Annals of Biomedical Engineering

, Volume 24, Issue 5, pp 595–605 | Cite as

A piconewton force transducer and its application to measurement of the bending stiffness of phospholipid membranes

  • Volkmar Heinrich
  • Richard E. Waugh
Article

Abstract

The bending stiffness of a phospholipid bilayer (kc) was measured by forming thin bilayer cylinders (tethers) from giant phospholipid vesicles. Based on the balance of forces, the tether force was expeeted to be proportional to the square root of the membrane tension, with a constant of proportionality containingk>c. The membrane tension was controlled via the aspiration pressure in a micropipette used to hold the vesicle. The force on the tether was generated by an electromagnet acting on a paramagnetic bead attached to the vesicle surface. The magnitude of the force was determined from measurements on the magnet current which was adjusted to maintain the position of the bead. Measurements were performed on vesicles composed of stearoyl-oleoyl-phosphatidylcholine plus 5% (by mole) biotinylated phosphatidylethanolamine to mediate adhesion to streptavidin-coated beads. From each vesicle, tethers were formed repeatedly at different values of the membrane tension. The expected relationship between membrane tension and tether force was observed. The mean value ofkc for 10 different vesicles was 1.17×10−19 J (SD=0.08×10−19 J). The precision of these data demonstrates the reliability of this approach, which avoids uncertainties of interpretation and measurement that may be associated with other methods for determiningkc.

Keywords

Magnetic particles Bilayer membrane Mechanics Micromanipulation Curvature elasticity 

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References

  1. 1.
    Angelova, M. I., S. Soléau, Ph. Méléard, 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.Google Scholar
  2. 2.
    Ashkin, A., and J. M. Dziedzic. Optical trapping and manipulation of viruses and bacteria,Science 235:1517–1520, 1987.PubMedCrossRefGoogle Scholar
  3. 3.
    Bo, L., and R. E. Waugh. Determination of bilayer membrane bending stiffness by tether formation from giatn, thin-walled vesicles,Biophys. J. 55:509–517, 1989.PubMedGoogle Scholar
  4. 4.
    Božič, B., S. Svetina, B. Žekš, and R. E. Waugh. The role of lamellar membrane structure in tether formation from bilayer vesicles,Biophys. J. 61:963–973, 1992.PubMedGoogle Scholar
  5. 5.
    Döbereiner, H.-G., E. Evans, U. Seifert, and M. Wortis. Spinodal fluctuations of budding vesicles,Phys. Rev. Lett. 75:3360–3363, 1995.PubMedCrossRefGoogle Scholar
  6. 6.
    Evans, E. A. Minimum energy analysis of membrane deformation applied to pipet aspiration and surface adhesion of red blood cell,Biophys. J. 30:265–284, 1980.PubMedCrossRefGoogle Scholar
  7. 7.
    Evans, E., and D. Needham. Physical properties of surfactant bilayer membranes: Thermal transitions, elasticity, rigidity, cohesion, and colloidal interactions,J. Phys. Chem. 91:4219–4228, 1987.CrossRefGoogle Scholar
  8. 8.
    Evans, E., and W. Rawicz. Entropy-driven tension and bending elasticity in condensed-fluid membranes,Phys. Rev. Lett. 64:2094–2097, 1990.PubMedCrossRefGoogle Scholar
  9. 9.
    Evans, E., K. Ritchie, and R. Merkel. Sensitive force technique to probe molecular adhesion and structural linkages at biological interfaces,Biophys. J. 68:2580–2587, 1995.PubMedGoogle Scholar
  10. 10.
    Evans, E. A., and R. Skalak. Mechanics and thermodynamics of biomembranes,CRC Crit. Rev. Bioeng. 3:181–418, 1979.PubMedGoogle Scholar
  11. 11.
    Evans, E., and A. Yeung. Hidden dynamics in rapid changes of bilayer shape.Chem. Phys. Lipids 73:39–56, 1994.CrossRefGoogle Scholar
  12. 12.
    Evans, E., A. Yeung, R. Waugh, and J. Song. Dynamic coupling and nonlocal curvature elasticity in bilayer membranes. In:The Structure and Conformation of Amphiphilic Membranes, edited by R. Lipowsky, D. Richter, and K. Kremer, Berlin, Heidelberg: Springer-Verlag, 1992, pp. 148–153.Google Scholar
  13. 13.
    Faucon, J. F., M. D. Mitov, P. Meleard, I. Bivas, and P. Bothorel. Bending elasticity and thermal fluctuations of lipid membranes. Theoretical and experimental requirements.J. Phys. France 50:2389–2414, 1989.CrossRefGoogle Scholar
  14. 14.
    Guilford, W. H., and R. W. Gore. A novel remote-sensing isometric force transducer for micromechanics studies.Am. j. Physiol. 263:C700-C707, 1992.PubMedGoogle Scholar
  15. 15.
    Guilford, W. H., R. C. Lantz, and R. W. Gore. Locomotive forces produced by single leukocytes in vivo and in vitro.Am. J. Physiol. 268:C1308-C1312, 1995.PubMedGoogle Scholar
  16. 16.
    Heinrich, V., M. Brumen, R. heinrich, S. Svetina, and B. Žekš. Nearly spherical vesicle shapes calculated by use of spherical harmonics: Axisymmetric and nonaxisymmetric shapes and their stability.J. Phys. France 2:1081–1108, 1992.CrossRefGoogle Scholar
  17. 17.
    Heinrich, V., S. Svetina, and B. Žekš. Nonaxisymmetric vesicle shapes in a generalized bilayer-couple model and the transition between oblate and prolate axisymmetric shapes.Phys. Rev. E 48:3112–3123, 1993).CrossRefGoogle Scholar
  18. 18.
    Helfrich, W. Tension-induced mutual adhesion and a conjectured superstructure of lipid membranes. In:Handbook of Biological Physics, Vol. 1. edited by R. Lipowsky, and E. Sackmann, Amsterdam, Elsevier Science B.V., 1995, pp. 691–721.Google Scholar
  19. 19.
    Lipowsky, R. The conformation of membranes,Nature 349:475–481, 1991.PubMedCrossRefGoogle Scholar
  20. 20.
    McIntosh, T. J., and S. A. Simon. Hydration force and bilayer deformation: A reevaluation,Biochemistry 25:4048–4066, 1986.Google Scholar
  21. 21.
    Needham, D., and R. S. Nunn. Elastic deformation and failure of lipid bilayer membranes containing cholesterol.Biophys. J. 58:997–1009, 1990.PubMedGoogle Scholar
  22. 22.
    Niggemann, G., M. Kummrow, and W. Helfrich. The bending rigidity of phosphatidylcholine bilayers: Dependences on experimental method, sample cell sealing and temperature,J. Phys. France 5:413–425, 1995.CrossRefGoogle Scholar
  23. 23.
    Reeves, J. P., and R. M. Dowben. Formation and properties of thin-walled phospholipid vesicles,J. Cell. Physiol. 73:49–60, 1969.PubMedCrossRefGoogle Scholar
  24. 24.
    Sackmann, E. Physical basis of self-organization and function of membranes: Physics of vesicles. In:Handbook of Biological Physics, Vol. 1. edited by R. Lipowsky and E. Sackmann. Amsterdam: Elsevier Science B.V., 1995, pp. 213–304.Google Scholar
  25. 25.
    Seifert, U., K. Berndl, and R. Lipowsky. Shape transformation of vesicles: Phase diagram for spontaneous-curvature and bilayer-coupling models,Phys. Rev. A 44: 1182–1202, 1991.PubMedCrossRefGoogle Scholar
  26. 26.
    Schneider, M. B., J. T. Jenkins, and W. W. Webb. Thermal fluctuations of large cylindrical phospholipid vesicles.Biophys. J. 45:891–899, 1984.PubMedGoogle Scholar
  27. 27.
    Servuss, R. M., W. Harbich, and W. Helfrich. Measurement of the curvature-elastic modulus of egg lecithin bilayers.Biochim. Biophys. Acta 436:900–903, 1976.PubMedCrossRefGoogle Scholar
  28. 28.
    Song, J. B., and R. E. Waugh. Bending rigidity of SOPC membranes containing cholesterol—brief communication.Biophys. J. 64:1967–1970, 1993.PubMedGoogle Scholar
  29. 29.
    Svetina, S., and B. Žekš. Elastic properties of closed bilayer membranes and the shapes of giant phospholipid vesicles. In:Handbook of Nonmedical Applications of Liposomes, Vol. 1, edited by D. D. Lasic, and Y. Barenholz. Boca Raton, New York, London, Tokyo: CRC Press, 1996, pp. 13–42.Google Scholar
  30. 30.
    Waugh, R. E., and R. M. Hochmuth. Mechanical equilibrium of thick hollow liquid membrane cylinders,Biophys. J. 52:391–400, 1987.PubMedGoogle Scholar
  31. 31.
    Waugh, R. E., J. Song, S. Svetina, and B. Žekš. Monolayer coupling and curvature elasticity in bilayer membranes by tether formation from lecithin vesicles.Biophys. J. 61: 974–982, 1992.PubMedGoogle Scholar

Copyright information

© Biomedical Engineering Society 1996

Authors and Affiliations

  • Volkmar Heinrich
    • 1
  • Richard E. Waugh
    • 1
  1. 1.Department of BiophysicsUniversity of Rochester School of Medicine and DentistryRochesterNY

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