Mathematical Approach to the Platonic  Solid Structure of MS2 Particles

Nai-Chia Shi; Chun-Chun Wu; Jui-Sen Yang

doi:10.4236/am.2015.64059

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Applied Mathematics > Vol.6 No.4, April 2015

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 PDF HTML XML 2,502 Downloads 2,943 Views

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

Share and Cite:

Shi, N. , Wu, C. and Yang, J. (2015) Mathematical Approach to the Platonic Solid Structure of MS2 Particles. Applied Mathematics, 6, 655-662. doi: 10.4236/am.2015.64059.

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	Janner, A. (2006) Towards a Classification of Icosahedral Viruses in Terms of Indexed Polyhedral. Acta Crystallographica, Section A, 62, 319-330.
[2]	Golmohammadi, R., Valegård, K., Fridborg, K. and Liljas, L. (1993) The Refined Structure of Bacteriophage MS2 at 2.8 Å Resolution. Journal of Molecular Biology, 234, 620-639.
[3]	Valegård, K., Liljas, L., Fridborg, K. and Unge, T. (1990) The Three-Dimensional Structure of the Bacterial Virus MS2. Nature, 345, 36-41. http://dx.doi.org/10.1038/345036a0
[4]	Baker, T.S., Olson, N.H. and Fuller, S.D. (1999) Adding the Third Dimension to Virus Life Cycles: Three-Dimensional Reconstruction of Icosahedral Viruses from Cryo-Electron Micrographs. Microbiology and Molecular Biology Reviews, 63, 862-922.
[5]	Valegård, K., Murray, J.B., Stonehouse, N.J., van den Worm, S., Stockley, P.G. and Liljas, L. (1997) The Three-Dimensional Structures of Two Complexes between Recombinant MS2 Capsids and RNA Operator Fragments Reveal Sequence-Specific Protein-RNA Interactions. Journal of Molecular Biology, 270, 724-738.
[6]	Koning, R., van den Worm, S., Plaisier, J.R., van Duin, J., Abrahams, J.P. and Koerten, H. (2003) Visualization by Cryo-Electron Microscopy of Genomic RNA That Binds to the Protein Capsid inside Bacteriophage MS2. Journal of Molecular Biology, 332, 415-422.
[7]	Plevka, P., Tars, K. and Liljas, L. (2008) Crystal Packing of a Bacteriophage MS2 Coat Protein Mutant Corresponds to Octahedral Particles. Protein Science, 17, 1731-1739. http://dx.doi.org/10.1110/ps.036905.108
[8]	Caspar, D.L.D. and Klug, A. (1962) Physical Principles in the Construction of Regular Viruses. Cold Spring Harbor Symposia on Quantitative Biology, 27, 1-24.
[9]	Flint, S.J., Enquist, L.W., Krug, R.M., Racaniello, V.R. and Skaika, A.M. (2000) Principles of Virology: Molecular Biology, Pathogenesis, and Control. American Society for Microbiology Press, Washington DC, 58-98.
[10]	Reddy, V.S. and Johnson, J.E. (2005) Structure-Derived Insights into Assembly. Advances in Virus Research, 64, 45-68.
[11]	Gau, J.F. (2010) The Attachment of MS2 on E. coli. Master thesis, National Taiwan Ocean University, Keelung.
[12]	Plevka, P., Tars, K. and Liljas, L. (2009) Structure and Stability of Icosahedral Particles of a Covalent Coat Protein Dimer of Bacteriophage MS2. Protein Science, 18, 1653-1661. http://dx.doi.org/10.1002/pro.184
[13]	Schneemann, A. (2006) The Structural and Functional Role of RNA in Icosahedral Virus Assembly. Annual Review of Microbiology, 60, 51-67. http://dx.doi.org/10.1146/annurev.micro.60.080805.142304
[14]	Dr. Math, FAQ (1994-2009) (2009) Regular Polyhedral: Formulas. The Math Forum@Drexel. Drexel University, Philadelphia. http://mathforum.org
[15]	Cann, A.J., (Au & Ed) (2005) The Principles of Molecular Virology. Chap. 2, Particles. Elsevier Academic Press, San Diego, 25-55.
[16]	Shih, N.C. (2009) Mathematical Studies on the 3D Reconstruction of Phage MS2. Master Thesis, Feng-Chia University, Taichung.