On the motion of solitons in discrete molecular chains

Vakhnenko, Oleksiy O.; Gaididei, Yuri

doi:10.1007/bf01019387

Cited by 60 publications

(46 citation statements)

References 9 publications

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“…22,23 In this way the external influence on the equilibrium position of a chain molecule is modeled by oscillations around the bottom of the potential, and in a recent paper the existence of polaron states in such a Davydov model with on-site potential was investigated. 24 In our current study we take the steric arrangement of the peptide groups in the three-dimensional protein cage into account and discuss the energy transport within a threestrand Davydov model which we consider from the perspective of recent developments in polaron dynamics. 25,26 In particular, effective numerical methods to obtain the polaron ground state were developed and polaron properties such as their wave pattern and the energy are readily obtainable.…”

Section: Introductionmentioning

confidence: 99%

Energy transport in α-helical protein models: One-strand versus three-strand systems

Hennig

2002

Phys. Rev. B

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We study the transport of vibrational energy in ␣-helix forms of proteins within the frame of a steric Davydov model. Our main objective is the comparison of the localization and transport properties of the widely used one-strand approximation of the ␣ helix associated with a linear chain of hydrogen bonded peptide groups and the complete three-dimensional helical system consisting of three such strands being connected via covalent bonds. We construct polaron solutions of the set of discrete equations utilizing a nonlinear map method for finding the ground state. With respect to the polaron wave pattern, we found that while the excitonic wave function of the one-strand system is localized at a site and monotonically decaying apart from it on the three-strand system a multihump structure arises whose envelope exhibits monotonic decay. For the polaronic states the static deformations of the H bonds are stronger for an isolated strand than for a strand embedded in the three-dimensional protein cage. In the excited region the radius of the helix slightly decreases. The participation numbers show that the exciton localization is more strongly pronounced on the one-strand system than on its three-strand counterpart. In our dynamical studies we pay special attention to the mobility of the polarons when their internal pinning modes are initiated. The latter are identified as certain isolated Floquet eigenvalues obtained from the Floquet map, which is derived from the linearized equations in tangent space. It is shown that the polarons on the one-strand system move with higher velocity than on the three-strand system. In the latter case the preferred transport path proceeds across the hydrogen bonds and polaron motion along the covalent channel is suppressed.

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Section: Introductionmentioning

confidence: 99%

Energy transport in α-helical protein models: One-strand versus three-strand systems

Hennig

2002

Phys. Rev. B

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“…This allows e.g. the use of soliton perturbation theory 98,24 to elucidate the role of the on-site nonlinearity as a non-integrable perturbation to the integrable AL equation. The Salerno equation was extensively analyzed by Hennig and co-workers 50 and is also described in the book by Scott 92 .…”

Section: Introductionmentioning

confidence: 99%

The Discrete Nonlinear Schrödinger Equation — 20 Years On

Eilbeck¹,

Johansson²

2003

Localization and Energy Transfer in Nonlinear Systems

111

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“…Second, for a definite region of parameters, the DNLS equation can be treated as a perturbed version of the AL equation, thereby allowing for considerable progress in the analytical study in the framework of the AL soliton perturbation theory. This idea has been initiated in early papers by Vakhnenko and Gaididei [7] on a soliton motion in a discrete molecular chain, by Kivshar and Campbell [8] on a modeling of the Peierls-Nabarro potential barrier, and by Aceves et al [9] on the self-trapping phenomenon in one-dimensional waveguide arrays [10]. Recently, the same approach has been employed to study discrete soliton dynamics in random media [11], energy transport in ␣-helical proteins [12], and dissipative coherent structures in discrete systems [13,14].…”

Section: Introductionmentioning

confidence: 96%

Dynamics of the Ablowitz-Ladik soliton train

2004

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It is shown that dynamics of a train of N weakly interacting Ablowitz-Ladik solitons with (almost) equal velocities and masses is governed by the complex Toda chain model. The integrability of the complex Toda chain model provides the means to describe analytically various dynamical regimes of the N-soliton train and to predict initial soliton parameters responsible for each of the regimes. Numerical simulations corroborate well analytical predictions. A specific feature arising for the discrete soliton train system is the appearance of an additional (with respect to the lattice spacing) spatial scale-intersoliton distance. We comment on interplay between both spatial scales.

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On the motion of solitons in discrete molecular chains

Cited by 60 publications

References 9 publications

Energy transport in α-helical protein models: One-strand versus three-strand systems

Energy transport in α-helical protein models: One-strand versus three-strand systems

The Discrete Nonlinear Schrödinger Equation — 20 Years On

Dynamics of the Ablowitz-Ladik soliton train

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