Mathematical Approach to the Platonic Solid Structure of MS2 Particles

Nai-Chia Shi¹, Chun-Chun Wu¹, Jui-Sen Yang²

¹Department of Applied Mathematics, Feng-Chia University, Taichung, Taiwan.
²Institute of Marine Biology, National Taiwan Ocean University, Keelung, Taiwan.

DOI: 10.4236/am.2015.64059                

Abstract

Bacteriophage MS2 is a viral particle whose symmetrical capsid consists of 180 copies of asymmetrical coat proteins with triangulation number T = 3. The mathematical theorems in this study show that the phage particles in three-dimension (3D) might be an icosahedron, a dodecahedron, or a pentakis dodecahedron. A particle with 180 coat protein subunits and T = 3 requires some geometrical adaptations to form a stable regular polyhedron, such as an icosahedron or a dodecahedron. However, with mathematical reasons electron micrographs of the phage MS2 show that 180 coat proteins are packed in an icosahedron. The mathematical analysis of electron micrographs in this study may be a useful tool for surveying the platonic solid structure of a phage or virus particle before performing 3D reconstruction.

Keywords

MS2, Icosahedron, Mathematical Approach

Conflicts of Interest

The authors declare no conflicts of interest.

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