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Mechanical Modeling of Microtubules in Living Cells

  • Author / Creator
    Jin, MingZhao
  • Three important mechanical behaviors of microtubules in vivo, i.e., buckling, vibration and splitting are investigated with especial focus on their relevance to biological functions of microtubules. To study the vibration and buckling of a microtubule, we model a microtubule as an elastic beam and surrounding three dimensionally distributed biopolymers as springs by using finite element method. Our model predicts that the buckling and vibration of microtubule are highly localized within several microns. As a result the critical buckling force and the lowest vibration frequency are insensitive to the total length of microtubule. The localized buckling and vibration predicted by the present model agree with a number of experimental observations which cannot be well explained by the existing elastic foundation model. Compared with predictions from the existing elastic foundation model, some key parameters (e.g., critical buckling force, buckling wave length, vibration frequency and vibration wave length) obtained from the present model are also in better agreement with experiments. In addition to our finite element results, several empirical equations, which are unavailable from the existing elastic foundation model, are provided to calculate these key parameters in terms of mechanical and geometrical properties of microtubule and surrounding biopolymer. To investigate splitting of a microtubule into splayed protofilaments, we model protofilaments as individual elastic beams in parallel and laterally assembled to form a microtubule. Our analytical model shows that an axial compressive force could induce splitting of a microtubule shorter than 450 nm even if it is protected by a “cap” consisted of strongly bonded GTP dimers at the end. For a longer microtubule, the axial compressive force might cause overall buckling prior to splitting. On the other hand, after the strong “cap” at the end of microtubule is lost (not necessarily due to compressive force), a molecular ring coupled to the frayed end of microtubule could provide a pulling force with splitting propagation of microtubule to move chromosome during mitosis. Our model predicts that the splitting of microtubule will spontaneously propagate with splitting length around 15 ~ 18 nm, which is comparable with the frayed end in microtubule of 10 ~ 30 nm observed in experiments. By using the predicted splitting length, we estimate the theoretical upper limit of pulling force as 7 ~ 24 pN, which is close to the upper bound of the experimentally measured pulling force 0.5 ~ 5 pN with reasonable accuracy. In summary, our numerical simulations and analytical models offer plausible explanations to some important experiments of microtubules in vivo which have not been well explained by existing models. It is hoped that the present study could bring some new insights to the understanding of interacting between mechanics and biology of microtubule and spark further research interest in mechanical modeling of microtubules.

  • Subjects / Keywords
  • Graduation date
    2014-11
  • Type of Item
    Thesis
  • Degree
    Doctor of Philosophy
  • DOI
    https://doi.org/10.7939/R3PC2TH84
  • License
    This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for non-commercial purposes. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.
  • Language
    English
  • Institution
    University of Alberta
  • Degree level
    Doctoral
  • Department
    • Department of Mechanical Engineering
  • Supervisor / co-supervisor and their department(s)
    • Ru, Chongqing (Mechanical Engineering)
  • Examining committee members and their departments
    • Raboud, Donald (Mechancial Engineering)
    • Ayranci, Cagri (Mechancial Engineering)
    • Ru, Chongqing (Mechanical Engineering)
    • Wegner, Joanne (Mechanical Engineering)
    • Tuszynski, Jack (Physics)
    • Tang, Tian (Mechanical Engineering)