Publications

Articles in scientific journals

Books

Theses
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1. Articles in scientific journals
 Isometric bending requires local constraints on free edges
Jemal Guven, Martin Michael Müller, Pablo VázquezMontejo 
Abstract
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Math. Mech. Solids, 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 
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 
We 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.
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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 
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.
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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 
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 
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 
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 
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 
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 
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 
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).
