Some stochastic models have been proposed to account for the effects of positive supercoiling buildup (PSB) in gene expression dynamics (e.g. in bacterial gene expression), differing in, e.g., the level of detail. In general, the detail increases when adding processes affected by and affecting supercoiling. As this addition occurs, the complexity of the model increases.
For example, in  two models of different complexity are proposed. In the most detailed one, events were modeled at the nucleotide level, while in the other the events were modeled at the promoter region alone, and thus required much less events to be accounted for.
Examples of stochastic models that focus on the effects of PSB on a promoter's activity can be found in:. In general, such models include a promoter, Pro, which is the region of DNA controlling transcription and, thus, whose activity/locking is affected by PSB. Also included are RNA molecules (the product of transcription), RNA polymerases (RNAP) which control transcription, and Gyrases (G) which regulate PSB. Finally, there needs to be a means to quantify PSB on the DNA (i.e. the promoter) at any given moment. This can be done by having some component in the system that is produced over time (e.g., during transcription events) to represent positive supercoils, and that is removed by the action of Gyrases. The amount of this component can then be set to affect the rate of transcription.