Modeling of charge dynamics in synthetic DNA under the influence of an external electric field

N. S. Fialko

Matematičeskaâ biologiâ i bioinformatika, Tome 19 (2024) no. 2, pp. 439-452.

Résumé

Based on the Holstein polaron model, the problem of modeling Bloch oscillations of a quantum charged particle in a chain of classical sites placed in a uniform electric field is considered. As is known, in a rigid lattice, Bloch oscillations describe charge oscillations under the influence of a constant electric field. Biopolymers are considered as non-rigid lattice, and movement of lattice sites have significant effect on the charge dynamics. Most of the computational experiments were carried out with the parameters values of homogeneous polyguanine fragments of DNA. At the initial moment, the charge “arises” at one site of the chain placed in a field with constant intensity, so charge have no time to form a polaron. The dynamics of charge in an unperturbed chain (at zero temperature) is simulated. Minimum chain length is estimated, for which end effects have not influence on the charge dynamics during Bloch oscillations. For the center of mass motion of the charge, a comparative analysis was carried out with the dynamics of the polaron, previously studied by Korshunova and Lakhno. A simulation of Bloch charge oscillations at a finite temperature was performed. To determine the frequency of charge oscillations, in addition to visual control, a Fourier series expansion was used. It is shown that averaging over realizations leads to smoothing of oscillations, which complicates the study of the influence of temperature on Bloch oscillations. Based on the simulation results, we assume that it is necessary to study the dynamics of individual implementations in more detail, in order to determine the temperature at which Bloch oscillations are disrupted.