Skip to main content
Log in

Bending stiffness of biological membranes: What can be measured by neutron spin echo?

  • Regular Article
  • Published:
The European Physical Journal E Aims and scope Submit manuscript

Abstract

Large vesicles obtained by the extrusion method represent adequate membrane models to probe membrane dynamics with neutron radiation. Particularly, the shape fluctuations around the spherical average topology can be recorded by neutron spin echo (NSE). In this paper we report on the applicable theories describing the scattering contributions from bending-dominated shape fluctuations in diluted vesicle dispersions, with a focus on the relative relevance of the master translational mode with respect to the internal fluctuations. Different vesicle systems, including bilayer and non-bilayer membranes, have been scrutinized. We describe the practical ranges where the exact theory of bending fluctuations is applicable to obtain the values of the bending modulus from experiments, and we discuss about the possible internal modes that could be alternatively contributing to shape fluctuations.

Graphical abstract

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. W. Helfrich, Z. Naturforsch. c 28, 693 (1973).

    Google Scholar 

  2. J.F. Nagle, S. Tristram-Nagle, Biochim. Biophys. Acta 1469, 159 (2000).

    Article  Google Scholar 

  3. J. Lyatskaya, Y. Liu, S. Tristram-Nagle, J. Katsaras, J.F. Nagle, Phys. Rev. E 63, 011907 (2000).

    Article  ADS  Google Scholar 

  4. G. Brotons, L. Belloni, Th. Zemb, T. Salditt, Europhys. Lett. 75, 992 (2006).

    Article  ADS  Google Scholar 

  5. M.M. Blum, M. Mustyakimov, H. Rüterjans, K. Kehe, B.P. Schoenborn, P. Langan, J.C. Chen, Proc. Natl. Acad. Sci. U.S.A. 106, 713 (2009).

    Article  ADS  Google Scholar 

  6. E. Schneck, B. Demé, C. Gege, M. Tanaka, Biophys. J. 100, 2151 (2011).

    Article  ADS  Google Scholar 

  7. V.I. Gordeliy, M.A. Kiselev, Biophys. J. 69, 1424 (1995).

    Article  ADS  Google Scholar 

  8. J. Pencer, F.R. Hallett, Phys. Rev. E 61, 3003 (2000).

    Article  ADS  Google Scholar 

  9. P.C. Mason, B.D. Gaulin, R.M. Epand, G.D. Wignall, J.S. Lin, Phys. Rev. E 59, 3361 (1999).

    Article  ADS  Google Scholar 

  10. N. Kucerka, J.F. Nagle, S.E. Feller, P. Balgavý, Phys. Rev. E 69, 051903 (2004).

    Article  ADS  Google Scholar 

  11. L.R. Arriaga, I. López-Montero, F. Monroy, G. Orts-Gil, B. Farago, T. Hellweg, Biophys. J. 96, 3629 (2009).

    Article  ADS  Google Scholar 

  12. L.R. Arriaga, I. López-Montero, G. Orts-Gil, B. Farago, T. Hellweg, F. Monroy, Phys. Rev. E 80, 031908 (2009).

    Article  ADS  Google Scholar 

  13. E. Evans, A. Yeung, Chem. Phys. Lipids 73, 39 (1994).

    Article  Google Scholar 

  14. J.T. Jenkins, J. Math. Biol 4, 149 (1977).

    Article  MATH  Google Scholar 

  15. M.B. Schneider, J.T. Jenkins, W.W. Webb, J. Phys. (Paris) 45, 1457 (1984).

    Article  Google Scholar 

  16. D.A. Boal, Mechanics of the Cell, 2nd edition (Cambridge University Press, Cambridge, 2012).

  17. W. Helfrich, R.-M. Servuss, Nuovo Cimento D 3, 137 (1984).

    Article  ADS  Google Scholar 

  18. B.J. Berne, R. Pecora, Dynamic Light Scattering (Wiley, New York, 1976).

  19. S.W. Lovesey, P. Schofield, J. Phys. C: Solid State Phys. 9, 2843 (1976).

    Article  ADS  Google Scholar 

  20. S.T. Milner, S.A. Safran, Phys. Rev. A 36, 4371 (1987).

    Article  ADS  Google Scholar 

  21. T. Hellweg, D. Langevin, Phys. Rev. E 57, 6825 (1998).

    Article  ADS  Google Scholar 

  22. R. Messager, P. Bassereau, G. Porte, J. Phys. (Paris) 51, 1329 (1990).

    Article  Google Scholar 

  23. A.G. Zilman, R. Granek, Chem. Phys. 284, 195 (2002).

    Article  ADS  Google Scholar 

  24. J.S. Huang, S.T. Milner, B. Farago, D. Richter, Phys. Rev. Lett. 59, 2600 (1987).

    Article  ADS  Google Scholar 

  25. B. Farago, M. Monkenbusch, K.D. Goecking, D. Richter, J.S. Huang, Physica B 213-214, 712 (1995).

  26. T. Hellweg, A. Brulet, T. Sottmann, Phys. Chem. Chem. Phys. 2, 5168 (2000).

    Article  Google Scholar 

  27. S. Komura, T. Takeda, Y. Kawabata, S.K. Ghosh, H. Seto, M. Nagao, Phys. Rev. E 63, 041402 (2001).

    Article  ADS  Google Scholar 

  28. B. Farago, M. Gradzielski, J. Chem. Phys. 114, 10105 (2001).

    Article  ADS  Google Scholar 

  29. M. Mihailescu, M. Monkenbusch, J. Allgaier, H. Frielinghaus, D. Richter, B. Jakobs, T. Sottmann, Phys. Rev. E 66, 041504 (2002).

    Article  ADS  Google Scholar 

  30. A.C. Woodka, P.D. Butler, L. Porcar, B. Farago, M. Nagao, Phys. Rev. Lett. 109, 058102 (2012).

    Article  ADS  Google Scholar 

  31. E. Freyssingeas, D. Roux, F. Nallet, J. Phys.: Condens. Matter 8, 2801 (1996).

    Article  ADS  Google Scholar 

  32. E. Freyssingeas, F. Nallet, D. Roux, Langmuir 12, 6028 (1996).

    Article  Google Scholar 

  33. J.F. Faucon, M.D. Mitov, P. Méléard, I. Bivas, P. Bothorel, J. Phys. (Paris) 50, 2389 (1989).

    Article  Google Scholar 

  34. J. Pécréaux, H.G. Döbereiner, J. Prost, J.-F. Joanny, P. Bassereau, Eur. Phys. J. E 13, 277 (2004).

    Article  Google Scholar 

  35. A.G. Zilman, R. Granek, Phys. Rev. Lett. 77, 4788 (1996).

    Article  ADS  Google Scholar 

  36. R. Granek, Soft Matter 7, 5281 (2011).

    Article  ADS  Google Scholar 

  37. R. Granek, J. Phys. II 7, 1761 (1997).

    Article  Google Scholar 

  38. N.G. van Kampen, Stochastic Process in Physics and Chemistry (North-Holland, Amsterdam, 1992).

  39. R. Iñiguez-Palomares, H. Acuña-Campa, A. Maldonado, Phys. Rev. E 84, 011604 (2011).

    Article  ADS  Google Scholar 

  40. M.H. Nagao, H. Seto, Y. Kawabata, T. Takeda, J. Appl. Crystallogr. 33, 653 (2000).

    Article  Google Scholar 

  41. M. Mihailescu, M. Monkenbusch, H. Endo, J. Allgaier, G. Gompper, J. Stellbrink, D. Richter, B. Jakobs, T. Sottmann, B. Farago, J. Chem. Phys. 115, 9563 (2001).

    Article  ADS  Google Scholar 

  42. Z. Yi, M. Nagao, D. Bossev, J. Phys.: Condens. Matter 21, 155104 (2009).

    Article  ADS  Google Scholar 

  43. M. Imai, R. Mawatari, K. Nakaya, S. Komura, Eur. Phys. J. E 13, 391 (2004).

    Article  Google Scholar 

  44. M.C. Watson, F.L.H. Brown, Biophys. J. 98, L9 (2010).

    Article  Google Scholar 

  45. M.C. Watson, Y. Peng, Y. Zheng, F.L.H. Brown, J. Chem. Phys. 135, 194701 (2011).

    Article  ADS  Google Scholar 

  46. L.R. Arriaga, R. Rodríguez-García, I. López-Montero, B. Farago, T. Hellweg, F. Monroy, Eur. Phys. J. E 31, 105 (2010).

    Article  Google Scholar 

  47. U. Seifert, S.A. Langer, Europhys. Lett. 23, 71 (1993).

    Article  ADS  Google Scholar 

  48. M. Kraus, U. Seifert, J. Phys. II 4, 1117 (1994).

    Article  Google Scholar 

  49. T. Pott, P. Méléard, Europhys. Lett. 59, 87 (2002).

    Article  ADS  Google Scholar 

  50. R. Rodríguez-García, L.R. Arriaga, M. Mell, L.H. Moleiro, I. López-Montero, F. Monroy, Phys. Rev. Lett. 102, 128201 (2009).

    Article  Google Scholar 

  51. M. Nagao, Phys. Rev. E 80, 031606 (2009).

    Article  ADS  Google Scholar 

  52. B.J. Frisken, C. Asman, P.J. Patty, Langmuir 16, 928 (2000).

    Article  Google Scholar 

  53. Z. Li, E. Kesselman, Y. Talmon, M.A. Hillmyer, T.P. Lodge, Science 306, 98 (2004).

    Article  ADS  Google Scholar 

  54. A. Wittemann, M. Drechsler, Y. Talmon, M. Ballauff, J. Am. Chem. Soc. 127, 9688 (2005).

    Article  Google Scholar 

  55. S.W. Provencher, Comput. Phys. Commun. 27, 213 (1982).

    Article  ADS  Google Scholar 

  56. S.W. Provencher, Comput. Phys. Commun. 27, 229 (1982).

    Article  ADS  Google Scholar 

  57. A. Jakes, Collect. Czech. Chem. Commun. 60, 1781 (1995).

    Article  Google Scholar 

  58. P. Brocca, L. Cantù, M. Corti, E.D. Favero, Prog. Colloid Polym. Sci. 115, 181 (2000).

    Article  Google Scholar 

  59. P. Brocca, L. Cantù, M. Corti, E.D. Favero, S. Motta, Langmuir 20, 2141 (2004).

    Article  Google Scholar 

  60. P. Schleger et al., Physica B 266, 49 (1999).

    Article  ADS  Google Scholar 

  61. B. Farago, D. Richter, J.S. Huang, S.A. Safran, S.T. Milner, Phys. Rev. Lett. 65, 3348 (1990).

    Article  ADS  Google Scholar 

  62. D. Chapman, Q. Rev. Biophys. 8, 185 (1975).

    Article  Google Scholar 

  63. I. López-Montero, L.R. Arriaga, G. Rivas, M. Vélez, F. Monroy, Chem. Phys. Lipids 163, 56 (2010).

    Article  Google Scholar 

  64. W. Rawicz, K.C. Olbrich, T. McInstosh, D. Needham, E. Evans, Biophys. J. 79, 328 (2000).

    Article  Google Scholar 

  65. N. Kucerka, S. Tristram-Nagle, J.F. Nagle, J. Memb. Biol. 208, 193 (2005).

    Article  Google Scholar 

  66. A.C. Woodka, P.D. Butler, L. Porcar, B. Farago, M. Nagao, Phys. Rev. E 80, 031606 (2009).

    Article  Google Scholar 

  67. H. Seto, N.L. Yamada, M. Nagao, M. Hishida, T. Takeda, Eur. Phys. J. E 26, 217 (2008).

    Article  Google Scholar 

  68. R. Rodríguez-García, M. Mell, I. López-Montero, J. Netzel, T. Hellweg, F. Monroy, Soft Matter 7, 1532 (2011).

    Article  ADS  Google Scholar 

  69. R. Rodríguez-García, M. Mell, I. López-Montero, F. Monroy, Europhys. Lett. 94, 28009 (2011).

    Article  ADS  Google Scholar 

  70. H. Bermúdez et al., Macromolecules 35, 8203 (2002).

    Article  ADS  Google Scholar 

  71. M. Nagao, S. Chawang, T. Hawa, Soft Matter 7, 6598 (2011).

    Article  ADS  Google Scholar 

  72. M. Nagao, J. Chem. Phys. 135, 074704 (2011).

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Thomas Hellweg.

Additional information

Contribution to the Topical Issue “Neutron Biological Physics”, edited by Giovanna Fragneto and Frank Gabel.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Mell, M., Moleiro, L.H., Hertle, Y. et al. Bending stiffness of biological membranes: What can be measured by neutron spin echo?. Eur. Phys. J. E 36, 75 (2013). https://doi.org/10.1140/epje/i2013-13075-2

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epje/i2013-13075-2

Keywords

Navigation