Solitons in Yakushevich-like models of DNA dynamics with improved intrapair potential

The Yakushevich (Y) model provides a very simple pictures of DNA torsion dynamics, yet yields remarkably correct predictions on certain physical characteristics of the dynamics. In the standard Y model, the interaction between bases of a pair is modelled by a harmonic potential, which becomes anharmonic when described in terms of the rotation angles; here we substitute to this different types of improved potentials, providing a more physical description of the H-bond mediated interactions between the bases. We focus in particular on soliton solutions; the Y model predicts the correct size of the nonlinear excitations supposed to model the ``transcription bubbles'', and this is essentially unchanged with the improved potential. Other features of soliton dynamics, in particular curvature of soliton field configurations and the Peierls-Nabarro barrier, are instead significantly changed

DNA Torsional Solitons in Presence of localized Inhomogeneities

In the present paper we investigate the influence of inhomogeneities in the dynamics and stability of DNA open states, modeled as propagating solitons in the spirit of a Generalized Yakushevish Model. It is a direct consecuence of our model that there exists a critical distance between the soliton's center of mass and the inhomogeneity at which the interaction between them can change the stability of the open state.Furtherly from this results was derived a renormalized potential funtion.Comment: RevTex, 13 pages, 3 figures, final versio

Multi-site H-bridge breathers in a DNA--shaped double strand

We investigate the formation process of nonlinear vibrational modes representing broad H-bridge multi--site breathers in a DNA--shaped double strand. Within a network model of the double helix we take individual motions of the bases within the base pair plane into account. The resulting H-bridge deformations may be asymmetric with respect to the helix axis. Furthermore the covalent bonds may be deformed distinctly in the two backbone strands. Unlike other authors that add different extra terms we limit the interaction to the hydrogen bonds within each base pair and the covalent bonds along each strand. In this way we intend to make apparent the effect of the characteristic helicoidal structure of DNA. We study the energy exchange processes related with the relaxation dynamics from a non-equilibrium conformation. It is demonstrated that the twist-opening relaxation dynamics of a radially distorted double helix attains an equilibrium regime characterized by a multi-site H-bridge breather.Comment: 27 pages and 10 figure

Solitons in the Yakushevich model of DNA beyond the contact approximation

The Yakushevich model of DNA torsion dynamics supports soliton solutions, which are supposed to be of special interest for DNA transcription. In the discussion of the model, one usually adopts the approximation $\ell_0 \to 0$, where $\ell_0$ is a parameter related to the equilibrium distance between bases in a Watson-Crick pair. Here we analyze the Yakushevich model without $\ell_0 \to 0$. The model still supports soliton solutions indexed by two winding numbers $(n,m)$; we discuss in detail the fundamental solitons, corresponding to winding numbers (1,0) and (0,1) respectively

On the nonlinear dynamics of topological solitons in DNA

Dynamics of topological solitons describing open states in the DNA double helix are studied in the frameworks of the model which takes into account asymmetry of the helix. It is shown that three types of topological solitons can occur in the DNA double chain. Interaction between the solitons, their interactions with the chain inhomogeneities and stability of the solitons with respect to thermal oscillations are investigated.Comment: 16 pages, 16 figure

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

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.Comment: 4. Submitted to Phys. Rev.

A symmetry breaking mechanism for selecting the speed of relativistic solitons

We propose a mechanism for fixing the velocity of relativistic soliton based on the breaking of the Lorentz symmetry of the sine-Gordon (SG) model. The proposal is first elaborated for a molecular chain model, as the simple pendulum limit of a double pendulums chain. It is then generalized to a full class of two-dimensional field theories of the sine-Gordon type. From a phenomenological point of view, the mechanism allows one to select the speed of a SG soliton just by tuning elastic couplings constants and kinematical parameters. From a fundamental, field-theoretical point of view we show that the characterizing features of relativistic SG solitons (existence of conserved topological charges and stability) may be still preserved even if the Lorentz symmetry is broken and a soliton of a given speed is selected.Comment: 23 pages, no figure

Sine-Gordon solitons, auxiliary fields, and singular limit of a double pendulums chain

We consider the continuum version of an elastic chain supporting topological and non-topological degrees of freedom; this generalizes a model for the dynamics of DNA recently proposed and investigated by ourselves. In a certain limit, the non-topological degrees of freedom are frozen, and the model reduces to the sine-Gordon equations and thus supports well-known topological soliton solutions. We consider a (singular) perturbative expansion around this limit and study in particular how the non-topological field assume the role of an auxiliary field. This provides a more general framework for the slaving of this degree of freedom on the topological one, already observed elsewhere in the context of the mentioned DNA model; in this framework one expects such phenomenon to arise in a quite large class of field-theoretical models.Comment: 18 pages, 2 figure

Tautomeric mutation: A quantum spin modelling

A quantum spin model representing tautomeric mutation is proposed for any DNA molecule. Based on this model, the quantum mechanical calculations for mutational rate and complementarity restoring repair rate in the replication processes are carried out. A possible application to a real biological system is discussed.Comment: 7 pages (no figures

Bubble generation in a twisted and bent DNA-like model

The DNA molecule is modeled by a parabola embedded chain with long-range interactions between twisted base pair dipoles. A mechanism for bubble generation is presented and investigated in two different configurations. Using random normally distributed initial conditions to simulate thermal fluctuations, a relationship between bubble generation, twist and curvature is established. An analytical approach supports the numerical results.Comment: 7 pages, 8 figures. Accepted for Phys. Rev. E (in press