DOI QR코드

DOI QR Code

Bending behavior of microfilaments in living cell with nonlocal effects

  • Muhammad Safeer (Department of Mathematics, University of poonch Rawalakt) ;
  • Muhammad Taj (Department of Mathematics, University of poonch Rawalakt) ;
  • Mohamed A. Khadimallah (Department of Civil Engineering, College of Engineering in Al-Kharj, Prince Sattam Bin Abdulaziz University) ;
  • Muzamal Hussain (Department of Mathematics, Govt. College University Faisalabad) ;
  • Saima Akram (Department of Mathematics, Govt. College Women University) ;
  • Faisal Mehmood Butt (Department of Electrical Engineering, University of Azad Jammu and Kashmir Muzaffarabad) ;
  • Abdelouahed Tounsi (YFL (Yonsei Frontier Lab), Yonsei University)
  • Received : 2021.11.02
  • Accepted : 2023.01.26
  • Published : 2023.07.25

Abstract

Dynamics of protein filamentous has been an active area of research since the last few decades as the role of cytoskeletal components, microtubules, intermediate filaments and microfilaments is very important in cell functions. During cell functions, these components undergo the deformations like bending, buckling and vibrations. In the present paper, bending and buckling of microfilaments are studied by using Euler Bernoulli beam theory with nonlocal parametric effects in conjunction. The obtained results show that the nonlocal parametric effects are not ignorable and the applications of nonlocal parameters well agree with the experimental verifications.

Keywords

Acknowledgement

This study is supported via funding from Prince Satam bin Abdulaziz University project number (PSAU/2023/R/1444)

References

  1. Abouelregal, A.E., Mohammad-Sedighi, H., Faghidian, S.A. and Shirazi, A.H. (2021), "Temperature-dependent physical characteristics of the rotating nonlocal nanobeams subject to a varying heat source and a dynamic load", Facta Univ. Series Mech. Eng., 19(4), 633-656. https://doi.org/10.22190/FUME201222024A
  2. Ackbarow, T., Chen, X., Keten, S., and Buehler, M. J. (2007), " Hierarchies, multiple energy barriers, and robustness govern the fracture mechanics of α-helical and β-sheet protein domains", Proceedings of the National Academy of Sciences, 104(42), 16410-16415. https://doi.org/10.1073/pnas.0705759104
  3. Akbas S.D. (2017a), "Free vibration of edge cracked functionally graded microscale beams based on the modified couple stress theory", Int. J. Struct. Stabil. Dyn., 17(3), 1750033. https://doi.org/10.21923/jesd.553328
  4. Akbas, S.D. (2016a), "Forced vibration analysis of viscoelastic nanobeams embedded in an elastic medium", Smart Struct. Syst., 18(6), 1125-1143. https://doi.org/10.12989/sss.2016.18.6.1125
  5. Akbas, S.D. (2016b), "Analytical solutions for static bending of edge cracked micro beams", Struct. Eng. Mech., 59(3), 579-599. https://doi.org/10.12989/SEM.2016.59.3.579
  6. Akbas, S.D. (2017b), "Forced vibration analysis of functionally graded nanobeams", Int. J. Appl. Mech., 9(7), 1750100. https://doi.org/10.1142/S1758825117501009
  7. Akintewe, O.O., Roberts, E.G., Rim, N.G., Ferguson, M.A. and Wong, J.Y. (2017), "Design approaches to myocardial and vascular tissue engineering", Annual Rev. Biomed. Eng., 19, 389-414. https://doi.org/10.1146/annurev-bioeng-071516-044641
  8. Alberts, B., Bray, D., Hopkin, K., Johnson, A. D., Lewis, J., Raff, M., Roberts, K and Walter, P. (2013), Essential Cell Biology, Garland Science.
  9. AlSaleh, R.J. and Fuggini, C. (2020), "Combining GPS and accelerometers' records to capture torsional response of cylindrical tower", Smart Struct. Syst., 25(1), 111. https://doi.org/10.12989/sss.2020.25.1.111.
  10. Arani, A.G., Kolahchi, R. and Esmailpour, M. (2016), "Nonlinear vibration analysis of piezoelectric plates reinforced with carbon nanotubes using DQM", Smart Struct Syst, 18, 787-800. http://doi.org/10.12989/sss.2016.18.4.787
  11. Arefi, M. and Zenkour, A. M. (2017), "Nonlinear and linear thermo-elastic analyses of a functionally graded spherical shell using the Lagrange strain tensor", Smart Struct Syst, 19, 33-38. https://doi.org/10.12989/sss.2017.19.1.033
  12. Benmansour, D.L., Kaci, A., Bousahla, A.A., Heireche, H., Tounsi, A., Alwabli, A.S., Alhebshi, A.M., Al-ghmady, K. and Mahmoud, S.R. (2019), "The nano scale bending and dynamic properties of isolated protein microtubules based on modified strain gradient theory", Adv. Nano Res., 7(6), 443. 213840154
  13. Blobe, G.C., Schiemann, W.P. and Lodish, H.F. (2000), "Role of transforming growth factor β in human disease", New England J. Med., 342(18), 1350-1358. https://doi.org/10.1056/NEJM200005043421807
  14. Block, J., Schroeder, V., Pawelzyk, P., Willenbacher, N. and Koster, S. (2015), "Physical properties of cytoplasmic intermediate filaments", Biochimica et Biophysica Acta Mol. Cell Res., 1853, 3053-3064. https://doi.org/10.1016/j.bbamcr.2015.05.009.
  15. Bornheim, R., Muller, M., Reuter, U., Herrmann, H., Bussow, H. and Magin, T.M. (2008), "A dominant vimentin mutant upregulates Hsp70 and the activity of the ubiquitin-proteasome system, and causes posterior cataracts in transgenic mice", J. Cell Sci., 121(22), 3737-3746. https://doi.org/10.1242/jcs.030312
  16. Boussoula, A., Boucham, B., Bourada, M., Bourada, F., Tounsi, A., Bousahla, A.A. and Tounsi, A. (2019), "A simple nth-order shear deformation theory for thermomechanical bending analysis of different configurations of FG sandwich plates", Smart Struct. Syst., 25(2), 197. https://doi.org/10.12989/sss.2020.25.2.197
  17. Chang, L. and Goldman, R.D. (2004), "Intermediate filaments mediate cytoskeletal crosstalk", Nature Rev. Mol. Cell Biol., 5(8), 601-613. https://doi.org/10.1063/1.3050108
  18. Chen, T., Chiu, M.S. and Weng, C.N. (2006), "Derivation of the generalized Young-Laplace equation of curved interfaces in nanoscaled solids", J. Appl. Phys., 100(7), 074308. https://doi.org/10.1063/1.3050108
  19. Civalek, O . and Demir, C . (2011), "Bending analysis of microtubules using nonlocal Euler-Bernoulli beam theory", Appl. Math. Modell., 35(5), 2053-2067. https://doi.org/10.1016/j.apm.2010.11.004
  20. Crewther, W., Dowling, L., Steinert, P. and Parry, D. (1983), "Structure of intermediate filaments", Int. J. Biol. Macromol., 5(5), 267-274. https://doi.org/10.1242/jcs.089516
  21. Cuenot, S., Fretigny, C., Demoustier-Champagne, S. and Nysten, B. (2004), "Surface tension effect on the mechanical properties of nanomaterials measured by atomic force microscopy", Phys. Rev. B, 69(16), 165410. https://doi.org/10.1103/PhysRevB.69.165410
  22. Dickinson, R.B. and Purich, D.L. (2006), "Diffusion rate limitations in actin-based propulsion of hard and deformable particles", Biophys. J., 91(4), 1548-1563. https://doi.org/10.1529/biophysj.106.082362
  23. Dickinson, R.B. and Purich, D.L. (2007), "Nematode sperm motility: nonpolar filament polymerization mediated by end-tracking motors", Biophys. J., 92(2), 622-631. https://doi.org/10.1529/biophysj.106.090472
  24. Dickinson, R.B., Caro, L. and Purich, D.L. (2004), "Force generation by cytoskeletal filament end-tracking proteins", Biophys. J., 87(4), 2838-2854. https://doi.org/10.1529/biophysj.104.045211
  25. Dickinson, R.B., Southwick, F.S. and Purich, D.L. (2002), "A direct-transfer polymerization model explains how the multiple profilin-binding sites in the actoclampin motor promote rapid actin-based motility", Arch. Biochem. Biophys., 406(2), 296-301. https://doi.org/10.1016/s0003-9861(02)00212-6
  26. Ebrahimi, F., Dabbagh, A., Rabczuk, T. and Tornabene, F. (2019), "Analysis of propagation characteristics of elastic waves in heterogeneous nanobeams employing a new two-step porosity-dependent homogenization scheme", Adv. Nano Res., 7(2), 135. https://doi.org/10.12989/anr.2019.7.2.135
  27. Eltaher, M.A., Almalki, T.A., Ahmed, K.I. and Almitani, K.H. (2019), "Characterization and behaviors of single walled carbon nanotube by equivalent-continuum mechanics approach", Adv. Nano Res., 7(1), 39. https://doi.org/10.12989/anr.2019.7.1.039
  28. Eringen, A.C. (1972a), "Linear theory of nonlocal elasticity and dispersion of plane waves", Int. J. Eng. Sci., 10(5), 425-435. https://doi.org/10.1016/0020-7225(72)90050-X
  29. Eringen, A.C. (1972b), "Nonlocal polar elastic continua", Int. J. Eng. Sci., 10(1), 1-16. https://doi.org/10.1016/0020-7225(72)90070-5
  30. Eringen, A.C. (1984), "Theory of nonlocal elasticity and some applications", Res Mech., 21(4), 313-342. https://doi.org/10.21236/ADA145201
  31. Fletcher, D.A. and Mullins, R.D. (2010), "Cell mechanics and the cytoskeleton", Nature, 463, 485. https://doi.org/10.1038/nature08908
  32. Franke, W.W., Schmid, E., Osborn, M. and Weber, K. (1978), "Different intermediate-sized filaments distinguished by immunofluorescence microscopy", Proceedings of the National Academy of Sciences, 75(10), 5034-5038. https://doi.org/10.1073/pnas.75.10.5034
  33. Fuchs, E. and Cleveland, D.W. (1998), "A structural scaffolding of intermediate filaments in health and disease", Science, 279(5350), 514-519. https://doi.org/10.1126/science.279.5350.514.
  34. Fuchs, E. and Weber, K. (1994), "Intermediate filaments: structure, dynamics, function and disease", Annual Rev. Biochem., 63(1), 345-382. https://doi.org/10.1016/S0014-5793(98)01190-9
  35. Fudge, D.S., Gardner, K.H., Forsyth, V.T., Riekel, C. and Gosline, J.M. (2003), "The mechanical properties of hydrated intermediate filaments: insights from hagfish slime threads", Biophys. J., 85(3), 2015-2027. https://doi.org/10.1242/jeb.02067
  36. Galland, R., Leduc, P., Guerin, C., Peyrade, D., Blanchoin, L. and Thery, M. (2013), "Fabrication of three-dimensional electrical connections by means of directed actin self-organization", Nature Mater., 12(5), 416-421. https://doi.org/10.1038/nmat3569
  37. Gao, Y. and Lei, F.M. (2009), "Small scale effects on the mechanical behaviors of protein microtubules based on the nonlocal elasticity theory", Biochem. Biophys. Res. Commun., 387(3), 467-471. https://doi.org/10.1021/nl025724i
  38. Gervasi, M.G., Xu, X., Carbajal-Gonzalez, B., Buffone, M.G., Visconti, P.E. and Krapf, D. (2018), "The actin cytoskeleton of the mouse sperm flagellum is organized in a helical structure", J. Cell Sci., 131(11), jcs215897. https://doi.org/10.1242/jcs.215897
  39. Gittes, F., Mickey, B., Nettleton, J. and Howard, J. (1993), "Flexural rigidity of microtubules and actin filaments measured from thermal fluctuations in shape", J. Cell Biol., 120(4), 923-934. https://doi.org/10.1016/j.jmb.2012.08.006
  40. Gokhin, D.S. and Fowler, V.M. (2016), "Feisty filaments: actin dynamics in the red blood cell membrane skeleton", Curr. Opinion Hematol., 23(3), 206. https://doi.org/10.1097/MOH.0000000000000227
  41. Goldman, R.D., Cleland, M.M., Murthy, S.P., Mahammad, S. and Kuczmarski, E.R. (2012), "Inroads into the structure and function of intermediate filament networks", J. Struct. Biol., 177(1), 14-23. https://doi.org/10.1016/j.jsb.2011.11.017
  42. Goldman, R.D., Khuon, S., Chou, Y.H., Opal, P. and Steinert, P.M. (1996), "The function of intermediate filaments in cell shape and cytoskeletal integrity", J. Cell. Biol, 134(4), 971-983. https://doi.org/10.1083/jcb.134.4.971
  43. Gruenbaum, Y., Margalit, A., Goldman, R.D., Shumaker, D.K. and Wilson, K.L. (2005), "The nuclear lamina comes of age", Nature Rev. Mol. Cell Biol., 6(1), 21-31. https://doi.org/10.1053/j.gastro.2018.03.026
  44. 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.
  45. Guzman, C., Jeney, S., Kreplak, L., Kasas, S., Kulik, A., Aebi, U. and Forro, L. (2006), "Exploring the mechanical properties of single vimentin intermediate filaments by atomic force microscopy", J. Mol. Biol., 360(3), 623-630. https://doi.org/10.1016/j.jmb.2006.05.030
  46. Hanukoglu, I. and Ezra, L. (2014), "Proteopedia entry: Coiled-coil structure of keratins", Biochem. Mol. Biol. Educ., 42(1), 93-94. https://doi.org/10.1002/bmb.20746
  47. Hanukoglu, I. and Fuchs, E. (1983), "The cDNA sequence of a type II cytoskeletal keratin reveals constant and variable structural domains among keratins", Cell, 33(3), 915-924. https://doi.org/10.1016/0092-8674(83)90034-X
  48. Herrmann, H., Bar, H., Kreplak, L., Strelkov, S. V. and Aebi, U. (2007), "Intermediate filaments: From cell architecture to nanomechanics", Nature Rev. Mol. Cell Biol., 8(7), 562-573. https://doi.org/10.1038/ncb1886
  49. Pieper, K., Grimbacher, B. and Eibel, H. (2013), "B-cell biology and development", J. Allergy Clin. Immunol., 131(4), 959-971. https://doi.org/10.1016/j.jaci.2013.01.046.
  50. Ishikawa, H., Bischoff, R. and Holtzer, H. (1968), "Mitosis and intermediate-sized filaments in developing skeletal muscle", J. Cell Biol., 38(3), 538-555. https://doi.org/10.1016/0012
  51. Koochi, A. and Goharimanesh, M. (2021), "Nonlinear oscillations of CNT nano-resonator based on nonlocal elasticity: The energy balance method", Rep. Mech. Eng., 2(1), 41-50. https://doi.org/10.31181/RME200102041G
  52. Lazar, M., Maugin, G.A. and Aifantis, E.C. (2006), "On a theory of nonlocal elasticity of bi-Helmholtz type and some applications", Int. J. Solids Struct., 43(6), 1404-1421. https://doi.org/10.1016/j.ijsolstr.2005.04.027
  53. Lim, C., Zhang, G. and Reddy, J. (2015), "A higher-order nonlocal elasticity and strain gradient theory and its applications in wave propagation", J. Mech. Phys. Solid, 78, 298-313. https://doi.org/10.1016/j.jmps.2015.02.001
  54. Mehar, K. and Panda, S.K. (2016a), "Geometrical nonlinear free vibration analysis of FG-CNT reinforced composite flat panel under uniform thermal field", Compos. Struct., 143, 336-346. https://doi.org/10.1016/J.COMPSTRUCT.2016.02.038
  55. Mehar, K. and Panda, S.K. (2016b), "Free vibration and bending behaviour of CNT reinforced composite plate using different shear deformation theory", In IOP Conference Series: Materials Science and Engineering, 115(1), 012014. IOP Publishing. https://doi.org/10.1088/1757-899X/115/1/012014
  56. Mofrad, M.R. and Kamm, R.D. (2006), Cytoskeletal Mechanics: Models and Measurements in Cell Mechanics, Cambridge University Press. https://doi.org/10.1017/CBO9780511607318
  57. Mullins, R.D., Heuser, J.A. and Pollard, T.D. (1998), "The interaction of Arp2/3 complex with actin: nucleation, high affinity pointed end capping, and formation of branching networks of filaments", Proceedings of the National Academy of Sciences, 95(11), 6181-6186. https://doi.org/10.1073/pnas.95.11.6181
  58. Ouakad, H.M., Valipour, A., Zur, K.K., Sedighi, H.M. and Reddy, J.N. (2020), "On the nonlinear vibration and static deflection problems of actuated hybrid nanotubes based on the stress-driven nonlocal integral elasticity", Mech. Mater., 148, 103532. https://doi.org/10.1016/j.mechmat.2020.103532
  59. Pieper, K., Grimbacher, B. and Eibel, H. (2013), "B-cell biology and development", J. Allergy Clin., 131(4), 959-971. https://doi.org/10.1016/j.jaci.2013.01.046.
  60. Reddy, J.N. (2006), Theory and Analysis of Elastic Plates and Shells, CRC press. https://doi.org/10.1201/9780849384165.
  61. Reddy, J. and Pang, S. (2008), "Nonlocal continuum theories of beams for the analysis of carbon nanotubes", J. Appl. Phys., 103(2), 023511.
  62. Rudan, M.V., Barrington, C., Henderson, S., Ernst, C., Odom, D.T., Tanay, A. and Hadjur, S. (2015), "Comparative Hi-C reveals that CTCF underlies evolution of chromosomal domain architecture", Cell Rep., 10(8), 1297-1309. https://doi.org/10.1016/j.celrep.2015.02.004.
  63. Sadegh, S., Higgins, J.L., Mannion, P.C., Tamkun, M.M. and Krapf, D. (2017), "Plasma membrane is compartmentalized by a self-similar cortical actin meshwork", Phys. Rev. X, 7(1), 011031. https://doi.org/10.1103/PhysRevX.7.011031
  64. Sae-Long, W., Limkatanyu, S., Sukontasukkul, P., Damrongwiriyanupap, N., Rungamornrat, J. and Prachasaree, W. (2021), "Fourth-order strain gradient bar-substrate model with nonlocal and surface effects for the analysis of nanowires embedded in substrate media.", Facta Univ. Series Mech. Eng., 19(4), 657-680. 10.1002/zamm.201700311
  65. Safaei, B., Khoda, F.H. and Fattahi, A.M. (2019), "Non-classical plate model for single-layered graphene sheet for axial buckling", Adv Nano Res, 7(4), 265-275. https://doi.org/10.12989/anr.2019.7.4.265
  66. Sedighi, H.M. and Malikan, M. (2020), "Stress-driven nonlocal elasticity for nonlinear vibration characteristics of carbon/ boron-nitride hetero-nanotube subject to magneto-thermal environment", Physica Scripta, 95(5), 055218. https://doi.org/10.1088/1402-4896/ab7a38
  67. Sedighi, H.M., Malikan, M., Valipour, A. and Zur, K.K. (2020), "Nonlocal vibration of carbon/boron-nitride nano-hetero-structure in thermal and magnetic fields by means of nonlinear finite element method", J. Comput. Des. Eng., 7(5), 591-602. https://doi.org/10.1093/jcde/qwaa041
  68. Shahsavari, D., Karami, B. and Janghorban, M. (2019), "Size-dependent vibration analysis of laminated composite plates", Adv. Nano Res., 7(5), 337-349. https://doi.org/10.12989/anr.2019.7.5.337
  69. Pradhan, S.C. and Phadikar, J.K. (2009), "Nonlocal elasticity theory for vibration of nanoplates", J. Sound Vib., 325(1-2), 206-223.https://doi.org/10.1016/j.jsv.2009.03.007
  70. Wayne, R.O. (2009), "Plant cell biology", Astronom. Zool., 106(4). https://doi.org/10.1093/aob/mcq161
  71. Xu, K., Zhong, G. and Zhuang, X. (2013), "Actin, spectrin, and associated proteins form a periodic cytoskeletal structure in axons", Science, 339(6118), 452-456. https://doi.org/10.1126/science.1232251.
  72. Zhang, Y., Liu, G. and Xie, X. (2005),"Free transverse vibrations of double-walled carbon nanotubes using a theory of nonlocal elasticity", Phys. Rev. B, 71(19), 195404. https://doi.org/10.1103/PhysRevB.71.195404