Stochastic Modelling Of Viral Assembly Efficiency Across Capsid Geometries

Viruses are a form of obligate parasite which require the metabolism of a host cell to replicate. During infection of the host cell, viruses need to efficiently assemble new viral progeny and have evolved many strategies to achieve this. For icosahedral ssRNA viruses, capsid proteins and genomic ssRNA co-assemble without the need for subsequent packaging by a terminase. Two features that are critical for efficient assembly are the capsid’s overall geometry and the arrangement of possible contacts between the RNA and capsid proteins. Thus, a natural question is whether there exist pairings of capsid geometries and arrangements of RNA contacts which result in high assembly efficiency. In this thesis, a mathematical and computational framework is developed which uses the symmetry of capsids to generate the adjacencies of all capsomers, based only on the information from one fundamental domain. This allows the enumeration of all possible icosahedral capsid geometries and RNA arrangements up to isomorphism, which can be used alongside a combinatorics program to count the possible RNA paths within a given pairing. This is implemented alongside a version of Gillespie’s SSA algorithm, which stochastically models the assembly of a capsid with these geometries and RNA arrangements, generalizing the simulation of capsid assembly in ssRNA viruses. The first capsid investigated is STNV, a T = 1 virus. During this investigation, a set of limitations on the RNA arrangement which resulted in high efficiency assembly and repetition of arrangements was identified, showing similarity to experimental results. Next, by modelling each of the three T = 3 capsid geometries or tilings, significant effects on assembly for different RNA arrangements were identified, with some arrangements leading to higher assembly yields. Finally, disassembly is shown to have significant differences with assembly in the T = 3 class of capsid geometries, which has important consequences for understanding the uncoating process during infection.