Markov chain models of coupled calcium channels: Kronecker representations and iterative solution methods.

Mathematical models of calcium release sites derived from Markov chain models of intracellular calcium channels exhibit collective gating reminiscent of the experimentally observed phenomenon of stochastic calcium excitability (i.e., calcium puffs and sparks).

Calcium release site ultrastructure and the dynamics of puffs and sparks.

When Markov chain models of 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. Interestingly, some single-channel models that include Ca(2+) inactivation are not particularly sensitive to channel density, so long as the requirement for inter-channel communication is satisfied, while other single-channel models that do not include Ca(2+) inactivation open and close synchronously only when the channel density is in a prescribed range. This observation led us to hypothesize that single-channel models with Ca(2+) inactivation would be less sensitive to the details of release site ultrastructure than models that lack a slow Ca(2+) inactivation process.

Markov chain models of coupled intracellular calcium channels: Kronecker structured representations and benchmark stationary distribution calculations.

Mathematical models of calcium release sites derived from Markov chain models of intracellular calcium channels exhibit collective gating reminiscent of the experimentally observed phenomenon of stochastic calcium excitability (i.e., calcium puffs and sparks).

The dynamics of stochastic attrition viewed as an absorption time on a terminating Markov chain.

Localized Ca(2+) elevations known as Ca(2+) puffs and sparks are cellular signals that arise from the cooperative activity of clusters of inositol 1,4,5-trisphosphate receptors and ryanodine receptors 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 Ca(2+) microdomain, simulated Ca(2+) release sites may exhibit the phenomenon of "stochastic Ca(2+) excitability" where the inositol 1,4,5-trisphosphate receptors (IP(3)Rs) or ryanodine receptors (RyRs) open and close in a concerted fashion. Interestingly, under some conditions simulated puffs and sparks can be observed even when the single-channel model used does not include slow Ca(2+) inactivation or, indeed, any long-lived closed/refractory state [V.