Continuous step model of expression of genes controlled by closely spaced tandem promoters

We investigate the impact of the physical phenomenon of occlusion by a sitting RNA Polymerase (RNAP) on the dynamics of closely spaced promoters in tandem formation (Fig. 1A and Fig. 1B). From the single-cell statistics of protein numbers of 20 natural genes controlled by tandem promoters in E. coli, we find that those genes whose tandem promoters are distanced (dTSS) by less base pairs than what a sitting RNAP occupies have lower expression levels than the others (Fig. 1C). We then propose an analytical model accounting for this form of transcription interference. The model is based on a continuous step function with respect to dTSS, and its parameters are obtained by fitting it to the empirical data by R2 maximization. Finally, we use this model to predict that the time-length of steps following the commitment to open complex formation in transcription initiation can be a key regulatory mechanism of the influence of RNAP occlusion in tandem promoters (Fig. 1D).

Fig. 1. Tandem promoters’ dynamics in Escherichia coli. (A) Illustration of the phenomenon of transcription interference in tandem promoters due to occlusion by a sitting RNA Polymerase (RNAP), when the two promoters are located in close proximity and (B) Transcription interference due to a ‘sitting duck’ phenomenon, where the elongation of the RNAP from the upstream promoter is hindered by an RNAP bound to the transcription start site of the downstream promoter. Green and blue clouds are RNAPs, purple bar is the gene, and green and blue arrows are the transcription start sites (TSS) of the promoters pointing towards the direction where transcription will occur. (C) Empirical data on mean protein expression levels (log10) plotted against the distance between TSSs (dTSS in base pairs). Data points are grouped into 3 boxplots based on different ranges of dTSS. The red lines in the boxes mark the medians. The bottom and top of the boxes are 25th and 75th quantiles, respectively. The black curve is the best fitting curve of the continuous step interference model. The grey line is the best zero order fitting line. The preferred continuous step function was selected based on its R2 values, reported in the black boxes. (D) Mean Protein expression, predicted by the model, varies as a function of the rate constant of the events prior to open complex formation (kprior) and the rate constant of events after committing to open complex formation (kafter) in transcription initiation. The dark blue surface is the predicted mean protein expression for tandem promoters with dTSS ≤ 35, while the light blue surface is the predicted mean expression when dTSS > 35.