How does supercoiling regulation on a battery of RNA polymerases impact on bacterial transcription bursting?

Transcription plays an essential role in gene expression. The transcription bursting in bacteria has been suggested to be regulated by positive supercoiling accumulation in front of a transcribing RNA polymerase (RNAP) together with gyrase binding on DNA to release the supercoiling. In this work, we study the supercoiling regulation in the case of a battery of RNAPs working together on DNA by constructing a multi-state quantitative model, which allows gradual and stepwise supercoiling accumulation and release in the RNAP transcription. We solved for transcription characteristics under the multi-state bursting model for a single RNAP transcription, and then simulated for a battery of RNAPs on DNA with T7 and Escherichia coli RNAP types of traffic, respectively, probing both the average and fluctuation impacts of the supercoiling regulation. Our studies show that due to the supercoiling accumulation and release, the number of RNAP molecules loaded onto the DNA vary significantly along time in the traffic condition. Though multiple RNAPs in transcription promote the mRNA production, they also enhance the supercoiling accumulation to suppress the production. In particular, the fluctuations of the mRNA transcripts become highly pronounced for a battery of RNAPs transcribing together under the supercoiling regulation, especially for a long process of transcription elongation. In such an elongation process, though a single RNAP can work at a high duty ratio, multiple RNAPs are hardly able to do so. Our multi-state model thus provides a systematical characterization of the quantitative features of the bacterial transcription bursting; it also supports improved physical examinations on top of this general modeling framework.