Calcium-dependent inactivation and the dynamics of calcium puffs and sparks

Localized intracellular Ca 2 + elevations known as puffs and sparks arise from the cooperative activity of inositol 1,4,5-trisphosphate receptor Ca 2 + channels ( IP 3 R s) and ryanodine receptor Ca 2 + channels (RyRs) clustered at Ca 2 + release sites on the surface of the endoplasmic reticulum or sarcoplasmic reticulum. When Markov chain models of these intracellular Ca 2 + -regulated Ca 2 + channels are coupled via a mathematical representation of a Ca 2 + microdomain, simulated Ca 2 + release sites may exhibit the phenomenon of “stochastic Ca 2 + excitability” reminiscent of Ca 2 + puffs and sparks where channels open and close in a concerted fashion. To clarify the role of Ca 2 + inactivation of IP 3 R s and RyRs in the dynamics of puffs and sparks, we formulate and analyze Markov chain models of Ca 2 + release sites composed of 10–40 three-state intracellular Ca 2 + channels that are inactivated as well as activated by Ca 2 + . We study how the statistics of simulated puffs and sparks depend on the kinetics and dissociation constant of Ca 2 + inactivation and find that puffs and sparks are often less sensitive to variations in the number of channels at release sites and strength of coupling via local [ Ca 2 + ] when the average fraction of inactivated channels is significant. Interestingly, we observe that the single channel kinetics of Ca 2 + inactivation influences the thermodynamic entropy production rate of Markov chain models of puffs and sparks. While excessively fast Ca 2 + inactivation can preclude puffs and sparks, moderately fast Ca 2 + inactivation often leads to time-irreversible puffs and sparks whose termination is facilitated by the recruitment of inactivated channels throughout the duration of the puff/spark event. On the other hand, Ca 2 + inactivation may be an important negative feedback mechanism even when its time constant is much greater than the duration of puffs and sparks. In fact, slow Ca 2 + inactivation can lead to release sites with a substantial fraction of inactivated channels that exhibit puffs and sparks that are nearly time-reversible and terminate without additional recruitment of inactivated channels.