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Solitary wavelike solutions in nonlinear dynamics of damped DNA systems

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Abstract.

The internal mobility of the DNA molecule, in a weakly damped medium, is studied. Inspired by the microscopic Peyrard-Bishop-Dauxois model, a zigzag model, which considers longitudinal and transverse vibrations of base pairs is used. The damped limit is considered and the whole system is shown to be governed by a dissipative nonlinear Schrödinger equation. The linear stability analysis of a plane wave solution is thereafter performed. The oscillations and open states of the DNA duplex are also addressed, where two hyperbolic functions are used to construct DNA bubbles in the form of bright- and kink-type soliton solutions. The confirmation of analytical predictions is verified through direct numerical experiments. There are good accuracy and good agreement between the quantitative and qualitative influence of damping forces on the width and amplitude of the moving soliton. Such relevant results could be used to predict the generation of moving bubbles along the DNA molecule, and to explain energy transfer and localization processes during the fundamental processes of DNA replication and transcription.

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Author information

Authors and Affiliations

  1. Laboratory of Biophysics, Department of Physics, Faculty of Science, University of Yaounde I, P.O. Box 812, Yaounde, Cameroon

    Joseph Brizar Okaly

  2. African Center of Excellence in Information and Communication Technologies, University of Yaounde I, P.O. Box 812, Yaounde, Cameroon

    Joseph Brizar Okaly, Fabien II Ndzana, Rosalie Laure Woulaché & Timoléon Crépin Kofané

  3. International Center for Complex Systems, Faculty of Science, University of Yaoundé I, P.O. Box 812, Yaounde, Cameroon

    Fabien II Ndzana

  4. Complex Systems, Faculty of Science, University of Maroua, P.O. Box 814, Maroua, Cameroon

    Fabien II Ndzana

  5. Laboratory of Mechanics, Department of Physics, Faculty of Science, University of Yaounde I, P.O. Box 812, Yaounde, Cameroon

    Rosalie Laure Woulaché & Timoléon Crépin Kofané

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  1. Joseph Brizar Okaly
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  2. Fabien II Ndzana
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  3. Rosalie Laure Woulaché
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  4. Timoléon Crépin Kofané
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Correspondence to Joseph Brizar Okaly.

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Okaly, J.B., Ndzana, F.I., Woulaché, R.L. et al. Solitary wavelike solutions in nonlinear dynamics of damped DNA systems. Eur. Phys. J. Plus 134, 598 (2019). https://doi.org/10.1140/epjp/i2019-12992-3

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