Continuation of discrete breathers from infinity in a nonlinear model for DNA breathing

Abstract

We study the existence of discrete breathers (time-periodic and spatially localized oscillations) in a chain of coupled nonlinear oscillators modelling the breathing of DNA. We consider a modification of the Peyrard–Bishop model introduced by Peyrard et al. [Nonlinear analysis of the dynamics of DNA breathing, J. Biol. Phys. 35 (2009), 73–89], in which the reclosing of base pairs is hindered by an energy barrier. Using a new kind of continuation from infinity, we prove for weak couplings the existence of large amplitude and low frequency breathers oscillating around a localized equilibrium, for breather frequencies lying outside resonance zones. These results are completed by numerical continuation. For resonant frequencies (with one multiple belonging to the phonon band) we numerically obtain discrete breathers superposed on a small oscillatory tail.

Keywords:

• discrete breathers
• Peyrard–Bishop model for DNA
• continuation from infinity
• numerical continuation
• resonances with phonons
• breathers with oscillatory tails

AMS Subject Classifications::

• 37L60
• 37K60
• 92B99
• 34C25
• 34C37

Acknowledgements

C. Ferreira acknowledges support from the CAPES (Coordenação de Aperfeiçoamento de Pessoal de Nivel Superior-Brasil, www.capes.gov.br). This work was supported by the CNRS program PEPS PTI (Physique Théorique et ses Interfaces).