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Molecular structural mechanics model for the mechanical properties of microtubules

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Abstract

The aim of this paper was to develop a structural mechanics (SM) model for the microtubules (MTs) in cells. The technique enables one to study the configuration effect on the mechanical properties of MTs and enjoys greatly improved computational efficiency as compared with molecular dynamics simulations. The SM model shows that the Young’s modulus has nearly a constant value around 0.83 GPa, whereas the shear modulus, two orders of magnitude lower, varies considerably with the protofilament number \(N\) and helix-start number \(S\). The dependence of the bending stiffness and persistence length on the MT length and protofilament number \(N\) is also examined and explained based on the continuum mechanics theories. Specifically, the SM model is found to be in good agreement with available simulation and experiment results, showing its robustness in studying the static deformation of MTs and the potential for characterizing the buckling and vibration of MTs as well as the mechanical behaviour of intermediate and actin filaments.

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References

  • Alberts B, Johnson A, Lewis J, Raff M, Roberts K, Walter P (2002) Molecular biology of the cell, 4th edn. Garland Science, New York

    Google Scholar 

  • Brangwynne CP, Koenderink GH, Barry E, Dogic Z, MacKintosh FC, Weitz DA (2007) Bending dynamics of fluctuating biopolymers probed by automated high-resolution filament tracking. Biophys J 93:346–359

    Article  Google Scholar 

  • Chandran PL, Mofrad MRK (2009) Rods-on-string idealization captures semiflexible filament dynamics. Phys Rev E 79:011906

    Article  MathSciNet  Google Scholar 

  • Chretien D, Wade RH (1991) New data on the microtubule surface lattice. Biol Cell 71:161–174

    Article  Google Scholar 

  • Chretien D, Fuller SD (2000) Microtubules switch occasionally into unfavorable configurations during elongation. J Mol Biol 298:663–676

    Article  Google Scholar 

  • Chu JW, Voth GA (2005) Allostery of actin filaments: molecular dynamics simulations and coarse-grained analysis. Proc Natl Acad Sci USA 102:13111–13116

    Article  Google Scholar 

  • de Pablo PJ, Schaap IAT, MacKintosh FC, Schmidt CF (2003) Deformation and collapse of microtubules on the nanometer scale. Phys Rev Lett 91:098101

    Article  Google Scholar 

  • Deriu MA, Enemark S, Soncini M, Montevecchi FM, Redaelli A (2007) Tubulin: from atomistic structure to supramolecular mechanical properties. J Mater Sci 42:8864–8872

    Article  Google Scholar 

  • Deriu MA, Soncini M, Orsi M, Patel M, Essex JW, Montevecchi FM, Redaelli A (2010) Anisotropic elastic network modeling of entire microtubules. Biophys J 99:2190–2199

    Article  Google Scholar 

  • Donhauser ZJ, Jobs WB, Binka EC (2010) Mechanics of microtubules: effects of protofilament orientation. Biophys J 99:1668–1675

    Article  Google Scholar 

  • Enemark S, Deriu MA, Soncini M, Redaelli A (2008) Mechanical model of the tubulin dimer based on molecular dynamics simulations. J Biomech Eng 130:041008

    Article  Google Scholar 

  • Felgner H, Frank R, Schliwa M (1996) Flexural rigidity of microtubules measured with the use of optical tweezers. J Cell Sci 109:509–516

    Google Scholar 

  • Gao YW, Lei FM (2009) Small scale effects on the mechanical behaviors of protein microtubules based on the nonlocal elasticity theory. Biochem Biophys Res Commun 387:467–471

    Article  Google Scholar 

  • Gebremichael Y, Chu JW, Voth GA (2008) Intrinsic bending and structural rearrangement of tubulin dimer: molecular dynamics simulations and coarse-grained analysis. Biophys J 95:2487–2499

    Article  Google Scholar 

  • Gere JM (2003) Mechanics of Materials, 5th edn. Brooks/Cole, Pacific Grove California

    Google Scholar 

  • Gittes F, Mickey B, Nettleton J, Howard J (1993) Flexural rigidity of microtubules and actin filaments measured from thermal fluctuations in shape. J Cell Biol 120:923–934

    Article  Google Scholar 

  • Hawkins T, Mirigian M, Yasar MS, Ross JL (2010) Mechanics of microtubules. J Biomech 43:23–30

    Article  Google Scholar 

  • Hawkins TL, Mirigian M, Li J, Yasar MS, Sackett DL, Sept D, Ross JL (2012) Perturbations in microtubule mechanics from tubulin preparation. Cell Mol Bioeng 5:227–238

    Article  Google Scholar 

  • Hawkins TL, Sept D, Mogessie B, Straube A, Ross JL (2013) Mechanical properties of doubly stabilized microtubule filaments. Biophys J 104:1517–1528

    Article  Google Scholar 

  • Howard J (2001) Mechanics of motor proteins and the cytoskeleton. Sunderland, MA

    Google Scholar 

  • Howard J, Hyman AA (2003) Dynamics and mechanics of the microtubule plus end. Nature 422:753–758

    Article  Google Scholar 

  • Hunyadi V, Chretien D, Janosi IM (2005) Mechanical stress induced mechanism of microtubule catastrophes. J Mol Biol 348:927–938

    Article  Google Scholar 

  • Hunyadi V, Chretien D, Flyvbjerg H, Janosi IM (2007) Why is the microtubule lattice helical? Biol Cell 99:117–128

    Article  Google Scholar 

  • Janosi IM, Chretien D, Flyvbjerg H (1998) Modeling elastic properties of microtubule tips and walls. Eur Biophys J 27:501–513

    Article  Google Scholar 

  • Janson ME, Dogterom M (2004) A bending mode analysis for growing microtubules: evidence for a velocity-dependent rigidity. Biophys J 87:2723–2736

    Article  Google Scholar 

  • Ji XY, Feng XQ (2011a) Coarse-grained mechanochemical model for simulating the dynamic behavior of microtubules. Phys Rev E 84:031933

    Article  Google Scholar 

  • Ji XY, Feng XQ (2011b) Mechanochemical modeling of dynamic microtubule growth involving sheet-to-tube transition. PLoS ONE 6:e29049

    Article  Google Scholar 

  • Kasas S, Kis A, Riederer BM, Forro L, Dietler G, Catsicas S (2004) Mechanical properties of microtubules explored using the finite elements method. Chem Phys Chem 5:252–257

    Google Scholar 

  • Kawaguchi K, Yamaguchi A (2010) Temperature dependence rigidity of non-taxol stabilized single microtubules. Biochem Biophys Res Commun 402:66–69

    Article  Google Scholar 

  • Kikumoto M, Kurachi M, Tosa V, Tashiro H (2006) Flexural rigidity of individual microtubules measured by a buckling force with optical traps. Biophys J 90:1687–1696

    Article  Google Scholar 

  • Li CY, Chou TW (2003) A structural mechanics approach for the analysis of carbon nanotubes. Int J Solids Struct 40:2487–2499

    Article  MATH  Google Scholar 

  • Li T (2008) Mechanics model of microtubule buckling in living cells. J Biomech 41:1722–1729

    Article  Google Scholar 

  • Mehrbod M, Mofrad MRK (2011) On the significance of microtubule flexural behavior in cytoskeletal mechanics. PLoS ONE 6:e25627

    Article  Google Scholar 

  • Mitra A, Sept D (2008) Taxol allosterically alters the dynamics of the tubulin dimer and increases the flexibility of microtubules. Biophys J 95:3252–3258

    Article  Google Scholar 

  • Mizushima-Sugano J, Maeda T, Miki-Noumura T (1983) Flexural rigidity of singlet microtubules estimated from statistical analysis of their contour lengths and end-to-end distances. Biochim Biophys Acta 755:257–262

    Google Scholar 

  • Molodtsov MI, Ermakova EA, Shnol EE, Grishchuk EL, McIntosh JR, Ataullakhanov FI (2005) A molecular-mechanical model of the microtubule. Biophys J 88:3167–3179

    Article  Google Scholar 

  • Pampaloni F, Florin EL (2008) Microtubule architecture: inspiration for novel carbon nanotube-based biomimetic materials. Trends Biotechnol 26:302–310

    Article  Google Scholar 

  • Pampaloni F, Lattanzi G, Jonas A, Surrey T, Frey E, Florin EL (2006) Thermal fluctuations of grafted microtubules provide evidence of a length-dependent persistence length. Proc Natl Acad Sci USA 103:10248–10253

    Article  Google Scholar 

  • Schaap IAT, Hoffmann B, Carrasco C, Merkel R, Schmidt CF (2007) Tau protein binding forms a 1 nm thick layer along protofilaments without affecting the radial elasticity of microtubules. J Struct Biol 158:282–292

    Article  Google Scholar 

  • Sept D, MacKintosh FC (2010) Microtubule elasticity: connecting all-atom simulations with continuum mechanics. Phys Rev Lett 104:018101

    Article  Google Scholar 

  • Shen HS (2010) Nonlocal shear deformable shell model for postbuckling of axially compressed microtubules embedded in an elastic medium. Biomech Model Mechanobiol 9:345–357

    Article  Google Scholar 

  • Sirenko YM, Stroscio MA, Kim KM (1996) Elastic vibrations of microtubules in a fluid. Phys Rev E 53:1003–1010

    Article  Google Scholar 

  • Valdman D, Atzberger PJ, Yu D, Kuei S, Valentine MT (2012) Spectral analysis methods for the robust measurement of the flexural rigidity of biopolymers. Biophys J 102:1144–1153

    Article  Google Scholar 

  • VanBuren V, Cassimeris L, Odde DJ (2005) Mechanochemical model of microtubule structure and self-assembly kinetics. Biophys J 89:2911–2926

    Article  Google Scholar 

  • Van Buren V, Odde DJ, Cassimeris L (2002) Estimates of lateral and longitudinal bond energies within the microtubule lattice. Proc Natl Acad Sci USA 99:6035–6040

    Article  Google Scholar 

  • Van den Heuvel MGL, de Graaff MP, Dekker C (2008) Microtubule curvatures under perpendicular electric forces reveal a low persistence length. Proc Natl Acad Sci USA 105:7941–7946

    Article  Google Scholar 

  • Venier P, Maggs AC, Carlier MF, Pantaloni D (1994) Analysis of microtubule rigidity using hydrodynamic flow and thermal fluctuations. J Biol Chem 269:13353–13360

    Google Scholar 

  • Wang CM, Kitipornchai S, Lim CW, Eisenberger M (2008) Beam bending solutions based on nonlocal Timoshenko beam theory. J Eng Mech 134:475–481

    Article  Google Scholar 

  • Wang CY, Ru CQ, Mioduchowski A (2006a) Vibration of microtubules as orthotropic elastic shells. Physica E 35:48–56

    Article  Google Scholar 

  • Wang CY, Ru CQ, Mioduchowski A (2006b) Orthotropic elastic shell model for buckling of microtubules. Phys Rev E 74:052901

    Article  Google Scholar 

  • Wang CY, Li CF, Adhikari S (2009) Dynamic behaviors of microtubules in cytosol. J Biomech 42:1270–1274

    Article  Google Scholar 

  • Wang CY, Zhang LC (2008) Circumferential vibration of microtubules with long axial wavelength. J Biomech 41:1892–1896

    Article  Google Scholar 

  • Weaver W Jr, Gere JM (1990) Matrix analysis of framed structures, 3rd edn. Van Nostrand Reinhold, New York

    Book  Google Scholar 

  • Wu ZH, Nogales E, Xing JH (2012) Comparative studies of microtubule mechanics with two competing models suggest functional roles of alternative tubulin lateral interactions. Biophys J 102:2687–2696

    Article  Google Scholar 

  • Zhang J, Wang CY, Adhikari S (2013) Molecular structure-dependent deformations in boron nitride nanostructures subject to an electrical field. J Phys D: Appl Phys 46:235303

    Article  Google Scholar 

Download references

Acknowledgments

JZ acknowledges the support from the China Scholarship Council (CSC).

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Authors and Affiliations

  1. College of Engineering, Swansea University, Singleton Park, Swansea, Wales , SA2 8PP, UK

    Jin Zhang & Chengyuan Wang

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  1. Jin Zhang
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  2. Chengyuan Wang
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Correspondence to Chengyuan Wang.

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Zhang, J., Wang, C. Molecular structural mechanics model for the mechanical properties of microtubules. Biomech Model Mechanobiol 13, 1175–1184 (2014). https://doi.org/10.1007/s10237-014-0564-x

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