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Mechanical Modeling of Microtubules in Living Cells Open Access


Other title
Finite element method
Elastic beam
Type of item
Degree grantor
University of Alberta
Author or creator
Jin, MingZhao
Supervisor and department
Ru, Chongqing (Mechanical Engineering)
Examining committee member and department
Wegner, Joanne (Mechanical Engineering)
Ayranci, Cagri (Mechancial Engineering)
Raboud, Donald (Mechancial Engineering)
Tuszynski, Jack (Physics)
Ru, Chongqing (Mechanical Engineering)
Tang, Tian (Mechanical Engineering)
Department of Mechanical Engineering

Date accepted
Graduation date
Doctor of Philosophy
Degree level
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.
Permission is hereby granted to the University of Alberta Libraries to reproduce single copies of this thesis and to lend or sell such copies for private, scholarly or scientific research purposes only. Where the thesis is converted to, or otherwise made available in digital form, the University of Alberta will advise potential users of the thesis of these terms. The author reserves all other publication and other rights in association with the copyright in the thesis and, except as herein before provided, neither the thesis nor any substantial portion thereof may be printed or otherwise reproduced in any material form whatsoever without the author's prior written permission.
Citation for previous publication
Jin, M.Z., Ru, C.Q., 2013. Localized buckling of a microtubule surrounded by randomly distributed cross linkers, Physical Review E 88, 012701.Jin, M.Z. & Ru, C.Q. 2014. Localized Vibration of a Microtubule Surrounded by Randomly Distributed Cross Linkers, Journal of biomechanical engineering, 136, 071002.Jin, M.Z., Ru, C.Q., 2012. Compressed microtubules: Splitting or buckling, Journal of Applied Physics 111, 604701.

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