Abstract
Experiments have reached a monumental capacity for designing and synthesizing
microscopic particles for self-assembly, making it possible to precisely
control particle concentrations, shapes, and interactions. However, we lack a
comprehensive inverse-design framework for tuning these particle-level
attributes to obtain desired system-level assembly outcomes, like the yield of
a user-specified target structure. This severely limits our ability to take
full advantage of this vast design space to assemble nanomaterials with complex
structure and function. Here we show that a hidden mathematical architecture
controls equilibrium assembly outcomes and provides a single comprehensive view
of the entire design space. This architecture predicts which structures can be
assembled at high yield and reveals constraints that govern the coexistence of
structures, which we verify through detailed, quantitative assembly experiments
of nanoscale particles synthesized using DNA origami. Strong experimental
agreement confirms the importance of this underlying architecture and motivates
its use as a predictive tool for the rational design of self-assembly. These
results uncover a universal core logic underpinning all equilibrium
self-assembly that forms the basis for a robust inverse-design framework,
applicable to a wide array of systems from biological protein complexes to
synthetic nanomachines.