Frequency-Selective Anharmonic Mode Analysis of Thermally Excited Vibrations in Proteins

Low-frequency molecular vibrations at far-infrared frequencies are thermally excited at room temperature. As a consequence, thermal fluctuations are not limited to the immediate vicinity of local minima on the potential energy surface, and anharmonic properties cannot be ignored. The latter is particularly relevant in molecules with multiple conformations, such as proteins and other biomolecules. However, existing theoretical and computational frameworks for the analysis of molecular vibrations have so far been limited by harmonic or quasi-harmonic approximations, which are ill-suited to describe anharmonic low-frequency vibrations. Here, we introduce a fully anharmonic analysis of molecular vibrations based on a time correlation formalism that eliminates the need for harmonic or quasi-harmonic approximations. We use molecular dynamics simulations of a small protein to demonstrate that this new approach, in contrast to harmonic and quasi-harmonic normal modes, correctly identifies the collective degrees of freedom associated with molecular vibrations at any given frequency. This allows us to unambiguously characterize the anharmonic character of low-frequency vibrations in the far-infrared spectrum.