Fig. 4.

Effects of RNAP-promoter binding affinity fluctuation on non-Poisson mRNA noise in constitutive expression. a Transcription model of a constitutive gene without promoter strength fluctuation. The overall transcription rate of a single-gene copy is modeled by $R_1=\left[K{N}_{\mathrm{Rp}}\mathrm{∕}\left(1+K{N}_{\mathrm{Rp}}\right)\right]k_{\mathrm{TX}}\left(\Gamma \right)$, where the number $N_{\mathrm{Rp}}$ of RNAP is a stochastic variable, but the RNAP binding affinity $K$ of the promoter is a constant. b Transcription model of constitutive gene with promoter strength fluctuation due to conformational dynamics of DNA. The overall transcription rate is given by the same formula as transcription model a, but with $K$ being a dichotomous stochastic variable whose value takes either 0 or $K_0$. Our analysis shows fluctuation in the value of $K_0$ is negligible (Supplementary Note 20). c (circles) Experimental results for the mean number $⟨{n⟩}_1$ of mRNA per gene copy and non-Poisson noise $Q_n\mathrm{∕}{⟨n⟩}_1\left(=⟨g⟩Q_n\mathrm{∕}⟨n⟩\right)$ from the constitutive expression data reported in Fig. 2 of ref. ²³. (red dot-dash) Prediction of the previous model proposed in ref. ²³. (solid line) Result of transcription model a best fitted to the experimental data. d (solid line) Result of transcription model b best fitted to the experimental data. Binding affinity fluctuation in the constitutive expression occurs much faster than in the repressor-regulated gene expression (Supplementary Figs. 2 and 10). For constitutive gene expression, transcription model b provides a better quantitative explanation of the experimental data than Model III. However, in the absence of fluctuation in N_Rp, transcription model b becomes equivalent to Model III (Supplementary Fig. 12)