The optimal design of DNA origami systems that assemble rapidly and robustly is hampered by the lack of a model capable of simulating the self-assembly process that is sufficiently detailed yet computationally tractable. In this thesis, we propose a model for DNA origami that strikes a balance between these two criteria by representing DNA origami systems on a lattice at the level of binding domains. Particular attention is paid to the constraints imposed by the double-helical twist, as they determine where strand crossovers between adjacent helices can occur.

Because of the highly specific types of interaction and the length of the scaffold, standard Monte Carlo simulation methods for polymeric systems are found to be ineffective at sampling the dense, near-assembled states considered here. In order to address the issue of sampling such states, we develop Monte Carlo methods that extend the configurational bias and recoil growth methods, and consider the sampling of scaffold conformations independently from the sampling of staple binding states. We demonstrate the validity of our model and the feasibility of our sampling methods with simulations of a small origami design previously studied with the oxDNA model, as well as with designs that include staples that span longer scaffold segments.

In other self-assembling systems, it is often the case that nucleation barriers control the self-assembly behaviour. We investigate whether there is a nucleation barrier along the self-assembly pathway of DNA origami. Our simulations reveal that for simple systems, stacking interactions govern a nucleation barrier, albeit one that is never prohibitively large relative to thermal fluctuations. These findings may prove useful in the design of DNA origami structures capable of controllable reversible folding for functional purposes and in assisting the optimization of assembly pathways at the design stage.