Homepage of Martin Michael Müller

Publications

Articles in scientific journals
Books
Theses

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1. Articles in scientific journals

Conformational Space of the Translocation Domain of Botulinum Toxin: Atomistic Modeling and Mesoscopic Description of the Coiled-Coil Helix Bundle

Alexandre Delort, Grazia Cottone, Thérèse E. Malliavin, Martin Michael Müller

Abstract

Int. J. Mol. Sci., 25: 2481, 2024.

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.

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.

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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 self-induced filament buckling via a surface stress located at the outside of the cross-section. 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 Ez-Zahraouy, 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 (contact-circle solutions) or on a surface (contact-area solutions). All solutions without adhesion are up-down symmetric. When the container is adhesive, the phase diagram is altered and new kinds of solution without up-down symmetry are found. For increasing values of adhesion the region of contact-circle 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

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Eur. Phys. J. E, 39: 114, 2016. See also arXiv:1606.03611.

How bio-filaments 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

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Phys. Rev. E, 92: 032721, 2015. See also arXiv:1509.00765.

Non-linear buckling and symmetry breaking of a soft elastic sheet sliding on a cylindrical substrate

Norbert Stoop, Martin Michael Müller

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Int. J. Non-Linear Mech., 75: 115, 2015. See also arXiv:1503.05030.

Crunching Biofilament Rings

Julien Fierling, Martin Michael Müller, Hervé Mohrbach, Albert Johner, Igor M. Kulić

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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

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Soft Matter, 10(16): pp. 2836-2847, 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, 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.

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

The sarcoplasmic reticulum (SR) is a specialized form of endoplasmic reticulum (ER) in skeletal muscle and is essential for calcium homeostasis. The mechanisms involved in SR remodeling and maintenance of SR subdomains are elusive. In this study, we identified myotubularin (MTM1), a phosphatase mutated in X-linked centronuclear myopathy (XLCNM), as a key regulator of phosphoinositide-3-monophosphate (PtdIns3P) levels at the SR. Mtm1 deficient mouse muscles and myoblasts from XLCNM patients exhibit abnormal SR/ER networks. In vivo modulation of MTM1 enzymatic activity in muscle using ectopic expression of wild-type or a dead-phosphatase MTM1 protein leads to differential SR remodeling. Active MTM1 is associated to flat membrane stacks, while dead-phosphatase MTM1 mutant promotes highly curved cubic membranes originating from the SR and enriched in PtdIns3P. Moreover, expression of the PtdIns3P binding module 2XFYVE also modified the SR shape at triads. Our findings, supported by the parallel analysis of the Mtm1- null mouse and in vivo study, reveal a direct function of MTM1 enzymatic activity in SR remodeling and a key role for its substrate PtdIns3P in promoting SR membrane curvature in skeletal muscle. We propose that alteration in SR remodeling is a primary cause of X-linked centronuclear myopathy. The tight regulation of PtdIns3P on specific membrane subdomains may be a general mechanism to control membrane curvature.

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J. Cell Sci., 126(8): 1806, 2013.

Dipoles in thin sheets

Jemal Guven, J. A. Hanna, Osman Kahraman, Martin Michael Müller

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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 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.

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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 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.

Morphogenesis of membrane invaginations in spherical confinement

Osman Kahraman, Norbert Stoop, Martin Michael Müller

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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 Vázquez-Montejo

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J. Phys. A: Math. Theor., 45(1): 015203, 2012. See also arXiv:1107.5008.

Interface-mediated interactions: Entropic forces of curved membranes

Pierre Gosselin, Hervé Mohrbach, Martin Michael Müller

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Phys. Rev. E, 83(5): 051921, 2011. See also arXiv:1011.1221.

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
We investigate the morphology of thin discs and rings growing in circumferential direction. Recent analytical results suggest that this growth produces symmetric excess cones (e-cones). We study the stability of such solutions considering self-contact and bending stress. We show that, contrary to what was assumed in previous analytical solutions, beyond a critical growth factor, no symmetric e-cone solution is energetically minimal any more. Instead, we obtain skewed e-cone 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

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Prog. Theor. Phys. Suppl., 184: pp. 351-363, 2010.

Hamiltonian formulation of surfaces with constant Gaussian curvature

Miguel Trejo, Martine Ben Amar, Martin Michael Müller

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J. Phys. A: Math. Theor., 42(42): 425204, 2009.

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.

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

The mechanics of cellular membranes is governed by a non-equilibrium composite framework consisting of the semiflexible filamentous cytoskeleton and extracellular matrix proteins linked to the lipid bilayer. While elasticity information of plasma membranes has mainly been obtained from whole cell analysis, techniques that allow to address local mechanical properties of cell membranes are desirable to learn how their lipid and protein composition is reflected in the elastic behavior on local length scales. Here, we introduce an approach based on basolateral membranes of polar epithelial Madin-Darby canine kidney (MDCK) II cells, prepared on a highly ordered porous substrate that allows elastic mapping on a submicrometer length scale. A strong correlation between the density of actin filaments and the measured membrane elasticity is found. Spatially resolved indentation experiments carried out with atomic force and fluorescence microscope permit to relate the supramolecular structure to the elasticity of cellular membranes. It is shown that the elastic response of the pore-spanning cell membranes is governed by the local bending modules rather than the lateral tension.

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Small, 5(7): pp. 832-838, 2009.

Conical Defects in Growing Sheets

Martin Michael Müller, Martine Ben Amar, Jemal Guven
A growing or shrinking disc will adopt a conical shape, its intrinsic geometry characterized by a surplus angle φ_e at the apex. If growth is slow, the cone will find its equilibrium. Whereas this is trivial if φ_e≤0, the disc can fold into one of a discrete infinite number of states if φ_e is positive. We construct these states in the regime where bending dominates, determine their energies and how stress is distributed in them. For each state a critical value of φ_e is identified beyond which the cone touches itself. Before this occurs, all states are stable; the ground state has twofold symmetry.

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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
A variational framework is introduced to describe how a surface bends when it is subject to local constraints on its geometry. This framework is applied to describe the patterns of a folded sheet of paper. The unstretchability of paper implies a constraint on the surface metric; bending is penalized by an energy quadratic in mean curvature. The local Lagrange multipliers enforcing the constraint are identified with a conserved tangential stress that couples to the extrinsic curvature of the sheet. The framework is illustrated by examining the deformation of a flat sheet into a generalized cone.

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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

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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.

Balancing torques in membrane-mediated interactions: Exact results and numerical illustrations

Martin Michael Müller, Markus Deserno, Jemal Guven

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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.

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

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Nature 447(7143): pp. 461-464, 2007.

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

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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.

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

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.

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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.

Geometry of surface-mediated interactions

Martin Michael Müller, Markus Deserno, Jemal Guven

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Europhys. Lett., 69(3): pp. 482-488, 2005. See also cond-mat/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).