Nonlinear breathing modes due to a defect in a DNA chain.

Recent molecular-dynamics simulations of a DNA duplex containing the 'rogue' base difluorotoluene (F) in place of a thymine (T) base show that breathing events can occur on the nanosecond time-scale, whereas breathing events in a normal DNA duplex take place on the microsecond time-scale. The main aim of this paper is to analyse a nonlinear Klein-Gordon lattice model of the DNA duplex, including both nonlinear interactions between opposing bases and a defect in the interaction at one lattice site, each of which can cause localization of energy. Solutions for a breather mode either side of the defect are derived using multiple-scales asymptotics and are pieced together across the defect to form a solution which includes the effects of the nonlinearity and the defect. We consider defects in the inter-chain interactions and in the along-chain interactions. In most cases we find in-phase breather modes and/or out-of-phase breather modes, with one case displaying a shifted mode.