Comparative simulation results for a reversible reaction with feedback controls. In all panels, the x-axis denotes time in seconds and the y-axis represents the number of molecules of species S1. The upper and lower panels use two different sets of initial numbers of molecules, namely: (x1(0), x2(0), x3(0), U) = (5, 5, 6, 1μm3) and (x1(0), x2(0), x3(0), U) = (100, 100, 120, 20μm3), respectively. Other simulation parameters are (f1, f2, f3, g1, g3, k
) = (1.3, 1.8, -1, 1, 1, 0.5, 0.5). In both the upper and lower panels, the first column compares the time evolution of S1 molecules by different methods: the black line shows the ODE solution of Equation (52) for x1 ; the blue lines are the solutions of Equation (53) for μ1 and for μ1 ± σ1, respectively. The red dotted lines framing the mean indicate the 95% confidence interval. The second column shows the propensity adjustment functions for the forward reaction (solid line) and the backward reaction (dashed line). The third column shows 100 independent stochastic simulations with propensity adjustment (blue means and error bars), in comparison with the ODE (Equation (52)) prediction (black line). The fourth column shows a second set of 100 independent stochastic simulations without propensity adjustment (blue means and error bars), in comparison with the ODE (Equation (52)) prediction (black line). The red dotted lines framing the mean in columns 3 and 4 again indicate the 95% confidence intervals.