Retrovirus capsid is a fullerene-like lattice consisting of capsid protein hexamers and pentamers. Mathematical models for the lattice structure help understand the underlying biological mechanisms in the formation of viral capsids. It is known that viral capsids could be categorized into three major types: icosahedron, tube, and cone. While the model for icosahedral capsids is established and well-received, models for tubular and conical capsids need further investigation. This paper proposes new models for the tubular and conical capsids based on an extension of the Capser-Klug quasi-equivalence theory. In particular, two and three generating vectors are used to characterize respectively the lattice structures of tubular and conical capsids. Comparison with published HIV-1 data demonstrates a good agreement of our modeling results with experimental data.
@article{bwmeta1.element.doi-10_2478_mlbmb-2014-0009, author = {Farrah Sadre-Marandi and Jiangguo Liu and Simon Tavener and Chaoping Chen}, title = {Generating Vectors for the Lattice Structures of Tubular and Conical Viral Capsids}, journal = {Molecular Based Mathematical Biology}, volume = {2}, year = {2014}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_mlbmb-2014-0009} }
Farrah Sadre-Marandi; Jiangguo Liu; Simon Tavener; Chaoping Chen. Generating Vectors for the Lattice Structures of Tubular and Conical Viral Capsids. Molecular Based Mathematical Biology, Tome 2 (2014) . http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_mlbmb-2014-0009/
[1] J. Benjamin, B.K. Ganser-Pornillos,W.F. Tivol,W.I. Sundquist, and G.J. Jensen, Three-dimensional structure of HIV-1 virus-like particles by electron cryotomography. J. Mol. Biol. 346(2005), 577–588.
[2] J. Briggs, K. Grünewald, B. Glass, F. Förster, H-G. Kräusslich, and S.D. Fuller, The mechanism of HIV-1 core assembly: Insights from three-dimensional reconstructions of authentic virions. Structure 14(2006), 15–20.
[3] J. Briggs and H. Krausslich, The molecular architecture of HIV. J. Mol. Biol. 410(2011), 491–500.
[4] J. Briggs, T. Wilk, R. Welker, H-G. Kräusslich, and S.D. Fuller, Structural organization of authentic, mature HIV-1 virions and cores. EMBO 22(2003), 1707–1715.
[5] C. Büchen-Osmond, ICTVdB - The universal virus database, Version 4, ICTVdB Management, New York, 2006.
[6] I.L. Byeon, X. Meng, J. Jung, G. Zhao, R. Yang, J. Ahn, J. Shi, J. Concel, C. Aiken, P. Zhang, and A.M. Gronenborn, Structural convergence between cryo-EM and NMR reveals intersubunit interations critical for HIV-1 capsid function. Cell 139(2009), 780–790. [WoS]
[7] D. Caspar and A. Klug, Physical principles in the construction of regular viruses. Cold Spring Harb. Symp. Quant. Biol. 27(1962), 1–24. [Crossref]
[8] T. Douglas and M. Young, Virus: Making friends with old foes. Science 312(2006), 873–875.
[9] O.M. Elrad and M.F. Hagan, Encapsulation of a polymer by an icosahedral virus. Phys. Biol. 7(2010), 045003. [Crossref][WoS][PubMed]
[10] A. de la Escosura, R. Nolte, and J. Cornelissen, Viruses and protein cages as nanocontainers and nanoreactors. J. Mater. Chem. 19(2009), 2274–2278. [WoS]
[11] B.K. Ganser, S. Li, V.Y. Klishko, J.T. Finch, and W.I. Sundquist, Assembly and analysis of conical models for the HIV-1 core. Science 80(1999), 80–83.
[12] B.K. Ganser-Pornillos, M. Yeager, and O. Pornillos, Assembly and architecture of HIV. Adv. Exp. Med. Biol. 726(2012), 441– 465.
[13] Y. Gogotsi, Nanomaterial Handbook, Taylor & Francis Group, Florida, 2006.
[14] J. Heymann, C. Butan, D. Winkler, R. Craven, and A. Steven, Irregular and semi-regular polyhedral models for Rous sarcoma virus cores. Comput. Math. Meth. Med. 9(2008), 197–210. [WoS][Crossref] | Zbl 1160.92021
[15] Y. Hu, R. Zandi, A. Anavitarte, C.M. Knobler, andW.M. Gelbart, Packaging of a polymer by a viral capsid: The interplay between polymer length and capsid size. Biophys. J. 94(2008), 1428–1436. [Crossref][WoS]
[16] J. Liu, F. Sadre-Marandi, S. Tavener, and C. Chen, Curvature concentrations on the HIV-1 capsid. Preprint, Colorado State University, (2014).
[17] A. Luque and D. Reguera, The structure of elongated viral capsids. Biophys. J. 98(2010), 2993–3003. [WoS][PubMed][Crossref]
[18] E.R. May, J. Feng, and C.L. Brooks III, Exploring the symmetry and mechanism of virus capsid maturation via an ensemble of pathways. Biophys. J. 102(2012), 606–612. [WoS][Crossref]
[19] M.F. Moody, The shape of the T-even bacteriophage head. Virology 26(1965), 567–576. [Crossref]
[20] M.F. Moody, Geometry of phage head construction. J. Mol. Biol. 293(1999), 401–433.
[21] T.T. Nguyen, R.F. Bruinsma, and W.M. Gelbart, Elasticity theory and shape transitions of viral shells. Phys. Rev. E 72(2005), 1–19. [WoS]
[22] J.K. Pokorski and N.F. Steinmetz, The art of engineering viral nanoparticles. Mol. Pharma. 8(2011), 29–43. [Crossref]
[23] O. Pornillos, B.K. Ganser-Pornillos, and M. Yeager, Atomic-level modelling of the HIV capsid. Nature (Letter) 469(2011), 424– 428. [WoS]
[24] A. Siber, Continuum and all-atom description of the energetics of graphene nanocones. Nanotech. 18(2007), 1–6.
[25] Y. Tao, N.H. Olson,W. Xu, D.L. Anderson, M.G. Rossmann, and T.S. Baker, Assembly of a tailed bacterial virus and its genome release studied in there dimensions. Cell 95(1998), 431–437. [Crossref][PubMed]
[26] B. Turner and M. Summers, Structural biology of HIV. J. Mol. Biol. 285(1999), 1–32.
[27] R. Welker, H. Hohenberg, U. Tessmer, C. Huckhagel, and H-G. Kräusslich, Biochemical and structural analysis of isolated mature cores of human immunodeficiency virus type 1. J. Virol. 74(2000), 1168–1177. [Crossref]
[28] F.F. Xu, Y. Bando, and D. Golberg, The tubular conical helix of graphitic boron nitride. New J. Phys. 5(2003), 1–16.
[29] R. Zandi, D. Reguera, R. Bruinsma, W. Gelbart, and J. Rudnick, Origin of icosahedral symmetry in viruses. PNAS 101(2004), 15556–15560.
[30] G. Zhao, J. Perilla, E. Yufenyuy, X. Meng, B. Chen, J. Ning, J. Ahn, A. Gronenborn, K. Schulten, C. Aiken, and P. Zhang, Mature HIV-1 capsid structure by cryo-electron microscopy and all-atom molecular dynamics. Nature (Letter) 497(2013), 642–646.
[31] www.thebacteriophages.org/chapters/0180_figure_003.htm