  In contrast to most self-assembling synthetic materials, which undergo
unbounded growth, many biological self-assembly processes are self-limited.
That is, the assembled structures have one or more finite dimensions that are
much larger than the size scale of the individual monomers. In many such cases,
the finite dimension is selected by a preferred curvature of the monomers,
which leads to self-closure of the assembly. In this article, we study an
example class of self-closing assemblies: cylindrical tubules that assemble
from triangular monomers. By combining kinetic Monte Carlo simulations, free
energy calculations, and simple theoretical models, we show that a range of
programmable size scales can be targeted by controlling the intricate balance
between the preferred curvature of the monomers and their interaction
strengths. However, their assembly is kinetically controlled - the tubule
morphology is essentially fixed shortly after closure, resulting in a
distribution of tubule widths that is significantly broader than the
equilibrium distribution. We develop a simple kinetic model based on this
observation and the underlying free-energy landscape of assembling tubules that
quantitatively describes the distributions. Our results are consistent with
recent experimental observations of tubule assembly from triangular DNA origami
monomers. The modeling framework elucidates design principles for assembling
self-limited structures from synthetic components, such as artificial
microtubules that have a desired width and chirality.
