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Virus shapes and buckling transitions in spherical shells.
Jack Lidmar1, Leonid Mirny, David R Nelson
1Department of Physics, Royal Institute of Technology, AlbaNova, SE-106 91 Stockholm, Sweden.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 20, 2003
Summary
Large spherical viruses become unstable and facet due to their size, similar to 2D crystals. This shape change is modeled by elastic shell physics, fitting virus structures and large vesicle shapes.
Area of Science:
- Biophysics
- Materials Science
- Structural Biology
Background:
- Icosahedral symmetry is common in spherical viruses, as proposed by Caspar and Klug.
- The stability of these structures at larger sizes is not fully understood.
Purpose of the Study:
- To investigate the stability of icosahedral virus structures at larger sizes.
- To model the three-dimensional shape of large spherical viruses using elastic shell theory.
Main Methods:
- Developed a nonlinear physics model for thin elastic shells.
- Analyzed the buckling instability of disclinations in 2D crystals.
- Used a dimensionless Foppl-von Kármán number (gamma) to characterize shell properties.
- Applied spherical harmonic expansion for shape parametrization.
Main Results:
- Icosahedral packings become unstable to faceting for large virus sizes.
- The model accurately fits the 3D shapes of large spherical viruses with one parameter (gamma).
- Faceted shape is determined by the Foppl-von Kármán number (gamma = YR^2/kappa).
- Elastic shell theory for large gamma (10^3-10^8) applies to large vesicle shapes.
Conclusions:
- Virus size influences the stability of their icosahedral protein shell structure.
- Elasticity theory provides a quantitative framework for understanding virus and vesicle shapes.
- The Foppl-von Kármán number is a key parameter governing the faceting transition.