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We study the nonlinear dynamics of a protein-DNA molecular system by treatingDNA as a set of two coupled linear chains and protein in the form of a singlelinear chain sliding along the DNA at the physiological temperature in aviscous medium. The nonlinear dynamics of the above molecular system in generalis governed by a perturbed nonlinear Schr\"{o}dinger equation. In thenon-viscous limit, the equation reduces to the completely integrable nonlinearSchr\"{o}dinger (NLS) equation which admits N-soliton solutions. The solitonexcitations of the DNA bases make localized base pair opening and travel alongthe DNA chain in the form of a bubble. This may represent the bubble generatedduring the transcription process when an RNA-polymerase binds to a promotersite in the DNA double helical chain. The perturbed NLS equation is solvedusing a perturbation theory by treating the viscous effect due to surroundingas a weak perturbation and the results show that the viscosity of the solventin the surrounding damps out the amplitude of the soliton.

Base pair opening and bubble transport in a DNA double helix induced by a protein molecule in a viscous medium