Moving electron–vibron breathers in random protein models

We consider the electron transfer (ET) in random helical protein models. The steric molecular structure of the protein matrix is modeled by a network of coupled oscillators. The latter, representing the peptide groups, are coupled via point–point interaction potentials describing the covalent and hydrogen bonds which stabilize the secondary structure of the helical protein scaffold. The electronic degree of freedom, expressed in terms of a tight-binding system, is coupled to intramolecular as well as bond vibrations. The effects of disorder and imperfections present in any real protein system are simulated by randomness in the system parameters and/or random equilibrium lengths of the bonds yielding a random protein cage. Interest is focused on the mobility of breather solutions accomplishing ET. We demonstrate that the coupling of the electron to the vibrational dynamics of the protein matrix is vital for the initiation of coherent ET. Furthermore, it is shown that the moving electron breathers of the ordered system may sustain the impact of randomness in the system parameters and persist as chaotic breathers establishing long-ranged ET along the transfer channels of the protein scaffold. The comparative analysis in dependence on the source of the randomness integrated into the breather dynamics is quantitatively performed with the help of transport coefficients. Interestingly, for relatively large degree of disorder in the system parameters the coupling of the polaron to the randomly distorted protein matrix leads even to enhanced ET in comparison with the case when randomness is only included in the system parameters and the bonds have equal equilibrium lengths. Particularly the last result concerning the amplifying modification of ET operations attributed to protein-inherent modes of the random protein matrix is exemplary for the constructive and yet paradoxical role played by disorder for the improvement of transport properties in biological systems.