Topological Design of Heterogeneous Self-Assembly

Recent advances in encoding specific interactions on microscopic particles allow programming self-assembly of complex multiscale structures. However, this programming is currently limited by two factors: off-target particle binding, or cross-talk, and lack of computational tools for design of heterogeneous particle sets. Here we use statistical mechanics, combinatorics, and spectral methods to directly relate the properties of particle sets to the yields of all structures they self-assemble. We derive analytical limits on the largest structures reliably assembled for a given level of cross-talk. These results allow us to formulate specific design rules for particle sets that optimally self-assemble structures of two different topologies: rings and chains.