Abstract
The charge transport in the modified DNA model is studied by taking into account the factor of solvent and the effect of coupling motions of nucleotides. We report on the presence of the modulational instability (MI) of a plane wave for charge migration in DNA and the generation of soliton-like excitations in DNA nucleotides. By applying the continuum approximation, we show that the original differential-difference equation for the DNA dynamics can be reduced to a set of three coupled nonlinear equations. The linear stability analysis of wave solutions of the coupled systems is performed and the growth rate of instability is found numerically. We also investigate the impact of solvent interaction. The solvent factor introduces a new behavior to the wave patterns, modifying also the intrinsic properties of localized structures. In the numerical simulations, we show that the solitons exists when taking into account the effect of solvent and confirms an highest propagation of localized structures in the systems. The effect of solvent forces introduces a robustness behavior to the formed patterns, reinforcing the idea that the information in the DNA model is confined and concentrated to specific regions for efficiency. We also show that the localized structures can be disappeared with the highest value of solvent factor and thereafter the information within the molecule is not perceptible or not transmitted to another sites.
Highlights
Charge transfer through biomolecular systems is one of the most promising ongoing investigations in biophysics and nanotechnology
By applying the continuum approximation, we show that the original differential-difference equation for the DNA dynamics can be reduced to a set of three coupled nonlinear equations
The linear stability has been studied under the continuum approximation and the emergence of localized structures in DNA model have been displayed
Summary
Charge transfer through biomolecular systems is one of the most promising ongoing investigations in biophysics and nanotechnology. In recent years, localized and nonlinear excitations [8,9,10,11,12,13,14,15,16], (solitons, discrete breathers, intrinsic localized modes) have been drawing increasing attention and are widely believed to be responsible for several effects in molecular chains, such as charge and thermal conductivity, energy transfer, and localization. Fialko and Laklno [20, 21]has studied the transport of charge and hole along the short DNA molecule by using the Peyrard–Bishop–Holstein (PBH) model [22, 23] These authors investigate the impact of long-range transfer of charges through the DNA molecule.
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