We analyse transcriptional bursting within a stochastic non-equilibrium model which accounts for the coupling between the dynamics of DNA supercoiling and gene transcription. We find a clear signature of bursty transcription when there is a separation between the timescales of transcription initiation and supercoiling dissipation - the latter may either be diffusive or mediated by topological enzymes, such as type I or type II topoisomerases. In multigenic DNA domains we observe either bursty transcription, or transcription waves; the type of behaviour can be selected for by controlling gene activity and orientation. In the bursty phase, the statistics of supercoiling fluctuations at the promoter are markedly non-Gaussian.
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