Abstract
Mathematical models of Ca2+ release sites derived from Markov chain models of intracellular Ca2+ channels exhibit collective gating reminiscent of the experimentally observed phenomenon of stochastic Ca2+ excitability (i.e., puffs and sparks). Ca2+ release site models are composed of a number of individual channel models whose dynamic behavior depends on the local Ca2+ concentration which is influenced by the state of all channels. We consider this application area to illustrate how stochastic Petri nets and in particular stochastic activity networks can be used to model dynamical phenomena in cell biology. We highlight how state-sharing composition operations as supported by the Mobius framework can represent both mean-field and spatial coupling assumptions in a natural manner. We investigate how state-of-the-art techniques for the numerical and simulative analysis of Markov chains associated with stochastic Petri nets scale when modeling Ca2+ signaling complexes of physiological size and complexity.
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