Model parameter definitions and values.

DNA supercoiling (SC), the over- and under-winding of DNA, is generated by transcription as described in the twin-domain model. Conversely, SC also impacts transcription through torsional stress. SC therefore regulates transcription dynamically and independently of transcription factor binding, particularly in the context of chromosomal topological domains and the activity of topoisomerases in bacteria. In this work, we develop numerical simulations of SC-coupled transcription of a single gene within a topological domain, based on a model incorporating stochastic transcription and activities of topoisomerase I and gyrase. We explore the effect of several parameters not systematically assessed in previous works (role of topoisomerase activities, topological domain size, gene expression strength) and compare the simulation results to a diverse set of experimental observations ranging from in vitro transcription assays to transcriptomics datasets from various species. This model recapitulates the non-monotonic dependence of transcription in vitro with the superhelical density of the plasmid template. Simulations of in vivo transcription in a closed domain exhibit a qualitatively different role for the two topoisomerases, as well as qualitatively different regulatory behaviors depending on the promoter strength. Specifically, topoisomerase I is required for strongly expressed genes that may be hindered by stalled RNA Polymerase, whereas gyrase activity favors the expression of all genes by enhancing transcription initiation and modulating the burstiness of transcription. The simulations exhibit a new mechanism for transcription bursting mediated by negative SC accumulating at the promoter region and modulating the initiation rate, resulting in levels of burstiness compatible with values reported in cells. Finally, we analyze several transcriptomics datasets from a range of evolutionarily distant species and show that topoisomerase inhibition is systematically associated with the repression of highly expressed genes. Simulations show this behavior to occur within a limited parameter range and thus indicate a biologically relevant regime for the simulations. Overall, this work provides a more quantitative description of how SC contributes to differential gene regulation and transcriptional bursting in bacteria.