When building models that simulate biological systems at different levels of abstraction, we need to compare their output parameters with measurements from lab experiments. Before we can do that, we need a way to parameterise the models themselves. Here, we investigate parameterising an abstract computational model of plasmid circuits operated by DNA supercoiling (TORCComp), using a more detailed biophysical model (TORCPhys). TORCComp is built as a high speed low fidelity model, which will allow us to explore many variations of parameters in our modelled systems, at the higher abstract level of circuit components. This is aimed at increasing our ability to design supercoiling operated plasmid circuits. TORCPhys is a slower more detailed model, whose parameters are derived from physical concepts and lab experiments, designed to simulate the detailed action of a single circuit at the lower biomolecular level. It cannot be used as an exploratory tool for circuit construction due to longer run times. To explore the feasibility of using TORCPhys to parameterise TORCComp, here, we compare the models of a simple supercoiling controlled plasmid circuit operational in bacteria ( Escherichia coli or Salmonella enterica ) through the mappings of their states. We parameterise TORCComp based on parameter values that are physiologically observable in both lab experiments and TORCPhys, and also those that are not observable in the lab, but can be observed in TORC-Phys. Our results demonstrate the difficulty of parameterising a model based on limited highly contextual observations, and the difficulty of comparing models at different abstraction levels.

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.