arXiv subjects

Martin Lenz

Publications and source records attributed to Martin Lenz.

At least 19 recordsLinked to original sources

arXiv2026

Designing corrugated surfaces to guide colloidal self-assembly

The self-assembly of colloidal particles enables the creation of structured materials with programmable functionalities; however, controlling interaction specificity and aggregate morphology in a reversible and scalable manner remains a major challenge. Here, we investigate the selective depletion-induced self-assembly of 3D-printed flat polygonal colloids, where nanoscale surface topography is engineered through precise modeling in two-photon polymerization. By designing anisotropic lateral surfaces, we direct specific interactions that govern aggregate morphology, yielding dimers, chains, zigzag, and honeycomb structures depending on the surface configuration. The specificity of interaction is tuned by varying the length scale of the topographic surfaces, the depletant concentration and the ionic strength of the solution, revealing a transition from selective to non-selective aggregation regimes. The relative placement of lateral interacting surfaces on the colloids enables assembly into aggregates spanning a broad range of sizes, while tuning the interaction strength selectively stabilizes distinct structural motifs. We demonstrate this interplay between geometric arrangement and interaction energy experimentally and corroborate through both theory and simulations for specifically hexagonal shaped colloids. This study establishes a versatile framework for programming colloidal interactions via micro-architectural design, offering new routes for fabricating reconfigurable and functional soft materials.

cond-mat.soft↗

arXiv2026

High-symmetry ill-fitting subunits in 3D form aggregates of all dimensions

Proteins can combine into functional elements in living cells or self-assemble into unwanted structures in a number of diseases. The resulting aggregates often display filamentous morphologies across a large range of protein shapes and molecular interactions. This has led to the suggestion that filament formation could be a generic outcome of the aggregation of geometrically complex, ill-fitting objects, although such a mechanism has not been demonstrated in three dimensions. To address this problem, we theoretically study the self-assembly of three-dimensional identical, ill-fitting deformable subunits mimicking globular proteins in solution. In our model, self-assembling subunits incur deformations that accumulate as the aggregate size increases and can eventually hamper further assembly. We analytically predict the ground state morphologies of the resulting aggregates as a function of the subunit adhesivity and elasticity by mapping their mechanics onto those of two incompatible, interconnected networks. We find that zero-dimensional clusters, three-dimensional bulks as well as symmetry-broken one-dimensional filaments and two-dimensional layers can all form depending on assembly parameters. Poorly compressible, moderately adhesive subunits favor filaments. These findings hint at a generic pathway to control self-assembly in three dimensions and suggests that such mechanisms could be investigated in more realistic protein models.

cond-mat.soft↗

arXiv2025

A Microfluidic Platform for Actin-Based Membrane Remodeling Reveals the Stabilizing Role of Branched Actin Networks on Lipid Microdomains

Cell shape changes, essential for processes such as motility or division, are controlled by the actomyosin cortex that actively remodels biological membranes. Their mechanisms can be deciphered in___vitro using biomimetic reconstituted systems, such as giant unilamellar vesicles (GUVs) with controlled lipid composition coupled to reconstituted actin networks. These assays allow mimicking cell shape changes in controlled biochemical and biophysical environments. However, studying the dynamics of these shape changes on statistically significant populations of GUVs with the possibility to sequentially modify the protein composition of the assay is a major experimental challenge. To address these issues, a microfluidic approach is used to immobilize several dozens of isolated GUVs and monitor membrane and actin network evolution. The loading of the chamber with GUVs and actin is first characterized. Then, the actin-induced remodeling of populations of homogeneous and phase-separated GUVs is monitored and shows that actin networks prevent the coalescence of lipid microdomains and that, in return, the number of domains affects the actin network structure. This microfluidic-based experimental strategy, thus, allows for studying actin-induced membrane deformation in___vitro and can be adapted to other studies on membrane remodeling processes.

cond-mat.soft↗

arXiv2025

Topological defect engineering enables size and shape control in self-assembly

The self-assembly of complex structures from engineered subunits is a major goal of nanotechnology, but controlling their size becomes increasingly difficult in larger assemblies. Existing strategies present significant challenges, among which the use of multiple subunit types or the precise control of their shape and mechanics. Here we introduce an alternative approach based on identical subunits whose interactions promote crystals, but also favor crystalline defects. We theoretically show that topological restrictions on the scope of these defects in large assemblies imply that the assembly size is controlled by the magnitude of the defect-inducing interaction. Using DNA origami, we experimentally demonstrate both size and shape control in two-dimensional disk- and fiber-like assemblies. Our basic concept of defect engineering could be generalized well beyond these simple examples, and thus provide a broadly applicable scheme to control self-assembly.

cond-mat.soft↗

arXiv2024

Stress Isotropization in Weakly Jammed Granular Packings

When sheared, granular media experience localized plastic events known as shear transformations which generate anisotropic internal stresses. Under strong confining pressure, the response of granular media to local force multipoles is essentially linear, resulting in quadrupolar propagated stresses. This can lead to additional plastic events along the direction of relative stress increase. Closer to the unjamming transition however, as the confining pressure and the shear modulus vanish, nonlinearities become relevant. Yet, the consequences of these nonlinearities on the stress response to plastic events remains poorly understood. We show with granular dynamics simulations that this brings about an isotropization of the propagated stresses, in agreement with a previously developed continuum elastic model. This could significantly modify the yielding transition of weakly-jammed amorphous media, which has been conceptualized as an avalanche of such plastic events.

cond-mat.soft↗

arXiv2024

Transient contacts between filaments impart its elasticity to branched actin

Branched actin networks exert pushing forces in eukaryotic cells, and adapt their stiffness to their environment. The physical basis for their mechanics and adaptability is however not understood. Indeed, here we show that their high density and low connectivity place them outside the scope of standard elastic network models for actin. We combine high-precision mechanical experiments, molecular dynamics simulations and a mean-field elastic theory to show that they are instead dominated by the proliferation of interfilament contacts under compression. This places branched actin in the same category as undercoordinated, fibrous materials such as sheep's wool. When the network is grown under force, filaments entangle as if knitted together and trap contacts in their structure. Trapped contacts play a similar role as crosslinkers in rigidifying the network, and are thus key to its active adaptive mechanics.

cond-mat.soft↗

arXiv2024

Specific yet transient bonds between anisotropic colloids

Self-assembly of colloidal particles is a promising avenue to control the shape and dynamics of larger aggregates. However, achieving the necessary fine control over the dynamics and specificity of the bonds between such particles remains a challenge. Here we demonstrate such control in bonds mediated by depletion interactions between anisotropic colloids that we 3D-print in the shape of half disks with sub-micron resolution. When brought together by diffusion, the particles interact in different configurations but the interaction through the flat faces is by far the longest-lasting. All bonds are flexible and transient, and we demonstrate control over their life time through the depletant concentration in quantitative agreement with a simple physical model. This basic design could be extended to manufacture particles with multiple binding sites to engineer directional assembly with multiple particles.

cond-mat.soft↗

arXiv2023

How do particles with complex interactions self-assemble?

In living cells, proteins self-assemble into large functional structures based on specific interactions between molecularly complex patches. Due to this complexity, protein self-assembly results from a competition between a large number of distinct interaction energies, of the order of one per pair of patches. Current self-assembly models however typically ignore this aspect, and the principles by which it determines the large-scale structure of protein assemblies are largely unknown. Here, we use Monte-Carlo simulations and machine learning to start to unravel these principles. We observe that despite widespread geometrical frustration, aggregates of particles with complex interactions fall within only a few categories that often display high degrees of spatial order, including crystals, fibers, and oligomers. We then successfully identify the most relevant aspect of the interaction complexity in predicting these outcomes, namely the particles' ability to form periodic structures. Our results provide a first extensive characterization of the rich design space associated with identical particles with complex interactions, and could inspire engineered self-assembling nanoobjects as well as help understand the emergence of robust functional protein structures.

cond-mat.soft↗

arXiv2023

Transverse fluctuations control the assembly of semiflexible filaments

The kinetics of the assembly of semiflexible filaments through end-to-end annealing is key to the structure of the cytoskeleton, but is not understood. We analyze this problem through scaling theory and simulations, and uncover a regime where filaments ends find each other through bending fluctuations without the need for the whole filament to diffuse. This results in a very substantial speed-up of assembly in physiological regimes, and could help understand the dynamics of actin and intermediate filaments in biological processes such as wound healing and cell division.

cond-mat.soft↗

arXiv2022

Runaway Transition in Irreversible Polymer Condensation with Cyclisation

The process of polymer condensation, i.e. the formation of bonds between reactive end-groups, is ubiquitous in both industry and biology. Here we study generic systems undergoing polymer condensation in competition with cyclisation. Using a generalised Smoluchowski theory, molecular dynamics simulations and experiments using DNA and T4 ligase, we find that this system displays a transition, from a regime with finite-length chains at infinite time and dominated by rings to one dominated by linear polymers that grow in time. Finally, we show that fluids prepared close to the transition may have profoundly different compositions and rheology at large condensation times.

cond-mat.soft↗

arXiv2022

Generic Stress Rectification in Nonlinear Elastic Media

Stress propagation in nonlinear media is crucial in cell biology, where molecular motors exert anisotropic force dipoles on the fibrous cytoskeleton. While the force dipoles can be either contractile or expansile, a medium made of fibers which buckle under compression rectifies these stresses towards a biologically crucial contraction. A general understanding of this rectification phenomenon as a function of the medium's elasticity is however lacking. Here we use theoretical continuum elasticity to show that rectification is actually a very general effect in nonlinear materials subjected to anisotropic internal stresses. We analytically show that both bucklable and constitutively linear materials subjected to geometrical nonlinearities rectify small forces towards contraction, while granular-like materials rectify towards expansion. Using simulations, we moreover show that these results extend to larger forces. Beyond fiber networks, these results could shed light on the propagation of stresses in brittle or granular materials following a local plastic rearrangement.

cond-mat.soft↗

arXiv2021

Valence can control the nonexponential viscoelastic relaxation of multivalent reversible gels

Gels made of telechelic polymers connected by reversible crosslinkers are a versatile design platform for biocompatible viscoelastic materials. Their linear response to a step strain displays a fast, near-exponential relaxation when using low valence crosslinkers, while larger supramolecular crosslinkers bring about much slower dynamics involving a wide distribution of time scales whose physical origin is still debated. Here, we propose a model where the relaxation of polymer gels in the dilute regime originates from elementary events in which the bonds connecting two neighboring crosslinkers all disconnect. Larger crosslinkers allow for a greater average number of bonds connecting them, but also generate more heterogeneity. We characterize the resulting distribution of relaxation time scales analytically, and accurately reproduce stress relaxation measurements on metal-coordinated hydrogels with a variety of crosslinker sizes including ions, metal-organic cages, and nanoparticles. Our approach is simple enough to be extended to any crosslinker size and could thus be harnessed for the rational design of complex viscoelastic materials.

cond-mat.soft↗

arXiv2021

Twist-induced local curvature of filaments in DNA toroids

DNA toroidal bundles form upon condensation of one or multiple DNA filaments. DNA filaments in toroidal bundles are hexagonally packed, and collectively twist around the center line of the toroid. In a previous study, we and our coworkers argue that the filaments' curvature locally correlates with their density in the bundle, with the filaments less closely packed where their curvature appears to be higher. We base our claim on the assumption that twist has a negligible effect on the local curvature of filaments in DNA toroids. However, this remains to be proven. We fill this gap here, by calculating the distribution of filaments' curvature in a geometric model of twisted toroidal bundle, which we use to describe DNA toroids by an appropriate choice of parameters. This allows us to substantiate our previous study and suggest directions for future experiments.

cond-mat.soft↗

arXiv2020

Chiral active hexatics: Giant number fluctuations, waves and destruction of order

Active materials, composed of internally driven particles, have properties that are qualitatively distinct from matter at thermal equilibrium. However, the most spectacular departures from equilibrium phase behaviour are thought to be confined to systems with polar or nematic asymmetry. In this paper, we show that such departures are also displayed in more symmetric phases such as hexatics if, in addition, the constituent particles have chiral asymmetry. We show that chiral active hexatics whose rotation rate does not depend on density have giant number fluctuations. If the rotation rate depends on density, the giant number fluctuations are suppressed due to a novel orientation-density sound mode with a linear dispersion which propagates even in the overdamped limit. However, we demonstrate that beyond a finite but large lengthscale, a chirality and activity-induced relevant nonlinearity invalidates the predictions of the linear theory and destroys the hexatic order. In addition, we show that activity modifies the interactions between defects in the active chiral hexatic phase, making them non-mutual. Finally, to demonstrate the generality of a chiral active hexatic phase we show that it results from the melting of chiral active crystals in finite systems.

cond-mat.soft↗

arXiv2019

Geometry of martensite needles in shape memory alloys

We study the geometry of needle-shaped domains in shape-memory alloys. Needle-shaped domains are ubiquitously found in martensites around macroscopic interfaces between regions which are laminated in different directions, or close to macroscopic austenite/twinned-martensite interfaces. Their geometry results from the interplay of the local nonconvexity of the effective energy density with long-range (linear) interactions mediated by the elastic strain field, and is up to now poorly understood. We present a two-dimensional shape optimization model based on finite elasticity and discuss its numerical solution. Our results indicate that the tapering profile of the needles can be understood within finite elasticity, but not with linearized elasticity. The resulting tapering and bending reproduce the main features of experimental observations on NiAl.

physics.comp-ph↗

arXiv2019

Spontaneous rotation can stabilise ordered chiral active fluids

Active hydrodynamic theories are a powerful tool to study the emergent ordered phases of internally driven particles such as bird flocks, bacterial suspension and their artificial analogues. While theories of orientationally ordered phases are by now well established, the effect of chirality on these phases is much less studied. In this paper, we present the first complete dynamical theory of orientationally ordered chiral particles in two-dimensional incompressible systems. We show that phase-coherent states of rotating chiral particles are remarkably stable in both momentum-conserved and non-conserved systems in contrast to their non-rotating counterparts. Furthermore, defect separation -- which drives chaotic flows in non-rotating active fluids -- is suppressed by intrinsic rotation of chiral active particles. We thus establish chirality as a source of dramatic stabilization in active systems, which could be key in interpreting the collective behaviours of some biological tissues, cytoskeletal systems and collections of bacteria.

cond-mat.soft↗

arXiv2019

Swimmer suspensions on substrates: anomalous stability and long-range order

We present a comprehensive theory of the dynamics and fluctuations of a two-dimensional suspension of polar active particles in an incompressible fluid confined to a substrate. We show that, depending on the sign of a single parameter, a state with polar orientational order is anomalously stable (or anomalously unstable), with a nonzero relaxation (or growth) rate for angular fluctuations at zero wavenumber. This screening of the broken-symmetry mode in the stable state does lead to conventional rather than giant number fluctuations as argued by Bricard et al., Nature ${\bf 503}$, 95 (2013), but their bend instability in a splay-stable flock does not exist and the polar phase has long-range order in two dimensions. Our theory also describes confined three-dimensional thin-film suspensions of active polar particles as well as dense compressible active polar rods, and predicts a flocking transition without a banding instability

cond-mat.soft↗

arXiv2018

Fiber plucking by molecular motors yields large emergent contractility in stiff biopolymer networks

The mechanical properties of the cell depend crucially on the tension of its cytoskeleton, a biopolymer network that is put under stress by active motor proteins. While the fibrous nature of the network is known to strongly affect the transmission of these forces to the cellular scale, our understanding of this process remains incomplete. Here we investigate the transmission of forces through the network at the individual filament level, and show that active forces can be geometrically amplified as a transverse motor-generated force force "plucks" the fiber and induces a nonlinear tension. In stiff and densely connnected networks, this tension results in large network-wide tensile stresses that far exceed the expectation drawn from a linear elastic theory. This amplification mechanism competes with a recently characterized network-level amplification due to fiber buckling, suggesting that that fiber networks provide several distinct pathways for living systems to amplify their molecular forces.

cond-mat.soft↗