SR Ca(2+) release is tightly regulated not only by cytosolic Ca(2+) but also by intra-store Ca(2+) concentration. Specifically, Ca(2+)-induced Ca(2+) release (CICR) that relies on auto-catalytic action of Ca(2+) at the cytosolic side of RyR2s is precisely balanced and counteracted by RyR2 deactivation dependent on a reciprocal decrease of Ca(2+) at the luminal side of RyR2s. Dysregulation of this inherently unstable Ca(2+) signaling is considered to be an underlying cause of triggered arrhythmias, and is associated with genetic and acquired forms of sudden cardiac death. In this article, we present an overview of recent advances in our understanding of the regulatory role luminal Ca(2+) plays in Ca(2+) handling, with a particular emphasis on the role of Ca(2+)release refractoriness in aberrant Ca(2+) release.

Decoding myocardial Ca²⁺ signals across multiple spatial scales: a role for sensitivity analysis

Numerous studies have employed mathematical modeling to quantitatively understand release of Ca(2+) from the sarcoplasmic reticulum (SR) in the heart. Models have been used to investigate physiologically important phenomena such as triggering of SR Ca(2+) release by Ca(2+) entry across the cell membrane and spontaneous leak of Ca(2+) from the SR in quiescent heart cells. In this review we summarize studies that have modeled myocardial Ca(2+) at different spatial scales: the sub-cellular level, the cellular level, and the multicellular level. We discuss each category of models from the standpoint of parameter sensitivity analysis, a common simulation procedure that can generate quantitative, comprehensive predictions about how changes in conditions influence model output. We propose that this is a useful perspective for conceptualizing models, in part because a sensitivity analysis requires the investigator to define the relevant parameters and model outputs. This procedure therefore helps to illustrate the capabilities and limitations of each model. We further suggest that in future studies, sensitivity analyses will aid in simplifying complex models and in suggesting experiments to differentiate between competing models built with different assumptions. We conclude with a discussion of unresolved questions that are likely to be addressed over the next several years.

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

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

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

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

Calsequestrin 2 and arrhythmias

Calsequestrin is the most abundant Ca-binding protein of the specialized endoplasmic reticulum found in muscle, the sarcoplasmic reticulum (SR). Calsequestrin binds Ca with high capacity and low affinity and importantly contributes to the mobilization of Ca during each contraction both in skeletal and cardiac muscle. Surprisingly, mutations in the gene encoding the cardiac isoform of calsequestrin (Casq2) have been associated with an inherited form of ventricular arrhythmia triggered by emotional or physical stress termed catecholaminergic polymorphic ventricular tachycardia (CPVT). Despite normal cardiac contractility and normal resting ECG, CPVT patients present with a high risk of sudden death at a young age. Here, we review recent new insights regarding the role of calsequestrin in genetic and acquired arrhythmia disorders. Mouse models of CPVT have shed light on the pathophysiological mechanism underlying CPVT. Casq2 is not only a Ca-storing protein as initially hypothesized, but it has a far more complex function in Ca handling and regulating SR Ca release channels. The functional importance of Casq2 interactions with other SR proteins and the importance of alterations in Casq2 trafficking are also being investigated. Reports of altered Casq2 trafficking in animal models of acquired heart diseases such as heart failure suggest that Casq2 may contribute to arrhythmia risk beyond genetic forms of Casq2 dysfunction.