Moving breather collisions in the Peyrard-Bishop DNA model

We consider collisions of moving breathers (MBs) in the Peyrard-Bishop DNA model. Two identical stationary breathers, sep- arated by a fixed number of pair-bases, are perturbed and begin to move approaching to each other with the same module of velocity. The outcome is strongly dependent of both the velocity of the MBs and the number of pair-bases that initially separates the stationary breathers. Some col- lisions result in the generation of a new stationary trapped breather of larger energy. Other collisions result in the generation of two new MBs. In the DNA molecule, the trapping phenomenon could be part of the complex mechanisms involved in the initiation of the transcription pro- cesses

Nonsymmetric moving breather collisions in the Peyrard-Bishop DNA model

We study nonsymmetric collisions of moving breathers (MBs) in the Peyrard-Bishop DNA model. In this paper we have considered the following types of nonsymmetric collisions: head-on collisions of two breathers traveling with different velocities; collisions of moving breathers with a stationary trapped breather; and collisions of moving breathers traveling with the same direction. The various main observed phenomena are: one moving breather gets trapped at the collision region, and the other one is reflected; breather fusion without trapping, with the appearance of a new moving breather; and breather generation without trapping, with the appearance of new moving breathers traveling either with the same or different directions. For comparison we have included some results of a previous paper concerning to symmetric collisions, where two identical moving breathers traveling with opposite velocities collide. For symmetric collisions, the main observed phenomena are: breather generation with trapping, with the appearance of two new moving breathers with opposite velocities and a stationary breather trapped at the collision region; and breather generation without trapping, with the appearance of new moving breathers with opposite velocities. A common feature for all types of collisions is that the collision outcome depends on the internal structure of the moving breathers and the exact number of pair-bases that initially separates the stationary breathers when they are perturbed. As some nonsymmetric collisions result in the generation of a new stationary trapped breather of larger energy, the trapping phenomenon could play an important part of the complex mechanisms involved in the initiation of the DNA transcription processes.MICIN

Breather trapping and breather transmission in a DNA model with an interface

We study the dynamics of moving discrete breathers in an interfaced piecewise DNA molecule. This is a DNA chain in which all the base pairs are identical and there exists an interface such that the base pairs dipole moments at each side are oriented in opposite directions. The Hamiltonian of the Peyrard--Bishop model is augmented with a term that includes the dipole--dipole coupling between base pairs. Numerical simulations show the existence of two dynamical regimes. If the translational kinetic energy of a moving breather launched towards the interface is below a critical value, it is trapped in a region around the interface collecting vibrational energy. For an energy larger than the critical value, the breather is transmitted and continues travelling along the double strand with lower velocity. Reflection phenomena never occur. The same study has been carried out when a single dipole is oriented in opposite direction to the other ones. When moving breathers collide with the single inverted dipole, the same effects appear. These results emphasize the importance of this simple type of local inhomogeneity as it creates a mechanism for the trapping of energy. Finally, the simulations show that, under favorable conditions, several launched moving breathers can be trapped successively at the interface region producing an accumulation of vibrational energy. Moreover, an additional colliding moving breather can produce a saturation of energy and a moving breather with all the accumulated energy is transmitted to the chain.Comment: 15 pages, 11 figure

Discrete moving breather collisions in a Klein-Gordon chain of oscillators

We study collision processes of moving breathers with the same frequency, traveling with opposite directions within a Klein-Gordon chain of oscillators. Two types of collisions have been analyzed: symmetric and non-symmetric, head-on collisions. For low enough frequency the outcome is strongly dependent of the dynamical states of the two colliding breathers just before the collision. For symmetric collisions, several results can be observed: breather generation, with the formation of a trapped breather and two new moving breathers; breather reflection; generation of two new moving breathers; and breather fusion bringing about a trapped breather. For non-symmetric collisions the possible results are: breather generation, with the formation of three new moving breathers; breather fusion, originating a new moving breather; breather trapping with also breather reflection; generation of two new moving breathers; and two new moving breathers traveling as a ligand state. Breather annihilation has never been observed.Comment: 19 pages, 12 figure

Energy funneling in a bent chain of Morse oscillators with long-range coupling

A bent chain of coupled Morse oscillators with long-range dispersive interaction is considered. Moving localized excitations may be trapped in the bending region. Thus chain geometry acts like an impurity. An energy funneling effect is observed in the case of random initial conditions.Comment: 6 pages, 12 figures. Submitted to Physical Review E, Oct. 13, 200

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.

Discrete Breathers

Nonlinear classical Hamiltonian lattices exhibit generic solutions in the form of discrete breathers. These solutions are time-periodic and (typically exponentially) localized in space. The lattices exhibit discrete translational symmetry. Discrete breathers are not confined to certain lattice dimensions. Necessary ingredients for their occurence are the existence of upper bounds on the phonon spectrum (of small fluctuations around the groundstate) of the system as well as the nonlinearity in the differential equations. We will present existence proofs, formulate necessary existence conditions, and discuss structural stability of discrete breathers. The following results will be also discussed: the creation of breathers through tangent bifurcation of band edge plane waves; dynamical stability; details of the spatial decay; numerical methods of obtaining breathers; interaction of breathers with phonons and electrons; movability; influence of the lattice dimension on discrete breather properties; quantum lattices - quantum breathers. Finally we will formulate a new conceptual aproach capable of predicting whether discrete breather exist for a given system or not, without actually solving for the breather. We discuss potential applications in lattice dynamics of solids (especially molecular crystals), selective bond excitations in large molecules, dynamical properties of coupled arrays of Josephson junctions, and localization of electromagnetic waves in photonic crystals with nonlinear response.Comment: 62 pages, LaTeX, 14 ps figures. Physics Reports, to be published; see also at http://www.mpipks-dresden.mpg.de/~flach/html/preprints.htm

A discrete nonlinear model with substrate feedback

We consider a prototypical model in which a nonlinear field (continuum or discrete) evolves on a flexible substrate which feeds back to the evolution of the main field. We identify the underlying physics and potential applications of such a model and examine its simplest one-dimensional Hamiltonian form, which turns out to be a modified Frenkel-Kontorova model coupled to an extra linear equation. We find static kink solutions and study their stability, and then examine moving kinks (the continuum limit of the model is studied too). We observe how the substrate effectively renormalizes properties of the kinks. In particular, a nontrivial finding is that branches of stable and unstable kink solutions may be extended beyond a critical point at which an effective intersite coupling vanishes; passing this critical point does not destabilize the kink. Kink-antikink collisions are also studied, demonstrating alternation between merger and transmission cases.Comment: a revtex text file and 6 ps files with figures. Physical Review E, in pres