DNA Supercoiling Drives a Transition between Collective Modes of Gene Synthesis*

Transcription of genes can be affected by both biochemical and mechanical factors. Recent experiments tie the transition from cooperative to antagonistic group dynamics of RNA polymerases (RNAPs) on promoter repression to the mechanical stresses associated with transcription induced DNA supercoiling. To underpin the mechanism behind this drastic transition, we developed a continuum deterministic model for transcription under torsion with two novel features: (1) the number of RNAPs on the gene affects the torsional stress experienced by individual RNAPs and (2) transcription factors, when bound to the DNA, block the diffusion of supercoils at the promoter. We show that this model generates a fluid mode of RNAP group dynamics when the RNAP flux is continuous, and a torsionally-stressed mode when the flux is interrupted. At low flux conditions, a single RNAP transcribes with the same efficiency irrespective of the continuity in RNAP loading. The results of our minimal model are in quantitative agreement with experimental findings and elucidate the interplay of mechanical and biological factors in the collective dynamics of molecular machines involved in gene expression.