Skip to main content
SpringerLink
Log in

Influence of surface parameters and Poisson’s ratio on the buckling growth rate of a microtubule system using the modified couple stress theory

  • Published:
Pramana Aims and scope Submit manuscript

Abstract

We developed and obtained close-form solutions for the buckling growth rate of microtubule (MT) bundles using the Timoshenko beam theory. We took into consideration the surface effects and the Poisson’s ratio of the microtubules surrounded by neighbouring filaments in the viscous cytosol. We developed the motion equation by using the modified couple stress theory (MCST) which will take into account the small-scale effects of the microtubules. We then proceeded by studying the effects of various parameters on the buckling growth rate of microtubule bundles. Our results show that the internal material length scale parameter has a decreasing effect on the buckling growth rate of the microtubule bundle. And as microtubule added in the bundle increases, the buckling growth rate reduces further due to the effects of the surrounding microtubule-associated proteins (MAPs). On the contrary, the Poisson’s ratio has an increasing effect on the value of the buckling growth rate of the microtubule bundle. We also investigated the effects of other parameters such as surface energy on the buckling growth rates of microtubule bundles and showed the validity of our model by comparing our results with those obtained by previous researchers.

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
Fig. 11

Similar content being viewed by others

References

  1. D Boal and D H Boal, Mechanics of the cell (Cambridge University Press, 2012)

  2. J Howard and R Clark, Appl. Mech. Rev. 55, 39 (2002)

  3. F Gittes, B Mickey, J Nettleton and J Howard, J. Cell Biol. 120, 923 (1993)

    Article  Google Scholar 

  4. B Alberts, A Johnson, J Lewis, M Raff, K Roberts and P Walter, Mol. Biol. Cell 4 (2002)

  5. J M Berg, Chem. Eng. News 79, 130 (2001)

    Google Scholar 

  6. D Bray, Cell movements: From molecules to motility, 2nd edn (Routledge, New York, 2000)

    Book  Google Scholar 

  7. M A Jordan and L Wilson, Nat. Rev. Cancer 4, 253 (2004)

    Article  Google Scholar 

  8. M C Ekosso, A J Fotue, S C Kenfack, H Fotsin and L C Fai, Mod. Phys. Lett. B 33, 1950433 (2019)

    Article  ADS  Google Scholar 

  9. C P Brangwynne, F C MacKintosh, S Kumar, N A Geisse, J Talbot, L Mahadevan, K K Parker, D E Ingber and D A Weitz, J. Cell Biol. 173, 733 (2006)

    Article  Google Scholar 

  10. T Li, J. Biomech. 41, 1722 (2008)

    Article  Google Scholar 

  11. S R Heidemann, S Kaech, R E Buxbaum and A Matus, J. Cell Biol. 145, 109 (1999)

    Article  Google Scholar 

  12. D J Odde, L Ma, A H Briggs, A DeMarco and M W Kirschner, J. Cell Sci. 112, 3283 (1999)

    Article  Google Scholar 

  13. N Wang, K Naruse, D Stamenović, J J Fredberg, S M Mijailovich, I M Tolić-Nørrelykke, T Polte, R Mannix and D E Ingber, Proc. Natl. Acad. Sci. USA 98, 7765 (2001)

    Article  ADS  Google Scholar 

  14. A Tounsi, H Heireche, H Benhassaini and M Missouri, J. Theor. Biol. 266, 250 (2010)

    Article  ADS  Google Scholar 

  15. Y Fu and J Zhang, Physica E 42, 1741 (2010)

    Article  ADS  Google Scholar 

  16. A Ghorbanpour Arani, M Abdollahian and M H Jalaei, J. Theor. Biol. 367, 29 (2015)

    Article  Google Scholar 

  17. S K Park and X-L Gao, J. Micromech. Microeng. 16, 2355 (2006)

    Article  ADS  Google Scholar 

  18. B Akgöz and Ö Civalek, Curr. Appl. Phys. 11, 1133 (2011)

    Article  ADS  Google Scholar 

  19. F Ebrahimi and M R Barati, Compos. Struct. 159, 174 (2017)

    Article  Google Scholar 

  20. O Civalek and B Akgoz, Transaction B: Mech. Eng. 17, 367 (2010)

    Google Scholar 

  21. M Danesh, A Farajpour and M Mohammadi, Mech. Res. Commun. 39, 23 (2012)

    Article  Google Scholar 

  22. Y Gao and F-M Lei, Biochem. Biophys. Res. Commun. 387, 467 (2009)

    Article  Google Scholar 

  23. W Chen, H Li and X Wang, Proc. Inst. Mech. Eng. Part C J. Mech. Eng. Sci. 227, 2377 (2013)

    Article  Google Scholar 

  24. H M Ma, X-L Gao and J N Reddy, J. Mech. Phys. Solids 56, 3379 (2008)

    Article  ADS  MathSciNet  Google Scholar 

  25. A Imani Aria and H Biglari, Appl. Math. Comput. 321, 313 (2018)

    MathSciNet  Google Scholar 

  26. A Farajpour and A Rastgoo, Results Phys. 7, 1367 (2017)

    Article  ADS  Google Scholar 

  27. A Farajpour, A Rastgoo and M Mohammadi, Mech. Res. Commun. 57, 18 (2014)

    Article  Google Scholar 

  28. H Heireche, A Tounsi, H Benhassaini, A Benzair, M Bendahmane, M Missouri and S Mokadem, Physica E 42, 2375 (2010)

    Article  ADS  Google Scholar 

  29. S K Park and X-L Gao, Z. Angew. Math. Phys. 59, 904 (2008)

    Google Scholar 

  30. F Yang, A C M Chong, D C C Lam and P Tong, Int. J. Solids Struct. 39, 2731 (2002)

    Article  Google Scholar 

  31. J N Reddy and J N Reddy, Theory and analysis of elastic plates and shells (CRC Press, Boca Raton, 2007)

    Google Scholar 

  32. D J Steigmann, IMA J. Appl. Math. 48, 195 (1992)

    Article  ADS  MathSciNet  Google Scholar 

  33. X-L Gao and S Mall, Int. J. Solids Struct. 38, 855 (2001)

    Article  Google Scholar 

  34. S Timoshenko, Vibration problems in engineering (D Van Nostrand Company, 1937)

  35. S Hameroff and R Penrose, Math. Comput. Simul. 40, 453 (1996)

    Article  Google Scholar 

  36. Ö Civalek and Ç Demir, Appl. Math. Model. 35, 2053 (2011)

    Article  MathSciNet  Google Scholar 

  37. A S Zeiger and B E Layton, Biophys. J. 95, 3606 (2008)

    Article  ADS  Google Scholar 

  38. M Kurachi, M Hoshi and H Tashiro, Cell Motil. 30, 221 (1995)

    Article  Google Scholar 

  39. F Pampaloni, G Lattanzi, A Jonáš, T Surrey, E Frey and E-L Florin, Proc. Natl. Acad. Sci. 103, 10248 (2006)

    Article  ADS  Google Scholar 

  40. H Li, J Xiong and X Wang, Eur. J. Mech.-A Solids 39, 11 (2013)

    Article  ADS  MathSciNet  Google Scholar 

  41. X Wang, W D Yang and J T Xiong, Physica E 56, 342 (2014)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Condensed Matter and Nanomaterials, Faculty of Science, Department of Physics, University of Dschang, P.O. Box 67, Dschang, Cameroon

    C KENFACK-SADEM, S N WOPUNGHWO, W A NGANFO, M C EKOSSO, A J FOTUÉ & L C FAI

Authors
  1. C KENFACK-SADEM
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. S N WOPUNGHWO
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. W A NGANFO
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. M C EKOSSO
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. A J FOTUÉ
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. L C FAI
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

KENFACK-SADEM, C., WOPUNGHWO, S.N., NGANFO, W.A. et al. Influence of surface parameters and Poisson’s ratio on the buckling growth rate of a microtubule system using the modified couple stress theory. Pramana - J Phys 96, 16 (2022). https://doi.org/10.1007/s12043-021-02244-4

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s12043-021-02244-4

Keywords

PACS

Search

Navigation