Gillespie Simulation of Rare Events in a Genetic Regulatory Network

We perform a Gillespie simulation for a simple auto-catalytic gene regulatory network with a positive feedback loop. The chemical master equation for the same model has been solved directly, and after a transient period, proteins were shown to go extinct due to a rare event. We find these features are reproduced with the Gillespie simulation, and the time-dependent frequency of protein numbers shows excellent agreement with the time-dependent probability obtained by solving the master equation directly. The reproduction of the probability for a rare event with the Gillespie simulation reconfirms the feasibility of using the method for modelling the stochastic dynamics of more complex gene regulatory networks, where the direct solution of the master equation is no longer feasible due to computational costs.