"... Here we present a formalism by which mathematical models for Ca2+-regulated Ca2+ release sites
are derived from stochastic models of single-channel gating that include Ca2+ activation, Ca2+
inactivation, or both.
Such models are stochastic automata networks (SANs) that involve a large
number of functional transitions, that is, the transition probabilities of the infinitesimal generator
matrix of one of the automata (i.e., an individual channel) may depend on the local [Ca2+] and
thus the state of the other channels. Simulation and analysis of the SAN descriptors representing
homogeneous clusters of intracellular Ca2+ channels show that (1) release site density can modify
both the steady-state open probability and stochastic excitability of Ca2+ release sites, (2) Ca2+
inactivation is not a requirement for Ca2+ puffs or sparks, and (3) a single-channel model with a
bell-shaped open probability curve does not lead to release site activity that is a biphasic function of
release site density.
Nguyen V, Mathias R, Smith GD (2005) A stochastic automata network descriptor for Markov chain models of instantaneously coupled intracellular Ca2+ channels. Bull Math Biol 67:393-432 [PubMed]