Fast calculation of the infrared spectra of large biomolecules

Vibrational spectra of proteins potentially give insight into biologically significant molecular motion and the proportions of different types of secondary structure. Vibrational spectra can be calculated either from normal modes obtained by diagonalizing the mass-weighted Hessian or from the time autocorrelation function derived from molecular dynamics trajectories. The Hessian matrix is calculated from force fields because it is not practical to calculate the Hessian from quantum mechanics for large molecules. As an alternative to molecular dynamics the spectral response can be calculated from a time autocorrelation derived from numerical solution of the harmonic equations of motion, resulting in calculations at least 4 times faster. Because the calculation also scales linearly with number of atoms, N, it is faster than normal-mode calculations that scale as N (3) for proteins with more then 4,700 atoms. Using this method it is practical to perform all-atom calculations for large biological systems, for example viral capsids, with the order of 10(5) atoms.