Polaronic electron transfer in β-sheet protein models

We consider electron transfer (ET) along β-sheet forms of proteins. The secondary structure of the β-sheet proteins is modelled by a two-dimensional oscillator network whose constituents represent peptide units. Covalent and hydrogen bonds between the peptide units are represented by point-point interaction potentials. Intrapeptide vibrational degrees of freedom are taken into account by means of harmonic oscillators while the electronic motion is described within the framework of a tight-binding system. We construct polarons as stationary localized solution states utilizing a non-linear map approach. The polaron state represents a self-trapped electron in conjunction with its intrapeptide deformation field and the static deformation of the protein scaffolding. Furthermore, in the dynamical study we focus attention on the initiation of polaron motion, utilizing its pinning modes. We show that both the covalent and the hydrogen channel provide a path for coherent ET in β-sheet proteins. It is demonstrated that the interplay of the vibrations of the protein scaffolding and the electron dynamics promotes long-lived localized excitation patterns travelling coherently along the lattice of peptide units.