Cadherin cis and trans interactions are mutually cooperative

Significance

Cadherin-mediated intercellular adhesion involves both cis and trans interactions between cadherin extracellular domains. It has been hypothesized that the combination of these cis and trans interactions is critical for the formation of macroscopic adhesions. Here, we have used single-molecule microscopy to show that cis and trans interactions are mutually cooperative, in that cis interactions directly increase the stability of trans bonds and trans interactions similarly increase the stability of cis bonds. Furthermore, we show that this cooperativity directly results in cadherin accumulation to form macroscopic intermembrane junctions. This cooperativity occurs at the molecular level and suggests that trans dimers are allosterically stabilized by individual cis interactions. These results provide mechanistic insight into cadherin junction assembly, independent of cytoplasmic interactions.

Abstract

Cadherin transmembrane proteins are responsible for intercellular adhesion in all biological tissues and modulate tissue morphogenesis, cell motility, force transduction, and macromolecular transport. The protein-mediated adhesions consist of adhesive trans interactions and lateral cis interactions. Although theory suggests cooperativity between cis and trans bonds, direct experimental evidence of such cooperativity has not been demonstrated. Here, the use of superresolution microscopy, in conjunction with intermolecular single-molecule Förster resonance energy transfer, demonstrated the mutual cooperativity of cis and trans interactions. Results further demonstrate the consequent assembly of large intermembrane junctions, using a biomimetic lipid bilayer cell adhesion model. Notably, the presence of cis interactions resulted in a nearly 30-fold increase in trans-binding lifetimes between epithelial-cadherin extracellular domains. In turn, the presence of trans interactions increased the lifetime of cis bonds. Importantly, comparison of trans-binding lifetimes of small and large cadherin clusters suggests that this cooperativity is primarily due to allostery. The direct quantitative demonstration of strong mutual cooperativity between cis and trans interactions at intermembrane adhesions provides insights into the long-standing controversy of how weak cis and trans interactions act in concert to create strong macroscopic cell adhesions.

Cadherin adhesion proteins are essential for the hierarchical organization of all multicellular organisms, and their dysfunction is associated with several pathologies (1–8). For example, deficiencies in cadherin-mediated adhesion are correlated with the onset and metastasis of multiple cancers and tissue diseases (6–8). Cadherin-mediated adhesion involves the formation of adherens junctions (9, 10), which entail interactions between cadherin extracellular domains in cis and trans configurations, where cis interactions occur between proteins on the same cell membrane, and trans interactions occur between proteins on opposing membranes (11–26). Theory suggests that these cis and trans bonds form cooperatively (11–26). For example, cis interactions are believed to enhance molecular ordering (15) and may increase intercellular adhesion through cluster avidity (16, 27, 28), with potential applications related to angiogenesis and therefore cancer therapies (29–31). Early studies suggested that cis interactions enhanced the cadherin adhesive function (16). However, observations of lateral cis interactions between cadherin extracellular domains have been elusive because of their low affinity and the challenges of studying membrane-bound proteins (32–34). Observations of cis interactions in crystal structures and the disruption of cadherin organization within junctions by putative cis mutants suggested that they operate in tandem with trans interactions (15, 35). One hypothesis was that initial trans binding enhances the cis-binding affinity, leading to lateral clustering, junction nucleation, and growth (36). Such trans → cis cooperativity was predicted theoretically but not verified experimentally (37).

Recent single-molecule (SM) studies successfully demonstrated that cis interactions induced clustering between cadherin extracellular domains on a supported lipid bilayer (SLB) (38, 39). The latter result suggested that conformational constraints associated with membrane immobilization increased the cis-binding affinity sufficiently to induce clustering, even in the absence of trans interactions. This observation raised the possibility of the reciprocal cooperativity (i.e., cis → trans), in which initial cis binding may enhance adhesion. Although the probability (but not the strength) of trans binding was found to increase for cadherin dimer constructs, relative to the monomer (34), the connection to cis interactions, if any, remains unclear. Demonstrating cis/trans cooperativity would require demonstrating that the presence of cis interactions alters the strength of trans bonds quantitatively and vice versa.

In this study, we systematically identified and quantified cis/trans cooperativity, using dynamic SM Förster resonance energy transfer (FRET). These measurements determine whether cis interactions increase trans-binding lifetimes and, conversely, whether trans interactions increase cis-binding lifetimes. They further elucidated the putative role of cis/trans cooperativity in the formation and growth of cadherin junctions between opposing membranes. We find that cis and trans interactions are strongly and mutually cooperative. Most importantly, results show that cis interactions dramatically increase trans-binding lifetimes by more than an order of magnitude, and these cooperative interactions are shown to facilitate the assembly of large junctions. A detailed analysis of trans-binding kinetics as a function of cluster size provide insight into the molecular mechanism of the elevated trans lifetimes. The results presented suggest that specific cis interactions allosterically activate trans-binding interactions.

Results

Experiments to Probe Cis and Trans Interactions and Adhesive and Lateral Binding.

A biomimetic system was designed to model cadherin-mediated cell adhesion by investigating adhesion events between SLBs and giant unilamellar vesicles (GUVs) decorated with epithelial-cadherin (E-cad) extracellular domains. Cis or trans E-cad binding was directly observed using dynamic SM-FRET microscopy. In all experiments, donor-labeled E-cad was bound to the SLB and either lateral (cis) or adhesive (trans) binding was probed by tethering acceptor-labeled E-cad to the SLB or GUV, respectively (Fig. 1 A and B). To avoid cross-contamination of FRET-labeled E-cad species, orthogonal conjugation methods were employed to tether specific E-cad species to the SLB or GUV surface, respectively. To isolate the effects of particular interactions, wild-type (WT) E-cad was compared to both cis mutant (L175D) and trans mutant (W2A) constructs, in which the cis mutant is incapable of interaction through the specific cis interface (15), and the trans mutant is incapable of forming the strand-swapped adhesive dimer, which is the primary adhesive interaction (11, 40). We note that the W2A trans mutant is still capable of forming a so-called X-dimer, which involves a weak but force-dependent interaction at the EC1–EC2 junctions of opposing E-cad (40, 41). As summarized in Table 1, five E-cad configurations were studied to probe the effects of specific cis and trans interactions on trans- and cis-binding kinetics, respectively.

Fig. 1.

Observation of cis or trans binding via SM FRET. (A) Schematic showing the configuration used to probe trans binding, with acceptor E-cad bound to the GUV. (B) Schematic showing the configuration used to target cis binding, with acceptor E-cad bound to the SLB. (C) Representative heat map of donor and acceptor intensities showing two discrete populations at high- and low-FRET efficiency indicated by the asterisks. The black line is used to divide the two populations and assign each observation to the high- or low-FRET state. (D and E) Donor and acceptor intensities and X and Y Cartesian coordinates, respectively, for a representative trajectory showing a trans-binding event between WT E-cad. The gray background indicates the trajectory is in the low-FRET (unbound) state, and the teal background indicates the trajectory is in the high-FRET (bound) state.

Table 1.

E-cad configurations used to test for cis/trans cooperativity

Targeted binding	Identifier	E-cad on SLB	E-cad on GUV	Capable interactions	Restricted interactions
Trans binding	With cis interactions	WT-donor + WT	WT-acceptor + WT	Cis and trans interactions	None
	Without cis interactions	WT-donor + cis mutant	Cis mutant-acceptor + cis mutant	Trans interactions	Specific cis interactions
	Without strand-swap interactions	WT-donor + trans mutant	Trans mutant-acceptor + trans mutant	Cis interactions	Strand-swap trans interactions
Cis binding	With trans interactions	WT-donor + WT-acceptor + WT	WT	Cis and trans interactions	None
	Without strand-swap interactions	WT-donor + trans mutant-acceptor + trans mutant	Trans mutant	Cis interactions	Strand-swap trans interactions

Samples were imaged using a through-the-objective total internal reflection fluorescence (TIRF) microscope at E-cad conditions optimized for superresolution SM-FRET imaging and E-cad junction formation. The overall SLB surface coverage was in the approximate range of 1.75 to 2.75 E-cad/µm² (SI Appendix, Table S1). These surface coverages are modestly lower than those observed on average on cell surfaces (20, 26, 42) but high enough to observe cis- and trans-binding interactions and junction formation. Binding and cooperative effects that occur at lower surface coverage are expected to also occur at higher coverage. Also, by performing experiments at low E-cad coverage, we minimized confounding effects associated with large preformed clusters that could complicate the interpretation of experimental findings. Bright-field images, acquired immediately prior to TIRF imaging, established the GUV locations and enabled us to distinguish SM trajectories occurring in junction regions (between GUV and SLB) from those in free bilayer regions (SLB only).

Molecular observations from individual frames were linked into trajectories, and objects colocalized in donor and acceptor channels were identified as FRET pairs. Each observation was assigned to either a high-FRET or low-FRET efficiency state based on an analysis of donor and acceptor intensity populations (Fig. 1C and SI Appendix, Fig. S11). Fig. 1C shows a representative FRET map that shows two discrete populations present at high- and low-FRET efficiency. Thus, a given trajectory is a multivariate time series, comprising X and Y Cartesian coordinates (determined using superresolution localization) and donor and acceptor emission intensities versus time (see Fig. 1 D and E and SI Appendix, Fig. S10 for representative examples). Fig. 1 D and E show a trajectory exhibiting a trans-binding event between WT E-cad. Initially, the trajectory shows a donor monomer, diffusing rapidly, which then binds to an E-cad cluster via trans binding, resulting in an increase in acceptor emission intensity (and FRET efficiency) as well as a simultaneous decrease in positional fluctuations due to the greater drag experienced by the cluster. These trajectory data are analyzed to determine the effective thermal unbinding rate for the specific binding mode being probed in a given experiment in conjunction with the instantaneous effective diffusion coefficient. These parameters provide complementary information about the binding strength associated with a cluster of a particular size. For each experimental condition, more than 3,000 molecular trajectories were analyzed in junction regions (under GUVs) and free bilayer regions. For details on experimental sample size, see SI Appendix, Table S5. Further details on sample preparation, imaging procedures, and analysis are given in Methods and SI Appendix.

Mutual Cooperativity of Cis and Trans Interactions.

E-cad binding and unbinding was modeled using a heterogeneous, three-state Markov model that accounted for finite trajectory lengths to extract the average dissociation rate constant $\left({\overline{\text{k}}}_{\text{d}}\right)$. For a detailed explanation, see Methods, SI Appendix, and Thompson et al. (39). Fig. 2A shows the results of experiments probing the presence of cis → trans cooperativity, particularly the values of ${\overline{\text{k}}}_{\text{d}}$ for trans binding with cis interactions, without cis interactions, and without strand-swap trans interactions. Notably, the thermal dissociation of adhesive trans bonds is nearly 30-times slower in the presence versus the absence of cis interactions (${\overline{\text{k}}}_{\text{d}}$ values of $0.56\pm 0.07\hspace{0.17em}{s}^{-1}$ versus $16\pm 2\hspace{0.17em}{s}^{-1}$), suggesting that cis interactions drastically increase trans-binding lifetimes. In the absence of the strand-swapped trans interactions (W2A trans mutant), dissociation between opposing E-cad is even faster $\left({\overline{\text{k}}}_{\text{d}}=31\pm 6\hspace{0.17em}{s}^{-1}\right)$. Presumably, these interactions between W2A trans mutant E-cad result in the formation of the X-dimer. The X-dimer interaction is a postulated transient intermediate in the trans-binding mechanism, but it is also a catch bond, the lifetime of which increases with increasing force (40, 41, 43). Thermal fluctuations are the only source of force on trans bonds in this experimental system, such that the rapid dissociation of the trans bonds between W2A trans mutant E-cad is expected.

Fig. 2.

Cis and trans interactions are mutually cooperative. (A) Average dissociation rate constants for trans binding with cis interactions, without cis interactions, and without strand-swap trans interactions. Error bars were calculated as the square root of the Cramèr–Rao lower bound. (B) Average dissociation rate constants for cis binding with trans interactions and without strand-swap interactions. Error bars were calculated as the square root of the Cramèr–Rao lower bound. (C) ${\overline{D}}_{short}$ overall, and for trans-bound and trans-unbound populations, with cis interactions and without cis interactions in the trans configuration. Error bars represent the SD of fitting 100 samples using a bootstrap method with replacement.

Similarly, we tested for trans → cis cooperativity by measuring dissociation constants of cis binding using WT and trans-mutant E-cad. Specifically shown in Fig. 2B are the values of ${\overline{\text{k}}}_{\text{d}}$ for cis binding with trans interactions and without strand-swap trans interactions for E-cad in SLB–GUV junctions. The dissociation of lateral cis bonds was more than two-times slower in the presence of trans interactions (${\overline{\text{k}}}_{\text{d}}$ values of $2.2\pm 0.4\hspace{0.17em}{s}^{-1}$ versus $4.8\pm 0.6\hspace{0.17em}{s}^{-1}$), indicating that cis-binding lifetimes are significantly enhanced by the additional strand-swap interactions. To put this into context, we note that the lateral interactions observed for trans-mutant E-cad on free SLB dissociate more slowly than for the WT E-cad (SI Appendix, Table S8), suggesting that the W2A mutation inherently stabilizes lateral interactions. Therefore, the apparent factor of 2.2 enhancement of cis-binding lifetimes in the presence of strand-swap interactions represents a lower limit. The actual enhancement may be as large as eightfold. In any case, the enhancement of cis-binding lifetimes in the presence of trans interactions (factor of 2.2) is less dramatic than the increase in trans-binding lifetimes in the presence of cis interactions (factor of ∼30). Nevertheless, this indicates a second form of cooperativity, in which each type of binding is reciprocally enhanced by the other type of interactions, hence “mutual” cooperativity. Interestingly, the dissociation rate of cis bonds formed by the trans mutant in SLB–GUV junctions is similar to that of cis bonds on free SLBs alone (SI Appendix, Table S8), suggesting that the trans mutant effectively decouples E-cad bound to opposing membranes within the junction region. This is consistent with the extremely fast dissociation rate of the X-dimer formed by the W2A trans mutant (43). Again, under the low tension in this experimental system, the catch bond of the X-dimer would be too short lived to affect or nucleate cis binding between E-cad on an opposing bilayer. Furthermore, this suggests that the trans → cis cooperativity observed is due to strand-swap interactions as opposed to X-dimer intermediate interactions.

Observations of Diffusion Confirm Cis/Trans Cooperativity.

As mentioned previously, the in-plane motion of E-cad molecules is determined in conjunction with FRET observations and provides complementary information about the binding state of an E-cad probe molecule. This is because oligomers diffuse more slowly than monomers due to the presence of multiple protein–lipid interactions, which are the primary source of drag (44). Similarly, molecules or clusters bound across junctions experience additional drag compared to E-cad bound to only a single bilayer. To characterize diffusion, we calculated the short-time diffusion coefficient $\left({\overline{\text{D}}}_{\text{short}}\right)$ for trajectories observed in SLB–GUV junctions. The calculation details are described in the Methods, and all raw data and fitting parameters used in these calculations are included in SI Appendix, Fig. S7 and Table S2.

The FRET results described above demonstrate that trans-binding events are significantly more stable and long-lived in the presence of cis interactions. This suggests that the time-averaged diffusion should be slower in the presence of cis interactions because a given E-cad molecule will be found more frequently in a trans-bound state. Indeed, as shown in Fig. 2C, the overall value of ${\overline{\text{D}}}_{\text{short}}$ was significantly slower when cadherin can form cis interactions $\left(1.34\pm 0.01\hspace{0.17em}\mu m^2/s\right)$ than without cis interactions $\left(1.53\pm 0.01\hspace{0.17em}\mu m^2/s\right)$. Since these values reflect a time-weighted average of the diffusion of trans-bound and trans-unbound populations, the difference in the mean diffusion coefficient could, in principle, be related either to differences in the diffusion of these populations or to their relative population fractions. A more granular analysis shows that the difference is due to the greater prevalence of the trans-bound population in the presence of cis interactions. Specifically, with or without cis interactions, the diffusion of the low-FRET (trans unbound) populations is faster than that of the high-FRET (trans bound) populations. This difference reflects the greater drag experienced by clusters linked across the junction. However, the values of ${\overline{\text{D}}}_{\text{short}}$ in the high-FRET (trans bound) and low-FRET (trans unbound) states are indistinguishable for E-cad with and without cis interactions, suggesting that similar clusters exist in both cases. Therefore, the significant difference in the overall time-average diffusion is due to the “higher frequency” of high-FRET (trans bound) species in the presence of cis interactions. This observation is consistent with the cis → trans cooperativity indicated by the rate constants inferred from FRET transition data above. Conversely, the effect of trans interactions on cis binding was not significant in terms of diffusion (SI Appendix, Table S2). This behavior suggests that the trans → cis cooperativity is relatively modest. Details of the relationship between FRET and the different binding states are provided in SI Appendix, Relating FRET and Binding States.

Mutual Cis/Trans Cooperativity Enriches Cadherin Density in Junctions.

Trans interactions between E-cad on opposing membranes are proposed to generate a “diffusion trap” that results in the formation of a condensed phase in the adhesive zone and a dilute phase outside of the adhesive zone (27). The relative difference in surface coverage, or density, between the two phases is predicted to increase with either increasing frequency or lifetime of trans interactions as well as the presence of cis interactions causing lattice formation. Fig. 3A shows a heat map (two-dimensional histogram) of molecular observations for a WT E-cad field of view, and Fig. 3B shows the corresponding bright-field image, indicating the presence of GUVs. Visual inspection of these images suggests that the time-averaged concentration of E-cad is dramatically elevated in the region of the GUV and perhaps particularly at the edge of the GUV. Spontaneous accumulation at the rim of a two-cell junction has been predicted and observed previously (35, 45, 46).

Fig. 3.

Cis/trans cooperativity results in the formation of large junctions. (A) Two-dimensional histogram of all molecular observations for a single WT E-cad movie. (B) Bright-field image showing the location of the GUV for the same field of view. (C) Surface coverage enrichment ratio under GUVs to the free SLB for WT, cis-mutant, and trans-mutant E-cad samples. Error bars represent propagated molecule counting error.

In order to quantify the E-cad enrichment in SLB–GUV junctions, the average ratio of E-cad surface coverage in junction to nonjunction regions was calculated for WT, cis-mutant, and trans-mutant E-cad, and the resulting values are shown in Fig. 3C. Consistent with FRET and diffusion measurements, the greatest junction enrichment was observed for WT E-cad, followed by the cis mutant, and the W2A trans mutant exhibited the smallest enrichment. Thus, the junction apparently provided the strongest diffusion trap for WT E-cad, which was capable of forming both cis and trans interactions. Indeed, the mutual cooperativity described above is expected to result in a positive feedback loop, in which cis interactions cooperatively increase the frequency of trans binding, which then increases the frequency of cis binding and so on, thereby causing a high degree of enrichment under GUVs. The cis mutant, which is capable of forming strand-swap trans interactions between E-cad on opposing membranes, exhibited significantly less enrichment. This is presumably because, in the absence of cis interactions and the resulting lattice, trapping occurred only via trans binding. The W2A trans mutant, which is incapable of strand-swap trans interactions, exhibited only modest enrichment due to the low affinity of the residual X-dimer interaction in this system. Overall, this trend seen in the enrichment ratio for WT, cis-mutant, and trans-mutant E-cad agrees with the results discussed previously in this work. It illustrates the role of cis/trans cooperativity in junction formation. As discussed below, additional information is required to understand the molecular mechanisms underlying this cooperativity.

Cis/Trans Cooperativity Depends Only Weakly on Cluster Size.

What is the mechanism by which cis interactions enhance trans binding? One possibility involves an indirect effect: Cis interactions increase the size of cadherin clusters, and larger clusters exhibit stronger overall adhesion due to multivalent interactions between clusters on opposing membranes—a collective phenomenon known as avidity (34, 47). For WT cadherin, the specific cis interaction combined with antiparallel trans interactions results in the assembly of ordered clusters at intermembrane junctions (15, 26). Within these clusters, the lifetimes of both trans and cis bonds are expected to increase with increasing cluster size, as greater numbers of molecules become entrapped within larger clusters. Such an “avidity” effect would result generally from multivalent trans interactions between opposing clusters, regardless of whether the clusters are amorphous or ordered. Alternatively, the trans-binding affinity of an individual cadherin molecule could be enhanced allosterically by simultaneous cis binding (16, 34, 47). Of course, both mechanisms could also work in concert. To some extent, avidity is inevitable because the adhesion energy density is greater for large lateral clusters on opposing bilayers relative to monomeric E-cad. However, it is not clear whether this is the primary reason for the dramatic increase of trans-binding lifetimes for WT E-cad. In particular, SM-FRET measurements alone are not capable of distinguishing avidity effects from differences in individual bond dissociation kinetics. This is because molecular dissociation may not result in a complete loss of FRET if the donor and acceptor are within large clusters that are bound via other trans interactions. To address this question, we explored the dependence of trans-binding lifetimes on the cadherin cluster size. If avidity were the dominant mechanism by which cis interactions enhance the lifetime of trans bonds, then the lifetime would increase with cluster size. However, in the case of allosteric activation, the lifetime should depend only weakly on cluster size.

Specifically, we calculated the effective average lateral cluster size for each cadherin trajectory on the SLB, as described in the Methods. To focus only on trajectories associated with very small clusters, we employed a threshold corresponding to approximately trimeric E-cad. Cluster sizes refer to the number of E-cad on the SLB within a given cluster because cluster diffusion is primarily dictated by hydrodynamic drag from the SLB. We then analyzed the FRET data associated with this subset of trajectories in order to determine the dissociation rate of trans bonds corresponding to small oligomers. This analysis was performed for both WT (average cluster size of 1.39 ± 0.02) and cis-mutant (average cluster size of 1.33 ± 0.02) E-cad. These dissociation rates for small clusters were compared with the trans-binding dissociation rates determined for the entire ensemble of trajectories, which exhibited average cluster sizes of 4.2 ± 0.1 and 5.1 ± 0.1 in the absence and presence of cis interactions, respectively.

Fig. 4 shows the trans-binding dissociation rate constants for small oligomers compared to the trans-binding dissociation rate constants for all trajectories. Importantly, the dissociation rate constants for the small-oligomer data are statistically indistinguishable from the overall dissociation rate constants (for all trajectories) determined for both WT E-cad and cis-mutant E-cad. This result suggests that trans-binding lifetimes are insensitive to cluster size. Moreover, the presence of cis interactions greatly enhances trans binding in both data sets. A striking 30-fold enhancement of trans-binding lifetimes is observed, even for small oligomers. Finally, binding avidity effects are expected to be relatively small for trajectories with an average SLB cluster size of ∼1.35 E-cad, and any avidity effects that are present for these small oligomers should affect trans binding similarly for both E-cad with and without cis interactions. These combined observations suggest that allosteric activation is the primary cause of cooperativity and increased trans-binding lifetimes. Although the increased binding avidity between clusters must logically have an effect on trans-binding lifetimes for sufficiently large clusters, in practice, the effect appears to be small for the distribution of cluster sizes in this system.

Fig. 4.

Trans-binding lifetimes do not decrease for small E-cad clusters. Average dissociation rate constants for trans binding with and without cis interactions in the trans configuration resulting from modeling interactions using a Markov model using either all trajectories or only trajectories corresponding to small oligomers. Error bars were calculated as the square root of the Cramèr–Rao lower bound.

The trans → cis cooperativity could similarly be explained by avidity and/or allosteric activation, although directly separating these mechanisms using a cluster-size analysis is not straightforward. However, a similar cluster-size analysis of cis binding indicated that those lifetimes were modestly longer for both small and large clusters of WT E-cad (SI Appendix).

Discussion

The primary result from this work is the quantitative, experimental demonstration that E-cad cis and trans interactions are mutually cooperative, and this cooperativity enhances the accumulation of cadherins in adhesion zones between opposing membranes. We demonstrated this based on three independent measurements: dissociation constants (i.e., binding lifetimes) based on dynamic FRET trajectories, diffusion coefficients providing indirect information about binding, and model-free observations of cadherin enrichment within adhesion zones. These methods are self-consistent and provide complementary evidence for cooperativity. Furthermore, the reciprocal cooperativity of cis and trans interactions directly correlates with the formation of large junctions, independent of any cytoskeletal interactions.

Although mutual cis/trans cooperativity has been proposed, it has not previously been measured (27, 34, 37, 48, 49). Computational studies predicted that cadherin junction formation is a cooperative process dependent on both cis- and trans-binding affinities (27); however, experimental evidence to date has been indirect and sometimes ambiguous. In terms of cis → trans cooperativity, E-cad ectodomain cis dimers resulted in stronger cell adhesion than monomers (16), and junction accumulation and adhesion were modestly reduced with cis-mutant E-cad compared to WT (15). However, while atomic force microscopy studies observed an increase in the trans-binding probability using an engineered dimer construct, the strength of trans bonds was identical for monomer and dimer constructs, and trans-binding lifetimes could not be measured (34). In the other direction (trans → cis cooperativity), simulations predicted elevated cis-binding affinity for trans dimers compared to monomers (37). Indeed, in studies of cadherin-mediated cell–cell binding kinetics, after an initial rapid trans-binding step, WT cadherin (but not cis mutants) undergo a transition to a higher-probability binding state (50). Thus, while prior work suggests that cis and trans interactions are coupled, the details have been unclear and inconsistent. Our quantitative results now provide a detailed and nuanced picture of the direct, quantitative effects of specific interactions on cis and trans binding between E-cad extracellular domains that can be directly related to junction formation.

The apparent allosteric enhancement is consistent with previous reports that cadherin dimers support stronger cell adhesion than monomers (16, 51). This allostery may be due to conventional allostery, in which conformational changes induced by specific cis binding between E-cad on the same bilayer leads to stronger trans binding. Alternatively, a more subtle mechanism may involve the reduction of conformational entropy after cis binding (47). Such a decrease in conformational entropy would reduce the entropic penalty of trans binding. However, differentiating between these two allosteric mechanisms is difficult based on the results presented here.

Cadherin has been shown to exhibit allosteric modulation in a variety of ways, such as inside-out signaling, activation, or inhibition by antibodies that bind domains distal from the active site and the regulation of adhesion upon association with protocadherins (19, 52–55). Therefore, the potential for cis interactions to allosterically activate trans binding seems viable. Regardless of the mechanism, the results presented here suggest that the molecular synergy of cis and trans interactions occurs on the molecular level and potentiates the formation of macroscopic junctions. Future work is required to elucidate the molecular-level details of the allosteric mechanism responsible for the dramatic stabilization of the trans dimer upon activation through the cis interface.

Methods

Protein Preparation.

Chromosomal expression platform 4.2 plasmids encoding the hexahistidine-tagged WT E-cad, L175D mutant, and W2A mutant were obtained from Dr. Lawrence Shapiro (Columbia University). The Human Embryonic Kidney 293T (HEK293T) cell line was from the American Type Culture Collection. Cells were cultured in Dulbecco’s Minimum Eagle Medium containing 10% fetal bovine serum (Life Technologies) under 5% CO₂ atmosphere at 37 °C. Cell lines that stably expressed the soluble proteins were generated by transfecting HEK293T cells with the mutant construct using Lipofectamine 2000 (Invitrogen) according to the manufacturer’s instructions.

To create sortase-tagged WT E-cad, L175D E-cad, and W2A E-cad, the coding sequence for the sortase tag (LPETG) was inserted downstream of these constructs. Forward and reverse primers of LPETG were designed so that it would recognize the sequences before the hexahistidine-tag to add the LPETG motif. The LPETG sequence was inserted before the hexahistidine sequence in each construct so that the hexahistidine would be cleaved during sortase A–mediated conjugation. PCR amplification was used to incorporate the LPETG motif within the listed constructs. PCR products are then screened and verified using gel electrophoresis and DNA sequencing to ensure correct insertion within the E-cad C terminus.

Sortase-tagged WT E-cad, L175D E-cad, and W2A E-cad plasmids are then transfected into HEK293T cells using Lipofectamine 2000. HEK293T cell lines that stably expressed sortase-tagged WT E-cad, L175D E-cad, and W2A E-cad soluble ectodomains were selected with 200 µg/mL Hygromycin B (Invitrogen). Western blots of the culture medium confirmed protein expression by individual colonies. The colonies that expressed the highest levels of soluble protein were pooled for further protein production. Secreted hexahistidine-tagged cadherin constructs were then purified from filtered culture medium by affinity chromatography with an Affigel NTA affinity column, followed by ion-exchange chromatography (Aktapure). Protein purity was assessed by SDS polyacrylamide gel electrophoresis, and adhesive function was confirmed with bead aggregation assays (56).

Purified sortase-tagged WT E-cad extracellular domains were randomly labeled using an Alexa Fluor 488 (AF488) NHS-ester antibody labeling kit. Sortase-tagged WT, WT, L175D mutant, sortase-tagged W2A mutant, and W2A mutant were labeled using an Alexa 647 (AF647) NHS-ester antibody labeling kit (succinimidyl ester; Invitrogen). The protein was reacted with the dye for 2 h in buffer (25 mM Hepes, 100 mM NaCl, 10 mM KCl, 2 mM CaCl₂, 0.05 mM NiSO₄, and pH 8) at room temperature. Unreacted dye was removed via spin column. Based on absorbance measurements, using extinction coefficients of 71,000 cm⁻¹ ⋅ M⁻¹ for the AF488, 239,000 cm⁻¹ ⋅ M⁻¹ for the AF647, and 59,860 cm⁻¹ ⋅ M⁻¹ for the protein, the labeling stoichiometry was ∼1.4 for AF488 labeling of sortase-tagged WT E-cad and ∼1.6, ∼2.3, ∼1.3, ∼1.9, and ∼1.3 for AF647 labeling of sortase-tagged WT, WT, L175D mutant, sortase-tagged W2A mutant, and W2A mutant, respectively.

GUV Electroformation.

The standard electroformation method was used to form GUVs (57) using a custom-built electroformation cell. 1,2-Dioleoyl-sn-glycero-3-phosphocholine (DOPC) was purchased from Millipore Sigma. 1,2-dioleoyl-sn-glycero-3-[(N-(5-amino-1-carboxypentyl)iminodiacetic acid)succinyl] (nickel salt) (DGS-NTA(Ni)) and 1,2-dioleoyl-sn-glycero-3-phosphoethanolamine-N-(lissamine rhodamine B sulfonyl) (ammonium salt) (DOPE-LR) were purchased from Avanti Polar Lipids. A lipid solution containing DOPC and 10 mol percent DGS-NTA(Ni) was prepared with a total concentration of 5 mg/mL in chloroform, and 30 µL of the lipid solution was spread on two ITO-coated coverslips (Structure Probe, Inc.). Solvent was evaporated overnight under vacuum, and a 2.6-mm-thick, press-to-seal, silicone isolator (Grace Bio-Labs) was used to enclose the electroformation cell. The lipid film was then carefully hydrated with a 150-mM sucrose, 150-mM glucose solution, and copper tape was used to connect the ITO electrodes to an Arduino Uno, equipped with a 2A motor shield (Digi-Key) that was programmed to apply an alternating current of 3.12 V at 10 Hz for 2 h at room temperature. GUVs were carefully extracted with a syringe after a rest period of 1 h at 4 °C. GUVs ranging in size from 10 to 100 µm in diameter were obtained. GUV yield was verified via the addition of a small fraction of DOPE-LR. The extracted GUV solution (∼800 µL) was then diluted to 1.5 mL using a calcium-free buffer (25 mM Hepes, 100 mM NaCl, 10 mM KCl, 0.05 mM NiSO₄, and pH 8). After allowing the GUVs to sediment for 1 h, the top 1 mL was removed and the remaining GUV solution was again diluted to 1.5 mL with the calcium-free buffer. GUVs were allowed to sediment for 0.25 h, and the top 1 mL of solution was removed. This sedimentation process was repeated nine times, in addition to the initial 1-h sedimentation, effectively exchanging the GUVs into calcium-free buffer.

FRET Sample Preparation.

A custom DOPE peptide-modified lipid (DOPE-Sort) was designed and purchased from the Peptide/Protein Chemistry Core Facility at the University of Colorado Anschutz Medical Campus. This lipid contained a Gly-Gly-Gly-Gly-Cys peptide sequence that had been conjugated to a maleimide headgroup-functionalized DOPE lipid (1,2-dioleoyl-sn-glycero-3-phosphoethanolamine-N-[4-(p-maleimidomethyl)cyclohexane-carboxamide] (sodium salt)) (Avanti Polar Lipids) via the C-terminal Cys. This peptide-modified lipid was designed to allow for C-terminal covalent conjugation of sortase-tagged E-cad via the sortase enzyme (58). Sortase-mediated conjugation occurs via the sortase enzyme reacting with the Thr amino acid in the sortase recognition tag (LPETG) that has been inserted into the E-cad, cleaving the Gly amino acid and other downstream residues (58). The E-cad–conjugated sortase enzyme then reacts with the exposed N terminal of the Gly peptide attached to the lipid headgroup, covalently binding the E-cad to the DOPE lipid in the SLB (58). Therefore, the N terminal of the peptide was left free at the end of the Gly repeat to allow for site-specific sortase conjugation, and the carboxyl group at the Cys end of the peptide was modified to an amide to better mimic a native protein environment.

DOPC and DOPE-Sort were dissolved in chloroform in the molar ratio of 19:1 in a glass culture tube. Following solvent evaporation under a stream of nitrogen, a thin film of lipids was formed on the side of the tube. This lipid film was then hydrated with buffer, so the total lipid concentration was 3 mM. This suspension was mixed via vortex and sonicated for 0.5 h. The vesicles were then extruded through a 50-nm filter membrane (Whatman) 21 times to form unilamellar vesicles with a homogeneous size distribution.

Glass coverslips (Fisher Scientific) were cleaned with piranha solution for 2 h and treated by an ultraviolet ozone for 0.25 h. To form SLBs, a dispersion of unilamellar vesicles (3 mM total lipid concentration) was injected into a small-volume perfusion chamber (Grace Bio-Labs). Following a 1 h incubation period, vesicles spontaneously formed an SLB via vesicle fusion (59, 60). Following formation, the bilayer was rinsed with Ca-buffer (25 mM Hepes, 100 mM NaCl, 10 mM KCl, 2 mM CaCl₂, 0.05 mM NiSO₄, and pH 8) to remove excess vesicles. Sortase-tagged E-cad, sortase A pentamutant enzyme, and 10 M CaCl₂ were then injected into the perfusion chamber. The sortase A pentamutant with P94R, D160N, D165A, K190E, and K196T mutations was composed of amino acids 26 to 206 of Staphylococcus aureus and contained an N-terminal his-tag (BPS Bioscience). Sortase A pentamutant is a calcium-dependent enzyme, requiring the addition of 10 M CaCl₂ to elevate the Ca²⁺ concentration (61). SLB incubation conditions are described in SI Appendix, Table S3. For all configurations, SLB-bound, AF488-labeled WT E-cad served as the FRET donor and, to study cis binding, SLB-bound, AF647 labeled E-cad served as the FRET acceptor. An incubation period of 3 h was determined to be sufficient for a reasonable conjugation efficiency of sortase-tagged E-cad to the DOPE-Sort lipids. In order to verify covalent conjugation of sortase-tagged E-cad to the SLB, the apparent surface residence time of DOPE-LR within the SLB was compared to that of SLB-conjugated E-cad as well as the apparent surface residence time of his-tagged E-cad bound to SLB-incorporated DGS-NTA lipids. This comparison is shown in SI Appendix, Fig. S1 and confirms the covalent conjugation of E-cad to the SLB. See Methods and SI Appendix for details and discussion.

Following covalent binding of sortase-tagged E-cad, the SLB was extensively rinsed with buffer to completely remove all sortase enzymes and unconjugated E-cad. GUV solution (in Ca-free buffer) was then injected into the sample chamber, and GUVs were allowed to sediment for 0.25 h. His-tagged E-cad was injected and incubated with the GUVs in the Ca-free buffer for 2 h, permitting binding of his-tagged E-cad to the DGS-NTA lipids incorporated into the GUVs. Incubation was performed in Ca-free buffer to minimize GUV aggregation and allow for observation of E-cad under individual GUVs. GUV incubation conditions are included in SI Appendix, Table S4. For samples targeting trans binding, AF647-labeled E-cad served as the FRET acceptor while bound to GUVs. To facilitate adhesion between E-cad on the SLB and GUV, the CaCl₂ concentration was increased to 2 mM by adding 60 mM CaCl₂ 0.5 h before imaging (62).

The donor concentration of sortase-tagged E-cad was adjusted to allow for single molecule resolution, and the acceptor concentration of either sortase-tagged E-cad or his-tagged E-cad was optimized to allow for a large number of FRET events but an insignificant amount of acceptor direct excitation. Using the optimized donor and acceptor concentrations, donor bleed-through into the acceptor channel and direct excitation of the acceptor were both insignificant because of the spectral separation of AF488 and AF647 and the modest concentration of acceptor used. The addition of unlabeled E-cad both on the SLB and GUVs was necessary in order to reach a surface coverage high enough, such that frequent junction formation was observed. This resulted in a large number of high-FRET events, indicated by an acceptor intensity greater than that of the donor, due to lateral (cis) or adhesive (trans) binding. This surface coverage could not be achieved by adding donor and acceptor E-cad alone because of excess background in the acceptor channel due to direct excitation of the acceptor. Furthermore, an image background subtraction procedure removed any residual background.

SM TIRF FRET Imaging.

Imaging was accomplished using a through-the-objective TIRF microscope (Nikon N-STORM Eclipse Ti2 base, Plan-Apo 100× 1.5 NA oil-immersion objective). Samples were mounted on the microscope stage, and an Agilent MLC400B Monolithic laser combiner supplied a 488-nm 50 mW laser as an excitation source. This resulted in an exponentially decaying TIRF field propagating into solution, selectively exciting only donor fluorophores near the SLB–water interface. Fluorescent emissions from the donor and acceptor were separated using a Cairn Research Twin Cam beam splitter containing a dichroic mirror with a separation wavelength of 610 nm (Chroma). Fluorescence from the donor and acceptor were further filtered using a 529/28 bandpass filter and 685/40 bandpass filter (Semrock), respectively. Additionally, a quad bandpass (451/52, 523/39, 600/57, and 695/67) dichroic mirror was used to reflect the excitation laser toward the objective and allow both donor and acceptor emissions to transmit to the beam splitter (Chroma). The donor and acceptor channels were then projected onto separate Andor iXon Ultra DU897U-C50 EMCCD cameras (Oxford Instruments) maintained at −71 °C. An acquisition time of 50 ms was used to capture 20 time-lapse movies of each sample, and each movie was 1 min long. Two sample movie clips are included in Movies S1 and S2 of the donor and acceptor channels, respectively. Prior to TIRF imaging, a bright-field image was captured to observe GUV locations within the field of view. Because of the large size of the GUVs, they were observed to be immobile over the timescale of each movie. Additionally, to allow for accurate donor and acceptor colocalization, the donor and acceptor channels were aligned using images of a glass slide that had been scratched with sandpaper, resulting in an irregular alignment image visible in both channels. The details of this image alignment process are described previously (63).

Image Analysis.

Prior to any image analysis, a background image was subtracted from each frame, of each channel, where the background image for each channel was taken as the average of the first 1,000 frames in that channel. This greatly reduced the nonuniform image background as well as reduced the number of anomalously bright objects that were present and immobile for the entire duration of the movie. Following background subtraction, all two-channel movie analysis was performed using custom Matlab-based software, in which the methods for determining object identification, object positions and intensities, and linking trajectories have been described previously (63, 64). To briefly summarize, objects that were detected in consecutive frames that were within a user-defined tracking radius (8 pixels or 1.25 µm for this analysis) were linked into trajectories that could be further analyzed. Object identification was determined using a manual thresholding function that has been described previously (63). This manual thresholding software allowed for the use of a user-defined object radius (two pixels for this work). Objects that were identified within two pixels in separate channels were identified as a donor–acceptor pair undergoing FRET. The position of the FRET pair was determined using the object with the greatest signal-to-noise ratio. The FRET state (high- or low-FRET efficiency) of each trajectory at every frame was assigned using a method and algorithm described elsewhere (65). To summarize, two-dimensional heat maps showing the donor intensity $\left(I_D\right)$ versus acceptor intensity $\left(I_A\right)$ were constructed (SI Appendix, Fig. S11). It was apparent that two populations were present at high- and low-FRET efficiency. A linear threshold dividing these two populations was calculated by determining the slope and intercept that minimized the integrated heat map values along the dividing line.

Using the bright-field images of GUVs for each field of view, a binary image was created by manually selecting the areas of the SLB that were covered by a GUV. These binary images were then used to assign each observation of each trajectory a GUV state based on the position of the molecule, indicating if the molecule was within a junction (between a GUV and SLB) or on the free SLB for each frame.

Additionally, because of a combination of bright contaminants and inherent defects in SLBs, a permanently immobile (or highly confined) population was observed in the donor channel after background subtraction, which was readily distinguished from the mobile population of interest (66). To avoid inclusion of these anomalous trajectories, only trajectories with a median displacement greater than 0.2 µm were analyzed further. Additionally, to avoid the inclusion of anomalous trajectories due to noise objects, trajectories with a median displacement greater than 0.8 µm were removed. For short-time diffusion coefficient determination, only trajectories with a total surface residence time of 0.2 s (four frames) or longer were included to allow for significant statistical analysis. This surface residence time minimum of 0.2 s was not required for the FRET-state transition rate estimations. Therefore, all trajectories longer than 0.1 s (two frames) were included.

Surface Coverage Estimation and Enrichment Calculations.

The surface coverage in terms of number of E-cad per square micrometer was estimated under GUVs, not under GUVs, and overall, according to

$$\theta =\frac{n_D+n_A}{R_{D}A}\hspace{1em}\hspace{1em}\hspace{1em},$$ [1]

where $\theta$ is the surface coverage in terms of number of E-cad per square micrometer. $n_D$ is the number of fluorescent molecules in the donor channel either under GUVs, not under GUVs, or all together; $n_A$ is the number of fluorescent molecules in the acceptor channel either under GUVs, not under GUVs, or all together; $A$ is the area of the donor channel either under GUVs, not under GUVs, or all together; and $R_D$ is the ratio of donor-labeled protein to total protein. This estimate assumes a one-to-one transfer of energy from donor to acceptor and minimal anomalous objects in the acceptor channel. These assumptions are nearly valid for these experiments, primarily because the number of objects in the donor channel is much greater than the number of objects in the acceptor channel. Even so, the resulting surface coverage values should be treated as estimates. The surface coverage was averaged over the entire length of each movie to improve the precision of estimates. However, photobleaching significantly reduced the number of objects observed over the duration of the movie, causing an underestimation of surface coverage values. The photobleaching rate is the same for objects both under GUVs and not under GUVs. Thus, surface coverage comparison in both environments can still be compared. To further improve estimates, only objects which were tracked for two frames or more were included in surface coverage calculations. This greatly reduced the inclusion of single-frame noise objects. For surface coverage calculations, all 20 movies were tiled together and treated as one movie of 1 min in length but with a total field-of-view area 20-times that of a single field of view. This allowed for accurate weighting of GUV and non-GUV regions of each field of view based on size. Surface coverage estimates are shown in SI Appendix, Table S1 for all five protein conditions.

The surface coverage enrichment under GUVs was defined as the ratio of the surface coverage under GUVs to the surface coverage not under GUVs. For these calculations, the two WT configurations were analyzed together, and the two trans-mutant configurations were analyzed together. The total E-cad concentrations for both SLB and GUV incubation were the same for all conditions, allowing the combination of movies of like E-cad constructs for simple counting calculations. This allowed for a direct comparison of surface coverage enrichment only as a function of E-cad construct. Resulting surface-coverage enrichment ratios are tabulated in SI Appendix, Table S6.

Average Short-Time Diffusion Coefficient Determination.

All molecular displacements between consecutive frames that were localized under GUVs were separated based on FRET state. Complementary cumulative-squared displacement distributions were then calculated using histograms of all squared displacements in the high-FRET (bound) and low-FRET (unbound) states under GUVs, in which the squared displacement was defined as the square of the Euclidean distance between localizations in subsequent frames. Additional distributions were constructed using all molecular displacements under GUVs from both FRET states. These distributions were then fitted to a Gaussian mixture model:

$$P\left(R^2\ge r^2,\mathrm{\Delta }t\right)={\displaystyle \sum _{i=1}^M{c}_i{e}^{-r^2/4\mathrm{\Delta }t{D}_i}}\hspace{1em},$$ [2]

where $r$ is the Euclidean displacement between frames, $\mathrm{\Delta }t$ is the time between frames (0.05 s), $c_i$ is the fraction of displacements fitted by the $i$th Gaussian term, $D_i$ is the diffusion coefficient for the $i$th term, and $M$ is the number of terms included in the model. These data were best modeled by $M=2$ determined via residual analysis. Using the Gaussian mixture model parameters determined from nonlinear fitting, an average short-time diffusion coefficient $\left({\overline{\text{D}}}_{\text{short}}\right)$ was calculated for both FRET-states and overall:

$${\overline{\text{D}}}_{\text{short}}={\displaystyle \sum _{i=1}^M{c}_i{D}_i},$$ [3]

where ${\overline{\text{D}}}_{\text{short}}$ is representative of the average diffusion coefficient on the shortest time-scale assessable for these experiments.

Apparent Surface Residence Time Distributions.

In order to confirm the covalent conjugation of sortase-tagged E-cad to DOPE-Sort lipids in the SLB, complementary cumulative apparent surface residence time (observation time) distributions were constructed for sortase-conjugated E-cad, SLB-incorporated DOPE-LR, and his-tagged E-cad bound to SLB-incorporated DGS-NTA. The fraction of molecules that remained a given time after their initial observation $\left(t_s\right)$ was calculated for these three samples, directly comparing the apparent surface residence times of histag-NTA and sortase-conjugated E-cad to the surface residence times of a lipid in the SLB. These complementary cumulative apparent surface residence time distributions were then fit to an exponential mixture model:

$$P\left(t_s^{\text{'}}\ge t_s\right)={\displaystyle \sum _{i=1}^N{f}_i{e}^{-t/{\tau }_i}}\hspace{1em},$$ [4]

where $f_i$ and ${\tau }_i$ correspond to the fraction of trajectories and characteristic time constant associated with exponential $i$, respectively, and $i$ is summed over 1 to $N$, with $N$ being the number of exponential terms included. $N=2$ was determined to be sufficient for the two E-cad control samples, but for DOPE-LR, $N=1$ was sufficient. The average apparent residence time, $RT$, was calculated as the weighted average of the characteristic time constants:

$$RT\hspace{1em}={\displaystyle \sum _{i=1}^N{f}_i{\tau }_i}.$$ [5]

Complementary cumulative apparent surface residence time distributions and the exponential mixture model fits are shown in SI Appendix, Fig. S1A, and the resulting values of $RT$ are shown in SI Appendix, Fig. S1B. All fitting parameters are tabulated in SI Appendix, Table S7.

SLB Lateral Cluster Size Determination.

In order to calculate the lateral cluster size on the SLB for each trajectory within the GUV–SLB adhesive region, an effective diffusion coefficient $\left(D_T\right)$ was calculated for each trajectory that was underneath a GUV for the entire duration of the trajectory according to

$$D_T=\frac{1}{4T}{\displaystyle \sum _{i=1}^T\left[{\left(x_i-x_{i-1}\right)}^2+{\left(y_i-y_{i-1}\right)}^2\right]}\hspace{1em},$$ [6]

where $T$ is the duration of the trajectory and $x_i$ and $y_i$ are the Cartesian position coordinates of the trajectory after time $i$. The effective diffusion coefficient can then be related to the trajectory friction factor $\left(f\right)$ by the Einstein relation (67):

$$\frac{f}{k_{B}T}=\frac{1}{D_T},$$ [7]

where $k_B$ is the Boltzmann constant, $T$ is temperature, and $D_T$ is the effective diffusion coefficient for a single trajectory.

As lipid diffusion is much slower (approximately two to three times) in the SLB than in the GUV because of substrate coupling, increases in $f$ are primarily due to increased drag due to lateral clustering on the SLB (68), and changes in $\hspace{1em}f$ due to trans binding to E-cad on the GUV are assumed to be small. Considering that E-cad is covalently conjugated to a single lipid via the sortase enzymatic reaction, we can extract the size of E-cad clusters on the SLB-assuming additive friction factor contributions from each E-cad molecule in the cluster (66, 69). The apparent trajectory friction factor, $f$, can be expanded as

$$f={\displaystyle \sum _{i=1}^N{f}_i},$$ [8]

where $f_i$ is the friction factor contribution due to each E-cad molecule in the cluster, and N is the number of proteins in the cluster. The friction factor contribution of each protein is equal to the friction factor for an individual lipid in the free-draining limit, assuming bound lipids are well separated and each E-cad molecule tightly binds a single lipid and has minimal contact with additional lipids, all of which are true for this system after filtering trajectories (66). Therefore, the trajectory friction factor becomes

$$f=N{f}_L,$$ [9]

where $f_L$ is the friction factor of an individual lipid molecule diffusing in the SLB. The friction factor of an individual lipid molecule can be extracted from a DOPE-LR friction factor distribution, using the fact that the large peak at low friction factor corresponds to freely diffusing, individual lipids. It was determined that f_L = 0.3 s/µm² corresponded to the friction factor of a single lipid. This model allows for quantitative determination of the apparent cluster size corresponding to a single trajectory. The apparent SLB cluster size was calculated for each trajectory that was underneath the GUV for its entire duration. These calculations were only performed for WT and cis mutant E-cad in the trans configuration and WT and trans-mutant E-cad in the cis configuration. SI Appendix, Table S9 shows the resulting values of the average SLB lateral cluster size calculated using either all trajectories or only trajectories with an average lateral cluster size between one and three E-cad $\left(N\le 3\right)$.

FRET-State Transition Rate Determination.

Trajectories were separated into GUV and non-GUV trajectories for each E-cad configuration, where GUV trajectories were located underneath GUVs for their entire duration, and non-GUV trajectories were not under GUVs at any point during their trajectory. Any trajectories that transitioned between GUV states were not included in transition rate estimation. Additionally, non-GUV trajectories were discarded for samples in the trans configuration.

E-cad interactions were modeled using a three-state Markov model that has been previously used to model protein conformation and intermolecular interactions (39, 64). To summarize, this model allowed for three states: high-FRET (bound), low-FRET (unbound), or off. Therefore, the transition probability matrix has the form

$$TR=\left[\begin{array}{ccc}1-p_{LH}-p_{off}& p_{LH}& p_{off}\\ p_{HL}& 1-p_{HL}-p_{off}& p_{off}\\ 0& 0& 1\end{array}\right],$$ [10]

where $p_{LH}$, $p_{HL}$, and $p_{off}$ are the probabilities that a molecule will transition from the low-FRET state to the high-FRET state, transition from the high-FRET state to the low-FRET state, and terminate via photobleaching, respectively. The value of $p_{off}$ was determined independently by fitting the surface residence times to an exponential distribution. In order to determine the transitions probabilities between these three states, a maximum likelihood estimate was used based on all trajectory state sequences. To describe the heterogeneity in these transition probabilities, a likelihood function was defined to allow for beta-distributed transition probabilities. The resulting likelihood function was

$$LF\left(S|a_{LH},b_{LH},a_{HL},b_{HL}\right)={\displaystyle \prod _k\left[\frac{B\left(a_{LH}+N_{LH,k},b_{LH}+N_{LL,k}\right)B\left(a_{HL}+N_{HL,k},b_{HL}+N_{HH,k}\right)}{B\left(a_{LH},b_{LH}\right)B\left(a_{HL},b_{HL}\right)}{p}_{off}^{N_{off,k}}{\left(1-p_{off}\right)}^{N_{LL,k}+N_{LH,k}+N_{HH,k}+N_{HL,k}}\right]},$$ [11]

where $S$ is the sequence of observed FRET states for the $k$th trajectory; B is the beta function; and $N_{HL,k}$, $N_{LH,k}$, $N_{LL,k}$, $N_{HH,k}$, and $N_{off,k}$ are the number of times within the $k$th trajectory the molecule transitions from the high-FRET state to the low-FRET state, transitions from low-FRET state to the high-FRET state, remains in the low-FRET state, remains in the high-FRET state, and ends, respectively. The model is parameterized by $a_{LH},b_{LH},a_{HL},\hspace{0.17em}and\hspace{0.17em}{b}_{HL}$, which are the parameters defining the beta distribution of $p_{LH}$ and $p_{HL}$, respectively. The log of this likelihood function was maximized by iteratively changing the parameters defining the beta distributions describing the transition probabilities between the high and low-FRET states using either GUV trajectories or non-GUV trajectories. The average transition rates could then be estimated by

$$r_{LH}=-\left(\psi \left(b_{LH}\right)-\psi \left(a_{LH}+b_{LH}\right)\right)/\mathrm{\Delta }t$$ [12]

$$r_{HL}=-\left(\psi \left(b_{HL}\right)-\psi \left(a_{HL}+b_{HL}\right)\right)/\mathrm{\Delta }t,$$ [13]

where $\mathrm{\Delta }t$ is the experimental acquisition time, $\psi$ is the digamma function, and $r_{LH}$ and $r_{HL}\hspace{1em}$ are the average transition rates from the low-FRET state to the high-FRET state and from the high-FRET state to the low-FRET state, respectively. The transitions rates ($r_{LH}$ and $r_{HL}$) between FRET states were estimated separately using GUV or non-GUV trajectories for samples in the cis configuration and only GUV trajectories for samples in the trans configuration. For transitions from the high-FRET state to the low-FRET state, the transition rate is equivalent to the dissociation rate constant $\left({\overline{\text{k}}}_{\text{d}}\right)$, as dissociation is a unimolecular reaction. This is not the case for transitions from the low-FRET state to the high-FRET state, as the association rate is dependent on the acceptor surface coverage as well as the association rate constant and is complicated because of potential inclusion of bound E-cad in the low-FRET state.

An additional transition rate analysis was performed using only GUV trajectories corresponding to small lateral clusters. This analysis was conducted only for the WT and cis-mutant E-cad configurations targeting trans binding and the WT and trans-mutant configurations targeting cis binding. To specifically investigate the FRET-state transition rates for small clusters, only trajectories with an apparent SLB lateral cluster size approximately between one and three E-cad were used for maximum likelihood estimation. For all transition rate analyses, resulting beta distributions of state transition probabilities are shown in SI Appendix, Fig. S8, and the corresponding probability density functions for state transition rates are shown in SI Appendix, Fig. S9. The average transition rates are presented in SI Appendix, Table S8. After determining the most likely beta distribution parameters for the transition probabilities, FRET-state trajectories were simulated using these transition probability distributions and truncated by sampling from the experimental trajectory surface residence time distributions. Complementary cumulative FRET-state dwell time distributions were calculated using simulated and experimental trajectories, in which the apparent dwell time was defined as the number of consecutive frames a trajectory spent in a given state multiplied by the acquisition time. Theoretical dwell time distributions were compared to the experimental distributions for each estimation to check for model consistency (SI Appendix, Figs. S4 and S5). Furthermore, probability density functions of the fraction of a trajectory spent in the high-FRET state were calculated for both the experimental and simulated trajectories (SI Appendix, Figs. S2 and S3). A comparison of these simulated and experimental probability density functions generally serves as a better method of model verification than dwell time distributions because of the greater independence of trajectory length. See SI Appendix regarding model verification.

Data Availability

All study data are included in the article and/or SI Appendix. Two sample movies corresponding to one field of view are included, and all full-length raw movies are available upon request.