Publications

Articles in scientific journals

Books

Theses
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1. Articles in scientific journals
 Flexoelectric fluid membrane vesicles in spherical confinement
Niloufar Abtahi, Lila Bouzar, Nadia SaidiAmroun, Martin Michael Müller 
Abstract
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EPL, 131(1): 18001, 2020. See also arXiv:2006.04475.
 Isometric bending requires local constraints on free edges
Jemal Guven, Martin Michael Müller, Pablo VázquezMontejo 
Abstract
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Math. Mech. Solids, 24: 4051, 2019. See also arXiv:1904.05855.
 Helical Superstructure of Intermediate Filaments
Lila Bouzar, Martin Michael Müller, René Messina, Bernd Nöding, Sarah Köster, Hervé Mohrbach, Igor M. Kulić 
Intermediate filaments are the least explored among the large cytoskeletal elements.
We show here that they display conformational anomalies in narrow microfluidic channels.
Their unusual behavior can be understood as the consequence of a previously undetected, large scale
helically curved superstructure. Confinement in a channel orders the otherwise soft, strongly
fluctuating helical filaments and enhances their structural correlations, giving rise to experimentally
detectable, strongly oscillating tangent correlation functions. We propose an explanation for the detected
intrinsic curving phenomenon  an elastic shape instability that we call autocoiling. The mechanism
involves selfinduced filament buckling via a surface stress located at the outside of the
crosssection. The results agree with ultrastructural findings and rationalize for the commonly observed
looped intermediate filament shapes. Beyond curvature, explaining the molecular origin of the detected helical
torsion remains an interesting challenge.
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Phys. Rev. Lett., 122: 098101, 2019. See also arXiv:1803.04691.
 Vesicle dynamics in confined steady and harmonically modulated Poiseuille flows
Zakaria Boujja, Chaouqi Misbah, Hamid EzZahraouy, Abdelilah Benyoussef, Thomas John, Christian Wagner, Martin Michael Müller 
We present a numerical study of the timedependent motion of a membrane vesicle in a
channel under an imposed flow. In a Poiseuille flow the shape of the vesicle depends on the flow strength,
the mechanical properties of the membrane, and the width of the channel. In a wide parameter region, the
emerging snaking shape shows an oscillatory motion like a swimmer flagella even though the flow is
stationary. We quantify this behavior by the amplitude and frequency of the oscillations of the vesicle's
center of mass. The influence of an amplitude modulation of the imposed flow on the dynamics and shape of
the snaking vesicle is also investigated. We find that this modulationwhen sufficiently smallinduces
a modulation in amplitude and frequency of the center of mass of the snaking vesicle. For large
modulation amplitudes transitions to static shapes are observed.
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Phys. Rev. E, 98: 043111, 2018. See also arXiv:1810.04500.
 Confining a fluid membrane vesicle of toroidal topology in an adhesive hard sphere
Lila Bouzar, Ferhat Menas, Martin Michael Müller 
Abstract
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IOP Conf. Series: MSE, 186: 012021, 2017.
 Squeezed helical elastica
Lila Bouzar, Martin Michael Müller, Pierre Gosselin, Igor M. Kulić, Hervé Mohrbach 
Abstract
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Eur. Phys. J. E, 39: 114, 2016. See also arXiv:1606.03611.
 How biofilaments 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
biofilaments 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
biofilaments. In particular, we analyse interfacemediated interactions and membrane
wrapping when the filaments apply a local torque distribution on a tubular membrane.
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Soft Matter, 12: 5747, 2016.
 Toroidal membrane vesicles in spherical confinement
Lila Bouzar, Ferhat Menas, Martin Michael Müller 
Abstract
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Phys. Rev. E, 92: 032721, 2015. See also arXiv:1509.00765.
 Nonlinear buckling and symmetry breaking of a soft elastic sheet sliding on a cylindrical substrate
Norbert Stoop, Martin Michael Müller 
Abstract
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Int. J. NonLinear Mech., 75: 115, 2015. See also arXiv:1503.05030.
 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.
 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. 28362847, 2014. See also arXiv:1312.3106.
 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, generalizedconical sheet rotating about a fixed axis. Conservation laws are used to reduce the dynamics to a quadrature describing a particle in a threeparameter 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 skirtlike solutions. Fully nonlinear solutions with threefold 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.
 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.
 Dipoles in thin sheets
Jemal Guven, J. A. Hanna, Osman Kahraman, Martin Michael Müller 
Abstract
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Eur. Phys. J. E, 36: 106, 2013. See also arXiv:1212.3262.
 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 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.
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New J. Phys., 14: 095021, 2012.
 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 K_{G}.
In this paper, we construct the shapes of sympetalous bellshaped 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.
 Morphogenesis of membrane invaginations in spherical confinement
Osman Kahraman, Norbert Stoop, Martin Michael Müller 
Abstract
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Europhys. Lett., 97(6): 68008, 2012. See also arXiv:1201.2518.
 Conical instabilities on paper
Jemal Guven, Martin Michael Müller, Pablo VázquezMontejo 
Abstract
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J. Phys. A: Math. Theor., 45(1): 015203, 2012. See also arXiv:1107.5008.
 Interfacemediated 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.
 SelfContact 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.
 Cell Model Approach to Membrane Mediated Protein Interactions
Martin Michael Müller, Markus Deserno 
Membranedeforming proteins can interact through the curvature
fields they create. In the case of many such proteins a cell model
approach can be used to calculate the energy per protein and
predict, whether it would lead to phase segregation or
budformation. Using covariant differential geometry exact results
are derived for the lateral pressure in terms of geometric
properties at the cell boundary. Numerical solutions of the exact
shape equations in the highly nonlinear regime are found and it is
seen that both phase segregation and bud formation can occur.
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Prog. Theor. Phys. Suppl., 184: pp. 351363, 2010.
 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.
 Local Membrane Mechanics of PoreSpanning Bilayers
Ingo Mey, Milena Stephan, Eva K. Schmitt, Martin Michael Müller, Martine Ben Amar, Claudia Steinem, Andreas Janshoff 
Abstract
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J. Am. Chem. Soc., 131(20): pp. 70317039, 2009.
 Elasticity Mapping of PoreSuspending 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. 832838, 2009.
 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.
 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.
 Contact lines for fluid surface adhesion
Markus Deserno, Martin Michael Müller, Jemal Guven 
Abstract
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Phys. Rev. E, 76(1): 011605, 2007. See also condmat/0703019. Also featured in the Virtual Journal of Biological Physics Research.
 Balancing torques in membranemediated interactions: Exact results and
numerical illustrations
Martin Michael Müller, Markus Deserno, Jemal Guven 
Torques on interfaces can be described by a divergencefree tensor
which is fully encoded in the geometry. This tensor consists of two
terms, one originating in the couple of the stress, the other capturing
an intrinsic contribution due to curvature. In analogy to the description
of forces in terms of a stress tensor, the torque on a particle can be
expressed as a line integral along any contour surrounding the particle.
Interactions between particles mediated by a fluid membrane are studied
within this framework. In particular, torque balance places a strong
constraint on the shape of the membrane. Symmetric twoparticle
configurations admit simple analytical expressions which are valid
in the fully nonlinear regime; in particular, the problem may be
solved exactly in the case of two membranebound parallel cylinders.
This apparently simple system provides some flavor of the remarkably
subtle nonlinear behavior associated with membranemediated interactions.
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Phys. Rev. E, 76(1): 011921, 2007. See also condmat/0702340. Also featured in the Virtual Journal of Biological Physics Research.
 Aggregation and vesiculation of membrane proteins by curvaturemediated
interactions
Benedict J. Reynwar, Gregoria Illya, Vagelis A. Harmandaris, Martin Michael Müller, Kurt Kremer, Markus Deserno 
Membrane remodelling plays an important role in cellular tasks such as endocytosis, vesiculation and protein sorting, and in the biogenesis of organelles such as the endoplasmic reticulum or the Golgi apparatus. It is well established that the remodelling process is aided by specialized proteins that can sense as well as create membrane curvature, and trigger tubulation when added to synthetic liposomes. Because the energy needed for such largescale changes in membrane geometry significantly exceeds the binding energy between individual proteins and between protein and membrane, cooperative action is essential. It has recently been suggested that curvaturemediated attractive interactions could aid cooperation and complement the effects of specific binding events on membrane remodelling. But it is difficult to experimentally isolate curvaturemediated interactions from direct attractions between proteins. Moreover, approximate theories predict repulsion between isotropically curving proteins. Here we use coarsegrained membrane simulations to show that curvatureinducing model proteins adsorbed on lipid bilayer membranes can experience attractive interactions that arise purely as a result of membrane curvature. We find that once a minimal local bending is realized, the effect robustly drives protein cluster formation and subsequent transformation into vesicles with radii that correlate with the local curvature imprint. Owing to its universal nature, curvaturemediated attraction can operate even between proteins lacking any specific interactions, such as newly synthesized and still immature membrane proteins in the endoplasmic reticulum.
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Nature 447(7143): pp. 461464, 2007.
 How to determine local elastic properties of lipid bilayer membranes
from atomicforcemicroscope measurements: A theoretical analysis
Davood Norouzi, Martin Michael Müller, Markus Deserno 
Measurements with an atomic force microscope (AFM) offer a direct way to
probe elastic properties of lipid bilayer membranes locally: provided
the underlying stressstrain relation is known, material parameters such as
surface tension or bending rigidity may be deduced.
In a recent experiment a porespanning membrane was poked with an AFM tip,
yielding a linear behavior of the forceindentation curves. A theoretical
model for this case is presented here which describes these curves in the
framework of Helfrich theory. The linear behavior of the measurements is
reproduced if one neglects the influence of adhesion between tip and membrane.
Including it via an adhesion balance changes the situation significantly:
forcedistance curves cease to be linear, hysteresis and nonzero detachment
forces can show up. The characteristics of this rich scenario are discussed
in detail in this article.
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Phys. Rev. E, 74(6): 061914, 2006. See also condmat/0602662. Also featured in the Virtual Journal of Biological Physics Research.
 Mechanical Properties of PoreSpanning Lipid Bilayers Probed by Atomic Force Microscopy
Siegfried Steltenkamp, Martin Michael Müller, Markus Deserno, Christian Hennesthal, Claudia Steinem, Andreas Janshoff 
We measure the elastic response of a freestanding lipid membrane to a local indentation by using an atomic force microscope. Starting point is a planar
goldcoated alumina substrate with a chemisorbed 3mercaptopropionic acid
monolayer displaying circular pores of very well defined and tunable size, over
which bilayers composed of N,N, dimethyl N,N, dioctadecylammonium bromide or
1,2  dioleoyl  3  trimethylammonium  propane chloride were spread.
Centrally indenting these 'nanodrums' with an atomic force microscope tip yields
forceindentation curves, which we quantitatively analyze by solving the
corresponding shape equations of continuum curvature elasticity. Since the
measured response depends in a known way on the system geometry (pore size, tip
radius) and on material parameters (bending modulus, lateral tension), this opens
the possibility to monitor local elastic properties of lipid membranes in a
wellcontrolled setting.
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Biophys. J., 91(1): pp. 217226, 2006.
 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 divergencefree 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 twoparticle
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
forcedistance relations, several of which have originally been derived
by using an energy based approach.
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Phys. Rev. E, 72(6): 061407, 2005. See also condmat/0506019. Also featured in the Virtual Journal of Biological Physics Research.
 Geometry of surfacemediated interactions
Martin Michael Müller, Markus Deserno, Jemal Guven 
Abstract
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Europhys. Lett., 69(3): pp. 482488, 2005. See also condmat/0409043.
2. Books

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

Theoretical examinations of interface mediated interactions between colloidal particles,
diploma thesis (2004).

Theoretical studies of fluid membrane mechanics, dissertation (2007).

Symmetry breaking in bioelasticity, habilitation thesis (2015).
