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.
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W. Helfrich, Z. Naturforsch. c 28, 693 (1973).
J.F. Nagle, S. Tristram-Nagle, Biochim. Biophys. Acta 1469, 159 (2000).
J. Lyatskaya, Y. Liu, S. Tristram-Nagle, J. Katsaras, J.F. Nagle, Phys. Rev. E 63, 011907 (2000).
G. Brotons, L. Belloni, Th. Zemb, T. Salditt, Europhys. Lett. 75, 992 (2006).
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).
E. Schneck, B. Demé, C. Gege, M. Tanaka, Biophys. J. 100, 2151 (2011).
V.I. Gordeliy, M.A. Kiselev, Biophys. J. 69, 1424 (1995).
J. Pencer, F.R. Hallett, Phys. Rev. E 61, 3003 (2000).
P.C. Mason, B.D. Gaulin, R.M. Epand, G.D. Wignall, J.S. Lin, Phys. Rev. E 59, 3361 (1999).
N. Kucerka, J.F. Nagle, S.E. Feller, P. Balgavý, Phys. Rev. E 69, 051903 (2004).
L.R. Arriaga, I. López-Montero, F. Monroy, G. Orts-Gil, B. Farago, T. Hellweg, Biophys. J. 96, 3629 (2009).
L.R. Arriaga, I. López-Montero, G. Orts-Gil, B. Farago, T. Hellweg, F. Monroy, Phys. Rev. E 80, 031908 (2009).
E. Evans, A. Yeung, Chem. Phys. Lipids 73, 39 (1994).
J.T. Jenkins, J. Math. Biol 4, 149 (1977).
M.B. Schneider, J.T. Jenkins, W.W. Webb, J. Phys. (Paris) 45, 1457 (1984).
D.A. Boal, Mechanics of the Cell, 2nd edition (Cambridge University Press, Cambridge, 2012).
W. Helfrich, R.-M. Servuss, Nuovo Cimento D 3, 137 (1984).
B.J. Berne, R. Pecora, Dynamic Light Scattering (Wiley, New York, 1976).
S.W. Lovesey, P. Schofield, J. Phys. C: Solid State Phys. 9, 2843 (1976).
S.T. Milner, S.A. Safran, Phys. Rev. A 36, 4371 (1987).
T. Hellweg, D. Langevin, Phys. Rev. E 57, 6825 (1998).
R. Messager, P. Bassereau, G. Porte, J. Phys. (Paris) 51, 1329 (1990).
A.G. Zilman, R. Granek, Chem. Phys. 284, 195 (2002).
J.S. Huang, S.T. Milner, B. Farago, D. Richter, Phys. Rev. Lett. 59, 2600 (1987).
B. Farago, M. Monkenbusch, K.D. Goecking, D. Richter, J.S. Huang, Physica B 213-214, 712 (1995).
T. Hellweg, A. Brulet, T. Sottmann, Phys. Chem. Chem. Phys. 2, 5168 (2000).
S. Komura, T. Takeda, Y. Kawabata, S.K. Ghosh, H. Seto, M. Nagao, Phys. Rev. E 63, 041402 (2001).
B. Farago, M. Gradzielski, J. Chem. Phys. 114, 10105 (2001).
M. Mihailescu, M. Monkenbusch, J. Allgaier, H. Frielinghaus, D. Richter, B. Jakobs, T. Sottmann, Phys. Rev. E 66, 041504 (2002).
A.C. Woodka, P.D. Butler, L. Porcar, B. Farago, M. Nagao, Phys. Rev. Lett. 109, 058102 (2012).
E. Freyssingeas, D. Roux, F. Nallet, J. Phys.: Condens. Matter 8, 2801 (1996).
E. Freyssingeas, F. Nallet, D. Roux, Langmuir 12, 6028 (1996).
J.F. Faucon, M.D. Mitov, P. Méléard, I. Bivas, P. Bothorel, J. Phys. (Paris) 50, 2389 (1989).
J. Pécréaux, H.G. Döbereiner, J. Prost, J.-F. Joanny, P. Bassereau, Eur. Phys. J. E 13, 277 (2004).
A.G. Zilman, R. Granek, Phys. Rev. Lett. 77, 4788 (1996).
R. Granek, Soft Matter 7, 5281 (2011).
R. Granek, J. Phys. II 7, 1761 (1997).
N.G. van Kampen, Stochastic Process in Physics and Chemistry (North-Holland, Amsterdam, 1992).
R. Iñiguez-Palomares, H. Acuña-Campa, A. Maldonado, Phys. Rev. E 84, 011604 (2011).
M.H. Nagao, H. Seto, Y. Kawabata, T. Takeda, J. Appl. Crystallogr. 33, 653 (2000).
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).
Z. Yi, M. Nagao, D. Bossev, J. Phys.: Condens. Matter 21, 155104 (2009).
M. Imai, R. Mawatari, K. Nakaya, S. Komura, Eur. Phys. J. E 13, 391 (2004).
M.C. Watson, F.L.H. Brown, Biophys. J. 98, L9 (2010).
M.C. Watson, Y. Peng, Y. Zheng, F.L.H. Brown, J. Chem. Phys. 135, 194701 (2011).
L.R. Arriaga, R. Rodríguez-García, I. López-Montero, B. Farago, T. Hellweg, F. Monroy, Eur. Phys. J. E 31, 105 (2010).
U. Seifert, S.A. Langer, Europhys. Lett. 23, 71 (1993).
M. Kraus, U. Seifert, J. Phys. II 4, 1117 (1994).
T. Pott, P. Méléard, Europhys. Lett. 59, 87 (2002).
R. Rodríguez-García, L.R. Arriaga, M. Mell, L.H. Moleiro, I. López-Montero, F. Monroy, Phys. Rev. Lett. 102, 128201 (2009).
M. Nagao, Phys. Rev. E 80, 031606 (2009).
B.J. Frisken, C. Asman, P.J. Patty, Langmuir 16, 928 (2000).
Z. Li, E. Kesselman, Y. Talmon, M.A. Hillmyer, T.P. Lodge, Science 306, 98 (2004).
A. Wittemann, M. Drechsler, Y. Talmon, M. Ballauff, J. Am. Chem. Soc. 127, 9688 (2005).
S.W. Provencher, Comput. Phys. Commun. 27, 213 (1982).
S.W. Provencher, Comput. Phys. Commun. 27, 229 (1982).
A. Jakes, Collect. Czech. Chem. Commun. 60, 1781 (1995).
P. Brocca, L. Cantù, M. Corti, E.D. Favero, Prog. Colloid Polym. Sci. 115, 181 (2000).
P. Brocca, L. Cantù, M. Corti, E.D. Favero, S. Motta, Langmuir 20, 2141 (2004).
P. Schleger et al., Physica B 266, 49 (1999).
B. Farago, D. Richter, J.S. Huang, S.A. Safran, S.T. Milner, Phys. Rev. Lett. 65, 3348 (1990).
D. Chapman, Q. Rev. Biophys. 8, 185 (1975).
I. López-Montero, L.R. Arriaga, G. Rivas, M. Vélez, F. Monroy, Chem. Phys. Lipids 163, 56 (2010).
W. Rawicz, K.C. Olbrich, T. McInstosh, D. Needham, E. Evans, Biophys. J. 79, 328 (2000).
N. Kucerka, S. Tristram-Nagle, J.F. Nagle, J. Memb. Biol. 208, 193 (2005).
A.C. Woodka, P.D. Butler, L. Porcar, B. Farago, M. Nagao, Phys. Rev. E 80, 031606 (2009).
H. Seto, N.L. Yamada, M. Nagao, M. Hishida, T. Takeda, Eur. Phys. J. E 26, 217 (2008).
R. Rodríguez-García, M. Mell, I. López-Montero, J. Netzel, T. Hellweg, F. Monroy, Soft Matter 7, 1532 (2011).
R. Rodríguez-García, M. Mell, I. López-Montero, F. Monroy, Europhys. Lett. 94, 28009 (2011).
H. Bermúdez et al., Macromolecules 35, 8203 (2002).
M. Nagao, S. Chawang, T. Hawa, Soft Matter 7, 6598 (2011).
M. Nagao, J. Chem. Phys. 135, 074704 (2011).
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Contribution to the Topical Issue “Neutron Biological Physics”, edited by Giovanna Fragneto and Frank Gabel.
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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
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DOI: https://doi.org/10.1140/epje/i2013-13075-2