Numerical Approximation of Rare Event Probabilities in Biochemically Reacting Systems

In stochastic biochemically reacting systems, certain rare events can cause serious consequences, which makes their probabilities important to analyze. We solve the chemical master equation using a four-stage fourth order Runge-Kutta integration scheme in combination with a guided state space exploration and a dynamical state space truncation in order to approximate the unknown probabilities of rare but important events numerically. The guided state space exploration biases the system parameters such that the rare event of interest becomes less rare. For each numerical integration step, the portion of the state space to be truncated is then dynamically obtained using information from the biased model and the numerical integration of the unbiased model is conducted only on the remaining significant part of the state space. The efficiency and the accuracy of our method are studied through a benchmark model that recently received considerable attention in the literature.