Homepage of Martin Michael Müller

Elastic tubes and filaments

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.

Phys. Rev. Lett., 122: 098101, 2019. See also arXiv:1803.04691.

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.

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

Non-linear buckling and symmetry breaking of a soft elastic sheet sliding on a cylindrical substrate
Norbert Stoop, Martin Michael Müller
We consider the axial compression of a thin sheet wrapped around a rigid cylindrical substrate. In contrast to the wrinkling-to-fold transitions exhibited in similar systems, we find that the sheet always buckles into a single symmetric fold, while periodic solutions are unstable. Upon further compression, the solution breaks symmetry and stabilizes into a recumbent fold. Using linear analysis and numerics, we theoretically predict the buckling force and energy as a function of the compressive displacement. We compare our theory to experiments employing cylindrical neoprene sheets and find remarkably good agreement.

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
We discuss a curious example for the collective mechanical behavior of coupled non-linear 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 inter-unit interaction for efficient ring induced membrane fission.

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 man-made nano-world. 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 larger-scale quasipolymer superstructures exhibiting collective dynamic modes and giving rise to a hallmark behavior radically different from semiflexible beams.

Soft Matter, 10(16): pp. 2836-2847, 2014. See also arXiv:1312.3106.