Sampling of the stationary distribution for the bistable gene network (13) using different methods. (a) The 'true' stationary probability distribution π for the ME (13) calculated numerically with the approximate eigenvector method . The parameters are κ
= 25, κ
= 12, κA 0= κB 0= 60, κA 1= κB 1= 10, κA 2= κB 2= κA 3= κB 3= 1, and γ = 0.01. The locations of the two modes match the fixed points of the corresponding deterministic system. Note the extreme asymmetry of the bimodal probability distribution. (b) The estimate of π obtained from 104 samples of the DCFTP-SSA reproduces the presence of both modes and their relative weights. (c) Estimate of π from 104 samples of the SSA started at (0,0) with T
= 103. (d) Estimate of π obtained from 104 SSA simulations started from 104 different initial conditions chosen uniformly at random on the 100 × 100 lattice closest to the origin and run for T
= 103. (e) Estimate of π obtained from 104 SSA simulations, 5000 of them started from the origin and the other 5000 from the other mode and run for T
= 103. (f) Estimate of π obtained from 104 samples from a long SSA run sampled at interval Δt = 103. Note the different scale on the z-axis for (c) and (e) and how the SSA runs (c)-(f) do not capture the overall structure of π.