Membrane shape as a reporter for applied forces

doi:10.1073/pnas.0806814105

Membrane shape as a reporter for applied forces

^aDepartments of Applied Physics, Biochemistry and Molecular Biophysics, and Mechanical Engineering, California Institute of Technology, 1200 East California Boulevard, Pasadena, CA 91125;
^bDepartment of Mechanical and Aerospace Engineering and Program in Biomedical Engineering, University of California, Los Angeles, CA 90095; and
^cWhitehead Institute for Biomedical Research, 9 Cambridge Center, Cambridge, MA 02142

Edited by L. B. Freund, Brown University, Providence, RI, and approved October 22, 2008 (received for review July 15, 2008)

Abstract

Recent advances have enabled 3-dimensional reconstructions of biological structures in vivo, ranging in size and complexity from single proteins to multicellular structures. In particular, tomography and confocal microscopy have been exploited to capture detailed 3-dimensional conformations of membranes in cellular processes ranging from viral budding and organelle maintenance to phagocytosis. Despite the wealth of membrane structures available, there is as yet no generic, quantitative method for their interpretation. We propose that by modeling these observed biomembrane shapes as fluid lipid bilayers in mechanical equilibrium, the externally applied forces as well as the pressure, tension, and spontaneous curvature can be computed directly from the shape alone. To illustrate the potential power of this technique, we apply an axial force with optical tweezers to vesicles and explicitly demonstrate that the applied force is equal to the force computed from the membrane conformation.

Footnotes

¹To whom correspondence should be addressed. E-mail: wiggins{at}wi.mit.edu
Author contributions: H.J.L., E.L.P., R.P., and P.A.W. designed research; H.J.L., E.L.P., and P.A.W. performed research; H.J.L., E.L.P., W.S.K., and P.A.W. analyzed data; and H.J.L., E.L.P., R.P., W.S.K., and P.A.W. wrote the paper.
The authors declare no conflict of interest.
This article contains supporting information online at www.pnas.org/cgi/content/full/0806814105/DCSupplemental.
↵* We demonstrated the representation independence by making independent tracings of each dataset, which resulted in nearly identical measurements of physically observable quantities. For more information see the SI Appendix.