Bubble solitons in an inhomogeneous, helical DNA molecular chain with flexible strands

The influence of the DNA torque on the dynamics of transcription bubbles in plasmid PTTQ18

In this work, we study numerically the influence of the DNA torque on the movement of transcription bubbles in the potential field formed by the sequence of plasmid PTTQ18. To imitate the movement, we apply a modified sine-Gordon equation with the two additional terms that describe the effects of dissipation and the action of the DNA torsion torque, and with the coefficients that depend on the sequence of bases. We obtain the trajectories of the transcription bubbles and investigate the dependence of the trajectories on the initial bubble velocity and the DNA torsion torque. It is shown that not the initial bubble velocity but the DNA torsion torque governs the trajectories of the transcription bubbles.

Internal nonlinear dynamics of a short lattice DNA model in terms of propagating kink-antikink solitons

We study the internal nonlinear dynamics of an inhomogeneous short lattice DNA model by solving numerically the governing discrete perturbed sine-Gordon equations under the limits of a uniform and a nonuniform angular rotation of bases. The internal dynamics is expressed in terms of open-state configurations represented by kink and antikink solitons with fluctuations. The inhomogeneity in the strands and hydrogen bonds as well as nonuniformity in the rotation of bases introduce fluctuations in the profile of the solitons without affecting their robust nature and the propagation. These fluctuations spread into the tail regions of the soliton in the case of periodic inhomogeneity. However, the localized form of inhomogeneity generates amplified fluctuations in the profile of the soliton. The fluctuations are expected to enhance the denaturation process in the DNA molecule.

Long-range interactions between adjacent and distant bases in a DNA and their impact on the ribonucleic acid polymerase-DNA dynamics

When an inhomogeneous RNA-polymerase (RNAP) binds to an inhomogeneous DNA at the physiological temperature, we propose a spin-like model of DNA nonlinear dynamics with long-range interactions (LRI) between adjacent and distant base pairs to study RNAP-DNA dynamics. Using Holstein-Primakoff's representation and Glauber's coherent state representation, we show that the model equation is a completely integrable nonlinear Schrödinger equation whose dispersive coefficient depends on LRI's parameter. Inhomogeneities have introduced perturbation terms in the equation of motion of RNAP-DNA dynamics. Considering the homogeneous part of that equation, a detailed study of the solution shows that the number of base pairs which form the bubble, the height, and the width of that bubble depend on the long-range parameter. The results of the perturbation analysis show that the inhomogeneities due to the DNA and RNAP structures do not alter the velocity and amplitude of the soliton, but introduce some fluctuations in the localized region of the soliton. The events that happen in the present study may represent binding of an RNAP to a promoter site in the DNA during the transcription process.