Localized breather-like solution in a discrete Klein-Gordon model and application to DNA

Dauxois, Thierry; Peyrard, Michel; Willis, C. R.

doi:10.1016/0167-2789(92)90003-6

Cited by 104 publications

(69 citation statements)

References 27 publications

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“…This was done as nonlinear excitations are known to be generated from randomness [10,[36][37][38][39]. As the outcome of collisions between nonlinear excitations depends strongly on their relative phases, we made 500 different random initial conditions to be able to find effects independent of the random phases.…”

Section: ͑7͒mentioning

confidence: 99%

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Bubble generation in a twisted and bent DNA-like model

et al. 2004

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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.

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Section: ͑7͒mentioning

confidence: 99%

“…[10,12,[35][36][37][38][39], for example. In these references it was shown that solitons or discrete breathers can be generated from or exist among random thermal fluctuations.…”

Section: Introductionmentioning

confidence: 99%

Bubble generation in a twisted and bent DNA-like model

et al. 2004

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“…In the Peyrard-Bishop model, the existence of DBs has been demonstrated [7,8], and DBs are thought to be the precursors of the bubbles that appear prior to the transcription processes in which large fluctuations of energy have been experimentally observed. Some studies about the existence and properties of MBs in the Peyrard-Bishop model including dipole-dipole dispersive interaction are carried out in [9,10].…”

Section: Introduction and Model Set-upmentioning

confidence: 99%

Moving Breather Collisions in the Peyrard-Bishop DNA Model

Álvarez

Romero

Cuevas

et al. 2009

Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering

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Abstract. We consider collisions of moving breathers (MBs) in the Peyrard-Bishop DNA model. Two identical stationary breathers, separated 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 collisions 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 processes.

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“…In the Peyrard-Bishop model, the existence of DBs has been demonstrated [16], and DBs are thought to be the precursors of the bubbles that appear prior to the transcription processes in which large fluctuations of energy have been experimentally observed. Some studies about the existence and properties of MBs in the Peyrard-Bishop model including dipole-dipole dispersive interaction are carried out in [11] [4].…”

mentioning

confidence: 99%

“…Among them, it is worth remarking the Peyrard-Bishop model [27,16] introduced for the study of DNA thermal denaturation. In this model the DNA molecule is considered as a Klein-Gordon chain of oscillators, and have been used extensively for the study of the dynamical properties.…”

mentioning

confidence: 99%

Nonsymmetric moving breather collisions in the Peyrard-Bishop DNA model

Álvarez¹,

Romero²,

Romero³

et al. 2011

Discrete &Amp; Continuous Dynamical Systems - S

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Abstract. 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.

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Localized breather-like solution in a discrete Klein-Gordon model and application to DNA

Cited by 104 publications

References 27 publications

Bubble generation in a twisted and bent DNA-like model

Bubble generation in a twisted and bent DNA-like model

Moving Breather Collisions in the Peyrard-Bishop DNA Model

Nonsymmetric moving breather collisions in the Peyrard-Bishop DNA model

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