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Mathematical Biosciences and Engineering

2008, Volume 5, Issue 1: 205-216. doi: 10.3934/mbe.2008.5.205
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Soliton-like excitation in a nonlinear model of DNA dynamics with viscosity

  • 1.
    Laboratory of Mechanics, Department of Physics, Faculty of Science, University of Yaounde I, P. O. Box 812, Yaounde
  • 2.
    Condensed Matter Physics Laboratory, Department of Physics, Faculty of Science, University of Douala, P.O. Box 24157, Douala
  • Received: 01 May 2007 Accepted: 29 June 2018 Published: 01 January 2008

  • MSC : 37N25, 34J60, 34G34.

  • The study of solitary wave solutions is of prime significance for nonlinear physical systems. The Peyrard-Bishop model for DNA dynamics is generalized specifically to include the difference among bases pairs and vis- cosity. The small amplitude dynamics of the model is studied analytically and reduced to a discrete complex Ginzburg-Landau (DCGL) equation. Ex- act solutions of the obtained wave equation are obtained by the mean of the extended Jacobian elliptic function approach. These amplitude solutions are made of bubble solitons. The propagation of a soliton-like excitation in a DNA is then investigated through numerical integration of the motion equations. We show that discreteness can drastically change the soliton shape. The impact of viscosity as well as elasticity on DNA dynamic is also presented. The profile of solitary wave structures as well as the energy which is initially evenly distributed over the lattice are displayed for some fixed parameters.

    Citation: Conrad Bertrand Tabi, Alidou Mohamadou, Timoleon Crepin Kofane. Soliton-like excitation in a nonlinear model of DNA dynamics with viscosity[J]. Mathematical Biosciences and Engineering, 2008, 5(1): 205-216. doi: 10.3934/mbe.2008.5.205

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  • The study of solitary wave solutions is of prime significance for nonlinear physical systems. The Peyrard-Bishop model for DNA dynamics is generalized specifically to include the difference among bases pairs and vis- cosity. The small amplitude dynamics of the model is studied analytically and reduced to a discrete complex Ginzburg-Landau (DCGL) equation. Ex- act solutions of the obtained wave equation are obtained by the mean of the extended Jacobian elliptic function approach. These amplitude solutions are made of bubble solitons. The propagation of a soliton-like excitation in a DNA is then investigated through numerical integration of the motion equations. We show that discreteness can drastically change the soliton shape. The impact of viscosity as well as elasticity on DNA dynamic is also presented. The profile of solitary wave structures as well as the energy which is initially evenly distributed over the lattice are displayed for some fixed parameters.


  • This article has been cited by:

    1. H. Ngoubi, G. H. Ben-Bolie, T. C. Kofané, Charge transport in DNA model with vibrational and rotational coupling motions, 2017, 43, 0092-0606, 341, 10.1007/s10867-017-9455-6
    2. C.B. Tabi, T.G. Motsumi, C.D. Bansi Kamdem, A. Mohamadou, Nonlinear excitations of blood flow in large vessels under thermal radiations and uniform magnetic field, 2017, 49, 10075704, 1, 10.1016/j.cnsns.2017.01.024
    3. Slobodan Zdravković, Miljko V. Satarić, Ljupčo Hadžievski, DNA-RNA transcription as an impact of viscosity, 2010, 20, 1054-1500, 043141, 10.1063/1.3529360
    4. Dalibor Chevizovich, Davide Michieletto, Alain Mvogo, Farit Zakiryanov, Slobodan Zdravković, A review on nonlinear DNA physics, 2020, 7, 2054-5703, 200774, 10.1098/rsos.200774
    5. E S Shikhovtseva, V N Nazarov, Dynamics of conformational switchings of bistable quasi-one-dimensional macromolecules with nonlinear longitudinal stretching present, 2013, 46, 1751-8113, 225202, 10.1088/1751-8113/46/22/225202
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    7. Joseph Brizar Okaly, Fabien II Ndzana, Rosalie Laure Woulaché, Timoléon Crépin Kofané, Solitary wavelike solutions in nonlinear dynamics of damped DNA systems, 2019, 134, 2190-5444, 10.1140/epjp/i2019-12992-3
    8. Joseph Brizar Okaly, Fabien II Ndzana, Rosalie Laure Woulaché, Conrad Bertrand Tabi, Timoléon Crépin Kofané, Base pairs opening and bubble transport in damped DNA dynamics with transport memory effects, 2019, 29, 1054-1500, 093103, 10.1063/1.5098341
    9. Armand S. Etémé, Conrad B. Tabi, Alidou Mohamadou, Synchronized nonlinear patterns in electrically coupled Hindmarsh–Rose neural networks with long-range diffusive interactions, 2017, 104, 09600779, 813, 10.1016/j.chaos.2017.09.037
    10. H. Ngoubi, G. H. Ben-Bolie, T. C. Kofané, Charge transport in a DNA model with solvent interaction, 2018, 44, 0092-0606, 483, 10.1007/s10867-018-9503-x
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    13. C. B. Tabi, A. Mohamadou, T. C. Kofane, Modulational instability in the anharmonic Peyrard-Bishop model of DNA, 2010, 74, 1434-6028, 151, 10.1140/epjb/e2010-00062-1
    14. V. Vasumathi, M. Daniel, Base-pair opening and bubble transport in a DNA double helix induced by a protein molecule in a viscous medium, 2009, 80, 1539-3755, 10.1103/PhysRevE.80.061904
    15. Yulong Cao, Lei Gao, Stefan Wabnitz, Zhiqiang Wang, Qiang Wu, Lingdi Kong, Ziwei Li, Ligang Huang, Wei Huang, Tao Zhu, Experimental revealing of fiber laser soliton build-up activated by shaking-soliton triplets, 2022, 147, 00303992, 107677, 10.1016/j.optlastec.2021.107677
    16. A. Tripathy, S. Sahoo, New Dynamic Multiwave Solutions of the Fractional Peyrard–Bishop DNA Model, 2023, 18, 1555-1415, 10.1115/1.4063223
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