Anharmonic longitudinal motion of bases and dynamics of nonlinear excitation in DNA

The dynamics of the transcription bubble in DNA is studied by using a nonlinear model in which torsional and longitudinal conformations of the biomolecule are coupled. In the absence of forcing and dissipation the torsional dynamics is described by a perturbed kink of the Sine-Gordon DNA model, while the longitudinal conformational energy propagate as phonons. It was found that for random initial conditions of the longitudinal conformational field the presence of the kink promotes the creation of phonons propagating along the chain axis. Moreover, the presence of forcing, describing the active role of RNA polymerase, determines in agreement to the experimental data a modulation of the velocity of the transcription bubble. Lastly, it was shown that the presence of dissipation impacts the dynamic of the phonon by reducing the amplitude of the corresponding conformational field. On the contrary, dissipation and forcing modulate the velocity of the transcription bubble alone.