Breather solutions of a nonlinear DNA model including a longitudinal degree of freedom

We present a model of the DNA double helix assigning three degrees of freedom to each pair of nucleotides. The model is an extension of the Barbi–Cocco–Peyrard (BCP) model in the sense that the current model allows for longitudinal motions of the nucleotides parallel to the helix axis. The molecular structure of the double helix is modelled by a system of coupled oscillators. The nucleotides are represented by point masses and coupled via point–point interaction potentials. The latter describe the covalent and hydrogen bonds responsible for the secondary structure of DNA. We obtain breather solutions using an established method for the construction of breathers on nonlinear lattices starting from the anti-coupling limit. In order to apply this method we analyse the phonon spectrum of the linearised system corresponding to our model. The obtained breathing motion consists of a local opening and re-closing of base pairs combined with a local untwist of the helix. The motions in longitudinal direction are of much lower amplitudes than the radial and angular elongations.