One-dimensional nature of protein low-energy vibrations

Protein internal dynamics is crucial for its function. In particular, low-energy vibrational modes at 1-10 meV play important roles in the transportation of energy inside the protein molecule, and facilitate its enzymatic function and binding to ligands and other biomolecules. However, the microscopic spatiotemporal details of these modes have remained largely unknown, due to limitations of the experimental techniques. Here, by applying inelastic neutron scattering on a perdeuterated protein, we demonstrate that these vibration modes are correlated primarily through peptide bonds rather than noncovalent interactions (including hydrogen bonds), which is further confirmed by a complementary molecular dynamics simulation. More importantly, the complex spatiotemporal features of interatomic vibrations observed in an all-atom simulation are qualitatively reproduced by an ultrasimple toy model, a one-dimensional harmonic chain, where the vibrations propagate along the peptide chain, but are confined and damped by noncovalent interactions surrounding the chain. Our findings are fundamentally important for understanding many functional processes in proteins that are strongly coupled to low-energy vibrational modes. Moreover, the one-dimensional nature of low-energy vibrations discovered here should be applicable to other biomacromolecules and many ordinary polymeric materials.