Skip to main content
SpringerLink
Log in

Mechanical Behavior and Physical Properties of Protein Microtubules in Living Cells Using the Nonlocal Beam Theory

  • Published:
Physical Mesomechanics Aims and scope Submit manuscript

Abstract

A biomechanical model for vibrational analysis with characteristics of protein microtubules based on the nanobeam shape inside the cellular structure is presented. Young’s modulus of protein microtubules and unexplained length-dependent flexural rigidity are studied using a higher-order nonlocal shear deformation theory. The governing equations are provided by employing the principle of virtual work. The protein microtubules are considered simply supported for all numerical studies. The obtained results are critically discussed together with the theories as well as demonstrated in each case graphically.

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.

Similar content being viewed by others

REFERENCES

  1. Gerthoffer, W.T., Migration of Airway Smooth Muscle Cells, Proc. Am. Thorac. Soc., 2008, vol. 5, no. 1, pp. 97–105.

    Article  Google Scholar 

  2. Tang, D.D., Critical Role of Actin-Associated Proteins in Smooth Muscle Contraction, Cell Proliferation, Airway Hyper Responsiveness and Airway Remodeling, Respir. Res., 2015, vol. 16, p. 134.

    Article  Google Scholar 

  3. Cleary, R.A., Wang, R., Waqar, O., Singer, H.A., and Tang, D.D., Role of c-Abl Tyrosine Kinase in Smooth Muscle Cell Migration, Am. J. Physiol. Cell. Physiol., 2014, vol. 306, pp. 753–761.

    Article  Google Scholar 

  4. Tounsi, A., Heireche, H., and Benhassaini, H., Vibration and Length-Dependent Flexural Rigidity of Protein Microtubules Using Higher Order Shear Deformation Theory, J. Theor. Biol., 2010, vol. 266, no. 2, pp. 250–255.

    Article  ADS  Google Scholar 

  5. Schaap, I.A., Carrasco, C., de Pablo, P.J., MacKintosh, F.C., and Schmidt, C.F., Elastic Response, Buckling, and Instability of Microtubules under Radial Indentation, Biophys. J., 2006, vol. 91, no. 4, pp. 1521–1531.

    Article  ADS  Google Scholar 

  6. Wang, N., Naruse, K., Stamenović, D., Fredberg, J.J., Mijailovich, S.M., Tolić-Nørrelykke, I.M., Polte, T., Mannix, R., and Ingber, D.E., Mechanical Behavior in Living Cells Consistent with the Tensegrity Model, Proc. Nat. Acad. Sci., 2001, vol. 98, no. 14, pp. 7765–7770.

    Article  ADS  Google Scholar 

  7. Pirentis, A.P. and Lazopoulos, K.A., On the Singularities of a Constrained (Incompressible-Like) Tensegrity-Cytoskeleton Model under Equitriaxial Loading, Int. J. Solids Struct., 2010, vol. 47, no. 6, pp. 759–767.

    Article  Google Scholar 

  8. Hawkins, T., Mirigian, M., Yasar, M.S., and Ross, J.L., Mechanics of Microtubules, J. Biomech., 2010, vol. 43, no. 1, pp. 23–30.

    Article  Google Scholar 

  9. Li, T., A Mechanics Model of Microtubule Buckling in Living Cells, J. Biomechanics, 2008, vol. 41, no. 8, pp. 1722–1729.

    Article  Google Scholar 

  10. Shi, Y.J., Guo, W.L., and Ru, C.Q., Relevance of Timoshenko-Beam Model to Microtubules of Low Shear Modulus, Phys. E. Low-Dimens. Syst. Nanostruct., 2008, vol. 41, no. 2, pp. 213–219.

    Article  ADS  Google Scholar 

  11. Wagner, O.I., Rammensee, S., Korde, N., Wen, Q., Leterrier, J.F., and Janmey, P.A., Softness, Strength and Self-Repair in Intermediate Filament Networks, Exp. Cell Res., 2007, vol. 313, no. 10, pp. 2228–2235.

    Article  Google Scholar 

  12. Mehrbod, M. and Mofrad, M.R., On the Significance of Microtubule Flexural Behavior in Cytoskeletal Mechanics, PLoS one, 2011, vol. 6, no. 10, p. e25627.

  13. Aydogdu, M., A General Nonlocal Beam Theory: Its Application to Nanobeam Bending, Buckling and Vibration, Phys. E. Low-Dimens. Syst. Nanostruct., 2009, vol. 41, no. 9, pp. 1651–1655.

    Article  ADS  Google Scholar 

  14. Ishida, T., Thitamadee, S., and Hashimoto, T., Twisted Growth and Organization of Cortical Microtubules, J. Plant Res., 2007, vol. 120, no. 1, pp. 61–70.

    Article  Google Scholar 

  15. Lata, P. and Kaur, H., Interactions in a Homogeneous Isotropic Modified Couple Stress Thermoelastic Solid with Multi-Dual-Phase-Lag Heat Transfer and Two Temperature, Steel Compos. Struct., 2021, vol. 38, no. 2, pp. 213–221.

    Google Scholar 

  16. Boussoula, A., Boucham, B., Bourada, M., Bourada, F., Tounsi, A., Bousahla, A.A., and Tounsi, A., A Simple nth-Order Shear Deformation Theory for Thermomechanical Bending Analysis of Different Configurations of FG Sandwich Plates, Smart Struct. Syst., 2020, vol. 25, no. 2, pp. 197–218.

  17. Al-Basyouni, K.S., Ghandourah, E., Mostafa, H.M., and Algarni, A., Effect of the Rotation on the Thermal Stress Wave Propagation in Non-Homogeneous Viscoelastic Body, Geomech. Eng., 2020, vol. 21, no. 1, pp. 1–9.

    Google Scholar 

  18. Avcar, M., Free Vibration of Imperfect Sigmoid and Power Law Functionally Graded Beams, Steel Compos. Struct., 2019, vol. 30, no. 6, pp. 603–615.

    Google Scholar 

  19. Sahla, M., Saidi, H., Draiche, K., Bousahla, A.A., Bourada, F., and Tounsi, A., Free Vibration Analysis of Angle-Ply Laminated Composite and Soft Core Sandwich Plates, Steel Compos. Struct., 2019, vol. 33, no. 5, pp. 663–679.

    Google Scholar 

  20. Abualnour, M., Chikh, A., Hebali, H., Kaci, A., Tounsi, A., Bousahla, A.A., and Tounsi, A., Thermomechanical Analysis of Antisymmetric Laminated Reinforced Composite Plates Using a New Four Variable Trigonometric Refined Plate Theory, Comput. Concret., 2019, vol. 24, no. 6, pp. 489–498.

    Google Scholar 

  21. Belbachir, N., Draich, K., Bousahla, A.A., Bourada, M., Tounsi, A., and Mohammadimehr, M., Bending Analysis of Anti-Symmetric Cross-Ply Laminated Plates under Nonlinear Thermal and Mechanical Loadings, Steel Compos. Struct., 2019, vol. 33, no. 1, pp. 81–92.

    Google Scholar 

  22. Chaabane, L.A., Bourada, F., Sekkal, M., Zerouati, S., Zaoui, F.Z., Tounsi, A., Derras, A., Bousahla, A.A., Tounsi, A., Analytical Study of Bending and Free Vibration Responses of Functionally Graded Beams Resting on Elastic Foundation, Struct. Eng. Mech., 2019, vol. 71, no. 2, pp. 185–196. https://doi.org/10.12989/sem.2019.71.2.185

    Article  Google Scholar 

  23. Rakrak, K., Zidour, M., Heireche, H., Bousahla, A.A., and Chemi, A., Free Vibration Analysis of Chiral Double-Walled Carbon Nanotube Using Nonlocal Elasticity Theory, Adv. Nano Res., 2016, vol. 4, no. 1, p. 031.

    Article  Google Scholar 

  24. Ahmed, R.A., Fenjan, R.M., and Faleh, N.M., Analyzing Post-Buckling Behavior of Continuously Graded FG Nanobeams with Geometrical Imperfections, Geomech. Eng., 2019, vol. 17, no. 2, pp. 175–180.

    Google Scholar 

  25. Semmah, A., Heireche, H., Bousahla, A.A., Tounsi, A., Thermal Buckling Analysis of SWBNNT on Winkler Foundation by Nonlocal FSDT, Adv. Nano Res., 2019, vol. 7, no. 2, p. 89.

    Google Scholar 

  26. Schaap, I.A., Carrasco, C., de Pablo, P.J., MacKintosh, F.C., and Schmidt, C.F., Elastic Response, Buckling, and Instability of Microtubules under Radial Indentation, Biophys. J., 2006, vol. 91, no. 4, pp. 1521–1531.

    Article  ADS  Google Scholar 

  27. Felgner, H., Frank, R., and Schliwa, M., Flexural Rigidity of Microtubules Measured with the Use of Optical Tweezers, J. Cell Sci., 1996, vol. 109, no. 2, pp. 509–516.

    Article  Google Scholar 

  28. Kollar, L.P. and Springer, G.S., Mechanics of Composite Structures, Cambridge: Cambridge University Press, 2003.

  29. Heussinger, C., Bathe, M., and Frey, E., Statistical Mechanics of Semiflexible Bundles of Wormlike Polymer Chains, Phys. Rev. Lett., 2007, vol. 99, no. 4, p. 048101.

    Article  ADS  Google Scholar 

  30. Hunyadi, V., Chretien, D., and Janosi, I.M., Mechanical Stress Induced Mechanism of Microtubule Catastrophes, J. Molec. Biol., 2005, vol. 348, no. 4, pp. 927–938.

    Article  Google Scholar 

  31. Alberts, B., Bray, D., Hopkin, K., Johnson, A.D., Lewis, J., Raff, M., Roberts, K., and Walter, P., Essential Cell Biology, New York: Garland Publishing, 2015.

  32. Gittes, F., Mickey, B., Nettleton, J., and Howard, J., Flexural Rigidity of Microtubules and Actin Filaments Measured from Thermal Fluctuations in Shape, J. Cell Biol., 1993, vol. 120, no. 4, pp. 923–934. https://doi.org/10.1083/jcb.120.4.923

    Article  Google Scholar 

  33. Keller, P.J., Pampaloni, F., Lattanzi, G., and Stelzer, E.H., Three-dimensional microtubule behavior in Xenopus egg extracts reveals four dynamic states and state-dependent elastic properties, Biophys. J., 2008, vol. 95, no. 3, pp. 1474–1486. https://doi.org/10.1529/biophysj.107.128223

    Article  Google Scholar 

  34. Reddy, J.N. and Pang, S.D., Nonlocal Continuum Theories of Beams for the Analysis of Carbon Nanotubes, J. Appl. Phys., 2008, vol. 103, no. 2, p. 023511.

    Article  Google Scholar 

  35. Shen, H.S., Nonlocal Shear Deformable Shell Model for Torsional Buckling and Postbuckling of Microtubules in Thermal Environments, Mech. Res. Comm., 2013, vol. 54, pp. 83–95.

    Article  Google Scholar 

  36. Desai, A. and Mitchison, T.J., Microtubule Polymerization Dynamics, Annual Rev. Cell Develop. Biol., 1997, vol. 1, pp. 83–117.

    Article  Google Scholar 

  37. Ghandourah, E., Nonlocal Elasticity Theory for the Mechanical Behavior of Protein Microtubules, Phys. Mesomech., 2021, vol. 24, no. 3, pp. 319–325. https://doi.org/10.1134/S1029959921030103

    Article  Google Scholar 

  38. Kurachi, M., Hoshi, M., and Tashiro, H., Buckling of a Single Microtubule by Optical Trapping Forces: Direct Measurement of Microtubule Rigidity, Cell Motil. Cytoskeleton., 1995, vol. 30, no. 3, pp. 221–228.

    Article  Google Scholar 

  39. Alwabli, A.S., Kaci, A., Bellifa, H., Bousahla, A.A., Tounsi, A., Alzahrani, D.A., Abulfaraj, A.A., Bourada, F., Benrahou, K.H., Tounsi, A., and Mahmoud, S.R., The Nanoscale Buckling Properties of Isolated Protein Microtubules Based on Modified Strain Gradient Theory and a New Single Variable Trigonometric Beam Theory, Adv. Nano Res., 2021, vol. 10, no. 1, p. 15.

    Google Scholar 

  40. Mahmoud, S.R., Al-Solami, H.M., Alkenani, N., Alhebshi, A.M.S., Alwabli, A.S., and Bahieldin, A., Membrane, Water Treatment, 2020, vol. 11, no. 6, p. 399.

    Google Scholar 

  41. Ramady, A., Mahmoud, S.R., and Atia, H.A., A Theoretical Approach in 2D-Space with Applications of the Periodic Wave Solutions in the Elastic Body, Membrane Water Treatment, 2020, vol. 11, no. 4, pp. 295–302. https://doi.org/10.12989/mwt.2020.11.4.295

    Article  Google Scholar 

  42. Ramady, A., Dakhel, B., Balubaid, M., and Mahmoud, S.R., A Mathematical Approach for the Effect of the Rotation on Thermal Stresses in the Piezo-Electric Homogeneous Material, Comput. Concret., 2020, no. 5, pp. 471–478.

    Google Scholar 

  43. Benmansour, D.L., Kaci, A., Bousahla, A.A., Heireche, H., Tounsi, A., Alwabli, A.S., Alhebshi, A.M., Al-ghmady, K., and Mahmoud, S.R., The Nanoscale Bending and Dynamic Properties of Isolated Protein Microtubules Based on Modified Strain Gradient Theory, Adv. Nano Res., 2019, vol. 7, no. 6, pp. 443–457. https://doi.org/10.12989/anr.2019.7.6.443

    Article  Google Scholar 

  44. Al-Basyouni, K.S. and Mahmoud, S.R., Effect of the Magnetic Field, Initial Stress, Rotation, and Nonhomogeneity on Stresses in Orthotropic Material, Phys. Mesomech., 2021, vol. 24, no. 3, pp. 303–310. https://doi.org/10.1134/S1029959921030085

    Article  Google Scholar 

  45. Al-Basyouni, K.S., Dakhel, B., Ghandourah, E., and Ali Algarni, An Analytical Solution for the Problem of Stresses in Magneto-Piezoelectric Thermoelastic Material under the Influence of Rotation, Phys. Mesomech., 2020, vol. 23, no. 4, pp. 362–368. https://doi.org/10.1134/S1029959920040116

    Article  Google Scholar 

Download references

Funding

This work was funded by the Deanship of Scientific Research (DSR) at King Abdulaziz University, Jeddah (grant no. G-655-247-1439). The authors are grateful to the DSR for financial and technical support.

Author information

Authors and Affiliations

  1. Department of Biological Sciences, Faculty of Science, King Abdulaziz University, 21589, Jeddah, Saudi Arabia

    A. M. S. Alhebshi & H. M. Al-Solami

  2. Mathematics and Theoretical Physics Department, NRC, AEA, Inshas, 13759, Cairo, Egypt

    A. M. Metwally

  3. Mathematics Department, Faculty of Science, King Abdulaziz University, 21589, Jeddah, Saudi Arabia

    K. S. Al-Basyouni

  4. GRC Department, Applied College, King Abdulaziz University, 21589, Jeddah, Saudi Arabia

    S. R. Mahmoud

  5. Department of Biological Sciences, Rabigh College of Science and Arts, King Abdulaziz University, 21589, Jeddah, Saudi Arabia

    A. S. Alwabli

Authors
  1. A. M. S. Alhebshi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. M. Metwally
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. K. S. Al-Basyouni
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. S. R. Mahmoud
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. H. M. Al-Solami
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. A. S. Alwabli
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to S. R. Mahmoud.

Additional information

Translated from Fizicheskaya Mezomekhanika, 2021, Vol. 24, No. 6, pp. 99–102.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Alhebshi, A.M.S., Metwally, A.M., Al-Basyouni, K.S. et al. Mechanical Behavior and Physical Properties of Protein Microtubules in Living Cells Using the Nonlocal Beam Theory. Phys Mesomech 25, 181–186 (2022). https://doi.org/10.1134/S1029959922020096

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1029959922020096

Keywords:

Search

Navigation