Influence of taxol and CNTs on the stability analysis of protein microtubules

Document Type: Research Paper

Authors

1 Faculty of Health and Medical Sciences, Adelaide Medical School, University of Adelaide, Adelaide, Australia

2 Borjavaran Center of Applied Science and Technology, University of Applied Science and Technology, Tehran, Iran

Abstract

Microtubules are used as targets for anticancer drugs due to their crucial role in the process of mitosis. Recent studies show that carbon nanotubes (CNTs) can be classified as microtubule-stabilizing agents as they interact with protein microtubules (MTs), leading to interference in the mitosis process. CNTs hold a substantial promising application in cancer therapy in conjunction with other cancer treatments such as radiotherapy and chemotherapy. In the current study, a size-dependent model is developed for the stability analysis of CNT-stabilized microtubules under radial and axial loads. A nonlocal shell theory with strain gradient effects is employed to take size influences into account. Moreover, Van der Waals interactions between CNTs and MTs are simulated. An excellent agreement is observed between the present model and reported data from experiments on protein MTs. In addition, the effects of taxol, as another stabilizing agent, on the stability of microtubules are studied. It is found that both nonlocal and strain gradient effects are essential to accurately obtain the stability capacity of MTs. Furthermore, CNTs have an increasing effect on the critical loads of microtubules while the critical loads reduce in the presence of taxol.

Keywords

Main Subjects


[1]           Z. Liu, S. Tabakman, K. Welsher, H. Dai, Carbon nanotubes in biology and medicine: in vitro and in vivo detection, imaging and drug delivery, Nano research, Vol. 2, No. 2, pp. 85-120, 2009.

[2]           Z. Liu, W. Cai, L. He, N. Nakayama, K. Chen, X. Sun, X. Chen, H. Dai, In vivo biodistribution and highly efficient tumour targeting of carbon nanotubes in mice, Nature nanotechnology, Vol. 2, No. 1, pp. 47, 2007.

[3]           P.-C. Lee, Y.-C. Chiou, J.-M. Wong, C.-L. Peng, M.-J. Shieh, Targeting colorectal cancer cells with single-walled carbon nanotubes conjugated to anticancer agent SN-38 and EGFR antibody, Biomaterials, Vol. 34, No. 34, pp. 8756-8765, 2013.

[4]           S. Peretz, O. Regev, Carbon nanotubes as nanocarriers in medicine, Current Opinion in Colloid & Interface Science, Vol. 17, No. 6, pp. 360-368, 2012.

[5]           N. M. Bardhan, D. Ghosh, A. M. Belcher, Carbon nanotubes as in vivo bacterial probes, Nature communications, Vol. 5, pp. 4918, 2014.

[6]           A. Sharma, S. Hong, R. Singh, J. Jang, Single-walled carbon nanotube based transparent immunosensor for detection of a prostate cancer biomarker osteopontin, Analytica chimica acta, Vol. 869, pp. 68-73, 2015.

[7]           L. García-Hevia, F. Fernández, C. Grávalos, A. García, J. C. Villegas, M. L. Fanarraga, Nanotube interactions with microtubules: implications for cancer medicine, Nanomedicine, Vol. 9, No. 10, pp. 1581-1588, 2014.

[8]           L. Rodriguez-Fernandez, R. Valiente, J. Gonzalez, J. C. Villegas, M. n. L. Fanarraga, Multiwalled carbon nanotubes display microtubule biomimetic properties in vivo, enhancing microtubule assembly and stabilization, ACS nano, Vol. 6, No. 8, pp. 6614-6625, 2012.

[9]           F. Gittes, B. Mickey, J. Nettleton, J. Howard, Flexural rigidity of microtubules and actin filaments measured from thermal fluctuations in shape, The Journal of cell biology, Vol. 120, No. 4, pp. 923-934, 1993.

[10]         J. M. Berg, J. Tymoczko, L. Stryer, Glycolysis is an energy-conversion pathway in many organisms, Biochemistry. 5th ed. New York: WH Freeman, 2002.

[11]         J. A. Kaltschmidt, A. H. Brand, Asymmetric cell division: microtubule dynamics and spindle asymmetry, J Cell Sci, Vol. 115, No. 11, pp. 2257-2264, 2002.

[12]         H. Lodish, A. Berk, S. Zipursky, P. Matsudaira, D. Baltimore, J. Darnell, Collagen: the fibrous proteins of the matrix, Molecular Cell Biology, Vol. 4, 2000.

[13]         K. Dastani, M. Moghimi Zand, A. Hadi, Dielectrophoretic effect of nonuniform electric fields on the protoplast cell, Journal of Computational Applied Mechanics, Vol. 48, No. 1, pp. 1-14, 2017.

[14]         S. Suresh, Biomechanics and biophysics of cancer cells, Acta Materialia, Vol. 55, No. 12, pp. 3989-4014, 2007.

[15]         F. Pampaloni, G. Lattanzi, A. Jonáš, T. Surrey, E. Frey, E.-L. Florin, Thermal fluctuations of grafted microtubules provide evidence of a length-dependent persistence length, Proceedings of the National Academy of Sciences, Vol. 103, No. 27, pp. 10248-10253, 2006.

[16]         M. Kurachi, M. Hoshi, H. Tashiro, Buckling of a single microtubule by optical trapping forces: direct measurement of microtubule rigidity, Cell motility and the cytoskeleton, Vol. 30, No. 3, pp. 221-228, 1995.

[17]         A. I. Aria, H. Biglari, Computational vibration and buckling analysis of microtubule bundles based on nonlocal strain gradient theory, Applied Mathematics and Computation, Vol. 321, pp. 313-332, 2018.

[18]         Q. Wang, V. Varadan, Application of nonlocal elastic shell theory in wave propagation analysis of carbon nanotubes, Smart Materials and Structures, Vol. 16, No. 1, pp. 178, 2007.

[19]         M. Ece, M. Aydogdu, Nonlocal elasticity effect on vibration of in-plane loaded double-walled carbon nano-tubes, Acta Mechanica, Vol. 190, No. 1-4, pp. 185-195, 2007.

[20]         M. Danesh, A. Farajpour, M. Mohammadi, Axial vibration analysis of a tapered nanorod based on nonlocal elasticity theory and differential quadrature method, Mechanics Research Communications, Vol. 39, No. 1, pp. 23-27, 2012.

[21]         M. Aydogdu, I. Elishakoff, On the vibration of nanorods restrained by a linear spring in-span, Mechanics Research Communications, Vol. 57, pp. 90-96, 2014.

[22]         M. Z. Nejad, A. Hadi, A. Rastgoo, Buckling analysis of arbitrary two-directional functionally graded Euler–Bernoulli nano-beams based on nonlocal elasticity theory, International Journal of Engineering Science, Vol. 103, pp. 1-10, 2016.

[23]         M. Z. Nejad, A. Hadi, Non-local analysis of free vibration of bi-directional functionally graded Euler–Bernoulli nano-beams, International Journal of Engineering Science, Vol. 105, pp. 1-11, 2016.

[24]         A. Hadi, M. Z. Nejad, M. Hosseini, Vibrations of three-dimensionally graded nanobeams, International Journal of Engineering Science, Vol. 128, pp. 12-23, 2018.

[25]         M. Z. Nejad, A. Hadi, A. Farajpour, Consistent couple-stress theory for free vibration analysis of Euler-Bernoulli nano-beams made of arbitrary bi-directional functionally graded materials, Structural Engineering and Mechanics, Vol. 63, No. 2, pp. 161-169, 2017.

[26]         M. R. Farajpour, A. Shahidi, A. Farajpour, Resonant frequency tuning of nanobeams by piezoelectric nanowires under thermo-electro-magnetic field: a theoretical study, Micro & Nano Letters, Vol. 13, No. 11, pp. 1627-1632, 2018.

[27]         A. Farajpour, M. Mohammadi, A. Shahidi, M. Mahzoon, Axisymmetric buckling of the circular graphene sheets with the nonlocal continuum plate model, Physica E: Low-dimensional Systems and Nanostructures, Vol. 43, No. 10, pp. 1820-1825, 2011.

[28]         M. Farajpour, A. Shahidi, A. Hadi, A. Farajpour, Influence of initial edge displacement on the nonlinear vibration, electrical and magnetic instabilities of magneto-electro-elastic nanofilms, Mechanics of Advanced Materials and Structures, Vol. DOI: 10.1080/15376494.2018.1432820, 2018.

[29]         M. Farajpour, A. Shahidi, A. Farajpour, A nonlocal continuum model for the biaxial buckling analysis of composite nanoplates with shape memory alloy nanowires, Materials Research Express, Vol. 5, No. 3, pp. 035026, 2018.

[30]         M. R. Farajpour, A. R. Shahidi, A. Farajpour, Frequency behavior of ultrasmall sensors using vibrating SMA nanowire-reinforced sheets under a non-uniform biaxial preload, Materials Research Express, Vol. 6, pp. 065047, 2019.

[31]         M. R. Farajpour, A. R. Shahidi, A. Farajpour, Frequency behavior of ultrasmall sensors using vibrating SMA nanowire-reinforced sheets under a non-uniform biaxial preload, Materials Research Express, Vol. 6, No. 6, pp. 065047, 2019/03/29, 2019.

[32]         C. Wang, C. Ru, A. Mioduchowski, Orthotropic elastic shell model for buckling of microtubules, Physical Review E, Vol. 74, No. 5, pp. 052901, 2006.

[33]         H. Jiang, L. Jiang, J. D. Posner, B. D. Vogt, Atomistic-based continuum constitutive relation for microtubules: elastic modulus prediction, Computational Mechanics, Vol. 42, No. 4, pp. 607-618, 2008.

[34]         T. Li, A mechanics model of microtubule buckling in living cells, Journal of biomechanics, Vol. 41, No. 8, pp. 1722-1729, 2008.

[35]         B. Akgöz, Ö. Civalek, Application of strain gradient elasticity theory for buckling analysis of protein microtubules, Current Applied Physics, Vol. 11, No. 5, pp. 1133-1138, 2011.

[36]         M. Taj, J. Zhang, Analysis of wave propagation in orthotropic microtubules embedded within elastic medium by Pasternak model, journal of the mechanical behavior of biomedical materials, Vol. 30, pp. 300-305, 2014.

[37]         A. Farajpour, A. Rastgoo, M. Mohammadi, Surface effects on the mechanical characteristics of microtubule networks in living cells, Mechanics Research Communications, Vol. 57, pp. 18-26, 2014.

[38]         A. G. Arani, M. Abdollahian, M. Jalaei, Vibration of bioliquid-filled microtubules embedded in cytoplasm including surface effects using modified couple stress theory, Journal of theoretical biology, Vol. 367, pp. 29-38, 2015.

[39]         Ö. Civalek, C. Demir, A simple mathematical model of microtubules surrounded by an elastic matrix by nonlocal finite element method, Applied Mathematics and Computation, Vol. 289, pp. 335-352, 2016.

[40]         M. A. Jordan, L. Wilson, Microtubules as a target for anticancer drugs, Nature Reviews Cancer, Vol. 4, No. 4, pp. 253, 2004.

[41]         C. Lim, G. Zhang, J. Reddy, A higher-order nonlocal elasticity and strain gradient theory and its applications in wave propagation, Journal of the Mechanics and Physics of Solids, Vol. 78, pp. 298-313, 2015.

[42]         M. R. Farajpour, A. Rastgoo, A. Farajpour, M. Mohammadi, Vibration of piezoelectric nanofilm-based electromechanical sensors via higher-order non-local strain gradient theory, Micro & Nano Letters, Vol. 11, No. 6, pp. 302-307, 2016.

[43]         L. Li, Y. Hu, L. Ling, Wave propagation in viscoelastic single-walled carbon nanotubes with surface effect under magnetic field based on nonlocal strain gradient theory, Physica E: Low-dimensional Systems and Nanostructures, Vol. 75, pp. 118-124, 2016.

[44]         A. Farajpour, A. Rastgoo, M. Mohammadi, Vibration, buckling and smart control of microtubules using piezoelectric nanoshells under electric voltage in thermal environment, Physica B: Condensed Matter, Vol. 509, pp. 100-114, 2017.

[45]         M. Mohammadi, A. Farajpour, M. Goodarzi, R. Heydarshenas, Levy type solution for nonlocal thermo-mechanical vibration of orthotropic mono-layer graphene sheet embedded in an elastic medium, Journal of Solid Mechanics, Vol. 5, No. 2, pp. 116-132, 2013.

[46]         S. R. Asemi, A. Farajpour, Vibration characteristics of double-piezoelectric-nanoplate-systems, IET Micro & Nano Letters, Vol. 9, No. 4, pp. 280-285, 2014.

[47]         S. R. Asemi, A. Farajpour, M. Borghei, A. H. Hassani, Thermal effects on the stability of circular graphene sheets via nonlocal continuum mechanics, Latin American Journal of Solids and Structures, Vol. 11, No. 4, pp. 704-724, 2014.

[48]         M. Hosseini, A. Hadi, A. Malekshahi, M. Shishesaz, A review of size-dependent elasticity for nanostructures, Journal of Computational Applied Mechanics, Vol. 49, No. 1, pp. 197-211, 2018.

[49]         N. Kordani, A. Fereidoon, M. Divsalar, A. Farajpour, Forced vibration of piezoelectric nanowires based on nonlocal elasticity theory, Journal of Computational Applied Mechanics Vol. 47, pp. 137-150, 2016.

[50]         A. Farajpour, A. Rastgoo, M. Farajpour, Nonlinear buckling analysis of magneto-electro-elastic CNT-MT hybrid nanoshells based on the nonlocal continuum mechanics, Composite Structures, Vol. 180, pp. 179-191, 2017.

[51]         M. Goodarzi, M. Mohammadi, A. Farajpour, M. Khooran, Investigation of the effect of pre-stressed on vibration frequency of rectangular nanoplate based on a visco-Pasternak foundation, Journal of Solid Mechanics, Vol. 6, pp. 98-121, 2014.

[52]         S. R. Asemi, M. Mohammadi, A. Farajpour, A study on the nonlinear stability of orthotropic single-layered graphene sheet based on nonlocal elasticity theory, Latin American Journal of Solids and Structures, Vol. 11, No. 9, pp. 1515-1540, 2014.

[53]         M. Mohammadi, A. Farajpour, M. Goodarzi, H. Mohammadi, Temperature effect on vibration analysis of annular graphene sheet embedded on visco-Pasternak foundation, Journal of Solid Mechanics, Vol. 5, No. 3, pp. 305-323, 2013.

[54]         A. Farajpour, A. Rastgoo, Influence of carbon nanotubes on the buckling of microtubule bundles in viscoelastic cytoplasm using nonlocal strain gradient theory, Results in physics, Vol. 7, pp. 1367-1375, 2017.

[55]         M. Farajpour, A. Shahidi, F. Tabataba’i-Nasab, A. Farajpour, Vibration of initially stressed carbon nanotubes under magneto-thermal environment for nanoparticle delivery via higher-order nonlocal strain gradient theory, The European Physical Journal Plus, Vol. 133, No. 6, pp. 219, 2018.

[56]         A. C. Eringen, 2002, Nonlocal continuum field theories, Springer Science & Business Media,

[57]         C. Li, C. Ru, A. Mioduchowski, Length-dependence of flexural rigidity as a result of anisotropic elastic properties of microtubules, Biochemical and biophysical research communications, Vol. 349, No. 3, pp. 1145-1150, 2006.

[58]         W. D. Cornell, P. Cieplak, C. I. Bayly, I. R. Gould, K. M. Merz, D. M. Ferguson, D. C. Spellmeyer, T. Fox, J. W. Caldwell, P. A. Kollman, A second generation force field for the simulation of proteins, nucleic acids, and organic molecules, Journal of the American Chemical Society, Vol. 117, No. 19, pp. 5179-5197, 1995.