Nonlinear dynamics of damped DNA systems with long-range interactions

Okaly, Joseph Brizar; Mvogo, Alain; Woulaché, Rosalie Laure; Kofané, Timoléon Crépin

doi:10.1016/j.cnsns.2017.06.017

Cited by 31 publications

(6 citation statements)

References 38 publications

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“…The number of DNA damages in a single human cell exceeds 10, 000 every day [39], and must be counteracted by special DNA repair processes. Long-range interactions (LRI) are ubiquitous in DNA molecule, they play a crucial role in the stabilization of the molecule [25]. Hence, it is important to understand the interplay between inhomogeneity and LRI [40].…”

Section: Discussionmentioning

confidence: 99%

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Nonlinear dynamics of DNA systems with inhomogeneity effects

Okaly

Mvogo

Woulaché

et al. 2018

Chinese Journal of Physics

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We investigate the nonlinear dynamics of the Peyrard-Bishop DNA model taking into account site dependent inhomogeneities. By means of the multiple-scale expansion in the semi-discrete approximation, the dynamics is governed by the perturbed nonlinear Schrödinger equation. We carry out a multiple-scale soliton perturbation analysis to find the effects of the variety of nonlinear inhomogeneities on the breatherlike soliton solution. During the crossing of the inhomogeneities, the coherent structure of the soliton is found stable. The global shape of the inhomogeneous molecule is merged with the shape of the homogeneous molecule. However, the velocity, the wavenumber and the angular frequency undergo a time-dependent correction that is proportional to initial width of the soliton and depends on the nature of the inhomogeneities.

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Section: Discussionmentioning

confidence: 99%

“…The values of parameters used to describe the motions of the two strands are those from the dynamical and denaturation properties of DNA. They are [25,26]: m = 300 amu, K = 0.06 eV/ Å2 , D = 0.03 eV and a = 4.5 Å−1 . Our system of units (amu, Å, eV) defines a time unit (t.u.)…”

Section: Model Hamiltonian Of Dna Dynamics and Equations Of Motionmentioning

confidence: 99%

Nonlinear dynamics of DNA systems with inhomogeneity effects

Okaly

Mvogo

Woulaché

et al. 2018

Chinese Journal of Physics

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“…where γ S and γ H are the Stokes and hydrodynamic damping constants, respectively [41,42]. According to Raman spectroscopy measurements, the viscous effects can be confidently neglected in the study of H-bond related stretching oscillations, since the very small amplitude of the motion within the hydrogen bond well (0.12 − 0.2 Å) should not induce significant rearrangements of surrounding water molecules responsible for viscosity [21].…”

Section: Environmental Effects In the Dna Dynamicsmentioning

confidence: 99%

Synchronized Oscillations in Double-Helix B-DNA Molecules with Mirror-Symmetric Codons

Maciá

2021

Symmetry

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A fully analytical treatment of the base-pair and codon dynamics in double-stranded DNA molecules is introduced, by means of a realistic treatment that considers different mass values for G, A, T, and C nucleotides and takes into account the intrinsic three-dimensional, helicoidal geometry of DNA in terms of a Hamitonian in cylindrical coordinates. Within the framework of the Peyrard–Dauxois–Bishop model, we consider the coupling between stretching and stacking radial oscillations as well as the twisting motion of each base pair around the helix axis. By comparing the linearized dynamical equations for the angular and radial variables corresponding to the bp local scale with those of the longer triplet codon scale, we report an underlying hierarchical symmetry. The existence of synchronized collective oscillations of the base-pairs and their related codon triplet units are disclosed from the study of their coupled dynamical equations. The possible biological role of these correlated, long-range oscillation effects in double standed DNA molecules containing mirror-symmetric codons of the form XXX, XX’X, X’XX’, YXY, and XYX is discussed in terms of the dynamical equations solutions and their related dispersion relations.

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“…Introducing additional degrees of freedom into nonlinear chains helps capture some of the new physical effects [39,40].…”

Section: Introductionmentioning

confidence: 99%

Rotobreathers in a chain of coupled elastic rotators

Savin,

Sunagatova,

Dmitriev

2021

Preprint

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Rotobreathers in the chain of coupled linearly elastic rotators are analyzed. Each rotator is a particle connected by a massless elastic rod with a frictionless pivot; it has two degrees of freedom, length and angle of rotation. The rods of the rotators and the elastic bonds between the nearest rotators are linearly elastic, and the nonlinearity of the system is of a purely geometric nature. It is shown that long-lived rotobreathers can exist if the stiffness of the rods is high enough to create a relatively wide gap in the phonon spectrum of the chain. The frequency of angular rotation of the rotobreather cannot be above the optical band of the phonon spectrum and is in the spectrum gap. Generally speaking, the rotation of the rotobreather is accompanied by radial oscillations, however, one can choose such initial conditions so that the radial oscillations are minimal. Some parameters of rotobreathers with minimal radial vibrations are presented on the basis of numerical simulations. The results obtained qualitatively describe the behavior of physical systems with coupled rotators.

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Nonlinear dynamics of damped DNA systems with long-range interactions

Cited by 31 publications

References 38 publications

Nonlinear dynamics of DNA systems with inhomogeneity effects

Nonlinear dynamics of DNA systems with inhomogeneity effects

Synchronized Oscillations in Double-Helix B-DNA Molecules with Mirror-Symmetric Codons

Rotobreathers in a chain of coupled elastic rotators

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