Publications (37)123.96 Total impact
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ABSTRACT: We simulate randomly crosslinked networks of biopolymers, characterizing linear and nonlinear elasticity under different loading conditions (uniaxial extension, simple shear, and pure shear). Under uniaxial extension, and upon entering the nonlinear regime, the network switches from a dilatant to contractile response. Analogously, under isochoric conditions (pure shear), the normal stresses change their sign. Both effects are readily explained with a generic weakly nonlinear elasticity theory. The elastic moduli display an intermediate superstiffening regime, where moduli increase much stronger with applied stress σ than predicted by the forceextension relation of a single wormlikechain (). We interpret this superstiffening regime in terms of the reorientation of filaments with the maximum tensile direction of the deformation field. A simple model for the reorientation response gives an exponential stiffening, , in qualitative agreement with our data. The heterogeneous, anisotropic structure of the network is reflected in correspondingly heterogeneous and anisotropic elastic properties. We provide a coarsegraining scheme to quantify the local anisotropy, the fluctuations of the elastic moduli, and the local stresses as a function of coarsegraining length. Heterogeneities of the elastic moduli are strongly correlated with the local density and increase with applied strain. © 2015 IOP Publishing Ltd and Deutsche Physikalische Gesellschaft. 
Article: RheoChaos of Frictional Grains
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ABSTRACT: A twodimensional dense fluid of frictional grains is shown to exhibit timechaotic, spatially heterogeneous flow in a range of stress values, $\sigma$, chosen in the unstable region of sshaped flow curves. Stress controlled simulations reveal a phase diagram with reentrant stationary flow for small and large stress $\sigma$. In between no steady flow state can be reached, instead the system either jams or displays time dependent heterogeneous strain rates $\dot\gamma({\bf r},t)$. The results of simulations are in agreement with the stability analysis of a simple hydrodynamic model, coupling stress and microstructure which we tentatively associate with the frictional contact network. 
Article: Free volume under shear
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ABSTRACT: Using an athermal quasistatic simulation protocol, we study the distribution of free volumes in sheared hardparticle packings close to, but below, the randomclose packing threshold. We show that under shear, and independent of volume fraction, the free volumes develop features similar to closepacked systems  particles selforganize in a manner as to mimick the isotropically jammed state. We compare athermally sheared packings with thermalized packings and show that thermalization leads to an erasure of these structural features. The temporal evolution, in particular the openingup and the closing of freevolume patches is associated with the singleparticle dynamics, showing a crossover from ballistic to diffusive behavior.  [Show abstract] [Hide abstract]
ABSTRACT: Actin binding proteins (ABPs) not only set the structure of actin filament assemblies but also mediate the frequencydependent viscoelastic moduli of crosslinked and bundled actin networks. Point mutations in the actin binding domain of those ABPs can tune the association and dissociation dynamics of the actin/ABP bond and thus modulate the network mechanics both in the linear and nonlinear response regime. We here demonstrate how the exchange of a single charged amino acid in the actin binding domain of the ABP fascin triggers such a modulation of the network rheology. Whereas the overall structure of the bundle networks is conserved, the transition point from strainhardening to strainweakening sensitively depends on the crosslinker offrate and the applied shear rate. Our experimental results are consistent both with numerical simulations of a crosslinked bundle network and a theoretical description of the bundle network mechanics which is based on nonaffine bending deformations and forcedependent crosslink dynamics. Graphical abstract  [Show abstract] [Hide abstract]
ABSTRACT: Modeling approaches of suspended, rodlike particles and recent experimental data have shown that depletion forces display different signatures depending on the orientation of these particles. It has been shown that axial attraction of two rods yields contractile forces of 0.1pN that are independent of the relative axial shift of the two rods. Here, we measured depletioncaused interactions of actin bundles extending the phase space of single pairs of rods to a multiparticle system. In contrast to a filament pair, we found forces up to 3pN . Upon bundle relaxation forces decayed exponentially with a mean decay time of 3.4s . These different dynamics are explained within the frame of a mathematical model by taking pairwise interactions to a multifilament scale. The macromolecular content employed for our experiments is well below the crowding of cells. Thus, we propose that arising forces can contribute to biological force generation without the need to convert chemical energy into mechanical work.  [Show abstract] [Hide abstract]
ABSTRACT: We study the response of Factin bundles to driving forces through a simple analytical model. We consider two filaments connected by reversibly bound crosslinks and driven by an external force. Two failure modes under load can be defined. Brittle failure is observed when crosslinks suddenly and collectively unbind, leading to catastrophic loss of bundle integrity. During ductile failure, on the other hand, bundle integrity is maintained, however at the cost of crosslink reorganization and defect formation. We present phase diagrams for the onset of failure, highlighting the importance of the crosslink stiffness for these processes. Crossing the phase boundaries, forcedeflection curves display (frequencydependent) hysteresis loops, reflecting the firstorder character of the failure processes. We evidence how the introduction of defects can lead to complex elastoplastic relaxation processes, once the force is switched off. Depending on, both the timescale for defect motion and the crosslink stiffness, bundles can remain in a quasipermanent plastically deformed state for a very long time. Graphical abstract  [Show abstract] [Hide abstract]
ABSTRACT: We propose a phase diagram for the shear flow of dry granular particles in two dimensions based on simulations and a phenomenological Landau theory for a nonequilibrium firstorder phase transition. Our approach incorporates both frictional as well as frictionless particles. The most important feature of the frictional phase diagram is reentrant flow and a critical jamming point at finite stress. In the frictionless limit the regime of reentrance vanishes and the jamming transition is continuous with a critical point at zero stress. The jamming phase diagrams derived from the model agree with the experiments of Bi et al. [Nature (London) 480, 355 (2011)] and brings together previously conflicting numerical results.  [Show abstract] [Hide abstract]
ABSTRACT: We use computer simulations to study highly dense systems of granular particles that are driven by oscillating forces. We implement different dissipation mechanisms that are used to extract the injected energy. In particular, the action of a simple local Stokes' drag is compared with nonlinear and historydependent frictional forces that act either between particle pairs or between particles and an external container wall. The Stokes' drag leads to particle motion that is periodic with the driving force, even at high densities around close packing where particles undergo frequent collisions. With the introduction of interparticle frictional forces this "interacting absorbing state" is destroyed and particles start to diffuse around. By reducing the density of the material we go through another transition to a "noninteracting" absorbing state, where particles independently follow the forceinduced oscillations without collisions. In the system with particlewall frictional interactions this transition has signs of a discontinuous phase transition. It is accompanied by a diverging relaxation time, but not by a vanishing order parameter, which rather jumps to zero at the transition.  [Show abstract] [Hide abstract]
ABSTRACT: Using numerical simulations, the rheological response of an athermal assembly of soft particles with tunable attractive interactions is studied in the vicinity of jamming. At small attractions, a fragile solid develops and a finite yield stress is measured. Moreover, the measured flow curves have unstable regimes, which lead to persistent shearbanding. These features are rationalized by establishing a link between the rheology and the interparticle connectivity, which also provides a minimal model to describe the flow curves.  [Show abstract] [Hide abstract]
ABSTRACT: We study, by computer simulations, the role of different dissipation forces on the rheological properties of highlydense particleladen flows. In particular, we are interested in the closepacking limit (jamming) and the question if "universal" observables can be identified that do not depend on the details of the dissipation model. To this end, we define a simplified lubrication force and systematically vary the range $h_c$ of this interaction. For fixed $h_c$ a crossover is seen from a Newtonian flow regime at small strain rates to inertiadominated flow at larger strain rates. The same crossover is observed as a function of the lubrication range $h_c$. At the same time, but only at high densities close to jamming, particle velocity as well as local density distributions are unaffected by changes in the lubrication range  they are "universal". At densities away from jamming, this universality is lost: shortrange lubrication forces lead to pronounced particle clustering, while longerranged lubrication does not. These findings highlight the importance of "geometric" packing constraints for particle motion  independent of the specific dissipation model. With the free volume vanishing at randomclose packing, particle motion is more and more constrained by the ever smaller amount of free space. On the other side, macroscopic rheological observables, as well as higherorder correlation functions retain the variability of the underlying dissipation model. 
Article: Shear thickening in granular suspensions: Interparticle friction and dynamically correlated clusters
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ABSTRACT: We consider the shear rheology of concentrated suspensions of nonBrownian frictional particles. The key result of our study is the emergence of a pronounced shearthickening regime, where frictionless particles would normally undergo shearthinning. We clarify that shear thickening in our simulations is due to enhanced energy dissipation via frictional interparticle forces. Moreover, we evidence the formation of dynamically correlated particleclusters of size $\xi$, which contribute to shear thickening via an increase in \emph{viscous} dissipation. A scaling argument gives $\eta\sim \xi^2$, which is in very good agreement with the data. 
Article: Melting a Granular Glass by Cooling
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ABSTRACT: Driven granular systems readily form glassy phases at high particle volume fractions and low driving amplitudes. We use computer simulations of a driven granular glass to evidence a reentrance melting transition into a fluid state, which, contrary to intuition, occurs by \emph{reducing} the amplitude of the driving. This transition is accompanied by anomalous particle dynamics and superdiffusive behavior on intermediate timescales. We highlight the special role played by frictional interactions, which help particles to escape their glassy cages. Such an effect is in striking contrast to what friction is expected to do: reduce particle mobility by making them stick.  [Show abstract] [Hide abstract]
ABSTRACT: The mechanical properties of cells are dominated by the cytoskeleton, an interconnected network of long elastic filaments. The connections between the filaments are provided by crosslinking proteins, which constitute, next to the filaments, the second important mechanical element of the network. An important aspect of cytoskeletal assemblies is their dynamic nature, which allows remodeling in response to external cues. The reversible nature of crosslink binding is an important mechanism that underlies these dynamical processes. Here, we develop a theoretical model that provides insight into how the mechanical properties of cytoskeletal networks may depend on their underlying constituting elements. We incorporate three important ingredients: nonaffine filament deformations in response to network strain; interplay between filament and crosslink mechanical properties; reversible crosslink (un)binding in response to imposed stress. With this we are able to selfconsistently calculate the nonlinear modulus of the network as a function of deformation amplitude and crosslink as well as filament stiffnesses. During loading crosslink unbinding processes lead to a relaxation of stress and therefore to a reduction of the network modulus and eventually to network failure, when all crosslink are unbound. This softening due to crosslink unbinding generically competes with an inherent stiffening response, which may either be due to filament or crosslink nonlinear elasticity.  [Show abstract] [Hide abstract]
ABSTRACT: We consider a biopolymer bundle consisting of filaments that are crosslinked together. The crosslinks are reversible: they can dynamically bind and unbind adjacent filament pairs as controlled by a binding enthalpy. The bundle is subjected to a bending deformation and the corresponding distribution of crosslinks is measured. For a bundle consisting of two filaments, upon increasing the bending amplitude, a firstorder transition is observed. The transition is from a state where the filaments are tightly coupled by many bound crosslinks, to a state of nearly independent filaments with only a few bound crosslinks. For a bundle consisting of more than two filaments, a series of firstorder transitions is observed. The transitions are connected with the formation of an interface between regions of low and high crosslink densities. Combining umbrella sampling Monte Carlo simulations with analytical calculations, we present a detailed picture of how the competition between crosslink shearing and filament stretching drives the transitions. We also find that, when the crosslinks become soft, collective behavior is not observed: the crosslinks then unbind one after the other leading to a smooth decrease of the average crosslink density.  [Show abstract] [Hide abstract]
ABSTRACT: The dynamical mechanisms controlling the rheology of dense suspensions close to jamming are investigated numerically, using simplified models for the relevant dissipative forces. We show that the velocity fluctuations control the dissipation rate and therefore the effective viscosity of the suspension. These fluctuations are similar in quasistatic simulations and for finite strain rate calculations with various damping schemes. We conclude that the statistical properties of grain trajectories  in particular the critical exponent of velocity fluctuations with respect to volume fraction \phi  only weakly depend on the dissipation mechanism. Rather they are determined by steric effects, which are the main driving forces in the quasistatic simulations. The critical exponent of the suspension viscosity with respect to \phi can then be deduced, and is consistent with experimental data.  [Show abstract] [Hide abstract]
ABSTRACT: Inspired by the complex influence of the globular crosslinking proteins on the formation of biofilament bundles in living organisms, we study and analyze a theoretical model for the structure and thermodynamics of bundles of helical filaments assembled in the presence of crosslinking molecules. The helical structure of filaments, a universal feature of biopolymers such as filamentous actin, is shown to generically frustrate the geometry of crosslinking between the "grooves" of two neighboring filaments. We develop a coarsegrained model to investigate the interplay between the geometry of binding and mechanics of both linker and filament distortion, and we show that crosslinking in parallel bundles of helical filaments generates intrinsic torques, of the type that tend to wind the bundle superhelically about its central axis. Crosslinking mediates a nonlinear competition between the preference for bundle twist and the sizedependent mechanical cost of filament bending, which in turn gives rise to feedback between the global twist of selfassembled bundles and their lateral size. Finally, we demonstrate that above a critical density of bound crosslinkers, twisted bundles form with a thermodynamically preferred radius that, in turn, increases with a further increase in crosslinking bonds. We identify the stiffness of crosslinking bonds as a key parameter governing the sensitivity of bundle structure and assembly to the availability and affinity of crosslinkers.  [Show abstract] [Hide abstract]
ABSTRACT: Combining simulations and theory I study the interplay between bundle elastic degrees of freedom and crosslink binding propensity. By slowly driving bundles into a deformed configuration, and depending on the mechanical stiffness of the crosslinking agent, the binding affinity is shown to display a sudden and discontinuous drop. This indicates a cooperative unbinding process that involves the crossing of a freeenergy barrier. Choosing the proper crosslinker therefore not only allows us to change the composite elastic properties of the bundle but also the relevant time scales which can be tuned from the single crosslink binding rate to the much longer escape time over the freeenergy barrier.  [Show abstract] [Hide abstract]
ABSTRACT: Factin bundles are prominent cytoskeletal structures in eukaryotes. They provide mechanical stability in stereocilia, microvilli, filopodia, stress fibers and the sperm acrosome. Bundles are typically stabilized by a wide range of specific crosslinking proteins, most of which exhibit offrates on the order of 1s(1). Yet Factin bundles exhibit structural and mechanical integrity on time scales that are orders of magnitude longer. By applying large deformations to reconstituted Factin bundles using optical tweezers, we provide direct evidence of their differential mechanical response in vitro: bundles exhibit fully reversible, elastic response on short time scales and irreversible, elastoplastic response on time scales that are long compared to the characteristic crosslink dissociation time. Our measurements show a broad range of characteristic relaxation times for reconstituted Factin bundles. This can be reconciled by considering that bundle relaxation behavior is also modulated by the number of filaments, crosslinking type and occupation number as well as the consideration of defects due to filament ends. 
Article: Semiflexible Filamentous Composites
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ABSTRACT: Inspired by the ubiquity of composite filamentous networks in nature we investigate models of biopolymer networks that consist of interconnected floppy and stiff filaments. Numerical simulations carried out in three dimensions allow us to explore the microscopic partitioning of stresses and strains between the stiff and floppy fractions c_s and c_f, and reveal a nontrivial relationship between the mechanical behavior and the relative fraction of stiff polymer: when there are few stiff polymers, nonpercolated stiff ``inclusions`` are protected from large deformations by an encompassing floppy matrix, while at higher fractions of stiff material the stiff network is independently percolated and dominates the mechanical response.  [Show abstract] [Hide abstract]
ABSTRACT: Bundles of filamentous polymers are primary structural components of a broad range of cytoskeletal structures, and their mechanical properties play key roles in cellular functions ranging from locomotion to mechanotransduction and fertilization. We give a detailed derivation of a wormlike bundle model as a generic description for the statics and dynamics of polymer bundles consisting of semiflexible polymers interconnected by crosslinking agents. The elastic degrees of freedom include bending as well as twist deformations of the filaments and shear deformation of the crosslinks. We show that a competition between the elastic properties of the filaments and those of the crosslinks leads to renormalized effective bend and twist rigidities that become modenumber dependent. The strength and character of this dependence is found to vary with bundle architecture, such as the arrangement of filaments in the cross section and pretwist. We discuss two paradigmatic cases of bundle architecture, a uniform arrangement of filaments as found in F actin bundles and a shelllike architecture as characteristic for microtubules. Each architecture is found to have its own universal ratio of maximal to minimal bending rigidity, independent of the specific type of crosslinkinduced filament coupling; our predictions are in reasonable agreement with available experimental data for microtubules. Moreover, we analyze the predictions of the wormlike bundle model for experimental observables such as the tangenttangent correlation function and dynamic response and correlation functions. Finally, we analyze the effect of pretwist (helicity) on the mechanical properties of bundles. We predict that microtubules with different number of protofilaments should have distinct variations in their effective bending rigidity.
Publication Stats
804  Citations  
123.96  Total Impact Points  
Top Journals
Institutions

20142015

Universitätsmedizin Göttingen
Göttingen, Lower Saxony, Germany


20112015

GeorgAugustUniversität Göttingen
 Institute for Theoretical Physics
Göttingen, Lower Saxony, Germany


20092011

University of Lyon
Lyons, RhôneAlpes, France


2010

Claude Bernard University Lyon 1
 Laboratoire de la matière condensée et nanostructures (LPMCN)
Villeurbanne, RhôneAlpes, France


20062010

LudwigMaximilianUniversity of Munich
 • Department of Physics
 • Arnold Sommerfeld Center for Theoretical Physics (ASC)
München, Bavaria, Germany
