The Mechanical Properties of Icosahedral Viral Shells

Figure 1: Southern Bean Mosaic Virus (SBMV) is composed of 60 subunits, each of which contains protein A (red), protein B (blue), and protein C (green). Black symbols denote fivefold, threefold, and twofold symmetry axes. Triangle (black outline) marks one subunit. The approaching tip-sphere
(orange) is located close to the surface, and is attached to a 'virtual' spring that pushes the tip-sphere against the viral shell.

The mechanical properties of viral shells are crucial for viral assembly and infection. To study their distribution and heterogeneity on the viral surface, we have carried out atomistic force-probe molecular dynamics simulations of the complete shell of Southern Bean Mosaic Virus (SBMV), a prototypical T=3 virus, in explicit solvent. The simulation system comprises over 4,500,000 atoms. To facilitate direct comparison with atomic force microscopy measurements, a Lennard-Jones sphere was used as a model of the AFM tip and pushed with different velocities towards the capsid protein at 19 different positions on the triangular subunit of the viral surface.

A detailed picture of the spatial distribution of elastic constants and yielding forces determined at the rupture point is obtained which can explain corresponding heterogeneities observed in previous AFM experiments. Our simulations showed that the capsid behaved highly elastic upon indentation with the tip-sphere. Only the residues close to the indentation position deformed plastically.

Figure 2: Sketch of SU 12 (yellow) and adjacent subunits (white). Black dots mark grid points at which elastic properties were determined by force-probe simulations in which the tip-sphere was pushed at a probe velocity of 0.01 nm/ps against the capsid. The obtained elastic constants are shown in red, green, and blue; different colors of numbers denote different push-vector directions perpendicular to the viral surface.

Figure 1 gives an overview of the composition of the complete virus particle. The movie below shows a force-probe simulation in which the tip-sphere (orange sphere) was pushed along the 5-fold symmetry axis though the center of a pentamer (tube representation). The single residues are color-coded showing the degree of deformation (red: no deformation, blue: high deformation).

The obtained elastic constants are shown in Figure 2. The largest stiffness was seen at the pentamer center along the 5-fold symmetry axis. The weakest position was found at the subunit center and along the 2-fold symmetry axis.

Figure 3: Obtained yielding forces (in Nm). Colour code: low stability, blue; high stability, red.

The largest yielding forces were obtained between two A-proteins surrounding the pentamer center. The hexamer center around the 3-fold symmetry axes exhibits a larger stability compared to the pentamer center, although here the largest stiffness was found. The softest capsid positions were seen at the subunit center and along the 2-fold symmetry axis.

Publications

Zink, M.; Grubmueller, H.: Primary changes of the mechanical properties of Southern Bean Mosaic Virus upon calcium removal. Biophysical Journal 98 (4), pp. 687 - 695 (2010)

Zink, M.; Grubmueller, H.: Mechanical properties of the icosahedral shell of southern bean mosaic virus: A molecular dynamics study. Biophysical Journal 96 (4), pp. 1350 - 1363 (2009)
Zink, M.: Mechanical properties of icosahedral viral shells. A molecular dynamics study. Dissertation, Universität Göttingen, Göttingen (2009)

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