Probability distribution function (PDF) of species X and species Y in network (B4). (a) PDF of species X using the SSA (solid line) and the HyMSMC method (triangles), generated at 1000 s using 10000 trajectories. The PDFs of the HyMSMC method were generated at 1000 s, using temporal averaging for 0.1 s followed by ensemble average (open triangles) and without temporal sampling (just ensemble average; filled triangles). (b) Corresponding PDF of species Y in network (B4) generated using the SSA (solid line) and the HyMSMC (open symbols) and the slow-scale SSA (SS-SSA)  (filled symbols) methods. The SS-SSA method uses the mean-field approximation of the fast network to evaluate the slow-scale propensities. The PDFs were generated using XQE = 5 (filled squares) and XQE = 50 (filled triangles) as the quasi-equilibrium solution of fast network (B2)-(B4). See text for a detailed explanation.