Modeling gain and gradedness of Ca$^2+$ release in the functional unit of the cardiac diadic space.
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Biophys. J. 77 (4): 1871--1884 (October 1999)

A model of the functional release unit (FRU) in rat cardiac muscle consisting of one dihydropyridine receptor (DHPR) and eight ryanodine receptor (RyR) channels, and the volume surrounding them, is formulated. It is assumed that no spatial Ca$^2+$ gradients exist in this volume, and that each FRU acts independently. The model is amenable to systematic parameter studies in which FRU dynamics are simulated at the channel level using Monte Carlo methods with Ca$^2+$ concentrations simulated by numerical integration of a coupled system of differential equations. Using stochastic methods, Ca$^2+$-induced Ca$^2+$ release (CICR) shows both high gain and graded Ca$^2+$ release that is robust when parameters are varied. For a single DHPR opening, the resulting RyR Ca$^2+$ release flux is insensitive to the DHPR open duration, and is determined principally by local sarcoplasmic reticulum (SR) Ca$^2+$ load, consistent with experimental data on Ca$^2+$ sparks. In addition, single RyR openings are effective in triggering Ca$^2+$ release from adjacent RyRs only when open duration is long and SR Ca$^2+$ load is high. This indicates relatively low coupling between RyRs, and suggests a mechanism that limits the regenerative spread of RyR openings. The results also suggest that adaptation plays an important modulatory role in shaping Ca$^2+$ release duration and magnitude, but is not solely responsible for terminating Ca$^2+$ release. Results obtained with the stochastic model suggest that high gain and gradedness can occur by the recruitment of independent FRUs without requiring spatial Ca$^2+$ gradients within a functional unit or cross-coupling between adjacent functional units.
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