Abstract
We describe a new, high-resolution technique for determining the local viscoelastic response of polymer gels on a micrometer scale. This is done by monitoring thermal fluctuations of embedded probe particles. We derive the relationship between the amplitude of fluctuations and the low-frequency storage modulus G′, as well as the relationship between the fluctuation power spectrum, measured between 0.1 Hz and 25kHz, and the complex shear modulus G(ω). For both, semiflexible F-actin solutions and flexible polyacrylamide (PAAm) gels we observe high-frequency power-law dependence in the spectra, which reflects the behavior of the shear modulus. However, we observe distinctly different scaling exponents for G(ω) in F-actin and PAAm gels — presumably due to the semiflexible nature of the actin filaments.
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References
T.P. Stessei, Sci Am 271, 54–5, 58-63 (1994).
J. Kas, H. Strey, J.X. Tang et al., Biophysical Journal 70, 609 (1996).
O. Muller, et al., Macromolecules 24, 3111 (1991); R. Ruddies, et al, Eur Biophys J 22, 309 (1993).
P.A. Janmey, S. Hvidt, J. Kas et al., J Biol Chem 269, 32503 (1994).
P.A. Janmey, et al., Biochemistry 27, 8218 (1988); P.A. Janmey, J Biochem and Biophys Meth 22, 41 (1991).
F.C. MacKintosh, J. Kas, and P.A. Janmey, Physical Review Letters 75, 4425 (1995).
T.D. Pollard, I. Goldberg, and W.H. Schwarz, J Biol Chem 267, 20339 (1992); D.H. Wachsstock, W.H. Schwartz, and T.D. Pollard, Biophys J 65, 205 (1993); 66, 801 (1994); M. Sato, et al., J Biol Chem 260, 8585 (1985); K.S. Zaner and J.H. Hartwig, J Biol Chem 263, 4532 (1988); J. Newman, et al, Biophys 64, 1559 (1993).
F. Ziemann, J. Radier, and E. Sackmann, Biophys J 66, 2210 (1994).
F.G. Schmidt, F. Ziemann, and E. Sackmann, Eur Biophys J 24, 348 (1996).
F. Amblard, et al., Physical Review Letters 77, 4470 (1996).
T.G. Mason and D.A. Weitz, Physical Review Letters 74, 1250 (1995).
L.D. Landau and E.M. Lifshitz, Fluid mechanics (Pergamon Press, Reading, MA, 1959).
The shear stress σ and displacement field u in a viscoelastic medium are related in the same way as σ and the velocity field in a viscous fluid, provided that both are incompressible.
L.D. Landau and E.M. Lifshitz, Theory of elasticity, 2d ed. (Pergamon Press, New York, 1970).
B. Schnurr, et al., to be published.
F. Brochard and P.G. de Gennes, Macromolecules 10, 1157 (1977).
S.T. Milner, Physical Review E 48, 3674 (1993).
L.D. Landau, E.M. Lifshitz, and L.P. Pitaevskii, Statistical physics (Pergamon Press, New York, 1980).
M. Doi and S.F. Edwards, The Theory of Polymer Dynamics (Clarendon Press, Oxford, 1988).
J.D. Pardee and J.A. Spudich, in Structural and Contractile Proteins (PartB: The Contractile Apparatus and the Cy to skeleton), ed. by D W Frederiksen and L W Cunningham (Academic Press, San Diego, 1982).
Bio-Rad Laboratories, US/EG Bulletin 1156.
W. Denk and W.W. Webb, Applied Optics 29, 2382 (1990).
K. Svoboda, C.F. Schmidt, B.J. Schnapp et al., Nature 365, 721 (1993).
F. Gittes and C.F. Schmidt, in Laser tweezers in cell biology, ed. M. P. Sheetz (Academic Press, San Diego, 1997).
C.F. Schmidt, et al., Macromolecules 22, 3638 (1989).
In analogy with the Rouse model, one might have expected a scaling Gs(ω)), G′(ω) ∝ ω1/4 for semiflexible polymers. This would result in a ω-5/4 dependence of the power spectrum
J.S. Fawcett and C.J.O.R. Morris, Separation Science 1, 9 (1966).
Y. Cohen, et ai, Journal of Polymer Science, Part B (Polymer Physics) 30, 1055 (1992).
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Schnurr, B., Gittes, F., Olmsted, P.D. et al. Local Viscoelasticity of Biopolymer Solutions. MRS Online Proceedings Library 463, 15–20 (1996). https://doi.org/10.1557/PROC-463-15
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DOI: https://doi.org/10.1557/PROC-463-15