Muhammad Taj, ZHANG Jun-qian. Buckling of Embedded Microtubules in Elastic Medium[J]. Applied Mathematics and Mechanics, 2011, 32(3): 279-285. doi: 10.3879/j.issn.1000-0887.2011.03.004
Citation: Muhammad Taj, ZHANG Jun-qian. Buckling of Embedded Microtubules in Elastic Medium[J]. Applied Mathematics and Mechanics, 2011, 32(3): 279-285. doi: 10.3879/j.issn.1000-0887.2011.03.004

Buckling of Embedded Microtubules in Elastic Medium

doi: 10.3879/j.issn.1000-0887.2011.03.004
  • Received Date: 2010-09-21
  • Rev Recd Date: 2011-01-21
  • Publish Date: 2011-03-15
  • Motivated by the application of Winkler-like model for buckling analysis of embedded carbon nanotubes,an orthotropic Winkler-like model was developed to study buckling behavior of embedded cytoskeletal microtubules within cytoplasm.Experimental observations of buckling of embedded cytoskeletal microtubules reveal that embedded microtubules bear a large compressive force as compared to free microtubules.Our theoretical model predicts that embedded microtubules in elastic medium bear large compressive forces than free microtubules.The estimated critical pressure is found not only in good agreement with the experimental values of pressure-induced buckling of microtubules[Needleman D J,Ojeda-Lopez M A,Kai Ewert U R,Miller H P,Wilson L,Safiny C R.Biophys J,2005,89(5):3410-3423; Needleman D J,Ojeda-Lopez M A,Raviv U,Ewert K,Jones J B,Miller H P L,Wilso L,Safinya C R.Phys Rev Lett,2004,93(19):1981041-1981044.].But also,due to mechanical coupling of microtubules with surrounding elastic medium,critical buckling force has increased considerably,which well explains the theory that mechanical coupling of microtubules with the elastic medium increases compressive forces that microtubules can sustain[Brangwynne C P,MacKintosh F C,Kumar S,Geisse N A,Talbot J,Mahadevan L,Parker K K,Ingber D E,Weitz D A.The Journal of Cell Biology,2006,173 (5):733-741] suggesting that the present model is a good approximation for buckling analysis of embedded microtubules.
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  • [1]
    Nogales E. Structural insights into microtubule function[J].Annu Rev Biochem, 2000, 69(1): 277-302. doi: 10.1146/annurev.biochem.69.1.277
    Alberts B, Johnson A, Lewis J, Raff M, Roberts K, Roberts P.Molecular Biology of the Cell[M]. 4th ed. New York:Garland Science Publishing, 2005, 1463.
    Carter N J, Cross R A. Mechanics of the kinesin step[J] Nature, 2005, 435(3):308-312.
    Schoutens J E J. A model describing bending in flagella[J]. J Biol Phys, 2004, 30(2): 97-122. doi: 10.1023/B:JOBP.0000035852.95326.79
    Boal D. Mechanics of the Cell[M]. Cambridge: Cambridge University Press, 2002.
    Kolodney M S, Wysolmerski R B. Isometric contraction by fibroblasts and Endothelial cells in tissue culture: a quantitative study[J]. J Cell Biol, 1992, 117(1):73-82. doi: 10.1083/jcb.117.1.73
    Stamenovic D, Liang Z L, Chen J X, Wang N. Effect of the cytoskeletal prestress on the mechanical impedance of cultured airway smooth muscle cells[J]. J Appl Physiol, 2002, 92(4): 1443-1450.
    Zheng J, Buxbaum R E, Heidemann S R. Investigation of microtubule assembly and organization accompanying tension-induced neurite initiation[J] J Cell Sci,1993, 104(4): 1239-1250.
    Odde D J, Ma L, Briggs A H, Demarco A, Kirschner M W. Microtubule bending and breaking in living cells[J]. J Cell Sci, 1999, 112(19): 3283-3288.
    Needleman D J, Ojeda-Lopez M A, Raviv U, Ewert K, Miller H P , Wilson L, Safinya C R. Radial compression of microtubules and the mechanism of action of taxol and associated proteins[J].Biophys J, 2005, 89(5): 3410-3423. doi: 10.1529/biophysj.104.057679
    Needleman D J, Ojeda-Lopez M A, Raviv U, Ewert K, Jones J B, Miller H P L, Wilso L, Safinya C R. Synchrotron X-ray diffraction study of microtubules buckling and bundling under osmotic stress: a probe of interprotofilament interactions[J]. Phys Rev Lett, 2004, 93(19): 1981041-1981044.
    Felgner H, Frank R, Biernat J, Mandelkow E M, Madelkow E, Ludin B, Matus A, Schliwa M. Domains of neuronal microtubule-associated proteins and flexural rigidity of microtubules[J]. J Cell Biol,1997, 138(5):1067-1075. doi: 10.1083/jcb.138.5.1067
    Brangwynne C P, MacKintosh F C, Kumar S, Geisse N A, Talbot J, Mahadevan L, Parker K K, Ingber D E, Weitz D A. Microtubules can bear enhanced compressive loads in living cells because of lateral reinforcement[J]. The Journal of Cell Biology, 2006, 173(5): 733-741. doi: 10.1083/jcb.200601060
    Li T. A mechanics model of microtubule buckling in living cells[J]. J Biomech, 2008, 41 (8): 1722-1729. doi: 10.1016/j.jbiomech.2008.03.003
    Wang C Y, Ru C Q, Mioduchowski A. Orthotropic elastic shell model for buckling of microtubules[J]. Physical Review E, 2006, 74(5): 052901. doi: 10.1103/PhysRevE.74.052901
    Kis A, Kasas S, Babicˇ B, Kulik A J, Benot W, Briggs G A D, Schnenberger C, Catsicas S, Forr L. Nanomechanics of microtubules[J]. Physical Review Letters, 2002, 89(24): 248101. doi: 10.1103/PhysRevLett.89.248101
    Nogales E, Whittaker M, Milligan R A, Downing K H. High-resolution model of the microtubule[J] Cell, 1999, 96(1): 79-88.
    Qian X S, Zhang J Q, Ru C Q. Wave propagation in orthotropic microtubules[J]. J Appl Phys, 2007, 101(8): 084702. doi: 10.1063/1.2717573
    Lourie O, Cox D M, Wagner H D. Buckling and collapse of embedded carbon nanotubes[J]. Phys Rev Lett, 1998, 81(8): 1638-1641. doi: 10.1103/PhysRevLett.81.1638
    Yoon J, Ru C Q, Mioduchowski A. Sound wave propagation in multiwall carbon nanotubes [J]. J Appl Phys, 2003, 93(8): 4801-4806. doi: 10.1063/1.1559932
    Ventsel E, Krauthammer T. Thin Plates and Shells[M]. New York: Marcel Dekker, 2004.
    Pablo de P J, Schaap I A T , Mackintosh F C, Schmidt C F. Deformation and collapse of microtubules on the nanometer scale[J]. Physical Review Letters, 2003, 91(9): 098101- 098114. doi: 10.1103/PhysRevLett.91.098101
    Sirenko M, Stroscio M, Kim K W. Elastic vibrations of microtubules in a fluid[J]. Phys Rev E, 1996, 53 (1): 1003-1010. doi: 10.1103/PhysRevE.53.1003
    Flugge W. Stresses in Shells[M]. Berlin: Springer-Verlag, 1960.
    Ofek G, Natoli R M, Athanasiou K A. In situ mechanical properties of the chondrocyte cytoplasm and nucleus[J]. J Biomech, 2009, 42(7): 873-877. doi: 10.1016/j.jbiomech.2009.01.024
    Leipzing N D, Athanasiou K A. Unconfined creep compression of chondrocytes[J]. J Biomech, 2005, 38(1): 77-85. doi: 10.1016/j.jbiomech.2004.03.013
    Peng Z H, Yang J M, Si S H, Fang D C, Chen W S, Luo Y H. Effects of metastasis-suppressor gene KAI1 on viscoelastic properties of hepatocellular carcinoma MHCC97-H cells with high metastatic potential[J]. World Chin J Digestol, 2004, 12(5): 1040.
    Chajes A. Principles of Structural Stability Theory[M]. Englewood Cliffs NJ: Prentice-Hall, 1974.
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