Sains Malaysiana 48(12)(2019): 2841–2847

http://dx.doi.org/10.17576/jsm-2019-4812-25

Vibrational Analysis of Microtubules Embedded within Viscoelastic Medium using Orthotropic Kelvin like Model

(Analisis Getaran Bermikrotubul Tertanam dalam Medium Likat Kenyal menggunakan Model seperti Ortotropisme Kelvin)

MUHAMMAD SAFEER^1,2 & MUHAMMAD TAJ¹*

¹Department of Mathematics, The University of Azad Kashmir, Muzaffarabad 13100, Pakistan

²Department of Mathematics, University of Poonch Rawalwkot, Azad Kashmir

Received: 5 March 2019/Accepted: 23 December 2019

ABSTRACT

Microtubules, the key components of cytoskeleton of all living cells, are important for maintaining the cell shape and transporting the cellular organelles. Understanding the mechanics of microtubules is very important for these functions. Mechanics of these components are greatly affected when they are embedded in cells. To understand the mechanical properties of microtubules in living cells, we developed an orthotropic-Kelvin like model and investigated the vibrational behavior when they are embedded in surrounding elastic medium. We considered them as orthotropic elastic shell and its surrounding elastic matrix as Kelvin model. We found that due to mechanical coupling of these components with the elastic medium, the flexural vibration is increased and radial frequencies in all modes are increased considerably while other vibrational modes are not affected that much.

Keywords: Elastic medium; Kelvin foundation; microtubules; vibration

ABSTRAK

Mikrotubul merupakan komponen utama sita rangka bagi semua sel hidup dan adalah penting untuk mengekalkan bentuk sel dan membawa organel sel. Memahami mekanik mikrotubul adalah sangat penting bagi fungsi tersebut. Mekanik untuk komponen ini adalah sangat terkesan apabila mereka terbenam di dalam sel. Untuk memahami sifat mekanik mikrotubul dalam sel hidup, kami telah membangunkan model seperti Ortotropik-Kelvin dan mengkaji tingkah laku getaran apabila ia dibenamkan di persekitaran medium kenyal. Kami menganggap ia sebagai kelongsong kenyal Ortotropik dan persekitaran matrik kenyal sebagai model Kelvin. Kami telah mendapati bahawa kesan daripada gandingan mekanik oleh komponen ini dengan medium kenyal dan getaran lentur adalah meningkat dan frekuensi radial di dalam semua mod adalah meningkat dengan ketara manakala mod-mod getaran yang lain tidak begitu banyak yang terkesan.

Kata kunci: Asas Kelvin; getaran; medium kenyal; mikrotubul

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*Corresponding author; email: Muhammad_taj75@yahoo.com