Stochastic Petri net models of Ca signaling complexes and their analysis

Mathematical models of Ca release sites derived from Markov chain models of intracellular Ca channels exhibit collective gating reminiscent of the experimentally observed phenomenon of stochastic Ca excitability (i.e., puffs and sparks). Ca release site models are composed of a number of individual channel models whose dynamic behavior depends on the local Ca 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 Möbius 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 Ca signaling complexes of physiological size and complexity.