Discrete energy transport in the perturbed Ablowitz-Ladik equation for Davydov model of α-helix proteins

Ondoua, R. Y.; Tabi, Conrad Bertrand; Fouda, H. P. Ekobena; Mohamadou, Alidou; Kofané, Timoléon C.

doi:10.1140/epjb/e2012-21076-5

Cited by 22 publications

(15 citation statements)

References 15 publications

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“…Trial solutions for these perturbation equations can be adopted in the form (20) where Q and are the wavenumber and complex frequency of perturbation. We then obtain a homogeneous system of equations for B 1 , B 2 , B 3 and B 4 in the form…”

Section: Linear Stability Analysismentioning

confidence: 99%

“…This is addressed in this work, with a particular interest on energy localization. A direct mechanism leading to spontaneous energy localization in nonlinear systems is modulational instability (MI), which is the result of the interplay between nonlinear and dispersive effects, inherent to DNA and protein nonlinear models [17][18][19][20]. The way solvent interactions affect the emergence of energy patterns, under the activation of MI, in the twist-opening model of DNA is the main focus of the present contribution.…”

Section: Introductionmentioning

confidence: 99%

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Energy patterns in twist-opening models of DNA with solvent interactions

2015

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Energy localization, via modulation instability, is addressed in a modified twistopening model of DNA with solvent interactions. The Fourier expansion method is used to reduce the complex roto-torsional equations of the system to a set of discrete coupled nonlinear Schrödinger equations, which are used to perform the analytical investigation of modulation instability. We find that the instability criterion is highly influenced by the solvent parameters. Direct numerical simulations, performed on the generic model, further confirm our analytical predictions, as solvent interactions bring about highly localized energy patterns. These patterns are also shown to be robust under thermal fluctuations.

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Section: Linear Stability Analysismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Energy patterns in twist-opening models of DNA with solvent interactions

2015

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“…The determinant of the corresponding system is zero owing to the dispersion relation (17). The system will further have a solution for the Fredholm solvability condition, which is fulfilled for…”

Section: Mathematical Background and Linear Stability Analysismentioning

confidence: 99%

“…The later has been shown to naturally emerge in nonlinear systems through the activation of modulational instability (MI). MI is mainly due to the interplay between dispersive and nonlinear effects, and its realization spans a diverse set of disciplines including fluid dynamics, 10,11 plasma physics, 12 nonlinear optics, 13 Bose-Einsten condensation, 14 and molecular models, [15][16][17][18] just to name a few. MI is a general feature of continuum as well as discrete nonlinear equations.…”

Section: Introductionmentioning

confidence: 99%

Modulated pressure waves in large elastic tubes

Yone¹,

Tabi²,

Mohamadou³

et al. 2013

Chaos

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Modulational instability is the direct way for the emergence of wave patterns and localized structures in nonlinear systems. We show in this work that it can be explored in the framework of blood flow models. The whole modified Navier-Stokes equations are reduced to a difference-differential amplitude equation. The modulational instability criterion is therefore derived from the latter, and unstable patterns occurrence is discussed on the basis of the nonlinear parameter model of the vessel. It is found that the critical amplitude is an increasing function of α, whereas the region of instability expands. The subsequent modulated pressure waves are obtained through numerical simulations, in agreement with our analytical expectations. Different classes of modulated pressure waves are obtained, and their close relationship with Mayer waves is discussed.

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“…Thus, comes out the importance of discrete solitons in explaining local openings of the hydrogen bonds and formation of denaturation bubbles. Discrete solitons in nonlinear lattices have been the focus of considerable attention in diverse branches of science [16][17][18] and they are possible in several physical settings, such as biological systems [19][20][21][22][23], atomic chains [24,25], solid state physics [26], electrical lattices [27] and BoseEinstein condensates [28]. In DNA, such waves have been shown to carry the energy necessary for the initiation of the complex and key phenomena of replication and transcription [11][12][13][14].…”

Section: Introductionmentioning

confidence: 99%

Formation and Interaction of Bright Solitons with Shape Changing in a DNA Model

Tabi¹

2014

J Phys Chem Biophys

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I explore the collision of localized structures that arise from a general initial solutions in the Peyrard-Bishop model. By means of the semi-discrete approximation, it is shown that the amplitudes of waves are described by the the discrete nonlinear Schrödinger equation. The corresponding soliton solutions of this equation are obtained through the Hirota's bilinearization method. These solutions include the one-as well as the two-soliton solutions. Particular attention is paid to the behaviors displayed by the two-soliton solution. Taking one of the soliton as a pump and the other as the bubble that describes the local opening of the two strands of DNA, I show that, the enhancement of the bubbles is due to energy transfer from the pump to the bubble within the collision process. It is also shown that the underlying solitons undergo fascinating shape changing (intensity redistribution) collision.

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Discrete energy transport in the perturbed Ablowitz-Ladik equation for Davydov model of α-helix proteins

Cited by 22 publications

References 15 publications

Energy patterns in twist-opening models of DNA with solvent interactions

Energy patterns in twist-opening models of DNA with solvent interactions

Modulated pressure waves in large elastic tubes

Formation and Interaction of Bright Solitons with Shape Changing in a DNA Model

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