Low Frequency Mechanical Modes of Viral Capsids: An Atomistic Approach

We present a method for the calculation of the low frequency vibrational modes and frequencies of viral capsids, or other large molecules, where the modes are modeled with atomic detail. Extending ideas from electronic structure theory, an energy functional is used to find modes of a classical dynamical matrix below a fixed (pseudo-Fermi) level. The icosahedral satellite tobacco necrosis virus is modeled as an example. We find that atoms around the $C5$ and $C3$ axis have small relative displacement while the $\beta$ sheet body shows gliding motion.

Figure 1

Structure of a single protein building block of the satellite tobacco necrosis virus (2BUK). Not shown are the 3 ${\mathrm{Ca}}^{+2}$ atoms that bind the protein with itself, ${\mathrm{H}}_2\mathrm{O}$, and symmetry related copies.

Figure 2

Displacement pattern of the breathing $A$ mode at $2.4{\mathrm{cm}}^{-1}$ of STNV. Displacements are shown using arrows. Each beta sheet is shaded (colored online) differently for clarity. (a) The backbone displacements within a single protein unit with the $C5$ axis vertically aligned. (b) The displacement of the center of mass of the entire protein unit for the five units around the $C5$ axis. (c) Similar to (a) but looking down the $C5$ axis. (d) Similar to (b) but looking down the $C5$ axis. (e) Displacement of the center of mass of each peptide in the full virus.

Figure 3

Low frequency irrep. $H$ mode of STNV located at $4.1{\mathrm{cm}}^{-1}$. Arrows indicate the center of mass motion of each peptide in the full virus.

Figure 4

The relative Raman intensity of $A$ (solid line) and $H$ (dashed line) vibrational modes of STNV calculated from a bond polarizability model.