Deflection of a cell membrane under application of a local force

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volumn 57, Issue 2, 1998, Pages 2123-2128

  Boulbitch, A A ^a  

^a TECHNICAL UNIVERSITY OF MUNICH   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 85002435307     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.57.2123     Document Type: Article

References (46)

1. L. D. Landau and E. M. Lifshitz, Theory of Elasticity (Pergamon Press, New York, 1959).
2. W. Helfrich, Z. Naturforsch. 28c, 693 (1973).
3. S. Svetina and B. Zeks, Biochim. Biophys. Acta 42, 86 (1983); BBACAQ
4. L. Miao, U. Seifert, M. Wortis, and H.-G. Döbereiner, Phys. Rev. E 49, 5389 (1994).
5. E. A. Evans and R. Skalak, Mechanics and Thermodynamics of Biomembranes (CRC Press, Boca Raton, FL, 1980).
6. M. Ziegler, M. Peterson, and E. Sackmann (private communication).
7. E. Evans, K. Ritchie, and R. Merkel, Biophys. J. 68, 2580 (1995)
8. M. Duszug, B. Schwab III, G. I. Zahalak, H. Qian, and E. L. Elson, Biophys. J. 55, 683 (1989); BIOJAU
9. C. Pasternak, S. Wong, and E. L. Elson, J. Cell Biol. 128, 355 (1995).
10. M. Radmacher, M. Fritz, C. M. Kacher, J. P. Cleveland, and P. K. Hansma, Biophys. J. 70, 556 (1996)
11. E. Henderson, Prog. Surf. Sci. 46, 39 (1994); PSSFBP
12. H. Oberleitner, E. Brinckmann, G. Giebisch, and J. Geibel, Kidney Intern. 48, 923 (1995).
13. A. M. Fra, E. Williamson, K. Simmons, and R. G. Parton, Proc. Natl. Acad. Sci. USA 92, 8655 (1995); PNASA6
14. I. Nickola and M. Frimmer, Cell Tissue Res. 245, 635 (1986);
15. A. Jungbluth, V. von Arnim, E. Biegelmann, B. Humbel, A. Schweiger, and G. Gerisch, J. Cell. Sci. 107, 117 (1994); JNCSAI
16. J. Simon, M. Kühner, H. Ringsdorf, and E. Sackmann, Chem. Phys. Lipids 76, 241 (1995); CPLIA4
17. S. E. Zweig, K. T. Tokuyasu, and S. J. Singer, J. Supramol. Struct. Cell. Biochem. 17, 163 (1981);
18. I. Laffafian and M. B. Hallett, J. Cell. Sci. 108, 3199 (1995)
19. N. Mohandas and E. Evans, Annu. Rev. Biophys. Biomol. Struct. 23, 787 (1994).
20. Here the usual notation for the second Lame coefficient λ and the shear modulus μ is kept. λ is related to the compressibility modulus K as λ=K-2μ/3. Note that all these values λ, K, and μ are integrated over the membrane width h (Ref. 1). For membranes λ and K are usually much larger than μ (Refs. 211).
21. G. W. Schmid-Schönbein, T. Kosawada, R. Skalak, and Shu Chien, J. Biomech. Eng. 117, 171 (1995).
22. D. Simson, R. Simson, K. Maier, R. Merkel, and E. Sackmann (private communication).
23. The extensional rigidity of erythrocytes emanates from protein scaffolding underneath the bilayer 11. For present purposes its origin is not important. Note that μ and λ characterize the whole membrane property rather than that of some of its parts. For the sake of simplicity we take into account only dilatation. However, since in most cases μ≪λ the contribution of shear deformation is often negligible.
24. The lateral elasticity of a membrane together with its bending elasticity was considered by R. Bruinsma, in Proceedings of NATO Advanced Institute on Physics of Biomaterials, Geilo, 1995, Vol. 322 of NATO Advanced Studies Institute Ser. E: Applied Sciences, edited by T. Riste and D. Sherrington (Kluwer, Dordrecht, 1996);
25. and—in another manner—by M. Petersen, J. Math. Phys. 26, 711 (1985)
26. Ou-Yang Zhong-can and W. Helfrich, Phys. Rev. A 39, 5280 (1989)
27. B. Alberts, D. Bray, J. Lewis, M. Raff, K. Roberts, and J. D. Watson, Molecular Biology of the Cell (Garland Publishing, New York, 1989);
28. E. Sackmann, Macromol. Chem. Phys. 195, 7 (1994); MCHPES
29. T. Okanoue, M. Ohta, S. Fushiki, O. Ou, K. Kachi, T. Okuno, T. Takino, and S. W. French, Hepatology 5, 1 (1985);
30. J. H. Hartwig and M. DeSisto, J. Cell Biol. 112, 407 (1991).
31. N. Dan, P. Pincus, and S. A. Safran, Langmuir 9, 2768 (1993); LANGD5
32. N. Dan, A. Berman, P. Pincus, and S. A. Safran, J. Phys. II 4, 1713 (1994)
33. M. Goulian, R. Bruinsma, and P. Pincus, Europhys. Lett. 22, 145 (1993)
34. J. C. Lelièvre, C. Bucherer, S. Geiger, C. Lacombe, and V. Vereycken, J. Phys. III 5, 1689 (1995)
35. E. Evans and A. Yeung, Biophys. J. 56, 151 (1989); BIOJAU
36. D. Needham and R. M. Hochmuth, Biophys. J. 61, 1664 (1992)
37. The opposite limit kψΔ2ψ∼BψΔψ∼Dψ2 takes place under p∼10 Pa and corresponds to the case when a spherical shape is globally unstable. In this case the complete expression Eq. (6) for the square part of the free energy should be held and further simplifications are not valid.
38. Note that the elastic charge q is independent of the angle φ. Dependence of the parameters, a, s, and f0 on φ should be introduced in order to take into account the possible in-plane asymmetry and the tilt of integral proteins. The tilt takes place in particular under interaction of two proteins (Ref. 20). For the sake of simplicity this dependence is neglected here. This approach also does not take into account the phenomena arising due to the hydrophobic mismatch (Ref. 19).
39. L. D. Landau and E. M. Lifshitz, Statistical Physics (Pergamon Press, New York, 1959).
40. U. Seifert, Phys. Rev. E 49, 3124 (1994;); PLEEE8
41. U. Seifert and S. A. Langer, Europhys. Lett. 23, 71 (1993); EULEEJ
42. U. Seifert, Habilitation theses, Ludwig Maximilians Universität München, 1994.
43. M. Radmacher, M. Fritz, and P. K. Hansma, Biophys. J. 69, 264 (1995)
44. U. G. Hofmann, C. Rotsch, W. J. Parak, and M. Radmacher, J. Struct. Biol. (to be published).
45. M. Radmacher, IEEE Eng. Med. Biol. Mag. 16, 47 (1997)
46. W. Xu, P. J. Mulhern, B. L. Blackford, M. H. Jericho, M. Firtel, and T. J. Beveridge, J. Bacteriology 178, 3106 (1996).