Synthetic biology is one facet of Artificial Life which designs novel biological components, e.g. DNA, RNA, membranes, to produce new behaviours. Here, we are interested in DNA “circuits”: DNA engineered to have particular computational properties. During gene transcription, the DNA double-helix undergoes supercoiling changes, which affects transcription of nearby genes. There is limited mathematical, as opposed to physical, modelling of DNA circuits, and supercoiling is not considered. In many current synthetic circuits, supercoiling has to be carefully removed, particularly in in vivo systems, to prevent unmodelled side effects. However, supercoiling is an intrinsic property of DNA that impacts gene expression, and could be exploited if included in models. Here, we present a new π-calculus formalism for modelling DNA circuits with supercoiling, and demonstrate its use on a simple genetic circuit. The state transition diagrams normally associated with π-calculus are not accessible when the number of states becomes large. We present a new circular visualisation of the π-calculus circuit components that is more intuitive and readable for biologists familiar with the circular visualisations of plasmids.

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