Abstract
An understanding of whole-cell mechanical behavior can provide insight into cellular responses to mechanical loading and diseases in which such responses are altered. However, this aspect of cellular mechanical behavior has received limited attention. In this study, we used the atomic force microscope (AFM) in conjunction with several mechanical characterization methods (Hertz contact theory, an exponential equation, and a parallel-spring recruitment model) to establish a mechanically rigorous method for measuring and characterizing whole-cell mechanical behavior in the deformation range 0–500 nm. Using MC3T3-E1 osteoblasts, measurement repeatability was assessed by performing multiple loading cycles on individual cells. Despite variability in measurements, repeatability of the measurement technique was statistically confirmed. The measurement technique also proved acceptable since only 5% of the total variance across all measurements was due to variations within measurements for a single cell. The parallel-spring recruitment model, a single-parameter model, accurately described the measured nonlinear force–deformation response (R 2 > 0.99) while providing a mechanistic explanation of whole-cell mechanical behavior. Taken together, the results should improve the capabilities of the AFM to probe whole-cell mechanical behavior. In addition, the success of the parallel-spring recruitment model provides insight into the micromechanical basis of whole-cell behavior.
Similar content being viewed by others
REFERENCES
A-Hassan, E., W. F. Heinz, M. D. Antonik, N. P. D’Costa, S. Nageswaran, C. Schoenenberger, and J. H. Hoh. Relative microelastic mapping of living cells by atomic force microscopy. Biophys. J. 74:1564–1578, 1998.
Alcaraz, J., L. Buscemi, M. Grabulosa, X. Trepat, B. Fabry, R. Farre, and D. Navajas. Microrheology of human lung epithelial cells measured by atomic force microscopy. Biophys. J. 84:2071–2079, 2003.
Bland, J. M., and D. G. Altman. Statistical methods for assessing agreement between two methods of clinical measurement. Lancet 1:307–310, 1986.
Burr, D. B., A. G. Robling, and C. H. Turner. Effects of biomechanical stress on bones in animals. Bone 30:781–786, 2002.
Butt, H. J., and M. Jaschke. Calculation of thermal noise in atomic force microscopy. Nanotechnology 6:1–7, 1995.
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.
Charras, G. T., and M. A. Horton. Single cell mechanotransduction and its modulation analyzed by atomic force microscope indentation. Biophys. J. 82:2970–2981, 2002.
Charras, G. T., P. P. Lehenkari, and M. A. Horton. Atomic force microscopy can be used to mechanically stimulate osteoblasts and evaluate cellular strain distributions. Ultramicroscopy 86:85–95, 2001.
Collinsworth, A. M., S. Zhang, W. E. Kraus, and G. A. Truskey. Apparent elastic modulus and hysteresis of skeletal muscle cells throughout differentiation. Am. J. Physiol. Cell Physiol. 283:C1219–C1227, 2002.
Costa, K. D., and F. C. Yin. Analysis of indentation: Implications for measuring mechanical properties with atomic force microscopy. J. Biomech. Eng. 121:462–471, 1999.
Coughlin, M. F., and D. Stamenovic. A prestressed cable network model of the adherent cell cytoskeleton. Biophys. J. 84:1328–1336, 2003.
Cucina, A., A. V. Sterpetti, G. Pupelis, A. Fragale, and S. Lepidi. Shear stress induces changes in the morphology and cytoskeleton organisation of arterial endothelial cells. Eur. J. Vasc. Endovasc. Surg. 9:86–92, 1995.
Davies, P. F., A. Robotewskyj, and M. L. Griem. Quantitative studies of endothelial cell adhesion. Directional remodeling of focal adhesion sites in response to flow forces. J. Clin. Invest. 93:2031–2038, 1994.
Dimitriadis, E. K., F. Horkay, J. Maresca, B. Kachar, and R. S. Chadwick. Determination of elastic moduli of thin layers of soft material using the atomic force microscope. Biophys. J. 82:2798–2810, 2002.
Domke, J., and M. Radmacher. Measuring the elastic properties of thin polymer films with the atomic force microscope. Langmuir 14:3320–3325, 1998.
Freshney, R. I. Culture of Animal Cells. New York: Wiley-Liss, 2000.
Frisen, M., M. Magi, L. Sonnerup, and A. Viidik. Rheological analysis of soft collagenous tissue. J. Biomech. 2:13–20, 1969.
Fung, Y. C. Biomechanics: Motion, Flow, Stress, and Growth. New York: Springer-Verlag, 1990.
Fung, Y. C. Biomechanics: Mechanical Properties of Living Tissues. New York: Springer-Verlag, 1993.
Grubbs, F. E. Procedures for detecting outlying observations in samples. Technometrics 11:1–21, 1969.
Haga, H., S. Sasaki, K. Kawabata, E. Ito, T. Ushiki, and T. Sambongi. Elasticity mapping of living fibroblasts by AFM and immunofluorescence observation of the cytoskeleton. Ultramicroscopy 82:253–258, 2000.
Hategan, A., R. Law, S. Kahn, and D. E. Discher. Adhesively-tensed cell membranes: Lysis kinetics and atomic force microscopy probing. Biophys. J. 85:2746–2759, 2003.
Hofmann, U. G., C. Rotsch, W. J. Parak, and M. Radmacher. Investigating the cytoskeleton of chicken cardiocytes with the atomic force microscope. J. Struct. Biol. 119:84–91, 1997.
Howard, J. Mechanics of Motor Proteins and the Cytoskeleton. Sunderland, MA: Sinauer Associates, 2001.
Hutter, J. L., and J. Bechhoefer. Calibration of atomic-force microscope tips. Rev. Sci. Instrum. 64:1868–1873, 1993.
Jaasma, M. J. Osteoblast Mechanical Behavior and Its Adaptation to Mechanical Loading. PhD Dissertation, University of California, Berkeley, CA, 2004.
Janmey, P. A. The cytoskeleton and cell signaling: Component localization and mechanical coupling. Physiol. Rev. 78:763–781, 1998.
Johnson, K. L. Contact Mechanics. Cambridge, MA: Cambridge University Press, 1985.
Lee, C. A., and T. A. Einhorn. The bone organ system. In: Osteoporosis, edited by R. Marcus, D. Feldman, and J. Kelsey, Vol. 1. New York: Academic, 2001, pp. 3–20.
Mahaffy, R. E., S. Park, E. Gerde, J. Kas, and C. K. Shih. Quantitative analysis of the viscoelastic properties of thin regions of fibroblasts using atomic force microscopy. Biophys. J. 86:1777–1793, 2004.
Mahaffy, R. E., C. K. Shih, F. C. MacKintosh, and J. Kas. Scanning probe-based frequency-dependent microrheology of polymer gels and biological cells. Phys. Rev. Lett. 85:880–883, 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.
Mathur, A. B., G. A. Truskey, and W. M. Reichert. Atomic force and total internal reflection fluorescence microscopy for the study of force transmission in endothelial cells. Biophys. J. 78:1725–1735, 2000.
McElfresh, M., E. Baesu, R. Balhorn, J. Belak, M. J. Allen, and R. E. Rudd. Combining constitutive materials modeling with atomic force microscopy to understand the mechanical properties of living cells. Proc. Natl. Acad. Sci. U.S.A. 99(Suppl 2):6493–6497, 2002.
Miyazaki, H., and K. Hayashi. Atomic force microscopic measurement of the mechanical properties of intact endothelial cells in fresh arteries. Med. Biol. Eng. Comput. 37:530–536, 1999.
Ohashi, T., Y. Ishii, Y. Ishikawa, T. Matsumoto, and M. Sato. Experimental and numerical analyses of local mechanical properties measured by atomic force microscopy for sheared endothelial cells. Biomed. Mater. Eng. 12:319–327, 2002.
Pavalko, F. M., N. X. Chen, C. H. Turner, D. B. Burr, S. Atkinson, Y. F. Hsieh, J. Qiu, and R. L. Duncan. Fluid shear-induced mechanical signaling in MC3T3-E1 osteoblasts requires cytoskeleton–integrin interactions. Am. J. Physiol. 275:C1591–C1601, 1998.
Petersen, N. O., W. B. McConnaughey, and E. L. Elson. Dependence of locally measured cellular deformability on position on the cell, temperature, and cytochalasin B. Proc. Natl. Acad. Sci. U.S.A. 79:5327–5331, 1982.
Radmacher, M., M. Fritz, C. M. Kacher, J. P. Cleveland, and P. K. Hansma. Measuring the viscoelastic properties of human platelets with the atomic force microscope. Biophys. J. 70:556–567, 1996.
Raucher, D., and M. P. Sheetz. Characteristics of a membrane reservoir buffering membrane tension. Biophys. J. 77:1992–2002, 1999.
Rotsch, C., and M. Radmacher. Drug-induced changes in cytoskeletal structure and mechanics in fibroblasts: An atomic force microscopy study. Biophys. J. 78:520–535, 2000.
Sato, M., K. Nagayama, N. Kataoka, M. Sasaki, and K. Hane. Local mechanical properties measured by atomic force microscopy for cultured bovine endothelial cells exposed to shear stress. J. Biomech. 33:127–135, 2000.
Sneddon, I. N. The relation between load and penetration in the axisymmetric Boussinesq problem for a punch of arbitrary profile. Int. J. Eng. Sci. 3:47–57, 1965.
Sugawara, M., Y. Ishida, and H. Wada. Local mechanical properties of guinea pig outer hair cells measured by atomic force microscopy. Hear. Res. 174:222–229, 2002.
Sugawara, M., Y. Ishida, and H. Wada. Mechanical properties of sensory and supporting cells in the organ of Corti of the guinea pig cochlea—study by atomic force microscopy. Hear. Res. 192:57–64, 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., K. Naruse, D. Stamenovic, J. J. Fredberg, S. M. Mijailovich, I. M. Tolic-Norrelykke, T. Polte, R. Mannix, and D. E. Ingber. Mechanical behavior in living cells consistent with the tensegrity model. Proc. Natl. Acad. Sci. U.S.A. 98:7765–7770, 2001.
Wu, H. W., T. Kuhn, and V. T. Moy. Mechanical properties of L929 cells measured by atomic force microscopy: Effects of anticytoskeletal drugs and membrane crosslinking. Scanning 20:389–397, 1998.
You, J., C. E. Yellowley, H. J. Donahue, Y. Zhang, Q. Chen, and C. R. Jacobs. Substrate deformation levels associated with routine physical activity are less stimulatory to bone cells relative to load-induced oscillatory fluid flow. J. Biomech. Eng. 122:387–393, 2000.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Jaasma, M.J., Jackson, W.M. & Keaveny, T.M. Measurement and Characterization of Whole-Cell Mechanical Behavior. Ann Biomed Eng 34, 748–758 (2006). https://doi.org/10.1007/s10439-006-9081-0
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10439-006-9081-0