Fig. 2.

Dynamics of transcription rate fluctuation consistent with cell-to-cell variation in the number of mRNA expressed from repressor-regulated lacZ in E. coli. a (circles) Experimental data for the mean mRNA number $⟨{n⟩}_1$ per single-gene copy and non-Poisson mRNA noise $Q_n\mathrm{∕}{⟨n⟩}_1\left(=⟨g⟩Q_n\mathrm{∕}⟨n⟩\right)$ for various concentrations of inducer IPTG³⁶. The decay rate, $\gamma$, of the lacZ mRNA is 1/120 Hz³⁶. The red circles represent the data obtained from slowly growing cells with doubling times greater than 45 min. The experimental data were reported in Fig. 3 of ref. ³⁶. (dotted line) The result of Model I, for which $Q_n\mathrm{∕}{⟨n⟩}_1$ is the same as the Fano factor $\left(F_g\cong 0.21\right)$ of the gene copy number variation (Supplementary Note 16). (dot-dash line) Result of Model II. Non-Poisson mRNA noise also emerges from the gene-state switching process. (blue solid line) Result of Model III. The fluctuation in transcription rate κ produces additional mRNA noise. By comparing Model III and the entire data, we extract the time profile of the TCF, ${\varphi }_{\kappa }\left(t\right)$, of transcription rate κ. (red line) Result of Model III with ${\varphi }_{\kappa }\left(t\right)$ modeled as $exp\left(-\lambda t\right)$, which is in good agreement with only the red circle data. The optimized value of $\lambda \mathrm{∕}\gamma$ is 306. The major contributors to non-Poisson mRNA noise are those from the gene-state switching process and its bilinear coupling with the ensuing transcription process, corresponding to the last two terms on the R.H.S. of Eq. (2) (Supplementary Note 17 and Supplementary Fig. 16a). b (blue line) ${\varphi }_{\kappa }\left(t\right)$ extracted from the entire data shown in a using Model III. (red line) Exponential TCF, ${\varphi }_{\kappa }\left(t\right)={\mathrm{e}}^{-\lambda t}$, extracted from the red circle data in a, obtained from the slowly growing cells. The dependence of the non-Poisson mRNA noise on the mean mRNA level is consistent with the known mechanism of IPTG-regulated transcription (see Supplementary Note 6)