Protein container disassembly pathways depend on geometric design

Abstract: 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.