Distribution profiles in gene transcription activated by the cross-talking pathway

Figure 1.  Three modes of mRNA distribution generated by the two-state modal. (a) The decaying distribution for which $P_m$ deceases in $m$ for $m = 0, 1, 2, \cdots$. (b) The unimodal distribution for which $P_m$ takes exactly one peak at some $m>0$. (c) The bimodal distribution for which $P_m$ takes exactly two peaks with the first one at $m = 0$, and the other one at some $m > 0$. The parameter sets $(k_{on}, k_{off}, k_b, k_d)$ in (a), (b), and (c) are chosen as $(0.5, 1.5, 20, 1), (2, 2, 10, 1)$, and $(0.1, 0.2, 15, 1)$, respectively

Figure 2.  Gene transcription modulated by the cross-talking pathway [31]

Figure 3.  Cross-talking pathway can generate bimodal distribution when the gene is (a) easily turned on (${\rm T}_{{\rm off}}<1$) and easily turned off (${\rm T}_{{\rm on}}<1$); (b) easily turned on (${\rm T}_{{\rm off}}<1$) but hardly turned off (${\rm T}_{{\rm on}}>1$); and (c) hardly turned on (${\rm T}_{{\rm off}}<1$) and hardly turned off (${\rm T}_{{\rm on}}>1$). mRNA synthesis rate $v = 30$ and the other parameters are set to be $(\lambda_1, \lambda_2, \gamma, q_1) = (0.6, 6, 2, 0.2)$ in (a), $(\lambda_1, \lambda_2, \gamma, q_1) = (0.2, 4, 0.2, 0.1)$ in (b), and $(\lambda_1, \lambda_2, \gamma, q_1) = (0.2, 4, 0.2, 0.2)$ in (c)

Figure 4.  The transcriptional transition pattern of osmostress-responsive genes in yeast [22]. (a) At low salt concentrations (below 0.05 M NaCl solution), the weak basal pathway is more frequently selected, and therefore most cells are off, giving rise to the decaying distribution. (b) At intermediate salt concentrations, the stress-induced strong signaling pathway is more likely to be activated, leading to the bimodal distribution with two distinct cell identities representing silent and highly expressed cells. (c) At the highest salt concentrations (above 0.15 M NaCl solution), the strong pathway dominates the gene activation, giving rise to the most on cells and the unimodal distribution.