The Collapse of Viruses: Graph-Based Percolation Theory in the Wolfram Language

Graph-based percolation theory may be done in the Wolfram Language, here to aid in the understanding of viruses, their disassembly and eventual collapse. Capsids are protein nanocontainers that store and protect a virus’s genetic material in transit between hosts. Capsids consist of hundreds of subunits biochemically bound in a mathematically precise tiling. This subunit-bond network has evolved to not only provide their cargo protection, but also readily disassemble after cellular entry via organized or random subunit removal, eventually leading to a virus’s collapse. The subunit-bond networks are well understood in terms of an overarching classification scheme involving Archimedean lattices. We utilize this knowledge of subunit-bond network topologies, represented by graphs, to conduct percolation-theoretical comparisons of the disassembly and relative stability of different virus architectures. Automatic parallelization functionality in the Wolfram Language facilitates rapid Monte Carlo of the maximum number of subunits that may be randomly removed from each tiling without—on average—inducing fragmentation of the remaining shell. This fragmentation threshold is unique to each capsid tiling’s topology. After forming predictions in the Wolfram Language, we previously confirmed the fragmentation threshold prediction for the hepatitis B virus in vitro using “molecular breadboard” subunit removal strategies and single-particle charge detection mass spectroscopy and nanofluidic devices. We expect other fragmentation thresholds predicted here will be verified experimentally in due time. This comparative analysis demonstrates which virus architectures are the most stable (and which the weakest) to random subunit dissociation, also illustrating the extent to which “molecular breadboard” techniques may be used in nanotechnology.

Видео The Collapse of Viruses: Graph-Based Percolation Theory in the Wolfram Language канала Wolfram