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# Arrested demixing opens route to bigels

Edited by David A. Weitz, Harvard University, Cambridge, MA, and approved October 2, 2012 (received for review September 7, 2012)

## Abstract

Understanding and, ultimately, controlling the properties of amorphous materials is one of the key goals of material science. Among the different amorphous structures, a very important role is played by colloidal gels. It has been only recently understood that colloidal gels are the result of the interplay between phase separation and arrest. When short-ranged attractive colloids are quenched into the phase-separating region, density fluctuations are arrested and this results in ramified amorphous space-spanning structures that are capable of sustaining mechanical stress. We present a mechanism of aggregation through arrested demixing in binary colloidal mixtures, which leads to the formation of a yet unexplored class of materials––bigels. This material is obtained by tuning interspecies interactions. Using a computer model, we investigate the phase behavior and the structural properties of these bigels. We show the topological similarities and the geometrical differences between these binary, interpenetrating, arrested structures and their well-known monodisperse counterparts, colloidal gels. Our findings are supported by confocal microscopy experiments performed on mixtures of DNA-coated colloids. The mechanism of bigel formation is a generalization of arrested phase separation and is therefore universal.

The properties of a self-assembled material are ultimately controlled by the interactions among its building blocks and by the conditions in which they are prepared. It is by tuning these two properties that different structures can be obtained. Short-ranged attractive colloidal systems, for example, can form crystals, two glasses of different origin, or gels. The latter have great technological importance. Colloidal gels find applications in synthetic colloid porous materials (1, 2), functionalization of surfaces and films production (3, 4), ceramics processing (5, 6), protein assemblies (7, 8), food science (9, 10), and soft matter (11, 12). Although they have been known for some time (13, 14), it has only recently been understood that the colloidal gels arise as a result of arrested phase separation (15⇓⇓–18).

The gels are characterized by a ramified amorphous space-spanning structure that is capable of sustaining mechanical stress. The colloidal density plays a crucial role in the aggregation and therefore in the resulting structure. At low densities, irreversible aggregation leads to fractal gels. At intermediate densities more compact porous structures are observed, whereas a homogeneous glass emerges when the solute occupies more than 50% of the volume (11, 10, 14, 19).

It has been proven that when colloidal particles are quenched into the gas–liquid phase separation region, gelation occurs as a consequence of dynamic arrest that interferes with phase separation (15, 18). After the quench, the system is thermodynamically unstable and strong density fluctuations set in, favoring the separation of the fluid into two coexisting phases. Instead, after an initial transient, these fluctuations are arrested due to the long bonding time among colloids. Thus, rearrangements slow down and, as soon as a percolating structure is formed, a gel is observed. This mechanism, observed experimentally (7, 20, 21) and by computer simulations (16, 22, 23), is now accepted as universal (15).

The arrested phase separation scenario for one-component mixtures (1CM) can be envisaged for mixtures made up of two or more components. In the case of a two-component mixture (2CM) there is already a fundamental increase in complexity. According to Gibbs’ phase rule, in a binary mixture a two-phase region has two degrees of freedom. For colloidal systems, a good choice is the total density ϕ_{tot} and the composition *c* = *N*_{X}/*N*_{tot} of a reference species *X* with respect to the total population. Fluctuations in these two observables drive the thermodynamic instability which leads to phase separation. Depending on whether the two phases differ more in ϕ or *c*, the phase separation is called condensation or demixing, respectively.

In this paper, we address the question of whether it is possible to arrest composition fluctuations for 2CM systems in a manner similar to the arrest of density fluctuations in 1CMs. Our aim is to obtain a different form of colloidal gelation. To this end, we investigate a binary mixture of colloidal particles of the same size but different in intra- and interspecies attractions. We choose this route because it represents an efficient way to enhance composition fluctuations and, consequently, demixing. In fact, when the interspecies attraction is reduced, the system has a strong tendency to demix (12).

## Results

### Thermodynamic Stability.

We consider binary hard spheres with a square-well (SW) potential and the same diameter *σ*:

The intraspecies attraction is chosen with unit depth *u*_{ii} = 1, whereas the interspecies attraction *u*_{i≠j} acts as a tuning parameter: It is chosen to range from unit depth (recovering the 1CM system) to pure repulsion (*u*_{i≠j} = 0). We will see, by means of thermodynamic perturbation theory (TPT), simulations, and experiments how the interspecies pure repulsion enhances the demixing.

We calculate the onset of demixing in the framework of TPT (12, 24, 25), a formalism well suited when fluctuations in both ϕ and *c* take place at the same time. We use a first-order perturbative Helmholtz free energy per particle *f*. To determine whether the instability is mainly driven by density or composition fluctuations, one can diagonalize the stability matrix [*f*] of its partial derivatives (25, 26). At an instability boundary, [*f*] becomes singular as its determinant det[*f*] ≡ λ_{+}λ_{−} vanishes, λ_{±} being the largest and smaller eigenvalues, respectively. The nature of the instability can be characterized by the anglebetween the eigenvector corresponding to the smallest eigenvalue and the axis representing composition fluctuations (*SI Text*; *Materials and Methods*). Therefore, the instability will be either predominantly of the demixing type when its value is close to *α* = 0, indicating that composition fluctuations dominate, or of the condensation type when it is close to *α* = ±π/2, for which only density fluctuations are present.

The results for a binary mixture of SW colloidal particles with different interspecies attraction strengths are shown in Fig. 1. The spinodal surfaces, evaluated as a function of temperature *T*, density ϕ, and composition *c*, indicate boundaries between the stability and instability regions of the phase diagram. Moreover, the calculation indicates whether the system is more prone to condensation (density fluctuations) or demixing (composition fluctuations). This information is encoded by means of a color gradient for *α*. For identical interspecies and intraspecies attractions the result is trivial (Fig. 1, *Top*) and corresponds to a 1CM. In this case, the diagram is invariant with respect to a change of *c*, and only ϕ fluctuations drive the spinodal separation. As soon as the interspecies attraction is reduced, a demixing region emerges around the symmetry line *c* = 0.5 (Fig. 1, *Middle*). When the mutual attraction is completely eliminated (Fig. 1, *Bottom*), a pronounced demixing region takes over most of the spinodal surface.

### Computer Simulations.

To investigate the properties of the arrested structures, we use a computer model of a binary colloidal mixture in which the interspecies attraction is completely absent. We use the same SW model with tunable interspecies attraction introduced in Eq. **1**. Particle interaction via a hard-sphere (HS) potential with a short-ranged attractive part is widely used to model colloidal systems and gels (15, 16, 27⇓–29). The total packing fraction is ϕ_{tot} and the range is set to λ = 1.03, a value often used in colloidal modeling (30, 31) (*SI Text*). In what follows, we label the two species as red (R) and green (G) to be consistent with the color of the fluorescent dye used in the experiments. The composition *c* = *N*_{R}/*N*_{tot} is the concentration of the red species relative to the total population. The interspecies (R–G) and intraspecies (R–R, G–G) attractions are specified by the depth *u*_{ij}. To enhance demixing and in accordance with TPT results, we focus on the symmetric 2CM system where *u*_{RR} = *u*_{GG} = 1 and *u*_{RG} = 0.

We performed molecular dynamics simulations (32) for several 2CMs and 1CMs at different compositions and densities. Initial configurations equilibrated at a temperature *T* ≫ *u*_{ij}, high enough to eliminate the effect of attraction, are instantaneously quenched down to a temperature *T*_{q} ≪ *T*_{c}, where *T*_{c} is the critical temperature known for the 1CM case (33). Under this protocol the 1CM system undergoes a gel transition and remains trapped in an arrested phase separation (34). Because the dynamics is arrested, the system falls out of equilibrium and consequently undergoes aging. For this reason we consider averages over 10 independent realizations of the initial conditions instead of time averages (*SI Text*).

Several spatial configurations of the arrested symmetric 2CM structures obtained from simulations are shown in Fig. 2 for different compositions and densities. Although demixing is observed at all densities, we clearly distinguish two regimes. In the vicinity of the single-component regime *c* ∼ 0 or *c* ∼ 1, the majority species percolates and forms a gel structure, whereas the other one forms isolated clusters. Close to the symmetric composition *c* ∼ 0.5, interpenetrating branching is observed, and each species forms an independent gel. Composition fluctuations act on relatively short time scales compared with the arrest, thus each of these subgels contains only one species. We name this material composed of two arrested interpenetrating gels a bigel.

### Percolation from Arrested Fluctuations.

To further characterize bigels, we investigate the percolation properties of the arrested structure as a function of *c* and ϕ. We construct the cluster size distribution of the arrested configurations, distinguishing between the two species. If one of the clusters spans the simulation box, we consider the species as percolating (*SI Text*). If only one species percolates we have single percolation, and when both percolate we speak of double percolation. In the former case, the nonpercolating species forms clusters that are trapped within the cavities of the gel formed by the other component. The analysis reveals three different types of arrested structures. Below roughly 5% in density, most of the final configurations are made of disconnected clusters and no gel is observed, in agreement with previous observations from simulations in 1CM systems (18). Experimentally this finite size effect is absent. At higher densities either single or double percolation is always observed. The results are shown in Fig. 2: squares indicate no percolation, circles are single-percolation regions, and diamonds are double-percolation regions. These different regimes can be related to the spinodal surface of Fig. 1 (*Bottom*), the top view of which is redrawn in Fig. 2. The nature of the percolation at the simulated state points closely reflects the TPT calculations. Clearly, the interplay between the fluctuations in composition and in density gives rise to the different percolation regimes. When the *c* fluctuations prevail, both the components tend to percolate, whereas only one component percolates when density fluctuations dominate. This indicates how the underlying thermodynamic instabilities influence the final arrested structure. From Fig. 2 it is evident that the role of composition fluctuations is predominant at *c* = 0.5. Because we are interested in the double-percolation scenario, we focus on this symmetric case in the remainder of the paper. Several snapshots of such simulated systems are shown in Fig. 2 (*Left*) for different densities.

As for a gel, the structure is more open at lower densities and becomes compact at higher densities. At the highest density investigated here, ϕ_{tot} = 0.5, there are no more density inhomogeneities, in agreement with the behavior observed in gels (18). Bigels, however, significantly differ from gels because the two species are always completely demixed.

### Structural Properties.

To understand the structural analogies between a bigel and a gel, we will focus on bigels at a total density ϕ_{tot} and compare their two components separately (subgels) with gels at density ϕ = ϕ_{tot}/2. As an illustration, in Fig. 3 (*Upper*) we show two gel-like substructures that compose a bigel at ϕ_{tot} = 0.125 compared with gels at half the density, ϕ = 0.0625. We use two methods to investigate the structural properties. First, we consider the static structure factor *S*(*q*). This quantity can be measured in scattering experiments and is directly related to the Fourier transform of the radial distribution function (35). Structure factors have been discussed in the context of gels both for experiments (13, 15, 36⇓–38) and simulations (16, 39⇓–41). Our second analysis is based on surface reconstruction, which gives access to information about the topology and the geometry of the structures. These two methods provide complementary information. The former gives an insight into the mass distribution at different length scales, whereas the latter gives information about the porosity.

For the bigels, we take advantage of the *c* = 0.5 symmetry and evaluate the partial structure factors of the two species separately. The results for three representative densities are shown in Fig. 4*A*. In all cases, the structure factor of the gels agrees in a semiquantitative fashion with the structure factor of the bigels.

A difference in the local peak between the gels and bigels emerges at ϕ = 0.25, which corresponds to the critical density of the 1CM case (42). At small interparticle distances (large *q*), the differences are minimal, whereas at large length scales (small *q*) the differences are more significant. This is a consequence of steric effects, as the interpenetrating nature of the two subgels reduces density fluctuations. In other words, the two subgels are restraining each other and this effect is stronger at higher packing fractions.

It is natural to ask if this behavior being similar at each density can be simply attributed to steric effects due to the presence of a second species, and if its gel structure plays an important role. To clarify this point, we have performed simulations of a binary mixture in which one of the two species is purely repulsive and behaves as a simple crowding agent. More specifically, we set *u*_{RR} = 1, *u*_{GG} = 0, *u*_{RG} = 0 simulating a mixture of SW and HS particles (SW + HS) with the same protocol used for the bigels. The resulting structure factors, in Fig. 4*A*, show small *q* deviations in good agreement with the bigels. We can conclude that such differences are due to general steric effects and not to the interpenetrating nature of the two subgels. Instead, we note that the behavior of the SW + HS system is very similar to that of 1CM gels.

We now turn to the study of the geometry and the topology. Here, we develop and use a technique based on surface reconstruction (*SI Text*), which closely follows the one successfully applied to study amphiphilic systems (43). More specifically, we construct a surface enveloping the arms of the gel. An example of the resulting surfaces for gels and bigels is shown in Fig. 3 (*Lower*). Each point on the surface is characterized by a pair of principal curvatures *C*_{1,2} that determine the Gaussian curvature *K* = *C*_{1}⋅*C*_{2}, which describes the local geometry (44). We consider an overall property of the surface––its topology––in the sense of the Euler characteristic

The value of *χ* is a topological invariant that quantifies the number of objects, handles, and holes in a surface. In our case, it is directly related to the porosity of the gel, as already pointed out for dipolar colloidal gels (45). The distributions of the Gaussian curvature *K* for the reconstructed surfaces are shown in Fig. 4*B*, and the corresponding normalized Euler characteristic values are shown in Fig. 4*C*. The *K* distributions exhibit several local features: the *K* < 0 domain corresponds to saddle-like geometries due to branching areas; *K* = 0 reflects the cylindrical geometry typically found along the arms of the gel; and the *K* ∼ 1/*R*^{2} peak serves as a measure of local undulations. Here, *R* = σ/2 is the radius of the colloids. At higher densities, both an increase of the *K* ≤ 0 part of the distributions and a decrease of is observed. This shows that both the gels and the subgels become more porous. It is also evident from the distributions of Gaussian curvature that the geometrical difference between the gels and bigels grows, whereas essentially equal Euler characteristics show that topologically the structures remain very similar. The growing deviations in the *K* ∼ 0 and *K* ∼ 1/*R*^{2} regions point toward the compaction and straightening of the individual arms of the subgels. We note the almost perfect superposition of the *K* distributions for the SW + HS with the ones of the relative 1CM gels. This implies that steric effects do not affect the features of the surfaces enveloping the structures, as they rely on the local geometry, in agreement with the results for the structure factor (Fig. 4*A*). Finally, regardless of the presence of a second species, these observations allow us to conclude that the porosity of gels and single components of bigels are quantitatively similar.

### Experimental Results.

Interspecies interactions were shown to play a fundamental role in binary protein mixtures. Eye-lens protein systems, for example, can pass from condensation to demixing by a single point mutation, which is believed to alter the interspecies attraction (12, 46). Although this selective interaction is a result of the complex structure of the proteins, research on functionalized colloids unveils unprecedented possibilities of synthesizing particles with tunable interactions. Recently, experimental works on coated colloids have brought the real possibility of having species with selective interactions by grafting highly specific single-stranded DNA (ssDNA) (47⇓⇓⇓⇓⇓⇓–54).

We present experiments on a binary mixture of DNA-coated colloids with selective intraspecies attraction, which represents the ideal candidate to best reproduce the theoretical results of this work. We used two species of polystyrene colloids with diameters of 0.5 μm. The species are labeled with different R and G fluorescent dyes, which makes them distinguishable in confocal microscopy experiments. The DNA coatings are designed such that attraction is possible only between R and R or G and G, whereas G–R interaction is repulsive. This is achieved by using the four different strands, labeled A, A′, B and B′. Each of the four strands consists of a section of double-stranded DNA (dsDNA) with a length of ∼20 nm, which is grafted to the surface of the colloids and terminates with a “sticky end,” i.e., a short sequence of ssDNA (Fig. 5 *A* and *B*). The dsDNA acts as an inert spacer and allows the sticky end to explore a larger volume around the grafting point. The sticky ends of the strands A and B are complementary to those of A′ and B′, respectively. The binding free energies of the nonspecific interactions A–B, A–B′, A′–B, and A′-B′ are negligible compared with the hybridization free energies of A–A′ and B–B′. The surface of G colloids is coated with strands A and A′ in equal concentrations; analogously the surface of R colloids is coated with B and B′. Complementary strands A–A′ (or B–B′) grafted on the surface of different colloids of the same species can hybridize forming “bridges,” which cause the intraspecies attraction. Binding is also possible between complementary strands grafted within a certain distance on the surface of the same colloid, producing “loops” (55). The overall intraspecies attraction results from the competition between bridges and loops. A schematic of this interaction is shown in Fig. 5*B*.

The DNA-mediated colloidal aggregation is thermo-reversible and melting occurs sharply at the temperature . The value of is larger than the melting temperature *T*_{m} of free sticky ends in solution, and it is easily tuned by changing the DNA grafting density using inert polymers.

For the packing fractions of interest, multiple scattering highly reduces the quality of confocal image in bulk. For this reason, we confine the colloidal samples in quasi-2D chambers with a thickness of a few micrometers. In this way we can image systems with volume fractions close to those we simulate.

We report results obtained for samples with ϕ_{tot} ∼ 0.1 and symmetric composition (*c* ∼ 0.5), as indicated in Fig. 2. Once sealed into the chambers, the samples are heated up from room temperature (RT, ∼22 °C) to and left until a homogeneous gas phase is formed. The samples are then quenched to RT. At about 45 °C large-scale aggregation initiates and within 5 min a demixed bigel is formed, as shown by the confocal image in Fig. 5*C*. A double-percolating network is observed and in Fig. 5*D* we show detail where the G and R components are separately visualized. To guarantee that our binary system is completely symmetric, all of the experiments have been repeated after exchanging the DNA coatings between the fluorescent species, i.e., by using A–A′ on R colloids and B–B′ on G colloids. Details in *SI Text*.

## Conclusions

In this paper, we have proposed a mechanism for the assembly of colloidal gels. In 2CMs, phase separation is a consequence of the interplay between density and composition fluctuations. We have shown that when composition fluctuations occur, demixing can be arrested to create gel-like structures.

We focused on the case of symmetric binary mixtures. The gel structures, arrested after the quench, are made up of two interpenetrating gels. We name these materials bigels. As in a bicontinuous phase, each of the two subgels is made solely of one species. The structure of the bigel is a result of an out-of-equilibrium process and consequently is very hard to predict. However, we have shown that the underlying phase diagram provides important insights, which can be used to tune the properties of these materials. We have analyzed bigels through metric and topological observables, which give complementary information. We have carried out a comparison of the structural properties of the bigels to those of the monodisperse gels. Our analysis shows that gels and bigels share the same porosity, although differences due to steric effects emerge at local (nearest-neighbor) length scales from the structure factors.

We envision that the gelation mechanism we propose can be further tuned to customize the properties of the resulting materials even more. In the present paper we have mainly investigated the simple symmetric case but the next step could involve the relaxation of this constraint. For example, it is possible to change the size ratio between the components. In this case the two interpenetrating networks could be characterized by different building blocks and this could be exploited to change the characteristic length scale or porosity of the arrested structures. The properties of the gels can be tuned even further by modifying the strength of the attractions. In the case of the present experimental realization system, this can be achieved by changing the amount of grafted DNA between different species or the length of the sticky ssDNA. This asymmetry in attraction could be tuned to model the nature of the two subgels by making, for example, one gel as the result of a shallow quench and one as the result of a deep quench. In this case it has been shown that the two gel networks have different characteristic length scales (56). Finally, using mixtures with more than two components will enrich the possibilities even further. For a binary mixture, it is possible to tune like interactions and the interspecies interaction for a total of three possible parameters. However, increasing the number of components *n*, the number of tunable parameters would rapidly grow as *n*⋅(*n* + 1)/2, offering a large palette of interaction patterns to explore.

In summary, our results provide a route to the creation of bigels, a material characterized by a bicontinuous structure. The aggregation mechanism we propose is universal and only requires the manipulation of the interactions between colloidal particles. We proved the feasibility of this program experimentally with DNA-coated colloids.

## Materials and Methods

### Thermodynamic Perturbation Theory.

We use a first-order perturbative Helmholtz free energy , where *F*_{0} and are the free energy and the partial radial distribution function, respectively, of the unperturbed system β = 1/*k*_{B}*T* and ρ = *N*_{tot}/*V*. The reference state entering is a HS binary mixture. The reference free energy *F*_{0} is calculated using the Mansoori–Carnahan–Starling–Leland equation of state for multicomponent mixtures of HS. The partial radial distribution functions of the reference system have been evaluated within the Percus–Yevick approximation with the Gurdkje–Henderson modification to correct the thermodynamics inconsistency. The composition *x*_{R} = *c* = *N*_{R}/*N*_{tot} of a reference species over the total population is to be specified in addition to the overall density ϕ_{tot}. The matrix of the second-order partial derivatives of the free energy is calculated numerically by finite differences and this allows us to evaluate the loci where the system becomes unstable––the spinodal surface. The general procedure is described in ref. 57.

### Computer Simulations and Analysis.

Event-driven molecular dynamics simulations are performed in a cubic box with periodic boundary conditions. The diameter and the mass of the colloids are σ = 1 and *m* = 1, respectively, and we set *k*_{B} = 1. Thus, the temperature is measured in units of the well depth. All of the constant temperature simulations were performed for a total of *n* = 10^{4} particles in a fixed volume. The initial configurations were prepared by equilibrating at high temperature, *T* = 100, where the system behaves as a monodisperse HS fluid. Afterward, the system is instantaneously quenched to *T* = 0.05, well below the 1CM known critical temperature *T*_{c} = 0.3. For every set of parameters we simulate 10 independent realizations. The static structure factor is calculated using the definition , where the is defined on all particles for 1CM and on separated species for 2CM. Averages of *S*(*q*) are calculated on up to 300 independent directions of the scattering vector . A structure is considered to percolate when at least one cluster spans the whole simulation box and, replicating the box, such a cluster touches with all its replicated images.

For the surface reconstruction, we adopt the following space-filling procedure: each unbound colloid is represented by a sphere, and each pair of bound colloids is assumed to be connected by a cylinder. We do not apply periodic boundary conditions. Instead, we assume that the colloidal structure is embedded in empty space. Next, we define a distance function which represents the shortest distance from any point in space to the structure, namely the center of a colloid for unbound colloids or the axis of a cylinder for bound colloids. Then, the enveloping surface is computed as an isosurface where *R* is the colloidal radius. We calculated the Gaussian curvatures *K* at any point on the surface by finite differences (implemented in the Gnu Triangulated Surface library) and the Euler characteristic is evaluated using the Gauss–Bonnet theorem, Eq. **3**.

### Experimental Methods.

The DNA is attached to the surface of the streptavidin-coated colloids via biotin–streptavidin linkage. The structure of the strands is:Biotin–5′–TTTTT–dsDNA spacer–TTTTT–ssDNA sticky end–3′. The dsDNA rigid spacer is made of 60 base pairs (~20 nm in length) and the sequences of 5 thymine bases are added to confer more flexibility to the construct. The four sticky ends are A = 5′–AT CCC GGC C–3′, A′=5′–GG CCG GGA T–3′, B = 5′–CG CAG CAC C–3′, and B′=5′–GG TGC TGC G–3′. The *T*_{m} of the complementary strands A–A′ and B–B′ are, respectively, 33.3 °C and 33.5 °C at 26-mM ionic strength, whereas the nonspecific bonding probability between strands is negligible. The colloids, from Microparticles GmbH, are fluorescently coated in red (R) and green (G). All of the combinations (R–A′A, G–A′A, R–B′B, G–B′B) have been tested to ensure the elimination of spectra overlaps (details in *SI Text*). The experiments are carried out in 10-mM Tris-HCl pH 8 + 1-mM EDTA buffer with the addition of 20-mM NaCl. The density of the solution is matched to that of polystyrene (1.05 g/cm^{3}) by adding sucrose. To avoid nonspecific attraction we add free biotin to the solution. Due to high diffusivity and concentration, biotin would bind, before free DNA strands, to any free grafting site on the colloid’s surface. The experiments are carried out in a quasi-2D environment to allow optical imaging of high-density solutions. The sample chambers are designed with a wedge-like structure, which allows us to optimize the imaging of each sample by choosing the region of the sample with optimal thickness. The chambers are sealed to avoid any evaporation. For the imaging we use a Leica TCS SP5 inverted confocal microscope equipped with an HCX PL APO CS 100× 1.4 oil immersion objective.

## Acknowledgments

The authors thank N. Geerts and S. Manley for useful discussions. F.V., M.B., and G.F. acknowledge financial support from Swiss National Science Foundation (SNSF) Grants PP0022_119006 and PP00P2_140822/1. N.D. acknowledges support from SNSF Grant PBELP2-130895. L.D.M. acknowledges support from Marie Curie Initial Training Network Grant ITN-COMPLOIDS 234810.

## Footnotes

- ↵
^{1}To whom correspondence should be addressed. E-mail: giuseppe.foffi{at}epfl.ch.

Author contributions: G.F. designed research; E.E. designed experiments; F.V., L.D.M., S.H.N., and E.E. performed research; M.B. and N.D. contributed analytic tools; F.V., L.D.M., and G.F. analyzed data; and F.V., L.D.M., E.E., and G.F. wrote the paper.

The authors declare no conflict of interest.

This article is a PNAS Direct Submission.

This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1214971109/-/DCSupplemental.

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