Wave propagation along protein microtubule: Via strain gradient and orthotropic elastic model

Muhammad Taj, Mohammad Amien Khadimallah, Shahzad Ali Shahid Chatha, Ikram Ahmad, Sami Alghamdi, Muzamal Hussain, Rana Muhammad Akram Muntazir, Faisal Al-Thobiani, Muhammad Safeer, Muhammad Naeem Mohsin, Faisal Mehmood Butt and Zafer Iqbal

Abstract

Microtubules in the cell are influenced by internal and external stimulation and play an important part in conveying protein substances and in carrying out medications to the intended targets. Waves are produced during these functions and in order to control the biological cell functions, it is important to know the wave velocities of microtubules. Owing to cylindrical shell shaped and mechanically elastic and orthotropic, cylindrical shell model based on gradient elasticity theory has been used. Wave velocities of the protein microtubule are carried out by considering Love's thin shell theory and Navier solution. Also, the effect of size parameter and other variables on the results are investigated.

Key Words

Love's thin shell theory; microtubules; Navier solution; wave propagation

Address

(1) Muhammad Taj, Muhammad Safeer: Department of Mathematics, University of Azad Jammu and Kashmir, Muzaffarabad, 1300, Azad Kashmir, Pakistan; (2) Mohammad Amien Khadimallah: Department of Civil Engineering, College of Engineering in Al-Kharj, Prince Sattam Bin Abdulaziz University, Al-Kharj, 11942, Saudi Arabia; (3) Shahzad Ali Shahid Chatha: Department of Chemistry, Government College University Faisalabad, 38000, Pakistan; (4) Ikram Ahmad: Department of Chemistry, University of Sahiwal, Sahiwal, 57000, Faisalabad, Pakistan; (5) Sami Alghamdi: Electrical and Computer Engineering Department, King Abdulaziz University, Jeddah, Saudi Arabia; (6) Muzamal Hussain: Department of Mathematics, University of Sahiwal, Sahiwal, 57000, Faisalabad, Pakistan; (7) Rana Muhammad Akram Muntazir: Department of Mathematics, Lahore Leads University, 54792, Lahore, Pakistan; (8) Faisal Al-Thobiani: Marine Engineering Department, Faculty of Maritime Studies, King Abdulaziz University, Jeddah, Saudi Arabia; (9) Muhammad Naeem Mohsin: Institute for Islamic Theological Studies, University of Vienna, Schenkenstrabe 8-10,1010, Vienna, Austria; (10) Faisal Mehmood Butt: Department of Electrical Engineering, University of Azad Jammu and Kashmir, Pakistan; (11) Zafer Iqbal: Department of Mathematics, University of Sargodha, Sargodha, Punjab, Pakistan; (12) Zafer Iqbal: Department of Mathematics, University of Mianwali, Punjab, Pakistan.

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