Figure 2.

Comparison of the behaviour of M(t) between the classical chemical kinetics (CCK) model and the stochastic chemical kinetics (SCK) model of the simplified gene expression reactions. (a) A sample trajectory of M(t) from the SCK model. (b) Comparison between M(t) of the CCK model (red solid line) and 〈M(t)〉 of the SCK model (blue dashed line). (c) Stationary mean of M with respect to various combinations of k_p and k_d. The circles represent the data points sampled via simulations. (d) Log–log heat map to show the ratio of M_∞ to M_E for various combinations of k_p and k_d. The numbers shown in the x- and y-axis are k_d and k_p in log scale (base 10), respectively. The ratio in the z-axis is given by log₁₀ (M_∞/M_E). The values of the parameters used in this numerical analysis are k₁ = 10, k₂ = 1 and M(0) = 100. In the simulation of (a) and (b), the values of k_d and k_p are set to 0.1 and 0.01, respectively.