Vibron-polaron in alpha-helices. I. Single-vibron states.

The vibron dynamics associated to amide-I vibrations in a three-dimensional alpha-helix is described according to a generalized Davydov model. The helix is modeled by three spines of hydrogen-bonded peptide units linked via covalent bonds. To remove the intramolecular anharmonicity of each amide-I mode and to renormalize the vibron-phonon coupling, two unitary transformations have been applied to reach the dressed anharmonic vibron point of view. It is shown that the vibron dynamics results from the competition between interspine and intraspine vibron hops and that the two kinds of hopping processes do not experience the same dressing mechanism. Therefore, at low temperature (or weak vibron-phonon coupling), the polaron behaves as an undressed vibron delocalized over all the spines whereas at biological temperature (or strong vibron-phonon coupling), the dressing effect strongly reduces the vibrational exchanges between different spines. As a result the polaron propagates along a single spine as in the one-dimensional Davydov model. Although the helix supports both acoustical and optical phonons, this feature originates in the coupling between the vibron and the acoustical phonons only. Finally, the lattice distortion which accompanies the polaron has been determined and it is shown that residues located on the excited spine are subjected to a stronger deformation than the other residues.