Nonlinear waves in DNA and regulation of transcription

Polozov, R. V.; Yakushevich, L. V.

doi:10.1016/s0022-5193(88)80207-8

Cited by 32 publications

(13 citation statements)

References 29 publications

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“…The temporal evolution of waves depict that, as θ increases, the width of the pulse becomes more narrow while the amplitude of the pulse grows. The transmission of conformational changes over large distances along the double helix have been discussed by Polozov and Yakushevich [27]. They show that nonlinear solitary waves are a suit-able model for describing the transmission.…”

Section: Numerical Analysis and Twist Angle/solvent Effectmentioning

confidence: 99%

Breather-Like Solutions of the Twisted DNA with Solvent Interaction

Toko¹,

Woulache²

2013

J Phys Chem Biophys

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We study the propagation of localized excitations in a DNA molecule which takes into account helicity and solvent interaction. The small amplitude dynamics of the model is described by envelope solutions made of breathers. Our solutions drastically depends on the twist angle and solvent interaction. It is found that increasing the twist angle decreases the width of the pulse which can be used for the transportation of energy. Increase the solvent interaction term, increases the width of the pulses while the number of waves train decreases with time. The stability of the solutions has been checked through numerical simulations.

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Section: Numerical Analysis and Twist Angle/solvent Effectmentioning

confidence: 99%

Breather-Like Solutions of the Twisted DNA with Solvent Interaction

Toko¹,

Woulache²

2013

J Phys Chem Biophys

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“…[11]) using Toda lattice model in which two types of internal motions namely, transverse motion along the hydrogen bond direction and longitudinal motion along the backbone direction were found to contribute to DNA denaturation process in terms of travelling solitary waves and standing waves. These localized nonlinear excitations further explain conformation transition [12,13,14], long range interaction of kink solitons in the double chain [15,16], regulation of transcription [15,17], denaturation [10] and charge transport in terms of polarons and bubbles [18]. Some of them have been successfully used for interpreting experimental data related to microwave absorption [19,20].…”

Section: Introductionmentioning

confidence: 99%

Perturbed soliton excitations in the DNA double helix

Daniel

Vasumathi

2007

Physica D: Nonlinear Phenomena

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We study nonlinear dynamics of inhomogeneous DNA double helical chain under dynamic plane-base rotator model by considering angular rotation of bases in a plane normal to the helical axis. The DNA dynamics in this case is found to be governed by a perturbed sine-Gordon equation while taking into account the interstrand hydrogen bonding energy between bases and the intrastrand inhomogeneous stacking energy and by making an analogy with the Heisenberg model of the Hamiltonian of an inhomogeneous anisotropic spin ladder with ferromagnetic legs and antiferromagnetic rung coupling. In the homogeneous limit the dynamics is governed by the kink-antikink soliton of the sine-Gordon equation which represents the formation of open state configuration in DNA double helix. The effect of inhomogeneity in stacking energy in the form of localized and periodic variations on the formation of open states in DNA is studied under perturbation. The perturbed soliton is obtained using a multiple scale soliton perturbation theory by solving the associated linear eigen value problem and by constructing the complete set of eigen functions. The inhomogeneity in stacking energy is found to modulate the width and speed of the soliton depending on the nature of inhomogeneity. Also it introduces fluctuations in the form of train of pulses or periodic oscillations in the open state configuration.

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“…The perturbation of fluxons by dipole current devices in JJ's is a typical example of a strong and local external influence with the same topological form as expression (2) [8]. This forcing term may be also relevant for 1D models of biological molecules, like DNA chains, where 1D sG systems have been considered as a suitable model to explain the formation of open states or bubbles in the double helix [27][28][29]. Thus, results obtained in this work can be generalized to other topologically equivalent systems [11].…”

Section: Two-dimensional Model and The One-dimensional Theory Of mentioning

confidence: 99%

Bubblelike structures generated by activation of internal shape modes in two-dimensional sine-Gordon line solitons

2017

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Nonlinear waves that collide with localized defects exhibit complex behavior. Apart from reflection, transmission, and annihilation of an incident wave, a local inhomogeneity can activate internal modes of solitons, producing many impressive phenomena. In this work we investigate a two-dimensional sine-Gordon model perturbed by a family of localized forces. We observed the formation of bubblelike and droplike structures due to local internal shape mode instabilities. We describe the formation of such structures on the basis of a one-dimensional theory of activation of internal modes of sine-Gordon solitons. An interpretation of the observed phenomena, in the context of phase transition theory, is given. Implications in Josephson junctions with a current dipole device are discussed.

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Nonlinear waves in DNA and regulation of transcription

Cited by 32 publications

References 29 publications

Breather-Like Solutions of the Twisted DNA with Solvent Interaction

Breather-Like Solutions of the Twisted DNA with Solvent Interaction

Perturbed soliton excitations in the DNA double helix

Bubblelike structures generated by activation of internal shape modes in two-dimensional sine-Gordon line solitons

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