DNA duplex cage structures with icosahedral symmetry

A construction method for duplex cage structures with icosahedral symmetry made out of single-stranded DNA molecules is presented and applied to an icosidodecahedral cage. It is shown via a mixture of analytic and computer techniques that there exist realisations of this graph in terms of two circular DNA molecules. These blueprints for the organisation of a cage structure with a noncrystallographic symmetry may assist in the design of containers made from DNA for applications in nanotechnology

Protein container disassembly pathways depend on geometric design

The majority of viruses are organised according to the structural blueprints of the seminal Caspar-Klug theory. However, there are a number of notable exceptions to this geometric design principle. Prominent examples are the cancer-causing papilloma viridae and the \textit{de novo} designed AaLS cages that exhibit non-quasiequivalent capsid structures with protein numbers excluded by Caspar-Klug theory. The biophysical properties of these geometrically distinct architectures and the fitness advantages driving their evolution are currently unclear. We investigate here the resilience to fragmentation and disassembly behaviour of these capsid geometries by introducing a percolation theory on weighted graphs. We show that these cage architectures follow one of two distinct disassembly pathways, preferring either hole formation or capsid fragmentation. This suggests that preference for specific disassembly scenarios could be a driving force for the evolution of the non Caspar-Klug protein container architectures.Comment: 15 pages, 10 figure