DOI QR코드

DOI QR Code

The effects of the surrounding viscoelastic media on the buckling behavior of single microfilament within the cell: A mechanical model

  • Khadimallah, Mohamed A. (Prince Sattam Bin Abdulaziz University, College of Engineering, Civil Engineering Department) ;
  • Safeer, Muhammad (Department of Mathematics, University of Azad Jammu and Kashmir) ;
  • Taj, Muhammad (Department of Mathematics, University of Azad Jammu and Kashmir) ;
  • Ayed, Hamdi (Department of Civil Engineering, College of Engineering, King Khalid University) ;
  • Hussain, Muzamal (Department of Mathematics, Govt. College University Faisalabad) ;
  • Bouzgarrou, Souhail Mohamed (Civil Engineering Department, Faculty of Engineering, Jazan University) ;
  • Mahmoud, S.R. (GRC Department, Faculty of Applied studies, King Abdulaziz University) ;
  • Ahmad, Manzoor (Department of Mathematics University of Poonch Rawalwkot) ;
  • Tounsi, Abdelouahed (Materials and Hydrology Laboratory University of Sidi Bel Abbes, Algeria Faculty of Technology Civil Engineering Department)
  • Received : 2020.03.09
  • Accepted : 2020.08.01
  • Published : 2020.08.25

Abstract

In the present study, a mechanical model is applied to account the effects of the surrounding viscoelastic media on the buckling behavior of single microfilament within the cell. The model immeasurably associates filament's bending rigidity, neighboring system elasticity, and cytosol viscosity with buckling wavelengths, buckling growth rates and buckling amplitudes of the filament. Cytoskeleton components in living cell bear large compressive force and are responsible in maintaining the cell shape. Actually these filaments are surrounded by viscoelastic media consisting of other filaments network and viscous cytosole within the cell. This surrounding, viscoelastic media affects the buckling behavior of these filaments when external force is applied on these filaments. The obtained results, indicate that the coupling of viscoelastic media with the viscous cytosol greatly affect the buckling behavior of microfilament. The buckling forces increased with the increase in the intensity of surrounding viscoelastic media.

Keywords

References

  1. Alberts, B., Johnson, A., Lewis, J., Raff, M., Roberts, K. and Walter, P. (2002), Cell Movements and the Shaping of the Vertebrate Body. In Molecular Biology of the Cell, 4th Edition, Garland Science.
  2. Almor, J.M., Baulies, M.D., Urgell, J.D., Colet, J.C., Capdevila, M.C. and Cortada, J.B. (2004), "Prevalence and clinical course of patients in Spain with acute myocardial infarction and severely depressed ejection fraction who meet the criteria for automatic defibrillator implantation", Revista Espanola de Cardiologia, 57(7), 705-708. https://doi.org/10.1016/S1885-5857(06)60297-1.
  3. Bennett, V. and Baines, A.J. (2001), "Spectrin and ankyrin-based pathways: metazoan inventions for integrating cells into tissues", Physiol. Rev., 81(3), 1353-1392. https://doi.org/10.1152/physrev.2001.81.3.1353.
  4. Carter, N.J. and Cross, R. (2005), "Mechanics of the kinesin step", Nature, 435(7040), 308-312. https://doi.org/10.1038/nature03528.
  5. Crowley, C.A., Curnutte, J.T., Rosin, R.E. andre-Schwartz, J., Gallin, J.I., Klempner, M., ... & Babior, B.M. (1980), "An inherited abnormality of neutrophil adhesion: its genetic transmission and its association with a missing protein", New England J. Medic., 302(21), 1163-1168. https://doi.org/10.1056/NEJM198005223022102.
  6. Elzinga, M., Collins, J.H., Kuehl, W.M. and Adelstein, R.S. (1973), "Complete amino-acid sequence of actin of rabbit skeletal muscle", Proc. Nat. Acad. Sci., 70(9), 2687-2691. https://doi.org/10.1073/pnas.70.9.2687.
  7. Gardel, M.L., Shin, J.H., MacKintosh, F.C., Mahadevan, L., Matsudaira, P. and Weitz, D.A. (2004), "Elastic behavior of cross-linked and bundled actin networks", Sci., 304(5675), 1301-1305. https://doi.org/10.1126/science.1095087.
  8. Gardel, M.L., Shin, J.H., MacKintosh, F.C., Mahadevan, L., Matsudaira, P. and Weitz, D.A. (1993), "Flexural rigidity of microtubules and actin filaments measured from thermal fluctuations in shape", J. Cell. Biol., 120(4), 923-934. https://doi.org/10.1529/biophysj.103.038877.
  9. Glazov, M.M., Sherman, E.Y. and Dugaev, V.K. (2010), "Two-dimensional electron gas with spin-orbit coupling disorder", Physica E: Low Dimens. Syst. Nanostruct., 42(9), 2157-2177. https://doi.org/10.1038/srep45346.
  10. Gu, B., Mai, Y.W. and Ru, C.Q. (2009), "Mechanics of microtubules modeled as orthotropic elastic shells with transverse shearing", Acta Mechanica, 207(3-4), 195-209. https://doi.org/10.1007/s00707-008-0121-8.
  11. Gunning, P., Ponte, P., Okayama, H., Engel, J., Blau, H. and Kedes, L (1983), "Isolation and characterization of full-length cDNA clones for human alpha- beta-, and gamma-actin mRNAs: skeletal but not cytoplasmic actins have an amino-terminal cysteine that is subsequently removed", Molecul. Cell. Bio., 3(5), 787-795. https://doi.org/10.1128/mcb.3.10.1783.
  12. Gunning, P.W., Ghoshdastider, U., Whitaker, S., Popp, D. and Robinson, R.C. (2015), "The evolution of compositionally and functionally distinct actin filaments", J. Cell Sci., 128(11), 2009-2019. https://doi.org/10.1242/jcs.165563.
  13. Gurovich, V.T. and Fel, L.G. (2009), "Landau-Stanyukovich rule and the similarity parameter for converging shocks", JETP Lett., 89(1), 14-18. https://doi.org/10.1134/S0021364009010044.
  14. Hanukogle, I., Tanese, N. and Fuchs, E. (1983), "Complementary DNA sequence of a human cytoplasmic actin: interspecies divergence of 3' non-coding regions", J. Molecul. Biol., 163(4), 673-678. https://doi.org/10.1016/0022-2836(83)90117-1.
  15. Helbig, D., Silva, C.C.C.D., Real, M.D.V., Santos, E.D.D., Isoldi, L.A. and Rocha, L.A.O. (2016), "Study about buckling phenomenon in perforated thin steel plates employing computational modeling and constructal design method", Lat. Am. J. Solid. Struct., 13(10), 1912-1936. http://dx.doi.org/10.1590/1679-78252893.
  16. Herrmann, H., Bar, H., Kreplak, L., Strelkov, S.V. and Aebi, U. (2007), "Intermediate filaments: from cell architecture to nanomechanics", Nat. Rev. Molecul. Cell Biol., 8(7), 562-573. https://doi.org/10.1038/nrm2197.
  17. Hussain, M. and Naeem, M. (2019a), "Vibration characteristics of single-walled carbon nanotubes based on non-local elasticity theory using wave propagation approach (WPA) including chirality", Perspective of Carbon Nanotubes, IntechOpen. https://doi.org/10.5772/intechopen.85948.
  18. Hussain, M. and Naeem, M. (2019d), "Rotating response on the vibrations of functionally graded zigzag and chiral single walled carbon nanotubes", Appl. Math. Model., 75, 506-520. https://doi.org/10.1016/j.apm.2019.05.039.
  19. Hussain, M. and Naeem, M.N. (2019b), "Effects of ring supports on vibration of armchair and zigzag FGM rotating carbon nanotubes using Galerkin's method", Compo. Part B. Eng., 163, 548-561. https://doi.org/10.1016/j.compositesb.2018.12.144.
  20. Hussain, M. and Naeem, M.N. (2019c), "Vibration characteristics of zigzag and chiral FGM rotating carbon nanotubes sandwich with ring supports", J. Mech. Eng. Sci., Part C, 233(16), 5763-5780. https://doi.org/10.1177/0954406219855095.
  21. Hussain, M. and Naeem, M.N. (2020b), "Vibration characteristics of zigzag FGM single-walled carbon nanotubes based on Ritz method with ring-stiffeners", Indian Journal of Physics.
  22. Hussain, M. and Naeem, M.N. (2020c), "Accurate compact solution of fluid-filled FG cylindrical shell inducting fluid term: Frequency analysis", Journal of Sandwich Structures and Materials.
  23. Hussain, M. and Naeem., M.N. (2017), "Vibration analysis of single-walled carbon nanotubes using wave propagation approach", Mech. Sci., 8(1), 155-164. https://doi.org/10.5194/ms-8-155-2017.
  24. Hussain, M. and Naeem, M.N. (2020), "Mass density effect on vibration of zigzag and chiral SWCNTs: A theoretical study", Journal of Sandwich Structures & Materials, 1099636220906257. https://doi.org/10.1177/1099636220906257.
  25. Ishida, T., Thitamadee, S. and Hashimoto, T. (2007), "Twisted growth and organization of cortical microtubules", J. Plant Res., 120(1), 61-70. https://doi.org/10.1371/journal.pone.0160202.
  26. Jerusalem, A. and Dao, M. (2012), "Continuum modeling of a neuronal cell under blast loading", Acta Biomaterialia, 8(9), 3360-3371. https://doi.org/10.1016/j.actbio.2012.04.039.
  27. Jiang, H. and Zhang, J. (2008), "Mechanics of microtubule buckling supported by cytoplasm", J. Appl. Mech., 75(6), 061019. https://doi.org/10.1115/1.2966216.
  28. Kar, V.R. and Panda, S.K. (2016), "Post-buckling behaviour of shear deformable functionally graded curved shell panel under edge compression", Int. J. Mech. Sci., 115, 318-324. https://doi.org/10.1016/j.ijmecsci.2016.07.014.
  29. Katariya, P.V. and Panda, S.K. (2016), "Thermal buckling and vibration analysis of laminated composite curved shell panel", Aircraft Eng. Aerosp. Technol., 88(1), 97-107. https://doi.org/10.1108/AEAT-11-2013-0202.
  30. Katariya, P.V., Das, A. and Panda, S.K. (2018), "Buckling analysis of SMA bonded sandwich structure-using FEM", IOP Conf. Ser.: Mater. Sci. Eng., 338(1), 012035. https://doi.org/10.1088/1757-899X/338/1/012035
  31. Katariya, P.V., Panda, S.K. and Mahapatra, T.R. (2017), "Nonlinear thermal buckling behaviour of laminated composite panel structure including the stretching effect and higher-order finite element", Adv. Mater. Res., 6(4), 349. http://dx.doi.org/10.12989/amr.2017.6.4.349.
  32. Kikumoto, M., Kurachi, M., Tosa, V. and Tashiro, H. (2006), "Flexural rigidity of individual microtubules measured by a buckling force with optical traps", Biophys. J., 90(5), 1687-1696. https://doi.org/10.1529/biophysj.104.055483.
  33. Li, T. (2008), "A mechanics model of microtubule buckling in living cells", J. Biomech., 41(8), 1722-1729. https://doi.org/10.1016/j.jbiomech.2008.03.003.
  34. Lodish, H., Berk, A., Kaiser, C. A., Krieger, M., Scott, M. P., Bretscher, A., ... & Matsudaira, P. (2008), Molecular Cell Biology, Garland Science, New York.
  35. Lundin, V.F., Leroux, M.R. and Stirling, P.C. (2010), "Quality control of cytoskeletal proteins and human disease", Trend. Biochem. Sci., 35(5), 288-297. https://doi.org/10.1007/s00709-012-0403-9.
  36. Mehar, K. and Panda, S.K. (2019), "Multiscale modeling approach for thermal buckling analysis of nanocomposite curved structure", Adv. Nano Res., 7(3), 181. http://dx.doi.org/10.12989/anr.2019.7.3.181.
  37. Mehar, K., Panda, S.K., Devarajan, Y. and Choubey, G. (2019), "Numerical buckling analysis of graded CNT-reinforced composite sandwich shell structure under thermal loading", Compos. Struct., 216, 406-414. https://doi.org/10.1016/j.compstruct.2019.03.002
  38. Mirny, L. and Shakhnovich, E. (2001), "Protein folding theory: from lattice to all-atom models", Ann. Rev. Biophys. Biomolec. Struct., 30(1), 361-396. https://doi.org/10.1146/annurev.biophys.30.1.361.
  39. Netter, F.H. and Colacino, S. (1989), Atlas of Human Anatomy, Ciba-Geigy Corporation.
  40. Noria, S., Xu, F., McCue, S., Jones, M., Gotlieb, A.I. and Langille, B.L. (2004), "Assembly and reorientation of stress fibers drives morphological changes to endothelial cells exposed to shear stress", Am. J. Pathol., 164(4), 1211-1223. https://doi.org/10.1371/journal.pone.0004853.
  41. Pan, X., Hobbs, R.P. and Coulombe, P.A. (2013), "The expanding significance of keratin intermediate filaments in normal and diseased epithelia", Curr. Opin. Cell Bio., 25(1), 47-56. https://doi.org/10.1016/j.ceb.2012.10.018.
  42. Panda, S.K. and Katariya, P.V. (2015), "Stability and free vibration behaviour of laminated composite panels under thermo-mechanical loading", Int. J. Appl. Comput. Math., 1(3), 475-490. https://doi.org/10.1007/s40819-015-0035-9.
  43. Panda, S.K. and Singh, B.N. (2009), "Thermal post-buckling behaviour of laminated composite cylindrical/hyperboloid shallow shell panel using nonlinear finite element method", Compos. Struct., 91(3), 366-374. https://doi.org/10.1016/j.compstruct.2009.06.004.
  44. Panda, S.K. and Singh, B.N. (2010), "Thermal post-buckling analysis of a laminated composite spherical shell panel embedded with shape memory alloy fibres using non-linear finite element method", Proc. Inst. Mech. Eng., Part C: J. Mech. Eng. Sci., 224(4), 757-769. https://doi.org/10.1243/09544062JMES1809.
  45. Parekh, S.H., Chaudhuri, O., Theriot, J.A. and Fletcher, D.A. (2005), "Loading history determines the velocity of actin-network growth", Nat. Cell Bio., 7(12), 1219-1223. https://doi.org/10.1038/s41598-017-15638-5.
  46. Pokorny, J., Jelinek, F., Trkal, V., Lamprecht, I. and Holzel, R. (1997), "Vibrations in microtubules", J. Biolog. Phys., 23(3), 171-179. https://doi.org/10.1023/A:1005092601078.
  47. Qian, X.S., Zhang, J.Q. and Ru, C.Q. (2007), "Wave propagation in orthotropic microtubules", J. Appl. Phys., 101(8), 084702. https://doi.org/10.1063/1.2717573.
  48. Raff, M., Alberts, B., Lewis, J., Johnson, A. and Roberts, K. (2002). Molecular Biology of the Cell, 4th Edition, National Center for Biotechnology InformationOs Bookshelf.
  49. Safeer, M., Taj, M. and Abbas, S.S. (2019), "Effect of viscoelastic medium on wave propagation along protein microtubules", AIP Adv., 9(4), 045108. https://doi.org/10.1063/1.5086216.
  50. Schliwa, M. and Woehlke, G. (2003), "Molecular motors", Nat., 422(6933), 759-765. https://doi.org/10.1016/j.cub.2007.04.025.
  51. Sirenko, Y.M., Stroscio, M.A. and Kim, K.W. (1996), "Elastic vibrations of microtubules in a fluid", Phys. Rev. E, 53(1), 1003. https://doi.org/10.1103/PhysRevE.53.1003.
  52. Stehn, J.R., Haass, N.K., Bonello, T., Desouza, M., Kottyan, G., Treutlein, H., ... & Allanson, M (2013), "A novel class of anticancer compounds targets the actin cytoskeleton in tumor cells", Cancer Res., 73(16), 5169-5182. https://doi.org/10.1158/0008-5472.
  53. Taj, M. and Zhang, J. (2011), "Buckling of embedded microtubules in elastic medium", Appl. Math. Mech., 32(3), 293-300. https://doi.org/10.1007/s10483-011-1415-x.
  54. Taj, M. and Zhang, J. (2012), "Analysis of vibrational behaviors of microtubules embedded within elastic medium by Pasternak model", Biochem. Biophys. Res. Commun., 424(1), 89-93. https://doi.org/10.1016/j.bbrc.2012.06.072.
  55. Taj, M. and 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. https://doi.org/10.1016/j.jmbbm.2013.11.011.
  56. Taj, M., Safeer, M., Hussain, M., Naeem, M.N., Ahmad, M., Abbas, K., ... & Tounsi, A. (2020), "Effect of external force on buckling of cytoskeleton intermediate filaments within viscoelastic media", Comput. Concrete, 25(3), 205-214. https://doi.org/10.12989/cac.2020.25.3.205.
  57. Taj, M.S.M. (2019), "Vibrational analysis of microtubules embedded within viscoelastic, edium using orthotropic Kelvin like model", Sains Malaysiana, 48(12), 2841-2847. http://dx.doi.org/10.17576/jsm-2019-4812-25.
  58. Takasone, T., Juodkazis, S., Kawagishi, Y., Yamaguchi, A., Matsuo, S., Sakakibara, H., ... & Misawa, H. (2002), "Flexural rigidity of a single microtubule", JPN J. Appl. Phys., 41(5R), 3015. https://doi.org/10.1143/JJAP.41.3015.
  59. Timoshenko, S.P. and Woinowsky-Krieger, S. (1959), Theory of Plates and Shells, McGraw-hill.
  60. Tseng, Y., Schafer, B.W., Almo, S.C. and Wirtz, D. (2002), "Functional synergy of actin filament cross-linking proteins", J. Biolog. Chem., 277(28), 25609-25616. https://doi.org/10.1017/CBO9780511809217.
  61. Tuszynski, J.A., Luchko, T., Portet, S. and Dixon, J.M. (2005), "Anisotropic elastic properties of microtubules", Eur. Phys. J. E, 17(1), 29-35. https://doi.org/10.1140/epje/i2004-10102-5.
  62. van der Lebenskraft, G.D.L. "Biological science" redirects here. It is not to be confused with life science. For other uses, see Biology (disambiguation).
  63. Vaziri, A., Lee, H. and Mofrad, M.K. (2006), "Deformation of the cell nucleus under indentation: mechanics and mechanisms", J. Mater. Res., 21(8), 2126-2135. https://doi.org/10.1557/JMR.2006.0262.
  64. Venier, P., Maggs, A.C., Carlier, M.F. and Pantaloni, D. (1994), "Analysis of microtubule rigidity using hydrodynamic flow and thermal fluctuations", J. Biolog. Chem., 269(18), 13353-13360. https://doi.org/10.1529/biophysj.103.038877.
  65. Wang, C.Y., Ru, C.Q. and Mioduchowski, A. (2006), "Orthotropic elastic shell model for buckling of microtubules", Phys. Rev. E, 74(5), 052901. https://doi.org/10.1103/PhysRevE.74.052901.
  66. Zhang, Q., Jiang, B., Xiao, Z., Cui, W. and Liu, J. (2019), "Post-buckling analysis of compressed rods in cylinders by using dynamic relaxation method", Int. J. Mech. Sci., 159, 103-115. https://doi.org/10.1016/j.ijmecsci.2019.05.040.

Cited by

  1. Mathematical approach for the effect of the rotation, the magnetic field and the initial stress in the non-homogeneous an elastic hollow cylinder vol.79, pp.5, 2020, https://doi.org/10.12989/sem.2021.79.5.593