Virus shapes and buckling transitions in spherical shells

Jack Lidmar, Leonid Mirny, and David R. Nelson
Phys. Rev. E 68, 051910 – Published 25 November 2003
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Abstract

We show that the icosahedral packings of protein capsomeres proposed by Caspar and Klug for spherical viruses become unstable to faceting for sufficiently large virus size, in analogy with the buckling instability of disclinations in two-dimensional crystals. Our model, based on the nonlinear physics of thin elastic shells, produces excellent one-parameter fits in real space to the full three-dimensional shape of large spherical viruses. The faceted shape depends only on the dimensionless Foppl–von Kármán number γ = Y R 2 / κ , where Y is the two-dimensional Young’s modulus of the protein shell, κ is its bending rigidity, and R is the mean virus radius. The shape can be parametrized more quantitatively in terms of a spherical harmonic expansion. We also investigate elastic shell theory for extremely large γ , 10 3 < γ < 10 8 , and find results applicable to icosahedral shapes of large vesicles studied with freeze fracture and electron microscopy.

  • Received 27 June 2003

DOI:https://doi.org/10.1103/PhysRevE.68.051910

©2003 American Physical Society

Authors & Affiliations

Jack Lidmar

  • Department of Physics, Royal Institute of Technology, AlbaNova, SE-106 91 Stockholm, Sweden

Leonid Mirny

  • Harvard-MIT Division of Health Science and Technology, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA

David R. Nelson

  • Lyman Laboratory of Physics, Harvard University, Cambridge, Massachusetts 02138, USA

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Issue

Vol. 68, Iss. 5 — November 2003

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