  Inspired by recent successes using single-stranded DNA tiles to produce
complex structures, we develop a two-step coarse-graining approach that uses
detailed thermodynamic calculations with oxDNA, a nucleotide-based model of
DNA, to parametrize a coarser kinetic model that can reach the time and length
scales needed to study the assembly mechanisms of these structures. We test the
model by performing a detailed study of the assembly pathways for a
two-dimensional target structure made up of 334 unique strands each of which
are 42 nucleotides long. Without adjustable parameters, the model reproduces a
critical temperature for the formation of the assembly that is close to the
temperature at which assembly first occurs in experiments. Furthermore, the
model allows us to investigate in detail the nucleation barriers and the
distribution of critical nucleus shapes for the assembly of a single target
structure. The assembly intermediates are compact and highly connected
(although not maximally so) and classical nucleation theory provides a good fit
to the height and shape of the nucleation barrier at temperatures close to
where assembly first occurs.
