Viscoelastic properties of actin-coated membranes

E. Helfer; S. Harlepp; L. Bourdieu; J. Robert; F. C. MacKintosh; D. Chatenay

doi:10.1103/PhysRevE.63.021904

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Viscoelastic properties of actin-coated membranes

E. Helfer¹, S. Harlepp¹, L. Bourdieu^1,*, J. Robert¹, F. C. MacKintosh², and D. Chatenay¹

¹Laboratoire de Dynamique des Fluides Complexes, U.M.R. 7506, 3 rue de l’Université, 67084 Strasbourg Cedex, France
²Department of Physics, University of Michigan, Ann Arbor, Michigan 48109-1120

^*Author to whom correspondence should be addressed.

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Phys. Rev. E 63, 021904 – Published 19 January, 2001

DOI: https://doi.org/10.1103/PhysRevE.63.021904

Abstract

In living cells, cytoskeletal filaments interact with the plasma membrane to form structures that play a key role in cell shape and mechanical properties. To study the interaction between these basic components, we designed an in vitro self-assembled network of actin filaments attached to the outer surface of giant unilamellar vesicles. Optical tweezers and single-particle tracking experiments are used to study the rich dynamics of these actin-coated membranes (ACM). We show that microrheology studies can be carried out on such an individual microscopic object. The principle of the experiment consists in measuring the thermally excited position fluctuations of a probe bead attached biochemically to the membrane. We propose a model that relates the power spectrum of these thermal fluctuations to the viscoelastic properties of the membrane. The presence of the actin network modifies strongly the membrane dynamics with respect to a fluid, lipid bilayer one. It induces first a finite (ω=0) two-dimensional (2D) shear modulus $G_{2 D}^{0} \sim 0.5$ to 5 μN/m in the membrane plane. Moreover, the frequency dependence at high frequency of the shear modulus $[G_{2 D}^{'} (f) \sim f^{0.85 \pm 0.07}]$ and of the bending modulus $(κ_{ACM} (f) \sim f^{0.55 \pm 0.21})$ demonstrate the viscoelastic behavior of the composite membrane. These results are consistent with a common exponent of 0.75 for both moduli as expected from our model and from prior measurements on actin solutions.

References (44)

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[c1] B. Alberts et al., Molecular Biology of the Cell (Garland, New York, 1994).

[c2] F. Nédelec et al., Nature (London) 389, 305 (1997).

[c3] H. Hotani and M. Miyamoto, Adv. Biophys. 26, 135 (1990); M. Elbaum, D. K. Fygenson, and A. Libchaber, Phys. Rev. Lett. 76, 4078 (1996); D. K. Fygenson et al., Phys. Rev. E 55, 850 (1997).

[c4] J. D. Cortese et al., Proc. Natl. Acad. Sci. U.S.A. 86, 5773 (1989); ibid.H. Miyata and H. Hotani, 89, 11 547 (1992); W. Häckl, M. Bärmann, and E. Sackmann, Phys. Rev. Lett. 80, 1786 (1998).

[c5] A. Ott et al., Phys. Rev. E 48, 1642 (1993).

[c6] F. Gittes et al., J. Cell Biol. 120, 923 (1993).

[c7] F. Gittes et al., Phys. Rev. Lett. 79, 3286 (1997); B. Schnurr et al., Macromolecules 30, 7781 (1997).

[c8] A. Palmer et al., Biophys. J. 76, 1063 (1999).

[c9] T. Gisler and D. A. Weitz, Phys. Rev. Lett. 82, 1606 (1999).

[c10] D. C. Morse, Phys. Rev. E 58, 1237 (1998); ibid.F. Gittes and F. C. MacKintosh, 58, 1241 (1998).

[c11] R. Ruddies et al., Eur. Biophys. J. 64, 1559 (1993).

[c12] M. Doi and S. F. Edwards, The Theory of Polymer Dynamics (Clarendon, Oxford, 1986).

[c13] K. A. Beck and W. J. Nelson, Biochim. Biophys. Acta 1404, 153 (1998).

[c14] W. Helfrich, Z. Naturforsch. C 28, 693 (1973).

[c15] For a review, see U. Seifert, Adv. Phys. 46, 13 (1997).

[c16] E. A. Evans and W. Rawicz, Phys. Rev. Lett. 64, 2094 (1990); H. P. Duwe, J. Käs, and E. Sackmann, J. Phys. (France) 51, 945 (1990).

[c17] J. F. Faucon et al., J. Phys. (France) 50, 2389 (1989).

[c18] R. Waugh and E. Evans, Biophys. J. 26, 115 (1979).

[c19] R. M. Hochmuth, N. Mohandas, and P. L. Blackshear, Biophys. J. 13, 747 (1973).

[c20] S. Hénon et al., Biophys. J. 76, 1145 (1999).

[c21] F. Brochard and J. F. Lennon, J. Phys. (France) 36, 1035 (1975).

[c22] H. Strey, M. Peterson, and E. Sackmann, Biophys. J. 69, 478 (1995).

[c23] E. A. Evans, Biophys. J. 43, 27 (1983).

[c24] M. B. Schneider, J. T. Jenkins, and W. W. Webb, J. Phys. (France) 45, 1457 (1984); S. T. Milner and S. A. Safran, Phys. Rev. A 36, 4371 (1987).

[c25] E. Helfer et al., Phys. Rev. Lett. 85, 457 (2000).

[c26] F. Gittes and C. F. Schmidt, Methods Cell Biol. 55, 129 (1998).

[c27] R. R. C. New, Liposomes, Practical Approach Series (Oxford University Press, Oxford, 1990).

[c28] M. I. Angelova et al., Springer Proc. Phys. 66, 178 (1992).

[c29] L. Mathivet, P. F. Devaux, and S. Cribier, Biophys. J. 70, 1112 (1996).

[c30] J. D. Pardee and J. A. Spudich, Methods Cell Biol. 24, 271 (1982).

[c31] N. M. Green, Adv. Protein Chem. 29, 85 (1975).

[c32] A. Laliberte and C. Gicquaud, J. Cell Biol. 106, 1221 (1988).

[c33] J. E. Molloy, Methods Cell Biol. 55, 205 (1998).

[c34] K. Velikov et al., Europhys. Lett. 40, 405 (1997); R. Dimova et al., Eur. Phys. J. B 12, 589 (1999); K. Velikov et al., Colloids Surf. A 149, 245 (1999).

[c35] R. D. Kornberg and H. M. McConnel, Proc. Natl. Acad. Sci. U.S.A. 68, 2564 (1971); J. F. Tocanne, L. Dupou-Cezanne, and A. Lopez, Prog. Lipid Res. 33, 203 (1994).

[c36] R. Everaers et al., Phys. Rev. Lett. 82, 3717 (1999). Here, the authors show that at short times, the dynamics differ from those shown previously in Ref. [10]. This is due to the finite speed of propagation of tension. In a time t, the tension propagates a length $l_{1} \approx \sqrt{l_{p} l (t)},$ where $l_{p}$ is the persistence length and $l (t) \approx (4 κ t / η)^{1 / 4}$ represents the longest wavelength bending mode that can relax in time t. These authors show that for a filament segment of length L, the initial longitudinal mean-square displacement of a filament end grows with time as $δ x^{2} \approx t^{7 / 8}$ until $l_{1}$ exceeds L. This occurs in a time of order $(η L^{4} / κ {) (L / l}_{p})^{4}$ which, for instance, is approximately $10^{- 6} s$ for a segment of length 1 μm.

[c37] L. Landau and E. Lifchitz, Théorie de l’élasticité (Mir, Moscow, 1967).

[c38] A. E. H. Love, A Treatise on the Mathematical Theory of Elasticity (Dover, New York, 1944).

[c39] R. Granek, J. Phys. II 7, 1761 (1997).

[c40] D. Forster, Hydrodynamic Fluctuations, Broken Symmetry and Correlation Function (Addison Wesley, Reading, MA, 1983).

[c41] F. C. MacKintosh, J. Käs, and P. A. Janmey, Phys. Rev. Lett. 75, 4425 (1995).

[c42] C. F. Schmidt et al., Macromolecules 22, 3638 (1989).

[c43] D. Needham and E. Evans, Biochemistry 27, 8261 (1988).

[c44] R. Dimova, B. Pouligny, and C. Dietrich, Biophys. J. 79, 340 (2000).

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Viscoelastic properties of actin-coated membranes

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Flexibility of Cell Membranes

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