Simple models of non-linearDNA dynamics

Gaeta, Giuseppe; Reiss, Claude; Peyrard, Michel; Dauxois, Thierry

doi:10.1007/bf02724511

Cited by 110 publications

(113 citation statements)

References 66 publications

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“…The unitmass potential for kinks, initially at rest, moving in a slowly-varying background was derived by Salerno and Kivshar [8]. The sequence variation is contained in a term analogous to (13), however the weighting function is This coincides with the breather function for small tan 2 μ, illustrating why similar results for the major T7 promoter sequences are obtained for both kink [6][7][8] and breather solitons.…”

Section: Correlationsmentioning

confidence: 68%

Salerno's Model of DNA Re-Analysed: Could Breather Solitons have Biological Significance?

Bashford

2006

J Biol Phys

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Abstract.We investigate the sequence-dependent behaviour of localised excitations in a toy, nonlinear model of DNA base-pair opening originally proposed by Salerno. Specifically we ask whether "breather" solitons could play a role in the facilitated location of promoters by RNA polymerase (RNAP). In an effective potential formalism, we find excellent correlation between potential minima and Escherichia coli promoter recognition sites in the T7 bacteriophage genome. Evidence for a similar relationship between phage promoters and downstream coding regions is found and alternative reasons for links between AT richness and transcriptionally-significant sites are discussed. Consideration of the soliton energy of translocation provides a novel dynamical picture of sliding: steep potential gradients correspond to deterministic motion, while "flat" regions, corresponding to homogeneous AT or GC content, are governed by random, thermal motion. Finally we demonstrate an interesting equivalence between planar, breather solitons and the helical motion of a sliding protein "particle" about a bent DNA axis.

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Section: Correlationsmentioning

confidence: 68%

Salerno's Model of DNA Re-Analysed: Could Breather Solitons have Biological Significance?

Bashford

2006

J Biol Phys

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“…The DNA molecule encodes the information that organisms need to live and reproduce themselves. The DNA structure has been studied last decades (see for example [22][23][24][25][26][27][28][29][30][31][32]). The discovery of the double-helix structure of the DNA molecule has been established a strong relationship between its structure and function.…”

Section: Introductionmentioning

confidence: 99%

Exact Solutions for the Nonlinear PDE Describing the Model of DNA Double Helices using the Improved (G′/G)- Expansion Method

Zayed¹,

Amer²,

Shohib³

2014

Math. Sci. Lett.

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Abstract:The objective of this article is to apply the improved (G ′ /G)-expansion method for constructing many exact solutions with parameters of the nonlinear partial differential equation (PDE) describing the model of DNA double helices. The stretch of the hydrogen bonds is considered as a nonlinear chain with cubic and quadratic potential. When the parameters take special values, many solitary wave solutions and periodic wave solutions can be found. Comparison between some of our new results and the well-known results are given.

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Section: Introductionmentioning

confidence: 99%

“…Several models have been proposed in this direction; references and some detail on these can be found in [19,34]. 1 A particularly simple model (Y model) was proposed by Yakushevich [32,33]; see also [13,14,16,19]. Despite its simplicity, the Y-model succeeds in describing several relevant features of the DNA nonlinear (and linear) dynamics related to the relevant processes [19,34,36], and is thus the subject of continuing interest.…”

Section: Introductionmentioning

confidence: 99%

“…1 A particularly simple model (Y model) was proposed by Yakushevich [32,33]; see also [13,14,16,19]. Despite its simplicity, the Y-model succeeds in describing several relevant features of the DNA nonlinear (and linear) dynamics related to the relevant processes [19,34,36], and is thus the subject of continuing interest. In recent works it has been shown that all the (sometimes, very crude) approximations introduced by Yakushevich in her model -some of these substantially affecting the dispersion relations for the model [20] -have very little impact on the fully nonlinear dynamics and in particular on solitons' shape [17,18].…”

Section: Introductionmentioning

confidence: 99%

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Solitons in a double pendulums chain model, and DNA roto-torsional dynamics

Cadoni

Лео

Gaeta

2007

JNMP

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It was first suggested by Englander et al to model the nonlinear dynamics of DNA relevant to the transcription process in terms of a chain of coupled pendulums. In a related paper [4] we argued for the advantages of an extension of this approach based on considering a chain of double pendulums with certain characteristics. Here we study a simplified model of this kind, focusing on its general features and nonlinear travelling wave excitations; in particular, we show that some of the degrees of freedom are actually slaved to others, allowing for an effective reduction of the relevant equations.

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Simple models of non-linearDNA dynamics

Cited by 110 publications

References 66 publications

Salerno's Model of DNA Re-Analysed: Could Breather Solitons have Biological Significance?

Salerno's Model of DNA Re-Analysed: Could Breather Solitons have Biological Significance?

Exact Solutions for the Nonlinear PDE Describing the Model of DNA Double Helices using the Improved (G′/G)- Expansion Method

Solitons in a double pendulums chain model, and DNA roto-torsional dynamics

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