Figure 2From: A Dominated Coupling From The Past algorithm for the stochastic simulation of networks of biochemical reactionsSampling 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 [15]. The parameters are κ B = 25, κ A = 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 s = 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 s = 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 s = 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.Back to article page