Effects of elastic medium on buckling of microtubules due to bending and torsion

Muhammad Taj , Muzamal Hussain , Muhammad A. Afsar , Muhammad Safeer , Manzoor Ahmad , Muhammad N. Naeem , Noor Badshah , Arshad Khan , Abdelouahed Tounsi

Abstract

Microtubules buckle under bending and torsion and this property has been studied for free microtubules before using orthotropic elastic shell model. But as microtubules are embedded in other elastic filaments and it is experimentally showed that these elastic filaments affect the critical buckling moment and critical buckling torque of the microtubules. To prove that, we developed orthotropic Winkler like model and demonstrated that the critical buckling moment and critical buckling torque of the microtubules are orders of higher magnitude than those found for free microtubules. Our results show that Critical buckling moment is about 6.04 nNnm for which the corresponding curvature is about o=1.33 rad /um for embedded MTs, and critical buckling torque is 0.9 nNnm for the angle of 1.33 rad/um. Our results well proved the experimental findings.

Key Words

microtubule; orthotropic material; buckling; bending; torsion; winkler like model; orthotropic elastic shell model; wave propagation approach

Address

Muhammad Taj, Muhammad A. Afsar, Muhammad Safeer, Manzoor Ahmad — Department of Mathematics, University of Azad Jammu and Kashmir, Muzaffarabad, 1300, Azad Kashmir, Pakistan
Muzamal Hussain, Muhammad N. Naeem — Department of Mathematics, Govt. College University Faisalabad, 38000, Faisalabad, Pakistan
Noor Badshah — Department of Basic Science, University of Engineering and Technology, Peshawer
Arshad Khan — Institute of Computer Science and Information Technology, The University of Agriculture, Peshawar
Abdelouahed Tounsi — Materials and Hydrology Laboratory, Algeria Faculty of Technology Civil Engineering Department, University of Sidi Bel Abbes, Algeria; Department of Civil and Environmental Engineering, King Fahd University of Petroleumand Minerals, 31261 Dhahran, Eastern Province, Saudi Arabia

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