A novel stochastic reaction-diffusion model of Ca2+ blink in cardiac myocytes

A stochastic mathematical model for coupling the cytosolic and sarcoplasmic calcium movements in diseased cardiac myocytes

Several computational studies have been undertaken to explore the Ca²⁺-induced Ca²⁺ release (CICR) events in cardiac myocytes and along with experimental studies it has given us invaluable insight into the mechanism of CICR from spark/blink initiation to termination and regulation, and their interplay under normal and pathological conditions. The computational modelling of this mechanism has mainly been investigated using coupled differential equations (DEs). However, there is a lack of computational investigation into (1) how the different formulation of coupled DEs capture the Ca²⁺ movement in the cytosol and sarcoplasmic reticulum (SR), (2) the buffer and dye inclusion in both compartments, and (3) the effect of buffer and dye properties on the calcium behaviour. This work is set out to explore (1) the effect of different coupled formulation of DEs on spark/blink occurrence, (2) the inclusion of improved sarcoplasmic buffering properties, and (3) the effects of cytosolic and sarcoplasmic dye and buffer properties on Ca²⁺ movement. The simulation results show large discrepancies between different formulations of the governing equations. Additionally, extension of the model to include sarcoplasmic buffering properties show normalised fluorescent dye profiles to be in good agreement with experimental and amongst its one- and two-dimensional representations.

Estimation of stochastic behaviour in cardiac myocytes: I. Ca2+ movements inside the cytosol and sarcoplasmic reticulum on curvilinear domains

Since the discovery of Ca2+ sparks and their stochastic behaviour in cardiac myocytes, models have focused on the inclusion of stochasticity in their studies. While most models pay much attention to the stochastic modelling of cytosolic Ca2+ concentration the coupling of Ca2+ sparks and blinks in a stochastic model has not been explored fully. The cell morphology in in silico studies in the past is assumed to be Cartesian, spherical or cylindrical. The application on curvilinear grids can easily address certain restrictions posed by such grid set up and provide more realistic cell morphology. In this paper, we present a stochastic reaction-diffusion model that couples Ca2+ sparks and blinks in realistic shapes of cells in curvilinear domains. Methodology: Transformation of the model was performed to the curvilinear coordinate system. The set of equations is used to produce Ca2+ waves initiated from sparks and blinks. A non-buffered and non-dyed version as well as a buffered and dyed version of these equations were studied in light of observing the dynamics on the two different systems. For comparison, results for both the Cartesian and curvilinear grids are provided. Results and conclusions: A successful demonstration of the application of curvilinear grids serving as basis for future developments.

Effects of rogue ryanodine receptors on Ca2+ sparks in cardiac myocytes

Ca2+ sparks and Ca2+ quarks, arising from clustered and rogue ryanodine receptors (RyRs), are significant Ca2+ release events from the junctional sarcoplasmic reticulum (JSR). Based on the anomalous subdiffusion of Ca2+ in the cytoplasm, a mathematical model was developed to investigate the effects of rogue RyRs on Ca2+ sparks in cardiac myocytes. Ca2+ quarks and sparks from the stochastic opening of rogue and clustered RyRs are numerically reproduced and agree with experimental measurements. It is found that the stochastic opening Ca2+ release units (CRUs) of clustered RyRs are regulated by free Ca2+ concentration in the JSR lumen (i.e. [Ca2+]lumen). The frequency of spontaneous Ca2+ sparks is remarkably increased by the rogue RyRs opening at high [Ca2+]lumen, but not at low [Ca2+]lumen. Hence, the opening of rogue RyRs contributes to the formation of Ca2+ sparks at high [Ca2+]lumen. The interplay of Ca2+ sparks and Ca2+ quarks has been discussed in detail. This work is of significance to provide insight into understanding Ca2+ release mechanisms in cardiac myocytes.

Role of FK506-binding protein in Ca2+ spark regulation

The elementary Ca²⁺ release events, Ca²⁺ sparks, has been found for a quarter of century. However, the molecular regulation of the spark generator, the ryanodine receptor (RyR) on the sarcoplasmic reticulum, remains obscure. Although each subunit of the RyR homotetramer has a site for FK506-binding protein (FKBP), the role of FKBPs in modifying RyR Ca²⁺ sparks has been debated for long. One of the reasons behind the controversy is that most previous studies detect spontaneous sparks, where the mixture with out-of-focus events and local wavelets prevents an accurate characterization of Ca²⁺ sparks. In the present study, we detected Ca²⁺ sparks triggered by single L-type Ca²⁺ channels (LCCs) under loose-seal patch clamp conditions in FK506-treated or FKBP12.6 knockout cardiomyocytes. We found that FKBP dissociation both by FK506 and by rapamycin decreased the Ca²⁺ spark amplitude in ventricular cardiomyocytes. This change was neither due to decreased releasable Ca²⁺ in the sarcoplasmic reticulum, nor explained by changed RyR sensitivity. Actually FK506 increased the LCC-RyR coupling probability and curtailed the latency for an LCC to trigger a RyR Ca²⁺ spark. FKBP12.6 knockout had similar effects as FK506/rapamycin treatment, indicating that the decreased spark amplitude was attributable to the dissociation of FKBP12.6 rather than FKBP12. We also explained how decreased amplitude of spontaneous sparks after FKBP dissociation sometimes appears to be increased or unchanged due to inappropriate data processing. Our results provided firm evidence that without the inter-RyR coordination by functional FKBP12.6, the RyR recruitment during a Ca²⁺ spark would be compromised despite the sensitization of individual RyRs.