Self-folding polyhedra and analogies to biomolecular assembly

We detail model studies aimed at uncovering design principles that govern the self-assembly of polyhedral structures from two-dimensional precursors using surface tension forces. For a given polyhedron, there are a very large number of two-dimensional precursor nets that can be utilized, and remarkably many of these will self-assemble but with varying yields. We uncovered design rules that suggest striking analogies to biomolecular assembly such as observed in proteins and viruses. For example our studies revealed that the compactness of two-dimensional nets determines the yield of self-folding polyhedra and that certain intermediates and pathways were preferred. Consequently, a search algorithm was implemented to screen the large numbers of nets (e.g. 2.3 million for the truncated octahedron) and find high-yielding precursors. This assembly process represents a model system that can be utilized to design and then visualize self-assembly processes. The model system, design rules and findings will be discussed. References: S. Pandey, M. Ewing, A. Kunas, N. Nguyen, D. H. Gracias and G. Menon, Algorithmic design of self-folding polyhedra, \textit{PNAS }108, 50, 19885-19890 (2011).