Vibrons in a one-dimensional lattice of hydrogen-bonded peptide units: Influence of the inhomogeneous mass distribution in the amino acid sequence

Abstract

The influence of the inhomogeneous mass distribution in the amino acid sequence on amide-I vibrons in alpha-helices is studied within the small polaron approach in a one-dimensional (1D) model. It is shown that inhomogeneities in the sequence favor a randomness in the polaron Hamiltonian via the dressing mechanism. The polaron dynamics is thus described by a 1D tight binding model with correlated off-diagonal disorder. At low temperature, the polaron hopping constants exhibit small fluctuations around a large average value so that the polaron Hamiltonian appears weakly disordered. Extended states occur over a wide range of energies around the band center whereas the states close to the band edges appear localized. By contrast, at biological temperature, a stronger disorder takes place which originates in a drastic decrease of the average hopping constant. The number of localized states increases but few states close to the band center exhibit a localization length about to or greater than the lattice size. The extended nature of these latter states is attributed to the occurrence of short range correlations in the random hopping constants.