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 
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 arclength 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.
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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 
Abstract
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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 
Abstract
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 
Abstract
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 
We discuss a curious example for the collective mechanical behavior of coupled nonlinear monomer units entrapped in a circular filament. Within a simple model we elucidate how multistability of monomer units and exponentially large degeneracy of the filament's ground state emerge as a collective feature of the closed filament. Surprisingly, increasing the monomer frustration, i.e., the bending prestrain within the circular filament, leads to a conformational softening of the system. The phenomenon, that we term polymorphic crunching, is discussed and applied to a possible scenario for membrane tube deformation by switchable dynamin or FtsZ filaments. We find an important role of cooperative interunit interaction for efficient ring induced membrane fission.
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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 
Tubular lattices are ubiquitous in nature and technology. Microtubules and nanotubes of all
kinds act as important pillars of biological cells and the manmade nanoworld. We show that
when prestress is introduced in such structures, localized conformational quasiparticles emerge and
govern the collective shape dynamics of the lattice. When coupled via cooperative interactions these
quasiparticles form largerscale quasipolymer superstructures exhibiting collective dynamic modes
and giving rise to a hallmark behavior radically different from semiflexible beams.
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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 
Abstract
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 
Abstract
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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 
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 fourthorder 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 nfold symmetry labeled by an integer, n ≥ 2. A
nonlinear stability analysis shows that the 2fold 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.
 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 
We investigate the morphology of thin discs and rings growing in circumferential direction. Recent analytical results suggest that this growth produces symmetric excess cones (econes). We study the stability of such solutions considering selfcontact and bending stress. We show that, contrary to what was assumed in previous analytical solutions, beyond a critical growth factor, no symmetric econe solution is energetically minimal any more. Instead, we obtain skewed econe solutions having lower energy, characterized by a skewness angle and repetitive spiral winding with increasing growth. These results are generalized to discs with varying thickness and rings with holes of different radii.
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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 
Abstract
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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 
Dirac's method for constrained Hamiltonian systems is used to describe surfaces of constant Gaussian curvature. A geometrical free energy, for which these surfaces are equilibrium states, is introduced and interpreted as an action. An equilibrium surface can then be generated by the evolution of a closed space curve.
Since the underlying action depends on second derivatives, the velocity of the curve and its conjugate momentum must be included in the set of phase space variables. Furthermore, the action is linear in the acceleration of the curve and possesses a local symmetryreparametrization invariancewhich implies primary constraints in the canonical formalism. These constraints are incorporated into the Hamiltonian through Lagrange multiplier functions, that are identified as the components of the acceleration of the curve. The formulation leads to four first order partial differential equations, one for each canonical variable.
With the appropriate choice of parametrization only one of these equations has to be solved to obtain the surface which is swept out by the evolving space curve. To illustrate the formalism, several evolutions of pseudospherical surfaces are discussed.
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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 
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 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 
Abstract
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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 
Abstract
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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 
Abstract
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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 
Abstract
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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 
Soft interfaces can mediate interactions between particles bound to
them. The force transmitted through the surface geometry on a
particle may be expressed as a closed line integral of the surface
stress tensor around that particle. This contour may be deformed to
exploit the symmetries present; for two identical particles, one
obtains an exact expression for the force between them in terms of
the local surface geometry of their midplane; in the case of a
fluid membrane the sign of the interaction is often evident. The
approach, by construction, is adapted directly to the surface and is
independent of its parameterization. Furthermore, it is applicable
for arbitrarily large deformations; in particular, it remains valid
beyond the linear smallgradient regime.
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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).
