Elastic modulus of viral nanotubes

We report an experimental and theoretical study of the radial elasticity of tobacco mosaic virus (TMV) nanotubes. An atomic force microscope tip is used to apply small radial indentations to deform TMV nanotubes. The initial elastic response of TMV nanotubes can be described by finite-element analysis in $5\mathrm{nm}$ indentation depths and Hertz theory in $1.5\mathrm{nm}$ indentation depths. The derived radial Young’s modulus of TMV nanotubes is $0.92\pm 0.15\mathrm{GPa}$ from finite-element analysis and $1.0\pm 0.2\mathrm{GPa}$ from the Hertz model, which are comparable with the reported axial Young’s modulus of $1.1\mathrm{GPa}$ [Falvo et al., Biophys. J. 72, 1396 (1997)].

Figure 1

(Color online) AFM images of TMV nanotubes (a) before and (b) after indentation. The high profile across a nanotube is inset in (a). The white arrow shown in (b) indicates the collapse of the nanotube after indentation.

Figure 2

Force–$Z$ piezo distance (FZ) curve (gray) taken on a TMV nanotube, together with the FZ curve (black) on a glass substrate. Both FZ curves were performed under AFM contact mode in a liquid cell with the same AFM tip.

Figure 3

(Color online) Simulated deformation of a nanotube with an outer radius of $9\mathrm{nm}$ and an inner radius of $2\mathrm{nm}$ at indentations of (a) 0.65, (b) 1.45, (c) 1.50, (d) 3.95, and (e) $5.00\mathrm{nm}$, respectively. The von Mises stress is indicated by color contours (f).

Figure 4

Experimental data (circular dots) of force vs indentation for TMV nanotubes within $5\mathrm{nm}$ indentation. Young’s modulus was calculated from the best fitting of simulated force-indentation data (square dots) with finite-element analysis.

Figure 5

Experimental data (circular dots) of force vs indentation for TMV nanotubes in $1.5\mathrm{nm}$ indentation. The solid lines represent the fits of the experimental data with the Hertz model. The Young’s modulus from these optimized fitting results is 1.2, 0.9, and $0.8\mathrm{GPa}$, respectively.