Impact of regulatory proteins on the nonlinear dynamics of DNA

In this paper we examine the nonlinear dynamics of a DNA chain whose exciton modes are affected by regulatory proteins that may become bound to the DNA chain by hydrogen bonds. The dynamics of the DNA chain is described by the Peyrard-Bishop model. Since this model gives rise to large-amplitude broad oscillations of base pairs, we consider the impact of attached regulatory proteins on the so-called breathers or bubbles. Assuming that an ideal gas of bubbles may exist in the DNA chain at physiological temperatures we adopt a statistical approach to calculate the average size of base-pair stretching under the prevailing conditions.