Adhesion as a trigger of droplet polarization in flowing emulsions
Iaroslava Golovkova, Lorraine Montel, Franck Pan, Elie Wandersman, Alexis M. Prevost, Thibault Bertrand, Léa-Laetitia Pontani
AAdhesion as a trigger of droplet polarization in flowing emulsions
Iaroslava Golovkova, ∗ Lorraine Montel, ∗ Franck Pan, Elie Wandersman, Alexis M. Prevost, Thibault Bertrand, and L´ea-Laetitia Pontani † Sorbonne Universit´e, CNRS, Institut de Biologie Paris-Seine (IBPS),Laboratoire Jean Perrin (LJP), 4 place Jussieu, F-75005 Paris, France. Department of Mathematics, Imperial College London,South Kensington Campus, London SW7 2AZ, England, UK.
Tissues are subjected to large external forces and undergo global deformations during morphogen-esis. We use synthetic analogues of tissues to study the impact of cell-cell adhesion on the responseof cohesive cellular assemblies under such stresses. In particular, we use biomimetic emulsions inwhich the droplets are functionalized in order to exhibit specific droplet-droplet adhesion. We flowthese emulsions in microfluidic constrictions and study their response to this forced deformationvia confocal microscopy. We find that the distributions of avalanche sizes are conserved betweenrepulsive and adhesive droplets. However, adhesion locally impairs the rupture of droplet-dropletcontacts, which in turn pulls on the rearranging droplets. As a result, adhesive droplets are a lotmore deformed along the axis of elongation in the constriction. This finding could shed light on theorigin of polarization processes during morphogenesis.
INTRODUCTION
During morphogenesis, cells both differentiate and self-assemble into tissues and organs with specific formsand functions. For instance, during gastrulation, theDrosophila embryo folds onto itself to produce the ventralfurrow that eventually becomes the first tubular shapeof the embryo, thus defining the inside-outside geometryof the future organism. This extensive remodeling of tis-sues is controlled by both biochemical pathways, throughsoluble morphogens [1–3], and biomechanical processes,through forces [4–6] and the regulation of cellular ad-hesion [7, 8]. The behavior of tissues during morpho-genesis is thus strongly determined by their mechanicalresponse, which is controlled by a feedback loop betweencellular adhesion and biochemical signaling through thecytoskeleton [9–13]. Figuring out the properties of thetissue from a materials standpoint is therefore of the ut-most importance to fully understand the role of the var-ious processes at play during morphogenesis.The mechanical properties of tissues and their archi-tecture depend on the properties of the individual cellsbut also on the adhesion energy between the cells andwith the extracellular matrix. As a matter of fact, inthe absence of interactions with the extracellular matrix,the level of cell-cell adhesion is directly related to thesurface tension of cellular aggregates. As a result it wasshown that the level of intercellular adhesion controls theshape and hierarchical organization of cells in aggregates in vitro [10, 14–17]. These processes were described in theframework of the differential adhesion hypothesis [18], inwhich the cohesive cell aggregates are considered as fluidsthat tend to minimize their interface as a function of therelative strength of cellular adhesion. It was also shownthat cell aggregates exhibit mechanical behaviors thatdepend on the adhesion between cells. For instance, ad-hesive cell aggregates spread on solid substrates like vis- coelastic droplets at short times, but display distinct longtime wetting properties when the adhesion is impaired[19]. In epithelial monolayers, the correlated rearrange-ments and cell deformations also indicate that the tissuebehaves as a viscoelastic liquid [20]. Those experimentalobservations, together with theoretical frameworks [21],suggest that soft tissues can be described within a softmatter framework [22].Following this idea, interfacial energy models derivedfrom soap foams were shown to efficiently predict thehighly organized cellular structure in organs such as theDrosophila eye [23]. The behavior of foams, in analogywith tissues, have thus been widely studied under var-ious mechanical constraints. These studies revealed theimportance of plastic rearrangements for yielding in thosematerials [24]. Other approaches consist in treating thetissues as fluid-like materials, leading to the modeling ofmorphogenetic movements based on hydrodynamic theo-ries [25, 26]. Similarly, descriptions borrowed from glassymaterials have been recently implemented to describe thecollective behavior of cells in developing tissues [27]. Inthis context, the jamming of cells, evidenced by a de-crease of fluctuations in the topology of the tissue, di-rectly tunes the material properties of tissues. In turn,it is believed that the jamming transition controls thetissue response to the large stresses during morphogen-esis. Another approach aims to infer the fate of tissuesfrom their static topologies. In this case, the shape ofthe cells and their packing topology were used to predictthe fluidization of tissues [28–33].Here, we propose to bridge the gap between biologicalsystems and soft matter frameworks by using biomimeticemulsions to decipher the collective dynamics and mate-rial properties of tissues during remodeling. In partic-ular, we address the impact of cell-cell adhesion on themechanical properties of tissues by using functionalizedadhesive emulsions. In our previous work, we showed a r X i v : . [ c ond - m a t . s o f t ] J a n outputROI silicon oil EggPC streptavidin DSPE-PEG-biotin aqueous buffer
38 µm5 mm5 mm 1.28 mm1000 µmPressure pump
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FIG. 1. Experimental setup – (A) The oil in water emulsion is pushed using a pressure pump (P = 15-60 mbar depending onadhesion) through the microfluidic channel that consists of three parts: a 1000 µ m wide channel, a constriction, and 38 µ m widechannel. The depth of the channel is 30 µ m over the whole length, and the diameter of the droplets is ≈ µ m. We film theemulsion flow in the area of the constriction situated right before the beginning of the thin channel (see red dashed square forregion of interest). (B) Schematic representation of biotin-streptavidin-biotin bonds forming between the contacting surfacesof the droplets stabilized with phospholipids. (C) Progressive formation of adhesive patches over time. The top confocalimage shows that Alexa-555 streptavidin fluorescence is more homogeneously distributed over the surface of the droplets atthe beginning of the experiment. Over time, biotin-streptavidin-biotin bonds form at the droplet-droplet contacts (middleimage) until they enrich into clear adhesive patches with an increased fluorescence signal, allowing to isolate them throughimage analysis. Note that the formation of the patches depletes the fluorescence level on the free edge of the droplets makingit appear more red over time. that weakly attractive droplets displayed impaired plas-tic rearrangements under flow [34]. Here, we proposeto directly mimic intercellular adhesion by introducingspecific interactions between the droplets [35–37]. Suchbiomimetic systems have already been shown to repro-duce the minimal adhesive and mechanical properties oftissues in static experiments [35]. Their specific inter-actions are here introduced through biotin-streptavidin-biotin bonds that are allowed to form between the sur-faces of contacting droplets. The energy of those bindersis comparable to the one of cadherin homophilic interac-tions in tissues [38]. Moreover, the fluidity of the dropletssurface allows the binders to diffuse on the dropletssurface and to aggregate into adhesion patches at eachdroplet-droplet contact. At equilibrium, the size of thepatch can be roughly determined by the balance betweenthe gain in adhesion energy and the loss in elastic energydue to the flattening of the droplet surface in the patch[35].We study the response of these systems under mechan-ical stress. In order to impose a mechanical perturba-tion on the assembly of adhered droplets, we push themthrough a 2D microfluidic constriction (see Fig. 1A). Thisgeometry forces rearrangements in the emulsions, allow-ing us to study their elasto-plastic response, but also aims to mimic the convergent extension of epithelial tissuesthat is essential during embryogenesis [39]. We find thatadhesion does not affect the rearrangements topology andthat the size of avalanches exhibit the same statistics forall experimental conditions. This observation is furtherconfirmed in simulations that allow us to explore dif-ferent droplet size polydispersities, deformabilities andadhesion energies. These simulations similarly evidenceavalanche size statistics to be independent of adhesion.However, when exploring experimentally the individualT1 events, we find that the local dynamics are sloweddown in adhesive emulsions as the binding patches pre-vent droplet-droplet separation during rearrangements.In turn, we observe that adhesive patches lead to largescale deformations across all droplets in the constriction.In addition to being more deformed, we find that thedroplets are also more aligned with each other, whichcould be the signature of an adhesion-induced polariza-tion process in elongating tissues. MATERIALS AND METHODSEmulsion preparation
Oil in water emulsions were prepared using a pres-sure emulsifier, as described in [34]. After emulsification,the oil droplets were stabilized with phospholipids in or-der to make adhesive biomimetic emulsions, as shownin Fig.1B. Firstly, 9 mg of egg L- α -phosphatidylcholine(EPC) lipids and 1mg of DSPE-PEG(2000) biotinylatedlipids (Avanti Polar Lipids) were dried under nitrogenand dissolved in 500 µ L of dimethyl sulfoxide (DMSO,from Sigma Aldrich). This mixture was then added to5 mL of high SDS aqueous buffer (5mM SDS, 10mMTris, pH=7.5). The resulting solution was sonicated for30 minutes. We then added 2mL of emulsion cream tothe phospholipid containing buffer and left to incubateovernight at 4 ◦ C. After incubation the emulsion waswashed with 100 mL of high SDS buffer (5mM SDS,10mM Tris) in a separating funnel and set for a sec-ond round of stabilization. During this second round,the SDS concentration in the aqueous phase is loweredin order to favor the repartition of lipids at the dropletssurface, instead of SDS, while still keeping them fromcoalescing. The low SDS aqueous solution used for thislast round therefore contains 1mM (instead of 5mM) SDSwhile the rest of the procedure for lipid dissolution re-mains unchanged. After this last incubation, the emul-sion is washed again in 100 mL of low SDS buffer (1mMSDS, 10mM Tris) in a separating funnel. The resultingdroplets display an average diameter of 35 µ m (with asize polydispersity of 21%) and are stable over severalweeks at 4 ◦ C.Before running the experiments, the droplets are func-tionalized with streptavidin Alexa Fluor 555-conjugated(Invitrogen). To this end, 200 µ L of the emulsion cream ismixed with 3.6 µ L of streptavidin (1 mg/mL) and 200 µ Lof low SDS buffer. The resulting solution was incubatedfor 1 hour at room temperature to allow the strepta-vidin to bind to the biotinylated lipids on the surfaceof the droplets. The emulsion was then washed twicein the 800 µ L of low SDS buffer and once with 1 mLof a water/glycerol mixture (60:40 v:v) containing 1mMSDS, 10mM Tris, 10mM NaCl and 0.05 mg/mL casein( β -casein from bovine milk, Sigma Aldrich). The wa-ter/glycerol mixture ensures that the optical index ofthe continuous phase matches better the one of the oildroplets for transparency, while salt favors adhesion bydampening electrostatic repulsion between the droplets[35]. Experimental set-up
The microfluidic channels are engineered following thetechniques described in [34]. The channel consists of three sections: at the inlet the channel is first 1 mmwide over 5 mm length, then the width is reduced from1 mm to 38 µ m over a length of 5 mm, and then thechannel remains 38 µ m wide over 5 mm before the out-let (see Fig.1A). In order to maintain the droplets in amonolayer, the depth of the setup is adjusted to 30 µ m,thus facilitating image analysis.After passivating the channel with a solution of 0.25mg/mL casein for 40 minutes, the emulsion is flowedthrough the channel using a pressure pump (MFCS-8CFluigent). After the droplets fill the channel, the pres-sure is decreased to stop the emulsion flow (P = 5 mbar)and the droplets are left overnight to allow the droplets topack and the adhesion patches to grow (see Fig.1C). Afterthe incubation phase, the emulsion is flowed in the chan-nel under constant pressure (P = 15-60 mbar dependingon adhesion) and imaged in the constriction area throughconfocal microscopy with a 20x objective (exposure time= 20 ms, frame rate = 15 fps, see Fig.2A). Numerical Simulations
In order to explore a wide range of parameters, wedevelop a computational model for adhesive emulsionsthat is based on the deformable particle model (DPM)recently introduced by Boromand et al. [40, 41]. In thecase of 2D emulsions, particles deform in response to me-chanical stresses to minimize their perimeter while keep-ing their area fixed. Modeling each of the N emulsiondroplets as a deformable polygon with N v circulo-lineedges with width δ , our model relies on the minimizationof the following potential energy: U DP = γ N (cid:88) m =1 N v (cid:88) i =1 l m,i + k N (cid:88) m =1 ( a m − a m ) + U int (1)where l m,i is the length of the circulo-line between ver-tices i and i + 1 and a m is the area of droplet m . Thefirst term in U DP is proportional to the perimeter ofthe droplet with a proportionality constant equal to aline tension γ . The second term is a penalization termquadratic in the distance between the area of the dropletand a target area a m with compressibility coefficient k .Finally, U int represents the interaction potential en-ergy between two droplets; it is composed of a repulsiveterm and an attractive term (see details in SI † ). Uponcontact, overlaps between interacting droplets are penal-ized by introducing a purely repulsive interaction po-tential U r between all pairs of circulo-lines of differentdroplets. Upon contact, two droplets are also subjectedto contact mediated adhesion. For instance, after the ini-tial contact between a vertex of droplet i and a vertex oran edge of droplet j is made, droplets i and j are sub-ject to an attractive force derived from the interactionpotential U a [42]. See supplementary information † for B
30 µm 30 µm AD t t t +2.44s t +2.5s c d f
93 %90 %88 %84 %controladhesive - 1 C FIG. 2. Confocal imaging and analysis – (A) Confocal imageof an adhesive emulsion in the constriction. (B) Cumulativedistributions of deformation A - 1 for all droplets in the regionof interest for adhesive (dashed lines) and non-adhesive con-trol (solid lines) emulsions across packing fractions rangingfrom φ l = 84 to 93%. (C) Confocal images of four adhesivedroplets undergoing a T1 event. Droplets 1 and 2 are firstconnected through an adhesive patch (left panel), are thenpulled apart (middle panel) and are not neighbors anymore(right panel). In the meantime droplets 3 and 4 gain a contactat the end of the event. (D) Result of the image analysis per-formed on (C). Voronoi cells are drawn in white lines, dropletcontours are shown in red and the color of the disc inside eachdroplet codes for its deformation A . the detailed expressions of the repulsive and attractiveenergy terms.We use the same constriction angle as in the experi-ments (see movie † ). We flow the emulsion through theconstriction by subjecting each particle vertex to a con-stant force in the direction of the channel. We use peri-odic boundary conditions along the axis of the microflu-idic channel, i.e. that droplets exiting the constrictionre-enter the channel ahead of the constriction. Providedthese forces, we integrate the equations of motion for thevertices in the overdamped limit.We perform simulations with N = 128 deformabledroplets with N v = 16 vertices per droplet. We vary theline tension γ and the adhesion strength k a keeping allother parameters fixed for monodisperse emulsions andpolydisperse emulsions with 20% polydispersity (see inSI † ). We place ourselves in the limit of non-overlapping,nearly incompressible emulsion droplets. Data Analysis
Tesselation and tracking
Raw images are segmented using Ilastik [43]. The seg-mented images are then skeletonized and droplets aredetected using Fiji. Droplets, as well as channel bound-aries, are then indexed directly on the segmented im-age. A surface Voronoi tessellation is finally performedon these processed images to identify the Voronoi cellscorresponding to each droplet.A table of neighboring relationships between dropletsand Voronoi cells is generated using the Region Adja-cency Graphs from the Python Scikit-image package [44].We then obtain the list of neighbors at each time foreach droplet in the constriction and measure the sizeof droplet-droplet contacts as well as the length of theedge between neighboring Voronoi cells. The dropletsare tracked with a custom Python tracking algorithm al-lowing us to compute instant velocities of droplets andVoronoi cells.
Deformation
We measure droplet deformations following themethod used in [34]. To avoid artificial measurementnoise due to finite image resolution, we fit successionsof osculating arcs of circles around the droplet contours.The computed shape parameter A = p / πa , with p theperimeter and a the surface of the identified droplet, andlocal packing fraction φ l are then calculated from thisfitted contour, as shown in Fig.2D. Note that we excludethe droplets whose corresponding Voronoi cells touch thewalls of the channel. In parallel, we also fit each dropletwith an ellipse, and use its aspect ratio and orientationof the major axis to study elongation and alignment ofthe droplets in the constriction. Further details of theimage analysis can be found in SI † . T1 events detection
By tracking droplets and their neighborhood over time,we identify the formation or rupture of droplet-dropletcontacts and edges between Voronoi cells. This allowsus to identify individual T1 events by considering theneighborhood of droplet quadruplets as shown in Fig.2C.We then examine avalanche phenomena by consideringT1 events that occur during a given time window andthat are connected by neighboring droplets.To do so we define an adimensional time t = t ∗ (cid:104) V (cid:105) / (cid:104) R (cid:105) with t ∗ the elapsed time in seconds, (cid:104) V (cid:105) the mean flow ve-locity and (cid:104) R (cid:105) the mean radius of droplets that are bothaveraged over all droplets in all frames of each movie. T1events whose cells were neighbors to each other within aspecified time window (here, 0.4 in adimensional time)are grouped in a common avalanche event (see SI † ). Forsimulation data, the T1 were similarly identified from theloss and gain of physical contact between quadruplets ofdroplets, and grouped in avalanches using the same adi-mensional time window. We quantify avalanche sizes bymeasuring the total number of droplets participating inthe same avalanche.During a rearrangement, we also measure the speed atwhich contacts between voronoi cells are shrinking be-fore the actual neighbor exchange. To do so, we measure ∆ l e ∆ t / (cid:104) V (cid:105) , where l e is the contact length between neigh-boring Voronoi cells, ∆ l e = l e (frame n ) − l e (frame n + 1)and ∆ t the time between two consecutive frames. Wemeasure it for all the droplets involved in a T1 eventduring the adimensional time window [ t − , t ], t be-ing the exact moment of neighbor exchange. RESULTS
We inject and flow emulsions in a microfluidic con-striction as depicted in Fig.1A (see also supplementarymovie † ). In the large channel the emulsions spans about30 droplet diameters, and it progressively reduces to onedroplet in the thin channel. We experimentally testedboth non-adhesive and adhesive emulsions (see Materi-als and Methods). When the droplets are adhesive oneexpects their flow to be hindered and the emulsion tobehave more elastically, whereas an assembly of repul-sive droplets, for which rearrangements can be performedat lower energetic cost, should be more plastic. Indeed,when measuring the shape parameter A of all dropletsin the constriction, we find that they are globally moredeformed in the case of adhesive emulsions for all packing fractions (see Fig.2B), which is consistent with previouswork [34].In agreement with this global observation, much higherpressures need to be applied for adhesive emulsions toflow in the constriction compared to non-adhesive ones.On average, in our experimental conditions, one needsto apply about 15-20 mbar with the pressure controllerfor repulsive droplets, as opposed to 30 to 60 mbar foradhesive ones. At the macroscopic scale these two sys-tems therefore exhibit very distinct material properties.We explore in what follows the microscopic origin of thisdifference in behavior. Topology and local dynamics of rearrangements
We first study the properties of these two differentkinds of emulsions by examining the topology of dropletrearrangements such as T1 events depicted in Fig.2C-D. Indeed, it was previously shown that the rearrange-ments of monodisperse droplets are correlated and or-dered in space and time when going through a constric-tion [34, 45]. In particular, T1 events are aligned alongdisclination planes that are regularly spaced. Here, wedo not expect to see such patterns emerge in the constric-tion, even in the absence of adhesion, as our droplets ex-hibit a 21% size polydispersity. Instead, our experimentsdisplay a spatially heterogeneous and intermittent flowwhich is commonly observed in nature during avalanch-ing. Indeed, a large variety of physical systems [46–56]generically exhibit intermittent dynamics which is char-acterized by a slow build-up and a rapid release of stressin the system when subjected to a slow continuous load-ing. Few studies have looked at this intermittent dynam-ics at the local scale [46, 57–60]. Here, having access tothe whole dynamics during the emulsion flow, we exam-ine the statistics of avalanche sizes through a measure ofthe local plastic rearrangements.More specifically, we measure the size of the avalanchesfor different adhesion conditions. We define the avalanchesize as the number of droplets participating in spa-tially and temporally connected rearrangements duringa given time window. In particular, T1 events whosecells are neighbors at any point within the time windoware grouped in the same avalanche. Under all experi-mental conditions, the avalanches sizes are distributedaccording to power-law distributions and are surprisinglyindistinguishable with or without adhesion, as shown inFig.3A. Although one would expect adhesion to give riseto longer range effects, large avalanches do not seem toprevail in adhesive emulsions. Moreover, in both condi-tions the distribution of avalanche sizes reasonably fol-lows a power law with a − AB size of avalanches -4 -3 -2 -1 pd f controladhesion size of avalanches -4 -3 -2 -1 pd f controllow adhesionhigh adhesion -2 -2 ExperimentsSimulations
FIG. 3. Avalanche statistics for experimental data (A) andnumerical simulations (B) - (A) Distributions of avalanche sizefor adhesive (red dashed line) and non-adhesive (blue solidline) emulsions cannot be distinguished. (B) Distributions ofavalanche size for polydisperse packings of highly deformabledroplets (lowest γ ) without adhesion (blue solid line), with lowadhesion (purple dashed line) and high adhesion (red dashedline), see SI † for values of k a and γ . All curves are averagedover 5 repeats of simulations performed with the same param-eters. The distributions are not significantly different betweeneach other. The logarithmic binning as powers of two is usedfor the x-axis in both panels. The maximum cluster size thatwe measure corresponds to an avalanche over the entire fieldof view, indicating that the choice of time window does notartificially exclude large avalanches from the analysis. In bothpanels a line corresponding to a power law with exponent − to systematically vary the adhesion energy, droplet de-formability and polydispersity. We first examined pack-ings with the same polydispersity as in our biomimeticemulsions. We find that adhesion does not affect signif-icantly the distribution of avalanche sizes as shown in Fig.3B, which confirms our experimental findings. How-ever, in the lowest deformability condition, a differencebetween monodisperse and polydisperse packings clearlyexists (see SI † ). Indeed, our results show that monodis-perse packings exhibit an excess of large avalanches for alladhesion energies. This result is consistent with the ideathat low deformability monodisperse particles exhibit ahigher crystalline order leading to large rearrangementstaking place along disclination planes [45, 61].While we could not find evidence of the effect of adhe-sion on the statistics of avalanches sizes, the consequencesof adhesion can be evidenced locally by examining the dy-namics of individual rearrangements. To do so, we havefirst measured the speed at which the length of the dislo-cating edge decreases during a T1 event. We find that theedge length shrinks more slowly for adhesive droplets forall edge lengths, as shown in Fig.4A. Here, the presenceof adhesion helps stabilize short edges and slows downthe dislocation process by adding a strong energetic bar-rier to the formation of the rosette preceding the actualneighbor exchange [62]. However, once the contactingdroplets have been separated, the growth of a new edgetakes place faster for adhesive droplets (data not shown).This is due to the additional accumulated pressure nec-essary to break the adhesive contact, which pushes thenew droplets in contact more promptly.In conclusion, avalanche size statistics in flowing emul-sions is not affected by adhesion. In fact, the signa-ture of adhesion only lies in the local dynamics of T1events rather than in long range collective effects. Wenext study the impact of these local dynamics on dropletdeformations. Droplet deformations
As a consequence of impaired rearrangements, thedroplets should be more deformed during T1 events inadhesive emulsions. Indeed, the adhesion patches in-duce pulling forces on the droplets in addition to thecompressive forces induced by the constriction geome-try. To relate the locally slowed down rearrangementsto increased deformations, we have examined the defor-mation of droplets involved in T1 events by measuringtheir shape parameter A = p / πa over the course of therearrangement. In particular, we quantify the differencebetween the level of deformation before and after a T1by measuring ∆ A = A t − + A t − − A t +3 + A t +4 , where A , A are droplets that were in contact before a T1 event, and A , A are droplets that became in contact after the T1event. t − and t + are the frames just before and afterthe rearrangement respectively. For non-adhesive emul-sions, we find that the distribution of ∆ A is symmet-ric around zero, indicating that droplet deformations areidentical before and after the rearrangements (see SI † ).In contrast, we find that this distribution becomes asym- AB Patch intensity (a.u.) *10 -0.0100.010.020.030.040.050.06 adhesive adhesivecontrol FIG. 4. Properties of individual rearrangements - (A) Rateof change of shrinking for dislocating edges of length l e nor-malized by the average velocity of the flow (cid:104) V (cid:105) plotted as afunction of l e normalized by the global average edges length (cid:104) l e (cid:105) . For a given l e , a dislocating edge length is always disap-pearing more slowly for adhesive emulsions. (B) Difference indroplet deformation ∆ A before and after they undergo a T1event as a function of adhesive patch intensity. An increaseof patch intensity, i.e. an increase in binding energy, corre-sponds to higher values of droplet deformation accumulatedbefore a T1 event. metric when droplets interact through specific binders.However, after detachment, the droplets do not exhibitany excess in deformation and thus behave like repulsivedroplets. This makes sense because in our system adhe-sion is short range and dense adhesive patches form onthe timescale of hours.Considering this scenario, we finally relate the amountof excess deformation ∆ A during rearrangements to thebinding energy between droplets. To do so, we plot ∆ A as a function of the streptavidin fluorescence intensity atthe dislocating contact area and find that a higher inten- sity, meaning a higher binding energy, directly correlateswith droplets that are more deformed prior to rearrange-ments (Fig.4B). This directly links deformation levels inthe emulsion to binding energy between droplets.To track the global effect of this local excess of defor-mation during rearrangements, we have fitted ellipses toall droplets in the field of view and measured the aspectratio of the ellipses as well as the orientation of their ma-jor axis with respect to the horizontal x axis defined inFig.1A. As shown in the polar plot in Fig.5A, the aspectratio of the droplets is significantly higher for adhesiveemulsions for the whole range of orientations. Moreover,the distribution of ellipse orientations is more peaked inthe case of adhesive emulsions (Fig.5B), while controldroplets tend to follow the orientation of the flow fieldthat is measured by tracer particles in the constriction(see SI † ).In order to quantify droplets deformation indepen-dently of their orientation, we measure the shape param-eter A for all droplets in all experiments. When plottedalong the x axis, we observe that the shape parameter ofadhesive droplets is much higher for all considered pack-ing fractions (see Fig. 5C). In addition, this high de-formation does not relax back to the values measured fornon adhesive emulsions even far from the outlet (i.e. ≈ CONCLUSION
Intuitively, cell-cell adhesion is expected to rigidify bi-ological tissues, providing them with an elastic responseto an applied force. In cellular aggregates, the level ofcadherin expression has indeed been shown to controlthe wetting properties on 2D surfaces [19], while in de-veloping tissues loss of cadherin function can induce alowering of the yield stress [27]. This effect of adhesionon the bulk material properties of tissues is also observedindirectly in our biomimetic emulsions. Indeed, a muchhigher pressure is needed to induce flow in the case of ad-hesive emulsions. However, passed that threshold force,both repulsive and adhesive emulsions can flow and gothrough a constriction. We observed that the flow ofemulsions under continuous load exhibits a spatially andtemporally heterogeneous dynamics that are character-istic of yield-stress materials. Furthermore, our experi-ments and simulations both show that the avalanche sizestatistics is independent of adhesion but weakly depen-dent on the presence of crystalline order in the spatialstructure of the emulsions.However, the way those rearrangements take place dif-fers with or without adhesion. Indeed, adhesion prevents controladhesive A s pe c t R a t i o x (µm)
90 %88 %84 %adhesivecontrol C - -90 -60 -30 0 30 60 90 (º) e s t i m a t e d pd f controladhesive BA FIG. 5. Analysis of droplet deformation — (A) and (B) Analysis of the ellipses fitted to control (blue) and adhesive (pink)droplets in packings with average φ l = 88%. (A) Aspect ratios as a function of ellipse orientation. The aspect ratios foradhesive droplets are significantly larger for all considered angles. (B) Distributions of ellipse orientations θ with respect to thex axis in the constriction. Adhesive emulsions yield a narrower distribution than control ones. (C) Average deformation A -1of the droplets along the x axis of the channel for the adhesive (diamonds) and control (circles) emulsions at various packingfractions. The deformation is averaged in 35 µ m bins along the x axis, x=0 corresponding to the entry of the thin channel.The error bars correspond to the standard error of mean for the distribution of A obtained in each bin. the detachment of bound droplets, leading to sloweddown dynamics prior to the first droplet-droplet contactloss in T1 events. As a result, droplets exhibit largerdeformations and they tend to align with the directionof tissue elongation. These long-range cell elongationscould be the onset of symmetry breaking in tissues, thusinducing signaling pathways during morphogenesis. In-deed, tissue shape changes can be due to a combinationof external forces as well as intrinsic forces. This is thecase for the process of convergent extension that is veryconserved across metazoans [39]. These intrinsic forcesusually emerge from an anisotropy of contractility in in-dividual cells [63] and recent studies highlighted the im-portance of in-plane anisotropy [64, 65]. In this case, thecytoskeleton is remodeled and acto-myosin contractilitycan be increased at cell-cell junctions that are perpendic-ular to the extension axis [66, 67]. Interestingly, a recentstudy also evidenced the importance of cell alignment topredict the fate of tissues and highlighted its impact forrapid morphogenetic movements such as the convergentextension of the drosophila germband [68].In this context, our results suggest that adhesioncould participate to morphogenetic processes by inher-ently making the cells anisotropic when tissues start tobe elongated, thus providing a positive feedback loop be-tween external forces and the intracellular response. Be-yond these findings, our biomimetic approach paves thepath to unraveling other biological mechanisms in the fu-ture, such as the role of the extracellular matrix or thatof differential adhesion during morphogenetic processes. CONFLICTS OF INTEREST
There are no conflicts to declare.
ACKNOWLEDGEMENTS
The authors thank Gladys Massiera and LauraCasanellas for fruitful discussions, as well as Jacques Fat-taccioli for letting us use his pressure emulsifier. L.-L.Pontani also acknowledges financial support from AgenceNationale de la Recherche (BOAT, ANR-17-CE30-0001)as well as financial support from Emergence(s) Ville deParis. ∗ These two authors contributed equally † E-mail: [email protected][1] E. Kutejova, J. Briscoe, and A. Kicheva,
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