Skip to main content

Advertisement

SpringerLink
Log in

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

  • Original Paper
  • Published:
Journal of Biological Physics Aims and scope Submit manuscript

Abstract

Energy localization, via modulation instability, is addressed in a modified twist-opening 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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10

Similar content being viewed by others

References

  1. Englander, S.W., Kallenbanch, N.R., Heeger, A.J., Krumhansl, J.A., Litwin, S.: Proc. Natl. Acad. Sci. U.S.A 77, 7222 (1980)

    Article  ADS  Google Scholar 

  2. Yomosa, S.: Rev. Phys. A 27 (1983) 2120; ibid 30, 474 (1984)

    Google Scholar 

  3. Tabi, C.B., Mohamadou, A., Kofané, T.C.: Chaos 19, 043101 (2009)

  4. Tabi, C.B., Mohamadou, A., Kofané, T.C.: Eur. Phys. J. E 32, 327 (2010)

    Article  Google Scholar 

  5. Peyrard, M., Bishop, A.R.: Phys. Rev. Lett 62, 2755 (1989)

    Article  ADS  Google Scholar 

  6. Dauxois, T., Peyrard, M., Bishop, A.R.: Phys. Rev. E 47, R44 (1993)

    Article  ADS  Google Scholar 

  7. Dauxois, T., Peyrard, M.: Phys. Rev. E 51, 4027 (1995)

    Article  ADS  Google Scholar 

  8. Campa, A., Giansanti, A.: Phys. Rev. E 58, 3585 (1998)

    Article  ADS  Google Scholar 

  9. Cule, D., Hwa, T.: Phys. Rev. Lett. 79, 2375 (1997)

    Article  ADS  Google Scholar 

  10. Barbi, M., Cocco, S., Peyrard, M.: Phys. Lett. A 253, 358 (1999)

    Article  ADS  Google Scholar 

  11. Tabi, C.B., Mohamadou, A., Kofané, T.C.: Phys. Lett. A 373, 2476 (2009)

    Article  ADS  Google Scholar 

  12. Tabi, C.B.: J. Phys. Cond. Matter 22, 414107 (2010)

    Article  Google Scholar 

  13. Hammouda, B., Worcester, D.: Biophys. J. 91, 2237 (2006)

    Article  ADS  Google Scholar 

  14. Zhang, F., Collins, M.A.: Phys. Rev. E 52, 4217 (1995)

    Article  ADS  Google Scholar 

  15. Drukker, K., Wu, G., Schatz, G.C.: J. Chem. Phys 114, 579 (2001)

    Article  ADS  Google Scholar 

  16. Weber, G.: Europhys. Lett 73, 806 (2006)

    Article  ADS  Google Scholar 

  17. Tabi, C.B., Mohamadou, A., Kofané, T.C.: J. Phys. Cond. Matter 20, 415104 (2008)

    Article  Google Scholar 

  18. Tabi, C.B., Mohamadou, A., Kofané, T.C.: Comput. Theor. Nanosci. 5, 647 (2008)

    Google Scholar 

  19. Ekobena, H.P., Fouda, C.B., Tabi, A., Mohamadou, A., T. C. Kofané: J. Phys. Condens. Matter 23, 375104 (2011)

    Article  Google Scholar 

  20. Ondoua, R.Y., Tabi, C.B., Ekobena Fouda, H.P., Mohamadou, A., Kofané, T. C.: Eur. Phys. J. B 85, 318 (2012)

    Article  ADS  Google Scholar 

  21. Mefire, G.R.Y., Tabi, C.B., Mohamadou, A., Ekobena, H.P.F., Kofané, T.C.: Chaos 23, 033128 (2013)

    Article  ADS  Google Scholar 

  22. Remoissenet, M.: Rev. Phys. B 33, 2386 (1986)

    Article  Google Scholar 

  23. Tabi, C.B., Mohamadou, A., Kofané, T.C.: J. Comput. Theor. Nanosci. 5, 2201 (2008)

    Article  Google Scholar 

  24. Johansson, M.: Physica D 216, 62 (2006)

    Article  MathSciNet  ADS  Google Scholar 

  25. Lakshmanan, M., Rajasekar, S.: Nonlinear Dynamics: Integrability, Chaos and Patterns. Springer-Verlag, Berlin (2003)

    Book  MATH  Google Scholar 

  26. Akhmediev, N., Ankiewicz, A.: Solitons: Nonlinear Pulses and Beams. Chapman and Hall, London (1997)

    MATH  Google Scholar 

  27. Kivshar, Y., Agrawal, G.P.: Optical Solitons: From Fibers to Photonic Crystals. Academic Press, San Diego (2003)

    Google Scholar 

  28. Makhankov, V.G.: Soliton Phenomenology. Kluwer Academic, London (1990)

    Book  Google Scholar 

  29. Mimshe, J.C.F., Tabi, C.B., Edongue, H., Ekobena, H.P.F., Kofané, T.C.: Phys. Scr. 87, 025801 (2013)

    Article  ADS  Google Scholar 

  30. Tabi, C.B., Mimshe, J.C.F., Ekobena, H.P.F., Mohamadou, A., Kofané, T.C. Eur. Phys. J. B 86, 374 (2013)

    Article  MathSciNet  ADS  Google Scholar 

  31. Tsironis, G.P., Bishop, A.R., Savin, A.V., Zolotaryuk, A.V.: Phys. Rev. E 60, 6610 (1999)

    Article  ADS  Google Scholar 

  32. Muto, V., Scott, A.C., Christiansen, P.L.: Phys. Lett. A 136, 33 (1989)

    Article  ADS  Google Scholar 

  33. Muto, V., Scott, A.C., Christiansen, P.L.: Physica D 44, 75 (1990)

    Article  ADS  Google Scholar 

  34. Peyrard, M.: Physica D119, 184 (1998)

    ADS  Google Scholar 

Download references

Acknowledgments

CBT acknowledges the Claude Leon Foundation for research fellowship at Stellenbosch University, South Africa. Prof. K. K. Müller-Nedebock is also acknowledged for fruitful suggestions.

Author information

Authors and Affiliations

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

    Conrad Bertrand Tabi & Grégoire Bineli

  2. Institute of Theoretical Physics, Department of Physics, Faculty of Science, University of Stellenbosch, Private Bag X1 Matieland, Stellenbosch, 7602, South Africa

    Conrad Bertrand Tabi

  3. The African Institute for Mathematical Sciences, 6–8 Melrose Rd, Muizenberg, 7945, South Africa

    Conrad Bertrand Tabi

  4. Institute of Theoretical and Computational Physics, Department of Physics, College of Sciences Botwana International University of Science and Technology, Private Mail Bag 16, Palapye, Botswana

    Conrad Bertrand Tabi

  5. Department of Physics, Faculty of Science, University of Maroua, P.O. Box 46, Maroua, Cameroon

    Alidou Mohamadou

Authors
  1. Conrad Bertrand Tabi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Grégoire Bineli
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Alidou Mohamadou
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Conrad Bertrand Tabi.

Appendix

Appendix

$$\begin{array}{@{}rcl@{}} \begin{array}{llllll} r_{3}&=4[(P_{1} + P_{2})\sin(q)\sin(Q) + P_{3}\sin(2q)\sin(2Q)]\\ r_{2}&=-2\sigma_{2}|y_{0}|^{2}\sigma_{3}|x_{0}|^{2} + 4\sigma_{1}|x_{0}|^{2}P_{1}\cos(q)-4{P_{1}^{2}}\cos(q)^{2}-4\sigma_{1}|x_{0}|^{2}P_{1}\cos(q)\cos(Q)\\ &+8{P_{1}^{2}}\cos^{2}(q)\cos(Q)-4{P_{1}^{2}}\cos^{2}(q)\cos^{2}(Q)+ 16(P_{2} + 2P_{3}\cos(q) + 2P_{3}\cos(q - Q))\sin\left(q-\frac{Q}{2}\right)\\ &\times\left\{P_{1}\sin\left(q-\frac{Q}{2}\right)+(P_{1}+P_{2}+2P_{3}\cos(q)+2P_{3}\cos(q+Q))\sin\left(q+\frac{Q}{2}\right)\right\}\sin^{2}\left(\frac{Q}{2}\right)\\ &+4{P_{1}^{2}}\sin^{2}(q)\sin^{2}(Q)+16P_{1}(P_{2} + 2P_{3}\cos(q) + 2P_{3}\cos(q + Q))\sin(q)\sin^{2}\left(\frac{Q}{2}\right)\\&(\sin(q)+\sin(q + Q))\\ r_{1}&=-4\sigma_{2}|y_{0}|^{2}\sigma_{3}|x_{0}|^{2}P_{1}\cos(q)+4\sigma_{2}|y_{0}|^{2} \sigma_{3}|x_{0}|^{2}P_{1}\cos(q)\cos(Q)\\ &+2\sigma_{2}|y_{0}|^{2}\sigma_{3}|x_{0}|^{2}[\sigma_{1}|x_{0}|^{2}+(P_{2}-P_{1})\cos(q)+P_{3}\cos(2q)+P_{1}\cos(q-Q)\\ &-P_{2}\cos(q+Q)-P_{3}\cos(2(q+Q))]-2\sigma_{2}|y_{0}|^{2}\sigma_{3}|x_{0}|^{2}[\sigma_{1}|x_{0}|^{2}-(P_{1} + P_{2})\cos(q)-P_{3}\cos(2q)\\ &+P_{1}\cos(q+Q)+P_{2}\cos(q+Q)+P_{3}\cos(2(q+Q))]+32P_{1}(P_{2}+2P_{3}\cos(q)+ 2P_{3}\cos(q - Q))\\ &\times\bigg[-P_{2}-(\sigma_{1}|x_{0}|^{2} + P_{3})\cos(q)+(P_{1}+P_{2})\cos(2q)+P_{3}\cos(3q)-P_{1}\cos(Q)-P_{2}\cos(Q)\\ &-2P_{3}\cos(q+Q)+P_{2}\cos(2q+Q)+2P_{3}\cos(3q+Q)-P_{3}\cos(q+2Q)+P_{3}\cos(3q+2Q)\bigg]\\ &\times\sin\left(q-\frac{Q}{2}\right)\sin^{3}\left(\frac{Q}{2}\right)-32P_{1}\left[\sigma_{1}|x_{0}|^{2}\cos(q)+P_{1}(\cos(Q)-\cos(2q))\right]\\ &\times(P_{2}+2P_{3}\cos(q)+2P_{3}\cos(q + Q))\sin\left(q + \frac{Q}{2}\right)\sin^{3}\left(\frac{Q}{2}\right)\\ r_{0}&=\sigma_{3}|x_{0}|^{2}\bigg[-2(\sigma_{2}|y_{0}|^{2})^{2}\sigma_{3}|x_{0}|^{2}-8 \sigma_{2}|y_{0}|^{2}\left(\sigma_{1}|x_{0}|^{2}-P_{1}\cos(q)+P_{1}\cos(q-Q)\right)\\ &\times(P_{2} + 2P_{3}\cos(q) + 2P_{3}\cos(q + Q))\sin\left(q +\frac{Q}{2}\right)\sin\left(\frac{Q}{2}\right)\bigg]+2 \sigma_{2}|y_{0}|^{2}\sigma_{3}|x_{0}|^{2}\\ &\times\bigg(\sigma_{2}|y_{0}|^{2}\sigma_{3}|x_{0}|^{2}+4(\sigma_{1}|x_{0}|^{2}-P_{1}\cos(q)+P_{1}\cos(q+Q))(P_{2}+2P_{3}\cos(q)+2P_{3}\cos(q+Q))\\ &\times\sin\left(q+\frac{Q}{2}\right)\sin\left(\frac{Q}{2}\right)\bigg)+16P_{1}(P_{2}+2P_{3}\cos(q)+2P_{3}\cos(q-Q))\sin\left(q-\frac{Q}{2}\right)\sin\left(\frac{Q}{2}\right)\\ &\times\bigg(\sigma_{2}|y_{0}|^{2}\sigma_{3}|x_{0}|^{2}\cos(q)-\sigma_{2}|y_{0}|^{2}\sigma_{3}|x_{0}|^{2}\cos(q)\cos(Q)+8(\sigma_{1}|x_{0}|^{2}\cos(q)P_{1}(\cos(Q)-\cos(2q)))\\ &\times(P_{2}+2P_{3}\cos(q)+2P_{3}\cos(q+Q))\sin\left(q+\frac{Q}{2}\right)\sin^{3}\left(\frac{Q}{2}\right)\bigg) \end{array} \end{array} $$

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Tabi, C.B., Bineli, G. & Mohamadou, A. Energy patterns in twist-opening models of DNA with solvent interactions. J Biol Phys 41, 391–408 (2015). https://doi.org/10.1007/s10867-015-9386-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10867-015-9386-z

Keywords

Search

Navigation