  Self-assembly is one of the most promising strategies for making functional
materials at the nanoscale, yet new design principles for making self-limiting
architectures, rather than spatially unlimited periodic lattice structures, are
needed. To address this challenge, we explore the trade-offs between
addressable assembly and self-closing assembly of a specific class of
self-limiting structures: cylindrical tubules. We make triangular subunits
using DNA origami that have specific, valence-limited interactions and designed
binding angles, and study their assembly into tubules that have a self-limited
width that is much larger than the size of an individual subunit. In the
simplest case, the tubules are assembled from a single component by
geometrically programming the dihedral angles between neighboring subunits. We
show that the tubules can reach many micrometers in length and that their
average width can be prescribed through the dihedral angles. We find that there
is a distribution in the width and the chirality of the tubules, which we
rationalize by developing a model that considers the finite bending rigidity of
the assembled structure as well as the mechanism of self-closure. Finally, we
demonstrate that the distributions of tubules can be further sculpted by
increasing the number of subunit species, thereby increasing the assembly
complexity, and demonstrate that using two subunit species successfully reduces
the number of available end states by half. These results help to shed light on
the roles of assembly complexity and geometry in self-limited assembly and
could be extended to other self-limiting architectures, such as shells,
toroids, or triply-periodic frameworks.
