We study the propagation of localized excitations in a DNA molecule which takes into account helicity and solvent interaction. The small amplitude dynamics of the model is described by envelope solutions made of breathers. Our solutions drastically depends on the twist angle and solvent interaction. It is found that increasing the twist angle decreases the width of the pulse which can be used for the transportation of energy. Increase the solvent interaction term, increases the width of the pulses while the number of waves train decreases with time. The stability of the solutions has been checked through numerical simulations.
We analyze the possibility of coherent modes for DNA dynamics in a general model recently proposed by Joyeux and Florescu [J. Phys.: Condens. Matter 21, 034101 (2009)]. We show that the value they used for their results are not suitable to describe wave propagation in DNA. We therefore investigate parameter values in order to obtain coherent solitary waves with characteristics that are know experimentally.
We investigate the generation of soliton-like pulses along a DNA chain which takes into account both torsional and solvent interaction effects. Interactions between neighboring base pairs are described by a twist angle. Twisting is essential in the model to capture the importance of nonlinear effects for the thermodynamical properties. The nonlinear dynamics of the DNA is then modeled in the Hamiltonian approach by the generalized Dauxois–Peyrard–Bishop model (combination of several models). We introduce the generalized discrete nonlinear Schrödinger equation describing the dynamics of modulated wave through the twisted DNA with solvent interaction. The modulational instability is studied and we present an analytical expression for the MI gain to show the effects of twist angle on MI gain spectra as well as on stability diagram. With the increase of the twist angle the MI gain decreases then increases. Some interesting MI phenomena appear with an additional new MI region as the twist angle increases. The instability and stability diagrams are also affected. Numerical simulations are carried out to show the validity of the analytical approach. The result is that the initial wave breaks into a train of ultrashort pulses with repetition rates, which are trapped in some sites. The impact of the twist angle is investigated and we obtain that the twist angle affects the dynamics of stable patterns generated through the molecule. Thereafter, we study energy localization in the framework of twisted DNA with solvent interaction. While the twist angle leads to a stronger localization of energy, the solvent interaction delocalizes energy along the molecule.
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