A simple numerical model of calcium spark formation and detection in cardiac myocytes.
G. Smith, J. Keizer, M. Stern, W. Lederer, and H. Cheng.
Biophys. J. 75 (1): 15--32 (July 1998)

The elementary events of excitation-contraction coupling in heart muscle are Ca$^2+$ sparks, which arise from one or more ryanodine receptors in the sarcoplasmic reticulum (SR). Here a simple numerical model is constructed to explore Ca$^2+$ spark formation, detection, and interpretation in cardiac myocytes. This model includes Ca$^2+$ release, cytosolic diffusion, resequestration by SR Ca$^2+$-ATPases, and the association and dissociation of Ca$^2+$ with endogenous Ca$^2+$-binding sites and a diffusible indicator dye (fluo-3). Simulations in a homogeneous, isotropic cytosol reproduce the brightness and the time course of a typical cardiac Ca$^2+$ spark, but underestimate its spatial size (approximately 1.1 micron vs. approximately 2.0 micron). Back-calculating Ca$^2+$i by assuming equilibrium with indicator fails to provide a good estimate of the free Ca$^2+$ concentration even when using blur-free fluorescence data. A parameter sensitivity study reveals that the mobility, kinetics, and concentration of the indicator are essential determinants of the shape of Ca$^2+$ sparks, whereas the stationary buffers and pumps are less influential. Using a geometrically more complex version of the model, we show that the asymmetric shape of Ca$^2+$ sparks is better explained by anisotropic diffusion of Ca$^2+$ ions and indicator dye rather than by subsarcomeric inhomogeneities of the Ca$^2+$ buffer and transport system. In addition, we examine the contribution of off-center confocal sampling to the variance of spark statistics.
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