Abstract
We have introduced helicity in the revised Hamiltonian in which the dipole-dipole interaction and dipoleinduced- dipole interaction have taken into account. The system has been shown to be govern by a set of coupled discrete sine- Gordon equations, which describe the bending and oscillations of the hydrogen bonds. The multiple scale expansion has been used and the stability of planar waves, solutions of the system, has been investigated. We have brought out the effect of discreteness and have shown that helicity brings about wave switching in the two-component DNA model under study. PACS number(s): 87.14.gk, 05.45.Yv, 87.15.H.
Highlights
The complexity and role of DNA make it the most important molecule in nature
One sees that the model does not take helicity into account. It is the main purpose of the present work to modify the above-presented model and show, through the stability analysis of a plane wave, that helicity can bring about interesting features in the dynamics of DNA molecules
The main purpose of the present paper was to introduce the helicoidal coupling in a two-component helicoidal model of DNA, and to bring out the effectiveness of wave switching between the bending of the molecule and the opening of the base pairs
Summary
The complexity and role of DNA make it the most important molecule in nature. Describing its dynamics remains a fascinated task for modern physicists and biophysicists alike, because it is nowadays accepted that DNA undergoes dynamical features that are not yet fully unmasked. One sees that the model does not take helicity into account It is the main purpose of the present work to modify the above-presented model and show, through the stability analysis of a plane wave, that helicity can bring about interesting features in the dynamics of DNA molecules. These figures have been plotted for Sh < (β + D)/4 [panel (b)], Sh = (β + D)/4 [panel (c)] and Sh > (β + D)/4 [panel (d)], respectively. The following behaviors have been observed: 0.025
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