To exploit the potential of synthetic biology, we need engineering approaches, including computational tools and techniques, that work with, rather than against, biological complexity. Computational approaches have already provided many important advances in synthetic biology, allowing small `logic circuits' to be programmed and implemented in a cell's genetic make-up. In order to scale up the power of these approaches, we need a computational toolkit that is based on the full complexity of DNA processes. It is tempting to simplify genetics to a simple passive `code' along with genetic binary `switches' to control its expression. But the physical behaviour of the DNA itself is also implicated in gene regulation. Transcription generates positive supercoiling ahead of the transcription machinery and negative supercoiling behind, due to the topological changes required to separate the double helical DNA strands. Transcription induced supercoiling can both up and down-regulate expression of distal genes, however, in general negative supercoiling promotes transcription by destabling the DNA duplex, and facilitating the formation of the open RNA polymerase complex. This information transfer along the DNA strands can be modulated by DNA writhing to form plectonemic supercoils, by DNA binding proteins capable of removing (such as topoisomerases) or absorbing (such FIS) superhelical stress, or can be modified by bending (e.g. IHF) and bridging proteins (e.g. LacI) that stabilise plectonemes and by environmental or metabolic changes, such as the salt concentration or amount of ATP available. This behaviour is an inherent part of the information storage abilities of genomic DNA, and offers powerful new programming and control mechanisms for synthetic biology, but is not yet captured in any synthetic biology toolkit. Our vision is of a complete computational toolkit based on DNA writhe and twist properties, their information processing capabilities and their programmatic modulation. The toolkit, which we dub `TORC', would include a logic for reasoning, a language for expression, an interpreter for testing, and an API for synthetic biology. TORC would thereby provide both an engineering development approach for advanced synthetic biology, and a scientific language and logic for modelling biological genetics.