Reduction of calcium release site models via optimized state aggregation

Correspondence: [email protected] Math and Computer Science Department, Hobart and William Smith Colleges, 300 Pulteney St., Geneva, NY 14456, USA Abstract Background: Markov chain models of calcium release sites in living cells exhibit stochastic dynamics reminiscent of the experimentally observed phenomenon of calcium puffs and sparks. Such models often take the form of stochastic automata networks in which the transition probabilities for each of a large number of intercellular channel models depend on the local calcium concentration and thus the state of nearby channels. The state-space size in such compositionally defined calcium release site models increases exponentially as the number of channels increases, which is referred to as “state-space explosion”. Methods: In order to overcome the state-space explosion problem, we utilized the idea of “coarse graining” and implemented an automated procedure that reduces the state space by aggregating and lumping states of the full release site model. For a given state aggregation scheme, the transition rates between reduced states are chosen consistent with the conditional probability distribution among states within each group. A genetic algorithm-based approach is then applied to select the state aggregation schemes that lead to reduced models that approximate the observable behaviors of the full model.