Cis-clustering of cadherin-23 controls the kinetics of cell-cell adhesion

Cis and trans-interactions in cadherins are the foundations of multicellularity. While the transinteraction mediate cell-cell adhesion, the cis-interaction is postulated as strengthening to trans by clustering. The well-accepted model in cadherin-adhesion is that the ‘trans precedes cis’ via a diffusion-trap kinetic model. Here we report that cadherin-23, a non-classical cadherin with an extended extracellular region, undergoes clustering in solution via lateral interactions independent of trans and phase separate as liquid droplets. In cellulo using fluorescence-recovery after the photobleaching, we noticed a significantly slow-diffusion of cadherin-23 at the intercellular junctions, indicating the diffusion of a cluster. The cis-clustering accelerates the cell-cell adhesion and, thus, kinetically controls cell-adhesion via ‘cis precedes trans’ model. Though the connection of cis-clustering with the rapid adhesion is yet to explore, M2-macrophages that predominantly express cadherin-23 undergo fast attachments to circulatory tumor cells during metastasis.


Introduction
Cadherins predominantly maneuver the active cell-adhesion processes for both vertebrates and invertebrates. Two modes of binding are known for cadherins, trans-binding and cis-binding. While in trans-binding, the terminal extracellular (EC) domains of cadherins from opponent cells interact, the cis-binding is mediated by the lateral interactions among the rest of the EC domains of cadherins from the same cell surfaces (Harrison et al., 2011). Trans mediates direct contacts among opposing cells via a diffusion-trap kinetic approach and secures a cell-cell junction. For classical E(pithelial)-cadherins, approximately five independent protein molecules, clustered at the intracellular region by the cortical F-actin filaments, diffuse across the membrane and are trapped via trans-interactions with E-cadherins of neighboring cells and initiate the cell-cell adherin junctions (Wu et al., 2015). Lateral interactions, thereafter, influence the clustering of cadherins on the premature junctions and strengthen the association between cells. Cis-interaction is thus conceptually referred to as reinforcement to the trans-mediated cellular junctions for classical cadherins. However, this need not be universally true for all cadherins.
A sizeable conformational entropy and homotypic protein-protein repulsions against weak cisinteractions have been the limitations for cis clustering in solution. Results from molecular dynamics and Monte-Carlo simulations conceptualized the two-dimensional confinement of proteins as a solution to reduce the conformational entropy and neutralization of protein-protein repulsions, favoring independent cis clusters for classical cadherins. This is experimentally verified with E-cadherins on a supported lipid bilayer and monitored using single-particle tracking and FRET (Thompson et al., 2019, Thompson et al., 2020. However, capturing cadherin clusters mediated predominantly by cis-interactions in traditional solution-phase assays and studying their functional relevance has still been elusive yet demanding. Clustering of solute in a solution is a classical phase separation to condensed phase from the dilute phase. In cell biology, such a liquid-liquid phase separation (LLPS) is common in the cytoplasm. It is the developmental origin of the membrane-less liquid compartments like nucleoli (Latonen, 2019), centrosomes (Mahen and Venkitaraman, 2012), Cajal bodies (Gall, 2003), stress granules (Buchan and Parker, 2009). Relatively uncommon, but the existence of LLPS is also reported with proteins like Zonula Occludens (Beutel et al., 2019), nephrin (Banjade and Rosen, 2014) that are anchored to cell-membrane and mediate multiprotein cell-adhesion, signal transduction. Favorable interactions among like-neighbors are thermodynamically responsible for such phase separations. Such favorable interactions are also present in cadherins and drive cisclustering on two-dimensional confinement; however, the conformational entropy and proteinprotein repulsion often overpower the cis-clustering in solution. Intuitively, controlled tuning of the counterbalancing interactions may favour the clustering and subsequently, the LLPS with cadherins.
We performed an unbiased in silico search using the catGRANULE algorithm (Mitchell et al., 2013, Klus et al., 2014 across the cadherin-superfamily of proteins and identified cadherin-23 (Cdh23) (NP_075859) protein with a high propensity to undergo LLPS. Cdh23 is one of the long non-classical classes of cadherins with 27 extracellular domains. It mediates strong cell-cell adhesion among tissues like the heart, kidney, muscle, and testis homophilically , Singaraju et al., 2019, Sotomayor et al., 2012, and heterophilic interactions with protocadherin-15 in neuroepithelial cells (Sotomayor et al., 2010). Interestingly, with the potential for multivalent lateral interactions, Cdh23 engages in a stable spiral cis-dimerization (Kachar et al., 2000). The cis-interactions of Cdh23 facilitate clustering and phase separation to liquid droplets in solution. The phenomenon is critical to the ionic strength of the buffer. We quantitatively derived the relation of cis-clustering mediated LLPS of Cdh23.
To confirm the contribution of cis-interactions in LLPS, we specifically blocked the transinteractions of Cdh23 and measured the extent of LLPS. Further, we used chemical needles like 1,6-Hexanediol (HD) that rupture liquid droplets of biomacromolecules by non-specifically blocking interparticle interactions (Patel et al., 2017). We noticed no LLPS of Cdh23 in-vitro after 1,6-HD treatment. Free-standing cis-clustering of Cdh23 independent of trans-binding prompted us to study the effect on cell adhesion. We measured a significant acceleration in the rate of cellcell adhesions driven by cis-clustering. We noticed a substantial drop in cell-adhesion kinetics upon disruption of cis-clusters by 1,6-HD, supporting the functional implication of cis-clustering in cell-cell adhesion. Notably, while the toxicity of the phase-separated states has already been proposed for intrinsically disordered proteins(Elbaum-Garfinkle, 2019), the fast-aggregation of cells is a demonstration of the functional implication of LLPS in cell adhesion. Our fluorescence recovery after photobleaching (FRAP) experiments revealed the fluidic nature of the Cdh23clusters at the cell-cell junctions.

Cdh23 with 27 EC domains undergoes LLPS
The presence of Ca 2+ ions in the coordination sphere of cadherins reduces conformational variations. Further, inert polymers like polyethylene glycol (PEG) molecules often occupy the excluded protein volume and reduce protein entropy (Kaur et al., 2019, Delarue et al., 2018. Besides, Cdh23 EC1-27 has 440 negatively charged and 222 positively charged amino acid residues distributed throughout its structure, thus possessing coacervation propensity. It is, therefore, an interplay between the concentration of Ca 2+ ions, ionic strength of the buffer, and the protein proximity optimizes the lateral interactions in Cdh23 and drive phase separation in solution. Our in-silico search identified the EC regions in Cdh23 as more prone towards phase separation with a propensity score of 1.3. Usually, a propensity score higher than 1 is considered a good LLPS candidate (Ambadipudi et al., 2017). However, the propensity score for Cdh23 EC1-10, a truncated isoform, was measured lower than 1 (Fig. S1). Inference from the crystallographic studies has also revealed that EC domains 14,17,20,21,23,and 25 are predominantly responsible for cis-interactions in Cdh23 (Jaiganesh et al., 2018). To verify, we designed two variants of Cdh23: Cdh23 EC1-27, a variant with an entire EC region, thus possessing high-propensity for LLPS, and a truncated version, Cdh23 EC1-10, with a low-propensity for LLPS. Reportedly, Cdh23, apart from cis-interactions, can mediate both homophilic and heterophilic transinteractions. Two types of trans-interactions with two distinct binding affinities were reported between Cdh23 and Pcdh15 (Narui and Sotomayor, 2018). The most robust trans-conformation with a dissociation constant of < 1 M was notified for the canonical variant. The second transconformation with a higher dissociation constant of 5 M, was observed for a truncated variant. It was, therefore, necessary to block the interference of the trans-interactions to measure the strength of cis-binding. Notably, the heterophilic trans-interaction with Pcdh15 has the highest affinity (Table 1) (Choudhary et al., 2020, Singaraju et al., 2019, Sotomayor et al., 2012. To corroborate our in-silico observations on clustering propensity of Cdh23 EC1-27, we systematically varied the protein concentrations and the ionic strength of the buffer and checked the cis-clustering in solution. We recombinantly tagged eGFP at the C-terminal of each variant to visually track the cis-induced phase separations in real-time under a fluorescence microscope. 20 mM of HEPES buffer at pH 7.5 was used for all experiments, and 0.5% of PEG6000 was used as a crowding agent. We noticed the condensates of Cdh23 EC1-27 proteins for a range of protein concentrations, ionic strengths, and Ca 2+ concentrations ( Fig. 1 A, B and C). Association of the green fluorescence with the protein confirmed that the condensates are made of Cdh23 ( Fig. 1 B and Video 1 A). Fusion among floating droplets, the gold standard for liquid condensates, is also noticed among Cdh23 condensates, indicating the fluid nature of the droplets ( Attributing to the Hofmeister series, a standard theory to estimate protein stability and solubility, we systematically varied Na + & Ca 2+ ions to identify optimal conditions for the liquid-phase condensation of Cdh23 EC1-27 (Dignon et al., 2020). The rate of droplet growth was monitored for optimization ( Fig. 1 C). Towards this, we first varied Na + ions keeping Ca 2+ ions fixed at 4 mM. We noticed a gradual increase in droplet growth rate with increasing Na + ions, reaching an optimum at 500 mM ( Fig. 1 C). The phase separation of Cdh23 EC1-27 was noticed for 100 mM -1 M of NaCl. Next, we set the Na + ions to 500 mM and altered Ca 2+ ions, and obtained phase separation for a range of 4 mM -10 mM of CaCl2, and optimal at 6 mM of Ca 2+ (Fig. S3 A). Finally, we fixed the Ca 2+ ions to 6 mM and varied both [protein] and [Na + ] ions to obtain a complete phase separation diagram ( Fig. 1 D). The optimal growth rate of liquid droplets was obtained at 14 µM of proteins, 535 mM ionic strength, and 6 mM of Ca 2+ ions (Fig. 1 C and D and Fig. S3 B and Fig. S4). We noted a lower critical concentration of 2.5 µM for Cdh23 EC1-27 for in vitro cis-clustering ( Fig. 1 D). Also, Na + and Ca 2+ ions beyond the salting-out range showed no LLPS for Cdh23 EC1-27. It is important to note that the optimal Ca 2+ ions for in vitro LLPS of Cdh23 EC1-27 are within the scope of the extracellular region in physiology.
Interestingly, Cdh23 EC1-10 did not undergo phase separation for a wide range of buffer conditions, including the requirements maintained for Cdh23 EC1-27. We, therefore, considered the truncated version as the negative control. The point to note here is that both Cdh23 EC1-10 and Cdh23 EC1-27 have eGFP tags at their C-termini, and yet, Cdh23 EC1-27 is the only construct undergoing LLPS thus, withholding the contribution of eGFP in LLPS.
To validate the LLPS of Cdh23 EC1-27 as a resultant of exclusive cis-clustering, we repeated the phase transition experiment in the optimal condition, but by blocking the trans-interacting sites with ligand-protein, Pcdh15 EC1-2. As a precaution, we first facilitated the heterophilic transinteractions with an abundance of Pcdh15 EC1-2 (20 µM) in the experiment buffer and carefully altered the solution's ionic strength from an unfavorable phase separation condition to a favorable state via dialysis (Materials and Methods). We observed LLPS of Cdh23 EC1-27 and Pcdh15 EC1-2 complex, indicating that the droplets are predominantly due to lateral interactions of Cdh23 (Fig.  S5). Notably, the droplets of Cdh23 EC1-27 without Pcdh15 EC1-2 were more extensive than in Pcdh15 EC1-2, indicating that the additional trans-interactions contribute to the phase separation in vitro but are not essential for the LLPS. Overall, Cdh23 EC1-27 undergoes LLPS under physiological conditions, and the liquid droplets follow the characteristic feature of protein condensates.

LLPS helps in faster cell-cell aggregation
Liquid droplets of Cdh23 are not exclusive to in-vitro conditions. We observed mesoscopic liquidlike assemblies of Cdh23 in-cellulo in HEK293 cells stably expressing full-length Cdh23. Fulllength Cdh23, similar to the other cadherin family members, comprises a transmembrane domain and a cytosolic domain along with EC regions. Punctate structures in the mesoscopic to the microscopic regime were noticed at the cell-cell junctions of stably transfected HEK293 cells (Materials and Methods). The puncta structures were absent in control for immunofluorescence images, where only a secondary antibody was used for staining the cells (Fig. 2 A). Cellular droplets in cytosol separate homogeneous biomolecules into two phases, a condensed liquid droplet of specific biomolecules surrounded by a diluted phase. Since the foundation of the condensed phase is transient and weak intermolecular interactions, the liquid phase rapidly and reversibly undergoes de-mixing in response to chemical and physical cues, either triggered by incellulo activities or externally. 1,6-hexanediol (1,6-HD) is a widely used aliphatic alcohol in cell biology that weakens the hydrophobic interactions critical for LLPS and inhibits the condensation of solutes to liquid droplets (Itoh et al., 2021, Duster et al., 2021. Accordingly, we treated the stable HEK293 cells with 1,6-hexanediol and monitored the disruption of puncta structures, confirming the fluid nature of the Cdh23 clusters in cells (Fig. 2 A). Even in vitro, we noticed a complete demolishing of the condensed liquid phase in 1,6-HD (Fig. S6).
How do the liquid droplets of Cdh23 mediated by cis-clustering contribute to cells? Cadherins generally form anchoring junctions with the neighboring cells. Cdh23 is no different from the other family members and mediates vital cell-cell adhesion junctions in several tissues like the kidney, muscle, testes, and heart (Singaraju et al., 2019, Sotomayor et al., 2012. We, therefore, verified the effect of the liquid condensates of Cdh23 mediated by cisclustering in cell-cell adhesion, more importantly where cis-clustering precedes the transinteractions. We hypothesized that cis-clustering on a membrane would increase the effective intercellular interacting interface and accelerate cell-adhesion kinetics. We thus monitored the aggregation-kinetics of HEK293 cells exogenously expressing Cdh23 and fit the kinetics data to Von Bertalanffy model (West andNewton, 2019, Benzekry et al., 2014) to estimate the relative adhesion-rate constants (Materials and Methods). We used the same two recombinant variants, Cdh23 EC1-27, and Cdh23 EC1-10, but along with the transmembrane (TM) and cytosolic domains (CD) at their C-terminals (NP_075859). For monitoring the localization of proteins on cell junctions, we fused eGFP at the extreme C-terminals of the constructs. We transfected these chimeric constructs in HEK293 cells, where the cells were pre-treated with siRNA to silence the endogenous Cdh23 expression precisely (Materials and Methods). As expected, we observed a significant enhancement in the aggregation-kinetics of cells expressing Cdh23 EC1-27 ( , 0 = 2.1 × 10 −3 −1 ) (Fig. 2 B) than the cells overexpressing Cdh23 EC1-10 ( 0 = 3.4 × 10 −4 −1 ) (Fig. 2 C). Important to note that both types of cells formed Cdh23 mediated matured cell-cell junction after incubation, warranting the functional activity of both constructs. HEK293 cells treated with siRNA for endogenous Cdh23 showed no aggregation within the experiment time.
Does cis-clustering on cell membrane depend on the extent of surface coverage by Cdh23? To check, we monitored the cell-aggregation kinetics among cancer cell lines, HEK293, HeLa, HaCaT, and A549, that express endogenous Cdh23 differentially. Our results from qRT-PCR and western blot, in corroboration with TCGA, indicate higher endogenous expression of Cdh23 in A549, HaCaT cells and comparatively lower expression in HEK293, HeLa cell-lines (Fig. S7 A). Amongst all in the list, HeLa has the least expression. We performed the cell-aggregation assays in the previously optimized buffer condition and noticed significantly faster cell-aggregations for A549 and HaCat, than the low-expressing cell lines (HEK293 and HeLa). HeLa did not aggregate within the experiment time ( Fig. 3 A and B). To conclude the differences in aggregation kinetics based on the extent of the cis-clustering, we performed the aggregation kinetics of A549 and HEK293 cells in the presence of 1,6-HD. The aggregation kinetics of both cells dropped significantly in the presence of 1,6-HD ( Fig. 4 A and B) and became comparable among each other. Overall, the kinetic data w/o 1,6-HD indicate that the differences in cell-adhesion kinetics of A549 and HEK293 cells without 1,6-HD are due to differences in the extent of cis-clustering of Cdh23. When chemical treatments abolish the cis-clustering, the individual Cdh23 molecules on the cell membrane follow the trans-mediated diffusion-trap kinetics for cell adhesion, similar to classical cadherins. While cis-clustering increases the effective binding interface on a cell membrane and kinetically facilitates the cell adhesion, the diffusion trap is instead driven by the binding affinities between partners and, thus, independent of the surface coverage.

Fluidic nature of Cdh23 clusters on the cell membrane
Fluorescence recovery after photobleaching (FRAP) has been a valuable tool to decipher the fluidic nature of liquid droplets in in-vitro and in-cellulo conditions (Pincet et al., 2016, Kanaan et al., 2020. Accordingly, we performed FRAP experiments on the intercellular junctions of HEK293 cells that are stably transfected with Cdh23. The protein was recombinantly tagged with eGFP at the C-terminal. We noticed localization of eGFP at the cell-cell junctions as expected for Cdh23 (Fig. 5 A) and photobleached a confocal volume. Next, we monitored the fluorescence recovery along a line across the photobleaching spot (Fig. 5 B and C). This is to identify if the recovery is from the new Cdh23 exported and recruited to the membrane by cells or diffusion of membrane-bound proteins. The fluorescence intensity profile across the line is expected to follow an inverted Gaussian profile with a deep at the center of the photobleaching spot (Fig. 5 D). We noticed widening in the Gaussian profiles with recovery, characteristics of diffusion of active proteins from the surrounding membrane. Recruitment of new proteins, in general, recover the fluorescence intensity without diluting the surroundings, thus with a little widening of the Gaussian width (Erami et al., 2016). Next, we plotted the width of the Gaussian (σ 2 ) with time-lapsed after photobleaching and fit to the linear equation and estimated the diffusion-coefficient of Cdh23 clusters at the cell-cell junctions (Fig. 5 E) (Materials and Methods). The diffusion-coefficient of Cdh23 clusters at the cell-cell junctions is 0.6x10 -3 + 0.1x10 -3 µm 2 s -1 , 8-fold slower than the reported diffusion-coefficient of classical E-cadherin (Deff = 4.8x10 -3 + 0.3x10 -3 µm 2 s -1 ) clusters of ~1000 molecules (Erami et al., 2016). Overall, our FRAP data indicates that Cdh23 at the cellcell junction is fluidic and diffuse in clusters.

Discussion
Cdh23 can condensate to the punctate liquid phase at the cell membrane and, as super-adhesive, rapidly seizes the floating cells into aggregates. Though dense, short-range punctate junctions are widely noted for the cadherin family of proteins, the physiological implication of rapid cell-cell adhesion/communication is still elusive. Here, we deciphered that the punctate could be liquid droplets of cadherins. Though, in the family of cadherins, this is the first report to highlight the ability of the cadherin proteins to undergo LLPS. The LLPS mediated faster cell-cell adhesion is also the first demonstration of the physiological implication of LLPS on the membrane. Cdh23, among other cadherins, is significantly overexpressed in tumor-infiltrating M2-type macrophages (Poczobutt et al., 2016) and microglia , Zhang et al., 2014 (Fig.  S7 B). M2-type macrophages associate with the circulatory tumor cells (CTCs) on the go and help in metastasis. A quick cell-cell adhesion is thus essential in this process. Though speculative, the fast adhesion between M2 macrophages and CTCs is facilitated by the condensed Cdh23 droplets.
Usually, weak multimodal interactions are among the driving forces for LLPS. The ectodomains of Cdh23 possess such multiple interaction sites, witnessed from the previously reported puckered and extended coil conformation of Cdh23 cis-dimer (Jaiganesh et al., 2018, Di Palma et al., 2001. The specific cis-interacting sites beyond the ectodomain number of 10 (dom10) were also identified from the fragmented crystal structures of Cdh23 domains (Jaiganesh et al., 2018). Further, the catGRANULE algorithm that predicts the LLPS propensity of a protein from the primary structure identified several granules forming sites on the ectodomains of Cdh23, majorly beyond dom10. Accordingly, we observed LLPS for Cdh23 EC1-27 at the lowest concentration of 2.5 M in vitro but no condensed liquid-like phase for Cdh23 EC1-10 even at a very high concentration of 100 M. Our in-cellulo experiments also featured multifold faster rates ( 0 ) of cellular aggregation for cell-lines expressing full-length Cdh23 (Cdh23 EC1-27+TM+CD) ( 0 = 2.14 × 10 −3 −1 ) than the truncated form of Cdh23 (Cdh23 EC1-10+TM+CD) ( 0 = 3.4 × 10 −4 −1 ). Together, our data indicate that the EC domains beyond 10 (EC10 -27) is the key for LLPS. Data from FRAP experiments indicate that even at the cell-cell junctions, Cdh23 translocates as cis-clusters. Though we could not quantify the cluster size accurately, from the comparisons of the diffusion-coefficients, we noted approximately 8-fold mass-equivalence of Cdh23 clusters than the classical E-cadherins. It must be noted that the comparisons cannot be quantitative as cell lines under study are different.
The cis-dimerization of classical cadherins is generally considered the aftereffect of intercellular trans-interactions (Pontani et al., 2016). The physiological role of the cis-dimer is proposed to strengthen the trans-interactions at the cell-cell junction (Wu et al., 2010). The liquid phase condensate of Cdh23 on-membrane instead contributes to the kinetics of cell-cell adhesion. It drives the adhesion kinetics via the induced-fit model than the diffusion-trap as reported for classical cadherins. The adhesion kinetics is also dependent on the extent of surface coverage of Cdh23, so as the extent of cis-clustering. Interestingly, the extent of cis-clustering only affect the rate of cell-cell adhesion at the initial phase, and not the mature cell-cell junction. However, the physiological implication of such fast-snapping is still not well-understood.
Moreover, Cdh23 may not be the only cadherin in the family that can undergo LLPS. The Catgranule algorithm estimated the CDF score of more than 1 for many other cadherins (Table 2), considering only the ectodomains. In general, with a CDF of more than 1, the proteins show a tendency for LLPS. Accordingly, Fat-cadherin, Dacshous-cadherin, desmosomes, cadherin-22 have CDF scores of more than 1, and can undergo LLPS. Interestingly, most of these cadherins are associated with special cell-cell junctions. For instance, fat-cadherin and dacshous cadherinmediated heterophilic junctions exclusively regulate the epithelial cell-size dynamics (ECD) under the mechanical cues during morphogenesis (Kumar et al., 2020), desmoglein-2 forms heterophilic interactions with other isoforms of desmosomal cadherins and form Ca 2+ -independent hyperadhesive desmosomal junctions in tissues like skin, heart that are exposed to physical forces. Apart from cadherins, ZO1 that form tight-junctions (McNeil et al., 2006) also has a CDF score of more than 1 and undergoes LLPS (Beutel et al., 2019).

Conclusion
The distinctive features of liquid droplets, stretchable and tunable to different sizes and shapes, may be helpful in cell-cell junction, which routinely experiences mechanical assault. Our results address a functional feature that liquid condensates can achieve, but the individual functional counterparts cannot. Identifying the physiological or pathological cues that trigger such phase transitions is the next exciting step and may open up another exciting field of rapid cell-cell communication and adhesion.

Cloning of domain deletion mutants of Cdh23
The full-length Cdh23(NP_075859) consisting of 27 EC domains, a transmembrane domain, and a cytoplasmic domain was a generous gift from Dr. Raj Ladher, NCBS, Bangalore. Using this construct, we recombinantly generated domain deletion mutants. We have subcloned the same construct in pcDNA3.1 (+) plasmid, which code for Neomycin resistance. All the constructs were cloned between NheI and XhoI restriction sites with (S)-Sortase-tag (LPETGG)-(G)-eGFP-tag and (H)-His-tag; SGH-tag at downstream (C-terminus of the protein) in the same order. All the recombinant constructs were verified through double digestion, PCR amplification, and DNA sequencing.

Protein expression and purification
All recombinant Cdh23 variants for in-vitro studies were expressed in the ExpiCHO suspension cell system (A29129 ThermoFisher Scientific), following the prescribed protocol for transfection in ExpiCHO cells. After seven days, the culture media was collected by pelleting down the cells at 2000 rpm for 15 min at room temperature. The media was then extensively dialyzed against the dialysis buffer for 48 hours and intermittently changed the buffer every 8 hours. The dialyzed media with proteins were purified using affinity chromatography using Ni-NTA columns. The purity of the samples was checked using SDS-PAGE. Finally, the presence of protein was confirmed using western blotting with specific antibodies against GFP, Cadherin-23, and his-tag.

In vitro droplet formation assay
All purified proteins were prepared in buffer containing 20 mM HEPES, pH 7.5, 100 mM NaCl, 4 mM CaCl2. Before each experiment, the proteins were centrifuged at 15000 rpm at 4°C for 10 min to remove possible nonspecific aggregates. Then proteins were adjusted to reach designated concentrations. Each protein mixture (14 μM for each component) was injected into a homemade chamber and imaged using a Leica microscope (Leica DMi8) using 40X objective lens. The time-lapse images were taken under bright-field and fluorescence filters. All the assayed droplets were thicker than 6 μm in height, so the central layers of optical sections were chosen for quantification. Over 10 or more droplets were measured for each protein to generate the phase diagram of the condensed phase. The images were analyzed by ImageJ, and the quantification was performed by Origin software.
RNA from different cancer cell lines was extracted using RNA isolation kit (Bio Rad) and treated with DNAse using DNAse 1 kit (AMPD1, Sigma-Aldrich). cDNA synthesis was done using cDNA synthesis kit (Bio Rad). qRT-PCR was performed with the primers probing Cdh23 using the real time PCR system (CFX96 Bio Rad).

Cell-aggregation assay
After 30 hours of post-transfection, the cells were washed gently with PBS and then resuspended in Hank's buffer supplemented with 10mM Ca 2+ ions to a final cell count of 10 5 cells. Hank's buffer behaves like an incomplete media maintaining the osmolarity of the solution with the cells avoiding any bursting or shrinking of cells throughout the entire duration of the assay. After resuspending, the cells were imaged with a bright-field filter at 10X magnification using a Leica Inverted Microscope (Leica DMi8) over a time trace for 2 hours. The images were collected at 10 min, 15min, 30 min, 45 min, 60 min, and 120 min when all the cells aggregated completely. The image analysis for measuring the area of each aggregate was done in ImageJ software. The aggregates with atleast 5 cells are considered for the analysis. The mean area of aggregates over four different focal positions were measured and plotted against time. The aggregate size was compared over varying domain lengths for Cdh23. We performed all cell aggregation experiments at fixed cell-types and numbers. 1% (w/v) of 1,6-Hexanediol was added in the Hank's buffer for disrupting the LLPS during the cell-aggregation assays.

Fitting the cell aggregation data to a model
We have used Von Bertalanffy model (West andNewton, 2019, Benzekry et al., 2014) to quantify the rate of cell-cell aggregation for HEK293 cells transfected with Cdh23 EC1-10 and Cdh23 EC1-27 at different calcium concentrations. The net rate of cell aggregation is proportional to the total area of aggregate. In the absence of any dissociation in our experiment timescale, we have neglected the loss term in the equation (a special case of Von Bertalanffy model). Finally, we fit the cell aggregation data for anexperimental condition over time using the following rate-equation: The model is solved and written explicitly as, ( ) = ( 0 . . (1 − )) 1 1− , where, 0 represents the rate-constant, represents the area of aggregate, is the independent variable (time), and represents the growth of aggregate. 0 is an inherent property and is dependent on the cell types and their heterogeneity. While fitting, we, therefore, performed global fits and shared the value of (Table S1).

Live cell imaging and FRAP analysis
Stably expressing Cdh23 HEK293 cells grown for confluency on a 35mm glass-base petri dish were used for imaging. A super-resolution microscope (Zeiss LSM980 Airyscan 2) was used to image the cells maintained at 37 ºC and 5% CO2. FRAP was performed on a confocal volume of 1 µm diameter at the cell-cell junctions where localization of eGFP was noticed. ImageJ software was used to measure the fluorescence intensity profiles the line segment of 4 µm drawn across the photobleached region (line-scan analysis). The fluorescence intensity profiles (normalized) at different time points were fit to the Gaussian function in origin software. The fitted widths obtained at different time points were plotted against recovery time, and fit to linear regression to estimate the diffusion coefficient from slope (Erami et al., 2016).     Supplimentary Figures: Figure S1. The high propensity of Cdh23 EC1-27 to undergo liquid-liquid phase-separation than Cdh23 EC1-10. The plot of the propensity scores estimated using catGRANULE algorithm for Cdh23 EC1-27 (black) and Cdh23 EC1-10 (red) versus the number of residues shows that a higher number of EC domains is having a higher probability of undergoing LLPS. Propensity scores for Cdh23 EC1-27 and Cdh23 EC1-10 are 1.2932 and 0.8012, respectively. Fig. 1, A and B). The bright-field images with time capture one of the fusion events of liquid droplets of Cdh23 EC1-27. Arrows in black are highlighting the droplets undergoing fusion. Scale bar: 50 µm.       Fig. 2 D). The time-dependent growth of the cell-cell aggregation area (normalized) of HEK293 cells exogenously expressing Cdh23 EC1-27 at varying calcium concentrations. The error bars represent the standard error of the mean (SEM) for N=15 aggregates. Fig. 1 F). The fusion of liquid droplets of Cdh23 EC1-27 captured under a fluorescence (GFP) microscope.

Video 1 A. Fusion of droplets of Cdh23 EC1-27 (Supporting to
Video 1 B. Fusion of droplets of Cdh23 EC1-27 (Supporting to Fig. 1 E). The fusion of liquid droplets of Cdh23 EC1-27 captured under bright-field.