Challenging quantal calcium signaling in cardiac myocytes

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.

Quantitative analysis of calcium spikes in noisy fluorescent background

Intracellular calcium signals are studied by laser-scanning confocal fluorescence microscopy. The required spatio-temporal resolution makes description of calcium signals difficult because of the low signal-to-noise ratio. We designed a new procedure of calcium spike analysis based on their fitting with a model. The accuracy and precision of calcium spike description were tested on synthetic datasets generated either with randomly varied spike parameters and Gaussian noise of constant amplitude, or with constant spike parameters and Gaussian noise of various amplitudes. Statistical analysis was used to evaluate the performance of spike fitting algorithms. The procedure was optimized for reliable estimation of calcium spike parameters and for dismissal of false events. A new algorithm was introduced that corrects the acquisition time of pixels in line-scan images that is in error due to sequential acquisition of individual pixels along the space coordinate. New software was developed in Matlab and provided for general use. It allows interactive dissection of temporal profiles of calcium spikes from x-t images, their fitting with predefined function(s) and acceptance of results on statistical grounds, thus allowing efficient analysis and reliable description of calcium signaling in cardiac myocytes down to the in situ function of ryanodine receptors.

Construction of calcium release sites in cardiac myocytes

Local character of calcium release in cardiac myocytes, as defined by confocal recordings of calcium sparks, implies independent activation of individual calcium release sites based on ryanodine receptor (RyR) channel recruitment. We constructed virtual calcium release sites (vCRSs) composed of a variable number of RyR channels distributed in clusters in accordance with the experimentally observed cluster size distribution. The vCRSs consisted either of a single virtual calcium release unit (vCRU), in which all clusters shared a common dyadic space, or of multiple virtual calcium release units (CRUs) containing one cluster each and having separate dyadic spaces. We explored the stochastic behavior of vCRSs to understand the activation and recruitment of RyRs during calcium sparks. RyRs were represented by the published allosteric gating model that included regulation by cytosolic Ca(2+) and Mg(2+). The interaction of Mg(2+) with the RyR Ca(2+)-binding sites and the refractory period of vCRSs were optimized to accord with the experimentally observed calcium dependence of calcium spark frequency. The Mg(2+)-binding parameters of RyRs that provided the best description of spark frequency depended on the number of RyRs assembled in the vCRSs. Adequate inhibitory effect of Mg(2+) on the calcium dependence of RyR open probability was achieved if the vCRSs contained at least three clusters. For the distribution of the number of open RyRs in evoked calcium sparks to correspond to the experimentally observed distribution of spark calcium release fluxes, at least three clusters had to share a common virtual CRU, in which ∼3 RyRs open to form an average spark. These results reconcile the small cluster size and stochastic placement of RyRs in the release sites with the estimates of the amount of RyR protein, volume density of calcium release sites, and the size of calcium release sites in rat cardiac myocytes.

Calcium spike variability in cardiac myocytes results from activation of small cohorts of ryanodine receptor 2 channels

In mammalian cardiac myocytes, the elementary calcium releases triggered by step voltage stimuli manifest either as solitary or as twin spikes that vary widely in kinetics and amplitude for unknown reasons. Here we examined the variability of calcium spikes measured using line-scanning confocal microscopy in patch-clamped rat ventricular myocytes. Amplitude distributions of the single and of the first of twin spikes were broader than those of the second spikes. All could be best approximated by a sum of a few elementary Gaussian probability distribution functions. The latency distributions of the single and the first spikes were identical, much shorter and less variable than those of the second spikes. The multimodal distribution of spike amplitudes and the probability of occurrence of twin spikes were stochastically congruent with activation of only a few of the many RyR2 channels present in the release site cluster. The occurrence of twin release events was rare due to refractoriness of release, induced with a probability proportional to the number of RyR2s activated in the primary release event. We conclude that the variability of the elementary calcium release events supports a calcium signalling mechanism that arises from stochastics of RyR2 gating and from inactivation of local origin.

Automaticity in acute ischemia: bifurcation analysis of a human ventricular model

Acute ischemia (restriction in blood supply to part of the heart as a result of myocardial infarction) induces major changes in the electrophysiological properties of the ventricular tissue. Extracellular potassium concentration ([K(o)(+)]) increases in the ischemic zone, leading to an elevation of the resting membrane potential that creates an "injury current" (I(S)) between the infarcted and the healthy zone. In addition, the lack of oxygen impairs the metabolic activity of the myocytes and decreases ATP production, thereby affecting ATP-sensitive potassium channels (I(Katp)). Frequent complications of myocardial infarction are tachycardia, fibrillation, and sudden cardiac death, but the mechanisms underlying their initiation are still debated. One hypothesis is that these arrhythmias may be triggered by abnormal automaticity. We investigated the effect of ischemia on myocyte automaticity by performing a comprehensive bifurcation analysis (fixed points, cycles, and their stability) of a human ventricular myocyte model [K. H. W. J. ten Tusscher and A. V. Panfilov, Am. J. Physiol. Heart Circ. Physiol. 291, H1088 (2006)] as a function of three ischemia-relevant parameters [K(o)(+)], I(S), and I(Katp). In this single-cell model, we found that automatic activity was possible only in the presence of an injury current. Changes in [K(o)(+)] and I(Katp) significantly altered the bifurcation structure of I(S), including the occurrence of early-after depolarization. The results provide a sound basis for studying higher-dimensional tissue structures representing an ischemic heart.