Geometry in Nature


Confinement of lipid membranes


Relevant publications

  • Toroidal membrane vesicles in spherical confinement
    Lila Bouzar, Ferhat Menas, Martin Michael Müller

    We 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 Müller

    We 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 stomatocyte-like 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 Müller

    We 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, self-contact occurs: the invagination breaks symmetry and deforms into an ellipsoid-like 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.







     © Martin Michael Müller