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 SAFEER1,2 & MUHAMMAD TAJ1*

 

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

 

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

 

Diserahkan: 5 Mac 2019/Diterima: 23 Disember 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

RUJUKAN

Adames, N.R. & Cooper, J.A. 2000. Microtubule interactions with the cell cortex causing nuclear movements in Saccharomyces cerevisiae. J. Cell Biol. 149(4): 863-874.

Boykov, I., Boykova, A. & Ventsel, E. 2004. Fundamental solutions for thick sandwich plates. Engineering Analysis with Boundary Elements 28(12): 1437-1444.

Brangwynne, C.P., MacKintosh, F.C., Kumar, S., Geisse, N.A., Talbot, J., Mahadevan, L., Parker, K.K., Ingber, D.E. & Weitz, D.A. 2006. Microtubules can bear enhanced compressive loads in living cells because of lateral reinforcement. J. Cell Biol. 173(5): 733-741.

Burton, G.W. & Forbes, I. 1960. The genetics and manipulation of obligate apomixis in common Bahia grass Pas-palum notatum Flügge. Paper presented at the Proceedings of the Eighth International Grassland Congress held at the University of Reading, England, 11-21 July.

Chung-Davidson, Y.W., Huertas, M. & Li, W. 2010. A review of research in fish pheromones. In Chemical Communication in Crustaceans, edited by Breithaupt, T. & Thiel, M. New York: Springer. pp. 467-482.

Feldhendler, D. 2002. Augusto Boal and Jacob L.Moreno: Theatre and therapy. In Playing Boal: Theatre, Theraphy & Activitism, edited by Schutzman, M. & Cohen-Cruz, J. London: Routledge. pp. 97-119.

Felgner, P., Barenholz, Y., Behr, J., Cheng, S., Cullis, P., Huang, L., Jessee, J.A., Seymour, L., Szoka, F., Thierry, A.R., Wagner, E. & Thierry, A. 1997. Nomenclature for synthetic gene delivery systems. Human Gene Therapy 8(5): 511-512.

Forbes, J., Russell, J., Miyahara, S., Zhang, X., Palo, S., Mlynczak, M., Mertens. C.J. & Hagan, M. 2006. Troposphere-thermosphere tidal coupling as measured by the SABER instrument on TIMED during July-September 2002. Journal of Geophysical Research: Space Physics 111(A10). https:// doi.org/10.1029/2005JA011492.

Hardin, R. 2015. Collective Action. New York: RFF Press.

Kiyoi, H., Naoe, T., Nakano, Y., Yokota, S., Minami, S., Miyawaki, S., Asou, N., Kuriyama, K., Jinnai, I., Shimazaki, C., Akiyama, H., Saito, K., Oh, H., Motoji, T., Omoto, E., Saito, H., Ohno, R. & Ueda, R. 1999. Prognostic implication of FLT3 and N-RAS gene mutations in acute myeloid leukemia. Blood 93(9): 3074-3080.

Kreider, J.C. & Blumberg, M.S. 2005. Geotaxis and beyond: Commentary on Motz and Alberts. Neurotoxicology and Teratology 27(4): 535-538.

Leonova, A., Pokorny, J. & Smith, V.C. 2003. Spatial frequency processing in inferred PC-and MC-pathways. Vision Research 43(20): 2133-2139.

Meyers, M.A. & Chawla, K.K. 1999. Mechanical Behavior of Materials. Englewood Cliffs: Prentice-Hall.

Morehouse, B.J., Carter, R.H. & Sprouse, T.W. 2000. The implications of sustained drought for transboundary water management in Nogales, Arizona, and Nogales, Sonora. Natural Resources Journal 40(4): 783-817.

Nogales, E., Whittaker, M., Milligan, R.A. & Downing, K.H. 1999. High-resolution model of the microtubule. Cell 96(1): 79-88.

Pet-Soede, C., Cesar, H.S. & Pet, J. 1999. An economic analysis of blast fishing on Indonesian coral reefs. Environmental Conservation 26(2): 83-93.

Schoutens, W. 2005. Moment swaps. Quantitative Finance 5(6): 525-530.

Shah, S., Li, J., Moffatt, B.A. & Glick, B.R. 1998. Isolation and characterization of ACC deaminase genes from two different plant growth-promoting rhizobacteria. Canadian Journal of Microbiology 44(9): 833-843.

Sharma, P., Khatri, V.K., Gu, X., Song, Y., Shen, M.L., Riggs- Sauthier, J., Anand, N.K., Kozlowski, A., Odinecs, A. & Riley, T.A. 2019. Derivatives of 6-(2, 3-dichlorophenyl)-1, 2, 4-triazin-5-amine: Google Patents.

Shen, R. & Andrews, S.A. 2011. NDMA formation kinetics from three pharmaceuticals in four water matrices. Water Research 45(17): 5687-5694.

Sirenko, Y.M., Stroscio, M.A. & Kim, K. 1996. Elastic vibrations of microtubules in a fluid. Physical Review E 53(1): 1003.

Taj, M. & Zhang, J. 2014. Analysis of wave propagation in orthotropic microtubules embedded within elastic medium by Pasternak model. J. Mech. Behav. Biomed. Mater. 30: 300-305.

Taj, M. & Zhang, J. 2012. Analysis of vibrational behaviors of microtubules embedded within elastic medium by Pasternak model. Biochemical and Biophysical Research Communications 424(1): 89-93.

Taj, M. & Zhang, J.Q. 2011. Buckling of embedded microtubules in elastic medium. Applied Mathematics and Mechanics 32(3): 293-300.

Van Buren, M.E. & Erskine, W. 2002. The 2002 ASTD state of the industry report. Alexandria, VA: American Society of Training and Development.

Van Buren, V., Odde, D.J. & Cassimeris, L. 2002. Estimates of lateral and longitudinal bond energies within the microtubule lattice. Proceedings of the National Academy of Sciences 99(9): 6035-6040.

Wang, Y., Kong, L.J., Li, C. & Bureau, D.P. 2006. Effect of replacing fish meal with soybean meal on growth, feed utilization and carcass composition of cuneate drum (Nibea miichthioides). Aquaculture 261(4): 1307-1313.

Yang, X., Schadt, E.E., Wang, S., Wang, H., Arnold, A.P., Ingram- Drake, L., Drake, T.A. & Lusis, A.J. 2006. Tissue-specific expression and regulation of sexually dimorphic genes in mice. Genome Research 16(8): 995-1004.

Zhang, B., Georgiev, O., Hagmann, M., Günes, Ç., Cramer, M., Faller, P., Vasák, M. & Schaffner, W. 2003. Activity of metal-responsive transcription factor 1 by toxic heavy metals and H2O2 in vitro is modulated by metallothionein. Molecular and Cellular Biology 23(23): 8471-8485.

Zhao, Z., Dua, D. & Singh, S. 2017. Generating natural adversarial examples. arXiv preprint arXiv:1710.11342.

Zheng, J., Trafny, E.A., Knighton, D.R., Xuong, N.H., Taylor, S.S., Ten Eyck, L.F. & Sowadski, J.M. 1993. 2.2 Å refined crystal structure of the catalytic subunit of cAMP-dependent protein kinase complexed with MnATP and a peptide inhibitor. Acta Crystallographica Section D: Biological Crystallography 49(3): 362-365.

Zhou, Y., Wu, Y., Yang, L., Fu, L., He, K., Wang, S., Hao J., Chen, J. & Li, C. 2010. The impact of transportation control measures on emission reductions during the 2008 Olympic Games in Beijing, China. Atmospheric Environment 44(3): 285-293.

 

*Pengarang untuk surat-menyurat; email: Muhammad_taj75@yahoo.com

 

 

 

 

 

sebelumnya