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Rare Event Handling in Signalling Cascades

Signalling cascades are a recurrent pattern of biological regulatory systems whose analysis has deserved a lot of attention. It has been shown that stochastic Petri nets are appropriate to model such systems and evaluate the probabilities of specific properties. Such an evaluation can be done numerically when the combinatorial state space explosion is manageable or statistically otherwise. However, when the probabilities to be evaluated are too small, random simulation requires more sophisticated techniques for the handling of rare events. In this paper, we show how such involved methods can be successfully applied for signalling cascades. More precisely, we study three relevant properties of a signalling cascade with the help of the COSMOS tool. Our experiments point out interesting dependencies between quantitative parameters of the regulatory system and its transient behaviour. In addition, they demonstrate that we can go beyond the capabilities of MARCIE, which provides one of the most efficient numerical solvers.