  The observation by Ke et al. [Science 338, 1177 (2012)] that large numbers of
short, pre-designed DNA strands can assemble into three-dimensional target
structures came as a great surprise, as no colloidal self-assembling system has
ever achieved the same degree of complexity. That failure seemed easy to
rationalise: the larger the number of distinct building blocks, the higher the
expected error rate for self-assembly. The experiments of Ke et al. have
disproved this argument. Here, we report Monte Carlo simulations of the
self-assembly of a DNA brick cube, comprising approximately 1000 types of DNA
strand, using a simple model. We model the DNA strands as lattice tetrahedra
with attractive patches, the interaction strengths of which are computed using
a standard thermodynamic model. We find that, within a narrow temperature
window, the target structure assembles with high probability. Our simulations
suggest that mis-assembly is disfavoured because of a slow nucleation step. As
our model incorporates no aspect of DNA other than its binding properties,
these simulations suggest that, with proper design of the building blocks,
other systems, such as colloids, may also assemble into truly complex
structures.
