Periodic Table of Virus Capsids: Implications for Natural Selection and Design

Abstract

BackgroundFor survival, most natural viruses depend upon the existence of spherical capsids: protective shells of various sizes composed of protein subunits. So far, general evolutionary pressures shaping capsid design have remained elusive, even though an understanding of such properties may help in rationally impeding the virus life cycle and designing efficient nano-assemblies.Principal FindingsThis report uncovers an unprecedented and species-independent evolutionary pressure on virus capsids, based on the the notion that the simplest capsid designs (or those capsids with the lowest “hexamer complexity”, ) are the fittest, which was shown to be true for all available virus capsids. The theories result in a physically meaningful periodic table of virus capsids that uncovers strong and overarching evolutionary pressures, while also offering geometric explanations to other capsid properties (rigidity, pleomorphy, auxiliary requirements, etc.) that were previously considered to be unrelatable properties of the individual virus.SignificanceApart from describing a universal rule for virus capsid evolution, our work (especially the periodic table) provides a language with which highly diverse virus capsids, unified only by geometry, may be described and related to each other. Finally, the available virus structure databases and other published data reiterate the predicted geometry-derived rules, reinforcing the role of geometry in the natural selection and design of virus capsids.

Insights into Head-Tailed Viruses Infecting Extremely Halophilic Archaea

“…Thus, in addition to genome sequences, we report threedimensional (3D) cryo-electron microscopy (cryo-EM) reconstructions of the capsids for both viruses. Although HVTV-1 (Tϭ13) and HSTV-2 (Tϭ7) have different T-numbers, they belong to the same morphological class, class 2, of icosahedrally symmetric viruses (24). Furthermore, the genome size of HSTV-2 is considered large for a Tϭ7 capsid, and we show that HSTV-2 has solved this problem by inserting a minor protein into the capsid lattice.…”

“…The quasiequivalence theory places the capsomers in positions that can be described by subtriangulating the icosahedral facets. The triangulation number (T-number) is a parameter used to describe the capsomer (hexamer and pentamer) arrangement and can be calculated by using the formula T ϭ h 2 ϩ hk ϩ k 2 , where h and k are positive integers defining the pentameric and hexameric positions in the lattice (23,24).…”

A minimal representation of the self-assembly of virus capsids

“…Generalizations of the CK rules properly account for the geometry of some exceptional icosahedral capsids [3][4][5][6] and other elongated virus capsids that share coordination numbers with the icosahedral ones [7][8][9] . Recent work [10][11][12] provides important further development about the effect of the geometrical and topological constraints on the capsid structure.…”

Curvature Concentrations on the HIV-1 Capsid

“…Existing work [12,25,31,37,39,40] suggest that the pentamers introduce sharp declinations in the HIV-1 capsid. This agrees with our curvature calculations.…”