Charge diffusion in homogeneous molecular chains based on the analysis of generalized frequency spectra in the framework of the Holstein model

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Abstract

We analyzed numerically computed velocity autocorrelation functions and generalized frequency spectra of charge distribution in homogeneous DNA sequences at finite temperature. The autocorrelation function and generalized frequency spectrum (frequency-dependent diffusion coefficient) are phenomenologically introduced based on the functional of mean-square displacement of the charge in DNA. The charge transfer in DNA was modeled in the framework of the semi-classical Holstein model. In this model, DNA is represented by a chain of oscillators placed into thermostat at a given temperature that is provided by the additional Langevin term. Correspondence to the real DNA is provided by choice of the force parameters, which are calculated with quantum-chemical methods. We computed the diffusion coefficient for all homogenous DNA chains with respect to the temperature and found a special scaling of independent variables that the temperature dependence of the diffusion coefficient for different homogenous DNA is almost similar. Our calculations suggest that for all the sequences, only one parameter of the system is mainly responsible for the charge kinetics. The character of individual motions contributing to the charge mobility and temperature-dependent regimes of charge distribution is determined.

About the authors

Dmitry A Tikhonov

Institute of Mathematical Problems of Biology Branch of Keldysh Institute of Applied Mathematics of RAS; Institute of Theoretical and Experimental Biophysics of RAS

Email: dmitry.tikhonov@gmail.com
Candidate of Physical and Mathematical Sciences, Senior researcher, Institute of Mathematical Problems of Biology Branch of Keldysh Institute of Applied Mathematics Russian Academy of Sciences 1 Professor Vitkevich St., Pushchino, Moscow Region 142290, Russian Federation; 3 Institutskaya St., Pushchino, Moscow Region 142290, Russian Federation

Egor V Sobolev

Institute of Mathematical Problems of Biology Branch of Keldysh Institute of Applied Mathematics of RAS; European Molecular Biology Laboratory, Hamburg Unit

Email: egor@embl-hamburg.de
Candidate of Physical and Mathematical Sciences, Postdoctoral fellow, European Molecular Biology Laboratory, Hamburg Unit 1 Professor Vitkevich St., Pushchino, Moscow Region 142290, Russian Federation; c/o DESY, Building 25A, Notkestraße 85, 22607 Hamburg, Germany

Victor D Lakhno

Institute of Mathematical Problems of Biology Branch of Keldysh Institute of Applied Mathematics of RAS

Email: lak@impb.ru
Doctor of Physical and Mathematical Sciences, Scientific Director, Institute of Mathematical Problems of Biology Branch of Keldysh Institute of Applied Mathematics Russian Academy of Sciences 1 Professor Vitkevich St., Pushchino, Moscow Region 142290, Russian Federation

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