Fig. 2.

Analysis of a generalized model of constitutive gene expression without self-regulation, i.e.,${\psi }_1\left(t;n\right)$ is independent of $n$. (A) Schematic representation of the model. (B) Transitions between states. (C) Protein distributions at several different time points, where curves with empty circles correspond to the original nonmarkovian model, whereas colored curves correspond to the constructed markovian model. (D) Influences of memory index $L_1$ $\left(L_2\right)$ on mean protein levels, where empty circles represent the results obtained by the modified “first-reaction” Gillespie algorithm (41), whereas the lines represent the results obtained by theoretical predictions. (E) Stationary protein distributions for different values of $L_1$ and $L_2$. Parameter values are set as: $L_1=4,{\lambda }_1=120$, and $L_2=1,{\lambda }_2=1$ (C) and ${\lambda }_1=20L_1,{\lambda }_2=L_2$ (D and E).