Advertisement

Solitary wavelike solutions in nonlinear dynamics of damped DNA systems

  • Joseph Brizar OkalyEmail author
  • Fabien II Ndzana
  • Rosalie Laure Woulaché
  • Timoléon Crépin Kofané
Regular Article
  • 7 Downloads

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.

Notes

References

  1. 1.
    L. Styer, Biochemistry, 4th ed. (W. H. Freeman and Company, New York, 1995)Google Scholar
  2. 2.
    L.V. Yakushevich, A.V. Savin, L.I. Manevitch, Phys. Rev. E 66, 016614 (2002)ADSMathSciNetCrossRefGoogle Scholar
  3. 3.
    S.W. Englander, N.R. Kallenbach, A.J. Heeger, J.A. Krumhansl, S. Litwin, Proc. Natl. Acad. Sci. U.S.A. 77, 7222 (1980)ADSCrossRefGoogle Scholar
  4. 4.
    S. Yomosa, Phys. Rev. A 27, 2120 (1983)ADSMathSciNetCrossRefGoogle Scholar
  5. 5.
    S. Homma, S. Takeno, Prog. Theor. Phys. 70, 308 (1983)ADSCrossRefGoogle Scholar
  6. 6.
    S. Takeno, S. Homma, Prog. Theor. Phys. 72, 679 (1984)ADSCrossRefGoogle Scholar
  7. 7.
    M. Peyrard, A.R. Bishop, Phys. Rev. Lett. 62, 2755 (1989)ADSCrossRefGoogle Scholar
  8. 8.
    T. Dauxois, Phys. Lett. A l59, 390 (1991)ADSCrossRefGoogle Scholar
  9. 9.
    L.V. Yakushevich, Phys. Lett. A 136, 413 (1989)ADSCrossRefGoogle Scholar
  10. 10.
    T.A. Knotts IV, N. Rathore, D.C. Schwartz, J.J. de Pablo, J. Chem. Phys. 126, 084901 (2007)ADSCrossRefGoogle Scholar
  11. 11.
    L.V. Yakushevich, Phys. Lett. A 253, 358 (1999)CrossRefGoogle Scholar
  12. 12.
    M. Salerno, Phys. Rev. A 44, 5292 (1991)ADSMathSciNetCrossRefGoogle Scholar
  13. 13.
    V. Muto, P.S. Lomdahl, P.L. Christiansen, Phys. Rev. A 42, 7452 (1990)ADSCrossRefGoogle Scholar
  14. 14.
    K. De-Xing, L. Sen-Yue, Z. Jin, Commun. Theor. Phys. 36, 737 (2001)ADSCrossRefGoogle Scholar
  15. 15.
    A. Campa, A. Giansanti, Phys. Rev. E 58, 3585 (1998)ADSCrossRefGoogle Scholar
  16. 16.
    A.J. Sievers, S. Takeno, Phys. Rev. Lett. 61, 970 (1988)ADSCrossRefGoogle Scholar
  17. 17.
    R.S. MacKay, S. Aubry, Nonlinearity 7, 1623 (1994)ADSMathSciNetCrossRefGoogle Scholar
  18. 18.
    T.B. Benjamin, J.E. Feir, J. Fluid Mech. 27, 417 (1967)ADSCrossRefGoogle Scholar
  19. 19.
    C.B. Tabi, A. Mohamadou, T.C. Kofane, Math. Biosci. Eng. 5, 205 (2008)MathSciNetCrossRefGoogle Scholar
  20. 20.
    C.B. Tabi, A. Mohamadou, T.C. Kofane, J. Comput. Theor. Nanosci. 5, 647 (2008)CrossRefGoogle Scholar
  21. 21.
    C.B. Tabi, A. Mohamadou, T.C. Kofane, Chin. Phys. Lett. 26, 068703 (2009)CrossRefGoogle Scholar
  22. 22.
    S. Zdravković, M.V. Satarić, Phys. Scr. 64, 612 (2001)ADSCrossRefGoogle Scholar
  23. 23.
    S. Zdravković, M.V. Satarić, A.Yu. Parkhomenko, A.N. Bugay, Chaos 28, 113103 (2018)ADSMathSciNetCrossRefGoogle Scholar
  24. 24.
    S. Zdravković, M.V. Satarić, Chin. Phys. Lett. 24, 1210 (2007)ADSCrossRefGoogle Scholar
  25. 25.
    S. Zdravković, M.V. Satarić, L. Hadžievski, Chaos 20, 043141 (2010)ADSCrossRefGoogle Scholar
  26. 26.
    S. Zdravković, M.V. Satarić, J. Comput. Theor. Nanosci. 2, 1 (2005)CrossRefGoogle Scholar
  27. 27.
    A. Sulaimana, F.P. Zenb, H. Alatasc, L.T. Handoko, Physica D 241, 1640 (2012)ADSCrossRefGoogle Scholar
  28. 28.
    V. Vasumathi, M. Daniel, Phys. Rev. E 80, 061904 (2009)ADSCrossRefGoogle Scholar
  29. 29.
    T. Lipniacki, Phys. Rev. E 58, 7253 (1999)ADSCrossRefGoogle Scholar
  30. 30.
    G. Careri, M. Geraci, A. Ginansanti, J.A. Ruply, Proc. Natl. Acad. Sci. U.S.A. 82, 5342 (1985)ADSCrossRefGoogle Scholar
  31. 31.
    H. Khesbak, O. Savchuk, S. Tsushima, K. Fahmy, J. Am. Chem. Soc 82, 5834 (2011)CrossRefGoogle Scholar
  32. 32.
    W. Alka, A. Goyal, C.N. Kumar, Phys. Lett. A 375, 480 (2011)ADSCrossRefGoogle Scholar
  33. 33.
    J.B. Okaly, A. Mvogo, R.L. Woulaché, T.C. Kofané, Wave Motion 82, 1 (2018)MathSciNetCrossRefGoogle Scholar
  34. 34.
    M.A. Knyazev, D.M. Knyazev, J. Phys. Stud. 16, 1001 (2012)MathSciNetGoogle Scholar
  35. 35.
    H.M. Baskonus, C. Cattani, P. Agarwal, S.S. Dragomir, M. Jleli, B. Samet, in Advances in Mathematical Inequalities and Applications, (Birkhäuser, Singapore, Springer, Nature, Singapore, Pte Ltd., 2018)Google Scholar
  36. 36.
    F. II Ndzana, A. Mohamadou, Chaos 29, 013116 (2019)ADSMathSciNetCrossRefGoogle Scholar
  37. 37.
    E. Kengne, A. Lakhssassi, W.M. Liu, Phys. Rev. E 91, 062915 (2015)ADSCrossRefGoogle Scholar
  38. 38.
    S.B. Smith, Y. Cui, C. Bustamante, Science, New Series 271, 795 (1996)ADSGoogle Scholar
  39. 39.
    J.B. Okaly, A. Mvogo, R.L. Woulache, T.C. Kofane, Commun. Nonlinear Sci. Numer. Simul. 55, 183 (2018)ADSMathSciNetCrossRefGoogle Scholar
  40. 40.
    M. Peyrard, I. Daumont, Europhys. Lett. 59, 834 (2002)ADSCrossRefGoogle Scholar
  41. 41.
    I. Daumont, M. Peyrard, Chaos 13, 624 (2003)ADSMathSciNetCrossRefGoogle Scholar
  42. 42.
    C. Brunhuber, F.G. Mertens, Phys. Rev. E 73, 016614 (2006)ADSCrossRefGoogle Scholar
  43. 43.
    E. Arévalo, Y. Gaididei, F.G. Mertens, Eur. Phys. J. B 27, 63 (2002)ADSCrossRefGoogle Scholar
  44. 44.
    M. Peyrard, Nonlinearity 17, R1 (2004)ADSMathSciNetCrossRefGoogle Scholar
  45. 45.
    M. Remoissenet, Phys. Rev. B 33, 2386 (1986)ADSCrossRefGoogle Scholar
  46. 46.
    F.M. Moukam Kakmeni, E.M. Inack, E.M. Yamakou, Phys. Rev. E 89, 052919 (2014)ADSCrossRefGoogle Scholar
  47. 47.
    J.B. Okaly, A. Mvogo, R.L. Woulaché, T.C. Kofané, Chin. J. Phys. 56, 2613 (2018)CrossRefGoogle Scholar
  48. 48.
    C.B. Tabi, A. Mohamadou, T.C. Kofane, Eur. Phys. J. D 50, 307 (2008)ADSCrossRefGoogle Scholar
  49. 49.
    F. II Ndzana, A. Mohamadou, T.C. Kofane, Phys. Rev. E 78, 016606 (2008)ADSMathSciNetCrossRefGoogle Scholar
  50. 50.
    S. Abdoulkary, A.D. Aboubakar, M. Aboubakar, A. Mohamadou, L. Kavitha, Commun. Nonlinear Sci. Numer. Simul. 22, 1288 (2015)ADSMathSciNetCrossRefGoogle Scholar
  51. 51.
    M.J. Lighthill, J. Inst. Math. Appl. 1, 269 (1965)CrossRefGoogle Scholar
  52. 52.
    T.B. Benjamin, J.E. Feir, J. Fluid Mech. 27, 417 (1967)ADSCrossRefGoogle Scholar
  53. 53.
    V.E. Zakharov, Zh. Eksp. Teor. Fiz. 51, 688 (1966) (Sov. Phys. JETP 24Google Scholar
  54. 54.
    J.E. Feir, Proc. R. Soc. London, Ser. A 299, 54 (1967)ADSCrossRefGoogle Scholar
  55. 55.
    S. Nikitenkova, N. Singh, Y. Stepanyants, Chaos 25, 123113 (2015)ADSMathSciNetCrossRefGoogle Scholar
  56. 56.
    M.I. Fakhretdinov, F.K. Zakir'yanov, Russ. Phys. J. 54, 1304 (2012)CrossRefGoogle Scholar

Copyright information

© Società Italiana di Fisica / Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Laboratory of Biophysics, Department of Physics, Faculty of ScienceUniversity of Yaounde IYaoundeCameroon
  2. 2.African Center of Excellence in Information and Communication TechnologiesUniversity of Yaounde IYaoundeCameroon
  3. 3.International Center for Complex Systems, Faculty of ScienceUniversity of Yaoundé IYaoundeCameroon
  4. 4.Complex Systems, Faculty of ScienceUniversity of MarouaMarouaCameroon
  5. 5.Laboratory of Mechanics, Department of Physics, Faculty of ScienceUniversity of Yaounde IYaoundeCameroon

Personalised recommendations