Self-assembly of emulsion droplets through programmable folding.

In the realm of particle self-assembly, it is possible to reliably construct nearly arbitrary structures if all the pieces are distinct1-3, but systems with fewer flavours of building blocks have so far been limited to the assembly of exotic crystals4-6. Here we introduce a minimal model system of colloidal droplet chains7, with programmable DNA interactions that guide their downhill folding into specific geometries. Droplets are observed in real space and time, unravelling the rules of folding. Combining experiments, simulations and theory, we show that controlling the order in which interactions are switched on directs folding into unique structures, which we call colloidal foldamers8. The simplest alternating sequences (ABAB...) of up to 13 droplets yield 11 foldamers in two dimensions and one in three dimensions. Optimizing the droplet sequence and adding an extra flavour uniquely encodes more than half of the 619 possible two-dimensional geometries. Foldamers consisting of at least 13 droplets exhibit open structures with holes, offering porous design. Numerical simulations show that foldamers can further interact to make complex supracolloidal architectures, such as dimers, ribbons and mosaics. Our results are independent of the dynamics and therefore apply to polymeric materials with hierarchical interactions on all length scales, from organic molecules all the way to Rubik's Snakes. This toolbox enables the encoding of large-scale design into sequences of short polymers, placing folding at the forefront of materials self-assembly.

Refractive-index and density-matched emulsions with programmable DNA interactions.

Emulsion droplets on the colloidal length scale are a model system of frictionless compliant spheres. Direct imaging studies of the microscopic structure and dynamics of emulsions offer valuable insights into fundamental processes, such as gelation, jamming, and self-assembly. A microscope, however, can only resolve the individual droplets in a densely packed emulsion if the droplets are closely index-matched to their fluid medium. Mitigating perturbations due to gravity additionally requires the droplets to be density-matched to the medium. Creating droplets that are simultaneously index-matched and density-matched has been a long-standing challenge for the soft-matter community. The present study introduces a method for synthesizing monodisperse micrometer-sized siloxane droplets whose density and refractive index can be precisely and independently tuned by adjusting the volume fraction of three silane precursors. A systematic optimization protocol yields fluorescently labeled ternary droplets whose densities and refractive indexes match, to the fourth decimal place, those of aqueous solutions of glycerol or dimethylsiloxane. Because all of the materials in this system are biocompatible, we functionalize the droplets with DNA strands to endow them with programmed inter-droplet interactions. Confocal microscopy then reveals both the three-dimensional structure and the network of droplet-droplet contacts in a class of self-assembled droplet gels, free from gravitational effects. This experimental toolbox creates opportunities for studying the microscopic mechanisms that govern viscoelastic properties and self-assembly in soft materials.

DNA self-organization controls valence in programmable colloid design.

Just like atoms combine into molecules, colloids can self-organize into predetermined structures according to a set of design principles. Controlling valence-the number of interparticle bonds-is a prerequisite for the assembly of complex architectures. The assembly can be directed via solid "patchy" particles with prescribed geometries to make, for example, a colloidal diamond. We demonstrate here that the nanoscale ordering of individual molecular linkers can combine to program the structure of microscale assemblies. Specifically, we experimentally show that covering initially isotropic microdroplets with N mobile DNA linkers results in spontaneous and reversible self-organization of the DNA into Z(N) binding patches, selecting a predictable valence. We understand this valence thermodynamically, deriving a free energy functional for droplet-droplet adhesion that accurately predicts the equilibrium size of and molecular organization within patches, as well as the observed valence transitions with N Thus, microscopic self-organization can be programmed by choosing the molecular properties and concentration of binders. These results are widely applicable to the assembly of any particle with mobile linkers, such as functionalized liposomes or protein interactions in cell-cell adhesion.

Push-pull mechanics of E-cadherin ectodomains in biomimetic adhesions.

E-cadherin plays a central role in cell-cell adhesion. The ectodomains of wild-type cadherins form a crystalline-like two-dimensional lattice in cell-cell interfaces mediated by both trans (apposed cell) and cis (same cell) interactions. In addition to these extracellular forces, adhesive strength is further regulated by cytosolic phenomena involving α and ß catenin-mediated interactions between cadherin and the actin cytoskeleton. Cell-cell adhesion can be further strengthened under tension through mechanisms that have not been definitively characterized in molecular detail. Here we quantitatively determine the role of the cadherin ectodomain in mechanosensing. To this end, we devise an E-cadherin-coated emulsion system, in which droplet surface tension is balanced by protein binding strength to give rise to stable areas of adhesion. To reach the honeycomb/cohesive limit, an initial emulsion compression by centrifugation facilitates E-cadherin trans binding, whereas a high protein surface concentration enables the cis-enhanced stabilization of the interface. We observe an abrupt concentration dependence on recruitment into adhesions of constant crystalline density, reminiscent of a first-order phase transition. Removing the lateral cis interaction with a "cis mutant" shifts this transition to higher surface densities leading to denser, yet weaker adhesions. In both proteins, the stabilization of progressively larger areas of deformation is consistent with single-molecule experiments that show a force-dependent lifetime enhancement in the cadherin ectodomain, which may be attributed to the "X-dimer" bond.

A coarse-grained simulation model for colloidal self-assembly via explicit mobile binders.

Colloidal particles with mobile binding molecules constitute a powerful platform for probing the physics of self-assembly. Binding molecules are free to diffuse and rearrange on the surface, giving rise to spontaneous control over the number of droplet-droplet bonds, i.e., valence, as a function of the concentration of binders. This type of valence control has been realized experimentally by tuning the interaction strength between DNA-coated emulsion droplets. Optimizing for valence two yields droplet polymer chains, termed 'colloidomers', which have recently been used to probe the physics of folding. To understand the underlying self-assembly mechanisms, here we present a coarse-grained molecular dynamics (CGMD) model to study the self-assembly of this class of systems using explicit representations of mobile binding sites. We explore how valence of assembled structures can be tuned through kinetic control in the strong binding limit. More specifically, we optimize experimental control parameters to obtain the highest yield of long linear colloidomer chains. Subsequently tuning the dynamics of binding and unbinding via a temperature-dependent model allows us to observe a heptamer chain collapse into all possible rigid structures, in good agreement with recent folding experiments. Our CGMD platform and dynamic bonding model (implemented as an open-source custom plugin to HOOMD-Blue) reveal the molecular features governing the binding patch size and valence control, and opens the study of pathways in colloidomer folding. This model can therefore guide programmable design in experiments.

Emulsion patterns in the wake of a liquid-liquid phase separation front.

Miscible liquids can phase separate in response to a composition change. In bulk fluids, the demixing begins on molecular-length scales, which coarsen into macroscopic phases. By contrast, confining a mixture in microfluidic droplets causes sequential phase separation bursts, which self-organize into rings of oil and water to make multilayered emulsions. The spacing in these nonequilibrium patterns is self-similar and scale-free over a range of droplet sizes. We develop a modified Cahn-Hilliard model, in which an immiscibility front with stretched exponential dynamics quantitatively predicts the spacing of the layers. In addition, a scaling law predicts the lifetime of each layer, giving rise to a stepwise release of inner droplets. Analogously, in long rectangular capillaries, a diffusive front yields large-scale oil and water stripes on the time scale of hours. The same theory relates their characteristic length scale to the speed of the front and the rate of mass transport. Control over liquid-liquid phase separation into large-scale patterns finds potential material applications in living cells, encapsulation, particulate design, and surface patterning.

Multivalent, multiflavored droplets by design.

Nature self-assembles functional materials by programming flexible linear arrangements of molecules and then folding them to make 2D and 3D objects. To understand and emulate this process, we have made emulsion droplets with specific recognition and controlled valence. Uniquely monovalent droplets form dimers: divalent lead to polymer-like chains, trivalent allow for branching, and programmed mixtures of different valences enable a variety of designed architectures and the ability to subsequently close and open structures. Our functional building blocks are a hybrid of micrometer-scale emulsion droplets and nanoscale DNA origami technologies. Functional DNA origami rafts are first added to droplets and then herded into a patch using specifically designated "shepherding" rafts. Additional patches with the same or different specificities can be formed on the same droplet, programming multiflavored, multivalence droplets. The mobile patch can bind to a patch on another droplet containing complementary functional rafts, leading to primary structure formation. Further binding of nonneighbor droplets can produce secondary structures, a third step in hierarchical self-assembly. The use of mobile patches rather than uniform DNA coverage has the advantage of valence control at the expense of slow kinetics. Droplets with controlled flavors and valences enable a host of different material and device architectures.

Assembly and Dynamic Analysis of Square Colloidal Crystals via Templated Capillary Assembly.

Capillary assembly has the ability to engineer centimeter-sized regions of discrete colloidal superstructures and microarrays. However, its use as a tool for directing crystallization of colloids into surface-bound nonclose-packed arrays is limited. Furthermore, the use of quantitative particle tracking tools to investigate evaporative assembly dynamics is rarely employed. In this contribution, we use templated capillary assembly to fabricate square-packed lattices of spherical, organosilica colloids using designed patterned boundaries. Particle tracking algorithms reveal that the assembly of square-packed regions is controlled by the interplay between confinement-driven nuclei formation and osmotic pressure-driven restructuring. We find that the incorporation of a square template increases the yield of particles bearing four nearest neighbors (Zn = 4) from 4 to 39%, obtained using a heavier and more viscous solvent. Maximal square-packed domains occur at specific initial particle concentrations (1.75-2.25 wt % or φ = 0.013-0.017), indicating that rearrangements are a function of osmotic force. We use particle tracking methods to dynamically monitor conversions between square and hexagonal packing, revealing a cyclical transition between 4 and 6 coordinated particles throughout meniscus recession. Our method is highly scalable and inexpensive and can be adapted for use with different particle sizes and compositions, as well as for targeted open-packed geometries. Our findings will inform the large area, defect-free assembly of nonclose-packed lattices of unexplored varieties that are necessary for the continued expansion of colloid-based materials with vast applications in optical electronics.

Freely Jointed Polymers Made of Droplets.

An important goal of self-assembly is to achieve a preprogrammed structure with high fidelity. Here, we control the valence of DNA-functionalized emulsions to make linear and branched model polymers, or "colloidomers." The distribution of cluster sizes is consistent with a polymerization process in which the droplets achieve their prescribed valence. Conformational statistics reveal that the chains are freely jointed, so that the Kuhn length is close to one bead diameter. The end-to-end length scales with the number of bonds N as N^{ν}, where ν≈3/4, in agreement with the Flory theory in two dimensions. The chain diffusion coefficient D approximately scales as D∝N^{-ν}, as predicted by the Zimm model. Unlike molecular polymers, colloidomers can be repeatedly assembled and disassembled under temperature cycling, allowing for reconfigurable, responsive matter.

Cis and Trans Cooperativity of E-Cadherin Mediates Adhesion in Biomimetic Lipid Droplets.

The regulation of cell-cell adhesion is important in cell motility, tissue growth, and for the mechanical integrity of tissues. Although the role of active cytoskeleton dynamics in regulating cadherin interactions is crucial in vivo, here we present a biomimetic emulsion system to characterize the passive E-cadherin-mediated adhesion between droplets. The visualization of a three-dimensional assembly of lipid droplets, functionalized with extracellular E-cadherin domains, reveals a hierarchy of homophilic interactions. First, the high interfacial tension of droplets facilitates trans cadherin-cadherin adhesion, which is strong enough to stabilize looser than random close packing configurations. Second, fluorescence enhancement shows that adding clustering agents, such as calcium or chelating ligands, favor the lateral cis adhesion of the already bound cadherin pairs over the clustering of monomer cadherin on the surface. Finally, above a threshold cadherin and calcium concentration, the cis and trans protein interactions become strong enough to trigger and promote droplet fusion. While E-cadherin is not known to participate in cellular fusion, this mechanism is general because replacing calcium with cholesterol to cluster the cadherin-carrying lipids also promotes fusion. These results suggest that passive clustering, via calcium-induced dimerization or membrane ordering, may contribute to the reinforcement of cell-cell contacts. Alternatively, a molecular switch for fusion offers a route to mixing droplet contents and controlling their size in situ.

Evidence for Marginal Stability in Emulsions.

We report the first measurements of the effect of pressure on vibrational modes in emulsions, which serve as a model for soft frictionless spheres at zero temperature. As a function of the applied pressure, we find that the density of states D(ω) exhibits a low-frequency cutoff ω^{*}, which scales linearly with the number of extra contacts per particle δz. Moreover, for ω<ω^{*}, our results are consistent with D(ω)∼ω^{2}/ω^{*2}, a quadratic behavior whose prefactor is larger than what is expected from Debye theory. This surprising result agrees with recent theoretical findings [E. DeGiuli, A. Laversanne-Finot, G. A. Düring, E. Lerner, and M. Wyart, Soft Matter 10, 5628 (2014); S. Franz, G. Parisi, P. Urbani, and F. Zamponi, Proc. Natl. Acad. Sci. U.S.A. 112, 14539 (2015)]. Finally, the degree of localization of the softest low frequency modes increases with compression, as shown by the participation ratio as well as their spatial configurations. Overall, our observations show that emulsions are marginally stable and display non-plane-wave modes up to vanishing frequencies.

Biomimetic emulsions reveal the effect of mechanical forces on cell-cell adhesion.

Cell-cell contacts in tissues are continuously subject to mechanical forces due to homeostatic pressure and active cytoskeleton dynamics. In the process of cellular adhesion, the molecular pathways are well characterized but the role of mechanics is less well understood. To isolate the role of pressure we present a dense packing of functionalized emulsion droplets in which surface interactions are tuned to mimic those of real cells. By visualizing the microstructure in 3D we find that a threshold compression force is necessary to overcome electrostatic repulsion and surface elasticity and establish protein-mediated adhesion. Varying the droplet interaction potential maps out a phase diagram for adhesion as a function of force and salt concentration. Remarkably, fitting the data with our theoretical model predicts binder concentrations in the adhesion areas that are similar to those found in real cells. Moreover, we quantify the dependence of the area of adhesion on the applied force and thus reveal adhesion strengthening with increasing external pressure even in the absence of active cellular processes. This biomimetic approach reveals a physical origin of pressure-sensitive adhesion and its strength across cell-cell junctions.

Attractive emulsion droplets probe the phase diagram of jammed granular matter.

It remains an open question whether statistical mechanics approaches apply to random packings of athermal particles. Although a jamming phase diagram has recently been proposed for hard spheres with varying friction, here we use a frictionless emulsion system in the presence of depletion forces to sample the available phase space of packing configurations. Using confocal microscopy, we access their packing microstructure and test the theoretical assumptions. As a function of attraction, our packing protocol under gravity leads to well-defined jammed structures in which global density initially increases above random close packing and subsequently decreases monotonically. Microscopically, the fluctuations in parameters describing each particle, such as the coordination number, number of neighbors, and local packing fraction, are for all attractions in excellent agreement with a local stochastic model, indicating that long-range correlations are not important. Furthermore, the distributions of local cell volumes can be collapsed onto a universal curve using the predicted k-gamma distribution, in which the shape parameter k is fixed by the polydispersity while the effect of attraction is captured by rescaling the average cell volume. Within the Edwards statistical mechanics framework, this result measures the decrease in compactivity with global density, which represents a direct experimental test of a jamming phase diagram in athermal systems. The success of these theoretical tools in describing yet another class of materials gives support to the much-debated statistical physics of jammed granular matter.

Tailoring of high-order multiple emulsions by the liquid-liquid phase separation of ternary mixtures.

Multiple emulsions with an "onion" topology are useful vehicles for drug delivery, biochemical assays, and templating materials. They can be assembled by ternary liquid phase separation by microfluidics, but the control over their design is limited because the mechanism for their creation is unknown. Herein we show that phase separation occurs through self-similar cycles of mass transfer, spinodal decomposition or nucleation, and coalescence into multiple layers. Mapping out the phase diagram shows a linear relationship between the diameters of concentric layers, the slope of which depends on the initial ternary composition and the molecular weight of the surfactant. These general rules quantitatively predict the number of droplet layers (multiplicity), which we used to devise self-assembly routes for polymer capsules and liposomes. Moreover, we extended the technique to the assembly of lipid-stabilized droplets with ordered internal structures.

Metabolically intact nuclei are fluidized by the activity of the chromatin remodeling motor BRG1.

The structure and dynamics of the cell nucleus regulate nearly every facet of the cell. Changes in nuclear shape limit cell motility and gene expression. Although the nucleus is generally seen as the stiffest organelle in the cell, cells can nevertheless deform the nucleus to large strains by small mechanical stresses. Here, we show that the mechanical response of the cell nucleus exhibits active fluidization that is driven by the BRG 1 motor of the SWI/SNF/BAF chromatin-remodeling complex. Atomic force microscopy measurements show that the nucleus alters stiffness in response to the cell substrate stiffness, which is retained after the nucleus is isolated and that the work of nuclear compression is mostly dissipated rather than elastically stored. Inhibiting BRG 1 stiffens the nucleus and eliminates dissipation and nuclear remodeling both in isolated nuclei and in intact cells. These findings demonstrate a novel link between nuclear motor activity and global nuclear mechanics.

Domain-domain interactions in filamin A (16-23) impose a hierarchy of unfolding forces.

The quaternary structure of Filamin A (FLNa) 16-23 was recently shown to exhibit multiple domain-domain interactions that lead to a propeller-like construction. Here we present single-molecule force spectroscopy experiments to show a wide variety of mechanical responses of this molecule and compare it with its linear counterpart FLNa 1-8. The compact structure of FLNa 16-23 leads to a broad distribution of rupture forces and end-to-end lengths in the force-extension mode and multiple unraveling timescales in the force-clamp mode. Moreover, a subset of force-extension trajectories reveals a mechanical hierarchy in which the rupture of domain-domain interactions at high forces (>200 pN) liberates the unfolding of individual domains at low forces (∼100 pN). This mechanism may also explain the order-of-magnitude difference in the rates of the biexponential fits to the distribution of unfolding dwell times under force-clamp. Overall, FLNa 16-23 under a force of 100 pN is more compliant than the linear FLNa 1-8. Because a physiological role of FLNa is to crosslink actin filaments, this range of responses allows it to accommodate a broad spectrum of forces exerted by the cell and its environment.

Microscopic approach to the nonlinear elasticity of compressed emulsions.

Using confocal microscopy, we measure the packing geometry and interdroplet forces as a function of the osmotic pressure in a 3D emulsion system. We assume a harmonic interaction potential over a wide range of volume fractions and attribute the observed nonlinear elastic response of the pressure with density to the first corrections to the scaling laws of the microstructure away from the critical point. The bulk modulus depends on the excess contacts created under compression, which leads to the correction exponent α=1.5. Microscopically, the nonlinearities manifest themselves as a narrowing of the distribution of the pressure per particle as a function of the global pressure.

Force-dependent polymorphism in type IV pili reveals hidden epitopes.

Through evolution, nature has produced exquisite nanometric structures, with features unrealized in the most advanced man-made devices. Type IV pili (Tfp) represent such a structure: 6-nm-wide retractable filamentous appendages found in many bacteria, including human pathogens. Whereas the structure of Neisseria gonorrhoeae Tfp has been defined by conventional structural techniques, it remains difficult to explain the wide spectrum of functions associated with Tfp. Here we uncover a previously undescribed force-induced quaternary structure of the N. gonorrhoeae Tfp. By using a combination of optical and magnetic tweezers, atomic force microscopy, and molecular combing to apply forces on purified Tfp, we demonstrate that Tfp subjected to approximately 100 pN of force will transition into a new conformation. The new structure is roughly 3 times longer and 40% narrower than the original structure. Upon release of the force, the Tfp fiber regains its original form, indicating a reversible transition. Equally important, we show that the force-induced conformation exposes hidden epitopes previously buried in the Tfp fiber. We postulate that this transition provides a means for N. gonorrhoeae to maintain attachment to its host while withstanding intermittent forces encountered in the environment. Our findings demonstrate the need to reassess our understanding of Tfp dynamics and functions. They could also explain the structural diversity of other helical polymers while presenting a unique mechanism for polymer elongation and exemplifying the extreme structural plasticity of biological polymers.

Direct observation of an ensemble of stable collapsed states in the mechanical folding of ubiquitin.

Statistical theories of protein folding have long predicted plausible mechanisms for reducing the vast conformational space through distinct ensembles of structures. However, these predictions have remained untested by bulk techniques, because the conformational diversity of folding molecules has been experimentally unapproachable. Owing to recent advances in single molecule force-clamp spectroscopy, we are now able to probe the structure and dynamics of the small protein ubiquitin by measuring its length and mechanical stability during each stage of folding. Here, we discover that upon hydrophobic collapse, the protein rapidly selects a subset of minimum energy structures that are mechanically weak and essential precursors of the native fold. From this much reduced ensemble, the native state is acquired through a barrier-limited transition. Our results support the validity of statistical mechanics models in describing the folding of a small protein on biological timescales.

Solute-mediated interactions between active droplets.

Concentration gradients play a critical role in embryogenesis, bacterial locomotion, as well as the motility of active particles. Particles develop concentration profiles around them by dissolution, adsorption, or the reactivity of surface species. These gradients change the surface energy of the particles, driving both their self-propulsion and governing their interactions. Here, we uncover a regime in which solute gradients mediate interactions between slowly dissolving droplets without causing autophoresis. This decoupling allows us to directly measure the steady-state, repulsive force, which scales with interparticle distance as F∼1/r^{2}. Our results show that the dissolution process is diffusion rather than reaction rate limited, and the theoretical model captures the dependence of the interactions on droplet size and solute concentration, using a single fit parameter, l=16±3nm, which corresponds to the length scale of a swollen micelle. Our results shed light on the out-of-equilibrium behavior of particles with surface reactivity.