Soliton excitation in the DNA double helix

Abstract

We study the nonlinear dynamics of the DNA double-helical chain using the Peyrard-Bishop-Dauxois (PBD) model. By using the Fourier series approach, we have found that the DNA dynamics in this case is governed by the modified discrete nonlinear Schrödinger (MDNLS) equation. Through the Jacobian elliptic function method, we investigate a set of exact solutions of this model. These solutions include the Jacobian periodic solution as well as bubble solitons. The stability of these solutions is also studied.

High-order nonlinear excitations in the Joyeux-Buyukdagli model of DNA

“…The PBD model was also confirmed to be consistent with the formation of temporary sequencedependent openings observed by S1 nuclease cleavage experiments and with a multistep melting envisaged by experiments in heterogeneous DNA [23]. Some works have shown that the PBD model supports nonlinear local excitations [11,12,[24][25][26]. A few years ago, Joyeux and Buyukdagli [27] proposed a new dynamical model (JB model) for DNA, which is closer to the statistical ones than the PBD model.…”

“…DNA plays a vital role in all living organisms since it is the key molecule responsible for duplication, storage, and realization of genetic information [11]. DNA is basically a complex structure containing two strands of linear polymers of residues (nucleotides), where each strand is made up of sugars, purine [adenine (A) and guanine (G)] and pyrimidine [cytosine (C) and thymine (T)] bases, and phosphates [12].…”

Stability Analysis of the Jacobian Elliptic Solutions for the Twisted Peyrard-Bishop-Dauxois Model with Solvent Interaction

“…Evidently, the base-pairs can only de-naturate when the double helix is largely uncoiled and therefore we use a small angle [32,33]. One also consider the anharmonic Hamiltonian [34,35], where the same torsion angle dependence is introduced as in Equation 3 for the stacking interaction, (…”

Formation and Interaction of Bright Solitons with Shape Changing in a DNA Model

“…Among them, we have the tanh-function method [41], the elliptic function approach [42], and the Hirota'sbilinearization method [29][30][31][32], to name just few. Here, the Hirota'sbilinearization method is used to investigate exact solitons solution of the PB model.…”