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

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.

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

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

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

Nonlinearity-induced conformational instability and dynamics of biopolymers

We propose a simple phenomenological model for describing the conformational dynamics of biopolymers via the nonlinearity-induced buckling and collapse (i.e. coiling up) instabilities. Taking into account the coupling between the internal and mechanical degrees of freedom of a semiflexible biopolymer chain, we show that self-trapped internal excitations (such as amide-I vibrations in proteins, base-pair vibrations in DNA, or polarons in proteins) may produce the buckling and collapse instabilities of an initially straight chain. These instabilities remain latent in a straight infinitely long chain, because the bending of such a chain would require an infinite energy. However, they manifest themselves as soon as we consider more realistic cases and take into account a finite length of the chain. In this case the nonlinear localized modes may act as drivers giving impetus to the conformational dynamics of biopolymers. The buckling instability is responsible, in particular, for the large-amplitude localized bending waves which accompany the nonlinear modes propagating along the chain. In the case of the collapse instability, the chain folds into a compact three-dimensional coil. The viscous damping of the aqueous environment only slows down the folding of the chain, but does not stop it even for a large damping. We find that these effects are only weakly affected by the peculiarities of the interaction potentials, and thus they should be generic for different models of semiflexible chains carrying nonlinear localized excitations.Comment: 4 pages (RevTeX) with 5 figures (EPS

Propagation of twist solitons in real DNA chains

We report on numerical investigations concerning the propagation of solitons in a real DNA chain (the Human Adenovirus 2) using a realistic model of DNA torsional dynamics; this takes fully into account the inhomogeneities in the real chain. We find that twist solitons propagate for considerable distances (2-10 times their diameters) before stopping due to phonon emission. Our results show that twist solitons may exist in real DNA chains; and on a more general level that solitonic propagation can take place in highly inhomogeneous media.Comment: 6 pages, 3 figure

Bubble propagation in a helicoidal molecular chain

We study the propagation of very large amplitude localized excitations in a model of DNA that takes explicitly into account the helicoidal structure. These excitations represent the ``transcription bubble'', where the hydrogen bonds between complementary bases are disrupted, allowing access to the genetic code. We propose these kind of excitations in alternative to kinks and breathers. The model has been introduced by Barbi et al. [Phys. Lett. A 253, 358 (1999)], and up to now it has been used to study on the one hand low amplitude breather solutions, and on the other hand the DNA melting transition. We extend the model to include the case of heterogeneous chains, in order to get closer to a description of real DNA; in fact, the Morse potential representing the interaction between complementary bases has two possible depths, one for A-T and one for G-C base pairs. We first compute the equilibrium configurations of a chain with a degree of uncoiling, and we find that a static bubble is among them; then we show, by molecular dynamics simulations, that these bubbles, once generated, can move along the chain. We find that also in the most unfavourable case, that of a heterogeneous DNA in the presence of thermal noise, the excitation can travel for well more 1000 base pairs.Comment: 25 pages, 7 figures. Submitted to Phys. Rev.

Shape changing and accelerating solitons in integrable variable mass sine-Gordon model

Sine-Gordon model with variable mass (VMSG) appears in many physical systems, ranging from the current through nonuniform Josephson junction to DNA-promoter dynamics. Such models are usually nonintegrable with solutions found numerically or peturbatively. We construct a class of VMSG models, integrable both at classical and quantum level with exact soliton solutions, which can accelerate, change their shape, width and amplitude simulating realistic inhomogeneous systems at certain limits.Comment: 6 pages, 4 figures, revised with more physical input, to be published in Phys. Rev. Let