Chemically driven traveling waves in DNA

The nonlinear mechanical model constructed in a previous paper [Nuovo Cimento D 20, 833 (1998)] is developed in order to study the dynamics of the DNA double helix. It is assumed that the hydrophobic interaction between subsequent base pairs may be influenced by a RNA polymerase. The Lagrangian, constructed on the basis of "geometrical" properties of the DNA molecule, depends on time and contains first and second derivatives of the twist angle. The energy dissipation term is added to the dynamical equations resulting from the Lagrange formalism. It is proved that the system has pulse-like solitary wave solutions for which the dissipated energy is balanced by the energy pumped by the advancing RNA polymerase. The physical interpretation of our solution is the local untwisting of the DNA molecule during transcription of messenger RNA.