  We propose a stochastic model for gene transcription coupled to DNA
supercoiling, where we incorporate the experimental observation that
polymerases create supercoiling as they unwind the DNA helix, and that these
enzymes bind more favourably to regions where the genome is unwound. Within
this model, we show that when the transcriptionally induced flux of
supercoiling increases, there is a sharp crossover from a regime where
torsional stresses relax quickly and gene transcription is random, to one where
gene expression is highly correlated and tightly regulated by supercoiling. In
the latter regime, the model displays transcriptional bursts, waves of
supercoiling, and up-regulation of divergent or bidirectional genes. It also
predicts that topological enzymes which relax twist and writhe should provide a
pathway to down-regulate transcription. This article has been published in
Physical Review Letters, May 2016.
