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Morphological Diversity of Icosahedral Viruses

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Abstract—

The article is devoted to a morphological diversity of icosahedral viruses (individual capsids and the structure of the diversity in general). It was demonstrated that the fixation of capsid by triangulation numbers does not distinguish the isomers. The description of capsids with point symmetry groups Ih (with symmetry planes) and I (without them) was detailed. In their diversity, the similarity series connected in pairs by transitions to dual capsids were distinguished. Within the general biological problems, the similarity series were interpreted as homological series; dual transitions between them were interpreted as refrains. The concept of generator capsids generating the homological series and refrains and not being reducible to more simple forms was determined. It was hypothesized that not only the icosahedron and dodecahedron dual to it but all shapes of an icosahedral–dodecahedral system and their combinations can be the basic shapes of icosahedral viruses, and the homologous series and refrains of icosahedral viruses can indicate their phylogenetic kinship.

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Notes

  1. Strictly speaking, icosahedral p.s.g. are not crystallographic. Therefore, the International Union of Crystallography did not establish mandatory symbols for them. There are different variants in the literature. It is important that the symmetry planes m (Ih, –5–3m) are involved in one of the symbols, and only rotary axes (I, 532) in the other.

  2. In a dual transition, the points are taken at the centers of the polyhedron faces. Then, the points lying on neighboring faces are connected by segments. They form an edge network of the dual polyhedron. Thus, a cube is dual to an octahedron; an icosahedron, to a dodecahedron (and vice versa); a tetrahedron, to another tetrahedron.

  3. In crystallography, a set of faces obtained by multiplying the initial face by all elements of a given p.s.g. is called a simple shape. Simple shapes are open and closed (polyhedral), private (the initial face is parallel or orthogonal to any symmetry element), and general (the initial face is oblique to all symmetry elements). A combination of simple shapes is their intersection in the space. In this case, the faces of one simple shape cut off the vertices and edges of another one.

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ACKNOWLEDGMENTS

The author is grateful to a reviewer for qualified recommendations that contributed to a better presentation of the results.

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  1. Geological Institute, Federal Research Centre Kola Science Centre, Russian Academy of Sciences, 184209, Apatity, Russia

    Yu. L. Voytekhovsky

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Correspondence to Yu. L. Voytekhovsky.

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Translated by A. Barkhash

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Voytekhovsky, Y.L. Morphological Diversity of Icosahedral Viruses. Biol Bull Rev 13, 460–468 (2023). https://doi.org/10.1134/S2079086423050080

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  • DOI: https://doi.org/10.1134/S2079086423050080

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