Elementary excitations of biomembranes: Differential geometry of undulations in elastic surfaces

Physics Reports

Volumn 444, Issue 2, 2007, Pages 51-99

  van Hemmen, J Leo ^a   Leibold, Christian ^a  

^a TECHNICAL UNIVERSITY OF MUNICH   (Germany)

Author keywords

Biomembrane undulations; Excitations in soft matter

Indexed keywords

EID: 34249807309     PISSN: 03701573     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physrep.2006.12.007     Document Type: Review

References (106)

1. Anderson P.W. Concepts in Solids (1963), Benjamin, Reading, MA (Chapter 3)
2. Berndl K., Käs J., Lipowsky R., Sackmann E., and Seifert U. Europhys. Lett. 13 (1990) 659
3. Blair D.E. Inversion Theory and Conformal Mapping (2000), American Mathematical Society, Providence, RI
4. Boal D. Mechanics of the Cell (2002), Cambridge University Press, Cambridge (Chapter 6)
5. Boal D., Seifert U., and Shillcock J.C. Phys. Rev. B 48 (1993) 4274
6. Boruvka L., and Neumann A.W. J. Chem. Phys. 66 (1977) 5464
7. Boulbitch A., et al. Phys. Rev. E 62 (2000) 3974
8. Bowick M., Cacciuto A., Thorleifsson G., and Travesset A. Phys. Rev. Lett. 87 (2001) 148103
9. Brochard F., and Lennon J.F. J. Phys. (Paris) 36 (1975) 1035
10. Brouricz E. Zbl. Med. Wiss. 28 (1890) 625
11. Bruinsma R., and Sackmann E. C.R. Acad. Sci. Paris 2/Sér. IV (2001) 803
12. Buser P. Geometry and Spectra of Compact Riemann Surfaces (1992), Birkhäuser, Boston
13. Canham P.B. J. Theor. Biol. 26 (1970) 61
14. Coombs D., Huber G., Kessler J.O., and Goldstein R.E. Phys. Rev. Lett. 89 (2002) 118102
15. De Jeu W.H., Ostrovskii B.I., and Shalaginov A.N. Rev. Mod. Phys. 75 (2003) 181
16. Deuling H.J., and Helfrich W. J. Phys. (Paris) 37 (1976) 1335
17. Döbereiner H.-G., Evans E., Kraus M., Seifert U., and Wortis M. Phys. Rev. E 55 (1997) 4458
18. Dirac P.A.M. The Principles of Quantum Mechanics. fourth ed (1958), Oxford University Press, Oxford
19. Duplantier B. Physica A 168 (1990) 179
20. Duplantier B., Goldstein R.E., Romero-Rochin V., and Pesci A.I. Phys. Rev. Lett. 65 (1990) 508
21. Duwe H.P., and Sackmann E. Physica A 163 (1990) 410
22. Engelhardt H., Duwe H.P., and Sackmann E. J. Phys. (Paris) Lett. 46 (1985) L395
23. van Enter A.C.D., and van Hemmen J.L. Phys. Rev. A 29 (1984) 355 (especially, Sections II-III C and the appendix)
24. Evans E.A. Biophys. J. 14 (1974) 923
25. Frankel Th. The Geometry of Physics: An Introduction (1997), Cambridge University Press, Cambridge
26. Gantmacher F.R. The Theory of Matrices vol. 1 (1977), Chelsea, New York (IX. Sections 3 and IX. Section 5)
27. Gauss, C.F., 1827. Disquisitiones Generales circa Supervicies Curvas. in: Comm. soc. regiae sci. Gott. recentiores, vol. VI, pp. 1823-1827; translation Allgemeine Flächentheorie, 1900 (Engelmann, Leipzig) (See also Spivak (1979) Chapter 3).
28. Gerretsen J.C.H. Lectures on Tensor Calculus and Differential Geometry (1962), Noordhoff, Groningen
29. Goldstein R.E., Powers T.R., and Wiggins C.H. Phys. Rev. Lett. 80 (1998) 5232
30. Goldstein R.E., Goriely A., Huber G., and Wolgemuth C.W. Phys. Rev. Lett. 84 (2000) 1631
31. Gov, N., Zilman, A.G., Safran, S., 2003. Phys. Rev. Lett. 90, 228101.
32. Gov, N., Safran, S., 2005. Biophys. J. 88, 1859.
33. Guttenberg Z., Lorz B., Sackmann E., and Boulbitch A. Europhys. Lett. 54 (2001) 826
34. Head D.A., Levine A.J., and MacKintosh F.C. Phys. Rev. Lett. 91 (2003) 108102
35. Helfrich W. Z. Naturf. C 28 (1973) 693
36. Hilbert D., and Cohn-Vossen S. Geometry and the Imagination (1964), Chelsea, New York (Sections 26- 29)
37. Hildebrandt S., and Tromba A. The Parsimonious Universe: Shape and Form in the Natural World (1996), Springer, New York
38. Horn R.A., and Johnson C.R. Matrix Analysis (1985), Cambridge University Press, Cambridge (Sections 0.8.2 and 7.2.10)
39. Huang K. Statistical Mechanics. second ed (1987), Wiley, New York (Section 6.4)
40. Hyde S., et al. The Language of Shape: The Role of Curvature in Condensed Matter (1997), Elsevier, Amsterdam
41. Isenberg C. The Science of Soap Films and Soap Bubbles (1992), Dover, Mineola, NY (Chapters 5 and 6)
42. Jülicher F. J. Phys. II France 6 (1996) 1797
43. Jülicher F., Seifert U., and Lipowsky R. Phys. Rev. Lett. 71 (1993) 452
44. Kamien R.D. Rev. Mod. Phys. 74 (2002) 953
45. Kenmotsu K. Surfaces with Constant Mean Curvature (2003), American Mathematical Society, Providence, RI
46. Kleman M., and Lavrentovich O.D. Soft Matter Physics: An Introduction (2002), Springer, New York
47. Komura S., and Andelman D. Eur. Phys. J. E 3 (2000) 259
48. Kuzman D., Svetina S., Waugh R.E., and Žekš B. Eur. Biophys. J. 33 (2004) 1
49. Lakes R. Nature 414 (2001) 503
50. Landau L.D. J. Phys. U.S.S.R. 5 (1941) 71
51. Landau L.D., and Lifshitz E.M. Theory of Elasticity. third ed (1986), Pergamon, Oxford
52. Lim G.H.W., Wortis M., and Mukhopadhyay R. Proc. Natl. Acad. Sci. USA 99 (2002) 16766
53. Lipowsky R. Nature 349 (1991) 475
54. Liusternik L.A., and Sobolev V.J. Elements of Functional Analysis (1961), Ungar, New York
55. Marčelja S. Biochim. Biophys. Acta 367 (1974) 165 (see in particular the appendix)
56. Marx S., Schilling J., Sackmann E., and Bruinsma R. Phys. Rev. Lett. 88 (2002) 138102
57. Messiah A. Quantum Mechanics vol. I (1961), North-Holland, Amsterdam (Chapter V; Section 18, Chapter IX, Section 2), esp. (IX.9); Appendix B, Sections 9-11 esp. (B.98) and (B.81)
58. Miao L., Seifert U., Wortis M., and Döbereiner H.-G. Phys. Rev. E 49 (1994) 5389
59. Michalet X., and Bensimon D. Science 269 (1995) 666
60. Millman R.S., and Parker G.D. Elements of Differential Geometry (1977), Prentice-Hall, Englewood Cliffs, NJ
61. Milner S.T., and Safran S.A. Phys. Rev. A 36 (1987) 4371
62. Milnor J.W. Topology from the Differentiable Point of View (1997), Princeton University Press, Princeton, NJ (Section 1)
63. Misner, C.W., Thorne, K.S., Wheeler, J.A., 1973. Gravitation. Freeman, San Francisco.
64. Mukhopadhyay R., Lim G.H.W., and Wortis M. Biophys. J. 82 (2002) 1756
65. Nelson, D., Piran, T., Weinberg, S. (Eds.). 1989. Statistical Mechanics of Membranes and Surfaces. World Scientific, Singapore.
66. Nitsche J.C.C. Lectures on Minimal Surfaces vol. 1 (1989), Cambridge University Press, Cambridge
67. Oprea J. The Mathematics of Soap Films: Exploration with Maple (2000), American Mathematical Society, Providence, RI
68. Ou-Yang Z., and Helfrich W. Phys. Rev. A 39 (1989) 5280
69. Peliti L. In: David F., Ginsparg P., and Zinn-Justin J. (Eds). Les Houches LXII: Fluctuating Geometries in Statistical Mechanics and Field Theory (1996), North-Holland, Amsterdam
70. Peterson M.A. J. Math. Phys. 26 (1985) 711 Peterson, M.A., 1985. J. Appl. Phys. 57, 1739; Mol. Cryst. Liq. Cryst. 127, 159 and 257
71. Peterson M.A. Phys. Rev. Lett. 61 (1988) 1325
72. Peterson M.A. Phys. Rev. A 39 (1989) 2643
73. Peterson M.A. Phys. Rev. A 45 (1992) 4116
74. Peterson M.A., Strey H., and Sackmann E. J. Phys. II France 2 (1992) 1273
75. Pinkall U., and Stirling I. Math. Intell. 9 (1987) 38
76. Ponder E. Hemolysis and Related Phenomena (1948), Grune and Stratton, New York
77. Rayleigh, J.W.S., 1894. The Theory of Sound, second ed., vol. 1. Macmillan, London (Vol. 2 appeared two years later and both were republished by Dover (New York, 1945). For present purposes, see e.g. Sections 214 and 235 b. The convention of using h for the thickness of an elastic sheet goes back at least to Lord Rayleigh. His insight and clarity are amazing. We note that Rayleigh's thickness is 2 h whereas ours is h).
78. Reissner E. Quart. Appl. Math. 5 (1947) 55
79. Sackmann E. FEBS Lett. 346 (1994) 3
80. Sackmann E., Bausch A.R., and Vonna L. In: Flyvbjerg H., Jülicher F., Ormos P., and David F. (Eds). Les Houches LXXV (2002), EDP Sciences, Les Ulis and Springer, Berlin 237-284
81. Safran S.A. J. Chem. Phys. 78 (1983) 2073
82. Safran S.A. Statistical Thermodynamics of Surfaces, Interfaces, and Membranes (1994), Addison-Wesley, Reading, MA
83. Schäfer M. Z. Angew. Math. Mech. 32 (1952) 162
84. Segel L.A. Mathematics Applied to Continuum Mechanics (1977), Macmillan, New York (Chapter 11)
85. Schoen R., and Yau S.-T. Lectures on Differential Geometry (1994), International Press, Cambridge, MA (in particular, Chapter III)
86. Seifert U. J. Phys. A: Math. Gen. 24 (1991) L573 and Phys. Rev. Lett. 66, 2404
87. Seifert U. Z. Phys. B 97 (1995) 299
88. Seifert U. Adv. Phys. 46 (1997) 13
89. Seifert U., Berndl K., and Lipowsky R. Phys. Rev. A 44 (1991) 1182
90. Seifert U., and Lipowsky R. Phys. Rev. A 42 (1990) 4768
91. Sheetz M.P., and Singer S.J. Proc. Natl. Acad. Sci. USA 71 (1974) 4457
92. Spivak, M., 1979. A Comprehensive Introduction to Differential Geometry, second ed., vol. II. Publish or Perish, Berkeley, CA. (Chapters 3 and 4).
93. Stephani H. General Relativity: An Introduction to the Theory of the Gravitational Field (1990), Cambridge University Press, Cambridge
94. Strey H., Peterson M., and Sackmann E. Biophys. J. 69 (1995) 478
95. Struik D.J. Lectures on Classical Differential Geometry. second ed (1961), Addison-Wesley, Reading, MA (1988, reprint, Dover, New York)
96. Svetina S., and Žekš B. Eur. Biophys. J. 17 (1989) 101
97. Thomas G.B. Calculus and Analytic Geometry. third ed (1972), Addison-Wesley, Reading, MA (Sections 12.6, and 14.1-6)
98. Thomsen G. Abh. Math. Sem. Hamburg 3 (1924) 31-56
99. Thomson W., and Tait P.G. A Treatise on Natural Philosophy. second ed. (1878/1883), Cambridge University Press The second edition was published in two parts. See especially Sections 639, 642, and 720
100. Wilhelm J., and Frey E. Phys. Rev. Lett. 91 (2003) 108103
101. Willmore T.J. Total Curvature in Riemannian Geometry (1982), Ellis Horwood, Chichester (Section 5.2)
102. Willmore T.J. Riemannian Geometry (1993), Oxford University Press (Chapter 7)
103. Zeman K., Engelhardt H., and Sackmann E. Eur. Biophys. J. 18 (1990) 203
104. Zidovska, A., Sackmann, E., 2006. Phys. Rev. Lett. 96, 048103.
105. Zilker A., Engelhardt H., and Sackmann E. J. Phys. (Paris) 48 (1987) 2139
106. Zilker A., Ziegler M., and Sackmann E. Phys. Rev. A. 46 (1992) 7998