  The optimal design of DNA origami systems that assemble rapidly and robustly
is hampered by the lack of a model for self-assembly that is sufficiently
detailed yet computationally tractable. Here, we propose a model for DNA
origami that strikes a balance between these two criteria by representing these
systems on a lattice at the level of binding domains. The free energy of
hybridization between individual binding domains is estimated with a
nearest-neighbour model. Double helical segments are treated as rigid rods, but
we allow flexibility at points where the backbone of one of the strands is
interrupted, which provides a reasonably realistic representation of partially
and fully assembled states. Particular attention is paid to the constraints
imposed by the double helical twist, as they determine where strand crossovers
between adjacent helices can occur. To improve the efficiency of sampling
configuration space, we develop Monte Carlo methods for sampling scaffold
conformations in near-assembled states, and we carry out simulations in the
grand canonical ensemble, enabling us to avoid considering states with unbound
staples. We demonstrate that our model can quickly sample assembled
configurations of a small origami design previously studied with the oxDNA
model, as well as a design with staples that span longer segments of the
scaffold. The sampling ability of our method should allow for good statistics
to be obtained when studying the assembly pathways, and is suited to
investigating in particular the effects of design and assembly conditions on
these pathways and their resulting final assembled structures.
