Determination of Viral Capsid Elastic Properties From Equilibrium Thermal Fluctuations

We apply the theory of thin elastic shells to viral capsids to develop a framework for measuring elastic properties of viruses from equilibrium thermal fluctuations of the capsid surface. We show that the magnitudes of the long wave length modes of motion available in a simulation with all atomic degrees of freedom are recapitulated by an elastic network model. For the mode spectra to match, the elastic network model must be scaled appropriately by a factor which can be determined from an icosahedrally constrained all-atom simulation. By combining icosahedrally constrained molecular dynamics simulations with elastic network simulations we bypass the necessity of all-atom simulations with all degrees of freedom, when calculating elastic properties of viruses. With this method we calculate the two dimensional Young's modulus, Y , and bending modulus, κ, for the T=1 mutant of the Sesbania mosaic virus and for the T=7 HK97 virus in both immature and mature states. The values determined are in the range of previous theoretical estimates. We also observe a reduction in the bending modulus of HK97 from the immature to the mature state which would facilitate the structural buckling transition associated with maturation.