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Torsional frequency analyses of microtubules with end attachments
Author(s) -
Mustapha Khameel B.,
Wong Basil T.
Publication year - 2016
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.201500007
Subject(s) - torsion (gastropod) , torsion spring , oscillation (cell signaling) , microtubule , mechanics , vibration , stiffness , physics , added mass , torsional vibration , normal mode , softening , boundary value problem , chemistry , classical mechanics , acoustics , anatomy , medicine , biochemistry , quantum mechanics , biology , microbiology and biotechnology , thermodynamics
This study is concerned with the mathematical modeling of microtubules for torsional vibration analysis. Microtubules (MTs) are prone to mechanical torsion, and hence conductance oscillation, when they act as molecular pathways for cargo transport. The period of this torsional oscillation has an intimate, but yet‐to‐be‐understood relationship with the MTs’ stiffness and end conditions. In the spirit of the foregoing concern, this study embarks on the characterization of the shift in the torsional resonance of an isolated MT in the presence of an end attachment in the form of either outer kinetochores (treated as a torsional spring) or a linker molecule (treated as a concentrated mass). The MT is itself idealized as a strain gradient micro‐shaft, with its governing equation augmented by enriched boundary conditions due to the attachments. The solution of the model is then sought through the differential transformation method (DTM). Validation of the reduced form of the model is evaluated with benchmark results in the literature. Under a rapidly increasing magnitude of an attached rotary mass, the analyses indicate the existence of a drift of the frequency towards zero, a scenario that could induce a transition to rigid‐body motion. Conversely, in the presence of spring‐like elastic anchors, the analyses reveal a softening effect that increases the torsional resonant frequencies of the MT. Sensitivity assessments through Pareto analyses predict an interaction effect between the size‐effect and the magnitude of an attached mass.