Vibrational dynamics of folded proteins: Significance of slow and fast motions in relation to function and stability

A single-parameter harmonic Hamiltonian based on local packing density and contact topology is proposed for studying residue fluctuations in native proteins. The internal energy obeys an equipartition law, and free energy changes result from entropy fluctuations only. Frequency-wave-number maps show communication between residues involved in slow and fast modes. Fast modes are strongly localized, resulting from the geometric irregularity of the structure. Comparison with experiments shows that slow and fast modes are associated, respectively, with function and stability. Specifically, domain motions and folding cores of HIV-1 protease are accurately identified.