Abstract
Motivated by the application of Winkler-like models for the buckling analysis of embedded carbon nanotubes, an orthotropic Winkler-like model is developed to study the buckling behavior of embedded cytoskeletal microtubules within the cytoplasm. Experimental observations of the buckling of embedded cytoskeletal microtubules reveal that embedded microtubules bear a large compressive force as compared with free microtubules. The present theoretical model predicts that embedded microtubules in an elastic medium bear large compressive forces than free microtubules. The estimated critical pressure is in good agreement with the experimental values of the pressure-induced buckling of microtubules. Moreover, due to the mechanical coupling of microtubules with the surrounding elastic medium, the critical buckling force is increased considerably, which well explains the theory that the mechanical coupling of microtubules with an elastic medium increases compressive forces that microtubules can sustain. The model presented in the paper is a good approximation for the buckling analysis of embedded microtubules.
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References
Nogales, E. Structural insights into microtubule function. Annu. Rev. Biochem., 69(1), 277–302 (2000)
Alberts, B., Johnson, A., Lewis, J., Raff, M., Roberts, K., and Walter, P. Molecular Biology of the Cell, 4th ed., Garland Science, New York, 1463 (2005)
Carter, N. J. and Cross, R. A. Mechanics of the kinesin step. Nature, 435(3), 308–312 (2005)
Schoutens, J. E. J. A model describing bending in Flagella. J. Biol. Phys., 30(2), 97–122 (2004)
Boal, D. Mechanics of the Cell, Cambridge University Press, Cambridge (2002)
Kolodney, M. S. and Wysolmerski, R. B. Isometric contraction by fibroblasts and Endothelial cells in tissue culture: a quantitative study. J. Cell Biol., 117(1), 73–82 (1992)
Stamenovic, D., Liang, Z., Chen, J., and Wang, N. Effect of the cytoskeletal prestress on the mechanical impedance of cultured airway smooth muscle cells. J. Appl. Physiol., 92(4), 1443–1450 (2002)
Zheng, J., Buxbaum, R. E., and Heidemann, S. R. Investigation of microtubule assembly and organization accompanying tension-induced neurite initiation. J. Cell Sci., 104(4), 1239–1250 (1993)
Odde, D. J., Ma, L., Briggs, A. H., Demarco, A., and Kirschner, M. W. Microtubule bending and breaking in living cells. J. Cell Sci., 112(19), 3283–3288 (1999)
Needleman, D. J., Ojeda-Lopez, M. A., Ewert, K., Miller, H. P., Wilson, L., and Safinya, C. R. Radial compression of microtubules and the mechanism of action of taxol and associated proteins. Biophys. J., 89(5), 3410–3423 (2005)
Needleman, D. J., Ojeda-Lopez, M. A., Raviv, U., Ewert, K., Jones, J. B., Miller, H. P. L., Wilso, L., and Safinya, C. R. Synchrotron X-ray differection study of microtubules buckling and bundling under osmotic stress: a probe of interprotofilament interactions. Phys. Rev. Lett., 93(19), 1981041–1981044 (2004)
Felgner, H., Frank, R., Biernat, J., Mandelkow, E. M., Madelkow, E., Ludin, B., Matus, A., and Schliwa, M. Domains of neuronal microtubule-associated proteins and flexural rigidity of microtubules. J. Cell Biol., 138(5), 1067–1075 (1997)
Brangwynne, C. P., MacKintosh, F. C., Kumar, S., Geisse, N. A., Talbot, J., Mahadevan, L., Parker, K. K., Ingber, D. E., and Weitz, D. A. Microtubules can bear enhanced compressive loads in living cells because of lateral reinforcement. J. Cell Biol., 173(5), 733–741 (2006)
Li, T. A mechanics model of microtubule buckling in living cells. J. Biomech., 41(8), 1722–1729 (2008)
Wang, C. Y., Ru, C. Q., and Mioduchowski, A. Orthotropic elastic shell model for buckling of microtubules. Phys. Rev. E, 74(5), 052901 (2006)
Kis, A., Kasas, S., Babič, B., Kulik, A. J., Benoît, W., Briggs, G. A. D., Schönenberger C., Catsicas S., and Forrò, L. Nanomechanics of microtubules. Phys. Rev. Lett., 89(24), 248101 (2002)
Nogales, E., Whittaker, M., Milligan, R. A., and Downing, K. H. High-resolution model of the microtubule. Cell, 96(1), 79–88 (1999)
Qian, X. S., Zhang, J. Q., and Ru, C. Q. Wave propagation in orthotropic microtubules. J. Appl. Phys., 101(8), 084702 (2007)
Lourie, O., Cox, D. M., and Wagner, H. D. Buckling and collapse of embedded carbon nanotubes. Phys. Rev. Lett., 81(8), 1638–1641 (1998)
Yoon, J., Ru, C. Q., and Mioduchowski, A. Sound wave propagation in multiwall carbon nanotubes. J. Appl. Phys., 93(8), 4801–4806 (2003)
Ventsel, E. and Krauthammer, T. Thin Plates and Shells, Marcel Dekker, New York (2004)
Pablo, P. J., Schaap, I. A. T., Mackintosh, F. C., and Schmidt, C. F. Deformation and collapse of microtubules on the nanometer scale. Phys. Rev. Lett., 91(9), 098101–098114 (2003)
Sirenko, M., Stroscio, M., and Kim, K. W. Elastic vibrations of microtubules in a fluid. Phys. Rev. E, 53(1), 1003–1010 (1996)
Flugge, W. Stresses in Shells, Springer-Verlag, Berlin (1960)
Ofek, G., Natoli, R. M., and Athanasiou, K. In situ mechanical properties of the chondrocyte cytoplasm and nucleus. J. Biomech., 42(7), 873–877 (2009)
Leipzing, N. D. and Athanasiou, K. A. Unconfined creep compression of chondrocytes. J. Biomech., 38(1), 77–85 (2005)
Peng, Z. H., Yang, J. M., Si, S. H., Fang, D. C., Chen, W. S., and Luo, Y. H. Effects of metastasis-suppressor gene KAI1 on viscoelastic properties of hepatocellular carcinoma MHCC97-H cells with high metastatic potential. World Chin. J. Digestol., 12(5), 1040–1043 (2004)
Chajes, A. Principles of Structural Stability Theory, Prentice-Hall, Inc., New Jersey (1974)
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Project supported by the National Natural Science Foundation of China (No. 10772105) and the Shanghai Leading Academic Discipline Project (No. S30106)
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Taj, M., Zhang, Jq. Buckling of embedded microtubules in elastic medium. Appl. Math. Mech.-Engl. Ed. 32, 293–300 (2011). https://doi.org/10.1007/s10483-011-1415-x
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DOI: https://doi.org/10.1007/s10483-011-1415-x