Abstract
Recent advances in synthetic methods enable designing subunits that
self-assemble into structures with well-defined sizes and architectures, but
yields are frequently suppressed by the formation of off-target metastable
structures. Increasing the complexity (number of distinct inter-subunit
interaction types) can inhibit off-target structures, but leads to slower
kinetics and higher synthesis costs. Here, we use icosahedral shells formed of
programmable triangular subunits as a model system, and identify design
principles that produce the highest target yield at the lowest complexity. We
use a symmetry-based construction to create a range of design complexities,
starting from the maximal symmetry Caspar-Klug assembly up to the fully
addressable, zero-symmetry assembly. Kinetic Monte Carlo simulations reveal
that the most prominent defects leading to off-target assemblies are a class of
disclinations. We derive symmetry-based rules for identifying the optimal
(lowest-complexity, highest-symmetry) design that inhibits these disclinations,
leading to robust, high-fidelity assembly of targets with arbitrarily large
sizes. Optimal complexity varies non-monotonically with target size, with
`magic' sizes appearing for high-symmetry designs in which symmetry axes do not
intersect vertices of the triangular net. The optimal designs at magic sizes
require $12$ times fewer inequivalent interaction-types than the (minimal
symmetry) fully addressable construction.