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.

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.