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Developing a model for assembly of colloids with mobile binding sites, we probe the physics of assembly of adhesion patches between particles. We find design rules for assembly of low valence chains, and also study the folding behavior of these ‘colloidomers’.

In the realm of particle self-assembly, it is possible to reliably construct nearly arbitrary structures if all the pieces are distinct

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 inter-particle 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 microscopic 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.

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 (

We characterize the motility of athermal swimming droplets within the framework of a persistent random walk. Just like active colloids, their trajectories can be modeled with a constant velocity V and a slow angular diffusion, but the random changes in direction are not thermally driven. Instead, V is determined by the interfacial tension gradient along the droplet surface, while reorientation of the surfactant gradient leads to changes in direction with a persistence time τ. We show that the origin of locomotion is the difference in the critical micellar concentration in the front and the back of the droplet, ΔCMC. Tuning this parameter by salt controls V from 3 to 15 diameters d/s. Surfactant concentration has little effect on speed, but leads to a dramatic decrease in τ over 4 orders of magnitude. The corresponding range of the persistence length ℓ=Vτ extends beyond the realm of synthetic or living swimmers, in which V is limited by fuel consumption and τ is set by thermal fluctuations or biological activity, respectively. Our tunable swimmers are ideal candidates for the study of the departure from equilibrium to high levels of activity. We show that their collective behavior exhibits the formation of active clusters of a well-defined size.

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.

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.

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.

Peptides and proteins represent attractive building blocks for the development of new functional materials due to the biocompatibility and biodegradability of many naturally abundant proteins. In nature, sophisticated material functionality is commonly achieved through spatial control of protein localisation and structure on both the nano and micro scales. We approached this requirement in an artificial setting by exploiting the propensity of proteins to self-assemble into amyloid fibrils to achieve nano scale order, and utilised aqueous liquid/liquid phase separation to control the micron scale localization of the proteinaceous component under microconfinement. We show that in combination with droplet microfluidics, this strategy allows the synthesis of core-shell microgel particles composed of protein nanofibrils.

Complex structures and devices, both natural and manmade, are often constructed sequentially. From crystallization to embryogenesis, a nucleus or seed is formed and built upon. Sequential assembly allows for initiation, signaling, and logical programming, which are necessary for making enclosed, hierarchical structures. Although biology relies on such schemes, they have not been available in materials science. Here, we demonstrate programmed sequential self-assembly of DNA functionalized emulsions. The droplets are initially inert because the grafted DNA strands are pre-hybridized in pairs. Active strands on initiator droplets then displace one of the paired strands and thus release its complement, which in turn activates the next droplet in the sequence, akin to living polymerization. Our strategy provides time and logic control during the self-assembly process, and offers a new perspective on the synthesis of materials., Natural complex systems are often constructed by sequential assembly but this is not readily available for synthetic systems. Here, the authors program the sequential self-assembly of DNA functionalized emulsions by altering the DNA grafted strands.

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.

Marine-gel biopolymers were recently visualized at the molecular level using atomic force microscopy (AFM) to reveal fine fibril-forming networks with low to high degrees of cross-linking. In this work, we use force spectroscopy to quantify the intra- and intermolecular forces within the marine-gel network. Combining force measurements, AFM imaging, and the known chemical composition of marine gels allows us to identify the microscopic origins of distinct mechanical responses. At the single-fibril level, we uncover force-extension curves that resemble those of individual polysaccharide fibrils. They exhibit entropic elasticity followed by extensions associated with chair-to-boat transitions specific to the type of polysaccharide at high forces. Surprisingly, a low degree of cross-linking leads to sawtooth patterns that we attribute to the unraveling of polysaccharide entanglements. At a high degree of cross-linking, we observe force plateaus that arise from unzipping, as well as unwinding, of helical bundles. Finally, the complex 3D network structure gives rise to force staircases of increasing height that correspond to the hierarchical peeling of fibrils away from the junction zones. In addition, we show that these diverse mechanical responses also arise in reconstituted polysaccharide gels, which highlights their dominant role in the mechanical architecture of marine gels.

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(omega) exhibits a low-frequency cutoff omega*, which scales linearly with the number of extra contacts per particle delta(z). Moreover, for omega < omega*, our results are consistent with D(omega) similar to omega(2)/omega*(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. During, 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.

Force-clamp spectroscopy reveals the unfolding and disulfide bond rupture times of single protein molecules as a function of the stretching force, point mutations, and solvent conditions. The statistics of these times reveal whether the protein domains are independent of one another, the mechanical hierarchy in the polyprotein chain, and the functional form of the probability distribution from which they originate. It is therefore important to use robust statistical tests to decipher the correct theoretical model underlying the process. Here, we develop multiple techniques to compare the well-established experimental data set on ubiquitin with existing theoretical models as a case study. We show that robustness against filtering, agreement with a maximum likelihood function that takes into account experimental artifacts, the Kuiper statistic test, and alignment with synthetic data all identify the Weibull or stretched exponential distribution as the best fitting model. Our results are inconsistent with recently proposed models of Gaussian disorder in the energy landscape or noise in the applied force as explanations for the observed nonexponential kinetics. Because the physical model in the fit affects the characteristic unfolding time, these results have important implications on our understanding of the biological function of proteins.

We report a study of reversible adsorption of DNA-coated colloids on complementary functionalized oil droplets. We show that it is possible to control the surface coverage of oil droplets using colloidal particles by exploiting the fact that, during slow adsorption, compositional arrest takes place well before structural arrest occurs. As a consequence, we can prepare colloid-coated oil droplets with a "frozen" degree of loading but with fully ergodic colloidal dynamics on the droplets. We illustrate the equilibrium nature of the adsorbed colloidal phase by exploring the quasi-two-dimensional phase behavior of the adsorbed colloids under the influence of depletion interactions and present simulations of a simple model that illustrates the nature of the compositional arrest and the structural ergodicity., A.C. acknowledges support from the ETN-COLLDENSE (H2020-MCSA-ITN-2014, grant no. 642774). E.E. and J. Burelbach thank the Winton Programme for the Physics of Sustainability for the Pump Prime Grant and the scholarship award, respectively. D.J. thanks the Udayan Care-VCare grant, the Nehru Trust for Cambridge University, the Schlumberger Foundation’s Faculty for the Future Program, and Hughes Hall Santander Bursary Scholarship. Z.X. thanks the National University of Defense Technology Scholarship at Cambridge. A.S.N., D.E.P.P., and N.A.M.A. acknowledge financial support from the Portuguese Foundation for Science and Technology (FCT) (grants EXCL/FIS-NAN/ 0083/2012, UID/FIS/00618/2013, and IF/00255/2013). J. Brujic thanks the Materials Research Science and Engineering Center program of the National Science Foundation under Award DMR-1420073 and L. L. Pontani.

Paradigmatic model systems, which are used to study the mechanical response of matter, are random networks of point-atoms, random sphere packings, or simple crystal lattices; all of these models assume central-force interactions between particles/atoms. Each of these models differs in the spatial arrangement and the correlations among particles. In turn, this is reflected in the widely different behaviours of the shear (G) and compression (K) elastic moduli. The relation between the macroscopic elasticity as encoded in G, K and their ratio and the microscopic lattice structure/order, is not understood. We provide a quantitative analytical connection between the local orientational order and the elasticity in model amorphous solids with different internal microstructure, focusing on the two opposite limits of packings (strong excluded-volume) and networks (no excluded-volume). The theory predicts that, in packings, the local orientational order due to excluded-volume causes less nonaffinity (less softness or larger stiffness) under compression than under shear. This leads to lower values of G/K, a well-documented phenomenon which was lacking a microscopic explanation. The theory also provides an excellent one-parameter description of the elasticity of compressed emulsions in comparison with experimental data over a broad range of packing fractions.

Reconstructing free energy profiles is an important problem in bimolecular reactions, protein folding or allosteric conformational changes. Nonequilibrium trajectories are readily measured experimentally, but their statistical significance and relation to equilibrium system properties still call for rigorous methods of assessment and interpretation. Here we introduce methods to compute the equilibrium free energy profile of a given variable from a set of short nonequilibrium trajectories, obtained by externally driving a system out of equilibrium and subsequently observing its relaxation. This protocol is not suitable for the Jarzynski equality since the irreversible work on the system is instantaneous. Assuming that the variable of interest satisfies an overdamped Langevin equation, which is frequently used for modeling biomolecular processes, we show that the trajectories sample a nonequilibrium stationary distribution that can be calculated in closed form. This allows for the estimation of the free energy via an inversion procedure that is analogous to that used in equilibrium and bypasses more complicated path integral methods, which we derive for comparison. We generalize the inversion procedure to systems with a diffusion constant that depends on the reaction coordinate, as is the case in protein folding, as well as to protocols in which the trajectories are initiated at random points. Using only a statistical pool of tens of synthetic trajectories, we demonstrate the versatility of these methods by reconstructing double and multi-well potentials, as well as a proposed profile for the hydrophobic collapse of a protein.

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.

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.

The introduction of disulfide bonds into proteins creates additional mechanical barriers and limits the unfolded contour length (i.e., the maximal extension) measured by single-molecule force spectroscopy. Here, we engineer single disulfide bonds into four different locations of the human cardiac titin module (I27) to control the contour length while keeping the distance to the transition state unchanged. This enables the study of several biologically important parameters. First, we are able to precisely determine the end-to-end length of the transition state before unfolding (53 Angstrom), which is longer than the end-to-end length of the protein obtained from NMR spectroscopy (43 Angstrom). Second, the measured contour length per amino acid from five different methods (4.0 +/- 0.2 Angstrom) is longer than the end-to-end length obtained from the crystal structure (3.6 Angstrom). Our measurement of the contour length takes into account all the internal degrees of freedom of the polypeptide chain, whereas crystallography measures the end-to-end length within the "frozen" protein structure. Furthermore, the control of contour length and therefore the number of amino acids unraveled before reaching the disulfide bond (n) facilitates the test of the chain length dependence on the folding time (tau(F)). We find that both a power law scaling tau(F) lambda n(lambda) with lambda = 4.4, and an exponential scaling with n(0.6) fit the data range, in support of different protein-folding scenarios.

The conformational energy landscape of a protein out of equilibrium is poorly understood. We use single-molecule force-clamp spectroscopy to measure the kinetics of unfolding of the protein ubiquitin under a constant force. We discover a surprisingly broad distribution of unfolding rates that follows a power law with no characteristic mean. The structural fluctuations that give rise to this distribution reveal the architecture of the protein’s energy landscape. Following models of glassy dynamics, this complex kinetics implies large fluctuations in the energies of the folded protein, characterized by an exponential distribution with a width of 5–10kBT. Our results predict the existence of a ‘glass transition’ force below which the folded conformations interconvert between local minima on multiple timescales. These techniques offer a new tool to further test statistical energy landscape theories experimentally.

For packed i.e., “jammed”, hard and rough objects kinetic energy is a minor and ignorable quantity, as is elastic strain. Hence in the static case, the stress equations need supplementing by “missing equations” depending solely on configurations. A different pathway of analysis is the calculation of the probability distribution of interparticle forces. This paper presents the mini-review of recently obtained results in this field and poses a number of fundamental problems which are yet to be solved.

The micromechanics of a variety of systems experiencing a structural arrest due to their high density could be unified by a thermodynamic framework governing their approach to ‘jammed’ configurations. The mechanism of supporting an applied stress through the microstructure of these highly packed materials is important in inferring the features responsible for the inhomo- geneous stress transmission and testing the universality for all jammed matter. In this paper, we present a novel method for measuring the force distribution within the bulk of a compressed emulsion system using confocal microscopy and explain our results with a simple theoretical model and computer simulations. We obtain an exponential distribution at large forces and a small peak at small forces, in agreement with previous experimental and simulation data for other particulate systems.

The slow dynamics of granular flow is studied as an extension of static granular problems, which, as a consequence of shaking or related regimes, can be studied by the methods of statistical mechanics. For packed (i.e. 'jammed'), hard and rough objects, kinetic energy is a minor and ignorable quantity, as is strain. Hence, in the static case, the stress equations need supplementing by 'missing equations' depending solely on configurations. These are in the literature; this paper extends the equilibrium studies to slow dynamics, claiming that the strain rate (which is a consequence of flow, not of elastic strain) takes the place of stress, and as before, the analogue of Stokes's equation has to be supplemented by new 'missing equations' which are derived and which depend only on configurations.

Particulate packings in 3D are used to study the effects of compression and polydispersity on the geometry of the tiling in these systems. We find that the dependence of the neighbor number on cell size is quasilinear in the monodisperse case and becomes nonlinear above a threshold polydispersity, independent of the method of creation of the tiling. These size-topology relations can be described by a simple analytical theory, which quantifies the effects of positional disorder in the monodisperse case and those of size disorder in the polydisperse case and is applicable in two and three dimensions. The theory thus gives a unifying framework for a wide range of amorphous systems, ranging from biological tissues, foams, and bidisperse disks to compressed emulsions and granular matter.

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.

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.

International audience; We propose a statistical model for the random packing of frictionless polydisperse spheres in which the complexity of the global packing is distilled into a local stochastic process. We simplify the problem by considering the "granocentric" point of view of a single particle in the bulk, thereby reducing random packing to the assembly of nearest neighbours, followed by a random choice of contacts among them. The model is based on only two parameters, the available solid angle around each particle and the ratio of contacts to neighbors, which are both directly obtainable from experiments or simulations. As a result, the model analytically predicts the microscopic distributions of nearest neighbours and contacts, the local density fluctuations as well as the global density of the packing. We find that this granocentric view captures the essential properties of the polydisperse emulsion packing. This model suggests a general principle of organization for random packing and provides a statistical tool for quantifying the effect of the particle size distribution on the geometry of random packing in a variety of contexts of industrial relevance.

The nature of the random assembly of granular particles is a fundamental and ancient problem in physics and mathematics, with practical applications in situations as different as oil extraction through porous rocks, grain storage and the manufacture of tablets from powders. To date there is no known simple underlying mechanism for granular particles analogous to crystalline ordering. A team from the Center for Soft Matter Research at New York University has measured the packing of polydisperse emulsion droplets, finding that the complexity of the global packing structure can be understood in terms of a 'granocentric' view. A statistical model based on two simple, local parameters — the available space around a particle and the ratio of contacts to neighbours — successfully predicts both the local and global characteristics of packings, including their connectivity and density. A simple underlying mechanism for the random assembly of granular particles, analogous to crystalline ordering, remains unknown. Here however, three-dimensional measurements of packings of polydisperse emulsion droplets are used to build a statistical model where the complexity of the global packing can be understood in terms of two simple, local parameters — the available space around a particle and the ratio of contacts to neighbours. Packing problems are ubiquitous1,2, ranging from oil extraction through porous rocks to grain storage in silos and the compaction of pharmaceutical powders into tablets. At a given density, particulate systems pack into a mechanically stable and amorphous jammed state3,4. Previous theoretical studies have explored a connection between this jammed state and the glass transition4,5,6,7,8, the thermodynamics of jamming9,10,11,12 and geometric modelling of random packings13,14,15. Nevertheless, a simple underlying mechanism for the random assembly of athermal particles, analogous to crystalline ordering, remains unknown. Here we use three-dimensional measurements of packings of polydisperse emulsion droplets to build a simple statistical model in which the complexity of the global packing is distilled into a local stochastic process. From the perspective of a single particle, the packing problem is reduced to the random formation of nearest neighbours, followed by a choice of contacts among them. The two key parameters in the model—the available space around a particle and the ratio of contacts to neighbours—are directly obtained from experiments. We demonstrate that this ‘granocentric’ view captures the properties of the polydisperse emulsion packing—ranging from the microscopic distributions of nearest neighbours and contacts, to local density fluctuations, to the global packing density. Application of our results to monodisperse and bidisperse systems produces quantitative agreement with previously measured trends in global density16. Our model therefore reveals a general principle of organization for random packing and may provide the foundations for a theory of jammed matter.

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.

Jammed matter is by definition impenetrable to light, such that little is known about the geometry of jammed systems. Using confocal microscopy to image an emulsion in 3D, we first explain the origin of the enhanced fluorescence at the droplet contacts and then determine the contact network inside the model frictionless system. This enables the experimental determination of the average coordination number $⟨Z⟩$ which agrees with the isostatic predicted value of $⟨Z⟩\ensuremath{\approx}6$. Furthermore, we calculate the entropy of the packing from the network of contacts.

Single-protein force experiments have relied on a molecular fingerprint based on tethering multiple single-protein domains in a polyprotein chain. However, correlations between these domains remain an issue in interpreting force spectroscopy data, particularly during protein folding. Here we first show that force-clamp spectroscopy is a sensitive technique that provides a molecular fingerprint based on the unfolding step size of four single-monomer proteins. We then measure the force-dependent unfolding rate kinetics of ubiquitin and I27 monomers and find a good agreement with the data obtained for the respective polyproteins over a wide range of forces, in support of the Markovian hypothesis. Moreover, with a large statistical ensemble at a single force, we show that ubiquitin monomers also exhibit a broad distribution of unfolding times as a signature of disorder in the folded protein landscape. Furthermore, we readily capture the folding trajectories of monomers that exhibit the same stages in folding observed for polyproteins, thus eliminating the possibility of entropic masking by other unfolded modules in the chain or domain-domain interactions. On average, the time to reach the I27 folded length increases with increasing quenching force at a rate similar to that of the polyproteins. Force-clamp spectroscopy at the single-monomer level reproduces the kinetics of unfolding and refolding measured using polyproteins, which proves that there is no mechanical effect of tethering proteins to one another in the case of ubiquitin and I27.

Elastic and dissipative properties of granular assemblies under uniaxial compression are studied both experimentally and by numerical simulations. Following a novel compaction procedure at varying oscillatory pressures, the stress response to a step-strain reveals an exponential relaxation followed by a slow logarithmic decay. Simulations indicate that the latter arises from the coupling between damping and collective grain motion predominantly through sliding. We characterize an analogous "glass transition" for packed grains, below which the system shows aging in time-dependent sliding correlation functions., Comment: 5 pages, 5 figures

A thermodynamic formulation of jammed matter is reviewed. Experiments and simulations of compressed emulsions and granular materials are then used to provide a foundation for the thermodynamics., Comment: 51 pages, 21 figures

This chapter highlights the use of statistical mechanics tools in situations where the system is out of equilibrium and jammed. The chapter illustrates the derivation of Boltzmann equation for a jammed granular system and shows that the Boltzmann's analysis can be used to produce a “Second Law” for jammed systems. In a thermal system, the Brownian motion of the constituent particles implies that the system dynamically explores the available energy landscape, such that the notion of a statistical ensemble applies. For densely packed systems in which enduring contacts between particles are important, the potential energy barrier prohibits an equivalent random motion. At first sight it seems that the thermal statistical mechanics do not apply to these systems as there is no mechanism for averaging over the configurational states. Hence, these systems are inherently out of equilibrium. The chapter highlights the fundamental questions in this area of physics and points out the key quantities in characterizing a packing of particles, accessible through a novel experimentation method that is also presented.

We study the phase behavior of immiscible mixtures of phospholipids and cholesterol at the interface of oil-in-water emulsions. Such mixtures spontaneously decompose into domains on the surface of the droplets, similar to the presence of lipid rafts in cells, presenting the possibility of new biomimetic studies without constructing liposomes. Using a microfluidic device we control the production of monodisperse emulsions and map out a ternary immiscibility diagram allowing for the control of various surface morphologies, including spots, stripes, and hemispheres. All morphologies are found to be accessible using only binary mixtures of either cholesterol and DOPC or cholesterol and sphingomyelin. By functionalizing those controlled patterns with biotinylated lipids, we also make useful candidates for directed self-assembly with specific interactions via streptavidin. Using confocal microscopy and image analysis we find that domains grow to a maximum size and then remain stable against coarsening on a timescale of weeks. Surprisingly stability is not compromised by the presence of increasing amounts of salt, indicating that the stabilizing force is not of electrostatic origin. We investigate and discuss the potential driving forces for the stability of the domains and different lipid compositions could lead to different stabilization mechanisms.

Ubiquitous features of particle collections whose individual elements are locked in place haveinspired physicists tosearch for general principles that describe random packing.

We study the phase behavior of immiscible mixtures of phospholipids and cholesterol at the interface of oil-in-water emulsions, which governs the surface morphology of patchy droplets. Emulsification with lipid mixtures leads to domain formation with a variety of shapes, such as spots, disordered stripes, hemispheres and rings. We map out the ternary immiscibility diagram of our system, which allows one to control the geometry of patches on the droplet surface. By contrast to short-lived domains on liposomes, image analysis of the individual domains shows that emulsion spots grow towards a steady state size distribution and remain stable over weeks. These domains are functionalized with biotinylated lipids, which makes them useful candidates for directed self-assembly through specific interactions via streptavidin. Here we bind streptavidin coated beads to these lipids and find that the binder diffusion constant depends on the morphology of the droplet. These fluid patchy particles offer a versatile system in which the geometry and the dynamics of the sticky patches are under control.

We present a generalization of the granocentric model proposed in [Clusel et al., Nature, 2009, 460, 611–615] that is capable of describing the local fluctuations inside not only polydisperse but also monodisperse packings of spheres. This minimal model does not take into account the relative particle positions, yet it captures positional disorder through local stochastic processes sampled by efficient Monte Carlo methods. The disorder is characterized by the distributions of local parameters, such as the number of neighbors and contacts, filled solid angle around a central particle and the cell volumes. The model predictions are in good agreement with our experimental data on monodisperse random close packings of PMMA particles. Moreover, the model can be used to predict the distributions of local fluctuations in any packing, as long as the average number of neighbors, contacts and the packing fraction are known. These distributions give a microscopic foundation to the statistical mechanics framework for jammed matter and allow us to calculate thermodynamic quantities such as the compactivity in the phase space of possible jammed configurations.

Science moves forward when new techniques uncover unanticipated results, and the field of protein folding is no exception. Indeed, our force-clamp spectroscopy measurements of the folding of ubiquitin chains ([ 1 ][1]) revealed trajectories that departed from the expected two-state folding reactions

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.

A system’s equilibrium variance can be analyzed to probe its underlying dynamics at higher resolution. Here, using single-molecule atomic-force microscope techniques, we show how the variance in the length of a single dextran molecule can be used to establish thermodynamic equilibrium and to detect conformational changes not directly observable with other methods. Dextran is comprised of a chain of pyranose rings that each undergoes an Angstrom-scale transition from a chair to boat conformation under a stretching force. Our analysis of the variance of the molecule’s fluctuations verifies equilibrium throughout the force-extension curve, consistent with the expected thermodynamic ensemble. This validates further analysis of the variance in the transition region, which reveals an intermediate conformation between the chair and the boat on the sub-Angstrom scale. Our test of thermal equilibrium as well as our variance analysis can be readily extended to a wide variety of molecules, including proteins.

Using the recently developed single molecule force-clamp technique we quantitatively measure the kinetics of conformational changes of polyprotein molecules at a constant force. In response to an applied force of 110 pN, we measure the dwell times of 1647 unfolding events of individual ubiquitin modules within each protein chain. We then establish a rigorous method for analyzing force-clamp data using order statistics. This allows us to test the success of a history-independent, two-state model in describing the kinetics of the unfolding process. We find that the average unfolding trajectory is independent of the number of protein modules N in each trajectory, which varies between 3 and 12 (the engineered protein length), suggesting that the unfolding events in each chain are uncorrelated. We then derive a binomial distribution of dwell times to describe the stochastic dynamics of protein unfolding. This distribution successfully describes 81% of the data with a single rate constant of alpha = 0.6 s(-1) for all N. The remainder of the data that cannot be accounted for suggests alternative unfolding barriers in the energy landscape of the protein. This method investigates the statistical features of unfolding beyond the average measurement of a single rate constant, thus providing an attractive alternative for measuring kinetics by force-clamp spectroscopy.

In particulate materials, such as emulsions and granular media, a "jammed" system results if particles are packed together so that all particles are touching their neighbours, provided the density is sufficiently high. This paper studies through experiment, theory and simulation, the forces that particles exert upon one another in such a jammed state. Confocal microscopy of a compressed polydisperse emulsion provides a direct 3D measurement of the dispersed phase morphology within the bulk of the sample. This allows the determination of the probability distribution of interdroplet forces, P(f) where f is the magnitude of the force, from local droplet deformations. In parallel, the simplest form of the Boltzmann equation for the probability of force distributions predicts P(f) to be of the form e(-f/p), where p is proportional to the mean force f for large forces. This result is in good agreement with experimental and simulated data.

Determining the mechanism by which a protein folds remains a primary goal in biology. 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 experimentally, since the multiplicity of trajectories and folding structures is averaged out using bulk techniques. Moreover, most intermediate conformations are only transiently present, rendering their isolation and characterization difficult by commonly used spectroscopic methods. 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, mechanical stability and effect of solvent environment during each stage of folding. Here we discover that upon hydrophobic collapse, the protein rapidly selects a subset of non-native like, minimum energy structures that are mechanically weak and insensitive to the solvent environment. From this much reduced ensemble, the native state is acquired through a barrier-limited transition. The existence of such heterogeneous ensemble of minimum energy collapsed states was theoretically proposed by lattice simulations to be a milestone in the process of narrowing the available conformational space of a protein during its journey to the native fold, and a general feature of proteins that are naturally designed through evolution to fold on biological timescales. Here we demonstrate that such ensemble of collapsed states is also apparent in our experiments in the well-characterized I27 and Protein L proteins, albeit on different timescales, thus suggesting that their presence is ubiquitous to other mechanically stable proteins with a well-defined fold. Our results present the first experimental evidence for the validity of statistical mechanics models in describing the folding of small proteins on biological timescales.

In recent years reductionist biomimetic approaches have been able to reproduce complex biological phenomena, such as single cell locomotion or self-replication on the molecular scale. Here we address the effect of homeostatic pressure on cell-cell adhesion using densely packed emulsion droplets as a mimic for the mechanical and adhesive properties of biological tissues. 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. Furthermore, varying the 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, the adhesion size dependence on the applied force reveals adhesion strengthening with increasing homeostatic pressure even in the absence of active cellular processes. To further mimic the cell-cell adhesion we next replace the interdroplet biotin-streptavidin bonds with the extracellular domains of E-cadherins that are also grafted onto the lipid monolayer stabilizing the droplets. This new system of adhesive proteins unexpectedly leads to a very different behavior of the biomimetic emulsion: droplet fusion. This fusion involves the merging of the two lipid monolayers assembled on the surface of the droplets and can therefore shed light onto general fusion mechanisms. Our system reveals the role of both calcium ions and lipid domain segregation for the observed cadherin-mediated fusion. The variety of bio-inspired emulsions that can be designed with our system creates a rich playground for problems in biophysics.