Ryanodine receptor allosteric coupling and the dynamics of calcium sparks

Puffs and sparks are localized intracellular Ca2+ elevations that arise from the cooperative activity of Ca2+-regulated inositol 1,4,5-trisphosphate receptors and ryanodine receptors clustered at Ca2+ release sites on the surface of the endoplasmic reticulum or the sarcoplasmic reticulum. While the synchronous gating of Ca2+-regulated Ca2+ channels can be mediated entirely though the buffered diffusion of intracellular Ca2+, interprotein allosteric interactions also contribute to the dynamics of ryanodine receptor (RyR) gating and Ca2+ sparks. In this article, Markov chain models of Ca2+ release sites are used to investigate how the statistics of Ca2+ spark generation and termination are related to the coupling of RyRs via local [Ca2+] changes and allosteric interactions. Allosteric interactions are included in a manner that promotes the synchronous gating of channels by stabilizing neighboring closed-closed and/or open-open channel pairs. When the strength of Ca2+-mediated channel coupling is systematically varied (e.g., by changing the Ca2+ buffer concentration), simulations that include synchronizing allosteric interactions often exhibit more robust Ca2+ sparks; however, for some Ca2+ coupling strengths the sparks are less robust. We find no evidence that the distribution of spark durations can be used to distinguish between allosteric interactions that stabilize closed channel pairs, open channel pairs, or both in a balanced fashion. On the other hand, the changes in spark duration, interspark interval, and frequency observed when allosteric interactions that stabilize closed channel pairs are gradually removed from simulations are qualitatively different than the changes observed when open or both closed and open channel pairs are stabilized. Thus, our simulations clarify how changes in spark statistics due to pharmacological washout of the accessory proteins mediating allosteric coupling may indicate the type of synchronizing allosteric interactions exhibited by physically coupled RyRs. We also investigate the validity of a mean-field reduction applicable to the dynamics of a ryanodine receptor cluster coupled via local [Ca2+] and allosteric interactions. In addition to facilitating parameter studies of the effect of allosteric coupling on spark statistics, the derivation of the mean-field model establishes the correct functional form for cooperativity factors representing the coupled gating of RyRs. This mean-field formulation is well suited for use in computationally efficient whole cell simulations of excitation-contraction coupling.