A Study on Natural Frequencies of Spherical Viral Shells

A refined elastic shell model is used to study the effect of high structural heterogeneity on natural frequencies of spherical viral shells. With this model, the structural heterogeneity of a spherical viral shell is characterized by an effective bending thickness (which can be quite different from the average thickness) and the transverse shear modulus (which can be much lower than the in-plane shear modulus). The results show that actual natural frequencies of spheroidal modes of a spherical viral shell can be much lower than those predicted by the classical homogeneous shell model, although natural frequencies of torsional modes are close to those predicted by the classical model. For example, with physically realistic parameters for virus capsid STMV, the natural frequencies of spheroidal modes predicted by the present model are about 30-50% lower than those predicted by the classical model, in better agreement with known simulation results. These results suggest that the refined shell model could offer a relatively simple model to calculate natural frequencies of spherical viral shells of high structural heterogeneity. Keywords - Natural Frequency, Spherical Viral Shells, Structural Heterogeneity, Thickness Nonuniformity