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Lipid membrane deformations have been predicted to lead to indirect forces between the objects that induce these deformations. Recent experimental measurements have found an attractive interaction between spherical particles that all induce a deformation towards the inside of a giant unilamellar vesicle. Here, we complement these experimental observations by investigating the interactions between deformations pointing in opposite directions with respect to the membrane normal vector. This is experimentally realized by a particle deforming the membrane towards the inside of the GUV and pulling a membrane tube towards the outside of the membrane. Particles completely wrapped by the membrane are repelled from the tube with a strength of 3~k$_B$T at a distance of 0.5~$\mu$m. However, particles that strongly curve the membrane by adhering only to a patch of about 50~\% of its surface area are attracted to the center of the tube with a strength of -5.3~k$_B$T at a minimum distance of about 1~$\mu$m. We find that such Janus particles also experience attractive interactions when both deforming the membrane in the same way. These quantitative experimental observations provide new insights into interactions between oppositely membrane deforming objects, important for cooperative protein assembly at or interactions of microplastics with cell membranes.

Catalytic microswimmers typically swim close to walls due to hydrodynamic and/or phoretic effects. The walls in turn are known to affect their propulsion, making it difficult to single out the contributions that stem from particle-based catalytic propulsion only, thereby preventing an understanding of the propulsion mechanism. Here, we use acoustic tweezers to lift catalytically active Janus spheres away from the wall to study their motion in bulk and when approaching a wall. Mean-squared displacement analysis shows that diffusion constants at different heights match with Fax\'en's prediction for the near-wall hydrodynamic mobility. Both particles close to a substrate and in bulk show a decrease in velocity with increasing salt concentration, suggesting that the dominant factor for the decrease in speed is a reduction of the swimmer-based propulsion. The velocity-height profile follows a hydrodynamic scaling relation as well, implying a coupling between the wall and the swimming speed. The observed speed reduction upon addition of salt matches expectations from a electrokinetic theory, except for experiments in 0.1 wt% hydrogen peroxide in bulk, which could indicate contributions from a different propulsion mechanism. Our results help with the understanding of ionic effects on microswimmers in 3D and point to a coupling between the wall and the particle that affects its self-propulsion speed.

Flexibility governs the many properties of materials and is crucial for the function of proteins and biopolymers. However, how the self-assembly of flexibly bonded particles can lead to larger structures with global reconfigurability is unexplored. We here use a binary colloidal model system equipped with flexible DNA-based bonds to study how regular structures with tunable flexibility can be created through self-assembly. We find that the reconfigurability during lattice growth leads to lattices with square symmetry which are inherently mechanically unstable and hence thermally floppy. By considering the role of size ratio, number ratio, and directionality induced by particle shape, we identify the optimal pathways that maximize the yield and flexibility of these square lattices using a combination of experiments, analytical calculations, and simulations. Our study highlights the crucial role of reconfigurability in systems that are governed by enthalpic and entropic principles, from synthetic to biological, and might be useful for creating materials with novel or reconfigurable properties., Comment: 40 pages, 10 figures

Membrane-induced interactions have been predicted to be important for the organization of membrane proteins. Measurements of the interactions between two and three membrane deforming objects have revealed their non-additive nature. They are thought to lead to complex many-body effects, however, experimental evidence is lacking to date. We here present an experimental method to measure many-body effects in membrane-mediated interactions using colloidal spheres placed between a deflated giant unilamellar vesicles and a planar substrate. The thus confined colloidal particles cause a large deformation of the membrane while not being physochemically attached to it and interact through it. Two particles are found to attract with a maximum force of 0.2~pN. For three particles, we observe a preference for forming compact equilateral triangles over a linear arrangement. We use numerical energy minimization to establish that the attraction stems from a reduction in the membrane-deformation energy caused by the particles. Confining up to 36 particles, we find a preference for hexagonally close packed clusters. However, with increasing number of particles the order of the confined particles decreases, while at the same time, diffusivity of the particles increases. Our experiments for the first time show that the non-additive nature of membrane-mediated interactions affects the interactions and arrangements and ultimately leads to spherical aggregates with liquid-like order of potential importance for cellular processes.

Active colloidal microswimmers serve as archetypical active fluid systems, and as models for biological swimmers. Here, by studying in detail their velocity traces, we find robust power-law intermittency with system-dependent exponential cut off. We model the motion by an interplay of the field gradient-dependent active force and the locally fluctuating hydrodynamic drag, set by the wetting properties of the substrate. The model closely describes the velocity distributions of two disparate swimmer systems: AC field activated and catalytic swimmers. The generality is highlighted by the collapse of all data in a single master curve, suggesting the applicability to further systems, both synthetic and biological., Comment: 5 pages, 3figures

Cluster formation of microscopic swimmers is key to the formation of biofilms and colonies, efficient motion and nutrient uptake, but, in the absence of other interactions, requires high swimmer concentrations to occur. Here we experimentally and numerically show that cluster formation can be dramatically enhanced by an anisotropic swimmer shape. We analyze a class of model microswimmers with a shape that can be continuously tuned from spherical to bent and straight rods. In all cases, clustering can be described by Michaelis-Menten kinetics governed by a single scaling parameter that depends on particle density and shape only. We rationalize these shape-dependent dynamics from the interplay between interlocking probability and cluster stability. The bent rod shape promotes assembly even at vanishingly low particle densities and we identify the most efficient shape to be a semicircle. Our work provides key insights into how shape can be used to rationally design out-of-equilibrium self-organization, key to creating active functional materials and designing targeted two-component drug delivery.

Floppy microscale spring networks are widely studied in theory and simulations, but no well-controlled experimental system currently exists. Here, we show that square lattices consisting of colloid-supported lipid bilayers functionalized with DNA linkers act as microscale floppy spring networks. We extract their normal modes by inverting the particle displacement correlation matrix, showing the emergence of a spectrum of soft modes with low effective stiffness in addition to stiff modes that derive from linker interactions. Evaluation of the softest mode, a uniform shear mode, reveals that shear stiffness decreases with lattice size. Experiments match well with Brownian particle simulations and we develop a theoretical description based on mapping interactions onto linear response to describe the modes. Our results reveal the importance of entropic steric effects, and can be used for developing reconfigurable materials at the colloidal length scale.

Weak multivalent interactions govern a large variety of biological processes like cell-cell adhesion and virus-host interactions. These systems distinguish sharply between surfaces based on receptor density, known as superselectivity. Earlier experimental and theoretical work provided insights into the control of selectivity: Weak interactions and a high number of ligands facilitate superselectivity. Present experimental studies typically involve tens or hundreds of interactions, resulting in a high entropic contribution leading to high selectivities. However, if, and if so how, systems with few ligands, such as multi-domain proteins and virus binding to a membrane, show superselective behavior is an open question. Here, we address this question with a multivalent experimental model system based on star shaped branched DNA nanostructures (DNA nanostars) with each branch featuring a single stranded overhang that binds to complementary receptors on a target surface. Each DNA nanostar possesses a fluorophore, to directly visualize DNA nanostar surface adsorption by total internal reflection fluorescence microscopy (TIRFM). We observe that DNA nanostars can bind superselectively to surfaces and bind optimally at a valency of three. We quantitatively explain this optimum by extending the current theory with interactions between DNA nanostar binding sites (ligands). Our results add to the understanding of multivalent interactions, by identifying microscopic mechanisms that lead to optimal selectivity, and providing quantitative values for the relevant parameters. These findings inspire additional design rules which improve future work on selective targeting in directed drug delivery., Comment: 14 pages, 4 figures

Many cell functions require a concerted effort from multiple membrane proteins, for example, for signaling, cell division, and endocytosis. One contribution to their successful self-organization stems from the membrane deformations that these proteins induce. While the pairwise interaction potential of two membrane deforming spheres has recently been measured, membrane-deformation induced interactions have been predicted to be non-additive and hence their collective behavior cannot be deduced from this measurement. We here employ a colloidal model system consisting of adhesive spheres and giant unilamellar vesicles to test these predictions by measuring the interaction potential of the simplest case of three membrane-deforming spherical particles. We quantify their interactions and arrangements and for the first time experimentally confirm and quantify the non-additive nature of membrane-deformation induced interactions. We furthermore conclude that there exist two favorable configurations on the membrane: (1) a linear, and (2) a triangular arrangement of the three spheres. Using Monte Carlo simulation we corroborate the experimentally observed energy minima and identify a lowering of the membrane deformation as the cause for the observed configurations. The high symmetry of the preferred arrangements for three particles suggests that arrangements of many membrane-deforming objects might follow simple rules.

Endocytosis is a key cellular process involved in the uptake of nutrients, pathogens or the diagnosis and therapy of diseases. Most studies have focused on spherical objects, whereas biologically relevant shapes can be highly anisotropic. In this letter, we use an experimental model system based on Giant Unilamellar Vesicles (GUVs) and dumbbell-shaped colloidal particles to mimic and investigate the first stage of the passive endocytic process: engulfment of an anisotropic object by the membrane. Our model has specific ligand-receptor interactions realized by mobile receptors on the vesicles and immobile ligands on the particles. Through a series of experiments, theory and molecular dynamics simulations, we quantify the wrapping process of anisotropic dumbbells by GUVs and identify distinct stages of the wrapping pathway. We find that the strong curvature variation in the neck of the dumbbell as well as membrane tension are crucial in determining both the speed of wrapping and the final states.

Colloidal molecules are ideal model systems for mimicking real molecules and can serve as versatile building blocks for the bottom-up self-assembly of flexible and smart materials. While most colloidal molecules are rigid objects, the development of colloidal joints has made it possible to also include conformational flexibility into colloidal molecules. However, their unrestricted range of motion does not capture the restricted motion range and bond directionality that is typical of real molecules. In this work, we create flexible colloidal molecules with an in situ controllable motion range and bond directionality by assembling spherical particles onto cubes functionalized with complementary surface-mobile DNA. We assemble colloidal molecules with different coordination number of spheres by varying the size ratio and find that they feature a constrained range of motion above a critical size ratio. Using theory and simulations, we show that the particle shape together with the multivalent bonds create an effective free-energy landscape for the motion of the sphere on the surface of the cube. We quantify the confinement of the spheres on the surface of the cube and the probability to change facet. We find that temperature can be used as an extra control parameter to switch in situ between full and constrained flexibility of these colloidal molecules. These flexible colloidal molecules with temperature switching motion range can be used to investigate the effect of directional, yet flexible bonds in determining their self-assembly and phase behavior, and may be employed as constructional units in microrobotics and novel smart materials

Ring, or cyclic, polymers have unique properties compared to linear polymers, due to their topologically closed structure that has no beginning or end. Experimental measurements on molecular ring polymers are challenging due to their polydispersity in molecular weight and the presence of undesired side products such as chains. Here, we study an experimental model system for cyclic polymers, that consists of rings of flexibly-linked micron-sized colloids with $n$=4..8 segments. We characterize the conformations of these flexible colloidal rings and find that they are freely-jointed up to steric restrictions. We measure their diffusive behavior and compare it to hydrodynamic simulations. Interestingly, flexible colloidal rings have a larger translational and rotational diffusion coefficient compared to colloidal chains. In contrast to chains, their internal deformation mode shows slower fluctuations for $n\lesssim 8$ and saturates for higher values of $n$. We show that constraints stemming from the ring structure cause this decrease in flexibility for small $n$ and infer the expected scaling of the flexibility as function of ring size. Our findings could have implications for the behavior of both synthetic and biological ring polymers, as well as for the dynamic modes of floppy colloidal materials.

Hypothesis: Colloidal molecules with anisotropic shapes and interactions are powerful model systems for deciphering the behavior of real molecules and building units for creating materials with designed properties. While many strategies for their assembly have been developed, they typically yield a broad distribution or are limited to a specific type. We hypothesize that the shape and relative sizes of colloidal particles can be exploited to efficiently direct their assembly into colloidal molecules of desired valence. Experiments: We exploit electrostatic self-assembly of negatively charged spheres made from either polystyrene or silica onto positively charged hematite cubes. We thoroughly analyze the role of the shape and size ratio of particles on the cluster size and yield of colloidal molecules. Findings: Using a combination of experiments and simulations, we demonstrate that cubic particle shape is crucial to generate high yields of distinct colloidal molecules over a wide variety of size ratios. We find that electrostatic repulsion between the satellite spheres is important to leverage the templating effect of the cubes, leading the spheres to preferentially assemble on the facets rather than the edges and corners of the cube. Furthermore, we reveal that our protocol is not affected by the specific choice of the material of the colloidal particles. Finally, we show that the permanent magnetic dipole moment of the hematite cubes can be utilized to separate colloidal molecules from non-assembled satellite particles. Our simple and effective strategy might be extended to other templating particle shapes, thereby greatly expanding the library of colloidal molecules that can be achieved with high yield and purity.

Colloidal molecules are designed to mimic their molecular analogues through their anisotropic shape and interactions. However, current experimental realizations are missing the structural flexibility present in real molecules thereby restricting their use as model systems. We overcome this limitation by assembling reconfigurable colloidal molecules from silica particles functionalized with mobile DNA linkers in high yields. We achieve this by steering the self-assembly pathway towards the formation of finite-sized clusters by employing high number ratios of particles functionalized with complementary DNA strands. The size ratio of the two species of particles provides control over the overall cluster size, or, "valence", as well as the degree of reconfigurability. The bond flexibility provided by the mobile linkers allows the successful assembly of colloidal clusters with the geometrically expected maximum valence. We quantitatively examine the self-assembly dynamics of these flexible colloidal molecules by a combination of experiments, molecular dynamics simulations, and an analytical model. Our "flexible colloidal molecules" are exciting building blocks for investigating and exploiting the self-assembly of complex hierarchical structures, photonic crystals and colloidal meta-materials.

For biologically relevant macromolecules such as intrinsically disordered proteins, internal degrees of freedom that allow for shape changes have a large influence on both the motion and function of the compound. A detailed understanding of the effect of flexibility is needed in order to explain their behavior. Here, we study a model system of freely-jointed chains of three to six colloidal spheres, using both simulations and experiments. We find that in spite of their short lengths, their conformational statistics are well described by two-dimensional Flory theory, while their average translational and rotational diffusivity follow the Kirkwood-Riseman scaling. Their maximum flexibility does not depend on the length of the chain, but is determined by the near-wall in-plane translational diffusion coefficient of an individual sphere. Furthermore, we uncover shape-dependent effects in the short-time diffusivity of colloidal tetramer chains, as well as non-zero couplings between the different diffusive modes. Our findings may have implications for understanding both the diffusive behavior and the most likely conformations of macromolecular systems in biology and industry, such as proteins, polymers, single-stranded DNA and other chain-like molecules., Comment: 19 pages, 10 figures

Reliably distinguishing between cells based on minute differences in receptor density is crucial for cell-cell or virus-cell recognition, the initiation of signal transduction and selective targeting in directed drug delivery. Such sharp differentiation between different surfaces based on their receptor density can only be achieved by multivalent interactions. Several theoretical and experimental works have contributed to our understanding of this "superselectivity", however a versatile, controlled experimental model system that allows quantitative measurements on the ligand-receptor level is still missing. Here, we present a multivalent model system based on colloidal particles equipped with surface-mobile DNA linkers that can superselectively target a surface functionalized with the complementary mobile DNA-linkers. Using a combined approach of light microscopy and Foerster Resonance Energy Transfer (FRET), we can directly observe the binding and recruitment of the ligand-receptor pairs in the contact area. We find a non-linear transition in colloid-surface binding probability with increasing ligand or receptor concentration. In addition, we observe an increased sensitivity with weaker ligand-receptor interactions and we confirm that the time-scale of binding reversibility of individual linkers has a strong influence on superselectivity. These unprecedented insights on the ligand-receptor level provide new, dynamic information into the multivalent interaction between two fluidic membranes mediated by both mobile receptors and ligands and will enable future work on the role of spatial-temporal ligand-receptor dynamics on colloid-surface binding.

Cooperative motion in biological microswimmers is crucial for their survival as it facilitates adhesion to surfaces, formation of hierarchical colonies, efficient motion, and enhanced access to nutrients. Synthetic microswimmers currently lack truly cooperative behavior that originates from activity-induced interactions. Here, we demonstrate that catalytic microswimmers show a variety of cooperative behaviors along one-dimensional paths. We show that their speed increases with the number of swimmers, while the activity induces a preferred distance between swimmers. Using a minimal model, we ascribe this behavior to an effective activity-induced potential that stems from a competition between chemical and hydrodynamic coupling. These interactions further induce active self-assembly into trains as well as compact chains that can elongate, break-up, become immobilized and remobilized. We identify the crucial role that environment morphology and swimmer directionality play on these highly dynamic chain behaviors. These activity-induced interactions open the door towards exploiting cooperation for increasing the efficiency of, as well as provide temporal and spatial control over, microswimmer motion, thereby enabling them to perform intricate tasks inside complex environments.

The membrane curvature of cells and intracellular compartments continuously adapts to enable cells to perform vital functions, from cell division to signal trafficking. Understanding how membrane geometry affects these processes in vivo is challenging because of the membrane complexity as well as the short time and small length scales involved. By contrast, in vitro model membranes with engineered curvature provide a versatile platform for this investigation and applications to biosensing and biocomputing. However, a general route to the fabrication of lipid membranes with prescribed curvature and high spatial resolution is still missing. Here, we present a strategy that overcomes these challenges and achieve lipid membranes with designed shape by combining 3D micro-printing and replica-molding lithography to create scaffolds with virtually any geometry and high spatial resolution. The resulting supported lipid membranes are homogeneous, fluid, and can form chemically distinct lipid domains. These features are essential for understanding curvature-dependent cellular processes and developing programmable bio-interfaces for living cells and nanostructures.

Impurity-induced defects play a crucial role for the properties of crystals, but little is known about impurities with anisotropic shape. Here, we study how colloidal dumbbells distort and interact with a hexagonal crystal of charged colloidal spheres at a fluid interface. We find that subtle changes in the dumbbell length induce a transition from a local distortion to a particle-bound dislocation, and determine how the dumbbell moves inside the repulsive hexagonal lattice. Our results provide new routes towards controlling material properties through particle-bound dislocations.

Geometric confinement strongly influences the behavior of microparticles in liquid environments. However, to date, nonspherical particle behaviors close to confining boundaries, even as simple as planar walls, remain largely unexplored. Here, we measure the height distribution and orientation of colloidal dumbbells above walls by means of digital in-line holographic microscopy. We find that while larger dumbbells are oriented almost parallel to the wall, smaller dumbbells of the same material are surprisingly oriented at preferred angles. We determine the total height-dependent force acting on the dumbbells by considering gravitational effects and electrostatic particle-wall interactions. Our modeling reveals that at specific heights both net forces and torques on the dumbbells are simultaneously below the thermal force and energy, respectively, which makes the observed orientations possible. Our results highlight the rich near-wall dynamics of nonspherical particles, and can further contribute to the development of quantitative frameworks for arbitrarily-shaped microparticle dynamics in confinement., Comment: Ruben W. Verweij and Stefania Ketzetzi contributed equally to this work. 17 pages and 7 figures

Microswimmers typically move near walls, which can strongly influence their motion. However, direct experimental measurements of swimmer-wall separation remain elusive to date. Here, we determine this separation for model catalytic microswimmers from the height dependence of the passive component of their mean-squared displacement. We find that swimmers exhibit "ypsotaxis", a tendency to assume a fixed height above the wall for a range of salt concentrations, swimmer surface charges, and swimmer sizes. Our findings indicate that ypsotaxis is activity-induced, posing restrictions on future modeling of their still debated propulsion mechanism.

Shape changes resulting from segmental flexibility are ubiquitous in molecular and biological systems, and are expected to affect both the diffusive motion and (biological) function of dispersed objects. The recent development of colloidal structures with freely-jointed bonds have now made a direct experimental investigation of diffusive shape-changing objects possible. Here, we show the effect of segmental flexibility on the simplest possible model system, a freely-jointed cluster of three spherical particles, and validate long-standing theoretical predictions. We find that in addition to the rotational diffusion time, an analogous conformational diffusion time governs the relaxation of the diffusive motion, unique to flexible assemblies, and that their translational diffusivity differs by a small but measurable amount. We also uncovered a Brownian quasiscallop mode, where diffusive motion is coupled to Brownian shape changes. Our findings could have implications for molecular and biological systems where diffusion plays an important role, such as functional site availability in lock-and-key protein interactions., Comment: Ruben W. Verweij and Pepijn G. Moerman contributed equally to this work. 22 pages, 11 figures

Experiments on supported lipid bilayers featuring liquid ordered/disordered domains have shown that the spatial arrangement of the lipid domains and their chemical composition are strongly affected by the curvature of the substrate. Furthermore, theoretical predictions suggest that both these effects are intimately related with the closed topology of the bilayer. In this work, we test this hypothesis by fabricating supported membranes consisting of colloidal particles of various shapes lying on a flat substrate. A single lipid bilayer coats both colloids and substrate, allowing local lipid exchange between them, thus rendering the system thermodynamically open, i.e. able to exchange heat and molecules with an external reservoir in the neighborhood of the colloid. By reconstructing the Gibbs phase diagram for this system, we demonstrate that the free-energy landscape is directly influenced by the geometry of the colloid. In addition, we find that local lipid exchange enhances the pinning of the liquid disordered phase in highly curved regions. This allows us to provide estimates of the bending moduli difference of the domains. Finally, by combining experimental and numerical data, we forecast the outcome of possible experiments on catenoidal and conical necks and show that these geometries could greatly improve the precision of the current estimates of the bending moduli., Comment: 11 pages, 7 figures

We study the global influence of curvature on the free energy landscape of two-dimensional binary mixtures confined on closed surfaces. Starting from a generic effective free energy, constructed on the basis of symmetry considerations and conservation laws, we identify several model-independent phenomena, such as a curvature-dependent line tension and local shifts in the binodal concentrations. To shed light on the origin of the phenomenological parameters appearing in the effective free energy, we further construct a lattice-gas model of binary mixtures on non-trivial substrates, based on the curved-space generalization of the two-dimensional Ising model. This allows us to decompose the interaction between the local concentration of the mixture and the substrate curvature into four distinct contributions, as a result of which the phase diagram splits into critical sub-diagrams. The resulting free energy landscape can admit, as stable equilibria, strongly inhomogeneous mixed phases, which we refer to as antimixed states below the critical temperature. We corroborate our semi-analytical findings with phase-field numerical simulations on realistic curved lattices. Despite this work being primarily motivated by recent experimental observations of multi-component lipid vesicles supported by colloidal scaffolds, our results are applicable to any binary mixture confined on closed surfaces of arbitrary geometry., Comment: 20 Pages, 7 Figures; comments and references added, typos corrected

Catalytic colloidal swimmers that propel due to self-generated fluid flows exhibit strong affinity for surfaces. We here report experimental measurements of significantly different velocities of such microswimmers in the vicinity of substrates made from different materials. We find that velocities scale with the solution contact angle $\theta$ on the substrate, which in turn relates to the associated hydrodynamic substrate slip length, as $V\propto(\cos\theta+1)^{-3/2}$. We show that such dependence can be attributed to osmotic coupling between swimmers and substrate. Our work points out that hydrodynamic slip at the wall, though often unconsidered, can significantly impact the self-propulsion of catalytic swimmers.

The use of colloidal supported lipid bilayers (CSLBs) has recently been extended to create colloidal joints, that - in analogy to their macroscopic counterparts - can flexibly connect colloidal particles. These novel elements enable the assembly of structures with internal degrees of flexibility, but rely on previously unappreciated properties: the simultaneous fluidity of the bilayer, lateral mobility of inserted (linker) molecules and colloidal stability. Here we characterize every step in the manufacturing of CSLBs in view of these requirements using confocal microscopy and fluorescence recovery after photobleaching (FRAP). Specifically, we have studied the influence of different particle properties (roughness, surface charge, chemical composition, polymer coating) on the quality and mobility of the supported bilayer. We find that the insertion of lipopolymers in the bilayer can affect its homogeneity and fluidity. We improve the colloidal stability by inserting lipopolymers or double-stranded inert DNA into the bilayer. Finally, we include surface-mobile DNA linkers and use FRAP to characterize their lateral mobility both in their freely diffusive and bonded state. Our work offers a collection of experimental tools for working with CSLBs in applications ranging from controlled bottom-up self-assembly to model membrane studies., Comment: 23 pages, 12 figures (includes Supporting Information)

Motivated by recent experimental work on multicomponent lipid membranes supported by colloidal scaffolds, we report an exhaustive theoretical investigation of the equilibrium configurations of binary mixtures on curved substrates. Starting from the J\"ulicher-Lipowsky generalization of the Canham-Helfrich free energy to multicomponent membranes, we derive a number of exact relations governing the structure of an interface separating two lipid phases on arbitrarily shaped substrates and its stability. We then restrict our analysis to four classes of surfaces of both applied and conceptual interest: the sphere, axisymmetric surfaces, minimal surfaces and developable surfaces. For each class we investigate how the structure of the geometry and topology of the interface is affected by the shape of the substrate and we make various testable predictions. Our work sheds light on the subtle interaction mechanism between membrane shape and its chemical composition and provides a solid framework for interpreting results from experiments on supported lipid bilayers., Comment: 26 pages, 10 figures

Unravelling the physical mechanisms behind the organisation of lipid domains is a central goal in cell biology and membrane biophysics. Previous studies on cells and model lipid bilayers featuring phase-separated domains found an intricate interplay between the membrane geometry and its chemical composition. However, the lack of a model system with simultaneous control over the membrane shape and conservation of its composition precluded a fundamental understanding of curvature-induced effects. Here, we present a new class of multicomponent vesicles supported by colloidal scaffolds of designed shape. We find that the domain composition adapts to the geometry, giving rise to a novel "antimixed" state. Theoretical modelling allowed us to link the pinning of domains by regions of high curvature to the material parameters of the membrane. Our results provide key insights into the phase separation of cellular membranes and on curved surfaces in general., Comment: 5 pages, 3 figures

Understanding interactions between microparticles and lipid membranes is of increasing importance, especially for unraveling the influence of microplastics on our health and environment. Here, we study how a short-ranged adhesive force between microparticles and model lipid membranes causes membrane-mediated particle assembly. Using confocal microscopy, we observe the initial particle attachment to the membrane, then particle wrapping, and in rare cases spontaneous membrane tubulation. In the attached state, we measure that the particle mobility decreases by 26%. If multiple particles adhere to the same vesicle, their initial single-particle state determines their interactions and subsequent assembly pathways: 1) attached particles only aggregate when small adhesive vesicles are present in solution, 2) wrapped particles reversibly attract one another by membrane deformation, and 3) a combination of wrapped and attached particles form membrane-mediated dimers, which further assemble into a variety of complex structures. The experimental observation of distinct assembly pathways induced only by a short ranged membrane-particle adhesion, shows that a cellular cytoskeleton or other active components are not required for microparticle aggregation. We suggest that this membrane-mediated microparticle aggregation is a reason behind reported long retention times of polymer microparticles in organisms., Comment: 20 pages, 11 figures (including supporting material)

The miniaturization of machines towards the micron and nanoscales requires the development of joint-like elements that enable and constrain motion. We present a facile method to create colloidal joints, that is, anisotropic colloidal particles containing surface mobile DNA linkers that control the motion range of bonded particles. We demonstrate quantitatively that we can control the flexibility of these colloidal joints by tuning the DNA linker concentration in the bond area. We show that the colloidal shape controls the range of motion that these colloidal joints enable, due to the finite-sized patch of bonded linkers that cannot cross regions of high curvature. Finally we demonstrate the potential of the colloidal joints for programmable bottom-up self-assembly by creating flexible colloidal molecules and colloidal polymers. The reconfigurability and motion constraint offered by our colloidal joints make them promising building blocks for the development of switchable materials and nanorobots.

Quantitative tracking of features from video images is a basic technique employed in many areas of science. Here, we present a method for the tracking of features that partially overlap, in order to be able to track so-called colloidal molecules. Our approach implements two improvements into existing particle tracking algorithms. Firstly, we use the history of previously identified feature locations to successfully find their positions in consecutive frames. Secondly, we present a framework for non-linear least-squares fitting to summed radial model functions and analyze the accuracy (bias) and precision (random error) of the method on artificial data. We find that our tracking algorithm correctly identifies overlapping features with an accuracy below 0.2% of the feature radius and a precision of 0.1 to 0.01 pixels for a typical image of a colloidal cluster. Finally, we use our method to extract the three-dimensional diffusion tensor from the Brownian motion of colloidal dimers., Comment: 20 pages, 8 figures. Non-revised preprint version, please refer to http://dx.doi.org/10.1088/1361-648X/29/4/044001

The interplay of membrane proteins is vital for many biological processes, such as cellular transport, cell division, and signal transduction between nerve cells. Theoretical considerations have led to the idea that the membrane itself mediates protein self-organization in these processes through minimization of membrane curvature energy. Here, we present a combined experimental and numerical study in which we quantify these interactions directly for the first time. In our experimental model system we control the deformation of a lipid membrane by adhering colloidal particles. Using confocal microscopy, we establish that these membrane deformations cause an attractive interaction force leading to reversible binding. The attraction extends over 2.5 times the particle diameter and has a strength of three times the thermal energy (-3.3 kT). Coarse-grained Monte-Carlo simulations of the system are in excellent agreement with the experimental results and prove that the measured interaction is independent of length scale. Our combined experimental and numerical results reveal membrane curvature as a common physical origin for interactions between any membrane-deforming objects, from nanometre-sized proteins to micrometre-sized particles., Comment: 15 pages, 12 figures, Published in Scientific Reports (open access): http://www.nature.com/articles/srep32825 Supplementary Material available via the given URL

The self-assembly of anisotropic patchy particles with triangular shape was studied by experiments and computer simulations. The colloidal particles were synthesized in a two-step seeded emulsion polymerization process, and consist of a central smooth lobe connected to two rough lobes at an angle of $\sim$90$^{\circ}$, resembling the shape of a "Mickey Mouse" head. Due to the difference in overlap volume, adding an appropriate depletant induces an attractive interaction between the smooth lobes of the colloids only, while the two rough lobes act as steric constraints. The essentially planar geometry of the "Mickey Mouse" particles is a first geometric deviation of dumbbell shaped patchy particles. This new geometry is expected to form one-dimensional tube-like structures rather than spherical, essentially zero-dimensional micelles. At sufficiently strong attractions, we indeed find tube-like structures with the sticky lobes at the core and the non-sticky lobes pointing out as steric constraints that limit the growth to one direction, providing the tubes with a well-defined diameter but variable length both in experiments and simulations. In the simulations, we found that the internal structure of the tubular fragments could either be straight or twisted into so-called Bernal spirals.

We synthesize colloidal particles with various anisotropic shapes and track their orientationally resolved Brownian trajectories using confocal microscopy. An analysis of appropriate short-time correlation functions provides direct access to the hydrodynamic friction tensor of the particles revealing nontrivial couplings between the translational and rotational degrees of freedom. The results are consistent with calculations of the hydrodynamic friction tensor in the low-Reynolds-number regime for the experimentally determined particle shapes., Comment: 5 pages, 2 figures