Nonlinear Finite Element Analysis of Nanoindentation of Viral Capsids

Abstract

Recent Atomic Force Microscope (AFM) nanoindentation experiments measuring mechanical response of the protein shells of viruses have provided a quantitative description of their strength and elasticity. To better understand and interpret these measurements, and to elucidate the underlying mechanisms, this paper adopts a course-grained modeling approach within the framework of three-dimensional nonlinear continuum elasticity. Homogeneous, isotropic, elastic, thick shell models are proposed for two capsids: the spherical Cowpea Chlorotic Mottle Virus (CCMV), and the ellipsocylindrical bacteriophage $\varphi 29$. As analyzed by the finite element method, these models enable parametric characterization of the effects of AFM tip geometry, capsid dimensions, and capsid constitutive descriptions. The generally nonlinear force response of capsids to indentation is shown to be insensitive to constitutive details, and greatly influenced by geometry. Nonlinear stiffening and softening of the force response is dependent on the AFM tip dimensions and shell thickness. Fits of the models capture the roughly linear behavior observed in experimental measurements and result in estimates of Young's moduli of $\approx$280--360 MPa for CCMV and $\approx$4.5 GPa for $\varphi 29$.

24 pages, 10 figures, submitted to Biophysical Journal

References in corpus (2)

• Virus shapes and buckling transitions in spherical shells
• Mechanical Properties of Viral Capsids

Cited by in corpus (5)

• Contact Mechanics of a Small Icosahedral Virus
• Nanoindentation of virus capsids in a molecular model
• Fluctuating Nonlinear Spring Model of Mechanical Deformation of Biological Particles
• Self-assembly of model proteins into virus capsids
• Interplay between the mechanics of bacteriophage fibers and the strength of virus-host links