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The vibron dynamics associated to amide-I vibrations in a 3D alpha-helix isdescribed according to a generalized Davydov model. The helix is modeled bythree spines of hydrogen-bonded peptide units linked via covalent bonds. Toremove the intramolecular anharmonicity of each amide-I mode and torenormalized the vibron-phonon coupling, two unitary transformation have beenapplied to reach the dressed anharmonic vibron point of view. It is shown thatthe vibron dynamics results from the competition between inter-spine andintra-spine vibron hops and that the two kinds of hopping processes do notexperience the same dressing mechanism. Therefore, at low temperature (or weakvibron-phonon coupling), the polaron behaves as an undressed vibron delocalizedover all the spines whereas at biological temperature (or strong vibron-phononcoupling), the dressing effect strongly reduces the vibrational exchangesbetween different spines. As a result the polaron propagates along a singlespine as in the 1D Davydov model. Although the helix supports both acousticaland optical phonons, this feature originates in the coupling between the vibronand the acoustical phonons, only. Finally, the lattice distortion whichaccompanies the polaron has been determined and it is shown that residueslocated on the excited spine are subjected to a stronger deformation than theother residues.Comment: 13 pages, 7 figure

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