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Research Papers

Mechanics of Microtubule Buckling Supported by Cytoplasm

[+] Author and Article Information
Hanqing Jiang

Department of Mechanical and Aerospace Engineering, Arizona State University, Tempe, AZ 85287hanqing.jiang@asu.edu

Jiaping Zhang

Department of Mechanical and Aerospace Engineering, Arizona State University, Tempe, AZ 85287

J. Appl. Mech 75(6), 061019 (Aug 21, 2008) (9 pages) doi:10.1115/1.2966216 History: Received December 20, 2007; Revised May 22, 2008; Published August 21, 2008

The cytoskeleton provides the mechanical scaffold and maintains the integrity of cells. It is usually believed that one type of cytoskeleton biopolymer, microtubules, bears compressive force. In vitro experiments found that isolated microtubules may form an Euler buckling pattern with a long-wavelength for very small compressive force. This, however, does not agree with in vivo experiments where microtubules buckle with a short-wavelength. In order to understand the structural role of microtubules in vivo, we developed mechanics models that study microtubule buckling supported by cytoplasm. The microtubule is modeled as a linearly elastic cylindrical tube while the cytoplasm is characterized by different types of materials, namely, viscous, elastic, or viscoelastic. The dynamic evolution equations, the fastest growth rate, the critical wavelength, and compressive force, as well as equilibrium buckling configurations are obtained. The ability for a cell to sustain compressive force does not solely rely on microtubules but is also supported by the elasticity of cytoplasm. With the support of the cytoplasm, an individual microtubule can sustain a compressive force on the order of 100pN. The relatively stiff microtubules and compliant cytoplasm are combined to provide a scaffold for compressive force.

FIGURES IN THIS ARTICLE
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Copyright © 2008 by American Society of Mechanical Engineers
Topics: Force , Wavelength , Buckling
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Figures

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Figure 5

The relationship between the compressive force P that an individual microtubule bears before buckling and the shear modulus of the elastic cytoplasm

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Figure 6

The relationship of growth rate and wavelength for viscoelastic cytoplasm with different shear moduli

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Figure 7

The relationship of growth rate and wavelength for viscoelastic cytoplasm with different axial compressive forces

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Figure 1

The structure of a microtubule (1). (a) The microtubule is a hollow cylindrical tube formed from 13 protofilaments aligned in parallel. (b) One protofilament consists of a string α‐β heterodimers.

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Figure 2

(a) Microtubule buckles to a single long-wavelength pattern and (b) microtubule buckles to short-wavelength pattern

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Figure 3

The coordinate system used in the analysis

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Figure 4

The relationship of growth rate and wavelength for viscous cytoplasm. (a) Growth rate versus wavelength for small axial compressive force and (b) growth rate versus wavelength for large axial compressive force.

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