Analytical kinetic model of native tandem promoters in E. coli

Abstract

Closely spaced promoters in tandem formation are abundant in bacteria. We investigated the evolutionary conservation, biological functions, and the RNA and single-cell protein expression of genes regulated by tandem promoters in E. coli. We also studied the sequence (distance between transcription start sites 'dTSS', pause sequences, and distances from oriC) and potential influence of the input transcription factors of these promoters. From this, we propose an analytical model of gene expression based on measured expression dynamics, where RNAP-promoter occupancy times and dTSS are the key regulators of transcription interference due to TSS occlusion by RNAP at one of the promoters (when dTSS ≤ 35 bp) and RNAP occupancy of the downstream promoter (when dTSS > 35 bp). Occlusion and downstream promoter occupancy are modeled as linear functions of occupancy time, while the influence of dTSS is implemented by a continuous step function, fit to in vivo data on mean single-cell protein numbers of 30 natural genes controlled by tandem promoters. The best-fitting step is at 35 bp, matching the length of DNA occupied by RNAP in the open complex formation. This model accurately predicts the squared coefficient of variation and skewness of the natural single-cell protein numbers as a function of dTSS. Additional predictions suggest that promoters in tandem formation can cover a wide range of transcription dynamics within realistic intervals of parameter values. By accurately capturing the dynamics of these promoters, this model can be helpful to predict the dynamics of new promoters and contribute to the expansion of the repertoire of expression dynamics available to synthetic genetic constructs.

Fig 1. Interference between tandem promoters with different arrangements relative to each other.

(A) Interference by an RNAP occupying the downstream promoter on the activity of the elongating RNAP from upstream promoter. The TSSs need to be at least 36 bp apart (the length occupied by an RNAP when in OC, [23,25]) (B) Interference by occlusion of one of the promoter’s TSS by an RNAP on the TSS of the other promoter. The distance between the TSSs need to be ≤ 35 bp apart. Blue clouds are RNAPs. Black arrows sit on TSSs and point towards the direction of transcription elongation. Arrangements (I-II) of two promoters studied in the manuscript in tandem formation are represented. The red rectangles are the protein coding regions. We studied only the natural tandem promoters that neither overlap with nor have in between another gene (arrangements I and II, which differ based on whether the promoter regions overlap or not). Other arrangements (not considered in this study) are shown in Fig A in the S2 Appendix. Figure created with BioRender.com.

Fig 2. Workflow.

(I) We identified genes controlled by tandem promoters in Regulon DB. (II) Next, we measured the single-cell protein levels of those genes with arrangements I and II that are tagged in the YFP strain library [28]. We also measured the mean RNA fold changes of these genes over time (S1 Appendix, section ‘RNA-seq measurements and data analysis’). (III) We used the single-cell data to tune the model. (IV) Finally, we used the model to explore the state space of protein expression. Figure created with BioRender.com.

Fig 3. Events leading to transcriptional interference between tandem promoters.

(A) Sequence of events in transcription in isolated promoters. A similar set of events occurs in tandem promoters, if only one RNAP interacts with them at any given time. (B / C) Interference due to the occlusion of the downstream / upstream promoter by a bound RNAP, which will impede the incoming RNAP from binding to the TSS. (D) Interference of the activity of the RNAP incoming from the upstream promoter by the RNAP occupying the downstream promoter. One of these RNAPs will be dislodged by the collision. Created with BioRender.com.

Fig 4. Single cell protein numbers by microscopy and flow-cytometry.

(A) Example single-cell distributions (3 biological replicates) of fluorescence (in arbitrary units) of cells with a YFP tagged gene controlled by a pair of tandem promoters obtained by flow-cytometry, ‘FC’. (B) Example confocal microscopy image of cells overlapped by the results of cell segmentation from the corresponding phase contrast image. The two white arrows show the dimensions of the image, for scaling purposes. (C) Mean single-cell protein fluorescence of 10 genes (Table G in the S3 Appendix) when obtained by FC plotted against when obtained by microscopy, ‘Mic’. (D) Mean single-cell protein fluorescence (own measurements) plotted against the corresponding mean single-cell protein numbers reported in [28]. From the equation of the best fitting line without y-intercept (y-intercept = 0), we obtained a scaling factor, sf, equal to 0.09.

Fig 5. Relative RNAP concentrations along with the relationships between the moments of the single cell distributions of protein numbers.

(A) Relative RNAP levels measured by flow-cytometry (Section ‘flow-cytometry and data analysis’ in the S1 Appendix) in three media. (B) Scatter plot between M_P in M9 (1X) and diluted M9 (0.5X) media. Also shown are the best fitting line and standard error and p-value for the null hypothesis that the slope is zero. (C) M_P vs $C{V}_P^2$ and (D) M_P vs S_P of single-cell protein numbers of genes with tandem promoters in M9 (1X) and M9 diluted (0.5X) media. The lines and their shades are the best fitting lines and standard errors, respectively. ‘Merge’ stands for data from both 0.5X and 1X conditions.

Fig 6. Empirical data and analytical model of how d_TSS influences the single-cell protein numbers of genes controlled by tandem promoters.

(A) Mean, (B) CV², and (C) S of single protein numbers in the 1X media as a function of d_TSS. (D), (E), and (F) show the same for the 0.5X media, respectively. Each red dot is the mean from 3 biological repeats for a pair of promoters (S2 Table). The dots were also grouped in 3 ‘boxes’ based on their d_TSS. In each box, the red line is the median and the top and bottom are the 3^rd and 1^st quartiles, respectively. The vertical black bars are the range between minimum and maximum of the red dots. In A, all lines are best fits. In B, C, D, E, and F, all lines are model predictions, based on the parameters used to best fit A. The insets show the R² for each model fit and prediction.

Fig 7. Mean protein numbers produced as a function of other promoter’s occupancy.

M_P of the single-cell distribution of the number of proteins produced (A) by the upstream promoter alone, and (B) by the downstream promoter alone. Results are shown as a function of the fraction of times that the upstream (0.01 ≤ ω_u≤ 0.99) and the downstream (0.01 ≤ ω_d ≤ 0.99) promoter are occupied by RNAP. The null model is estimated by setting k_occlusion, k_occupy, and ω to zero.

Fig 8. Promoter occupancy ω estimated for the step model.

(A) ω as a function of the rate constant for a free RNAP to bind to the unoccupied promoter (k_bind⋅[R]) and of the time for that RNAP to start elongation after commitment to OC, $k_{after}^{-1}$. The horizontal black line at ω = 1, is the maximum fraction of time that the promoter can be occupied (i.e., the maximum promoter occupancy). (B) k_occlusion plotted as a function of ω and d_TSS. Since k_occlusion increases with ω if and only if d_TSS ≤ 35, it renders the simultaneous occupation of both TSS’s impossible.

Fig 9. Mean protein expression as a function of both promoters’ occupancy.

Expected mean protein numbers due to the activity of: (A) the upstream promoter alone, (B) the downstream promoter alone, and (C) both promoters. M_P is shown as a function of the fraction of times that the upstream (0 ≤ ω_u ≤ 1) and the downstream (0 ≤ ω_d ≤ 1) promoters are occupied by RNAP, when d_TSS > 35 (yellow) and d_TSS ≤ 35 (dark green) bp.