Eliot Fried, Ph.D.
Department of Mechanical Engineering
E-mail: mechanicist@uw...

TITLE:

"Wrinkling of a Lipid Vesicle in an Electric Field"


ABSTRACT:

Important applications in which lipid bilayer vesicles are subject to electric fields abound in
medicine and biotechnology. Electro-gene-transfer is used to transport genetic material across
a cell membrane. Electro-chemotherapy and irreversible electro-poration are employed in the
removal of cancerous tissues. Many disciplines are involved in the understanding of such
complex systems. However, mechanical effects are essential when addressing poration,
deformation, and wrinkling.

Knorr, Staykova, Gracia and Dimova [1] subjected giant unilamellar vesicles composed of DPPC
molecules in the gel phase to electric fields and observed the formation of wrinkles. To model
this experiment, we consider the tensile stress state induced in a spherical vesicle by a
uniform electric field and use an approach first proposed by Cerda, Ravi-Chandar and Mahadevan
[2] in a study the wrinkling of flat thin films in tension: the net potential energy to be
minimized is augmented by a constraint on the length of a reference curve in the deformed
configuration, thus allowing the possibility of wavy solutions to be explored.

The number of wrinkles that form is governed by the ratio between the in-plane stretching
stiffness and the bending stiffness and ultimately turns out to be proportional to the square
root of the ratio between the vesicle radius and the vesicle thickness. This number is one
order of magnitude higher than what observed by Knorr et al. We provide estimates for the
wavelength and amplitude of wrinkles that are consistent with analogous previous work by Finken
and Seifert [3] and that, in the limit for vanishing curvature, reduce to scalings obtained by
Cerda and Mahadevan [2].

We advocate further theoretical and experimental investigation on this subject. A refinement of
the proposed model accounting for the vesicle deformation is currently being considered.

References

[1]   Knorr, R. L.; Staykova, M.; Graci?, R. S. and Dimova, R. 2010, "Wrinkling and
electroporation of giant vesicles in the gel phase", Soft Matter, vol. 6, no. 9, pp. 1990-1996.

[2]   Cerda, E.; Ravi-Chandar, K. and Mahadevan, L. 2002, "Thin films: Wrinkling of an elastic
sheet under tension", Nature, vol. 419, pp. 579-580.

[3]   Finken, R. and Seifert, U. 2006, "Wrinkling of microcapsules in shear flow", Journal of
Physics: Condensed Matter, vol. 18, no. 15, pp. 185-191.