Bubble solitons in an inhomogeneous, helical DNA molecular chain with flexible strands

Abstract

Base pair opening in an inhomogeneous, DNA double helical molecular chain with flexible strands is investigated by studying its internal dynamics. For the study, a generalized model which takes into account the energies involved in stacking and hydrogen bonds along with inhomogeneity, helicity, and phonons coupled to the stacking and hydrogen bonds is proposed. The internal dynamics of the proposed DNA model is governed by a perturbed nonlinear Schrödinger equation. The unperturbed, completely integrable nonlinear Schrödinger equation which admits soliton solutions and forming a bubble corresponds to DNA dynamics with homogeneous and rigid strands. The results of the soliton perturbation analysis show that the inhomogeneity in stacking and hydrogen bonds in localized and periodic forms and the helicity do not alter the amplitude under perturbation. However, the flexibility of the strands diminishes the perturbed amplitude. On the other hand, the velocity of the soliton and bubble are unaltered due to all the above effects. However, the position and phase of the soliton and the bubble vary linearly in time. While the position of the soliton depends on the initial velocity, the phase depends on both the initial velocity and the initial amplitude of the soliton. The above effects introduce small fluctuation in the tail of the soliton, without affecting the robust nature of the soliton and the bubble during propagation. The soliton and the bubble obtained as solutions of the internal dynamics of the DNA molecule represent an opening of the base pairs which is essential for the transcription process.