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Mathematical modelling of axonal microtubule bundles under dynamic torsion

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Abstract

Owing to its viscoelastic nature, axon exhibits a stress rate-dependent me- chanical behavior. An extended tension-shear chain model with Kelvin-Voigt viscoelas- ticity is developed to illustrate the micromechanical behavior of the axon under dynamic torsional conditions. Theoretical closed-form expressions are derived to predict the de- formation, stress transfer, and failure mechanism between microtubule (MT) and tau protein while the axon is sheared dynamically. The results obtained from the present an- alytical solutions demonstrate how the MT-tau interface length, spacing between the tau proteins, and loading rate affect the mechanical properties of axon. Moreover, it is found that the MTs are more prone to rupture due to the contributions from the viscoelastic effects. Under the torsional force, the MTs are so long that the stress concentrates at the loaded end where axonal MTs will break. This MT-tau protein dynamics model can help to understand the underlying pathology and molecular mechanisms of axonal injury. Additionally, the emphasis of this paper is on the micromechanical behavior of axon, whereas this theoretical model can be equally applicable to other soft or hard tissues, owning the similar fibrous structure.

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Author information

Authors and Affiliations

  1. MOE Key Laboratory of Disaster Forecast and Control in Engineering, Institute of Applied Mechanics, Jinan University, Guangzhou, 510632, China

    J. Y. Wu & Hong Yuan

  2. School of Engineering, University of Plymouth, Plymouth, PL48AA, UK

    J. Y. Wu & L. Y. Li

Authors
  1. J. Y. Wu
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  2. Hong Yuan
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Correspondence to Hong Yuan.

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Project supported by the National Natural Science Foundation of China (No. 11032005), the Major Project of Department of Science and Technology of Guizhou Province (No. 2014-6024), and the Academician Workstation of Department of Science and Technology of Guizhou Province (No. 2015-4004)

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Wu, J.Y., Yuan, H. & Li, L.Y. Mathematical modelling of axonal microtubule bundles under dynamic torsion. Appl. Math. Mech.-Engl. Ed. 39, 829–844 (2018). https://doi.org/10.1007/s10483-018-2335-9

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  • DOI: https://doi.org/10.1007/s10483-018-2335-9

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