Skip to main content Accessibility help

Local Viscoelasticity of Biopolymer Solutions

  • B. Schnurr (a1), F. Gittes (a1), P. D. Olmsted (a2), C. F. Schmidt (a1) and F. C. Mackintosh (a1)...


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.



Hide All
1 Stessei, T.P., Sci Am 271, 54–5, 58–63 (1994).
2 Kas, J., Strey, H., Tang, J.X. et al., Biophysical Journal 70, 609 (1996).
3 Muller, O., et al., Macromolecules 24, 3111 (1991);
Ruddies, R., et al, Eur Biophys J 22, 309 (1993).
4 Janmey, P.A., Hvidt, S., Kas, J. et al., J Biol Chem 269, 32503 (1994).
5 Janmey, P.A., et al., Biochemistry 27, 8218 (1988);
Janmey, P.A., J Biochem and Biophys Meth 22, 41 (1991).
6 MacKintosh, F.C., Kas, J., and Janmey, P.A., Physical Review Letters 75, 4425 (1995).
7 Pollard, T.D., Goldberg, I., and Schwarz, W.H., J Biol Chem 267, 20339 (1992);
Wachsstock, D.H., Schwartz, W.H., and Pollard, T.D., Biophys J 65, 205 (1993); 66, 801 (1994);
Sato, M., et al., J Biol Chem 260, 8585 (1985);
Zaner, K.S. and Hartwig, J.H., J Biol Chem 263, 4532 (1988);
Newman, J., et al., Biophys J 64, 1559 (1993).
8 Ziemann, F., Radier, J., and Sackmann, E., Biophys J 66, 2210 (1994).
9 Schmidt, F.G., Ziemann, F., and Sackmann, E., Eur Biophys J 24, 348 (1996).
10 Amblard, F., et al., Physical Review Letters 77, 4470 (1996).
11 Mason, T.G. and Weitz, D.A., Physical Review Letters 74, 1250 (1995).
12 Landau, L.D. and Lifshitz, E.M., Fluid mechanics (Pergamon Press, Reading, MA, 1959).
13 The shear stress σ and displacement field it 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.
14 Landau, L.D. and Lifshitz, E.M., Theory of elasticity, 2d ed. (Pergamon Press, New York, 1970).
15 Schnurr, B., et al., to be published.
16 Brochard, F. and de Gennes, P.G., Macromolecules 10, 1157 (1977).
17 Milner, S.T., Physical Review E 48, 3674 (1993).
18 Landau, L.D., Lifshitz, E.M., and Pitaevskii, L.P., Statistical physics (Pergamon Press, New York, 1980).
19 Doi, M. and Edwards, S.F., The Theory of Polymer Dynamics (Clarendon Press, Oxford, 1988).
20 Pardee, J.D. and Spudich, J.A., in Structural and Contractile Proteins (PartB: The Contractile Apparatus and the Cy to skeleton), ed. by Frederiksen, D W and Cunningham, L W (Academic Press, San Diego, 1982).
21 Bio-Rad Laboratories, US/EG Bulletin 1156.
22 Denk, W. and Webb, W.W., Applied Optics 29, 2382 (1990).
23 Svoboda, K., Schmidt, C.F., Schnapp, B.J. et al., Nature 365, 721 (1993).
24 Gittes, F. and Schmidt, C.F., in Laser tweezers in cell biology, ed. Sheetz, M. P. (Academic Press, San Diego, 1997).
25 Schmidt, C.F., et al., Macromolecules 22, 3638 (1989).
26 In analogy with the Rouse model, one might have expected a scaling G′(ω)), G′(ω) ∝ ω 1/4 for semiflexible polymers. This would result in a ω −5/4 dependence of the power spectrum.
27 Fawcett, J.S. and Morris, C.J.O.R., Separation Science 1, 9 (1966).
28 Cohen, Y., et ai, Journal of Polymer Science, Part B (Polymer Physics) 30, 1055 (1992).


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed