Trapping and motion of polarons in weakly disordered DNA molecules

Polaron effects for charge migration in DNA molecules have been previously considered within the Peyrard-Bishop-Holstein model. When a uniform electric field is applied, the polaron moves asymptotically at a constant velocity, provided dissipative effects are taken into account, and then current flows through DNA. Disorder originating from interactions with a random environment of solute molecules and ions surrounding the DNA molecule could prevent charge migration due to the localization of the carrier wavefunction. We studied numerically the Peyrard-Bishop-Holstein model when the disordered DNA molecule is subjected to a uniform electric field. We found the threshold value of the electric field to observe polaron motion when disorder is present. We also calculated the fluctuations of the electric current and found that they provide valuable information about the polaron dynamics.