Figure 7

Stochastic focusing. The first panel from the top compares the time evolution of product molecules P obtained with different methods: the black line represents the solution of ODE model (64) for P; the blue solid line and blue dashed lines are the solutions of the moment-based model (65) for μ _P and μ _P ± σ _P , respectively. The second panel indicates that the stochastic simulations without propensity adjustment (blue error bar) diverge from the prediction by the ODE model (64) (black line). The third panel shows the propensity adjustment function paf4(t) = exp(-f _I f _S cov [log I(t), log S(t)]) for the reaction $R_4:I+S\underset{}{\overset{k_4}{\to }}S$. The bottom panel demonstrates that the propensity adjustment function paf₄ achieves convergence between the stochastic simulation and the ODE model (64) (black line): the blue error bars were computed from 100 independent stochastic simulations with propensity adjustment paf₄. The simulation parameters are (i(0), p(0), s(0), k₁, k₂, k₃, k₄, k₅, k₆, f _I , f _S ) = (0, 10, 100, 10⁴, 10³, 1, 9.9 × 10³, 10⁴, 10³, 1.1, 0.9); at t = 0.1, the value of k₅ changes from 10⁴ to 0.5 ×10⁴.