Mobile polaron solutions and nonlinear electron transfer in helical protein models - art. no. 041908

We consider the electron transfer along helical forms of proteins. The spat ial structure of the protein helices is modeled by three-dimensional oscill ator networks whose constituents represent peptide groups. Covalent and hyd rogen bonds between the peptide units are modeled by point-point interactio n potentials. The electronic degree of freedom is described by a tight-bind ing system including besides the nearest-neighbor exchange interactions bet ween covalently connected units also third- or fourth-nearest neighbor inte ractions between hydrogen-bonded sites. In addition each peptide unit posse sses an internal vibrational degree of freedom. The various dynamical degre es of freedom are coupled to each other making the exchange of electronic, intramolecular, and bond-vibrational energy possible. In the first part of the paper we investigate the static polaron formation resulting from strong interactions between the electron and the intramolecular vibrations. The 3 -10 helix and the a helix are investigated. Polaron states are constructed analytically on the basis of a variational approach. Compared to the a heli x the 3-10 helix supports stronger localized polarons. In the second part o f the paper we take the coupling of the polaron with the vibrations of the three-dimensional protein matrix into account focusing interest on the bond -assisted initiation of polaron motion. In detail it is demonstrated that t he interplay of the protein matrix and the polaron dynamics conspire to act ivate not only the polaron motion but also to maintain a long-lived coheren tly traveling localized pattern along the lattice of peptide units. Startin g from a nonequilibrium state it is shown that coexisting electron and bond -vibration breathers assist the relaxation dynamics towards energy equilibr ation and the attainment of a stationary regime.