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

Localized intracellular Ca²⁺ elevations known as puffs and sparks arise from the cooperative activity of inositol 1,4,5-trisphosphate receptor Ca²⁺ channels (IP₃Rs) and ryanodine receptor Ca²⁺ channels (RyRs) clustered at Ca²⁺ release sites on the surface of the endoplasmic reticulum or sarcoplasmic reticulum. When Markov chain models of these intracellular Ca²⁺-regulated Ca²⁺ channels are coupled via a mathematical representation of a Ca²⁺ microdomain, simulated Ca²⁺ release sites may exhibit the phenomenon of “stochastic Ca²⁺ excitability” reminiscent of Ca²⁺ puffs and sparks where channels open and close in a concerted fashion. To clarify the role of Ca²⁺ inactivation of IP₃Rs and RyRs in the dynamics of puffs and sparks, we formulate and analyze Markov chain models of Ca²⁺ release sites composed of 10–40 three-state intracellular Ca²⁺ channels that are inactivated as well as activated by Ca²⁺. We study how the statistics of simulated puffs and sparks depend on the kinetics and dissociation constant of Ca²⁺ 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 Ca²⁺] when the average fraction of inactivated channels is significant. Interestingly, we observe that the single channel kinetics of Ca²⁺ inactivation influences the thermodynamic entropy production rate of Markov chain models of puffs and sparks. While excessively fast Ca²⁺ inactivation can preclude puffs and sparks, moderately fast Ca²⁺ 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, Ca²⁺ 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 Ca²⁺ 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.