Termination of cardiac Ca2+ sparks:: An investigative mathematical model of calcium-induced calcium release

A Ca2+ spark arises when a cluster of sarcoplasmic reticulum (SR) channels (ryanodine receptors or RyRs) opens to release calcium in a locally regenerative manner. Normally triggered by Ca2+ influx across the sarcolemmal or transverse tubule membrane neighboring the cluster, the Ca2+ spark has been shown to be the elementary Ca2+ signaling event of excitation-contraction coupling in heart muscle. However, the question of how the Ca2+ spark terminates remains a central, unresolved issue. Here we present a new model, "sticky cluster," of SR Ca2+ release that simulates Ca2+ spark behavior and enables robust Ca2+ spark termination. Two newly documented features of RyR behavior have been incorporated in this otherwise simple model: "coupled gating" and an opening rate that depends on SR lumenal [Ca2+]. Using a Monte Carlo method, local Ca2+-induced Ca2+ release from clusters containing between 10 and 100 RyRs is modeled. After release is triggered, Ca2+ flux from RyRs diffuses into the cytosol and binds to intracellular buffers and the fluorescent Ca2+ indicator fluo-3 to produce the model Ca2+ spark. C2+ sparks generated by the sticky cluster model resemble those observed experimentally, and Ca2+ spark duration and amplitude are largely insensitive to the number of RyRs in a cluster. As expected from heart cell investigation, the spontaneous Ca2+ spark rate in the model increases with elevated cytosolic or SR lumenal [Ca2+]. Furthermore, reduction of RyR coupling leads to prolonged model Ca2+ sparks just as treatment with FK506 lengthens Ca2+ sparks in heart cells. This new model of Ca2+ spark behavior provides a "proof of principle" test of a new hypothesis for Ca2+ spark termination and reproduces critical features of Ca2+ sparks observed experimentally.