Gillespie’s approach for Monte Carlo simulation of the master equation. (a) The joint PDF that determines the reactions as function of time . Note that the variable is continuous and discrete. (b) shows two examples of deterministic (black lines) and associated stochastic (blue lines) simulations superimposed. The two cases start from a low and high initial value. The inset is a detail of how the stochastic solutions fluctuate around the deterministic ones. (c) The procedure of picking the time steps. (d) depicts how to determine the cell to update at each time step.