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

TL;DR

This paper models the nonlinear dynamics of protein-DNA interactions in a viscous medium, revealing how viscosity dampens soliton excitations that could facilitate DNA bubble formation during transcription.

Contribution

It introduces a perturbed nonlinear Schrödinger equation approach to describe protein-induced DNA bubble dynamics considering viscous effects, extending previous idealized models.

Findings

Viscosity dampens soliton amplitude in DNA bubble dynamics.

Soliton solutions model localized base pair opening during transcription.

Perturbed NLS equation effectively describes viscous effects on DNA dynamics.

Abstract

We study the nonlinear dynamics of a protein-DNA molecular system by treating DNA as a set of two coupled linear chains and protein in the form of a single linear chain sliding along the DNA at the physiological temperature in a viscous medium. The nonlinear dynamics of the above molecular system in general is governed by a perturbed nonlinear Schr\"{o}dinger equation. In the non-viscous limit, the equation reduces to the completely integrable nonlinear Schr\"{o}dinger (NLS) equation which admits N-soliton solutions. The soliton excitations of the DNA bases make localized base pair opening and travel along the DNA chain in the form of a bubble. This may represent the bubble generated during the transcription process when an RNA-polymerase binds to a promoter site in the DNA double helical chain. The perturbed NLS equation is solved using a perturbation theory by treating the viscous effect due to surrounding as a weak perturbation and the results show that the viscosity of the solvent in the surrounding damps out the amplitude of the soliton.