  Recent experiments showed that multiple copies of the molecular machine RNA
polymerase (RNAP) can efficiently synthesize mRNA collectively in the active
state of the promoter. However, environmentally-induced promoter repression
results in long-distance antagonistic interactions that drastically reduce the
speed of RNAPs and cause a quick arrest of mRNA synthesis. The mechanism
underlying this transition between cooperative and antagonistic dynamics
remains poorly understood. In this Letter, we introduce a continuum
deterministic model for the translocation of RNAPs, where the speed of an RNAP
is coupled to the local DNA supercoiling as well as the density of RNAPs on the
gene. We assume that torsional stress experienced by individual RNAPs is
exacerbated by high RNAP density on the gene and that transcription factors act
as physical barriers to the diffusion of DNA supercoils. We show that this
minimal model exhibits two transcription modes mediated by the torsional
stress: a fluid mode when the promoter is active and a torsionally stressed
mode when the promoter is repressed, in quantitative agreement with
experimentally observed dynamics of co-transcribing RNAPs. Our work provides an
important step towards understanding the collective dynamics of molecular
machines involved in gene expression.
