Nonlinear DNA dynamics: A new model

Yakushevich, L. V.

doi:10.1016/0375-9601(89)90425-8

Cited by 152 publications

(87 citation statements)

References 10 publications

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“…A simple model which has been studied in depth is the so called Y model [52]. This supports topological solitons (of sine-Gordon type) and provides correct orders of magnitude for several physically relevant quantities [26]; on the other hand, the soliton speed remains essentially a free parameter [22,23], and the speed of transverse phonons can be made to have a physical value only by assigning unphysical values to the coupling constants of the model [57].…”

Section: A Summary and Resultsmentioning

confidence: 92%

“…The standard Y model [52] can be seen as a particular limiting case of our model. Thus, a check of the validity of our model -and in particular of the fact we considered here physical assumptions which correspond to those by Y in her geometry -can be obtained by going to a limit in which our composite Y model reduces to the standard Y model.…”

Section: Comparison With the Yakushevich Modelmentioning

confidence: 99%

“…More recent advances are discussed in [39] and [5,12,51]) and the one by Yakushevich [52]; we will refer to these as the PB and the Y models respectively.…”

Section: Introductionmentioning

confidence: 99%

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Composite model for DNA torsion dynamics

2007

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DNA torsion dynamics is essential in the transcription process; a simple model for it, in reasonable agreement with experimental observations, has been proposed by Yakushevich (Y) and developed by several authors; in this, the DNA subunits made of a nucleoside and the attached nitrogen bases are described by a single degree of freedom. In this paper we propose and investigate, both analytically and numerically, a "composite" version of the Y model, in which the nucleoside and the base are described by separate degrees of freedom. The model proposed here contains as a particular case the Y model and shares with it many features and results, but represents an improvement from both the conceptual and the phenomenological point of view. It provides a more realistic description of DNA and possibly a justification for the use of models which consider the DNA chain as uniform. It shows that the existence of solitons is a generic feature of the underlying nonlinear dynamics and is to a large extent independent of the detailed modelling of DNA. The model we consider supports solitonic solutions, qualitatively and quantitatively very similar to the Y solitons, in a fully realistic range of all the physical parameters characterizing the DNA.

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Section: A Summary and Resultsmentioning

confidence: 92%

Section: Comparison With the Yakushevich Modelmentioning

confidence: 99%

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Composite model for DNA torsion dynamics

2007

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“…Surprisingly, the passage of the DNA kinks through the CDS region was not modeled by investigators, though the necessary mathematical formalism has been already developed. We can point out the model of Peyrard and Bishop [10] that takes into account the transverse motions of nucleotides, the Y-model [11][12][13] that takes into account the angular displacements of nitrous bases, the combined model [14] that takes into account both the angular and the transverse displacements, and numerous modifications of these models [15][16][17][18][19][20]. Any of them could be used for the purpose.…”

Section: Introductionmentioning

confidence: 99%

Траектории Кинков ДНК В Последовательностях, Содержащих Кодирующие Области Генов

Якушевич¹,

Yakushevich²

2017

Math.Biol.Bioinf.

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Coding regions (CDS) being an integral part of any gene sequence, play an important role in the process of transcription. One of the tasks associated with the CDS regions, consists in the modeling of the passage of transcription bubbles named also open states or DNA kinks through the coding regions. In this paper, we present a simple and convenient approach to the modeling of the passage. It includes the calculation of the energy profile of the sequence and reducing the initial task to the modeling of the movement of a quasi particle in the field with this energy profile. To illustrate the method, we present the results of the calculations of the trajectories of the DNA kinks moving in the sequence of gene coding interferon alpha 17 (IFNA17) that consists of the three regions: the coding region and the two regions with unknown functional properties. To analyze the kink dynamics, we apply approximation where the DNA parameters are being averaged separately over each of the three regions. In the absences of dissipation, the total kink energy is constant. At the same time the kink velocity is constant only inside each of the regions. In the presence of dissipation, the total kink energy decreases. It is shown that the greater the total initial energy of the kink, the faster the energy decrease. It is suggested that the proposed approach could be useful in finding the ways to govern the movement of transcription bubbles at the first stage of the process of transcription.

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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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Nonlinear DNA dynamics: A new model

Cited by 152 publications

References 10 publications

Composite model for DNA torsion dynamics

Composite model for DNA torsion dynamics

Траектории Кинков ДНК В Последовательностях, Содержащих Кодирующие Области Генов

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

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