# Virus shapes and buckling transitions in spherical shells.

@article{Lidmar2003VirusSA, title={Virus shapes and buckling transitions in spherical shells.}, author={Jack Lidmar and Leonid A. Mirny and David R. Nelson}, journal={Physical review. E, Statistical, nonlinear, and soft matter physics}, year={2003}, volume={68 5 Pt 1}, pages={ 051910 } }

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…

## 338 Citations

### Mechanical deformation of spherical viruses with icosahedral symmetry.

- EngineeringBiophysical journal
- 2006

The mechanical properties of crystalline shells of icosahedral symmetry on a substrate under a uniaxial applied force by computer simulations are studied to predict the elastic response for small deformations, and the buckling transitions at large deformations.

### Mechanical properties of icosahedral virus capsids

- Engineering
- 2007

Virus capsids are self-assembled protein shells in the size range of 10 to 100 nanometers. The shells of DNA-viruses have to sustain large internal pressures while encapsulating and protecting the…

### Relevance of capsid structure in the buckling and maturation of spherical viruses

- EngineeringPhysical biology
- 2012

This work studies how the capsid shape and the buckling transition depend on the triangulation number T and the icosahedral class P of the virus structure, and finds that, for small shells, capsids with P = 1 are most likely to produce polyhedral shapes that minimize their energy and accumulated stress, whereas viruses withP = 3 prefer to remain spherical.

### Elasticity theory and shape transitions of viral shells.

- PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2005

It is found that the transition from icosahedral to spherocylindrical symmetry is continuous or weakly first order near the onset of buckling, leading to extensive shape degeneracy.

### Buckling transitions and soft-phase invasion of two-component icosahedral shells.

- Materials SciencePhysical review. E
- 2020

The shapes of spherical viruses can be understood from the perspective of elasticity theory of thin two-component shells and a theory of shape transformations of an icosahedral shell upon addition of a softer, but still crystalline, material onto its surface is developed.

### Osmotically induced deformation of capsid-like icosahedral vesicles

- Biology
- 2011

Comparison of experimental results with Monte Carlo simulations provides a first estimate for the conditions of shell disruption, and suggests it is predominantly driven by curvature rather than two-dimensional stretching or compression.

### Elastic properties and mechanical stability of chiral and filled viral capsids.

- EngineeringPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2008

The elasticity and mechanical stability of empty and filled viral capsids under external force loading are studied in a combined analytical and numerical approach and it is found that generally skew shells have lower stretching energy than nonchiral ones.

### Kirigami and the Caspar-Klug construction for viral shells with negative Gauss curvature.

- BiologyPhysical review. E
- 2019

The Caspar-Klug construction is extended to the archaeal viruses and a buckling transition as a function of a modified Föppl-von Kármán number is described and it is shown how changes in γ^{★} may initiate the tail formation in the Acidianus two-tailed Archaeal virus.

### Buckling transition in icosahedral shells subjected to volume conservation constraint and pressure: relations to virus maturation.

- EngineeringPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2006

Several scenarios that may explain the experimentally observed feature of mature viruses being more aspherical (facetted) from their immature precursors are discussed, and predictions for the elastic properties of viral coatings are obtained on the basis of the presented studies.

### Soft modes near the buckling transition of icosahedral shells.

- PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2007

This work interprets the transition from smooth to faceted as a soft-mode transition inIcosahedral shells, and defines elastic susceptibilities as the response to forces applied at vertices, edges, and faces of an icosahedron.

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