Classification and Evolutionary Trends of Icosahedral Viral Capsids

Abstract

A classification of icosahedral viral capsids is proposed. We show how the self-organization of capsids during their formation implies a definite composition of their elementary building blocks. The exact number of hexamers with three different admissible symmetries is related to capsids' sizes, labelled by theirT-numbers. Simple rules determining these numbers for each value ofTare deduced and certain consequences concerning the probabilities of mutations and evolution of viruses are discussed.

Generalized Structural Polymorphism in Self-Assembled Viral Particles

“…The large spheres are repulsive providing volume exclusion. The small red spheres are attractive providing anisotropic inter-capsomer interactions if they are located on similar layers and belong to the interfaces that are specified according to the T capsid system as suggested by Kerner 23. For example, the T=1 system, without hexamers, requires pentamers to be attractive to one another at any interface.…”

“…The small red spheres are attractive providing anisotropic intercapsomer interactions if they are located on similar layers and belong to the interfaces that are specified according to the T capsid system as suggested by Kerner. 23 For example, the T ) 1 system, without hexamers, requires pentamers to be attractive to one another at any interface. Since pentamers are located further apart as T increases, each hexamer in T ) 3, 4, and 7 capsids is attractive to any pentamer at three, two, and one interfaces, respectively.…”

“…In capsid systems with enantiomorphism (T ) 7, 13, and 19), both versions are considered by imposing different pentamer/hexamer interaction schemes. 23 These models are used with discontinuous molecular dynamics (DMD), 24 an extremely fast alternative to traditional molecular dynamics. In the DMD simulation algorithm all potentials are discontinuous, i.e., based on hard-sphere or square-well interactions.…”

Self-Assembly of Icosahedral Viral Capsids: the Combinatorial Analysis Approach

“…Such "islands" exist also among the capsid types corresponding to higher values of T , even when one considers the Tables (17), (18) and (19) as cylinders, with their right and left borders glued together. There are single isolated species corresponding to T = 124; T = 196 and T = 268 (the last one beyond the range of observed types).…”

“…To define a notion of a distance between various types of capsids is a challenge for further research in this direction ( [18], [19], [20]). …”