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Extracting elastic properties and prestress of a cell using atomic force microscopy

Published online by Cambridge University Press:  31 January 2011

C.Y. Zhang*
Affiliation:
Shenzhen Institute of Advanced Technology, Chinese Academy of Science, Shenzhen 518067, China
Y.W. Zhang
Affiliation:
Department of Materials Science and Engineering, National University of Singapore, Singapore 119260
*
a) Address all correspondence to this author. e-mail: [email protected]
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Abstract

An analytical solution was derived for the indentation of a cell using atomic force microscopy. It was found that the contribution of the cell membrane to the overall indentation stiffness is dependent on the size of the indenter. When a small indenter [for example, an atomic force microscopy (AFM) tip] is used to probe the mechanical properties of cells, the cell membrane and its prestress were important in interpreting indentation data. The solution allows the partition of contributions from the membrane and the interior soft phase. The apparent elastic modulus of the cell and the prestress of the cell membrane can be extracted. In addition, the modulus of the cell membrane could be estimated from the extracted apparent modulus if the interior soft phase of the cell was known and vice versa. However, when a large indenter is used (for example, a microbead attached to the cantilever beam of the AFM), the contribution of the cell membrane is negligible.

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Articles
Copyright
Copyright © Materials Research Society 2009

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References

REFERENCES

1.Karcher, H., Lammerding, J., Huang, H., Lee, R.T., Kamm, R.D., and Mofrad, M.R.: A three-dimensional viscoelastic model for cell deformation with experimental verification. Biophys. J. 85, 3336 (2003).CrossRefGoogle ScholarPubMed
2.Binnig, G., Quate, C.F., and Gerber, C.: Atomic force microscope. Phys. Rev. Lett. 56, 930 (1986).CrossRefGoogle ScholarPubMed
3.Hoh, J.H. and Schoenenberger, C.A.: Microelastic mapping of living cells by atomic force microscopy. J. Cell Sci. 107, 1105 (1994).Google Scholar
4.Haydon, P.G., Lartius, R., Parpura, V., and Marchese-Ragona, S.P.: Membrane deformation of living glial cells using atomic force microscopy. J. Microsc. 182, 114 (1996).Google Scholar
5.Hassan, E.A., Heinz, W.F., Antonik, M.D., D'Costa, N.P., Nageswaran, S., Schoenenberger, C.A., and Hoh, J.H.: Relative microelastic mapping of living cells by atomic force microscopy. Biophys. J. 74, 1564 (1998).CrossRefGoogle Scholar
6.Mathur, A.B., Collinsworth, A.M., Reichert, W.M., Kraus, W.E., and Truskey, G.A.: Endothelial, cardiac muscle and skeletal muscle exhibit different viscous and elastic properties as determined by atomic force microscopy. J. Biomech. 34, 1545 (2001).Google Scholar
7.Sen, S., Subramanian, S., and Discher, D.E.: Indentation and adhesive probing of a cell membrane with AFM: Theoretical model and experiments. Biophys. J. 89, 3203 (2005).CrossRefGoogle ScholarPubMed
8.Rico, F., Cusachs, P.R., Gavara, N., Farré, R., Rotger, M., and Navajas, D.: Probing mechanical properties of living cells by atomic force microscopy with blunted pyramidal cantilever tips. Phys. Rev. E 72, 021914 (2005).CrossRefGoogle ScholarPubMed
9.Hertz, H.: On the contact of elastic solids. J. Reine Angew. Mathematik. 92, 156 (1881).Google Scholar
10.Johnson, K.L.: Contact Mechanics (Cambridge University Press, Cambridge, 1985).CrossRefGoogle Scholar
11.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 (1965).CrossRefGoogle Scholar
12.Zamir, E.A. and Taber, L.A.: Material Properties and residual stress in the stage 12 chick heart during cardiac looping. J. Biomech. Eng. 126, 276 (2004).Google Scholar
13.Weisenhorn, A.L., Maivald, P., Butt, H.J., and Hansma, P.K.: Measuring adhesion, attraction, and repulsion between surfaces in liquids with an atomic force microscope. Phys. Rev. B: Condens. Matter 45, 11226 (1992).Google Scholar
14.Sato, M., Nagayama, K., Kataoka, N., Sasaki, M., and Hane, K.: Local mechanical properties measured by atomic force microscopy for cultured bovine endothelial cells exposed to shear stress. J. Biomech. 33, 127 (2000).CrossRefGoogle ScholarPubMed
15.Rabinovich, Y., Esayanur, M., Daosukho, S., Byer, K., El-Shall, H., and Khan, S.: Atomic force microscopy measurement of the elastic properties of the kidney pithelial cells. J. Colloid Interface Sci. 285, 125 (2005).CrossRefGoogle Scholar
16.Costa, K.D. and Yin, F.C.P.: Analysis of indentation: Implications for measuring mechanical properties with atomic force microscopy. J. Biomech. Eng. 121, 462 (1999).CrossRefGoogle ScholarPubMed
17.Szilard, R.: Theory and Analysis of Plates (Prentice-Hall, Englewood Cliffs, NJ, 1974).Google Scholar
18.Timoshenko, S. and Goodier, J.N.: Theory of Elasticity (McGraw-Hill, New York, 1970).Google Scholar
19.Li, J. and Chou, T.W.: Elastic filed of a thin-film/substrate system under an axisymmetric loading. Int. J. Solids Struct. 34, 4463 (1997).CrossRefGoogle Scholar
20.Hajji, M.A.: Indentation of a membrane on an elastic half space. J. Appl. Mech. 45, 320 (1978).CrossRefGoogle Scholar
21.Mahaffy, R.E., Shih, C.K., MacKintosh, F.C., and Käs, J.: Scanning probe-based frequency-dependent microrheology of polymer gels and biological cells. Phys. Rev. Lett. 85, 880 (2000).Google Scholar
22.Dimitriadis, E.K., Horkay, F., Maresca, J., Kachar, B., and Chadwick, R.S.: Determination of elastic moduli of thin layers of soft material using the atomic force microscope. Biophys. J. 82, 2798 (2002).CrossRefGoogle ScholarPubMed
23.Chen, X. and Vlassak, J.J.: Numerical study on the measurement of thin film mechanical properties by means of nanoindentation. J. Mater. Res. 16, 2974 (2001).CrossRefGoogle Scholar
24.Fischer-Cripps, A.C.: Nanoindentation, 2nd Ed. (Springer, New York, 2004).CrossRefGoogle Scholar
25.Jung, Y.G., Lawn, B.R., Martyniuk, M., Huang, H., and Hu, X.Z.: Evaluation of elastic modulus and hardness of thin films by nanoindentation. J. Mater. Res. 19, 3076 (2004).CrossRefGoogle Scholar
26.Hofmann, U.G., Rotsch, C., Wolfgang, J.P., and Radmacher, M.: Investigating the cytoskeleton of chicken cardiocytes with the atomic force microscope. J. Struct. Biol. 119, 84 (1997).Google Scholar
27.Miyazaki, H. and Hayashi, K.: Atomic force microscopic measurement of the mechanical properties of intact endothelial cells in fresh arteries. Med. Biol. Eng. Comput. 37, 530 (1999).Google Scholar
28.Evans, E.A.: Bending elastic modulus of red blood cell membrane derived from buckling instability in micropipette aspiration tests. Biophys. J. 43, 27 (1983).CrossRefGoogle ScholarPubMed
29.Hochmuth, R.M. and Hampel, W.L.: Surface elasticity and viscosity of red cell membrane. J. Rheol. 23, 669 (1979).CrossRefGoogle Scholar
30.Sleep, J., Wilson, D., Simmons, R., and Gratzer, W.: Elasticity of the red cell membrane and its relation to hemolytic disorders: An optical tweezers study. Biophys. J. 77, 3085 (1999).CrossRefGoogle ScholarPubMed
31.Sheetz, M.P. and Dai, J.W.: Modulation of membrane dynamics and cell motility by membrane tension. Trends Cell Biol. 6, 85 (1996).Google Scholar