Modeling and analysis of a bacterial stochastic switch

Deterministic models fail to capture certain important dynamics in the subcellular environment due to the discrete stochastic nature of the molecular interactions at the gene level. Such discrete stochastic interactions are exploited in the cell to implement stochastic switches whose state are predictable only in a statistical sense. This absence of determinism and the inherent variability resulting from it play an important role in creating biological diversity that improves the chance for survivability. This paper will use a simplified model of the Pap switch in E. coli in order to illustrate a variety of computational methodologies. It will be shown that continuous time discrete-state Markov chains are natural tools for modeling this switch, and a review of these approaches will be provided. Using the recently introduced finite state projection algorithm, it is shown that the probability of a given switch position can be computed within any a-priori tolerance without resorting to the Monte-Carlo simulations, which generally lack accuracy guarantees