Abstract
Quantification of the cell elastic modulus is a central issue of micromanipulation techniques used to analyze the mechanical properties of living adherent cells. In magnetic twisting cytometry (MTC), magnetic beads of radius R, linked to the cell cytoskeleton through transmembrane receptors, are twisted. The relationships between imposed external torque and measured resulting bead rotation or translation only provide values of the apparent cell stiffness. Thus, specific correcting coefficients have to be considered in order to derive the cell elastic modulus. This issue has been highlighted in previous studies, but general relationships for handling such corrections are still lacking while they could help to understand and reduce the large dispersion of the reported values of cell elastic modulus. Thiswork establishes generalized abacuses of the correcting coefficients from which the Young’s modulus of a cell probed byMTCcan be derived. Based on a 3Dfinite element analysis of an hyperelastic (neo-Hookean) cell, we show that the dimensionless ratio hu/2R, where hu is the cell height below the bead, is an essential parameter for quantification of the cell elasticity. This result could partly explain the still intriguing question of the large variation of measured elastic moduli with probe size.
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Caille, N., O. Thoumine,Y. Tardy, and J. J. Meister. Contribution of the nucleus to the mechanical properties of endothelial cells. J. Biomech. 35:177–187, 2002.
Charras, G. T., and M. A. Horton. Determination of cellular strains by combined atomic force microscopy and finite element modeling. Biophys. J. 83:858–879, 2002.
Chen, J., B.Fabry, E.L.Schiffrin and N.Wang. Twisting integrin receptors increases endothelin-1 gene expression in endothelial cells. Am. J. Physiol. Cell Physiol. 280:C1475–C1484, 2001.
Djordjevic, V. D., J. Jaric, B. Fabry, J. J. Fredberg, and D. Stamenovic. Fractional derivatives embody essential features of cell rheological behavior. Ann. Biomed. Eng. 31:692–699, 2003.
Doornaert, B., V. Leblond, E. Planus, S. Galiacy, V. M. Laurent, G. Gras, D. Isabey, and C. Lafuma. Time course of actin cytoskeleton stifness and matrix adhesion molecules in human bronchial epithelial cell cultures. Exp. Cell Res. 287:199–208, 2003.
Engler, A., L. Bacakova, C. Newman, A. Hategan, M. Griffin, and D. Discher. Substrate compliance versus ligand density in cell on gel responses. Biophys. J. 86:617–628, 2004.
Fabry, B., G. N. Maksym, S. A. Shore, P. E. Moore, R. A. Panettieri Jr., J. P. Butler, and J. J. Fredberg. Selected contribution: time course and heterogeneity of contractile responses in cultured human airway smooth muscle cells. J. Appl. Physiol. 91:986–994, 2001a.
Fabry, B., G. N. Maksym, J. P. Butler,M. Glogauer, D. Navajas, and J. J. Fredberg. Scaling the microrheology of living cells. Phys. Rev. Lett. 87:148102-1–148102-4, 2001b.
Fabry, B., G. N. Maksym, J. P. Butler,M. Glogauer, D. Navajas, N. A. Taback, E. J. Millet, and J. J. Fredberg. Time scale and other invariants of integrative mechanical behavior in living cells. Phys. Rev. E 68:041914-1–041914-18, 2003.
Fodil, R., V. Laurent, E. Planus, and D. Isabey. Characterization of cytoskeleton mechanical properties and 3D-actin structure in twisted adherent epithelial cells. Biorheology 40:241–245, 2003.
Hamill, O. P., and B. Martinac. Molecular basis of mechanotransduction in living cells. Physiol. Rev. 81:685–740, 2001.
Holzapfel, G. A. Nonlinear Solid Mechanics. New York:Wiley, 2001.
Hu, S., J. Chen, B. Fabry, Y. Numaguchi, A. Gouldstone, D. E. Ingber, J. J. Fredberg, J. P. Butler, and N. Wang. Intracellular stress tomography reveals stress focusing and structural anisotropy in cytoskeleton of living cells, Am. J. Physiol. 285:C1082–C1090, 2003.
Hubmayr, R. D., S. A. Shore, J. J. Fredberg, E. Planus, R. A. Panettieri Jr, W. Moller, J. Heyder, and N. Wang. Pharmacological activation changes stiffness of cultured human airway smooth muscle cells. Am. J. Physiol. 271:C1660–C1668, 1996.
Janmey, P. A. The cytoskeleton and cell signaling: Component localization and mechanical coupling. Physiol. Rev. 78:763–781, 1998.
Karcher, H., J. Lammerding, H. Huang, R. T. Lee, R. D. Kamm, and M. R. Kaazempur-Mofrad. A three-dimensional viscoelastic model for cell deformation with experimental verification. Biophys. J. 85:3336–3349, 2003.
Laurent, V. M., S. Henon, E. Planus, R. Fodil, M. Balland, D. Isabey, and F. Gallet. Assessment of mechanical properties of adherent living cells by bead micromanipulation: Comparison of magnetic twisting cytometry vs optical tweezers. ASME J. Biomech. Eng. 124:408–421, 2002.
Laurent, V. M., R. Fodil, P. Cañadas, S. Féréol, B. Louis, E. Planus, and D. Isabey. Partitioning of cortical and deep cytoskeleton responses from transient magnetic bead twisting. Ann. J. Biomed. Eng. 31:1263–1278, 2003.
Maksym, G. N., B. Fabry, J. P. Butler, D. Navajas, D. J. Tschumperlin, J. D. Laporte, and J. J. Fredberg. Mechanical properties of cultured human airway smooth muscle cells from 0.05 to 0.4 Hz. J. Appl. Physiol. 89:1619–1632, 2000.
Maniotis, A. J., C. S. Chen, and D. E. Ingber. Demonstration of mechanical connections between integrins, cytoskeletal filaments, and nucleoplasm that stabilize nuclear structure. Proc. Natl. Acad. Sci. U.S.A. 94:849–854, 1997.
Mijailovich, S. M., M. Kojic, M. Zivkovic, B. Fabry, and J. J. Fredberg. A finite element model of cell deformation during magnetic bead twisting. J. Appl. Physiol. 93:1429–1436, 2002.
Ohayon, J., P. Tracqui, R. Fodil, S. Féréol, V. M. Laurent, E. Planus, and D. Isabey. Analysis of nonlinear responses of adherent epithelial cells probed by magnetic bead twisting: A finite element model based on an homogenization approach. J. Biomech. Eng. 126(6), 2004, in press.
Rahman, A., Y. Tseng, and D.Wirtz. Micromechanical coupling between cell surface receptors andRGDpeptides. Biochem. Biophys. Res. Commun. 296:771–778, 2002.
Schneider, S.W., P. Pagel, C. Rotsch, T. Danker,H. Oberleithner, M. Radmacher, and A. Schwab. Volume dynamics in migrating epithelial cells measured with atomic force microscopy. Pflugers Arch. 439:297–303, 2000.
Trickey, W. R., T. P. Vail, and F. Guilak. The role of the cytoskeleton in the viscoelastic properties of human articular chondrocytes, J. Orthop. Res. 22: 131–139, 2004.
Wang, N., J. P. Butler, and D. E. Ingber. Mechanotransduction across the cell surface and through the cytoskeleton. Science 260:1124–1127,1993.
Wang, N., and D. E. Ingber. Probing transmembrane mechanical coupling and cytomechanics using magnetic twisting cytometry. Biochem. Cell Biol. 73:327–335, 1995.
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Ohayon, J., Tracqui, P. Computation of Adherent Cell Elasticity for Critical Cell-Bead Geometry in Magnetic Twisting Experiments. Ann Biomed Eng 33, 131–141 (2005). https://doi.org/10.1007/s10439-005-8972-9
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DOI: https://doi.org/10.1007/s10439-005-8972-9