

Confinement of lipid membranes
Relevant publications
 Flexoelectric fluid membrane vesicles in spherical confinement
Niloufar Abtahi, Lila Bouzar, Nadia SaidiAmroun, Martin Michael MüllerThe morphology of spherically confined flexoelectric fluid membrane vesicles in an ex
ternal uniform electric field is studied numerically. Due to the deformations induced by
the confinement, the membrane becomes polarized resulting in an interaction with the
external field. The equilibrium shapes of the vesicle without electric field can be clas
sified in a geometrical phase diagram as a function of scaled area and reduced volume
[1, 2]. When the area of the membrane is only slightly larger than the area of the con
fining sphere, a single axisymmetric invagination appears. A nonvanishing electric field
induces an additional elongation of the confined vesicle which is either perpendicular or
parallel depending on the sign of the electric field parameter. Higher values of the surface
area or the electric field parameter can reduce the symmetry of the system leading to
more complex folding. We present the resulting shapes and show that transition lines
are shifted in the presence of an electric field. The obtained folding patterns could be of
interest for biophysical and technological applications alike.
EPL, 131(1): 18001, 2020. See also arXiv:2006.04475.
 Confining a fluid membrane vesicle of toroidal topology in an adhesive hard sphere
Lila Bouzar, Ferhat Menas, Martin Michael MüllerWe discuss how the equilibrium shapes of a confined toroidal fluid membrane vesicle
change when an adhesion between membrane and confining sphere is taken into account. The case without adhesion
was studied in Ref. [1]. Different types of solution were found and assembled in a phase diagram as a function of area
and reduced volume of the membrane. Depending on the degree of confinement the vesicle is either free, in contact along
a circle (contactcircle solutions) or on a surface (contactarea solutions). All solutions without adhesion are updown symmetric.
When the container is adhesive, the phase diagram is altered and new kinds of solution without updown symmetry are found.
For increasing values of adhesion the region of contactcircle solutions shrinks until it vanishes completely from the phase diagram.
IOP Conf. Series: MSE, 186: 012021, 2017.
 Toroidal membrane vesicles in spherical confinement
Lila Bouzar, Ferhat Menas, Martin Michael MüllerWe investigate the morphology of a toroidal fluid membrane vesicle confined inside a spherical container.
The equilibrium shapes are assembled in a geometrical phase diagram as a function of scaled area and
reduced volume of the membrane. For small area the vesicle can adopt its free form. When increasing
the area, the membrane cannot avoid contact and touches the confining sphere along a circular contact line,
which extends to a zone of contact for higher area. The elastic energies of the equilibrium shapes are
compared to those of their confined counterparts of spherical topology to predict under which conditions a
topology change is favored energetically.
Phys. Rev. E, 92: 032721, 2015. See also arXiv:1509.00765.
 Fluid membrane vesicles in confinement
Osman Kahraman, Norbert Stoop, Martin Michael MüllerWe numerically study the morphology of fluid membrane vesicles with prescribed volume and surface area in confinement.
For spherical confinement we observe axisymmetric invaginations that transform into ellipsoidal invaginations a the area of the
vesicle is increased, followed by a transition into stomatocytelike shapes.
We provide a detailed analysis of the axisymmetric shapes and investigate the effect of the spontaneous curvature of the membrane
as a possible mechanism for shape regulation. We show that the observed morphologies are stable under small geometric deformations
of the confinement. The results could help to understand the role of mechanics in the complex folding patterns of biological membranes.
New J. Phys., 14: 095021, 2012.
 Morphogenesis of membrane invaginations in spherical confinement
Osman Kahraman, Norbert Stoop, Martin Michael MüllerWe study the morphology of a fluid membrane in spherical confinement. When the
area of the membrane is slightly larger than the area of the outer container, a single axisymmetric
invagination is observed. For higher area, selfcontact occurs: the invagination breaks symmetry
and deforms into an ellipsoidlike shape connected to its outer part via a small slit. For even
higher areas, a second invagination forms inside the original invagination. The folding patterns observed
could constitute basic building blocks in the morphogenesis of biological tissues and organelles.
Europhys. Lett., 97(6): 68008, 2012. See also arXiv:1201.2518.




