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Alhebshi A.M.S., Metwally A.M., Al-Basyouni K.S. et al. / Физическая мезомеханика 24 6 (2021) 99-102 99
УДК 531.011
Исследование механического поведения и физических свойств белковых микротрубочек в живых клетках в рамках нелокальной теории балок
A.M.S. Alhebshi1, A.M. Metwally2, K.S. Al-Basyouni1, S.R. Mahmoud1, H.M. Al-Solami1, A.S. Alwabli3
1 Университет короля Абдулазиза, Джидда, 21589, Саудовская Аравия 2 Центр ядерных исследований при Агентстве по атомной энергетике, Иншас, Каир, P.O. 13759, Египет 3 Университет короля Абдулазиза, Рабиг, 25732, Саудовская Аравия
В статье представлена биомеханическая модель нанобалки внутри клеточной структуры для вибрационного анализа поведения белковых микротрубочек. Проведено исследование модуля Юнга белковых микротрубочек и зависимой от длины изгибной жесткости в рамках нелокальной теории сдвиговой деформации высшего порядка. Определяющие уравнения получены с использованием принципа работы на возможных перемещениях. Численные исследования проведены для свободно опертых белковых микротрубочек. Полученные результаты проанализированы и представлены графически для каждого случая.
Ключевые слова: жесткость на изгиб, деформационное поведение, физические свойства микротрубочек, механические свойства микротрубочек, вибрационный анализ
DOI 10.24412/1683-805X-2021-6-99-102
Mechanical behavior and physical properties of protein microtubules in living cells using the nonlocal beam theory
A.M.S. Alhebshi1, A.M. Metwally2, K.S. Al-Basyouni3, S.R. Mahmoud4, H.M. Al-Solami1, and A.S. Alwabli5
1 Department of Biological Sciences, Faculty of Science, King Abdulaziz University, Jeddah, 21589, Saudi Arabia 2 Mathematics and Theoretical Physics Department, NRC, AEA, Inshas, Cairo, P.O. 13759, Egypt 3 Mathematics Department, Faculty of Science, King Abdulaziz University, Jeddah, 21589, Saudi Arabia 4 GRC Department, Applied College, King Abdulaziz University, Jeddah, 21589, Saudi Arabia 5 Department of Biological Sciences, Rabigh College of Science and Arts, King Abdulaziz University, Rabigh, 25732, Saudi Arabia
A biomechanical model for vibrational analysis with characteristics of protein microtubules based on the nanobeam shape inside the cellular structure is presented. The study of Young's modulus of protein microtubules and unexplained length-dependent flexural rigidity using a higher-order nonlocal shear-deformation theory is presented. The governing equations are provided by employing the principle of virtual work. The protein microtubules are considered simply supported for all numerical studies. The obtained results are critically discussed together with the theories as well as demonstrated in each case graphically.
Keywords: flexural rigidity, deformation behavior, physical properties of microtubules, mechanical properties of microtubules, vibrational analysis
1. Introduction
Experimental investigations have been established in laboratories to study physical properties, mechanical properties, and the elastic characteristics and mechanics behavior of protein microtubules (MTs) under external force. Diminishing the structure's property dimensions to microscale leads to a different
mechanic response. Indeed, some experimental works have been shown that the scale effect plays a considerable role in the mechanic behaviors of small-scale structures. The conventional elasticity theories contain no intrinsic size parameters and do not permit predicting the size-dependent responses of nano- and microscaled structures. Consequently, various non-classical elasticity models have been introduced to
© Alhebshi A.M.S., Metwally A.M., Al-Basyouni K.S., Mahmoud S.R., Al-Solami H.M., Alwabli A.S., 2021
100 Alhebshi A.M.S., Metwally A.M., Al-Basyouni K.S. et al. / @u3uuecKan Me30MexanuKa 24 6 (2021) 99-102
examine the mechanic behaviors of structures on a reduced scale, such as the model of couple stress.
Smooth muscle cell movement plays a vital role in forming the tube of hollow organs, like the blood and airways vessels during growth. The motility of smooth muscle cells has also been concerned in the airway's pathogenesis remodeling, an essential kind of asthma. Additionally, the hypertrophy and hyper-plasia, airway plane muscle cell movement donate the expansion of airway renovation. The thickening of smooth muscle in the airways can stem from proliferating cell migration in the bundles of muscle or circulating recruitment of precursor cells in the flat muscle layer [1-3]. Microtubules (MTs), microfilaments, and intermediate filaments are three dissimilar kinds of filaments organized in the networks of eu-karyotic cells. Each of the filaments has particular physical properties and appropriate structures based on the cell functions. MTs contain compressive forces in living cells more than other filaments, which leads to the traction forces inside the cy-toskeleton of eukaryotic cells [4]. Three types of living cells are intermediate filaments, MTs, and actin [5]. The actins and intermediate filaments can tolerate only traction due to their minor cross-sections, but the MTs are generally under compression and behave like a rigid bar [6, 7]. Keeping in view, MTs provides support to the eukaryotic cell to preserve its shape [8-10]. MTs have essential roles in eukaryotic cell motility, meiosis, growth, and mitosis. MTs have highly dynamic structures based on rapid polymeri-zation/depolymerization and act within the eukaryotic cells for the proteins of motors to transmit car-
cgoes across the cytoplasm [11]. MTs have outer diameters 25 nm, inner diameters 17 nm, and length of MTs is between 10 nm-100 mm, illustrated in Fig. 1. In cytoskeleton, MTs don't need to exist straight; however, at least keep the magnitude less than its perseverance length that can be 0.2 to 9 mm [11]. The perseverance length of protein MT filaments is more significant than its length inside the eukaryotic cells.
MTs geometry is labeled by an integer's pair named N-S, which are protofilaments and starting plexus numbers. MTs 13-3 is one of the common types of MTs composed in the in vivo, as proto-filaments are taken as parallel to the longitudinal axis, i.e., deviation angle leads to zero [12-14]. Many exceptions in various kinds and models of cells have been observed and configured for typical MTs 13-3.
Recently, higher kinds of theories based on shear-deformation are applied to investigate the mechanical performance of structures in different scales [15-22]. These theories can be used for the biomechanical response of MTs. In addition, it should be noted that nonlocal elasticity theory and strain gradient theory are also used [23-25].
In this work, a biomechanical analysis of MTs is presented using a nonlocal higher-order shear-deformation beam model. This work deals with the vibration characteristics of MTs in the surrounding cytoplasm using a nonlocal continuum model. A higherorder shear deformation beam theory is very implemented rare and is still in the process of beginning. For the comparison, the previous and present nonlocal theories are presented along with the applications of thick supported MTs.
Fig. 1. The geometry of a microtubule [5, 8, 12] (color online)
Alhebshi A.M.S., Metwally A.M., Al-Basyouni K.S. et al. / Физическая мезомеханика 24 6 (2021) 99-102 101
Funding
This project was funded by the Deanship of Scientific Research (DSR) at King Abdulaziz University, Jeddah, using grant No. G-655-247-1439. The authors acknowledge with thanks the DSR for financial and technical support.
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Received 19.04.2021, revised 05.06.2021, accepted 05.06.2021
This is an excerpt of the article "Mechanical Behavior and Physical Properties of Protein Microtubules in Living Cells Using the Nonlocal Beam Theory". Full text of the paper is published in Physical Mesomechanics Journal. DOI: 10.1134/S1029959922020096
Сведения об авторах
Alawiah M.S. Alhebshi, Dr., Assoc. Prof., King Abdulaziz University, Saudi Arabia, [email protected]
Ahmed M. Metwally, Dr., Assoc. Prof., NRC, AEA, Egypt, [email protected]
Khalil Salem Al-Basyouni, Dr., Assist. Prof., King Abdulaziz University, Saudi Arabia, [email protected]
Samy Refahy Mahmoud, Prof., King Abdulaziz University, Saudi Arabia, [email protected]
Habeeb M. Al-Solami, Dr., Assist. Prof., King Abdulaziz University, Saudi Arabia, [email protected]
Afaf S. Alwabli, Dr., Assist. Prof., King Abdulaziz University, Saudi Arabia, [email protected], [email protected]
