Modelling and verification for DNA nanotechnology

DNA nanotechnology is a rapidly developing field that creates nanoscale devices from DNA, which enables novel interfaces with biological material. Their therapeutic use is envisioned and applications in other areas of basic science have already been found. These devices function at physiological conditions and, owing to their molecular scale, are subject to thermal fluctuations during both preparation and operation of the device. Troubleshooting a failed device is often difficult and we develop models to characterise two separate devices: DNA walkers and DNA origami. Our framework is that of continuous-time Markov chains, abstracting away much of the underlying physics. The resulting models are coarse but enable analysis of system-level performance, such as ‘the molecular computation eventually returns the correct answer with high probability’. We examine the applicability of probabilistic model checking to provide guarantees on the behaviour of nanoscale devices, and to this end we develop novel model checking methodology. We model a DNA walker that autonomously navigates a series of junctions, and we derive design principles that increase the probability of correct computational output. We also develop a novel parameter synthesis method for continuous-time Markov chains, for which the synthesised models guarantee a predetermined level of performance. Finally, we develop a novel discrete stochastic assembly model of DNA origami from first principles. DNA origami is a widespread method for creating nanoscale structures from DNA. Our model qualitatively reproduces experimentally observed behaviour and using the model we are able to rationally steer the folding pathway of a novel polymorphic DNA origami tile, controlling the eventual shape.