High-symmetry protein assemblies: patterns and emerging applications.

The accelerated elucidation of three-dimensional structures of protein complexes, both natural and designed, is providing new examples of large supramolecular assemblies with intriguing shapes. Those with high symmetry - based on the geometries of the Platonic solids - are particularly notable as their innately closed forms create interior spaces with varying degrees of enclosure. We survey known protein assemblies of this type and discuss their geometric features. The results bear on issues of protein function and evolution, while also guiding novel bioengineering applications. Recent successes using high-symmetry protein assemblies for applications in interior encapsulation and exterior display are highlighted.