Abstract

We use optical tweezers to trap a unilamellar phospholipid vesicle and measure the out-of-plane thermal fluctuations by using differential confocal microscopy. Bending moduli of the lipid membranes are calculated directly from the mean-square values of the fluctuation amplitudes. Owing to the refractive index contrast between the inner and outer solutions of the vesicle, optical tweezers trap the vesicle laterally and improve the reliability of the measured fluctuation amplitudes along the optical axis. Bending moduli of membranes in gel or fluid phases obtained by the combination of differential confocal microscopy and optical tweezers are close to those reported previously. We also obtain the bending modulus of sphingomyelin membranes in the gel phase, which was not reported previously.

© 2011 Optical Society of America

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  1. R. Dimova, S. Aranda, N. Bezlyepkina, V. Nikolov, K. A. Riske, and R. Lipowsky, “Practical guide to giant vesicles. Probing the membrane nanoregime via optical microscopy,” J. Phys. Condens. Matter 18, S1151–S1176 (2006).
    [CrossRef] [PubMed]
  2. G. Tresset and S. Takeuchi, “Utilization of cell-sized lipid containers for nanostructure and macromolecule handling in microfabricated devices,” Anal. Chem. 77, 2795–2801(2005).
    [CrossRef] [PubMed]
  3. A. P. Liu, D. L. Richmond, L. Maibaum, S. Pronk, P. L. Geissler, and D. A. Fletcher, “Membrane-induced bundling of actin filaments,” Nat. Phys. 4, 789–793 (2008).
    [CrossRef]
  4. C. B. Fox, R. A. Horton, and J. M. Harris, “Detection of drug-membrane interactions in individual phospholipid vesicles by confocal Raman microscopy,” Anal. Chem. 78, 4918–4924(2006).
    [CrossRef] [PubMed]
  5. R. Lipowsky, “Budding of membranes induced by intramembrane domains,” J. Phys. II 2, 1825–1840 (1992).
    [CrossRef]
  6. E. Evans and W. Rawicz, “Entropy-driven tension and bending elasticity in condensed-fluid membranes,” Phys. Rev. Lett. 64, 2094–2097 (1990).
    [CrossRef] [PubMed]
  7. H. P. Duwe, J. Kaes, and E. Sackmann, “Bending elastic moduli of lipid bilayers-modulation by solutes,” J. Phys. 51, 945–962 (1990).
    [CrossRef]
  8. M. D. Mitov, J. F. Faucon, P. Meleard, and P. Bothorel, “Thermal fluctuations of membranes,” in Advances in Supramolecular Chemistry, G.W.Gokel, ed. (JAI Press, 1992), Vol.  2, pp. 93–139.
  9. P. M. Chaikin and T. C. Lubensky, Principles of Condensed Matter Physics (Cambridge University, 1995), Section 10.4.
  10. C.-H. Lee and J. Wang, “Noninterferometric differential confocal microscopy with 2 nm depth resolution,” Opt. Commun. 135, 233–237 (1997).
    [CrossRef]
  11. T. Heimburg, “Mechanical aspects of membrane thermodynamics. Estimation of the mechanical properties of lipid membranes close to the chain melting transition from calorimetry,” Biochim. Biophys. Acta 1415, 147–162 (1998).
    [CrossRef] [PubMed]
  12. M. I. Angelova, S. Soleau, P. Meleard, J. F. Faucon, and P. Bothorel, “Preparation of giant vesicles by external AC electric fields: kinetics and applications,” Prog. Colloid Polym. Sci. 89, 127–131 (1992).
    [CrossRef]
  13. C.-H. Lee, Y.-F. Chang, C.-H. Tsai, and P.-H. Wang, “Optical measurement of the deformation of giant lipid vesicles driven by a micropipet electrode,” Langmuir 21, 7186–7190 (2005).
    [CrossRef] [PubMed]
  14. A. Ashkin, “Forces of a single-beam gradient laser trap on a dielectric sphere in the ray optics regime,” Biophys. J. 61, 569–582 (1992).
    [CrossRef] [PubMed]
  15. J. Henriksen, A. C. Rowat, and J. H. Ipsen, “Vesicle fluctuation analysis of the effects of sterols on membrane bending rigidity,” Eur. Biophys. J. 33, 732–741 (2004).
    [CrossRef] [PubMed]
  16. C.-H. Lee, W.-C. Lin, and J. Wang, “All-optical measurements of the bending rigidity of lipid-vesicle membranes across structural phase transitions,” Phys. Rev. E 64, 020901 (2001).
    [CrossRef]

2008

A. P. Liu, D. L. Richmond, L. Maibaum, S. Pronk, P. L. Geissler, and D. A. Fletcher, “Membrane-induced bundling of actin filaments,” Nat. Phys. 4, 789–793 (2008).
[CrossRef]

2006

C. B. Fox, R. A. Horton, and J. M. Harris, “Detection of drug-membrane interactions in individual phospholipid vesicles by confocal Raman microscopy,” Anal. Chem. 78, 4918–4924(2006).
[CrossRef] [PubMed]

R. Dimova, S. Aranda, N. Bezlyepkina, V. Nikolov, K. A. Riske, and R. Lipowsky, “Practical guide to giant vesicles. Probing the membrane nanoregime via optical microscopy,” J. Phys. Condens. Matter 18, S1151–S1176 (2006).
[CrossRef] [PubMed]

2005

G. Tresset and S. Takeuchi, “Utilization of cell-sized lipid containers for nanostructure and macromolecule handling in microfabricated devices,” Anal. Chem. 77, 2795–2801(2005).
[CrossRef] [PubMed]

C.-H. Lee, Y.-F. Chang, C.-H. Tsai, and P.-H. Wang, “Optical measurement of the deformation of giant lipid vesicles driven by a micropipet electrode,” Langmuir 21, 7186–7190 (2005).
[CrossRef] [PubMed]

2004

J. Henriksen, A. C. Rowat, and J. H. Ipsen, “Vesicle fluctuation analysis of the effects of sterols on membrane bending rigidity,” Eur. Biophys. J. 33, 732–741 (2004).
[CrossRef] [PubMed]

2001

C.-H. Lee, W.-C. Lin, and J. Wang, “All-optical measurements of the bending rigidity of lipid-vesicle membranes across structural phase transitions,” Phys. Rev. E 64, 020901 (2001).
[CrossRef]

1998

T. Heimburg, “Mechanical aspects of membrane thermodynamics. Estimation of the mechanical properties of lipid membranes close to the chain melting transition from calorimetry,” Biochim. Biophys. Acta 1415, 147–162 (1998).
[CrossRef] [PubMed]

1997

C.-H. Lee and J. Wang, “Noninterferometric differential confocal microscopy with 2 nm depth resolution,” Opt. Commun. 135, 233–237 (1997).
[CrossRef]

1992

A. Ashkin, “Forces of a single-beam gradient laser trap on a dielectric sphere in the ray optics regime,” Biophys. J. 61, 569–582 (1992).
[CrossRef] [PubMed]

M. I. Angelova, S. Soleau, P. Meleard, J. F. Faucon, and P. Bothorel, “Preparation of giant vesicles by external AC electric fields: kinetics and applications,” Prog. Colloid Polym. Sci. 89, 127–131 (1992).
[CrossRef]

R. Lipowsky, “Budding of membranes induced by intramembrane domains,” J. Phys. II 2, 1825–1840 (1992).
[CrossRef]

1990

E. Evans and W. Rawicz, “Entropy-driven tension and bending elasticity in condensed-fluid membranes,” Phys. Rev. Lett. 64, 2094–2097 (1990).
[CrossRef] [PubMed]

H. P. Duwe, J. Kaes, and E. Sackmann, “Bending elastic moduli of lipid bilayers-modulation by solutes,” J. Phys. 51, 945–962 (1990).
[CrossRef]

Angelova, M. I.

M. I. Angelova, S. Soleau, P. Meleard, J. F. Faucon, and P. Bothorel, “Preparation of giant vesicles by external AC electric fields: kinetics and applications,” Prog. Colloid Polym. Sci. 89, 127–131 (1992).
[CrossRef]

Aranda, S.

R. Dimova, S. Aranda, N. Bezlyepkina, V. Nikolov, K. A. Riske, and R. Lipowsky, “Practical guide to giant vesicles. Probing the membrane nanoregime via optical microscopy,” J. Phys. Condens. Matter 18, S1151–S1176 (2006).
[CrossRef] [PubMed]

Ashkin, A.

A. Ashkin, “Forces of a single-beam gradient laser trap on a dielectric sphere in the ray optics regime,” Biophys. J. 61, 569–582 (1992).
[CrossRef] [PubMed]

Bezlyepkina, N.

R. Dimova, S. Aranda, N. Bezlyepkina, V. Nikolov, K. A. Riske, and R. Lipowsky, “Practical guide to giant vesicles. Probing the membrane nanoregime via optical microscopy,” J. Phys. Condens. Matter 18, S1151–S1176 (2006).
[CrossRef] [PubMed]

Bothorel, P.

M. I. Angelova, S. Soleau, P. Meleard, J. F. Faucon, and P. Bothorel, “Preparation of giant vesicles by external AC electric fields: kinetics and applications,” Prog. Colloid Polym. Sci. 89, 127–131 (1992).
[CrossRef]

M. D. Mitov, J. F. Faucon, P. Meleard, and P. Bothorel, “Thermal fluctuations of membranes,” in Advances in Supramolecular Chemistry, G.W.Gokel, ed. (JAI Press, 1992), Vol.  2, pp. 93–139.

Chaikin, P. M.

P. M. Chaikin and T. C. Lubensky, Principles of Condensed Matter Physics (Cambridge University, 1995), Section 10.4.

Chang, Y.-F.

C.-H. Lee, Y.-F. Chang, C.-H. Tsai, and P.-H. Wang, “Optical measurement of the deformation of giant lipid vesicles driven by a micropipet electrode,” Langmuir 21, 7186–7190 (2005).
[CrossRef] [PubMed]

Dimova, R.

R. Dimova, S. Aranda, N. Bezlyepkina, V. Nikolov, K. A. Riske, and R. Lipowsky, “Practical guide to giant vesicles. Probing the membrane nanoregime via optical microscopy,” J. Phys. Condens. Matter 18, S1151–S1176 (2006).
[CrossRef] [PubMed]

Duwe, H. P.

H. P. Duwe, J. Kaes, and E. Sackmann, “Bending elastic moduli of lipid bilayers-modulation by solutes,” J. Phys. 51, 945–962 (1990).
[CrossRef]

Evans, E.

E. Evans and W. Rawicz, “Entropy-driven tension and bending elasticity in condensed-fluid membranes,” Phys. Rev. Lett. 64, 2094–2097 (1990).
[CrossRef] [PubMed]

Faucon, J. F.

M. I. Angelova, S. Soleau, P. Meleard, J. F. Faucon, and P. Bothorel, “Preparation of giant vesicles by external AC electric fields: kinetics and applications,” Prog. Colloid Polym. Sci. 89, 127–131 (1992).
[CrossRef]

M. D. Mitov, J. F. Faucon, P. Meleard, and P. Bothorel, “Thermal fluctuations of membranes,” in Advances in Supramolecular Chemistry, G.W.Gokel, ed. (JAI Press, 1992), Vol.  2, pp. 93–139.

Fletcher, D. A.

A. P. Liu, D. L. Richmond, L. Maibaum, S. Pronk, P. L. Geissler, and D. A. Fletcher, “Membrane-induced bundling of actin filaments,” Nat. Phys. 4, 789–793 (2008).
[CrossRef]

Fox, C. B.

C. B. Fox, R. A. Horton, and J. M. Harris, “Detection of drug-membrane interactions in individual phospholipid vesicles by confocal Raman microscopy,” Anal. Chem. 78, 4918–4924(2006).
[CrossRef] [PubMed]

Geissler, P. L.

A. P. Liu, D. L. Richmond, L. Maibaum, S. Pronk, P. L. Geissler, and D. A. Fletcher, “Membrane-induced bundling of actin filaments,” Nat. Phys. 4, 789–793 (2008).
[CrossRef]

Harris, J. M.

C. B. Fox, R. A. Horton, and J. M. Harris, “Detection of drug-membrane interactions in individual phospholipid vesicles by confocal Raman microscopy,” Anal. Chem. 78, 4918–4924(2006).
[CrossRef] [PubMed]

Heimburg, T.

T. Heimburg, “Mechanical aspects of membrane thermodynamics. Estimation of the mechanical properties of lipid membranes close to the chain melting transition from calorimetry,” Biochim. Biophys. Acta 1415, 147–162 (1998).
[CrossRef] [PubMed]

Henriksen, J.

J. Henriksen, A. C. Rowat, and J. H. Ipsen, “Vesicle fluctuation analysis of the effects of sterols on membrane bending rigidity,” Eur. Biophys. J. 33, 732–741 (2004).
[CrossRef] [PubMed]

Horton, R. A.

C. B. Fox, R. A. Horton, and J. M. Harris, “Detection of drug-membrane interactions in individual phospholipid vesicles by confocal Raman microscopy,” Anal. Chem. 78, 4918–4924(2006).
[CrossRef] [PubMed]

Ipsen, J. H.

J. Henriksen, A. C. Rowat, and J. H. Ipsen, “Vesicle fluctuation analysis of the effects of sterols on membrane bending rigidity,” Eur. Biophys. J. 33, 732–741 (2004).
[CrossRef] [PubMed]

Kaes, J.

H. P. Duwe, J. Kaes, and E. Sackmann, “Bending elastic moduli of lipid bilayers-modulation by solutes,” J. Phys. 51, 945–962 (1990).
[CrossRef]

Lee, C.-H.

C.-H. Lee, Y.-F. Chang, C.-H. Tsai, and P.-H. Wang, “Optical measurement of the deformation of giant lipid vesicles driven by a micropipet electrode,” Langmuir 21, 7186–7190 (2005).
[CrossRef] [PubMed]

C.-H. Lee, W.-C. Lin, and J. Wang, “All-optical measurements of the bending rigidity of lipid-vesicle membranes across structural phase transitions,” Phys. Rev. E 64, 020901 (2001).
[CrossRef]

C.-H. Lee and J. Wang, “Noninterferometric differential confocal microscopy with 2 nm depth resolution,” Opt. Commun. 135, 233–237 (1997).
[CrossRef]

Lin, W.-C.

C.-H. Lee, W.-C. Lin, and J. Wang, “All-optical measurements of the bending rigidity of lipid-vesicle membranes across structural phase transitions,” Phys. Rev. E 64, 020901 (2001).
[CrossRef]

Lipowsky, R.

R. Dimova, S. Aranda, N. Bezlyepkina, V. Nikolov, K. A. Riske, and R. Lipowsky, “Practical guide to giant vesicles. Probing the membrane nanoregime via optical microscopy,” J. Phys. Condens. Matter 18, S1151–S1176 (2006).
[CrossRef] [PubMed]

R. Lipowsky, “Budding of membranes induced by intramembrane domains,” J. Phys. II 2, 1825–1840 (1992).
[CrossRef]

Liu, A. P.

A. P. Liu, D. L. Richmond, L. Maibaum, S. Pronk, P. L. Geissler, and D. A. Fletcher, “Membrane-induced bundling of actin filaments,” Nat. Phys. 4, 789–793 (2008).
[CrossRef]

Lubensky, T. C.

P. M. Chaikin and T. C. Lubensky, Principles of Condensed Matter Physics (Cambridge University, 1995), Section 10.4.

Maibaum, L.

A. P. Liu, D. L. Richmond, L. Maibaum, S. Pronk, P. L. Geissler, and D. A. Fletcher, “Membrane-induced bundling of actin filaments,” Nat. Phys. 4, 789–793 (2008).
[CrossRef]

Meleard, P.

M. I. Angelova, S. Soleau, P. Meleard, J. F. Faucon, and P. Bothorel, “Preparation of giant vesicles by external AC electric fields: kinetics and applications,” Prog. Colloid Polym. Sci. 89, 127–131 (1992).
[CrossRef]

M. D. Mitov, J. F. Faucon, P. Meleard, and P. Bothorel, “Thermal fluctuations of membranes,” in Advances in Supramolecular Chemistry, G.W.Gokel, ed. (JAI Press, 1992), Vol.  2, pp. 93–139.

Mitov, M. D.

M. D. Mitov, J. F. Faucon, P. Meleard, and P. Bothorel, “Thermal fluctuations of membranes,” in Advances in Supramolecular Chemistry, G.W.Gokel, ed. (JAI Press, 1992), Vol.  2, pp. 93–139.

Nikolov, V.

R. Dimova, S. Aranda, N. Bezlyepkina, V. Nikolov, K. A. Riske, and R. Lipowsky, “Practical guide to giant vesicles. Probing the membrane nanoregime via optical microscopy,” J. Phys. Condens. Matter 18, S1151–S1176 (2006).
[CrossRef] [PubMed]

Pronk, S.

A. P. Liu, D. L. Richmond, L. Maibaum, S. Pronk, P. L. Geissler, and D. A. Fletcher, “Membrane-induced bundling of actin filaments,” Nat. Phys. 4, 789–793 (2008).
[CrossRef]

Rawicz, W.

E. Evans and W. Rawicz, “Entropy-driven tension and bending elasticity in condensed-fluid membranes,” Phys. Rev. Lett. 64, 2094–2097 (1990).
[CrossRef] [PubMed]

Richmond, D. L.

A. P. Liu, D. L. Richmond, L. Maibaum, S. Pronk, P. L. Geissler, and D. A. Fletcher, “Membrane-induced bundling of actin filaments,” Nat. Phys. 4, 789–793 (2008).
[CrossRef]

Riske, K. A.

R. Dimova, S. Aranda, N. Bezlyepkina, V. Nikolov, K. A. Riske, and R. Lipowsky, “Practical guide to giant vesicles. Probing the membrane nanoregime via optical microscopy,” J. Phys. Condens. Matter 18, S1151–S1176 (2006).
[CrossRef] [PubMed]

Rowat, A. C.

J. Henriksen, A. C. Rowat, and J. H. Ipsen, “Vesicle fluctuation analysis of the effects of sterols on membrane bending rigidity,” Eur. Biophys. J. 33, 732–741 (2004).
[CrossRef] [PubMed]

Sackmann, E.

H. P. Duwe, J. Kaes, and E. Sackmann, “Bending elastic moduli of lipid bilayers-modulation by solutes,” J. Phys. 51, 945–962 (1990).
[CrossRef]

Soleau, S.

M. I. Angelova, S. Soleau, P. Meleard, J. F. Faucon, and P. Bothorel, “Preparation of giant vesicles by external AC electric fields: kinetics and applications,” Prog. Colloid Polym. Sci. 89, 127–131 (1992).
[CrossRef]

Takeuchi, S.

G. Tresset and S. Takeuchi, “Utilization of cell-sized lipid containers for nanostructure and macromolecule handling in microfabricated devices,” Anal. Chem. 77, 2795–2801(2005).
[CrossRef] [PubMed]

Tresset, G.

G. Tresset and S. Takeuchi, “Utilization of cell-sized lipid containers for nanostructure and macromolecule handling in microfabricated devices,” Anal. Chem. 77, 2795–2801(2005).
[CrossRef] [PubMed]

Tsai, C.-H.

C.-H. Lee, Y.-F. Chang, C.-H. Tsai, and P.-H. Wang, “Optical measurement of the deformation of giant lipid vesicles driven by a micropipet electrode,” Langmuir 21, 7186–7190 (2005).
[CrossRef] [PubMed]

Wang, J.

C.-H. Lee, W.-C. Lin, and J. Wang, “All-optical measurements of the bending rigidity of lipid-vesicle membranes across structural phase transitions,” Phys. Rev. E 64, 020901 (2001).
[CrossRef]

C.-H. Lee and J. Wang, “Noninterferometric differential confocal microscopy with 2 nm depth resolution,” Opt. Commun. 135, 233–237 (1997).
[CrossRef]

Wang, P.-H.

C.-H. Lee, Y.-F. Chang, C.-H. Tsai, and P.-H. Wang, “Optical measurement of the deformation of giant lipid vesicles driven by a micropipet electrode,” Langmuir 21, 7186–7190 (2005).
[CrossRef] [PubMed]

Anal. Chem.

G. Tresset and S. Takeuchi, “Utilization of cell-sized lipid containers for nanostructure and macromolecule handling in microfabricated devices,” Anal. Chem. 77, 2795–2801(2005).
[CrossRef] [PubMed]

C. B. Fox, R. A. Horton, and J. M. Harris, “Detection of drug-membrane interactions in individual phospholipid vesicles by confocal Raman microscopy,” Anal. Chem. 78, 4918–4924(2006).
[CrossRef] [PubMed]

Biochim. Biophys. Acta

T. Heimburg, “Mechanical aspects of membrane thermodynamics. Estimation of the mechanical properties of lipid membranes close to the chain melting transition from calorimetry,” Biochim. Biophys. Acta 1415, 147–162 (1998).
[CrossRef] [PubMed]

Biophys. J.

A. Ashkin, “Forces of a single-beam gradient laser trap on a dielectric sphere in the ray optics regime,” Biophys. J. 61, 569–582 (1992).
[CrossRef] [PubMed]

Eur. Biophys. J.

J. Henriksen, A. C. Rowat, and J. H. Ipsen, “Vesicle fluctuation analysis of the effects of sterols on membrane bending rigidity,” Eur. Biophys. J. 33, 732–741 (2004).
[CrossRef] [PubMed]

J. Phys.

H. P. Duwe, J. Kaes, and E. Sackmann, “Bending elastic moduli of lipid bilayers-modulation by solutes,” J. Phys. 51, 945–962 (1990).
[CrossRef]

J. Phys. Condens. Matter

R. Dimova, S. Aranda, N. Bezlyepkina, V. Nikolov, K. A. Riske, and R. Lipowsky, “Practical guide to giant vesicles. Probing the membrane nanoregime via optical microscopy,” J. Phys. Condens. Matter 18, S1151–S1176 (2006).
[CrossRef] [PubMed]

J. Phys. II

R. Lipowsky, “Budding of membranes induced by intramembrane domains,” J. Phys. II 2, 1825–1840 (1992).
[CrossRef]

Langmuir

C.-H. Lee, Y.-F. Chang, C.-H. Tsai, and P.-H. Wang, “Optical measurement of the deformation of giant lipid vesicles driven by a micropipet electrode,” Langmuir 21, 7186–7190 (2005).
[CrossRef] [PubMed]

Nat. Phys.

A. P. Liu, D. L. Richmond, L. Maibaum, S. Pronk, P. L. Geissler, and D. A. Fletcher, “Membrane-induced bundling of actin filaments,” Nat. Phys. 4, 789–793 (2008).
[CrossRef]

Opt. Commun.

C.-H. Lee and J. Wang, “Noninterferometric differential confocal microscopy with 2 nm depth resolution,” Opt. Commun. 135, 233–237 (1997).
[CrossRef]

Phys. Rev. E

C.-H. Lee, W.-C. Lin, and J. Wang, “All-optical measurements of the bending rigidity of lipid-vesicle membranes across structural phase transitions,” Phys. Rev. E 64, 020901 (2001).
[CrossRef]

Phys. Rev. Lett.

E. Evans and W. Rawicz, “Entropy-driven tension and bending elasticity in condensed-fluid membranes,” Phys. Rev. Lett. 64, 2094–2097 (1990).
[CrossRef] [PubMed]

Prog. Colloid Polym. Sci.

M. I. Angelova, S. Soleau, P. Meleard, J. F. Faucon, and P. Bothorel, “Preparation of giant vesicles by external AC electric fields: kinetics and applications,” Prog. Colloid Polym. Sci. 89, 127–131 (1992).
[CrossRef]

Other

M. D. Mitov, J. F. Faucon, P. Meleard, and P. Bothorel, “Thermal fluctuations of membranes,” in Advances in Supramolecular Chemistry, G.W.Gokel, ed. (JAI Press, 1992), Vol.  2, pp. 93–139.

P. M. Chaikin and T. C. Lubensky, Principles of Condensed Matter Physics (Cambridge University, 1995), Section 10.4.

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Figures (5)

Fig. 1
Fig. 1

(a) Setup of the whole tweezers–DCM measurement system: MO, microscope objective; PBS, polarization beam splitter; IS, intensity stabilizer; QWP, quarter-wave plate; PD, photodiode; FO, fiber-optic light source; DM, dichromatic mirror; M, mirror; F, interference filters; L, lens. (b) Linear response of the DCM signal to the axial displacement of a reflection mirror. The standard deviation of the data points to the fitting straight line is 0.2%, corresponding to an axial positioning accuracy of 8 nm .

Fig. 2
Fig. 2

Center of a DOPC ULV with a 8.7 μm radius. (a) Tweezers off. (b) Tweezing power = 1.3 mW . (c) Tweezing power = 3.2 mW . The period of record is 60 s .

Fig. 3
Fig. 3

Thermal fluctuations of vesicles at 27 ° C measured by DCM. The radii of sphingomyelin, DPPC, and DOPC vesicle are 4.9 μm , 4.4 μm , and 4.9 μm , respectively.

Fig. 4
Fig. 4

Relations between the mean-square amplitudes of thermal fluctuations and the radius of the vesicles. The fitting curves are quadratic. The measurement on every vesicle was repeated seven times, and the error bars show the standard deviations.

Fig. 5
Fig. 5

Bending moduli of vesicles of various radii. Please note that the range of the bending modulus of DOPC is much smaller than those of sphingomyelin and DPPC.

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κ k B T R 2 2 π a 2 ,

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