**Dynamics of Large Radius Polaron in a Model Polynucleotide Chain with Random Perturbations**
**Nadezhda S. Fialko, Victor D. Lakhno**
*Institute of Mathematical Problems of Biology RAS – the Branch of Keldysh Institute of Applied Mathematics of Russian Academy of Sciences*

**Abstract**. We consider the dynamics of polaron in a chain using computational experiment. The temperature, which is simulated by random Langevin-type perturbations, and influence of external electric field are taking into account. In a sufficiently long unperturbed chain, the displacement of the center of mass of the polaron and its velocity does not depend on its length. In the semiclassical Holstein model, which is applied for simulations of charge transfer in DNA, the region of polaron existence in the thermodynamic equilibrium state depends not only on temperature, but also on the chain length. Therefore, when modeling dynamics from polaron initial data, the time dependences of the average displacement of the charge mass center at the same temperature are different for chains of different lengths. According to the results of computational experiment, for polaron of large radius the time dependence of the “average polaron displacement”, which takes into account only the polaron peak and its position, for chains of different lengths behaves almost equally at time intervals until the polaron will destroyed. The same slope of the polaron displacement allows us to estimate the average polaron velocity. The results of calculations demonstrate that in Holstein model at zero temperature, the mobility value of the large radius polaron is small but non-zero.

**Key words**: *Holstein model, Langevin thermostat, DNA, charge, electric field intensity, displacement of the charge center of mass, moving polaron*.