Skip to main content
SpringerLink
Log in

The Constitutive Equation for Membrane Tether Extraction

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

Abstract

Membrane tethers or nanotubes play a critical role in a variety of cellular and subcellular processes such as leukocyte rolling and intercellular mass transport. The current constitutive equations that describe the relationship between the pulling force and the tether velocity during tether extraction have serious limitations. In this article, we propose a new phenomenological constitutive equation that captures all known characteristics of nanotube formation, including nonlinearity, nonzero threshold force, and possible negative tether velocity. We used tether extraction from endothelial cells as a prototype to illustrate how to obtain the material constants in the constitutive equation. With the micropipette aspiration technique, we measured tether pulling forces at both positive and negative tether velocities. We also determined the threshold force of 55 pN experimentally for the first time. This new constitutive equation unites two established ones and provides us a unified platform to better understand not only the physiological role of tether extraction during leukocyte rolling and intercellular or intracellular transport, but also the physics of membrane tether growth or retraction.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Figure 1
Figure 2
Figure 3
Figure 4
Figure 5
Figure 6

Similar content being viewed by others

References

  1. Brochard-Wyart, F., N. Borghi, D. Cuvelier, and P. Nassoy. Hydrodynamic narrowing of tubes extruded from cells. Proc. Nat. Acad. Sci. U.S.A. 103:7660–7663, 2006.

    Article  CAS  Google Scholar 

  2. Chen, Y., G. Girdhar, and J. Y. Shao. Single membrane tether extraction from adult and neonatal dermal microvascular endothelial cells. Am. J. Physiol. Cell Physiol. 292:C1272–C1279, 2007.

    Article  CAS  PubMed  Google Scholar 

  3. Chen, Y., B. Liu, G. Xu, and J.-Y. Shao. Validation, in-depth analysis, and modification of the micropipette aspiration technique. Cell. Mol. Bioeng. 2:351–365, 2009.

    Article  PubMed  Google Scholar 

  4. Dai, J., and M. P. Sheetz. Mechanical properties of neuronal growth cone membrane studied by tether formation with laser optical tweezers. Biophys. J. 68:988–996, 1995.

    Article  CAS  PubMed  Google Scholar 

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

    Article  CAS  Google Scholar 

  6. Gelles, J., B. J. Schnapp, and M. P. Sheetz. Tracking kinesin-driven movements with nanometer-scale precision. Nature 331:450–453, 1988.

    Article  CAS  PubMed  Google Scholar 

  7. Girdhar, G., and J. Y. Shao. Membrane tether extraction from human umbilical vein endothelial cells and its implication in leukocyte rolling. Biophys. J. 87:3561–3568, 2004.

    Article  CAS  PubMed  Google Scholar 

  8. Girdhar, G., and J. Y. Shao. Simultaneous tether extraction from endothelial cells and leukocytes: observation, mechanics and significance. Biophys. J. 93:4041–4052, 2007.

    Article  CAS  PubMed  Google Scholar 

  9. Girdhar, G., Y. Chen, and J. Y. Shao. Double tether extraction from human umbilical vein and dermal microvascular endothelial cells. Biophys. J. 92:1035–1045, 2007.

    Article  CAS  PubMed  Google Scholar 

  10. Heinrich, V., A. Leung, and E. Evans. Nano- to microscale dynamics of P-selectin detachment from leukocyte interfaces. II. Tether flow terminated by P-selectin dissociation from PSGL-1. Biophys. J. 88:2299–2308, 2005.

    Article  CAS  PubMed  Google Scholar 

  11. Hochmuth, R. M., J. Y. Shao, J. Dai, and M. P. Sheetz. Deformation and flow of membrane into tethers extracted from neuronal growth cones. Biophys. J. 70:358–369, 1996.

    Article  CAS  PubMed  Google Scholar 

  12. Hwang, W. C., and R. E. Waugh. Energy of dissociation of lipid bilayer from the membrane skeleton of red blood cells. Biophys. J. 72:2669–2678, 1997.

    Article  CAS  PubMed  Google Scholar 

  13. Koster, G., M. VanDuijn, B. Hofs, and M. Dogterom. Membrane tube formation from giant vesicles by dynamic association of motor proteins. PNAS 100:15583–15588, 2003.

    Article  CAS  PubMed  Google Scholar 

  14. Leduc, C., O. Campas, K. B. Zeldovich, A. Roux, P. Jolimaitre, L. Bourel-Bonnet, B. Goud, J. F. Joanny, P. Bassereau, and J. Prost. From the cover: cooperative extraction of membrane nanotubes by molecular motors. PNAS 101:17096–17101, 2004.

    Article  CAS  PubMed  Google Scholar 

  15. Lee, C., and L. B. Chen. Dynamic behavior of endoplasmic reticulum in living cells. Cell 54:37–46, 1988.

    Article  CAS  PubMed  Google Scholar 

  16. Levin, J. D., H. P. Ting-Beall, and R. M. Hochmuth. Correlating the kinetics of cytokine-induced E-selectin adhesion and expression on endothelial cells. Biophys. J. 80:656–667, 2001.

    Article  CAS  PubMed  Google Scholar 

  17. Li, Z., B. Anvari, M. Takashima, P. Brecht, J. H. Torres, and W. E. Brownell. Membrane tether formation from outer hair cells with optical tweezers. Biophys. J. 82:1386–1395, 2002.

    Article  CAS  PubMed  Google Scholar 

  18. McCarty, O. J. T., S. A. Mousa, P. F. Bray, and K. Konstantopoulos. Immobilized platelets support human colon carcinoma cell tethering, rolling, and firm adhesion under dynamic flow conditions. Blood 96:1789–1797, 2000.

    CAS  PubMed  Google Scholar 

  19. Ramachandran, V., M. Williams, T. Yago, D. W. Schmidtke, and R. P. McEver. Dynamic alterations of membrane tethers stabilize leukocyte rolling on P-selectin. PNAS 101:13519–13524, 2004.

    Article  CAS  PubMed  Google Scholar 

  20. Rustom, A., R. Saffrich, I. Markovic, P. Walther, and H. H. Gerdes. Nanotubular highways for intercellular organelle transport. Science 303:1007–1010, 2004.

    Article  CAS  PubMed  Google Scholar 

  21. Schmidtke, D. W., and S. L. Diamond. Direct observation of membrane tethers formed during neutrophil attachment to platelets or P-selectin under physiological flow. J. Cell Biol. 149:719–729, 2000.

    Article  CAS  PubMed  Google Scholar 

  22. Shao, J. Y., and R. M. Hochmuth. Micropipette suction for measuring piconewton forces of adhesion and tether formation from neutrophil membranes. Biophys. J. 71:2892–2901, 1996.

    Article  CAS  PubMed  Google Scholar 

  23. Shao, J. Y., and R. M. Hochmuth. Mechanical anchoring strength of L-selectin, β2 integrins and CD45 to neutrophil cytoskeleton and membrane. Biophys. J. 77:587–596, 1999.

    Article  CAS  PubMed  Google Scholar 

  24. Shao, J. Y., and J. Xu. A modified micropipette aspiration technique and its application to tether formation from human neutrophils. J. Biomech. Eng. 124:388–396, 2002.

    Article  PubMed  Google Scholar 

  25. Shao, J. Y., H. P. Ting-Beall, and R. M. Hochmuth. Static and dynamic lengths of neutrophil microvilli. PNAS 95:6797–6802, 1998.

    Article  CAS  PubMed  Google Scholar 

  26. Sun, M., N. Northup, F. Marga, T. Huber, F. J. Byfield, I. Levitan, and G. Forgacs. The effect of cellular cholesterol on membrane-cytoskeleton adhesion. J. Cell Sci. 120:2223–2231, 2007.

    Article  CAS  PubMed  Google Scholar 

  27. White, J., L. Johannes, F. Mallard, A. Girod, S. Grill, S. Reinsch, P. Keller, B. Tzschaschel, A. Echard, B. Goud, and E. H. K. Stelzer. Rab6 coordinates a novel Golgi to ER retrograde transport pathway in live cells. J. Cell Biol. 147:743–760, 1999.

    Article  CAS  PubMed  Google Scholar 

  28. Xu, G. Mechanics of Single Microvilli and Double Tethers of Human Neutrophils and Lymphocytes. Saint Louis, MO: Washington University, 2006.

    Google Scholar 

  29. Xu, G., and J. Y. Shao. Double tether extraction from human neutrophils and its comparison with CD4+ T-lymphocytes. Biophys. J. 88:661–669, 2005.

    Article  CAS  PubMed  Google Scholar 

  30. Yago, T., A. Leppanen, H. Qiu, W. D. Marcus, M. U. Nollert, C. Zhu, R. D. Cummings, and R. P. McEver. Distinct molecular and cellular contributions to stabilizing selectin-mediated rolling under flow. J. Cell Biol. 158:787–799, 2002.

    Article  CAS  PubMed  Google Scholar 

Download references

Acknowledgments

This study was supported by the NIH (R01 HL069947 and R21/R33 RR017014).

Author information

Authors and Affiliations

  1. Department of Biomedical Engineering, Washington University, St. Louis, MO, 63130, USA

    Yong Chen, Da-Kang Yao & Jin-Yu Shao

Authors
  1. Yong Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Da-Kang Yao
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jin-Yu Shao
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jin-Yu Shao.

Additional information

Associate Editor Konstantinos Konstantopoulo oversaw the review of this article.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Chen, Y., Yao, DK. & Shao, JY. The Constitutive Equation for Membrane Tether Extraction. Ann Biomed Eng 38, 3756–3765 (2010). https://doi.org/10.1007/s10439-010-0117-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10439-010-0117-0

Keywords

Search

Navigation