Unlocking Internal Prestress from Protein Nanoshells

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Unlocking Internal Prestress from Protein Nanoshells

W. S. Klug, W. H. Roos, and G. J. L. Wuite

Phys. Rev. Lett. 109, 168104 – Published 19 October 2012

See Synopsis: Protein Shells Take a Strength Test

Abstract

The capsids of icosahedral viruses are closed shells assembled from a hexagonal lattice of proteins with fivefold angular defects located at the icosahedral vertices. Elasticity theory predicts that these disclinations are subject to an internal compressive prestress, which provides an explanation for the link between size and shape of capsids. Using a combination of experiment and elasticity theory we investigate the question of whether macromolecular assemblies are subject to residual prestress, due to basic geometric incompatibility of the subunits. Here we report the first direct experimental test of the theory: by controlled removal of protein pentamers from the icosahedral vertices, we measure the mechanical response of so-called “whiffle ball” capsids of herpes simplex virus, and demonstrate the signature of internal prestress locked into wild-type capsids during assembly.

Received 18 October 2011

DOI:https://doi.org/10.1103/PhysRevLett.109.168104

Synopsis

Protein Shells Take a Strength Test

Published 19 October 2012

The protein shells surrounding large viruses have built-in tension that determines their shapes.

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Authors & Affiliations

W. S. Klug¹, W. H. Roos^2,*, and G. J. L. Wuite²

¹Department of Mechanical and Aerospace Engineering, and California NanoSystems Institute, UCLA, Los Angeles, California 90095, USA
²Natuur- en Sterrenkunde & LaserLab, VU University, De Boelelaan 1081, 1081 HV Amsterdam, Netherlands

^*Corresponding author. wroos@few.vu.nl

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Issue

Vol. 109, Iss. 16 — 19 October 2012

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Images

Figure 1
HSV1 B capsids deposited on their threefold symmetry axis. The top AFM images (a),(b) are from a whiffle ball capsid and the bottom images (c),(d) are from an intact particle. The capsids are shown in a 3D-perspective rendering and the white arrows in (a),(c) indicate the icosahedral vertices. One can see three holes in image (a) at the places where the pentamers are removed. The particles are shown before (a),(c) and after (b),(d) nanoindentation. The insets in (b),(d) show the height profile (as taken along the gray arrows) before and after indentation, where $x$ denotes the lateral distance and $z$ the particle height.Reuse & Permissions
Figure 2
Asphericity as function of FvK number computed by finite-element analysis for “intact” (i.e., closed) and whiffle ball icosahedral elastic shells. Dashed lines show results using the shape of relaxed intact shells, but ignoring the pentons, i.e., making them “invisible.” Insets show the relaxed equilibrium shapes for shells having $γ = 1000$ , with color contours indicating stretching energy density. Results for closed shells are marked intact. Whiffle ball shells are labeled by the Caspar-Klug $T$ number defining the structure of the hexons and the removed pentons. For smaller $T$ numbers the holes at the pentameric sites are larger in proportion to the average shell radius. For the analysis, the finite-element discretizations were refined to a sufficient level that the results were insensitive to further refinement.Reuse & Permissions
Figure 3
Indentation curves (thin lines show individual curves) and their averages (thick lines) for whiffle ball $T = 16$ capsids (number of particles $n = 9$ ) and intact $T = 16$ capsids ( $n = 5$ , inset) along the threefold symmetry axis. Both averages are shown in both graphs; only the beginning of these curves are shown. The negative slope following on failure of most particles is $\sim 0.05 N / m$ , which equals the spring constant of the used cantilever and represents the relaxation of the cantilever after a breaking event.Reuse & Permissions
Figure 4
Normalized, simulated force-indentation responses of intact and whiffle ball icosahedral (prestressed) shells with $γ = 1500$ . Whiffle ball shells with triangulation numbers $T = 16$ , $T = 7$ , and $T = 4$ , have structures depicted in Fig. 2. Indentation loading was oriented along the threefold symmetry axis of the shells. The top left inset shows normalized stiffnesses, i.e., the derivatives of the curves in the main plot, corresponding to prestressed icosahedral shells. The bottom right inset shows the stiffness curves for shells with spherical (stress-free) reference states, revealing dramatically smaller differences between intact and whiffle ball shells than are seen for prestressed icosahedral shells.Reuse & Permissions

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