Skip to main content
Log in

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

  • Published:
Annals of Biomedical Engineering Aims and scope Submit manuscript

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.

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.

Similar content being viewed by others

References

  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.

    CAS  Google Scholar 

  2. Ashkin, A., and J. M. Dziedzic. Optical trapping and manipulation of viruses and bacteria,Science 235:1517–1520, 1987.

    Article  PubMed  CAS  Google Scholar 

  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.

    PubMed  CAS  Google Scholar 

  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.

    PubMed  Google Scholar 

  5. Döbereiner, H.-G., E. Evans, U. Seifert, and M. Wortis. Spinodal fluctuations of budding vesicles,Phys. Rev. Lett. 75:3360–3363, 1995.

    Article  PubMed  Google Scholar 

  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.

    Article  PubMed  CAS  Google Scholar 

  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.

    Article  CAS  Google Scholar 

  8. Evans, E., and W. Rawicz. Entropy-driven tension and bending elasticity in condensed-fluid membranes,Phys. Rev. Lett. 64:2094–2097, 1990.

    Article  PubMed  CAS  Google Scholar 

  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.

    PubMed  CAS  Google Scholar 

  10. Evans, E. A., and R. Skalak. Mechanics and thermodynamics of biomembranes,CRC Crit. Rev. Bioeng. 3:181–418, 1979.

    PubMed  CAS  Google Scholar 

  11. Evans, E., and A. Yeung. Hidden dynamics in rapid changes of bilayer shape.Chem. Phys. Lipids 73:39–56, 1994.

    Article  CAS  Google Scholar 

  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. 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.

    Article  Google Scholar 

  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.

    PubMed  CAS  Google Scholar 

  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.

    PubMed  CAS  Google Scholar 

  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.

    Article  CAS  Google Scholar 

  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).

    Article  CAS  Google Scholar 

  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. Lipowsky, R. The conformation of membranes,Nature 349:475–481, 1991.

    Article  PubMed  CAS  Google Scholar 

  20. McIntosh, T. J., and S. A. Simon. Hydration force and bilayer deformation: A reevaluation,Biochemistry 25:4048–4066, 1986.

    Google Scholar 

  21. Needham, D., and R. S. Nunn. Elastic deformation and failure of lipid bilayer membranes containing cholesterol.Biophys. J. 58:997–1009, 1990.

    PubMed  CAS  Google Scholar 

  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.

    Article  CAS  Google Scholar 

  23. Reeves, J. P., and R. M. Dowben. Formation and properties of thin-walled phospholipid vesicles,J. Cell. Physiol. 73:49–60, 1969.

    Article  PubMed  CAS  Google Scholar 

  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. 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.

    Article  PubMed  CAS  Google Scholar 

  26. Schneider, M. B., J. T. Jenkins, and W. W. Webb. Thermal fluctuations of large cylindrical phospholipid vesicles.Biophys. J. 45:891–899, 1984.

    PubMed  CAS  Google Scholar 

  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.

    Article  PubMed  CAS  Google Scholar 

  28. Song, J. B., and R. E. Waugh. Bending rigidity of SOPC membranes containing cholesterol—brief communication.Biophys. J. 64:1967–1970, 1993.

    PubMed  CAS  Google Scholar 

  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. Waugh, R. E., and R. M. Hochmuth. Mechanical equilibrium of thick hollow liquid membrane cylinders,Biophys. J. 52:391–400, 1987.

    PubMed  CAS  Google Scholar 

  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.

    PubMed  CAS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Heinrich, V., Waugh, R.E. A piconewton force transducer and its application to measurement of the bending stiffness of phospholipid membranes. Ann Biomed Eng 24, 595–605 (1996). https://doi.org/10.1007/BF02684228

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02684228

Keywords

Navigation