Solitonlike base pair opening in a helicoidal DNA: an analogy with a helimagnet and a cholesteric liquid crystal

Base pair opening in a damped helicoidal Joyeux-Buyukdagli model of DNA in an external force field

Upon the Joyeux-Buyukdagli model of DNA, the helicoidal interactions are introduced, and their effects on the dynamical behaviors of the molecule investigated. A theoretical framework for the analysis is presented in an external force field, taking into account Stokes and hydrodynamics viscous forces. In the semi-discrete approximation, the dynamics of the molecule is found governed by the cubic complex Ginzburg-Landau (CGL) equation. By choosing an appropriate decoupling ansatz, the cubic CGL equation is transformed into a nonlinear differential equation whose analytical solitary wave-like solutions can be explored by means of the direct method, which is more tractable in case where the form of soliton solutions is known. Based on this, a dissipative bright-like soliton solution is obtained. Numerical experiments have been done, and relevant results were brought out, such as the quantitative and qualitative influences of the helical interactions on the parameters of the traveling bubble. The important role-played by these interactions in the DNA biological processes is brought out, showing that depending on the wave number, their effects can increase, decrease, or keep constant the bubble angular frequency, velocity, amplitude, and width, as well as the energy involved by enzymes in the initiation of DNA biological processes. This can prevent some coding or reading errors and resulting genetic damages. Analytical predictions and numerical experiments were in good agreement.

A review on nonlinear DNA physics

The study and the investigation of structural and dynamical properties of complex systems have attracted considerable interest among scientists in general and physicists and biologists in particular. The present review paper represents a broad overview of the research performed over the nonlinear dynamics of DNA, devoted to some different aspects of DNA physics and including analytical, quantum and computational tools to understand nonlinear DNA physics. We review in detail the semi-discrete approximation within helicoidal Peyrard-Bishop model and show that localized modulated solitary waves, usually called breathers, can emerge and move along the DNA. Since living processes occur at submolecular level, we then discuss a quantum treatment to address the problem of how charge and energy are transported on DNA and how they may play an important role for the functioning of living cells. While this problem has attracted the attention of researchers for a long time, it is still poorly understood how charge and energy transport can occur at distances comparable to the size of macromolecules. Here, we review a theory based on the mechanism of 'self-trapping' of electrons due to their interaction with mechanical (thermal) oscillation of the DNA structure. We also describe recent computational models that have been developed to capture nonlinear mechanics of DNA in vitro and in vivo, possibly under topological constraints. Finally, we provide some conjectures on potential future directions for this field.

Stationary solitary and kink solutions in the helicoidal Peyrard-Bishop model of DNA molecule

We study nonlinear dynamics of the DNA molecule relying on a helicoidal Peyrard-Bishop model. We look for traveling wave solutions and show that a continuum approximation brings about kink solitons moving along the chain. This statement is supported by the numerical solution of a relevant dynamical equation of motion. Finally, we argue that an existence of both kinks and localized modulated solitons (breathers) could be a useful tool to describe DNA-RNA transcription.

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.

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

Base pair opening in an inhomogeneous, DNA double helical molecular chain with flexible strands is investigated by studying its internal dynamics. For the study, a generalized model which takes into account the energies involved in stacking and hydrogen bonds along with inhomogeneity, helicity, and phonons coupled to the stacking and hydrogen bonds is proposed. The internal dynamics of the proposed DNA model is governed by a perturbed nonlinear Schrödinger equation. The unperturbed, completely integrable nonlinear Schrödinger equation which admits soliton solutions and forming a bubble corresponds to DNA dynamics with homogeneous and rigid strands. The results of the soliton perturbation analysis show that the inhomogeneity in stacking and hydrogen bonds in localized and periodic forms and the helicity do not alter the amplitude under perturbation. However, the flexibility of the strands diminishes the perturbed amplitude. On the other hand, the velocity of the soliton and bubble are unaltered due to all the above effects. However, the position and phase of the soliton and the bubble vary linearly in time. While the position of the soliton depends on the initial velocity, the phase depends on both the initial velocity and the initial amplitude of the soliton. The above effects introduce small fluctuation in the tail of the soliton, without affecting the robust nature of the soliton and the bubble during propagation. The soliton and the bubble obtained as solutions of the internal dynamics of the DNA molecule represent an opening of the base pairs which is essential for the transcription process.

DNA-RNA transcription as an impact of viscosity

The impact of viscosity on DNA dynamics is studied both analytically and numerically. It is assumed that the viscosity exists at the segments where DNA molecule is surrounded by RNA polymerase. We demonstrate that the frictional forces destroy the modulation of the incoming solitonic wave. We show that viscosity, crucial for demodulation, is essential for DNA-RNA transcription.

Long-range interactions and wave patterns in a DNA model

We propose a spin-like model of DNA nonlinear dynamics with long-range interactions between adjacent base pairs. We show that the model equation is a modified sine-Gordon equation. We perform the linear stability analysis of a plane wave, which predicts high-amplitude and extended oscillating waves for high values of the long-range parameter. This is confirmed numerically and biological implications of the obtained patterns are suggested.

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

The protein-DNA interaction dynamics is studied by modeling the DNA bases as classical spins in a coupled spin system, which are bosonized and coupled to thermal phonons and longitudinal motion of the protein molecule in the nonviscous limit. The nonlinear dynamics of this protein-DNA complex molecular system is governed by the completely integrable nonlinear Schrödinger (NLS) equation which admits N -soliton solutions. The soliton excitations of the DNA bases in the two strands make localized base-pair opening and travel along the DNA chain in the form of a bubble. This may characterize the bubble generated during the transcription process, when an RNA polymerase binds to a promoter site in the DNA double helical chain. When the protein-DNA molecular system interacts with the surrounding viscous solvating water medium, the dynamics is governed by a perturbed NLS equation. This equation is solved using a multiple scale perturbation analysis, by treating the viscous effect as a weak perturbation, and the results show that the viscosity of the solvent medium damps out the soliton as time progresses.