Publications
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Articles in scientific journals
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Books
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Theses
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1. Articles in scientific journals
![](grafiken/33flexoelectric_icon.png) | Flexoelectric fluid membrane vesicles in spherical confinement
Niloufar Abtahi, Lila Bouzar, Nadia Saidi-Amroun, Martin Michael Müller | EPL, 131(1): 18001, 2020. See also arXiv:2006.04475.
![](grafiken/32tangentdev_icon.png) | Isometric bending requires local constraints on free edges
Jemal Guven, Martin Michael Müller, Pablo Vázquez-Montejo |
While the shape equations describing the equilibrium of an unstretchable thin sheet that is free
to bend are known, the boundary conditions that supplement these equations on free edges have remained elusive.
Intuitively, unstretchability is captured by a constraint on the metric within the bulk. Naïvely one would then
guess that this constraint is enough to ensure that the deformations determining the boundary conditions on these
edges respect the isometry constraint. If matters were this simple, unfortunately, it would imply unbalanced torques
(as well as forces) along the edge unless manifestly unphysical constraints are met by the boundary geometry. In this
article, we identify the source of the problem: not only the local arc-length but also the geodesic curvature need to
be constrained explicitly on all free edges. We derive the boundary conditions which follow. In contrast to conventional
wisdom, there is no need to introduce boundary layers. This framework is applied to isolated conical defects, both
with deficit as well, but more briefly, as surplus angles. Using these boundary conditions, we show that the lateral
tension within a circular cone of fixed radius is equal but opposite to the radial compression, and independent of
the deficit angle itself. We proceed to examine the effect of an oblique outer edge on this cone perturbatively
demonstrating that both the correction to the geometry as well as the stress distribution in the cone kicks in at
second order in the eccentricity of the edge.
Reduce
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Math. Mech. Solids, 24: 4051, 2019. See also arXiv:1904.05855.
![](grafiken/31squeelixsimulations_icon.jpg) | Helical Superstructure of Intermediate Filaments
Lila Bouzar, Martin Michael Müller, René Messina, Bernd Nöding, Sarah Köster, Hervé Mohrbach, Igor M. Kulić |
Abstract
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Phys. Rev. Lett., 122: 098101, 2019. See also arXiv:1803.04691.
![](grafiken/30vesicleflow_icon.png) | Vesicle dynamics in confined steady and harmonically modulated Poiseuille flows
Zakaria Boujja, Chaouqi Misbah, Hamid Ez-Zahraouy, Abdelilah Benyoussef, Thomas John, Christian Wagner, Martin Michael Müller |
Abstract
Phys. Rev. E, 98: 043111, 2018. See also arXiv:1810.04500.
![](grafiken/29confinementtorusadhesion_icon.png) | Confining a fluid membrane vesicle of toroidal topology in an adhesive hard sphere
Lila Bouzar, Ferhat Menas, Martin Michael Müller |
Abstract
Read more
IOP Conf. Series: MSE, 186: 012021, 2017.
![](grafiken/28squeelix_icon.png) | Squeezed helical elastica
Lila Bouzar, Martin Michael Müller, Pierre Gosselin, Igor M. Kulić, Hervé Mohrbach |
We theoretically study the conformations of a helical semi-flexible filament
confined to a two-dimensional surface. This squeezed helix exhibits a variety of unexpected shapes
resembling circles, waves or spirals depending on the material parameters. We explore the conformation
space in detail and show that the shapes can be understood as the mutual elastic interaction of
conformational quasi-particles. Our theoretical results are potentially useful to
determine the material parameters of such helical filaments in an experimental setting.
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Eur. Phys. J. E, 39: 114, 2016. See also arXiv:1606.03611.
![](grafiken/27dynamin_icon.png) | How bio-filaments twist membranes
Julien Fierling, Albert Johner, Igor M. Kulić, Hervé Mohrbach, Martin Michael Müller |
We study the deformations of a fluid membrane imposed by adhering stiff
bio-filaments due to the torques they apply. In the limit of small deformations, we
derive a general expression for the energy and the deformation field of the membrane.
This expression is specialised to different important cases including closed and helical
bio-filaments. In particular, we analyse interface-mediated interactions and membrane
wrapping when the filaments apply a local torque distribution on a tubular membrane.
Reduce
Soft Matter, 12: 5747, 2016.
![](grafiken/26confinementtorus_icon.png) | Toroidal membrane vesicles in spherical confinement
Lila Bouzar, Ferhat Menas, Martin Michael Müller |
Abstract
Read more
Phys. Rev. E, 92: 032721, 2015. See also arXiv:1509.00765.
![](grafiken/25sleeve_icon.png) | Non-linear buckling and symmetry breaking of a soft elastic sheet sliding on a cylindrical substrate
Norbert Stoop, Martin Michael Müller |
Abstract
Read more
Int. J. Non-Linear Mech., 75: 115, 2015. See also arXiv:1503.05030.
![](grafiken/24dynamin_icon.jpg) | Crunching Biofilament Rings
Julien Fierling, Martin Michael Müller, Hervé Mohrbach, Albert Johner, Igor M. Kulić |
Abstract
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Europhys. Lett., 107(6): 68002, 2014. See also arXiv:1408.6787.
![](grafiken/23microtubules_icon.png) | Confotronic dynamics of tubular filaments
Osman Kahraman, Hervé Mohrbach, Martin Michael Müller, Igor M. Kulić |
Abstract
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Soft Matter, 10(16): pp. 2836-2847, 2014. See also arXiv:1312.3106.
![](grafiken/22rotation_icon.png) | Whirling skirts and rotating cones
Jemal Guven, J. A. Hanna, Martin Michael Müller |
Steady, dihedrally symmetric patterns with sharp peaks may be observed on a spinning skirt, lagging behind the material flow of the fabric. These qualitative features are captured with a minimal model of traveling waves on an inextensible, flexible, generalized-conical sheet rotating about a fixed axis. Conservation laws are used to reduce the dynamics to a quadrature describing a particle in a three-parameter family of potentials. One parameter is associated with the stress in the sheet, aNoether is the current associated with rotational invariance, and the third is a Rossby number which indicates the relative strength of Coriolis forces. Solutions are quantized by enforcing a topology appropriate to a skirt and a particular choice of dihedral symmetry. A perturbative analysis of nearly axisymmetric cones shows that Coriolis effects are essential in establishing skirt-like solutions. Fully non-linear solutions with three-fold symmetry are presented which bear a suggestive resemblance to the observed patterns.
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New J. Phys., 15: 113055, 2013. See also arXiv:1306.2619.
![](grafiken/21cubicmembranes_icon.png) | Myotubularin and PtdIns3P remodel the sarcoplasmic reticulum in muscle in vivo
Leonela Amoasii, Karim Hnia, Gaëtan Chicanne, Andreas Brech, Belinda Simone Cowling, Martin Michael Müller, Yannick Schwab, Pascale Koebel, Arnaud Ferry, Bernard Payrastre, Jocelyn Laporte |
Abstract
J. Cell Sci., 126(8): 1806, 2013.
![](grafiken/20epole_icon.png) | Dipoles in thin sheets
Jemal Guven, J. A. Hanna, Osman Kahraman, Martin Michael Müller |
A flat elastic sheet may contain pointlike conical singularities that carry a metrical "charge" of Gaussian curvature. Adding such elementary defects to a sheet allows one to make many shapes, in a manner broadly
analogous to the familiar multipole construction in electrostatics. However, here the underlying field theory is non-linear,
and superposition of intrinsic defects is non-trivial as it must respect the immersion of the resulting surface in three
dimensions. We consider a "charge-neutral" dipole composed of two conical singularities of opposite sign.
Unlike the relatively simple electrostatic case, here there are two distinct stable minima and an infinity of unstable equilibria.
We determine the shapes of the minima and evaluate their energies in the thin-sheet regime where bending dominates
over stretching. Our predictions are in surprisingly good agreement with experiments on paper sheets.
Reduce
Read more
Eur. Phys. J. E, 36: 106, 2013. See also arXiv:1212.3262.
![](grafiken/19confinement_icon.png) | Fluid membrane vesicles in confinement
Osman Kahraman, Norbert Stoop, Martin Michael Müller |
Abstract
Read more
New J. Phys., 14: 095021, 2012.
![](grafiken/18flowermorpho_icon.png) | Petal shapes of sympetaleous flowers: the interplay between growth, geometry and elasticity
Martine Ben Amar, Martin Michael Müller, Miguel Trejo |
The growth of a thin elastic sheet imposes constraints on its geometry such as its Gaussian curvature KG.
In this paper, we construct the shapes of sympetalous bell-shaped flowers with a constant Gaussian curvature. Minimizing the bending energies
of both the petal and the veins, we are able to predict quantitatively the global shape of these flowers. We discuss two toy problems
where the Gaussian curvature is either negative or positive. In the former case the axisymmetric pseudosphere turns out to mimic the correct
shape before edge curling; in the latter case, singularities of the mathematical surface coincide with strong veins. Using a variational
minimization of the elastic energy, we find that the optimal number for the veins is either four, five or six, a number which is deceptively
close to the statistics on real flowers in nature.
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New J. Phys., 14: 085014, 2012. Also featured in the Highlights of 2012.
![](grafiken/17confinement_icon.png) | 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.
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Europhys. Lett., 97(6): 68008, 2012. See also arXiv:1201.2518.
![](grafiken/16econeunstab_icon.jpg) | Conical instabilities on paper
Jemal Guven, Martin Michael Müller, Pablo Vázquez-Montejo |
The stability of the fundamental defects of an unstretchable flat sheet is examined.
This involves expanding the bending energy to second order in deformations about the
defect. The modes of deformation occur as eigenstates of a fourth-order linear differential
operator. Unstretchability places a global linear constraint on these modes. Conical
defects with a surplus angle exhibit an infinite number of states. If this angle is below a
critical value, these states possess an n-fold symmetry labeled by an integer, n ≥ 2. A
nonlinear stability analysis shows that the 2-fold ground state is stable, whereas excited
states possess 2(n - 2) unstable modes which come in even and odd pairs.
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J. Phys. A: Math. Theor., 45(1): 015203, 2012. See also arXiv:1107.5008.
![](grafiken/15casimir_icon.png) | Interface-mediated interactions: Entropic forces of curved membranes
Pierre Gosselin, Hervé Mohrbach, Martin Michael Müller |
Abstract
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Phys. Rev. E, 83(5): 051921, 2011. See also arXiv:1011.1221.
![](grafiken/14econetouch_icon.jpg) | Self-Contact and Instabilities in the Anisotropic Growth of Elastic Membranes
Norbert Stoop, Falk K. Wittel, Martine Ben Amar, Martin Michael Müller, Hans J. Herrmann |
Abstract
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Phys. Rev. Lett., 105(6): 068101, 2010. See also arXiv:1007.1871.
![](grafiken/13cellmodel_icon.png) | Cell Model Approach to Membrane Mediated Protein Interactions
Martin Michael Müller, Markus Deserno |
Abstract
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Prog. Theor. Phys. Suppl., 184: pp. 351-363, 2010.
![](grafiken/12pseudo_icon.jpg) | Hamiltonian formulation of surfaces with constant Gaussian curvature
Miguel Trejo, Martine Ben Amar, Martin Michael Müller |
Abstract
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J. Phys. A: Math. Theor., 42(42): 425204, 2009.
![](grafiken/11indentstretch_icon.jpg) | Local Membrane Mechanics of Pore-Spanning Bilayers
Ingo Mey, Milena Stephan, Eva K. Schmitt, Martin Michael Müller, Martine Ben Amar, Claudia Steinem, Andreas Janshoff |
The mechanical behavior of lipid bilayers spanning the pores of highly ordered porous silicon substrates was studied by local indentation experiments as a function of surface functionalization, lipid composition, solvent content, indentation velocity, and pore radius. Solvent-containing nanoblack lipid membranes (nano-BLMs) as well as solvent-free pore-spanning bilayers were imaged by fluorescence and atomic force microscopy prior to force curve acquisition, which allows distinguishing between membrane-covered and uncovered pores. Force indentation curves on pore-spanning bilayers attached to functionalized hydrophobic porous silicon substrates reveal a predominately linear response that is mainly attributed to prestress in the membranes. This is in agreement with the observation that indentation leads to membrane lysis well below 5% area dilatation. However, membrane bending and lateral tension dominates over
prestress and stretching if solvent-free supported membranes obtained from spreading giant liposomes on hydrophilic porous silicon are indented.
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J. Am. Chem. Soc., 131(20): pp. 7031-7039, 2009.
![](grafiken/10substrate_icon.jpg) | Elasticity Mapping of Pore-Suspending Native Cell Membranes
Bärbel Lorenz, Ingo Mey, Siegfried Steltenkamp, Tamir Fine, Christina Rommel, Martin Michael Müller, Alexander Maiwald, Joachim Wegener, Claudia Steinem, Andreas Janshoff |
Abstract
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Small, 5(7): pp. 832-838, 2009.
![](grafiken/09econe_icon.png) | Conical Defects in Growing Sheets
Martin Michael Müller, Martine Ben Amar, Jemal Guven |
Abstract
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Phys. Rev. Lett., 101(15): 156104, 2008. See also arXiv:0807.1814.
![](grafiken/08drape_icon.png) | How paper folds: bending with local constraints
Jemal Guven, Martin Michael Müller |
Abstract
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J. Phys. A: Math. Theor., 41(5): 055203, 2008. See also arXiv:0712.0978.
![](grafiken/07vesad_icon.jpg) | Contact lines for fluid surface adhesion
Markus Deserno, Martin Michael Müller, Jemal Guven |
When a fluid surface adheres to a substrate, the location of the
contact line adjusts in order to minimize the overall energy. This
adhesion balance implies boundary conditions which depend on the
characteristic surface deformation energies. We develop a general
geometrical framework within which these conditions can be
systematically derived.
We treat both adhesion to a rigid substrate as well as adhesion
between two fluid surfaces, and illustrate our general results for
several important Hamiltonians involving both curvature and
curvature gradients. Some of these have previously been studied
using very different techniques, others are to our knowledge new.
What becomes clear in our approach is that, except for capillary
phenomena, these boundary conditions are not the manifestation
of a local force balance, even if the concept of surface stress is
properly generalized. Hamiltonians containing higher order surface
derivatives are not just sensitive to boundary translations but also
notice changes in slope or even curvature.
Both the necessity and the functional form of the corresponding
additional contributions follow readily from our treatment.
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Phys. Rev. E, 76(1): 011605, 2007. See also cond-mat/0703019. Also featured in the Virtual Journal of Biological Physics Research.
![](grafiken/06Eulerelastica_icon.png) | Balancing torques in membrane-mediated interactions: Exact results and
numerical illustrations
Martin Michael Müller, Markus Deserno, Jemal Guven |
Abstract
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Phys. Rev. E, 76(1): 011921, 2007. See also cond-mat/0702340. Also featured in the Virtual Journal of Biological Physics Research.
![](grafiken/05curvemedcover_icon.jpg) | Aggregation and vesiculation of membrane proteins by curvature-mediated
interactions
Benedict J. Reynwar, Gregoria Illya, Vagelis A. Harmandaris, Martin Michael Müller, Kurt Kremer, Markus Deserno |
Abstract
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Nature 447(7143): pp. 461-464, 2007.
![](grafiken/04tip_icon.jpg) | How to determine local elastic properties of lipid bilayer membranes
from atomic-force-microscope measurements: A theoretical analysis
Davood Norouzi, Martin Michael Müller, Markus Deserno |
Abstract
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Phys. Rev. E, 74(6): 061914, 2006. See also cond-mat/0602662. Also featured in the Virtual Journal of Biological Physics Research.
![](grafiken/03DODAB_icon.png) | Mechanical Properties of Pore-Spanning Lipid Bilayers Probed by Atomic Force Microscopy
Siegfried Steltenkamp, Martin Michael Müller, Markus Deserno, Christian Hennesthal, Claudia Steinem, Andreas Janshoff |
Abstract
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Biophys. J., 91(1): pp. 217-226, 2006.
![](grafiken/02multibody_icon.gif) | Interface mediated interactions between particles -- a geometrical approach
Martin Michael Müller, Markus Deserno, Jemal Guven |
Particles bound to an interface interact because they deform its shape.
The stresses that result are fully encoded in the geometry and described
by a divergence-free surface stress tensor. This stress tensor can be
used to express the force on a particle as a line integral along any
conveniently chosen closed contour that surrounds the particle. The
resulting expression is exact (i.e., free of any 'smallness' assumptions)
and independent of the chosen surface parametrization. Additional surface
degrees of freedom, such as vector fields describing lipid tilt, are readily
included in this formalism. As an illustration, we derive the exact force
for several important surface Hamiltonians in various symmetric two-particle
configurations in terms of the midplane geometry; its sign is evident in
certain interesting limits. Specializing to the linear regime, where the
shape can be analytically determined, these general expressions yield
force-distance relations, several of which have originally been derived
by using an energy based approach.
Reduce
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Phys. Rev. E, 72(6): 061407, 2005. See also cond-mat/0506019. Also featured in the Virtual Journal of Biological Physics Research.
![](grafiken/01surfacemed_icon.jpg) | Geometry of surface-mediated interactions
Martin Michael Müller, Markus Deserno, Jemal Guven |
Abstract
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Europhys. Lett., 69(3): pp. 482-488, 2005. See also cond-mat/0409043.
2. Books
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New Trends in the Physics and Mechanics of Biological Systems
Lecture Notes of the Les Houches Summer School, vol. 92 (Oxford University Press, 2011),
edited by Martine Ben Amar, Alain Goriely, Martin Michael Müller and Leticia Cugliandolo.
Chapter 9:
The physics of the cell membrane
Martin Michael Müller and Martine Ben Amar.
3. Theses
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Theoretical examinations of interface mediated interactions between colloidal particles,
diploma thesis (2004).
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Theoretical studies of fluid membrane mechanics, dissertation (2007).
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Symmetry breaking in bioelasticity, habilitation thesis (2015).
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