Skip to main content
SpringerLink
Log in

General model of microtubules

  • Original Paper
  • Published:
Nonlinear Dynamics Aims and scope Submit manuscript

Abstract

In the present work, we deal with nonlinear dynamics of microtubules. A new model, describing nonlinear dynamics of microtubules, is introduced. Its advantages over two existing models are demonstrated. We show that dynamics of microtubules can be explained in terms of kink solitons. Also, circumstances yielding to either subsonic or supersonic solitons are discussed.

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

Similar content being viewed by others

References

  1. Amos, L.A.: Focusing—in on microtubules. Curr. Opin. Struct. Biol. 10, 236–241 (2000)

    Article  Google Scholar 

  2. Satarić, M.V., Tuszyński, J.A., Žakula, R.B.: Kinklike excitations as an energy-transfer mechanism in microtubules. Phys. Rev. E 48, 589–597 (1993)

    Article  Google Scholar 

  3. Zdravković, S., Satarić, M.V., Zeković, S.: Nonlinear dynamics of microtubules—a longitudinal model. Europhys. Lett. 102, 38002 (2013)

    Article  Google Scholar 

  4. Satarić, M.V., Tuszyński, J.A.: Relationship between the nonlinear ferroelectric and liquid crystal models for microtubules. Phys. Rev. E 67, 011901 (2003)

    Article  Google Scholar 

  5. Krebs, A., Goldie, K.N., Hoenger, A.: Complex formation with kinesin motor domains affects the structure of microtubules. J. Mol. Biol. 335, 139–153 (2004)

    Article  Google Scholar 

  6. Zdravković, S., Kavitha, L., Satarić, M.V., Zeković, S., et al.: Modified extended tanh-function method and nonlinear dynamics of microtubules. Chaos Solitons Fract. 45, 1378–1386 (2012)

    Article  MATH  Google Scholar 

  7. Zdravković, S., Zeković, S., Bugay, A.N., Satarić, M.V.: Localized modulated waves and longitudinal model of microtubules. Appl. Math. Comput. 285, 248–259 (2016)

    MathSciNet  Google Scholar 

  8. Zdravković, S., Satarić, M.V., Maluckov, A., Balaž, A.: A nonlinear model of the dynamics of radial dislocations in microtubules. Appl. Math. Comput. 237, 227–237 (2014)

    MathSciNet  MATH  Google Scholar 

  9. Drabik, P., Gusarov, S., Kovalenko, A.: Microtubule stability studied by three-dimensional molecular theory of solvation. Biophys. J. 92, 394–403 (2007)

    Article  Google Scholar 

  10. Nogales, E., Whittaker, M., Milligan, R.A., Downing, K.H.: High-resolution model of the microtubule. Cell 96, 79–88 (1999)

    Article  Google Scholar 

  11. Ali, A.H.A.: The modified extended tanh-function method for solving coupled MKdV and coupled Hirota–Satsuma coupled KdV equations. Phys. Lett. A 363, 420–425 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  12. El-Wakil, S.A., Abdou, M.A.: New exact travelling wave solutions using modified extended tanh-function method. Chaos Solitons Fract. 31, 840–852 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  13. Kavitha, L., Akila, N., Prabhu, A., Kuzmanovska-Barandovska, O., et al.: Exact solitary solutions of an inhomogeneous modified nonlinear Schrödinger equation with competing nonlinearities. Math. Comput. Model. 53, 1095–1110 (2011)

    Article  MATH  Google Scholar 

  14. Sekulić, D.L., Satarić, M.V., Živanov, M.B.: Symbolic computation of some new nonlinear partial differential equations of nanobiosciences using modified extended tanh-function method. Appl. Math. Comput. 218, 3499–3506 (2011)

    MathSciNet  MATH  Google Scholar 

  15. Pokorný, J., Jelínek, J., Trkal, V., Lamprecht, I., et al.: Vibrations in microtubules. J. Biol. Phys. 23, 171–179 (1997)

    Article  Google Scholar 

  16. Havelka, D., Cifra, M., Kučera, O., Pokorný, J., et al.: High-frequency electric field and radiation characteristics of cellular microtubule network. Theor. Biol. 286, 31–40 (2011)

    Article  Google Scholar 

  17. Schoutens, J.E.: Dipole–dipole interactions in microtubules. J. Biol. Phys. 31, 35–55 (2005)

    Article  Google Scholar 

  18. Tuszyński, J.A., Brown, J.A., Crawford, E., Carpenter, E.J., et al.: Molecular dynamics simulations of tubulin structure and calculations of electrostatic properties of microtubules. Math. Comput. Model. 41, 1055–1070 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  19. Cifra, M., Pokorný, J., Havelka, D., Kučera, O.: Electric field generated by axial longitudinal vibration modes of microtubule. BioSystems 100, 122–131 (2010)

    Article  Google Scholar 

  20. Hunyadi, V., Chretien, D., Flyvbjerg, H., Janosi, I.M.: Why is the microtubule lattice helical? Biol. Cell. 99, 117–128 (2007)

    Article  Google Scholar 

  21. Sekulić, D.L., Satarić, B.M., Zdravković, S., Bugay, A.N., et al.: Nonlinear dynamics of C-terminal tails in cellular microtubules. Chaos 26, 073119 (2016)

    Article  MathSciNet  Google Scholar 

  22. Guigas, G., Kalla, C., Weiss, M.: Probing the nanoscale viscoelasticity of intracellular fluids in living cells. Biophys. J. 93, 316–323 (2007)

    Article  Google Scholar 

  23. Goychuk, I.: Fractional-time random walk subdiffusion and anomalous transport with finite mean residence times; faster, not slower. Phys. Rev. E 86, 021113 (2012)

    Article  Google Scholar 

  24. Sekulić, D.L., Satarić, B.M., Tuszyński, J.A., Satarić, M.V.: Nonlinear ionic pulses along microtubules. Eur. Phys. J. E 34, 49–59 (2011)

    Article  Google Scholar 

  25. Zdravković, S., Maluckov, A., Đekić, M., Kuzmanović, S., et al.: Are microtubules discrete or continuum systems? Appl. Math. Comput. 242, 353–360 (2014)

    MathSciNet  MATH  Google Scholar 

  26. Zdravković, S., Bugay, A.N., Aru, G.F., Maluckov, A.: Localized modulated waves in microtubules. Chaos 24, 023139 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  27. Zdravković, S., Bugay, A.N., Parkhomenko, AYu.: Application of Morse potential in nonlinear dynamics of microtubules. Nonlinear Dyn. 90, 2841–2849 (2017)

    Article  MathSciNet  Google Scholar 

  28. Kudryashov, N.A.: Exact solitary waves of the Fisher equation. Phys. Lett. A 342, 99–106 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  29. Kudryashov, N.A.: Simplest equation method to look for exact solutions of nonlinear differential equations. Chaos Solitons Fract. 24, 1217 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  30. Kudryashov, N.A., Loguinova, N.B.: Extended simplest equation method for nonlinear differential equations. Appl. Math. Comput. 205, 396–402 (2008)

    MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

This work was supported by funds from Serbian Ministry of Education, Sciences and Technological Development (Grants No. III45010), Project of AP Vojvodina No. 114-451-2708/2016-03 and Serbian Academy of Sciences and Arts.

Author information

Authors and Affiliations

  1. Institut za Nuklearne Nauke Vinča, Univerzitet u Beogradu, Beograd, 11001, Serbia

    Slobodan Zdravković

  2. Fakultet Tehničkih Nauka, Univerzitet u Novom Sadu, Novi Sad, 21000, Serbia

    Miljko V. Satarić

  3. Fizički Fakultet, Univerzitet u Beogradu, Beograd, 11001, Serbia

    Vladimir Sivčević

Authors
  1. Slobodan Zdravković
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Miljko V. Satarić
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Vladimir Sivčević
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Slobodan Zdravković.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zdravković, S., Satarić, M.V. & Sivčević, V. General model of microtubules. Nonlinear Dyn 92, 479–486 (2018). https://doi.org/10.1007/s11071-018-4069-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-018-4069-5

Keywords

Search

Navigation