Noncontact microrheology at acoustic frequencies using frequency-modulated atomic force microscopy

Abstract

We report an atomic force microscopy (AFM) method for assessing elastic and viscous properties of soft samples at acoustic frequencies under non-contact conditions. The method can be used to measure material properties via frequency modulation and is based on hydrodynamics theory of thin gaps we developed here. A cantilever with an attached microsphere is forced to oscillate tens of nanometers above a sample. The elastic modulus and viscosity of the sample are estimated by measuring the frequency-dependence of the phase lag between the oscillating microsphere and the driving piezo at various heights above the sample. This method features an effective area of pyramidal tips used in contact AFM but with only piconewton applied forces. Using this method, we analyzed polyacrylamide gels of different stiffness and assessed graded mechanical properties of guinea pig tectorial membrane. The technique enables the study of microrheology of biological tissues that produce or detect sound.

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Figure 1: Concept of FM-AFM to measure mechanical properties of soft samples.
Figure 2: Estimation of mechanical properties through measurement of frequency shifts.
Figure 3: Effective probe area of pyramidal-probe C-AFM versus FM-AFM.

References

  1. 1

    Pullarkat, P.A., Fernández, P.A. & Ott, A. Rheological properties of the eukaryotic cell cytoskeleton. Phys. Rep. 449, 29–53 (2007).

    CAS  Article  Google Scholar 

  2. 2

    Gardel, M.L., Valentine, M.T. & Weitz, D.A. Microrheology. in Microscale Diagnostic Techniques (ed., K. Breuer) 1–50 (Springer Verlag, New York, 2005).

  3. 3

    Ziemann, F., Rädler, J. & Sackmann, E. Local measurements of viscoelastic moduli of entangled actin networks using an oscillating magnetic bead micro-rheometer. Biophys. J. 66, 2210–2216 (1994).

    CAS  Article  Google Scholar 

  4. 4

    Block, S.M. Making light work with optical tweezers. Nature 360, 493–495 (1992).

    CAS  Article  Google Scholar 

  5. 5

    Ashkin, A. Forces of a single-beam gradient laser trap on a dielectric sphere in the ray optics regime. Biophys. J. 61, 569–582 (1992).

    CAS  Article  Google Scholar 

  6. 6

    Radmacher, M., Fritz, M., Kacher, C.M., Cleveland, J.P. & Hansma, P.K. Measuring the viscoelastic properties of human platelets with the atomic force microscope. Biophys. J. 70, 556–567 (1996).

    CAS  Article  Google Scholar 

  7. 7

    Sahin, O., Magonov, S., Su, C., Quate, C.F. & Solgaard, O. An atomic force microscope tip designed to measure time-varying nanomechanical forces. Nat. Nanotechnol. 2, 507–514 (2007).

    Article  Google Scholar 

  8. 8

    Alcaraz, J. et al. Microrheology of human lung epithelial cells measured by atomic force microscopy. Biophys. J. 84, 2071–2079 (2003).

    CAS  Article  Google Scholar 

  9. 9

    Hiratsuka, S. et al. The number distribution of complex shear modulus of single cells measured by atomic force microscopy. Ultramicroscopy 109, 937–941 (2009).

    CAS  Article  Google Scholar 

  10. 10

    Higgins, M.J. et al. Frequency modulation atomic force microscopy: a dynamic measurement technique for biological systems. Nanotechnology 16, S85–S89 (2005).

    CAS  Article  Google Scholar 

  11. 11

    Humphris, A.D.L., Tamayo, J. & Miles, M.J. Active quality factor control in liquids for force spectroscopy. Langmuir 16, 7891–7894 (2000).

    CAS  Article  Google Scholar 

  12. 12

    Chadwick, R.S. & Liao, Z. High-Frequency oscillations of a sphere in a viscous fluid near a rigid plane. SIAM Rev. 50, 313–322 (2008).

    Article  Google Scholar 

  13. 13

    Yeung, T. et al. Effects of substrate stiffness on cell morphology, cytoskeletal structure, and adhesion. Cell Motil. Cytoskeleton 60, 24–34 (2005).

    Article  Google Scholar 

  14. 14

    Morse, P.M. & Ingard, K.U. Theoretical Acoustics (McGraw-Hill, New York, 1968).

  15. 15

    Mathur, A.B., Collinsworth, A.M., Reichert, W.M., Kraus, W.E. & Truskey, G.A. Endothelial, cardiac muscle and skeletal muscle exhibit different viscous and elastic properties as determined by atomic force microscopy. J. Biomech. 34, 1545–1553 (2001).

    CAS  Article  Google Scholar 

  16. 16

    Hertz, H. Uber die beruhrung fester elastischer korper (On the contact of elastic solids). J. Reine Angew. Math. 92, 156–171 (1881).

    Google Scholar 

  17. 17

    Hodges, C.S. Measuring forces with the AFM: polymeric surfaces in liquids. Adv. Colloid Interface Sci. 99, 13–75 (2002).

    CAS  Article  Google Scholar 

  18. 18

    Weisenhorn, A.L., Maivald, P., Butt, H.J. & Hansma, P.K. Measuring adhesion, attraction, and repulsion between surfaces in liquids with an atomic-force microscope. Phys. Rev. B 45, 11226 (1992).

    CAS  Article  Google Scholar 

  19. 19

    Fritz, M., Radmacher, M. & Gaub, H.E. Granula motion and membrane spreading during activation of human platelets imaged by atomic force microscopy. Biophys. J. 66, 1328–1334 (1994).

    CAS  Article  Google Scholar 

  20. 20

    Gavara, N. & Chadwick, R.S. Collagen-based mechanical anisotropy of the tectorial membrane: implications for inter-row coupling of outer hair cell bundles. PLoS One 4, e4877 (2009).

    Article  Google Scholar 

  21. 21

    Richter, C.P., Emadi, G., Getnick, G., Quesnel, A. & Dallos, P. Tectorial membrane stiffness gradients. Biophys. J. 93, 2265–2276 (2007).

    CAS  Article  Google Scholar 

  22. 22

    Abnet, C.C. & Freeman, D.M. Deformations of the isolated mouse tectorial membrane produced by oscillatory forces. Hear. Res. 144, 29–46 (2000).

    CAS  Article  Google Scholar 

  23. 23

    Ghaffari, R., Aranyosi, A.J. & Freeman, D.M. Longitudinally propagating traveling waves of the mammalian tectorial membrane. Proc. Natl. Acad. Sci. USA 104, 16510–16515 (2007).

    CAS  Article  Google Scholar 

  24. 24

    Fabry, B. et al. Time scale and other invariants of integrative mechanical behavior in living cells. Phys. Rev. E 68, 041914 (2003).

    Article  Google Scholar 

  25. 25

    Novak, P. et al. Nanoscale live-cell imaging using hopping probe ion conductance microscopy. Nat. Methods 6, 279–281 (2009).

    CAS  Article  Google Scholar 

  26. 26

    Wang, Y.L., Pelham, R.J. & Richard, B.V. Preparation of a flexible, porous polyacrylamide substrate for mechanical studies of cultured cells. in Methods in Enzymology (eds., J. Abelson, R. Vallee & M. Simon) Vol. 298, 489 (Academic Press, 1998).

  27. 27

    Butt, H.J. & Jaschke, M. Calculation of thermal noise in atomic-force microscopy. Nanotechnology 6, 1–7 (1995).

    Article  Google Scholar 

  28. 28

    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).

    Article  Google Scholar 

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Acknowledgements

We thank T.B. Friedman and K.H. Iwasa for critical input. This work was supported by the Intramural Program of the US National Institute of Deafness and Other Communication Disorders.

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N.G. conceived, designed and performed the experiments, analyzed the data and wrote the paper. R.S.C. developed the hydrodynamic lubrication theory, conceived and designed the experiments and wrote the paper.

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Correspondence to Richard S Chadwick.

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The authors declare no competing financial interests.

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Supplementary Figures 1–4, Supplementary Table 1 and Supplementary Notes 1–3 (PDF 430 kb)

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Gavara, N., Chadwick, R. Noncontact microrheology at acoustic frequencies using frequency-modulated atomic force microscopy. Nat Methods 7, 650–654 (2010). https://doi.org/10.1038/nmeth.1474

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